Heat transfer engineering an international journal, tập 32, số 2, 2011

It is worth remembering that the lower the mass velocity, the higher is the experimental uncertainty of the heat transfer coefficient, due to the low local heat flux.. The heat transfer

Selected Papers From the Sixth

HEFAT Conference

JOSUA P MEYER

Department of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa

In 2002, the 1st International Conference on Heat Transfer, Fluid

Mechanics, and Thermodynamics (HEFAT2002) was hosted in

the Kruger National Park, South Africa In 2003, the 2nd

con-ference (HEFAT2003) was hosted at the Victoria Falls, Zambia

The 2004 conference (HEFAT2004) was in Cape Town and the

4th conference (HEFAT2005) took place in Cairo, while the 5th

conference (HEFAT2007) was at Sun City

The 6th International Conference on Heat Transfer, Fluid

Mechanics and Thermodynamics (HEFAT2008) was held in

Pretoria, South Africa, from 30 June to 2 July 2008 It was part

of the University of Pretoria’s 100-year celebrations with the

theme “A century in the service of knowledge.”

For this conference and proceedings, all papers were

peer-reviewed by at least two reviewers and almost 150 papers were

accepted The review policy was that only original research

pa-pers that were recommended unconditionally by two reviewers

who are distinguished subject specialists in the field of the

rel-evant paper were accepted The papers were read in 17 parallel

lecture sessions over a period of three days during which five

keynote papers were presented

The purpose of most conferences, including this one, was

to provide a forum at which specialists in heat transfer, fluid

mechanics, and thermodynamics from all corners of the globe

could present the latest progress and developments in the field

This not only allowed the dissemination of the state of the art,

but also served as a catalyst for discussions on future directions

and priorities in the areas of heat transfer, fluid mechanics,

and thermodynamics The additional purpose of this conference

Address correspondence to Prof Josua P Meyer, Department of Mechanical

and Aeronautical Engineering, University of Pretoria, Pretoria, 0002, South

Africa E-mail: jmeyer@up.ac.za

was to introduce Africa to the rest of the world and to initiatecollaboration in research

The current edition of Heat Transfer Engineering, therefore,

is a special issue covering the HEFAT2008 conference It tains nine papers that were nominated by the conference ses-sion chairs and co-chairs as the best papers from each session.These papers dealt with several topics as summarized by theauthors:

con-• The first paper was on condensation heat transfer and sure loss measurements of high- and low-pressure refrigerantsflowing in a 0.96-mm single minichannel The refrigerantsconsidered were R32 and R245fa, as they display a widerange of fluid properties and therefore they could be usedfor proper validation of predicting models The condensationtests were performed in a unique measuring test section, ataround 40◦C, and the pressure drop tests were performed inadiabatic flow conditions to measure only the pressure lossesdue to friction The experimental heat transfer data were com-pared with predicting models to provide a guideline for thedesign of minichannel condensers It has also been foundthat the heat transfer coefficients were roughly the same forthe two fluids at the same experimental conditions and thecondensation was shear stress dominated for most of the datapoints However, the frictional pressure drop was significantlyhigher in the case of the low-pressure refrigerant, as would beexpected

pres-• The second paper was on quantifying mixing in penetrativeconvection experiments where penetrative convection in a sta-ble stratified fluid has been reproduced under laboratory con-ditions It was done by employing a tank filled with water andsubjected to heating from below The purpose of the experi-ments was to predict the mixing layer growth as a function of

87

initial and boundary conditions and describing the outcome

of a tracer dissolved in the fluid phase The equipment used

made it possible to simultaneously provide temperatures

in-side the domain through thermocouples and Lagrangian

par-ticle trajectories by feature tracking The results demonstrate

the validity of Deardorff mixed-layer similarity for the

tur-bulent structure of the boundary layer Also, the comparison

with similar experiments described in literature shows good

agreement with measurements taken at both bench and real

scale, signifying the legitimacy of the experimental work and

applicability to the real atmospheric boundary layer and its

monitoring for environmental purposes

• The purpose of the third article was to determine

experi-mentally the local stretching rate distribution along the limit

methane/air and propane/air flames Particle image

velocime-try measurements were used to obtain moving flame velocity

fields in a standard flammability column and also to

recog-nize the flame structures The methodology that was

devel-oped proved to be reliable and able to supply analyses with

repeatable data From the experiments, it was possible to

de-rive the flame stretching rate that causes its extinction in both

mixtures

• Because of the heat capacity of pressure vessel walls, the heat

transfer from the compressed gas to the vessel wall strongly

influences the temperature field of the gas Until now, no

correlations were available for the heat transfer coefficient

between the inflowing gas and inner surface of the vessel

To develop such a correlation, in the fourth article

compu-tational fluid mechanics was used to determine the gas

ve-locities at the vicinity of the inner surface of the vessel for

a number of discrete surface elements A large number of

numerical experiments show that there exists a unique

rela-tionship between the gas velocity at the inlet and the

tan-gential fluid velocity at the vicinity of the inner surface of

a pressure vessel Once this unique relationship is known,

the complete velocity distribution at the vicinity of the

in-ner surface can be determined from the inlet gas velocity The

near-wall velocities at the outer limit of the boundary layer are

substituted into the heat transfer correlation for external flow

over flat plates The method was applied to the special case

of filling a 70-MPa composite vessel for hydrogen fuel cell

vehicles

• In the fifth article an air-side data analysis method was

de-veloped for flat-tube heat exchangers under partially wet

con-ditions It was done by making the simplification that

com-bined, sensible, and latent heat transfer assumed that drainage

paths developed such that, at steady state, water does not

spread to noncondensing surfaces, which therefore remain

dry The air dewpoint was compared with local fin-tip and

fin-base temperatures, and a partially wet flat-tube heat

ex-changer was divided into fully wet, partially wet, and

dry-fin regions, which were subsequently analyzed as separate

heat exchangers Using an enthalpy-based effectiveness NTU

method, the average fin efficiency was calculated for each

re-gion, and the locations of region boundaries were determined

iteratively The method was compared with experimental data

of a flat-tube louver-fin heat exchanger under various latentloads

• For temperature-dependent heat transfer coefficients and heatcapacities, fast approximation methods were considered forthe estimation of the effective overall heat transfer coeffi-cient in the sixth paper The heat transfer coefficients weredetermined for two, three, or four reference temperatures.For parallel and countercurrent flow, a known method wasdescribed, which used a hypothetical fluid temperature forthe iteration-free consideration of variable heat capacities.For the mixed–unmixed cross-flow, a previous method fortemperature-dependent heat transfer coefficients was refined

to allow also for variable heat capacities A new iterative fastdesign and rating method was developed for the mixed–mixedcrossflow, which was a suitable model for special multi-pass shell-and-tube heat exchangers The accuracy of themethods was tested against numerical calculations with goodresults

• The seventh paper is related to the operation of protonexchange membrane fuel cell stacks, which require carefulthermal and water management for optimal performance.Appropriate placement of cooling plates and appropriatecooling conditions are therefore essential To study the impact

of these design parameters, a two-phase model accounting forthe conservation of mass, momentum, species, energy, andcharge, a phenomenological model for the membrane, and anagglomerate model for the catalyst layer were developed andsolved The models were validated for a single cell, in terms ofboth the local and the global current density, and good agree-ment was found Four repetitive computational units werethen identified for the number of single cells placed betweenthe coolant plates varying from one to four cells The flowfields in the single cells and the cooling plates were of a nettype

• The thermodynamic stability of gas hydrates was gated in the presence of electrolyte solutions in the eightharticle The proposed model was based on the Van derWaals–Platteeuw model for gas hydrate equilibrium, and thePitzer and Mayorga model was employed to calculate thewater activity in electrolyte solutions Available values forthe Pitzer and Mayorga model parameters were usually ad-justed using experimental data at 25◦C, which was usuallyhigher than the gas hydrate formation temperature In order

investi-to eliminate this problem, those adjustable parameters werere-optimized using experimental data from the literature at thelowest temperature In the case of mixed electrolyte solutionsand without using any adjustable parameters, a mixing rulewas proposed to estimate the water activity The new mixingrule was based on the ionic strength of the mixture and es-timated the mixture water activity by using properties of thesingle electrolytes which constituted the mixture The resultsshow the proposed model can calculate hydrate equilibriumconditions with good accuracy, especially at low concentra-tions, which is the case for most industrial applications.heat transfer engineering vol 32 no 2 2011

changers The flow behaviors was studied in six geometrically

different configurations over a range of Reynolds numbers and

quantified using the concept of “fin angle alignment factorζ,”

which was related to the flow efficiencyη in louvered fins

The experimental data resulted in a discrete data set of local

ζ values, which was used to validate the simulations Using

these validated cases, it was shown that the graphical

measure-ment method can be distorted by recirculation zones resulting

in erroneous values Care should thus be taken when

per-forming graphical measurement of the mean flow angle based

on dye injection images The transition from steady laminar

to unsteady flow in inclined louvered fins was geometrically

triggered and occurred at lower Reynolds numbers compared

Mechanical and Aeronautical Engineering of the versity of Pretoria, South Africa He specializes in heat transfer, fluid mechanics, and thermodynamic aspects of heating, ventilation, and air conditioning.

Uni-He is the author and co-author of more than 250 cles, conference papers, and patents, and has received various prestigious awards for his research He is also

arti-a fellow or member of varti-arious professionarti-al institutes and societies and is regularly invited as a keynote speaker at local and inter- national conferences He has received various teaching awards as lecturer of the year, and he has received two awards from the University of Pretoria as an exceptional achiever In 2006, he was evaluated by the National Research Foun- dation (NRF) as an established researcher who enjoys considerable international recognition for the high quality and impact of his recent research outputs He is

an associate editor of Heat Transfer Engineering.

heat transfer engineering vol 32 no 2 2011

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457631003769104

Condensation Heat Transfer and

Pressure Losses of High- and

Low-Pressure Refrigerants Flowing

in a Single Circular Minichannel

ALBERTO CAVALLINI, STEFANO BORTOLIN, DAVIDE DEL COL,

MARKO MATKOVIC, and LUISA ROSSETTO

Dipartimento di Fisica Tecnica, University of Padova, Padova, Italy

A 0.96 mm circular minichannel is used to measure both heat transfer coefficients during condensation and two-phase

pressure losses of the refrigerants R32 and R245fa Test runs have been performed at around 40◦C saturation temperature,

corresponding to 24.8 bar saturation pressure for R32 and 2.5 bar saturation pressure for R245fa The pressure drop tests

have been performed in adiabatic flow conditions, to measure only the pressure losses due to friction The heat transfer

experimental data are compared against predicting models to provide a guideline for the design of minichannel condensers.

INTRODUCTION

A significant and still growing part of the engineering

re-search community has been devoted to scaling down devices

in the last few decades, while maintaining or improving their

functionality The introduction of minichannels in the field of

enhanced heat and mass transfer is surely one of those attempts

As a result, compact heat exchangers and heat pipes are used in

a wide variety of applications: from residential air conditioning

to the spacecraft thermal control Growing interest for different

solutions can also be found in electronic cooling, though these

applications are less interesting from the condensation point of

view due to its exothermal nature Compact elements work with

small refrigerant charge and can usually withstand extremely

high system pressures

Two-phase flow in rough minichannels is affected by gravity,

inertia, viscous shear, and surface tension forces These forces

influence flow regimes, pressure drop, and heat transfer

charac-teristics of minichannels

Some researchers reported flow regimes during condensation

of R134a in minichannels, but general flow regime maps have

Address correspondence to Dr Davide Del Col, Dipartimento di Fisica

Tecnica, University of Padova, Via Venezia 1, 35131 Padova, Italy E-mail:

davide.delcol@unipd.it

not been reported in the open literature Coleman and Garimella[1] reported flow patterns for R134a condensing inside horizon-tal tubes and square minichannels of hydraulic diameter ranging

from 1 to 4.9 mm At mass velocities G > 150 kg m−2s−1the

authors observed annular, wavy, intermittent (slug, plug), and

dispersed (bubble) flow patterns At hydraulic diameters D h=

1 mm the wavy regime was not observed, while at high flowrates and qualities annular film with mist core or mist flowswere observed The hydraulic diameter has a substantial effect

on flow transitions, but the tube shape was found to be less icant Several other authors have performed flow visualizations

signif-in msignif-inichannels, as reported signif-in Cavallsignif-ini et al [2], but no specificflow visualization with high-pressure fluids has been done.Considering the pressure drop behavior of minichannels, veryfew data are available in the open literature regarding high-pressure fluids In fact, most data refer to medium-pressure re-frigerants, such as R134a Cavallini et al [3] measured pressuredrops during adiabatic flows of R410A, R134a, and R236ea

at 40◦C inside a multiport minichannel having a square crosssection with hydraulic diameter 1.4 mm, length 1.13 m, andwith mass velocities ranging from 200 to 1400 kg m−2s−1 Themultiport minichannel tested is characterized by a square cross

section and a low value of surface roughness (Ra= 0.08 µm

and Rz= 0.43 µm), whose effect can thus be neglected.The authors compared their data against models, either devel-oped for conventional macrochannels or specifically developed

90

minichannels was then suggested by Cavallini et al [4].

