Differentiated Drying of the Mixtures Colloidal Components Used in the Construction of Underground Infrastructure Procedia Engineering 165 ( 2016 ) 806 – 816 1877 7058 © 2016 The Authors Published by[.]
Trang 1Procedia Engineering 165 ( 2016 ) 806 – 816
1877-7058 © 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license
( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).
Peer-review under responsibility of the scientific committee of the 15th International scientific conference “Underground Urbanisation as a
Prerequisite for Sustainable Development
doi: 10.1016/j.proeng.2016.11.779
ScienceDirect
15th International scientific conference “Underground Urbanisation as a Prerequisite for
Sustainable Development”
Differentiated drying of the mixtures colloidal components used in
the construction of underground infrastructure
a
Northern Trans-Ural State Agricultural University, Respubliki str 7, Tyumen, 625003, Russia
Abstract
Differentiated method of drying of the mixtures colloidal components used in the construction of underground infrastructure is proposed The theoretical analysis of the drying process of the colloidal components in the processes of heating and cooling at natural convection is completed
© 2016 The Authors Published by Elsevier Ltd
Peer-review under responsibility of the scientific committee of the 15th International scientific conference “Underground Urbanisation as a Prerequisite for Sustainable Development
Keywords: colloid body, building mixtures, drying of building mixtures, differentiated drying
1 Introduction
Stricter requirements apply to mixes used on underground infrastructure objects that are related to aggressive influence of moisture, salts and acids contained in the soil [11] The end product will depend on the requirements of the technological standards for the preparation of solutions for the construction of underground infrastructure
To meet the technical standards of the solutions preparation it is necessary to use mixtures of a certain faction, humidity and so on Changes in humidity component of the building mixes, depending on humid-temperature environmental parameters impede the compliance with technological standards of solutions preparation of mixes [10]
* Corresponding author Tel.: +7-3452-29-01-57
E-mail address: Impossible_@mail.ru
© 2016 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license
( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).
Peer-review under responsibility of the scientific committee of the 15th International scientific conference “Underground Urbanisation as a Prerequisite for Sustainable Development
Trang 2The most common and most sensitive to humid-temperature parameters of the environment component of mixes
is sand, as it applies to colloidal systems or colloids [14, 15] Sand, like colloid body, has equilibrium humidity, which depends on the temperature and humidity of the environment [6, 12]
Requirements for sand, as a component of mixes, [4, 5] regulate to use sand with a moisture content of not more than 2% for the preparation of acid solutions used in the construction of underground infrastructure The equilibrium moisture content of sand ranges from 0 to 20% depending on the temperature and humidity of the environment, therefore, before the preparation of mortars, the sand is dried [13]
The issue of maintaining the moisture content of the colloidal component mixes at the time of the solutions preparation, such as sand, is relevant in the construction of underground infrastructure
2 Subjects and Methods
The sand was chosen to study as a colloidal component mixes for the construction of underground infrastructure The main physical characteristics are taken from the standard documentation for carrying out of theoretical researches of differentiated sand drying process [5]
In the first approximation the grains of sand represent a sphere with diameter d
The process of sand drying (moisture transfer) as a colloid body in general is described by Lykov (1) [10, 12]:
) ( 4
ρ – density of matter, kg/m3
;
u – the gradient of moisture content, %/m;
δ – the coefficient of thermal diffusion, %/K;
Θ – the gradient of temperature, K/m
The direction of the temperature and humidity gradients for the processes of heating and cooling is presented in figure 1
