Tài liệu Handbook of Mechanical Engineering Calculations P17 doc

SECTION 17 SOLAR ENERGYAnalysis of Solar Electric Generating System Loads and Costs 17.1 Economics of Investment in an Industrial Solar-Energy System 17.4 Designing a Flat-Plate Solar-En

SECTION 17 SOLAR ENERGY

Analysis of Solar Electric Generating

System Loads and Costs 17.1

Economics of Investment in an

Industrial Solar-Energy System 17.4

Designing a Flat-Plate Solar-Energy

Heating and Cooling System 17.6

Determination of Solar Insolation on

Solar Collectors Under Differing

Conditions 17.13

Sizing Collectors for Solar-Energy

Heating Systems 17.15

F Chart Method for Determining Useful

Energy Delivery in Solar Heating 17.17 Domestic Hot-Water Heater Collector Selection 17.24

Passive Solar-Heating System Design 17.29

Determining if a Solar Water Heater Will Save Energy 17.36

Sizing a Photovoltaic System for Electrical Service 17.37

Economics and Applications

ANALYSIS OF SOLAR ELECTRIC GENERATING

SYSTEM LOADS AND COSTS

Analyze the feasibility of a solar electric generating system (SEGS) for a powersystem located in a sub-tropical climate Compare generating loads and costs withconventional fossil-fuel and nuclear generating plants

One successful solar electric generating system is located in the Mojave Desert

in southern California At this writing, it has operated successfully for some 12years with a turbine cycle efficiency of 37.5 percent for a solar field of more than2-million ft2(1,805,802 m2) A natural-gas backup system has a 39.5 percent effi-

17.2 ENVIRONMENTAL CONTROL

Cooling tower

Pre-heater

Steam generator Superheater Reheater

SI Values

FIGURE 1 Solar-generating-method schematic traces

flow of heat-transfer fluid (Luz International Ltd and Power.)

ciency Both these levels of efficiency are amongst the highest attainable today withany type of energy source

2. Sketch a typical cycle arrangement

Technology developed by Luz International Ltd uses a moderate-pressure the-art Rankine-cycle steam-generating system using solar radiation as its primaryenergy source, Fig 1 In the Mojave Desert plant mentioned above, a solar fieldcomprised of parabolic-trough solar collectors which individually track the sunusing sun sensors and microprocessors provides heat for the steam cycle

state-of-Collection troughs in the Mojave Desert plant are rear surface mirrors bent intothe correct parbolic shape These specially designed mirrors focus sunlight ontoheat-collection elements (HCE) Each mirror is washed every two weeks with de-mineralized water to remove normal dust blown off the desert The mirrors must

be clean to focus the optimal amount of the sun’s heat on the HCE

3. Detail the sun collector arrangement and orientation

With the parabolic mirrors described above, sun sensors begin tracking the sunbefore dawn Microprocessors prompt the troughs to follow the sun, rotating 180⬚each day A central computer facility at the Mojave Desert plant monitors andcontrols each of the hundreds of individual solar collectors in the field and all ofthe power plant equipment and systems

During summer months when solar radiation is strongest, some mirrors must beturned away from the sun because there is too much heat for the turbine capacity

Solar mode

FIGURE 2 Firing modes are shown for typical summer day, left, and typical winter day, right.

Correlation of solar generation to peaking power requirements is evident (Luz International Ltd and Power.)

When this occurs, almost every other row of mirrors must be turned away However,

in the winter, when solar radiation is the weakest, every mirror must be employed

to produce the required power

In the Mojave Desert plant, the mirrors focus the collected heat on theHCEs—coated steel pipes mounted inside vacuum-insulated glass tubes The HCEscontain a synthetic-oil heat-transfer fluid, which is heated by the focused energy toapproximately 735⬚F (390.6⬚C) and pumped through a series of conventional heatexchangers to generate superheated steam for the turbine-generator

In the Mojave Desert plant, several collectors are assembled into units calledsolar collector assemblies (SCA); generally, each 330-ft (100.6-m) row of collectorscomprises one SCA The SCAs are mounted on pylons and interconnected withflexible hoses An 80-MW field consists of 852 SCAs arranged in 142 loops EachSCA has its own sun sensor, drive motor, and local controller, and is comprised of