As is the case for flow visualization and pressure drop, most

of the heat transfer data available in the literature for

conden-sation inside minichannels were measured with R134a and in

most cases multiport channels have been used For multiport

tubes, averaged values over a number of parallel channels are

measured instead of in one single channel

It is not an easy task to measure local heat transfer

coeffi-cients during condensation inside a single minichannel, and it is

complicated as compared to the flow boiling case, where

electri-cal heating can be adopted In this context, a new experimental

apparatus for the measurement of the local heat transfer

coeffi-cients inside a single minichannel has been recently constructed

at the University of Padova With this apparatus, condensation

tests have been performed in a 0.96 mm diameter circular

chan-nel

The fluids investigated in this study are single-component

refrigerants R32 and R245fa, a high- and a low-pressure fluid,

respectively Their main physical properties at 40◦C compared to

the corresponding values of R134a are shown in Table 1 R32 is

considered a higher pressure refrigerant compared to R134a; its

vapor density exceeds R134a by 46%, while its liquid viscosity

is significantly lower R245fa has an opposite behavior It has

much lower vapor density and higher liquid viscosity Surface

tension force of R32 is slightly lower than that of R134a (by

20%), while its liquid thermal conductivity is higher by 50%

The surface tension force of R245fa is twice that of R134a and

2.7 times of R32

In practical applications, the use of a high-pressure

refriger-ant can mitigate a disadvrefriger-antage of the high pressure drop with

small channels R32 also has high thermal conductivity, which

is favorable to high heat transfer coefficients during

conden-sation On the contrary, R245fa displays much lower

satura-tion pressure and can be used when looking for low system

Liquid thermal conductivity [mW m −1K−1] 85.42 114.58 74.72

Vapor thermal conductivity [mW m −1K−1] 15.10 18.65 15.45

Note Corresponding saturation pressure is equal to 24.8 bar for R32, 2.5 bar

for R245fa, and 10.2 bar for R134a.

Figure 1 Experimental test rig (DESUP = desuperheater, MF = mechanical filter, HF = drier, PV = pressure vessel, CFM = Coriolis-effect mass flow meter, P = pressure transducer, T = temperature transducer, DP = differential pressure transducer).

The reason for studying those two fluids is that they display

a wide range of fluid properties and therefore they can be usedfor proper validation of predicting models

CONDENSATION TESTS

In order to investigate condensation heat transfer within asingle minichannel, a unique measuring test section has beenconstructed [5]

The test rig designed for heat transfer and pressure dropmeasurements during condensation is shown in Figure 1 Itconsists of the primary refrigerant loop and four auxiliary loops.The subcooled refrigerant is circulated through a filter drier, thenpasses into the gear pump that is coupled with a variable-speedelectric motor It is then pumped through the Coriolis-effectmass flow meter into the evaporator, where the fluid is heated

up, vaporized, and superheated At the evaporator exit, the state

of the superheated vapor is determined from temperature andpressure

The superheated vapor enters the test section, which is posed of two countercurrent heat exchangers The first heat ex-changer of the test section (desuperheater) is used to cool downthe fluid to saturation state before entering into the second heatexchanger, which is the actual measuring sector

com-The saturation temperature is obtained from the pressure inthe two adiabatic sectors upstream and downstream of the mea-suring sector There, the refrigerant temperature is also measured

by means of adiabatic wall temperature measurements After thetest section, the fluid is sent to the post-condenser, where it iscondensed and subcooled

The temperatures and flow rates of the secondary loops arecontrolled by a closed hot-water loop, two thermal baths, andheat transfer engineering vol 32 no 2 2011

Figure 2 Schematic of the experimental test section (the refrigerant flows from left to right).

an additional resistance heater arranged in series at the inlet

of the desuperheater In this way, it is possible to control the

temperatures of four different heat sinks or heat sources within

the test rig

A sketch of the test section is shown in Figure 2 The

mea-suring section is a commercial copper tube with inner diameter

0.96 mm

Single-phase tests and forced convective condensation and

flow boiling tests can be done with the present test facility

The test section is a straight, single minichannel with two

dia-batic sectors (desuperheater and measuring section in Figure

2) divided by an adiabatic capillary tube The two diabatic

sectors are made from an 8 mm external diameter copper rod

with a 0.9 mm internal bore The desuperheater has a length of

50 mm and the measuring section is 228.5 mm long The

thick-walled tube (8 mm diameter) was machined externally and then

closed with a plastic sheath in order to obtain a cooling water

channel within the wall thickness The tortuous path of the

sec-ondary fluid enables good water mixing and thus allows precise

local coolant temperature measurements In this test section,

15 T-thermocouples have been inserted into the water channel

along the measuring sector (MS) with 15 mm step to obtain the

coolant temperature profile The enhanced coolant heat

trans-fer surface area moves the dominant thermal resistance from

the external to the internal side; with this solution the internal

thermal resistance (refrigerant to wall) is increased and thus

the experimental heat transfer coefficient uncertainty due to the

refrigerant-to-wall temperature difference is reduced

In order to measure precise local heat transfer coefficient

values, 15 T-type thermocouples have been inserted into the

wall thickness, near the minichannel along the measuring

sec-tor, without having the thermocouple wires cross the coolant

path Furthermore, thermocouples are used to measure the

re-frigerant temperature in the adiabatic segments by recording the

external wall surface temperature of the stainless-steel capillary

tubes at the two extremes of the measuring section When

oper-ating in condensation mode, the first diabatic sector works as a

desuperheater To avoid large temperature gradients at the inlet

of the measuring sector, the desuperheater is used to cool down

the superheated refrigerant to the saturation state at the inlet of

the measuring sector Vapor quality is calculated from the

en-ergy balance on the coolant side, and saturation conditions are

checked using the adiabatic wall temperature and the pressure

measurement in the adiabatic sectors

The following three parameters are used for determination

of the local heat transfer coefficient: the local heat flux, tion temperature, and wall temperature The heat flux is de-termined from the temperature profile of the coolant in themeasuring sector The wall temperature is directly measuredalong the test section and the saturation temperature is ob-tained from the pressure measured at inlet and outlet of the testsection

satura-The coolant side temperature profile is obtained from thethermocouples inserted in the water channel along the measuringsector (Figure 3) The derivative of the temperature profile isproportional to the local heat flux:

thermocouples embedded in the wall

Figure 3 Temperature measurements within the single minichannel test tion.

sec-heat transfer engineering vol 32 no 2 2011

pressure at channel outlet and the pressure gradient profile is

multiplied by a constant factor to match the calculated and the

measured pressure drop The saturation temperature (T sat (z)) is

then evaluated, from the pressure, using Refprop7 [6]

By considering the conservation of energy in the sector, the

coolant temperature change is directly associated to the

corre-sponding enthalpy variation of the refrigerant Therefore, the

local vapor quality is calculated as follows:

In the present technique, the dominant thermal resistance

dur-ing the condensdur-ing process is on the refrigerant side, as shown in

Figure 3 This favors minimizing the experimental uncertainty

associated with the determination of the heat transfer

coeffi-cient In fact, one contribution of the experimental heat transfer

coefficient uncertainty is the saturation-to-wall temperature

dif-ference The other main uncertainty terms are associated to the

heat flux, the mass flow rate, and the hydraulic diameter Since

the heat flux is obtained from the temperature gradient of the

water, this uncertainty contribution depends on the operating

conditions, (mass flux and vapor quality), yielding higher

un-certainty at lower mass fluxes At highest mass velocity, 1200

kg m−2s−1, the total heat transfer coefficient uncertainty is

be-low 5%, while at the be-lowest mass velocity, 100 kg m−2s−1, it

ranges between 10% and 25% More details on the error analysis

are reported in Matkovic et al [5]

Prior to the tests, all instruments were carefully calibrated

Besides, several tests have been run to verify that the

nonde-pendency of heat transfer coefficient on the conditions of the

secondary fluid

The local heat transfer coefficient has been measured

dur-ing condensation of R32 and R245fa The R32 experiments

have been performed for the entire range of vapor quality at

40◦C saturation temperature and mass velocity ranging from 100

kg m−2s−1up to 1200 kg m−2s−1

The experimental heat transfer coefficients for condensation

of R32 are shown in Figure 4 As expected for forced convective

condensation inside conventional pipes, the heat transfer

coeffi-cient increases with mass velocity and vapor quality It is worth

remembering that the lower the mass velocity, the higher is the

experimental uncertainty of the heat transfer coefficient, due to

the low local heat flux

The heat transfer coefficient measured for R245fa, with mass

velocity ranging from 100 up to 500 kg m−2s−1, is shown in

Figure 5 By comparing the values measured for R32 and

R245fa, one can see that refrigerant R32 displays roughly the

same or a slightly higher coefficient at the same mass velocity

and vapor quality This may be surprising since, in the case of

0 5000 10000 15000

In the case of R32 data (Figure 4), the experimental heattransfer coefficients measured at 100 kg m−2s−1and those at

200 kg m−2 s−1 are very close to each other, showing littleeffect of mass velocity at these conditions This overlapping of

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5 Heat transfer coefficient measured during condensation of R245fa

in the channel versus vapor quality.

heat transfer engineering vol 32 no 2 2011

the heat transfer coefficients at the lower tested values of mass

velocity is not found with the refrigerant R245fa, whose trend at

low mass velocity is as expected from macroscale condensation

The behavior experienced with R32 may be explained with a

different flow pattern occurring in the channel

PRESSURE DROP TESTS

The present authors report here the pressure drop measured

during adiabatic two-phase flow of R32 and R245fa inside the

same test section previously described

For most of the frictional tests, the desuperheater is used

to achieve partial condensation of the refrigerant and then the

pressure drop is measured adiabatically in the following sector

Inlet vapor quality has been controlled through the thermal

bal-ance in the desuperheater Some frictional tests, at low vapor

qualities, have been performed bypassing the evaporator and

sending the refrigerant to the test section as a subcooled liquid;

the desuperheater is then used as a preheater for the liquid

In-deed, saturation conditions are achieved by partial vaporization

before the measuring sector

The present mini-tube has a much higher surface roughness

as compared to the previously tested multiport minichannel [3]

Therefore, the effect of tube wall roughness to the frictional

pressure drop was investigated

Some single-phase flow tests have previously been performed

with R134a to measure the friction factor in the minichannel

Experimental values of R134a friction factor have been

com-pared against equations for both laminar and turbulent flows

for rough tubes, and good agreement between calculated and

experimental values was found [4]

The test tube is the same as used for heat transfer tests The

arithmetical mean deviation of the assessed profile Ra of the

copper channel inner surface is Ra= 2.3 µm, the maximum

height of profile Rz is 18µm The inlet and outlet pressure ports

are inserted in two stainless-steel tubes 24 mm long, attached

to the ends of the copper tube (adiabatic sectors, Figure 2) The

stainless-steel tubes have 0.762 mm inner diameter, Ra= 2.0

µm, and Rz = 10.2 µm The total frictional pressure drop is

then the sum of the frictional pressure drop in the two

stainless-steel tubes, of the frictional pressure drop in the 228.5 mm long

copper tube, and of the pressure variations due to one abrupt

enlargement (from 0.762 mm diameter to 0.96 mm diameter)

and one contraction (from 0.96 mm to 0.762 mm) Pressure

losses due to abrupt geometry changes account for 4 to 8% of

total pressure drop in the R245fa data and for 6 to 10% in the

case of R32 data, according to the calculation by means of the

Paliwoda [7] equations

The experimental uncertainty for the measured pressure

dif-ference is±0.1 kPa, for the absolute pressure is ±3 kPa, for

the refrigerant flow rate is ±0.2%, and for the vapor quality

±1% The total experimental pressure drop for R32 at 40◦C

versus vapor quality, at mass velocities of 200, 400, 600, 800,

and 1000 kg m−2 s−1, is shown in Figure 6 In Figure 7, the

0 10 20 30 40 50 60 70 80 90 100

Figure 6 Cumulative experimental pressure drop in the test channel during adiabatic two-phase flow of R32.

cumulative pressure drop measured during adiabatic two-phaseflow of R245fa is reported

The combined effect of low vapor density and high liquidviscosity explains the significant pressure drop increase that ismeasured for R245fa as compared to R32, at the same massvelocity and vapor quality

0 10 20 30 40 50 60

Figure 7 Cumulative experimental pressure drop in the test channel during adiabatic two-phase flow of R245fa.

heat transfer engineering vol 32 no 2 2011

Figure 8 Calculated versus experimental heat transfer coefficient: The model

by Moser et al [8], modified by Zhang and Webb [9], is applied to R32 and

R245fa data.