Fig.1 The gradient of temperature and humidity in the grain of sand, a – heating; b – cooling
Trang 3The formula (1) shows the relationship of the moisture transfer process depending on the distribution of humidity and temperature on colloid body During convective heating (drying) of the body, a temperature gradient opposite to the gradient of moisture content on the sign and is directed from the center of the body to the surface, which leads to lower moisture transfer
According Filonenko G K the temperature gradient Θ = 1°C creates the intensity of moisture transfer that is comparable to the humidity gradient u in the range 5 8 %
a temperature gradient directed towards the center of the body (towards the gradient of humidity), that reduces the
the body (coinciding in direction with the gradient of humidity), that increases the speed of drying (if Θ<0,
Differential kinetics of drying is most effective with the alternation of heating and cooling processes with an exception condition of stationary state (if Θ→0)
The analysis of the Lykov formula (1) for heating processes (Fig.1A) and cooling processes (Fig.1B) indicates the contribution of the drying process during cooling Consequently, the process of drying the sand becomes more intense when using differentiated kinetics (alternating heating and cooling)
3 Results
Kinetics of differentiated drying - is alternating the processes of heating and cooling
In order to examine this process, the following assumptions are taken:
x - a grain of sand as a colloid body is an ellipsoid of rotation;
x - body geometry is not changed in the process of removing moisture;
x - the surface of the body is idealized (no inclusions and weeds);
x - the processes of heat and mass transfer with the body surface occur uniformly over the entire area;
x - evaporation is only possible from the surface of the body;
x - heat transfer processes occur in conditions of natural convection
The design schemes of the heating and cooling processes are shown in figures 2 and 3
Fig.2 A design scheme of the body heating process Q – the number of summed warmth; Q exp – the amount of heat expended in the removal of
surface moisture; Q h – the amount of heat for body heating
Fig.3 A design scheme of the body cooling process Q – the number of allocated warmth; Q exp – the amount of heat expended in the removal of
surface moisture; Q – the number of allocated heat to cool the body
Trang 4The heat balance of the heating process the colloid body (sand) (2):
)
;
; (
)
;
; (
)
;
;
;
; (
exp
T f
Q
T f
Q
T l c
f
Q
Q Q
Q
h
h
h
W D
W D
W D
(2)
Where are с – the specific heat of colloid bodies;
α – the heat transfer coefficient from the drying agent to the body;
τ – the time of heating the body;
l – the geometric characteristics of the body;
T – temperature
The heat balance during the cooling of the colloid body (3):
)
;
; (
)
;
; (
)
;
;
;
; (
exp
exp
T f
Q
T f
Q
T l c
f
Q
Q Q
Q
a
a
W D
W D
W D
(3)
Where is τ – cooling time colloid body
The amount of heat required for heating or cooling the colloid bodies is determined by Newton's-Richman law (4):
) (
)
Where are М – the mass of the colloid body (grain of sand);
ΔT – the change in body temperature;
с – the specific heat of body;
S – body surface area;
Тagent; Тbody – the temperature of the agent, the body temperature
The surface area of the colloid body is determined by the expression (5) [3, 7]
) 3 (
Where is l - length colloid body;
60 / ) 6 5
Where are a, b – the width and thickness of the colloid body as ellipsoid of revolution
The heat capacity of colloid bodies depends on heat capacity of solids, heat capacity of water contained in it, and the mass of water (humidity) The design scheme is drawn up to determine the heat capacity of the colloid of the body depending on humidity, see figure 4
Trang 5Fig.4 A design scheme of determining the heat capacity of colloid bodies М total – the mass of the colloid body, kg; m – weight moisture, kg; М – the dry mass, kg; сtotal – the specific heat of colloid bodies, J/kg°С; сw – the specific heat of water, J/kg°С; сdry – specific heat of solid (dry)
substance, J/kg°С
Every colloid body consists of dry matter and water contained in it temperature change in dry matter and moisture occurs in the counting of the thermal energy that is described by a heat balance There is a system of equations (7) to determine the equivalent specific heat capacity based on the data (Fig.4)