224 collector segments, or almost 5867 ft2 (545 m2) of mirrored surface and 24HCEs From this can be inferred that some (5867 / 80)⫽73.3 ft2(6.8 m2) per MW

is required at this installation

4. Plan for an uninterrupted power supply

To ensure uninterrupted power during peak demand periods, an auxiliary gas fired boiler is available at the Mojave Desert plant as a supplemental source ofsteam However, use of this boiler is limited to 25 percent of the time by federalregulations This boiler serves as a backup in the event of rain, for night productionwhen called for, or if ‘‘clean sun’’ is unavailable According to Luz International,clean sun refers to solar radiation untainted by smog, clouds, or rain Figure 2shows the firing modes for typical summer (left) and winter (right) days Correlation

natural-of solar generation to peaking-power requirements is evident

As shown in the cycle diagram, the balance-of-plant equipment consists of theturbine-generator, steam generator, solar superheater, two-cell cooling tower, and

an intertie with the local utility company, Southern California Edison Co TheMojave Desert installation represents some 90 percent of the world’s solar powerproduction Since installing it first solar electric generating system in 1984, a 13.8-

MW facility, Luz has built six more SEGS of 30 MW each Units 6 and 7 usethird-generation mirror technology

17.4 ENVIRONMENTAL CONTROL

5. Determine the costs of solar power

SEGS are suited to utility peaking service because they provide up to 80 percent

of their output during those hours of a utility’s greatest demand, with minimalproduction during low-demand hours

Cost of Luz’s solar-generated power is less than that of many nuclearplants—$0.08 / kWh, down from $0.24 / kWh for the first SEGS, according to com-pany officials Should the price of oil go up beyond $20 / barrel, solar will becomeeven more competitive with conventional power

But the advantages over conventional power sources include more than competitiveness Emissions levels are much lower—10 ppm—because the sun isessentially non-polluting SEGS are equipped with the best available technologyfor emissions cleanup during the hours they burn natural gas, the only time theyproduce emission

cost-Related Calculations. Luz International Ltd has installed more capacity at theMojave Desert plant mentioned here, proving the acceptance and success of itsapproach to this important technical challenge That data in this procedure can beuseful to engineers studying the feasibility of solar electric generation for other

sites around the world Luz received an Energy Conservation Award from Power

magazine, from which the data and illustrations in this procedure were obtained.There are estimates showing that the sunshine impinging the southwestern UnitedStates is more than enough to generate the entire electrical needs of thecountry—when efficient conversion apparatus is developed It may be that theequipment described here will provide the efficiency needed for large-scale pollu-tion-free power generation Results to date have been outstanding and promisegreater efficiency in the future

ECONOMICS OF INVESTMENT IN AN

INDUSTRIAL SOLAR-ENERGY SYSTEM

Determine the rate of return and after tax present value of a new industrial solarenergy system The solar installation replaces all fuel utilized by an existing fossil-fueled boiler when optimum weather conditions exist The existing boiler will

be retained as an auxiliary unit Assume a system energy output (E s) of 3⫻109Btu/ yr (3.17 kJ⫻109/ yr) an initial cost for the total system of $503,000 based on a

collector area (A c) of 10,060 ft2(934.6 m2), a depreciation life (DP) of 12 yr, a taxrate (␶) of 0.4840, a tax credit factor (TC) of 0.25, a system life of 20 yr, an

operating cost fraction (OMPI) of 0.0250, an initial fuel cost (P f 0) of $3.11 / MBtu

($3.11 / 947.9 MJ) and a fuel price escalation rate (e) of 0.1450.

Calculation Procedure:

1. Compute unit capacity cost (K s ) in $ / million Btu per year

initial cost of system $503,000

K s⫽ E s ⫽3⫻10 Btu / yr9

$167.67

⫽ ($167.67 / 947.9 MJ / yr)

1 million Btu / yr

2. Compute levelized coefficient of initial costs (M ) over the life of the system

CRFR,N TC

M⫽OMPI⫹ 1⫺␶ 冋 冉 冊1⫺ 1⫹R ⫺(␶ ⫻DEP)册

CRFR,N is the capital recovery factor which is a function of the market discount

rate (R)* over the expected lifetime of the system (20 yr) and is determined as

follows:

R

CRFR,20⫽1⫺(1⫹R)⫺20DEP is the depreciation which will be calculated by an accelerated method, thesum of the years digits (SOYD), in accordance with the following formula:

DEP⫽DP(DP⫹1)R冉DP⫺CRFR,DP冊

where DP is an allowed depreciation period, or tax life, of 12 yr

Prepare a tabulation (see below) of M values for various market discount rates (R).