ASSESSMENT OF HEAT TRANSFER CORRELATIONS

Experimental results have been compared against two models

available in the open literature developed for HTC predictions

inside macro-scale tubes

The first correlation has been presented by Moser et al [8],

and was initially developed for conventional pipes and later

modified by using the Zhang and Webb [9] method for pressure

drop calculation inside small-diameter tubes Although in this

paper all the experimental data points have been compared to

the models, the Moser et al [8] correlation was developed for

and should be applied only to annular flow condensation The

comparison between experimental and predicted data is depicted

in Figure 8 As one can see, the model by Moser et al [8]

modified with the Zhang and Webb [9] pressure drop correlation

is in good agreement with R32 data but overestimates R245fa

data by 30%

The heat transfer coefficients measured with R32 at 100

kg m−2 s−1are not in satisfactory agreement with the model

This may be due to the different flow pattern occurring in the

channel at these conditions As stated earlier, the correlation was

developed only for annular flow condensation and therefore it is

questionable whether the data at 100 kg m−2s−1mass velocity

may be included in the comparison

The second model used for comparison was developed

by Cavallini et al [10] for macroscale condensation It also

accounts for the transition from the
T-independent to

T-dependent region Here
T is the saturation minus wall

temperature difference However, this transition is defined for

0.010.101.00

10.001.00

0.100.01

X [/]tt

Jg

R245fa G100 R245fa G200 R245fa G400 R32 G100 R32 G200 R32 G400

Figure 9 Condensation test runs plotted on the flow pattern map (Cavallini

et al [10]).

conventional tubes, i.e., for channels with hydraulic diametershigher than or equal to 3 mm From flow pattern visualizationavailable in the open literature, one should expect that thestratified flow region is reduced in the case of minichannels, ascompared to conventional tubes

Matkovic et al [5] reported that the saturation to wall perature difference has no effect on the heat transfer coefficient

tem-at 200 kg m−2s−1mass velocity with R32, confirming that theeffect of gravity forces in a channel of around 1 mm diameter isnot significant in comparison with the other forces that influencethe condensation heat transfer at this mass velocity

In Figure 9, the test runs at mass velocity ranging between 100and 400 kg m−2s−1are plotted in the diagram of dimensionlessvapor velocity versus Martinelli parameter The transition curveprovided by Cavallini et al [10] for macro tubes is also plotted.This transition curve divides the map in two regions: the upperarea characterized by annular flow condensation (where the heattransfer coefficient does not depend on the saturation minus walltemperature difference), and the bottom area where the heattransfer coefficient is dependent on the temperature differencealready described The transition line is defined by Eq (4) forHFC refrigerants:

Figure 10 Calculated versus experimental heat transfer coefficient: The model

by Cavallini et al [10] is applied to R32 and R245fa data.

Figure 11 Ratio of calculated to experimental heat transfer coefficient versus

mass velocity: The model by Cavallini et al [10] is applied to R32 heat transfer

coefficients.

0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50

Nevertheless, one should remember that the transition in Eq (4)was developed for macroscale condensation and its extension tominichannels may require a proper validation.The comparisonbetween experimental heat transfer coefficients and predictions

by Cavallini et al [10] is shown in Figure 10 Both R32 andR245fa data are very well predicted by this correlation, which

is able to catch the experimental trend

The only data points that are not accurately estimated bythis model are the ones measured with R32 at 100 kg m−2s−1,

at moderate and high vapor quality This is clearly shown inFigure 11, where the ratio of calculated to experimental heattransfer coefficients is plotted versus mass velocity This dis-agreement is not found with R245fa data (Figure 12)

At mass velocity higher or equal to 200 kg m−2s−1, wherethe condensation heat transfer is likely to be dominated byshear stress, the macroscale model can accurately predict theheat transfer coefficient for both fluids At lower mass ve-locity, where, for instance, the agreement with R32 data isnot sufficiently accurate, the computation procedure based onmacroscale condensation data may not be always applicable tominichannels

re-heat transfer engineering vol 32 no 2 2011

HTC heat transfer coefficient, W m−2K−1

J G dimensionless gas velocity,= xG/[gDhρG(ρL—ρG)]0.5

˙

m mass flow rate, kg s−1

p pressure, Pa

Pr Prandtl number,= µcp/λ

q local heat flux, W m−2

Ra arithmetical mean deviation of the assessed profile

(ac-cording to ISO 4287 [1997]),µm

ReLO liquid only Reynolds number,= GD h /µL

Rz maximum height of profile (according to ISO 4287

Update on Condensation Heat Transfer and Pressure Drop

in Minichannels, Heat Transfer Engineering, vol 27, pp.

74–87, 2006

[3] Cavallini, A., Del Col, D., Doretti, L., Matkovic, M., setto, L., and Zilio, C., Two-Phase Frictional PressureGradient of R236ea, R134a and R410A Inside Multi-Port

Ros-Mini-Channels, Experimental Thermal and Fluid Science,

vol 29, pp 861–870, 2005

[4] Cavallini, A., Del Col, D., Matkovic, M., and Rossetto,L., Frictional Pressure Drop During Vapor–Liquid Flow

in Minichannels: Modelling and Experimental Evaluation,

International Journal of Heat and Fluid Flow, vol.30, pp.

131–139, 2009

[5] Matkovic, M., Cavallini, A., Del Col, D., and Rossetto, L.,Experimental Study on Condensation Heat Transfer Inside

a Single Circular Minichannel, International Journal of

Heat and Mass Transfer, vol 52, pp 2311–2323, 2009.

[6] National Institute of Standards and Technology (NIST),

Refprop Version 7.0, Boulder, CO, 2002.

[7] Paliwoda, A., 1992, Generalized Method of Pressure DropCalculation Across Pipe Components Containing Two-

Phase Flow of Refrigerants, International Journal of

[9] Zhang, M., and Webb, R L., Correlation of Two-Phase

Friction for Refrigerants in Small-Diameter Tubes,

Exper-imental Thermal and Fluid Science, vol 25, pp 131–139,

2001

[10] Cavallini, A., Censi, G., Del Col, D., Doretti, L., Matkovic,M., Rossetto, L., and Zilio, C., Condensation in HorizontalSmooth Tubes: A New Heat Transfer Model for Heat Ex-

changer Design, Heat Transfer Engineering, vol 27, pp.

31–38, 2006

Alberto Cavallini is full professor of energy

sci-ence at the Engineering Faculty of the University of Padova, Italy He has been director of the Department

of Fisica Tecnica of the University of Padova, and

of the Refrigeration Institute of the Italian Research Council He is a former president of the Scientific Council of the International Institute of Refrigeration

of Paris ASHRAE Fellow, and former president of AICARR, the Italian Society of Air Conditioning, Heating and Refrigerating Engineers His research activity concerns the field of energy management, heat transfer, refrigeration, and air conditioning with particular reference to problems related to the refrig- erant substitution issue He is the author or co-author of about 220 scientific and technical publications and of five textbooks.

heat transfer engineering vol 32 no 2 2011

Stefano Bortolin graduated in mechanical

engineer-ing at the University of Padova, Italy He is now a Ph.D student at the Department of Fisica Tecnica, University of Padova in Italy At present, his research

is focused on two-phase heat transfer with particular regard to condensation and vaporization of refriger- ants inside minichannels.

Davide Del Col took his Ph.D at the University of

Padova, Italy, and was a visiting scholar at sylvania State University, USA At present, he is an assistant professor in the Faculty of Engineering of the University of Padova, where he teaches the funda- mentals of thermodynamics and heat transfer He is a member of the Commission B1 of IIR and a member

Penn-of the ASME K-13 Committee His research activity deals with heat transfer during condensation and va- porization of new refrigerants, design of condensers and evaporators, and microscale heat transfer He is also active in the field of

heat pumps and solar energy conversion He is co-author of one book and more

than 100 papers, most of them published in international journals or presented

at international conferences.

Marko Matkovic graduated in mechanical

engineer-ing at the University of Ljubljana, where he gained first research experiences after graduation in Slove- nia He continued his research activity in Italy at the Department of Fisica Tecnica, University of Padova, where he completed his Ph.D in the field of con- densation heat transfer inside minichannels There,

he was involved in several international research projects, among them “Heat and Mass Transfer in- side Microchannels” funded through the Human Po- tential Program of the European Community, and “Enhanced Condensers for Microgravity” funded by ESA and “MOET” established between EC and Airbus France.

Luisa Rossetto is a professor of heat transfer She

teaches advanced heat transfer and applied namics to the engineering students at the University

thermody-of Padova Her research activity concerns the field

of enhanced heat transfer, particularly during phase flow or with condensation and vaporization of refrigerants (on integral fin tubes, in microfin tubes and mini- and microchannels) She is a member of ASHRAE (American Society of Heating, Refriger- ating, Air-Conditioning Engineers), of IIR (Interna- tional Institute of Refrigeration), and of UIT (Italian Society of Thermo-Fluid Dynamics) She is author or co-author of more than 150 papers, most published

single-in the single-international scientific press.

heat transfer engineering vol 32 no 2 2011

Convection Experiments

VALENTINA DORE, MONICA MORONI, and ANTONIO CENEDESE

Department of Hydraulics, Transportations and Roads, Sapienza University of Rome, Rome, Italy

Penetrative convection in a stably stratified fluid has been reproduced in laboratory by employing a tank filled with water

and subjected to heating from below The goal of the experiments is predicting the mixing layer growth as a function of

initial and boundary conditions and describing the fate of a tracer dissolved in the fluid phase The equipment employed

is suitable for simultaneously providing temperatures inside the domain through thermocouples and Lagrangian particle

trajectories by feature tracking The field of view is illuminated through a thin light sheet with suitable optical equipment To

fully characterize the transport feature of the phenomenon under investigation, the mixing layer growth is detected employing

both temperature data and statistics of the velocity field, i.e., the vertical velocity component standard deviation The velocity

spatial correlation allows the plume horizontal dimension to be determined This information coupled with the knowledge

of the mixing layer height allows the spatial extension of the convective region to be fully described.