total total
total total
M m
u
M m M
T c M
Q
/
'
(7)
Where are Q – the quantity of heat, J.;
ΔТ – temperature change, °С;
u – the moisture content (humidity), g/cube, m
From the system of equations (7), it follows that:
T c
M c m T c M T c m T c
so.,
dry w
total
Therefore:
total total
total total
total
total dry
w total
M u l M
u M m M
M
M u
m
M c M c m c
) (
/ ) (
(10)
The solution to this system of equations (10):
w dryl
Trang 6The specific heat of water is approximately cw≈4200 J/kg·°С
4200 )
( )
; ( u c l u c u
f
Specific heat of solid (dry) substance sand is 835 J/kg·°С
The heat capacity of the sand depending on humidity (13):
835 3365
4200 835
) ( )
f
The linear dependence of the specific heat capacity of colloid bodies (sand) is presented in figure 5
Fig.5 the dependence of the heat capacity of the sand from moisture
In natural convection the heat transfer coefficient α is determined from the expression (14): [2]
25 0 ) Pr (Pr/
Pr)
Where is Nu=α·l/λ – the Nusselt criterion, which characterizes the ratio between heat transfer by convection and heat transfer by conduction [1],
Where are l=2·L·A/(L+A) – the hydraulic diameter of the colloidal body, m;
L – length colloid body, m;
A – the thickness of the colloid body, m
– criterion Grashof;
ΔТ – the temperature difference between the heat exchange surfaces, °С;
Pr=ν/a=c·μ/λ – the Prandtl number;
с- specific heat, J/kg•K;
μ - dynamic viscosity, PA•s
λ – coefficient of thermal conductivity, W/m·K
С – for laminar regime С=1.18;
n – for laminar regime n=0,125
The heat transfer coefficient is determined from the expression (15):
Trang 725 0 625 0 25 0 375 0 125 0 125 0 125
18
The following heat transfer coefficient was obtained on the basis of physical data dry air:
) 10 6 9169 0 /(
) 234 11 0148
0 ( 49635 0 10
57
1 3 l0.625 ' T0.125 Tagent 5 T
Т – the surface temperature of the colloidal body, °С;
ΔT – the temperature difference between the agent and body, °С
Assuming uniform temperature changes of colloid bodies at various points, system heat balance of the process of heating and cooling are:
) 835 3365
( 10
4385 2 2502
10
) 10
1 ( 100
10 6 9 916
) 234 11 0148
0 ( 49635 0 )
20
6 5 1 ( 55 9
6 5 )
2 (
6
6 4
2 8
/ 9 625
0
'
'
'
'
'
u M
dt P
dT
T
dt P m
m u
M
m u
M u
u
T
T T
b a b
a a
l
a l P
h h
agent
K K
S
(17)
Where are P – input/exhaust heat power, W;
l, a, b – length, width, thickness of the colloid body, m;
ΔT – the temperature difference between the agent and body, °С;
Т – the temperature of the colloidal body, °С;
Тagent – temperature agent, °С;
u – humidity colloid body, %;
М – the mass of the colloid body, g;
Δm – the mass changes of the colloidal body, g;
dt – time change, sec;
The algorithm for solving the system of differential drying of colloidal bodies in a General view is presented in figure 6
Trang 8Fig.6 The algorithm for solving the system of differential equations of the drying kinetics Х0 – the original settings; Δt – step discrete (busted),с; τ – the total drying time, с; К – factors determined experimentally; Тc – cycle time, с; t current time, с; floor – the operator "integer part"» [9]; Р, Рc, Рh – thermal power, power exhaust, power input, W; Xt – current settings; Array Х=f(t) – formation of the parameter array
values in time
The results of solving the system of equations in a software environment MathCAD with application of the algorithm (Fig.6) are presented in figures 7-9 the temperature of the heating agent +40°C, the temperature of the cooling agent +5°C
Fig.7 The influence of efficiency of heating and evaporation on the temperature of the colloid body when differentiated drying (heating and cooling 60 sec) f(t;0,5;10) – the dependence of body temperature on the time in η h =0,5 g/cube, m and η e =10·10 -5 g/cube,m.; f(t;0,1;10) – the dependence of body temperature on the time in η h =0,1 g/cube, m and η e =10·10 -5 g/cube,m.; f(t;0,5;1) – the dependence of body temperature on the time in η h =0,5 g/cube, m and η e =1·10 -5 g/cube, m.; f(t;0,1;1) – the dependence of body temperature on the time in η h =0,1 g/cube, m and
η =1·10 -5 g/cube, m