3. Compute the levelized cost of solar energy (S), for the life cycle of the system in $ / million Btu ($ / MJ)

Use the relation, S ⫽(K s )(M) Since M varies with R, refer to the tabulation of S

for various market discount rates

4. Compute the levelized cost of fuel (F) in $ / million Btu ($ / MJ) and

compare to S

N

Pƒ 0 1⫹e 1⫹e

F⫽ ␩ 冋 冉 冊冉 冋 册 冊册CRFR,N R⫺e 1⫺ 1⫹R

where␩is the boiler efficiency for a fossil fuel system which supplies equivalent

heat Referring to the tabulation, the value of F is tabulated at various market

discount rates for␩values of 70, 80, and 100 percent The rate of return for the

solar installation is that value of R at which F ⫽ S For ␩ ⫽ 70 percent, R is

between 7.5 and 8.0 percent For␩ ⫽80 percent, R is between 6.5 and 7.0 percent.

These rates of return should exceed current interest (discount) rates to attain nomic feasibility

eco-5. Compute the after tax present value (PV) of the solar investment if the existing boiler installation has an efficiency of 70 percent

5 percent discount rate,

*See tabulation on page 17.6.

*As used in engineering economics, R, discount rate and interest rate refer to the same percentage The

only difference is that interest refers to a progression in time, and discount to a regression in time See

‘‘Engineering Economics for P.E Examinations,’’ Max Kurtz, McGraw-Hill.

REFERENCE

Brown, Kenneth C., ‘‘How to Determine the Cost-Effectiveness of Solar Energy Projects,’’

Power magazine, March, 1981.

DESIGNING A FLAT-PLATE SOLAR-ENERGY

HEATING AND COOLING SYSTEM

Give general design guidelines for the planning of a solar-energy heating and ing system for an industrial building in the Jacksonville, Florida, area to use solarenergy for space heating and cooling and water heating Outline the key factorsconsidered in the design so they may be applied to solar-energy heating and coolingsystems in other situations Give sources of pertinent design data, where applicable

cool-Calculation Procedure:

1. Determine the average annual amount of solar energy available at the site

Figure 3 shows the average amount of solar energy available, in Btu / (day䡠ft2)(W / m2) of panel area, in various parts of the United States How much energy iscollected depends on the solar panel efficiency and the characteristics of the storageand end-use systems

Tables available from the National Weather Service and the American Society

of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE) chart themonthly solar-radiation impact for different locations and solar insolation [totalradiation form the sun received by a surface, measured in Btu / (h䡠ft2) (W / m2);

FIGURE 3 Average amount of solar energy available, in Btu / (day 䡠 ft 2 ) (W / m 2 ), for different

parts of the United States (Power.)

insolation is the sum of the direct, diffuse, and reflected radiation] for key hours

of a day each month

Estimate from these data the amount of solar radiation likely to reach the surface

of a solar collector over 1 yr Thus, for this industrial building in Jacksonville,Florida, Fig 3 shows that the average amount of solar energy available is 1500Btu / (day䡠ft2) (4.732 W / m2)

When you make this estimate, keep in mind that on a clear, sunny day directradiation accounts for 90 percent of the insolation On a hazy day only diffuseradiation may be available for collection, and it may not be enough to power thesolar heating and cooling system As a guide, the water temperatures required forsolar heating and cooling systems are:

Space heating Up to 170⬚F (76.7⬚C)

Space cooling with absorption air

conditioning From 200 to 240⬚F (93.3 to 114.6⬚C)Domestic hot water 140⬚F (60⬚C)

2. Choose collector type for the system

There are two basic types of solar collectors: flat-plate and concentrating types Atpresent the concentrating type of collector is not generally cost-competitive withthe flat-plate collector for normal space heating and cooling applications It willprobably find its greatest use for high-temperature heating of process liquids, spacecooling, and generation of electricity Since process heating applications are not thesubject of this calculation procedure, concentrating collectors are discussed sepa-rately in another calculation procedure

17.8 ENVIRONMENTAL CONTROL

FIGURE 4 Construction details of flat-plate solar collectors (Power.)