INTRODUCTION

Penetrative convection is the motion of vertical plumes or

domes into a fluid layer of stable density and temperature

strati-fication, providing enough momentum for the plumes to extend

into the stable layer for a significant distance from the

sur-face at which they started In its initial stages, the convective

boundary layer is organized in coherent structures persisting

over time Subsequently the flow becomes turbulent and the

structures break up Penetrative convection is of importance in

several areas of geophysical fluid dynamics, most notably in the

lower atmosphere, the upper ocean, and lakes, i.e., fluid

bod-ies periodically stably stratified (their mean density decreases

upwards) in most regions

In most lakes, turbulent convective flow can be observed

when the free surface becomes cooler than the underlying

wa-ters, eroding the stable stratification on a daily or seasonal time

scale [1]

In the ocean under calm conditions, the upper 20 or 30 m

usually exhibits a continuous, moderately stable density

distri-bution When wind begins to blow over the surface, turbulence

in the water is generated both by shear and by sporadic breaking

waves With time, the turbulent layer becomes deeper as a result

Address correspondence to Valentina Dore, Department of Hydraulics,

Transportations and Roads, Sapienza University of Rome, Via Eudossiana 18,

00184 Rome, Italy E-mail: valentina.dore@uniroma1.it

of the entrainment across the interface between the turbulentand stable fluids [2] and erosion of the underlying denser water.Because of the relatively rapid mixing, the density distribution

is approximately uniform in the upper layer

An analogous phenomenon is observed in the atmospherewhen surface heating due to solar radiation results in a grow-ing unstable layer adjacent to the ground, which replaces thenocturnal inversion from below In this case, the initially stableenvironment near the ground is affected by convection, and fullinteraction between the two regions occurs [3, 4]

In lakes and oceans, domes with large downward velocitiesoriginate at the free surface, balanced by ascending domes withlower velocity but a larger area In the atmosphere, convection

is characterized by relatively narrow plumes in the form ofdomes of rising horizontal surfaces balanced by larger regions

of descending motion

Resulting oscillatory movements (internal waves) ated within the stable layer take place at or below theBrunt–V¨aiss¨al¨a frequency, which is related to the vertical tem-perature gradient [5, 6]

gener-The dynamic of penetrative convection in nature influencesthe transport and mixing features of stratified fluids; in fact, theflux through the interface between the mixing layer and the sta-ble layer plays a fundamental role in characterizing and forecast-ing the distribution of chemical species with implications for [7]:

• Air or water quality (pollutants, released inside the mixinglayer, remain confined inside it)

99

• Absorption of ultraviolet (UV) radiation (ozone, a natural

fil-ter for UV in the upper atmosphere, but a harmful contaminant

in the lower troposphere)

• Climate change (greenhouse gases)

• Water turnover, ecosystems, algal blooms and eutrofization

(oxygen and nutrients in oceans and lakes)

Dispersion in turbulent convective phenomena is mostly due

to transport by large organized structures, while molecular

diffu-sion can be neglected Knowledge of the horizontal and vertical

extension of the structures dominating the flow field is then

mandatory The vertical dimension is associated with the

mix-ing layer height In its calculation the entrainment has to be

taken into account to carefully determine the upper limit a

con-taminant can reach Furthermore, the spatial correlation of the

velocity field, providing the plume horizontal dimension, allows

the horizontal extension of the mixing region to be determined

The convective boundary layer development in a

continu-ously and linearly stratified atmosphere has been extensively

studied during field campaigns, in laboratory models, with bulk

convective boundary layer models, and by numerical

simula-tions Fedorovich and Conzemius [8] present a nice and

com-plete review of the literature published on this issue It appears

there is a lack of consensus on the dependence of integral

pa-rameters of convective entrainment (convective boundary layer

[CBL] growth rate, ratio of the buoyancy flux of entrainment to

the surface buoyancy flux, ratio of the entrainment layer depth

to that of the CBL) on the initial stratification strength and

con-vective phenomenon evolution

Here we present a laboratory model designed to reproduce

the penetrative convection phenomenon, to predict the mixing

layer growth as a function of initial and boundary conditions,

to understand the interaction between the mixing layer and the

stable layer, and to describe the fate of a contaminant dissolved

within the fluid phase Field experiments aimed at measuring

the turbulence budget of the convective boundary layer (CBL)

have shown that the mechanical generation of kinetic energy by

wind shear is often confined close to the ground, supporting the

validity of laboratory models in which no wind is present [3, 9]

The similarity proposed by Deardorff [3] is employed here

to compute scaling parameters, which are functions of time

Under the assumption of negligibility of mechanical

produc-tion of turbulence kinetic energy in comparison with buoyancy

production, the scaling parameters are:

Height of the mixing layer : zi (1a)

Convective velocity : w∗ =
3

gβqszi (1b)

Convective time : t∗= zi

where qsis the surface kinematic heat flux (wθat the boundary)

andβ the volume expansion coefficient Through normalizing

the quantities measured at different stages of the experiment,the phenomenon can be considered as a succession of steadystates, according to an evolution of the quantities of interest thatmay be defined quasi-steady [10]

The experimental apparatus employed to run the experimentspresented here is the same as in Cenedese and Querzoli [10],Querzoli [11], Cenedese and Querzoli [12], and Moroni andCenedese [5] The spatial resolution of velocity data is largelyincreased here by means of feature tracking used instead oflaser–Doppler anemometer or particle tracking velocimetry as

in references [10], [11], and [12] Furthermore, the combineduse of thermocouples and flow visualization techniques allowsemploying and cross-validating different methods to estimatethe mixing layer height evolution with time [5, 13] and theplume characteristic dimensions Feature tracking (FT) algo-rithms focus their attention on pixel luminosity intensity gradi-ents distributed within each image, recalling the “image bright-ness constancy constraint” and assuming the hypothesis of tracerparticles behaving as Lambertian surfaces The intensity gradi-ents are likely distributed around the particle border and thoseare tracked frame by frame The issues of properly separating aparticle from the image background and computing its centroidare overcome [14] FT is suitable for analyzing any particle den-sity images and it does not require a priori velocity estimates toidentify particle trajectories The technique employed for thisinvestigation implements a pure translation model [14–16]

a large heating rate and sufficient time to take measurements ofthe evolving thermal structure A fluid density stable stratifica-tion within the test section, e.g., a positive vertical temperaturegradient, is obtained employing the two tanks method The fluid

is initially equally distributed into two identical tanks set at thesame height The temperature inside the tanks is initially set to

TW(“warm” tank) and TC(“cold” tank) A pipe connecting the

“cold” tank and the test section fills the latter with a linearlyincreasing temperature working fluid In fact, the temperaturewithin the “cold” tank will increase with time because of theinput of warm water caused by the head difference between thetwo tanks An agitator placed within the cold tank homogenizesthe temperature inside The temperature at the upper boundary

is maintained at a constant value by an insulating polystyrenesheet The test section lower boundary is in contact with a cir-culating water bath connected to a cryostat, separated from theheat transfer engineering vol 32 no 2 2011

Figure 1 (a) Experimental setup (b) Sketch of the fluid configuration during filling procedure and during the experiment.

fluid by an aluminium sheet fitting the tank horizontal cross

section During the filling procedure, the cryostat maintains the

temperature of the lower boundary at a fixed value Ts0,

approxi-mately equal to TC(Figure 1b) The time required to fill the test

section ranges from 30 to 60 min, depending on the gradient

The experiment begins (time t= 0) when the cryostat

pro-vides heat to start and sustain convection by maintaining a

tem-perature always greater than the average temtem-perature within the

mixing layer (Figure 1b) In fact, thermal convection is

initi-ated upon replacing the cool water circulating under the lower

boundary with warm water of temperature greater than the per boundary temperature The temperature at the bottom, Ts,gradually increases approaching the final value Tsf

up-The fluid initial conditions are velocity equal to zero andincreasing temperature with height with a continuous approxi-mately linear trend of slope 1/γ Both velocity and temperatureare measured before convection is started to ensure stationaryconditions are reached

Temperature is detected through T-type thermocouplesplaced within the test section along a vertical line (array ofheat transfer engineering vol 32 no 2 2011

Figure 2 Initial conditions for the experiments (stratification profiles).

26 thermocouples of uncertainty less than 0.1◦C) to measure

vertical profiles and on the lower boundary to test horizontal

homogeneity in supplying heat T-thermocouples are made of

copper and a copper (60%)/nickel (40%) alloy The calibration

is performed by doing measurements in a thermostatic bath at

temperatures ranging between 5 and 40◦C It appears that slight

differences in output voltage between individual thermocouples

exist Therefore, every thermocouple is assigned its own

cali-bration parameters For the calicali-bration parameters, linear fits are

used (T≈ aV + b, with V the measured voltage) and optimized

by minimizing the sum of squared differences

Velocity is detected through an image analysis technique

(feature tracking) [15, 16]) Images of well-reflecting tracer

particles (pollen with average size equal to about Dp = 80

µm) were recorded by using a monochrome 8-bit CCD camera

with a time resolution of 25 fps, focused on the mixing layer

region (acquisition window of 15 cm side approximately) The

measuring plane is illuminated by a thin light sheet obtained

by collimating a divergent light beam, produced by a 150-W

halogen source, using a light-line fiber optic guide equipped

with a cylindrical lens

The acquisition procedure can be divided into two steps

Images are first stored on the mass memory of a computer (576

× 764 pixels as resolution) Then they are analyzed to detect

trajectories

Two experiments are presented here Their main features are

reported in Table 1 and the temperature initial conditions are

plotted in Figure 2 Both of the experiments show stratification

gradients that fit a linear trend well Experiment 2 presents a

temperature gradient (γ) lower than that of experiment 1, while

Table 1 Features of experiments

the final value of temperature reached at the test section bottom

is slightly larger for experiment 1

DATA PROCESSING

Thermocouples provide the instantaneous values of ature When heat is supplied from below, the linear temperatureprofile associated to the stratification inside the domain starts

temper-to break up and changes with time as far as the phenomenonevolves (Figure 3 for experiment 1 and Figure 4 for experiment2) Vertical temperature profiles acquired during the experimentallow the growth of the mixing layer to be measured at differenttime instants (zi(t)) The height can be calculated through the

following relation, where T(t) is the mean temperature within

the mixing layer (Figure 5):

Figure 5 Sketch of potential temperature vertical profiles inside the

atmo-spheric boundary layer The convective zone is divided into three layers, from

the bottom to the top we have: the surface layer (S.L.), the mixing layer (M.L.),

and the entrainment zone (E.Z.) Drawing not to scale.

T (t) is calculated by averaging the thermocouple outputs where

the temperature profile is uniform The upper limit of the

con-vective zone and the mixing layer height do not exactly

co-incide, and the temperature profile should exhibit an interface

layer, called the entrainment zone, where the temperature

ho-mogeneity overcomes the initial stratification line, as sketched

in Figure 5 Given the heating temperature, the vertical

ex-tension of the entrainment zone is expected to be greater for

lower temperature gradients of the initial stratification This is

due to the weaker resistance opposed by fluids presenting large

temperature gradients In both experiments presented here, the

temperature gradient is large and the entrainment interface is

negligible Equation (2) is then used to detect the mixing layer

height Moreover, when the entrainment zone thickness can be

neglected, the method just described coincides with the

well-known maximum gradient method, for which the mixed layer

depth is defined as the level of the largest increase in potential

temperature vertical gradient [17]

As mentioned before, the height of mixing layer is

compara-ble with the domes’ vertical dimension Starting from this idea

we can evaluate the mixing layer height with a given frequency

(anyway less than 25 Hz, the largest frame rate for image

ac-quisition) by dividing the domain into layers and computing

the vertical velocity standard deviation profiles The

horizon-tal homogeneity assumption, in fact, allows averaging velocity

data in each layer The degree of homogeneity was tested in

a statistical sense by analyzing sets of velocity data extracted

from different locations within the mixing layer at the same

height The reverse arrangement test [18] was performed and

repeated several times for different data sets, proving that the

horizontal homogeneity hypothesis holds with a 5% level of

significance

For each profile in Figure 6a, the height where the standard

deviation became, after the peak, 30% of the maximum value,

and where the profile slope is still gentle, is identified zi is

Figure 6 (a) Time evolution of vertical velocity standard deviation profiles for experiment 2 (b) Time evolution of σ w3/z profiles for experiment 2.

Figure 7 Comparison of mixing layer growth for experiments 1 and 2.

heat transfer engineering vol 32 no 2 2011

Figure 8 Time evolution of vertical velocity standard deviation profiles compared with mixing layer height evolution derived quantitatively from temperature measurement and qualitatively from trajectories observation (experiment 2).

empirically determined by using a larger set of experiments and

findings of Cenedese and Querzoli [10]

Moreover, inside a well-mixed layer where mechanical

pro-duction can be neglected, the Y= σw3/z profile versus z gives

an approximation for the local heat flux, which linearly creases with height vanishing by definition at z = zi [19], asshown in Figure 6b Thus, the extrapolation to zero of the linearregression of the Y profiles provides the mixing layer growthheat transfer engineering vol 32 no 2 2011

(if i= j we obtain the autocorrelation function), are measured at

points x1and x2, and at time t, p(ui, u

j, t) is the joint probability

density function Setting x1= x and x2= x + r, then

Ru

i uj(x1, x2, t) = Rij(x, r, t) (5)

If the assumption of horizontal homogeneity is satisfied, the

spatial correlation is only a function of|r|, the height z, and

time t, i.e., Rij(z, |r| , t).