Trang 9The change in the evaporation efficiency practically does not influence temperature changes of colloidal bodies (about 0.03°C) and the growth efficiency of the heating causes a slight increase in the average temperature of the colloid body (1.5 °C)
Fig.8 The influence of efficiency of heating and evaporation on the temperature of the colloid body when differentiated drying (heating and cooling for 120 s) f(t;0,5;10) – – the dependence of body temperature on the time in η h =0,5 g/cube, m and η e =10·10 -5 g/cube,m.; f(t;0,1;10) – – the dependence of body temperature on the time in η h =0,1 g/cube, m and η e =10·10 -5 g/cube,m.; f(t;0,5;1) – – the dependence of body temperature
on the time in η h =0,5 g/cube, m and η e =1·10 -5 g/cube, m.; f(t;0,1;1) – – the dependence of body temperature on the time in η h =0,1 g/cube, m and
η e =1·10 -5 g/cube, m
The change in the efficiency of the evaporation practically does not influence the change in body temperature (of the order of 0.07°C) and the growth efficiency of the heating causes a slight increase in average body temperature (about 2.5 °C)
Fig.9 The influence of efficiency of heating and evaporation on the temperature of the colloid body when differentiated drying (heating and cooling at 240 C) f(t;0,5;10) – the dependence of body temperature on the time in η h =0,5 g/cube, m and η e =10·10 -5 g/cube,m.; f(t;0,1;10) – the dependence of body temperature on the time in η h =0,1 g/cube, m and η e =10·10 -5 g/cube,m.; f(t;0,5;1) – the dependence of body temperature on the time in η h =0,5 g/cube, m and η e =1·10 -5 g/cube, m.; f(t;0,1;1) – the dependence of body temperature on the time in η h =0,1 g/cube, m and
η =1·10 -5 g/cube, m
Trang 10As can be seen from figures 7-9, the efficiency increase of heat causes an increase in the rate of temperature change , the efficiency change of evaporation has little influence on temperature of a colloidal body in the process of drying, which is reflected on the lines of the average value of the temperatures (the Trend line) Heating/cooling influences the maximum value of body temperature in the heating process and minimum values of the temperature
in the cooling process Therefore, reducing the time of heating/cooling helps to reduce the changes of body temperature in the process of differentiated drying (the inability to achieve steady-state values)
Fig.10 The efficiency influence of heating and evaporation speed of moisture removal from the colloid body with differentiated drying (heating and cooling 60 sec) f(t;0,5;10) – the dependence of the moisture removal rate of at η h =0,5 g/cube,m and η e =10·10 -5 g/cube,m.; f(t;0,1;10) – the dependence of the moisture removal rate of at η h =0,1 g/cube,m and η e =10·10 -5 g/cube,m.; f(t;0,5;1) – the dependence of the moisture removal rate of at η h =0,5 g/cube,m and η e =1·10 -5 g/cube,m.; f(t;0,1;1) – the dependence of the moisture removal rate of at η h =0,1 g/cube,m and η e =1·10 -5
g/cube,m
According to the average values (Fig.10) (Trend line) it can be seen that the efficiency increase of heating leads
to a slight decrease in the rate of moisture removal (up to 2•10-10 g/s), increasing the efficiency of evaporation in 10 times leads to higher average drying rate in 10 times
4 Conclusion
The theoretical studies indicate that differentiated drying of the colloidal components of the mixes, and in particular sand, can use sources of thermal energy with temperature settings that do not pose a danger to humans (the minimum agent temperature +5°C, the maximum temperature of the agent +40°C) Differentiated kinetics of sand drying is ensured by the alternating processes of heating and cooling without reaching the steady-state values
of temperatures
The results showed that for sand drying as a colloid body it is better to use differentiated drying with time heating and cooling t=60
The offered technique of parameters calculation differentiated the drying kinetics will allow for the daily fluctuations of the ambient temperature during storage and use of sand for making mixes in compliance with the required humidity value
References
[1] V A Gorshkov-Kantakuzen, S E Guperin, Effect GKZh, for large values of Ra in the calculation of the Nusselt number of convection Rayleigh-Benard, XXII international Symposium "Dynamic and technological problems of constructions mechanics and continuous media" named of A G Gorshkov 1 (2015) 85-86