Flat-plate collectors find their widest use for building heating, domestic waterheating, and similar applications Since space heating and cooling are the objective

of the system being considered here, a flat-plate collector system will be a tentativechoice until it is proved suitable or unsuitable for the system Figure 4 shows theconstruction details of typical flat-plate collectors

3. Determine the collector orientation

Flat-plate collectors should face south for maximum exposure and should be tilted

so the sun’s rays are normal to the plane of the plate cover Figure 5 shows theoptimum tilt angle for the plate for various insolation requirements at differentlatitudes

Since Jacksonville, Florida, is approximately at latitude 30⬚, the tilt of the platefor maximum year-round insolation should be 25⬚ from Fig 5 As a general rulefor heating with maximum winter insolation, the tilt angle should be 15⬚ plus theangle of latitude at the site; for cooling, the tilt angle equals the latitude (in thesouth, this should be the latitude minus 10⬚ for cooling); for hot water, the angle

of tilt equals the latitude plus 5⬚ For combined systems, such as heating, cooling,and hot water, the tilt for the dominant service should prevail Alternatively, the tiltfor maximum year-round insolation can be sued, as was done above

When collector banks are set in back of one another in a sawtooth arrangement,low winter sun can cause shading of one collector by another This can cause a

FIGURE 5 Spacing of solar flat-plate

collec-tors to avoid shadowing (Power.)

TABLE 1 Spacing to Avoid Shadowing, ft (m) ⬚

loss in capacity unless the units are carefully spaced Table 1 shows the minimumspacing to use between collector rows, based on the latitude of the installation andcollector tilt

4. Sketch the system layout

Figure 6 shows the key components of a solar system using flat-plate collectors tocapture solar radiation The arrangement provides for heating, cooling, and hot-water production in this industrial building with sunlight supplying about 60 percent

of the energy needed to meet these loads—a typical percentage for solar systems.For this layout, water circulating in the rooftop collector modules is heated to

160⬚F (71.1⬚C) to 215⬚F (101.7⬚C) The total collector area is 10,000 ft2(920 m2).Excess heated hot water not need for space heating or cooling or for domestic water

is directed to four 6000-gal (22,740-L) tanks for short-term energy storage ventional heating equipment provides the hot water needed for heating and coolingduring excessive periods of cloudy weather During a period of 3 h around noon

Con-on a clear day, the heat output of the collectors is about 2 milliCon-on Btu / h (586 kW),with an efficiency of about 50 percent at these conditions

17.10 ENVIRONMENTAL CONTROL

FIGURE 6 Key components of a solar-energy system using flat-plate collectors (Power.)

For this industrial building solar-energy system, a lithium-bromide absorptionair-conditioning unit (a frequent choice for solar-heated systems) develops 100 tons(351.7 kW) of refrigeration for cooling with a coefficient of performance of 0.71

by using heated water from the solar collectors Maximum heat input required bythis absorption unit is 1.7 million Btu / h (491.8 kW) with a hot-water flow of 240gal / min (909.6 L / min) Variable-speed pumps and servo-actuated valves controlthe water flow rates and route the hot-water flow from the solar collectors alongseveral paths—to the best exchanger for heating or cooling of the building, to theabsorption unit for cooling of the building, to the storage tanks for use as domestichot water, or to short-term storage before other usage The storage tanks holdenough hot water to power the absorption unit for several hours or to provideheating for up to 2 days

Another—and more usual—type of solar-energy system is shown in Fig 7 In

it a flat-plate collector absorbs heat in a water / antifreeze solution that is pumped

to a pair of heat exchangers

From unit no 1 hot water is pumped to a space-heating coil located in the ductwork of the hot-air heating system Solar-heated antifreeze solution pumped to unit

no 2 heats the hot water for domestic service Excess heated water is diverted tofill an 8000-gal (30,320-L) storage tank This heated water is used during periods

of heavy cloud cover when the solar heating system cannot operate as effectively

5. Give details of other techniques for solar heating

Wet collectors having water running down the surface of a tilted absorber plate andcollected in a gutter at the bottom are possible While these ‘‘trickle-down’’ collec-tors are cheap, their efficiency is impaired by heat losses from evaporation andcondensation

Air systems using rocks or gravel to store heat instead of a liquid find use inresidential and commercial applications The air to be heated is circulated via ducts

to the solar collector consisting of rocks, gravel, or a flat-plate collector From hereother ducts deliver the heated air to the area to be heated

In an air system using rocks or gravel, more space is needed for storage of thesolid media, compared to a liquid Further, the ductwork is more cumbersome and