TRENDS AND RESULTS

Figures 3 and 4 present vertical temperature profiles for

ex-periments 1 and 2 Each profile is associated with the acquisition

time given in the legend even though it was obtained through

averaging data acquired for 20 s at each thermocouple location

Three portions characterize each profile The portion of the

profile close to the boundary presents a negative gradient related

to the existence of the surface thermal boundary layer Its height

cannot be quantified because of the low spatial resolution of

thermocouples in the lower boundary region Then the profile

has a uniform temperature, T(t), where the mixing layer is

lo-cated Finally, above the mixing region, the temperature profile

practically collapses onto the straight line of the initial

stratifica-tion The temperature profile in the stable layer is not noticeably

affected by the growing mixing layer This holds even at late

stages when velocity data indicate internal wave activity in the

stable layer Profiles relative to the latest time intervals deviate

from the original stratification profile and become less stable

(the slope increases and the thermal gradient decreases)

The standard deviation profiles of the velocity vertical

com-ponent (Figure 6a) as well as the Y profiles in Figure 6b allow

the vertical extension of the mixing region and its evolution to

be detected and quantified (Figure 7) We expect values of the

velocity standard deviation to be larger inside the mixing region

than in the stable layer, where it should vanish According to

this expectation, profiles have a typical behavior with a

maxi-mum that became larger for longer time and an inflection point

moving upward All profiles change less as height increases

dy-by the plume In fact, for experiment 1 the mixing layer height

is much lower than for experiment 2 even if the heat provided

to start and maintain convection is slightly larger

Figure 8 compares three profiles, chosen among thosepresented in Figure 6a, with the snapshots of feature trajectories

up to the same times Each profile on the right-hand side isrelative to the given time, while the white straight line in theimages on the left-hand side indicates the height of mixinglayer computed from temperature measurements In particular,

it should be noticed that the mixing region spreads upward;

Figure 9 Normalized standard deviation of vertical velocity compared with atmospheric models, tank experiments (a), and field campaign data (b) found in literature.

heat transfer engineering vol 32 no 2 2011

Figure 10 Spatial autocorrelation of the vertical component of the velocity field for three times (experiment 2).

after 10 min approximately, the internal waves of increasing

amplitude with time can be recognized in the stable layer

The region occupied by domes (i.e., the region interested by

higher values of the standard deviation) overlaps very well with

the region of temperature homogeneity This evidence, coupled

with the comparison of temperature-based and velocity-based

methods to detect the mixing layer height, proves that both sets

of data allow the vertical extension of the convective region to

normal-22, 23]), and field campaign measurements (Figure 9B [24]).heat transfer engineering vol 32 no 2 2011

ponent of the velocity field for three instants of time Velocity

vectors belonging to a layer centred around the convective

re-gion centreline are taken into account The oscillating behavior

of each line allows the transverse dimension of the plumes within

the mixing layer, for a given time the correlation refers to, to

be evaluated The characteristic dimension of those structures

increases with time For small times, the number of velocity

samples belonging to the layer within the mixing region taken

into account to compute the correlation is inadequate to gather

a statistically acceptable result For large times, the structure

dimension becomes comparable to the test section side and the

wall effects are not negligible This then suggests the velocity

data analysis is meaningful since about 1000 s from the

begin-ning of the experiments

The correlation goes toward zero more quickly for smaller

time, congruently with the expected smaller dimension of the

structure; moreover, the dome horizontal characteristic

dimen-sion increases with time The distance between two peaks in

each plot is compared with the distance between two domes

Notice that the results are in a good agreement for each time

instant presented

CONCLUSIONS

Feature tracking is suitable for analyzing the large particle

density images acquired during the convective boundary layer

(CBL) experiments reported herein Structures characteristic of

the CBL have been observed: growing domes or turrets

present-ing an extremely sharp interface at their top, flat regions of large

horizontal extent after a dome has spread out or receded, and

cusp-shaped regions of entrainment

The mixing layer height was detected by employing

tem-perature data and the standard deviation profiles of the velocity

vertical component All methods determine comparable mixing

layer growth

The spatial covariance of the velocity field, providing the

plume horizontal dimension, allows the spatial extension of the

mixing region to be determined

Dome characteristic vertical dimension is of the same order

of magnitude as the mixing layer height, while their horizontal

dimension becomes similar to the vertical one at the end of the

experiment when the structure dimensions are comparable to the

test section side and border effects are not negligible anymore

Experimental data demonstrate the validity of Deardorff

mixed-layer similarity [5] for the turbulent structure of the

boundary layer Moreover the comparison with literature data

shows a good agreement with measurement taken at both bench

and real scale, demonstrating the validity of our experimental

D diameter of particles, m

g gravity acceleration, m/s2

p joint probability density function

q kinematic heat flux, m-K/s

z Cartesian vertical direction, m

zi mixing layer height, m

Greek Symbols

β thermal expansion coefficient, 1/K

γ temperature gradient before heating starts, K/m

interval

θ potential temperature, K

σ velocity standard deviation, m/s

Superscripts

∗ convective parameter scale

‘ parameter fluctuation part

- parameter mean part

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Atmo-spheric Science, vol 31, pp 1297–1307, 1974

[23] Deardorff, J W., and Willis, G E., Further Results From aLaboratory Model of the Convective Planetary Boundary

Layer, Boundary-Layer Methods, vol 35, pp 205–236,

Valentina Dore is a Ph.D student in the Fluid

Me-chanics Laboratory of the Department of Hydraulics, Transportation, and Roads of Sapienza University of Rome, Italy She received her master’s degree from Sapienza University of Rome in 2006 Currently, she

is working on investigating the convective boundary layer via image analysis techniques.

Monica Moroni is a researcher in the Department of

Hydraulics, Transportation, and Roads of Sapienza University of Rome, Italy She received her master’s degree from Sapienza University of Rome in 1996 She received her Ph.D from Sapienza University of Rome in 2000 Her main research interests are de- veloping novel image analysis techniques, laboratory investigation of the atmospheric boundary layer, and Lagrangian chaotic dynamics of mixing She has pub- lished more than 60 articles in well-recognized jour- nals, books, and proceedings.

Antonio Cenedese is a professor of

environmen-tal fluid mechanics at Sapienza University of Rome, Italy He received his master’s degree from Sapienza University of Rome in 1966 His main research inter- ests are developing novel image analysis techniques, laboratory and numerical investigation of the atmo- spheric boundary layer, hyperspectral image analysis, and bio fluid mechanics He has published more than

250 articles in well-recognized journals, books, and proceedings.

heat transfer engineering vol 32 no 2 2011

Experimental Study of Flame

Extinction in Standard Square

Flammability Column Resulting From Stretching

TADEUSZ R FODEMSKI and GRZEGORZ G ´ ORECKI

Department of Heat Technology and Refrigeration, Lodz Technical University, Lodz, Poland

The main goal of this work is to determine experimentally local stretching rate distribution along the limits of methane/air

and propane/air flames, using particle image velocimetry (PIV) This method allows obtaining necessary moving flame

velocity fields in a standard flammability column and also recognition of the flame structures For this purpose each mixture

was seeded with MgO particles (of known size) before entering the tube (column), using a special system The amount of

seeds in the mixture, their dispersion system, and the laser power producing a sheet of light penetrating the column were

carefully chosen (so as not to disrupt the combustion or flame propagation in it) After a learning process, this finally it

allowed us obtain good-quality velocity field images in the region of concern, images acceptable for further processing The

methodology developed for these experiments proved to be reliable and able to supply analyses with repeatable data On the

basis of performed experiments it was possible to derive the flame stretching rate that causes its extinction in both mixtures.

INTRODUCTION

The first theoretical concept of flammability limit was

for-mulated more than 200 years ago [1] and started to developed

significantly after 1930 [2–5] In the second part of the last

cen-tury important works, both theoretical and experimental, were

published (see monographs [6, 7] and those related to the present

paper [8–26]) After the introduction of flame stretch and

pref-erential diffusion concepts, better understanding and progress

could have been made For practical reasons (to bring down

a growing number of accidents in mines and various

indus-tries), flammability limits for different mixtures were measured

The methodology and results presented in this paper are from a

completed project supported by EU Marie Curie ToK ECHTRA (No

MTKD–CT–2005–509847) and also from currently conducted projects

sup-ported by the Polish State Committee for Scientific Research (Project

4607/B/T02/2008) and Technical University of Lodz, Engineering Faculty,

KT-CiCH (Projects K–15/701/BW and K–15/699/DzS).

Address correspondence to Prof Tadeusz R Fodemski, Department of Heat

Technology and Refrigeration, Mechanical Faculty, Lodz Technical University,

90-924 Lodz, Poland E-mail: tadeusz.fodemski@p.lodz.pl

in many laboratories in vessels of various shapes and were ratus dependent Therefore, a standard vertical tube of diameter

appa-d = 50–51 mm and length h = 1.8 m, closed at the upper end

and open to the atmosphere at the bottom, was proposed for thisflammability determination in 1952 [8] The gas concentration

at which the flame extinction occurs, before it reaches the topend of a standard column, is referred to as a flammability limit,and the flame in a standard tube at this concentration is called

a limit flame The optical experimental methods started to beemployed intensively [13] and, to make their application easier,this standard vertical tube has been often replaced by a verticalcolumn of the same length but with square (5 cm× 5 cm) crosssection [7] Although the flame shapes propagating in these twochannels, close to the walls, are different (see Figure 1 for twomixtures analyzed in this paper), these shapes and propagationconditions are very similar for both flame tips (in the centralcylinder around the symmetry axis of both columns, about half

of the tube diameter or channel width)

There are papers where analytical analyses for tubes are ported by results from experiments with square-cross-sectioncolumns [16–18] In particular, heat loss effects to cold walls,

sup-109

Figure 1 Stable lean limit flames pictures propagating in columns h= 1.8 m

long with different cross-sections: tube diameter 5 cm: (a) CH 4 /air; (b) C 3 H 8 /

air; square 5 cm × 5 cm: (c) CH 4 /air and (d) C 3 H 8 /air.

in both cross sections mentioned, are negligible in the flame

tip regions (see [11] and the most recent works, for example,

[27–29]) Some of these phenomena were also analyzed

focus-ing on the gravity, large centrifugal forces, and microgravity

conditions [25, 30, 31]

For a lean limit mixture, flames propagating in a standard

vertical 1.8-m-long column with square cross section 5 cm×

5 cm and (mainly as a reference) in a tube of 5 cm diameter

were analyzed in experiments with particle image velocimetry

(PIV) and are reported in this paper Two different combustible

mixtures, i.e., methane–air and propane–air (referred to here as

CH4/air and C3H8/air), were investigated Following the

igni-tion at the column open bottom end, the flame propagates up

toward the closed top end The experiments showed that the lean

limit flame extinction of CH4/air is similar to that of C3H8/air

(their concentrations are 5.25% or
= 0.528 and 2.05% or

= 0.498, respectively) It was reported by researchers (for

example [9], [16], [28]) that the extinction always starts at the

flame tip and then spreads down toward the flame skirt Since,

as mentioned, the heat loss effect to the cold walls, for both

cross sections mentioned, is negligible, it is claimed that

an-other reason is responsible for this limit flame extinction The

generalized approach to explain it was originally developed by

Karlovitz et al [9] It involves the idea of the flame stretching

rate to describe the local flame front propagation and

extinc-tion This approach is based on the analysis of the velocity field

in the mixture and in the combustion gases close to the flame

However, there is still a need for reliable experimental results

Figure 2 The plane laminar flame features.

Figure 3 Three zones of the plane laminar flame structure [5].