FIGURE 7 Solar-energy system using flat-plate collectors and an antifreeze solution in a pair of

heat exchangers (Power.)

occupies more space than the piping for liquid heat-transfer media And air systemsare generally not suitable for comfort cooling or liquid heating, such as domestichot water

Eutectic salts can be used to increase the storage capacity of air systems whilereducing the volume required for storage space But these salts are expensive, cor-rosive, and toxic, and they become less effective with repeated use Where it isdesired to store thermal energy at temperatures above 200⬚F (93.3⬚C), pressurizedstorage tanks are attractive

Solar ‘‘heat wheels’’ can be used in the basic solar heating and cooling system

in the intake and return passages of the solar system The wheels permit the transfer

of thermal energy from the return to the intake side of the system and offer a means

Solar collectors can be used as a heat source for heat-pump systems in whichthe pump transfers heat to a storage tank The hot water in the tank can then beused for heating, while the heat pump supplies cooling

In summary, solar energy is a particularly valuable source of heat to augmentconventional space-heating and cooling systems and for heating liquids The prac-tical aspects of system operation can be troublesome—corrosion, deterioration,freezing, condensation, leaks—but these problems can be surmounted Solar energy

is not ‘‘free’’ because a relatively high initial investment for equipment must bepaid off over a long period And the equipment requires some fossil-fuel energy tofabricate

17.12 ENVIRONMENTAL CONTROL

But even with these slight disadvantages, the more solar energy that can be put

to work, the longer the supply of fossil fuels will last And recent studies show thatsolar energy will become more cost-competitive as the price of fossil fuels continues

to rise

6. Give design guides for typical solar systems

To ensure the best performance from any solar system, keep these pointers in mind:

a For space heating, size the solar collector to have an area of 25 to 50 percent

of the building’s floor area, depending on geographic location, amount of sulation, and ratio of wall to glass area in the building design

in-b For space cooling, allow 250 to 330 ft2 (23.3 to 30.7 m2) of collector surfacefor every ton of absorption air conditioning, depending on unit efficiency andsolar intensity in the area Insulate piping and vessels adequately to provide fluidtemperatures of 200 to 240⬚F (93.3 to 115.6⬚C)

c Size water storage tanks to hold between 1 and 2 gal / ft2(3.8 to 7.6 L / m2) ofcollector surface area

d In larger collector installations, gang collectors in series rather than parallel Use

the lowest fluid temperature suitable for the heating or cooling requirements

e Insulate piping and collector surfaces to reduce heat losses Use an overall

heat-transfer coefficient of less than 0.04 Btu / (h䡠ft2䡠 ⬚F) [0.23 W / (m2䡠K)] for pipingand collectors

f Avoid water velocities of greater than 4 ft / s (1.2 m / s) in the collector tubes, or

else efficiency may suffer

g Size pumps handling antifreeze solutions to carry the additional load caused by

the higher viscosity of the solution

Related Calculations. The general guidelines given here are valid for solarheating and cooling systems for a variety of applications (domestic, commercial,and industrial), for space heating and cooling, and for process heating and cooling,

as either the primary or supplemental heat source Further, note that solar energy

is not limited to semitropical areas There are numerous successful applications ofsolar heating in northern areas which are often considered to be ‘‘cold.’’ And withthe growing energy consciousness in all field, there will be greater utilization ofsolar energy to conserve fossil-fuel use

Energy experts in many different fields believe that solar-energy use is here tostay Since there seems to be little chance of fossil-fuel price reductions (onlyincreases), more and more energy users will be looking to solar heat sources toprovide some of or all their energy needs For example, Wagner College in StatenIsland, New York, installed, at this writing, 11,100 ft2(1032.3 m2) of evacuated-tube solar panels on the roof of their single-level parking structure These panelsprovide heating, cooling, and domestic hot water for two of the buildings on thecampus Energy output of these evacuated-tube collectors is some 3 billion Btu (3.2