One of the most promising methods to analyze velocity fields isthe PIV method

The important features of the plane laminar flame, moving

in a stationary manner, are shown in Figures 2 and 3 (withthree zones, determined by the temperature distribution, result-ing from Eq (1)) This is used as a reference case for flamespropagating under other conditions; therefore, the most impor-tant information related to it is given in the following

The energy equation for this flame, moving with velocity

u L∞, has the form of a second-order differential equation [4, 18,

19]:

λd2T

d z2 − u L c pρd T

d z + q = 0 (1)

where I is the zone of mixture heating, combustion reaction

velocity = 0; II is the ignition zone, d 2 T/dz 2 ≈ 0; and III is the reaction zone in the final temperature, i.e., dT/dz ∼= 0.Figure 4 shows the measured temperature profile (curve 1determined by experimental points [19]) and, for comparison,the exponential profile (defined by equation in Figure 2, where

temperatures T i = eT O and T N = (e − 1)T O result from thesolution of Eq (1) in the mixture heating zone [4, 18]).The determination of the “flame thickness” is important On

the basis of the Eq (1) solution, in zone I, Zeldo’vich and

co-workers [4, 18] defined the laminar flame thickness δZel,

Figure 4 Temperature profiles: (1) experimental, in all zones [6]; (2) nential; in the heating zone, see Figure 2.

expo-heat transfer engineering vol 32 no 2 2011

Figure 5 Different laminar plane flame thickness definitions.

expressed by the formula:

δSp= (T G − T O)

The flame thickness δG-W, by Gaydon and Wolfhard [10], is

defined as a layer from the temperature inflection point (Figure

2) to the point where it differs by 1% from the fresh mixture

temperature The last flame thickness definition presented,δA-B

(by Andrews and Bradley [14]), is based on the experimental

measurements using a noninvasive interferometer, allowing one

to determine special points A and B (Figure 5)

All the thicknesses just mentioned are shown in Figure 5

One can find, neglecting the temperature changes of the

mate-rial parameters, thatδSp = 2 δZel;δG-W = 4.6 δZel and that the

experimentalδA-Bvalue is the largest one The lack of a unified

thickness definition results in difficulty in the flame stretching

rate determination (discussed later)

EXPERIMENTAL SETUP AND METHODOLOGY

The PIV System and Equipment

The PIV DANTEC Measurement Technology system was

used (Figure 6): two double-frequency Q-switched Nd:YAG

lasers with maximum 50 mJ energy output, digital video camera

CCD 80C60 HiSense PIV/PLIF (1280 × 1024 ≈ 1.3 × 106

pixels), special FlowManager double PIV processing unit, and

a computer controlling all units The maximum rate of the PIV

system operation was four measurements (four double frames)

per second In the experiments, different physical areas of the

column were recorded

Figure 6 The PIV setup.

The principles of this method are shown in Figure 7 Twopictures of any flow (with the seeding particles), coincidingwith the presence of the “sheet laser light,” are taken in a short

t time interval and are recorded Knowing particle positions in

both pictures (they are divided into “interrogation areas”; Figure7), and thet value, one velocity field is created and is ready

for further processing We usually used 16× 16 pixels in theinterrogation area Thus, four velocity pictures per second areacquired, in each area mentioned, giving information on howthis field changes with time It is important to state that in ourprocedure of processing good-quality velocity fields, to obtainthe local flame stretching rates for lean CH4/air and C3H8/airmixtures, we focused totally on the flame shapes by placingthese areas accordingly This procedure allowed achieving thehighest accuracy as far as the system used is concerned Themost important area for the analysis of the stretching rate is theflame tip region, where the flame extinction starts, and these rateshave maximum values (they result from the theoretical analysisand are confirmed by our results presented in this article)

Seeding Particles

MgO seed particles were used throughout all experimentsreported in this work Two particle volume distributions are pre-sented in Figures 8 and 9 The first, and the finest we couldpossibly have, with the averaged particle size of 2µm, was used

to acquire final velocity fields, from which the local

stretch-ing rates k along the flame front, presented in this paper, were

obtained

The bimodal particle size distribution was used in thepreparatory stage of our work The third one, not presentedhere (with the distribution shape similar to the one presented inFigure 8 but with the mean value of particle size being equal

to 5µm) was also used, mainly for comparison of the effects

Figure 7 The principle of the mixture (with seeding) velocity determination.

heat transfer engineering vol 32 no 2 2011

Figure 8 Volume distribution of the MgO seed particles (mean diameter 2

µm) used in all experiments presented in this paper.

of thermophoresis The use of the similar size of solid seeds

(1.6 µm spherical ceramic particles), in C3H8/air mixture at

an equivalence ratio
= 0.585, with the PIV experiments

in-volved, is reported in [32] It includes the assessment of the

effects of thermophoresis on the motion of seeding particles

surrounded by mixture Experimental conditions in the quoted

work (related to the unsteady effects on the propagating flame,

wrinkled by a vortex) and in the present one are different in two

aspects First, the equivalence ratios in two experiments differ

(0.585 and 0.498) Resulting from this, the ratio of temperature

differences across the flame is about 1.175 It is lower by about

17% in the flammability limit C3H8/air mixture analyzed in the

present paper Second, there is an additional effect of the flow

unsteadiness connected with this vortex—not occurring in the

present work—where the steady laminar limit flame movement

prevails Taking into account thorough and detailed estimations

related to the three potential effects of thermophoresis [32],

comparison of the sum of these effects in the two cases leads to

the conclusion that in the present work the theoretical accuracy

of the velocity field determined by the same PIV systems is

lower than 10% It is worth adding that velocities are not used

in the present work, but instead their gradients are important

Being aware of thermophoresis effects, we applied the same

procedures to determine velocity field and the resulting local

stretching rate using 5-µm MgO particles A set of values

sim-ilar to those for 2-µm particles was created The stretching rate

values obtained in our experiments with 2- and 5-µm particles

differ less than 4% (no similar attempt was reported to check

the influence of seed particles size on the experimental values in

available references) In other experiments, analyzing ethylene,

n-butane, and toluene flames, small droplets of silicone fluid as

Figure 9 Bimodal volume distribution of the MgO seed particles (used in

preparatory stage).

seeds were used (these droplets do not survive the post-flameregion [33]) Microscopic analysis of different sizes of MgOparticles was also done, using a scanning microscope (HitachiS-3000N), before and after their exposure to the flame propa-gating in the column No influence or sign of any effect on boththe particle surfaces and the volume distribution was noticed.Two important conclusions result from the detailed particlesanalysis: (i) There is no chemical reaction in the combustion inwhich the MgO particles are involved, and (ii) the influences ofthe combustion and the thermophoresis effects on the seedingpresence and movement in the mixture, using the PIV method

to determine these velocity fields and local stretching rates, are

in the range between 4% and 10% (i.e., within the experimentalerror of this study estimated as 10%)

The Flammability Column

In all our experiments different columns were used: two ofthem only for the analysis of the mixture flow with seeds tocheck supply conditions and the MgO particles distribution inthe flammability columns The analysis showed that the mix-ture with the seeding supply system at the top of the column issuperior Each mixture, without seeding, was initially prepared

by the partial pressure method and stored in a special tank Theprecision of this method, due to the use of digital electronicpressure gauges, was estimated as ±0.02% of CH4 or C3H8concentration in the respective mixture with air The mixtureswere stored for about 24 h before use The MgO seeding supply

to each mixture occurred when filling the column, using thereplacement method (not less than 6 column volumes) Afterclosing the valves, the mixture with seeding was allowed torest, in the column, for about 40 s to damp out residual flowsfrom the column filling Then the bottom valve was opened andmixture ignited near the column bottom end The flammabil-ity columns used in all combustion experiments are shown inFigure 10

Better results of seeding distribution in the mixtures insidethe column were achieved using the pressurized supply systemwith the shredder (Figure 10b)

It is worth mentioning that combustion in the column results

in the flow of reaction products toward the open bottom end,while fresh mixture is motionless between the flame and theclosed top, excluding the region very close to the flame Thiseffect is shown in Figures 11 and 12 (each has four pictures, for

CH4/air and C3H8/air, respectively) The MgO particles bution immediately below the flame front is lower by less than

distri-a hdistri-alf order of mdistri-agnitude Pictures distri-a distri-and b (in Figures 11 distri-and12) present the flame movement recorded without and with theoptical filter, respectively The presence of the filter, cutting allbut the laser light for the camera recording, is crucial Pictures cand d show two enlarged areas below the flame, where the suf-ficient presence of seeds can be seen (presented pictures qualitylowered in the processing for publication) This is important,since the PIV system used requires sufficient seeding particleheat transfer engineering vol 32 no 2 2011

Figure 10 Flammability columns and the mixture with seeding supply

sys-tems: (a) at atmospheric pressure and (b) pressurized.

Figure 11 The PIV camera pictures of moving flame in CH 4 /air, with 2- µm

MgO particles: (a) without an optical filter; (b) with the optical filter; (c) and

(d), two enlargements of chosen areas below the laminar flame.

Figure 12 The PIV camera pictures of the moving flame in C 3 H 8 /air, with

2- µm MgO particles: (a) without an optical filter; (b) with the filter; (c) and (d),

two enlargements of chosen areas below the laminar flame.

Figure 13 (a) Optical setup of the schlieren method flame pictures; (b) tracted part (used in all other schlieren pictures in the paper), which shows only propagating flame in the column.

ex-density in the interrogation areas of this region—greater than 5particles in each area—to obtain the proper, representative, andgood-quality velocity fields in all areas mentioned (the C3H8/aircase always required more attention and this request was satis-fied in all results presented in this paper)

The Seeding Particle Mass in the Column

Apart from the PIV system, the schlieren method was used

to record flame behavior Figure 13 presents its full set-up andthe interesting part of it related only to the flame (shown in allother pictures throughout this paper)

The analysis concentrated on pictures like the one presented

in Figure 13b, helping to analyze the influence of the seedingmass amount in the standard flammability column on the flamepropagation velocity in it This velocity can be determined forany mass and compared to the one without MgO The chosenset of pictures in Figure 14 presents recorded color changes,when the MgO particle mass in the mixture grows: Figures 14aand b show the mixture without seeding, taken by two differentcameras, and Figures 14c–h for specified mass of the MgOparticles in the column

Figure 14 Total seeding mass influence on flame velocity propagation umn 5 cm × 5 cm × 1.8 m Mixture CH 4 /air; average MgO particle size 2

Col-µm Pictures: (a) by ordinary camera, no seeding; (b) by schlieren method (no seeding); (c)–(h) schlieren method with growing seeding mass.

heat transfer engineering vol 32 no 2 2011

Figure 15 Influence of the seeding mass (average MgO particle size 2 µm), on

laminar flame velocity propagation in CH 4 /air and C 3 H 8 /air mixtures; column

size 5 cm × 5 cm × 1.8 m The maximum seeding masses A and B, for each

mixture, are determined.

The adopted solution to control seeding mass in the column

is actually presented in Figures 10a and b The total prepared

gas mixture flow is divided into two parallel flows The flow to

the seed container is controlled by the valve and rotameter The

mixture flow ˙m V blows away seeding mass m related to this flow.