⫻109kJ), producing a fuel-cost savings of $25,000 during the first year of lation The use of evacuated-tube collectors is planned in much the same way asdetailed above Other applications of such collectors include soft-drink bottlingplants, nursing homes, schools, etc More applications will be found as fossil-fuelprice increases make solar energy more competitive in the years to come Table 2gives a summary of solar-energy collector choices for quick preliminary use

instal-Data in this procedure are drawn from an article in Power magazine prepared

by members of the magazine’s editorial staff and from Owens-Illinois, Inc

TABLE 2 Solar-Energy Design Selection Summary

DETERMINATION OF SOLAR INSOLATION ON

SOLAR COLLECTORS UNDER DIFFERING

CONDITIONS

A south-facing solar collector will be installed on a building in Glasgow, Montana,

at latitude 48⬚13⬘N What is the clear-day solar insolation on this panel at 10 a.m

on January 21 if the collector tilt angle is 48⬚? What is the daily surface totalinsolation for January 21, at this angle of collector tilt? Compute the solar insolation

at 10:30 a.m on January 21 What is the actual daily solar insolation for thiscollector? Calculate the effect on the clear-day daily solar insolation if the collectortilt angle is changed to 74⬚

Calculation Procedure:

1. Determine the insolation for the collector at the specified location

The latitude of Glasgow, Montana, is 48⬚13⬘N Since the minutes are less than 30,

or one-half of a degree, the ASHRAE clear-day insolation table for 48⬚north itude can be used Entering Table 3 (which is an excerpt of the ASHRAE table)for 10 a.m on January 21, we find the clear-day solar insolation on a south-facingcollector with a 48⬚ tilt is 206 Btu / (h䡠ft2) (649.7 W / m2) The daily clear-daysurface total for January 21 is, from the same table, 1478 Btu / (day䡠ft2) (4661.6

lat-W / m2) for a 48⬚collector tilt angle

2. Find the insolation for the time between tabulated values

The ASHRAE tables plot the clear-day insolation at hourly intervals between 8a.m and 4 p.m For other times, use a linear interpolation Thus, for 10:30 a.m.,interpolate in Table 3 between 10:00 and 11:00 a.m values Or, (249⫺206) / 2⫹

206⫽227.5 Btu / (h䡠ft2) (717.5 W / m2), where the 249 and 206 are the insolationvalues at 11 and 10 a.m respectively Note that the difference can be either added

to or subtracted from the lower, or higher, clear-day insolation value, respectively

3. Find the actual solar insolation for the collector

ASHRAE tables plot the clear-day solar insolation for particular latitudes Dust,clouds, and water vapor will usually reduce the clear-day solar insolation to a valueless than that listed

To find the actual solar insolation at any location, use the relation i A ⫽ pi T,

where i A⫽actual solar insolation, Btu / (h䡠ft2) (W / m2); p ⫽ percentage of

clear-day insolation at the location, expressed as a decimal; i T ⫽ ASHRAE-tabulatedclear-day solar insolation, Btu / (h䡠ft2) (W / m2) The value of p ⫽ 0.3 ⫹ 0.65(S / 100), where S ⫽average sunshine for the locality, percent, from an ASHRAE orgovernment map of the sunshine for each month of the year For January, in Glas-

gow, Montana, the average sunshine is 50 percent Hence, p ⫽ 0.30 ⫹ 0.65(50 /100)⫽ 0.625 Then i A⫽0.625(1478)⫽923.75, say 923.5 Btu / (day䡠ft2) (2913.7

W / m2), by using the value found in step 1 of this procedure for the daily day solar insolation for January 21

clear-4. Determine the effect of a changed tilt angle for the collector

Most south-facing solar collectors are tilted at an angle approximately that of thelatitude of the location plus 15⬚ But if construction or other characteristics of thesite prevent this tilt angle, the effect can be computed by using ASHRAE tablesand a linear interpolation

Thus, for this 48⬚N location, with an actual tilt angle of 48⬚, a collector tilt angle

of 74⬚ will produce a clear-day solar insolation of i T ⫽ 1578[(74 ⫺ 68) / (90 ⫺68)](1578⫺1478)⫽ 1551.0 Btu / (day䡠ft2) (4894.4 W / m2), by the ASHRAE ta-bles In the above relation, the insolation values are for solar collector tilt angles

of 68⬚and 90⬚, respectively, with the higher insolation value for the smaller angle.Note that the insolation (heat absorbed) is greater at 74⬚ than at 48⬚ tilt angle

Related Calculations. This procedure demonstrates the flexibility and utility

of the ASHRAE clear-day solar insolation tables Using straight-line interpolation,the designer can obtain a number of intermediate clear-day values, including solarinsolation at times other than those listed, insolation at collector tilt angles differentfrom those listed, insolation on both normal (vertical) and horizontal planes, andsurface daily total insolation The calculations are simple, provided the designercarefully observes the direction of change in the tabulated values and uses thelatitude table for the collector location Where an exact-latitude table is not avail-able, the designer can interpolate in a linear fashion between latitude values lessthan and greater than the location latitude