The relation between the flow and the seeding mass taken by it

was derived for practical use The results of extensive

experi-ments to establish the seeding influence, on the laminar flame

moving up in column with 5.25% CH4/air or 2.05% C3H8/air

mixture (with MgO 2-µm particles), are shown in Figure 15

For each mixture, one can notice a fall in the flame velocity

measured when the seeding mass increases Lines A and B, for

CH4/air and C3H8/air, respectively, show the maximum seeding

mass in all our experiments The ratio of these masses is about 3,

but each value is far from the one to notice any practical change

in the laminar flame velocity measured for the respective mixture

free of seeding

The other important factor affecting the PIV recorded

veloc-ity field picture qualveloc-ity is the laser light impulse energy used in

a particular experiment In general, it is connected with the seed

numbers “seen” by the camera, and this depends upon the “sheet

laser light” thickness The latter grows with its energy impulse

and also with the distance between the laser and the analyzed

object Figure 16 shows comparison of two picture sets chosen

from a big number stored The top row presents the case with a

too small seeding mass in the mixture The bottom one shows

the acceptable combination of their values related to these two

factors mentioned Usually, there is a trade-off between these

factors in order to achieve the best quality velocity picture (this

applies to all experimental results presented in this article)

The last important experimental limitation, related to the

ob-served and undesired lack of the flame symmetry or even its

surface oscillations (occurring in columns in the preparatory

stage of experiments) during the flame propagation, was also

analyzed (general transition to unstable flames in different

mix-tures is discussed, for example, in [34]) The flame shape and its

Figure 16 Influence of the laser energy impulse and seeding mass on PIV flame velocity field picture quality Flame propagates in the column 5 cm ×

5 cm × 1.8 m with C 3 H 8 /air The laser impulse (mJ) and the total seeding mass (g) (average MgO particle size 2 µm) are given.

propagation in the column, for the local flame stretching rates termination, has to be always symmetrical and stable throughoutthe whole length of the standard flammability column, regard-less of its cross section and mixture The bubble-shaped limitflame propagating up moves with the velocity determined bythe buoyancy forces, like an air bubble in a column of water [5,

de-7, 13, 28] Since this velocity is independent of mixture

proper-ties, for the tube diameter d it can be calculated quite accurately from the simple formula U = 0.328√gd [5, 7, 28]) Figure 17

presents (a) pictures of symmetrical and nonsymmetrical flameshapes moving in the rectangular column cross section and (b)their three-dimensional (3-D) graphic models related to bothshapes, respectively

At the preparatory stage it was not certain what causes ble movements However, it was observed that the same flamebehavior occurs in mixtures without or with the seeding particles(2 or 5µm) It has been definitely found that this nonsymmet-rical flame shape and the flame oscillatory behavior result fromthe lack of thermal equilibrium of the column walls This refersparticularly to the square-cross-section columns; they are fromdifferent materials: aluminum and glass (Figures 13 and 17).The stable shape and movement of flames in our experimentalstand did not occur when the time gap between two consec-utive experiments was greater than 30 min Figure 1 showsthe stable flames in CH4/air and C3H8/air mixtures with seed-ing, moving in columns with circular (a and b) and rectan-gular (c and d) cross sections, respectively Close to the col-umn walls, a noticeable difference in the flame shapes resultsonly from their cross sections Determined local stretching ratespresented in this paper are for the stable flame movements in5.25% CH4/air and 2.05% C3H8/air mixtures with 2-µm MgOparticles

unsta-heat transfer engineering vol 32 no 2 2011

Figure 17 The stable and unstable surface flame shapes in the C 3 H 8 /air

mix-ture without seeding, during propagation in 5 cm × 5 cm × 1.8 m flammability

column The same flame behavior in the CH 4 /air mixture with no seeding in both

mixtures with the MgO particles (2 or 5 µm) (a) Camera pictures; top: stable

shape; bottom: unstable one; both for C 3 H 8 /air without seeding; (b) graphical

3-D model of the flame surfaces.

The experimental setup, described earlier, results from the

thorough analysis in the preparatory stage Some remarks related

also to the methodology are also presented there This setup

allowed us to assemble a reliable experimental stand and to

conduct wide, precise, and repeatable experiments with two

mixtures We achieved a repeatable experimental state of the

present only two examples of such fields Analysis based onthese fields and used in calculation allowed determining thelocal flame stretching rates

The Methodology

Important methodology contributions, which can be used inthe PIV picture processing, to obtain the local stretching ratesfrom the PIV vector velocity pictures, are presented in [22] andemployed elsewhere [28, 35–37] The latter consider detailedanalysis related to the lean limit flame movement, and uses astandard flammability tube, focusing on the temperature fieldanalysis in the CH4/air mixture only The cylindrical geome-try and the stable flame propagation represent a genuine casewhere all 3-D scalar and vector distribution fields (temperatureand velocity, respectively) are, in fact, two-dimensional (2-D)(see Figures 1a and 1b) It is worth noticing that this simplergeometry presents a few complications in the PIV system appli-cation The important ones are related to the laser sheet beamrecorded pictures: (i) The laser beam is scattered by internaland external tube surfaces (to avoid this, two parts of the tubewall were replaced by the narrow flat glass windows); (ii) dis-tortion of the PIV seeding particle images recorded through thecylindrical tube wall occurs; and (iii) the background reflec-tions of laser light pose problems (solved by a vertical slit aper-ture installed near the tube test section) The optical distortion

Figure 18 The good quality velocity picture of the flame in the CH 4 /air with the MgO seeding particles (the average size 2 µm); column 5 cm × 5 cm × 1.8 m; coordinate system bound to the flame Pictures: (left) seeding distribution in the mixture; (middle) velocity field (m/s) in the fresh mixture and in combustion products, on the white background and (right) superimposed pictures: (left) + (middle).

heat transfer engineering vol 32 no 2 2011

Figure 19 The good quality velocity picture of the flame in the C 3 H 8 /air with the MgO seeding particles (the average size 2 µm), column 5 cm × 5 cm × 1.8 m; coordinate system bound to the flame Pictures: (left) seeding distribution in the mixture; (middle) velocity field [m/s] in the fresh mixture and in combustion products, on the dark background and (right) superimposed pictures: (left) + (middle).

during the recording, mentioned in (ii), causes a systematic

er-ror in radial coordinate direction; it can be corrected in obtained

real fields by a multiplication factor adequate to their radial

placements in the tube A significant part of the experimental

problems mentioned is not present in the square-cross-section

channel with plane walls The main idea presented in [7] and

[22] has also been used in the work reported in this paper It is

based on the link—not only theoretical but in fact present in the

PIV measurements—between velocity and temperature fields in

the flame front undergoing stretching This is particularly

im-portant when the observed thickness of the studied flame front

cannot be defined precisely (despite different flame thickness

definitions presented earlier; see Figure 5) The analysis in [7]

and [22] leads to the determination of isotherms from T= 400

K up to 1000 K The first one is related to the region of the

forefront flame location It can be identified by the local

max-ima of the dilatation rate of the fresh (cold) mixture flow on

the way through the heating zone to the flame (see Figure 2

in the coordinate system bound to the flame) The proposition

is used to determine the location of 400 K isotherm, at which

the stretching rate should be calculated Figure 20 shows the

comparison of two temperature profiles determined in different

ways: (i) calculation based on the PIV measurements of the gas

velocity distribution in the flame front region, and (ii) measured

by a 10-µm platinum wire sensor Both profiles show good

agreement

This temperature profile was used to construct Figure 21 and

is also shown there together with the location of other isotherms

The dashed area covers the region where the isotherms cannot be

precisely determined by the described method [28] It is worth

mentioning that for the CH4/air mixture this region is, in fact,

a stagnant gas volume which moves together with the flame

tip (Figure 18) It results in the lower temperature in the

stag-nation zone in Figure 21—in the dilatation method obviously

related to low gas velocities with reference to the flame Thepresence of this region was also detected by the independent ofthe PIV temperature measurements there (see Figure 22 [28],particularly two temperature profiles at the flame tip region).They confirmed the temperature drop between the flame andthe stagnation zone Such flame structure indicates the normalconsequence, i.e., the local heat flux presence from the flame

to the surrounding gases with lower temperature below For theflame tip, the loss of heat by the radiation quite possibly leads

or strongly contributes to its extinction

To complete the presentation of the experimental stand andmethodology, it is worth showing examples of the velocity fieldsthat the PIV system and the FlowManager program create Apartfrom Figures 18 and 19, they are also shown in Figures 23 and

24, for the flammability limit CH4/air and C3H8/air mixtures.Figures 19 and 24, related to the latter mixture, show that in thiscase there is no stagnant gas volume below the flame tip thatmoves together with it

Figure 20 The temperature profile of the propagating lean limit flame front

(at the center of the flammability tube diameter d = 5 cm and length h = 1.8 m

long); lean limit CH 4 /air mixture [25–27] Comparison of two profiles: points, calculated temperature (from the PIV velocity field picture in mixture); dashed line, temperature measured by the 10- µm platinum wire sensor.

heat transfer engineering vol 32 no 2 2011

Figure 21 The flame tip region isotherms distribution in the lean CH 4 /air

mix-ture during propagation in the tube column (diameter d = 5 cm and length h =

1.8 m).

THEORY, PRACTICE, AND RESULTS

The important difference between lean limit CH4/air and

C3H8/air mixtures is the Le number value The former mixture

has Le < 1, and stretched flame propagating in it experiences

preferential diffusion resulting in a higher burning intensity

Mixture characterized by Le > 1, during stretching, reduces this

intensity [26, 38] The general and qualitative character of this

stretching influence on the flame temperature, in mixtures with

different Le, is shown in Figure 25 Detailed theoretical analysis

of flame extinction by stretching, in different combustion

con-ditions (for example, in the counterflow burners), is beyond the

scope of this paper The main qualitative differences between

velocity profiles in the flammability columns and in these

burn-ers refer to flows in the combustion product zones Only the

basic theoretical information allowing predicting the influences

of the flame stretching rate k and of the Le number values on

the flame extinction is presented in the following

The asymptotic analytical adiabatic model, for weakly

stretched flames [15, 38], predicts that the response of flame

front parameters (i.e., the temperature T and velocity u L)

de-pends on the sign of the following expression: W = k (1–Le)

Figure 22 Temperature profiles along the flame and below the flame in the

lean CH 4/air mixture; flammability column: tube diameter d= 5 cm and length

h= 1.8 m.

sign, based on the expression mentioned, gives the followingresults:

A For the positive stretching rates (i.e., k > 0) and two values

of the Le number, one gets:

1 When Le < 1 (lean CH4/air or rich C3H8/air), one obtains

the value of W > 0 and therefore the flame temperature

and its velocity should increase

2 When Le > 1 (rich CH4/air or lean C3H8/air), the value

W < 0 and flame parameters decrease.

B For the negative stretching rates (i.e., k < 0) and two

values of the Le number, one has:

3 When Le < 1 (lean CH4/air or rich C3H8/air)–value

of W < 0; flame parameters decrease.

4 When Le > 1 (rich CH4/air or lean C3H8/air)–value

of W >0; parameters should increase.

This simple method has been applied to too many cases,sometimes beyond its application range Therefore, the compar-ison of the preceding theoretical prediction with the particularexperimental result is paramount The repeatable experimentalresults of flames extinctions, during the undisturbed laminarflame propagations in the standard flammability column withflammability limit CH4/air and C3H8/air mixtures—starting atthe location where the flame stretching rates have the maxi-mum values—are in contradiction with the asymptotic theory ofstretched flames (see earlier discussion of theoretical predictionsfor cases A1 and B4, respectively) The main aim of this paper is

to report the determined flame stretching rate values resulting inextinctions of both limit flames analyzed However, during thecourse of this work some interesting direct visual observationshave been recorded and also obtained after their processing.They are not confined only to the small tip flame region

in both flammability limit mixtures and result from the wideruse of PIV and schlieren picture methods The chosen samples

of these observations and results are presented in Figures 26

to 29

Figure 26a shows the stable structure of the peculiar seedingparticles accumulation (before any extinction starts) in the topregion of the flame present in the flammability limit CH4/air

mixture (Le < 1) This structure is connected with the

stag-nant combustion product region, just below the central part ofthe bubble flame This region moves upward practically to-gether with the flame In consequence, the region content isnot replaced by the effective, convective combustion products

“fresh supply,” directly from the reaction zone Therefore, theheat transfer engineering vol 32 no 2 2011

Figure 23 The PIV limit flame propagation velocity pictures (all fields shown are in the coordinate system bound to the flame); its position is additionally marked

by white dots The lean 5.25% CH 4 /air mixture with MgO seeding (2 µm); square column: 5 cm × 5 cm × 1.8 m (a) Single PIV picture showing seeding; (b)

velocity field; (c) total velocity V c (m/s), scalar map; (d) V x component, scalar map (m/s); (e) V zcomponent (m/s), scalar map; (f) flow rotation ω (1/s), scalar map.

temperatures in this region, as shown in Figures 21 and 22, are

significantly below not only the flame temperature but also

be-low the temperature of gases outside this region The chosen

area of Figure 26a is also shown in Figures 11c and 11d (the

latter for Le > 1) to prove that the density of seeding

parti-cle distribution is sufficient to determine velocity field there by

the PIV system The developed methodology allows

construct-ing the streamlines, in the flame coordinate system, for this

flame bubble moving up; they are shown in Figure 26b The

same methodology is used to construct these streamlines for

the flammability limit C3H8/air mixture (Le > 1), presented in

Figure 26c The flame front positions identified by local ima of dilatation rate are shown in both streamlines The overallcomparison of these streamlines, for the two analyzed flamma-bility limit mixtures, gives the evidence that they differ signif-icantly; at the flame front inflow they are less divergent andconverge again more quickly in the C3H8/air mixture than inthe CH4/air one The PIV method is the most effective toolthat allows detecting the presence of the stagnation zone in theflammability limit CH4/air mixture and this zone absence in therespective C3H8/air mixture Finally, Figure 26d presents therich limit flame in C3H8/air mixture (characterized by Le < 1)

max-heat transfer engineering vol 32 no 2 2011

Figure 24 The PIV limit flame propagation velocity pictures (all fields shown are in the coordinate system bound to the walls); its position is additionally marked

by white dots The lean 2.05% C 3 H 8 /air mixture with MgO seeding (2µm); square column 5 cm × 5 cm and length h = 1.8 m (a) Single PIV picture showing seeding; (b) plane velocity field; (c) scalar map of the total velocity V c (m/s); (d) V x component, scalar map (m/s); (e) V zcomponent, scalar map (m/s);(f) flow rotation ω (1/s), scalar map.

obtained by the schlieren method with superimposed direct

photography Its structure is generally similar to the structure

presented in Figure 26a and related to the lean limit CH4/air

mixture (Le < 1) However, Figure 26d cannot provide any

information about the velocity field involved in this flame

prop-agation

Figures 27, 28, and 29 present recorded pictures of exactly

the same flame extinction process, occurring in the flammability

limit 5.25% CH4/air mixture in the square-cross-section 5 cm×

5 cm and 1.8-m-long standard flammability column This quite

spectacular and well repeatable process started in the top half ofthe column, where all optical equipment outside of the flamma-bility column has been mounted

It took some time to have start and completion of this lar extinction process exactly in this column location for the fullrecording using available equipment located just there Since

particu-we particu-were dealing, as already mentioned, with flammability limitflame, the repeatability of its extinction in the particular loca-tion cannot be forecasted; otherwise one can suspect that it istriggered by some special cause that might affect, in some way,heat transfer engineering vol 32 no 2 2011

Figure 25 The general, theoretical influence of the flame stretching on the

flame temperature.

the whole extinction process Figure 27 shows direct

photogra-phy negatives, taken at 0.02-s intervals (it determines also the

accuracy of the flame extinction beginning), which cover 0.26

s after the flame extinction start The dotted line in Figure 27

shows positions the flame should reach in the column when

propagating without extinction The flame disappearance can

be observed but without information about the details of

veloc-ity fields involved

Figure 28 shows four PIV velocity field pictures, in the

co-ordinate system bound to the column walls, and covers 0.75

s after the flame extinction starts (picture a) After 0.25 s

fol-lowing the start of PIV recording, velocities of hot gases close

to the disappearing flame have the maximum value of 0.4 m/s

(picture b), and in the next 0.25 s and 0.5 s, these velocities

are 0.9 m/s (picture c) and 1.3 m/s (picture d) Figure 29 shows

the same case as presented in Figure 28, but with the additional

scalar maps of all velocities in the coordinate system bound to

the flame

The Theory and Results of Flame Stretch Determination

The basic and important information related to the flame

stretching theory are given next The flame stretching rate k

(s−1) is determined by the formula [9]:

k= 1

A ·d A

where A is the flame area and t is time.

The stretch affects laminar flame velocity, and this effect isexpressed by the equation [17, 20]:

where u L∞ is the plane flame laminar velocity and u L is theflame (under stretch) laminar velocity

The last equation can be written also as the Markstein length

L Mdefinition It can be also rearranged to the following formula[17, 20]:

Only for Le = 1 one obtains δ = δZel, and no other flamethickness definitions presented earlier are involved in these con-siderations

The flame stretching rate calculation in a standard bility column case is considered the main goal of this paper

flamma-It can be determined by utilizing the PIV system and method

to obtain the velocity field For the 2-D case, and coordinatesbound to the moving flame, this stretch can be calculated using

Figure 26 Pictures related to experimental and computational results, for CH 4 /air and C 3 H 8/air mixtures, presenting the Le value influence on the flame propagations in a standard flammability tube diameter d = 5 cm and length h = 1.8 m: (a) the PIV seeding image picture in the lean limit CH4/air mixture (Le <

1), resulting from the limit flame propagation (coordinates bound to the flame); (b) streamlines pattern (coordinates bound to the flame) in the lean CH 4 /air mixture

(Le < 1), determined from the PIV limit flame velocity distribution propagation Flame front position, identified by local maxima of dilatation rate, is shown (c)

As in (b) but for limit flame in the C 3 H 8/air mixture (Le > 1); (d) superimposed schlieren and direct photography pictures of the upward propagating flame in the

rich limit C 3 H 8/air mixture (Le < 1).

heat transfer engineering vol 32 no 2 2011

Figure 27 Pictures of the limit flame extinction process in the flammability limit 5.25% CH 4 /air mixture Flammability column: square cross section 5 cm ×

5 cm and length h= 1.8 m Pictures (presented as negatives) were taken at 0.02-s intervals The black dotted line shows positions the flame should reach in the column when propagating without extinction.

the following equation [24]:

k= d V t

d L +V t· cos ϕ

where L is the length along the flame surface, V tis the tangential

velocity component,φ is the angle defining the chosen flame

point with velocity V t , and l is the distance of the chosen flame

point from the column symmetry axis

The coordinate system bound to the mowing flame is shown

in Figure 30, together with two different velocity components

of the total velocity V c These components are presented in two

forms: (i) appropriate for the use in Eq (9) (V t and V n–dashed

vectors) and (ii) by values determined by the PIV system used

(V x and V z, in Cartesian coordinates, shown as dotted vectors)

All quantities in Eq (9) have been calculated using MathCad

When the setting of all discussed earlier parameters is correct,

a full set of the PIV data covering the flame is obtained (a fewexample figures were presented earlier) The flame stretchingrates have been calculated for two flammability limit mixtures:5.25% CH4/air and 2.05% C3H8/air Obtained results of the localflame stretching rates in the standard flammability column (withsquare cross section 5 cm× 5 cm and 1.8 m long), for both leanlimit mixtures, are shown in Figures 31 and 32, respectively.Their maximum values, at the flame tips, are 35± 3 s−1and

30± 2.5 s−1, respectively (quoted accuracy ranges result from

calculation based on different experimental PIV velocity fieldpictures recorded) In both cases, after reaching a maximum, itgradually falls in the lower parts of the flame

It is worth adding that for the tube of diameter 5 cm and1.8 m length with 5.15% CH4/air (used in [36–38]), the

Figure 28 The PIV vector velocity fields [m/s] of the flame extinction process, propagation in the flammability column: square cross-section 5 cm × 5 cm and

h= 1.8 m length; lean 5.25% CH 4 /air mixture with 2- µm seeding Fields shown are in the coordinate system bound to the column walls The time interval pictures 0.25 s Existing flame position is marked by white dots.

heat transfer engineering vol 32 no 2 2011

Figure 29 The PIV vector velocity fields (a, b, c, and d; m/s) and their scalar maps (e, f, g, and h; m/s) of the flame extinction process The same case as presented

in Figure 28 but in the coordinate system bound to the flame and with additional scalar maps of all velocities.

Figure 30 Definition of parameters for the local stretch flame k calculation: (a) flame front coordinate L; angle of chosen flame point related to column axis; (b) column coordinates (Figure 2); and (c) total velocity V ccomponents: dashed, in the flame coordinates; dotted, from PIV.

heat transfer engineering vol 32 no 2 2011

Figure 31 Local stretch rate k along the flame front L: the lean 5.25% CH4 /air

mixture; column with square cross section 5 cm × 5 cm and 1.8 m long.

maximum stretching rate value obtained (using the same

methodology and described in this paper) was equal to 34±

2 s−1 The different lean limit CH4/air concentration in this tube

results from the fact that the flammability limit changes with

the column cross section (of the same 1.8 m length) For the

tube with diameter 5 cm and the square cross section 5 cm× 5

cm, the difference is small (0.1%) These concentration limits

for other inner tube diameters of 24 mm and 80 mm are 4.90%

and 5.50%, respectively There are, obviously, different visible

limit flame speeds in these tubes related to the quoted respective

flammability limit values—[22–24] and also measured in our

laboratory [35–37, 39, 40]—resulting from the extensive and

precise experiments conducted in recent years, i.e., 14.3± 0.2

cm/s, 21.5± 0.7 cm/s, and 28.0 ± 0.3 cm/s (for tube diameters

24, 50, and 80 mm, respectively) Direct experimental

determi-nation of laminar flame reported in [41] supports our quoted

values

Obtained values of the flame stretching rates are usually

associated with the flame curvature and the dilatation velocity,

with the latter resulting from the fresh mixture heating In both

cases the contribution of the former, in the total value of stretch

Figure 32 Local stretch rate k along the flame front L: the lean 2.05% C3 H 8 /air

mixture; column with square cross section 5 cm × 5 cm and 1.8 m long.

Although the stretch rate shapes look similar, calculation ofthese contributions in respective total stretch rates are about 3.5

s−1for the CH4/air flame and about 12 s−1for C3H8/air flame,i.e., about 10% and 40%, respectively Despite that, the mainstretch is due to the flow divergence, shown for both flames inFigures 26b and c, respectively

CONCLUSIONS

The results based on the PIV measurements for both limitflame CH4/air and C3H8/air mixtures analyzed in the squarecross section 5 cm× 5 cm and 1.8-m-long flammability columnshow that local stretch rates are maximum at the flame tip.The extinctions of both upward propagating limit flames aresimilar: They are not affected by the negligible heat losses to thecolumn walls, and always start at their flame tips and then spreaddown toward the flame These statements, based on repeatableexperiments performed, are in line with the earlier experimental[7, 13, 16, 28, 41, 42] and numerical modeling [35] results.Therefore, the possibility of the extinction of the lean limit

CH4/air flame in the square or round cross-section column, atthe location where the stretch is maximum, is in contradictionwith the asymptotic theory of stretched flames For this leanlimit mixture, a stagnant region situated below the flame tip,moving with the same velocity as the flame, has been detected.Since this theory does not include, for example, counterflowburner configurations, the development of a universal one israther unlikely

The methodology of PIV measurements is also described andaddresses:

1 Maximum MgO seeding mass in mixtures with no effect onthe laminar flame propagation

2 The range of laser light energy impulse that gives good ity for all PIV pictures; this energy impulse has to be adjusted

qual-to the mixture seeding particles density distribution

3 The conditions for stable flame propagation in the bility column were determined, particularly for square-cross-section walls from different materials

flamma-4 The comparison of pictures obtained by schlieren and PIVmethods adds some relevant information to the investigation

5 To understand the extinction mechanism of limit CH4/airand C3H8/air flames, further investigation is necessary Thecolumn cross section size can also influence this mechanism

6 This recently developed methodology is general enough to beapplied not only to combustion, but also to flows in complexgeometry

heat transfer engineering vol 32 no 2 2011

a thermal diffusivity, m2/s

A flame surface area, m2

c p specific heat at constant pressure, J/kg-K

Ka Karlowitz number, k δ/u L

l distance of the chosen flame point from the column

q reaction heat, J/kmol

R curvature radius of the flame spherical cap, m

t time, s

T temperature, K

u L laminar flame velocity, m/s

W = k(1 – Le); expression [15] predicting flame front

λ heat conductivity coefficient, W/m-K

ϕ angle defining the chosen flame point with velocity V t

f value for the flame

G value for the combustion gas final temperature

G–W Gaydon and Wolfhard value

i value for the inflection or ignition temperature

L laminar flame value

m value for mixture

Zel Zeldo’vich value

∞ value for the laminar, not stretched plane flame

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Tadeusz R Fodemski holds a chair in

thermody-namics, heat transfer, fluid mechanics, and power gineering at Technical University of Ł´od´z, Poland Since 2001 he has been head of the Department of Heat Engineering and Refrigeration At present he

en-is head of the Thermodynamic Section in the Polen-ish Academy of Science Thermodynamics and Combus- tion Committee and is a fellow or member of vari- ous professional bodies and societies He received an M.Sc (1970) and holds the Ph.D (1977) and D.Sc (1986) degrees, all in mechanical engineering from the Technical University

heat transfer engineering vol 32 no 2 2011