Remember that the ASHRAE tables give clear-day insolation values To mine the actual solar insolation, the clear-day values must be corrected for dust,water vapor, and clouds, as shown above This correction usually reduces theamount of insolation, requiring a larger collector area to produce the required heat-ing or cooling ASHRAE also publishes tables of the average percentage of sun-shine for use in the relation for determining the actual solar insolation for a givenlocation

deter-SIZING COLLECTORS FOR SOLAR-ENERGY

HEATING SYSTEMS

Select the required collector area for a solar-energy heating system which is tosupply 70 percent of the heat for a commercial building situated in Grand Forks,

17.16 ENVIRONMENTAL CONTROL

TABLE 4 Solar Energy Available for Heating

Minnesota, if the computed heat loss 100,000 Btu / h (29.3 kW), the design indoortemperature is 70⬚F (21.1⬚C), the collector efficiency is given as 38 percent by themanufacturer, and collector tilt and orientation are adjustable for maximum solar-energy receipt

Calculation Procedure:

1. Determine the heating load for the structure

The first step in sizing a solar collector is to compute the heating load for thestructure This is done by using the methods given for other procedures in thishandbook in Sec 16 under Heating, Ventilating and Air Conditioning, and in Sec

16 under Electric Comfort Heating Use of these procedures would give the hourlyheating load—in this instance, it is 100,000 Btu / h (29.3 kW)

2. Compute the energy insolation for the solar collector

To determine the insolation received by the collector, the orientation and tilt angle

of the collector must be known Since the collector can be oriented and tilted formaximum results, the collector will be oriented directly south for maximum inso-lation Further, the tilt will be that of the latitude of Grand Forks, Minnesota, or

48⬚, since this produces the maximum performance for any solar collector

Next, use tabulations of mean percentage of possible sunshine and solar positionand insolation for the latitude of the installation Such tabulations are available inASHRAE publications and in similar reference works List, for each month of theyear, the mean percentage of possible sunshine and the insolation in Btu / (day䡠ft2)(W / m2), as in Table 4

Using a heating season of September through May, we find total solar energyavailable from the collector for these months is 103,627.6 Btu / ft2(326.9 kW / m2),found by taking the heat energy per month (⫽ mean sunshine, percent)[total in-solation, Btu / (ft2䡠day)](collector efficiency, percent) and summing each month’stotal Heat available during the off season can be used for heating water for use inthe building hot-water system.

3. Find the annual heating season heat load

Since the heat loss is 100,000 Btu / h (29.3 kW), the total heat load during the

9-month heating season from September through May, or 273 days, is H a ⫽ (24h)(273 days)(100,000)⫽655,200,000 Btu (687.9 MJ)

4 Determine the collector area required

The calculation in step 2 shows that the total solar energy available during theheating season is 103,627.6 Btu / ft2 (326.9 kW / m2) Then the collector area re-

quired is A ft2 (m2) ⫽ H a / S a , where S a ⫽ total solar energy available during theheating season, Btu / ft2 Or A⫽655,200,000 / 103,627.6⫽ 6322.64 ft2(587.4 m2)

if the solar panel is to supply all the heat for the building However, only 70 percent

of the heat required by the building is to be supplied by solar energy Hence, therequired solar panel area⫽0.7(6322.6)⫽4425.8 ft2(411.2 m2)

With the above data, a collector of 4500 ft2(418 m2) would be chosen for thisinstallation This choice agrees well with the precomputed collector sizes published

by the U.S Department of Energy for various parts of the United States

Related Calculations. The procedure shown here is valid for any type of solarcollector—flat-plate, concentrating, or nonconcentrating The two variables whichmust be determined for any installation are the annual heat loss for the structureand the annual heat flow available from the solar collector Once these are known,the collector area is easily determined

The major difficulty in sizing solar collectors for either comfort heating or waterheating lies in determining the heat output of the collector Factors such as collectortilt angle, orientation, and efficiency must be carefully evaluated before the collectorfinal choice is made And of these three factors, collector efficiency is probably themost important in the final choice of a collector

F CHART METHOD FOR DETERMINING USEFUL

ENERGY DELIVERY IN SOLAR HEATING

Determine the annual heating energy delivery of a solar space-heating system using

a double-glazed flat-plate collector if the building is located in Bismarck, NorthDakota, and the following specifications apply:

Building

Location: 47⬚N latitude

Space-heating load: 15,000 Btu / (⬚F䡠day) [8.5 kW / (m2䡠K䡠day)]

Solar System

Collector loss coefficient: F R U C⫽0.80 Btu / (h䡠ft2䡠 ⬚F) [4.5 W / (m2䡠K)]

Collector optical efficiency (average): F R(␶␣)⫽0.70

Collector tilt:␤ ⫽L⫹15⬚ ⫽62⬚

17.18 ENVIRONMENTAL CONTROL

TABLE 5 Climatic and Solar Data for Bismarck, North

Dakota

Collector area: A c⫽600 ft2(55.7 m2)

Collector fluid flow rate:m˙c / A c⫽11.4 lb / (h䡠ft )(water) [0.0155 kg / (s2c 䡠m2)]

Collector fluid heat capacity—specific gravity product: c pc⫽0.9 Btu / (lb䡠 ⬚F) [3.8

kJ / (kg䡠K)] (antifreeze)

Storage capacity: 1.85 gal / ft (water) (75.4 L / m2 2)

c

Storage fluid flow rate:m˙s / A c⫽20 lb / (h䡠ft2)(water) [0.027 kg / (s䡠m2)]

Storage fluid heat capacity: c ps ⫽1 Btu / (lb䡠 ⬚F)(water) [4.2 kJ / (kg䡠K)]

Heat-exchanger effectiveness: 0.75

Climatic Data

Climatic data from the NWS are tabulated in Table 5

Calculation Procedure:

1. Determine the solar parameter P s

The F chart is a common calculation procedure used in the United States to tain the useful energy delivery of active solar heating systems The F chart applies

ascer-only to the specific system designs of the type shown in Fig 8 for liquid systemsand Fig 9 for air systems Both systems find wide use today

The F chart method consists of several empirical equations expressing the

monthly solar heating fraction ƒsas a function of dimensionless groups which relatesystem properties and weather data for a month to the monthly heating requirement.The several dimensionless parameters are grouped into two dimensionless groups

call the solar parameter P s and the loss parameter P L

The solar parameter P s is the ratio of monthly solar energy absorbed by thecollector divided by the monthly heating load, or

FIGURE 8 Liquid-based solar space- and water-heating system (DOE / CS-0011.)

FIGURE 9 Air-based solar space- and water-heating system (DOE /

CS-0011.)

17.20 ENVIRONMENTAL CONTROL

FIGURE 10 Heat-exchanger penalty factor F hx When no exchanger is present, F⫽

1 (Kreider—The Solar Heating Design Process, McGraw-Hill.)

where F hx⫽heat-exchanger penalty factor (see Fig 10)

F R␶␣ ⫽average collector optical efficiency ⫽ 0.95 ⫻ collector efficiency

curve intercept F R(␶␣)n

I monthly average insolation on collector surface from a listing ofmonthly solar and climatic data

N⫽number of days in a month

L⫽monthly heating load, net of any passive system delivery as calculated

by the P chart, solar load ratio (SLR), or any other suitable method,

Btu / month

K ldhx⫽load-heat-exchanger correction factor for liquid systems, Table 6

(The P chart method and the SLR method are both explained in Related

Calcula-tions below.)

The value of P sis found for each month of the year by substituting appropriateunit values in the above equation and tabulating the results (Table 7)

2. Determine the loss parameter P L

The loss parameter P Lis related to the long-term energy losses from the collectordivided by the monthly heating load:

TABLE 6 F Chart K Factors

where F R U c⫽magnitude of collector efficiency curve slope (can be modified to

include piping and duct losses)

T monthly average ambient temperature,⬚F (⬚C)1

⌬t⫽number of hours per month⫽24N

T r⫽reference temperature⫽212⬚F (100⬚C)

Kstor⫽storage volume correction factor, Table 6

Kflow⫽collector flow rate correction factor, Table 6

KDHW⫽conversion factor for parameter P L when only a water heating system

is to be studied, Table 6

3. Determine the monthly solar fraction

The monthly solar fraction ƒs depends only on these two parameters, P s and P L.For liquid heating systems using solar energy as their heat source, the monthly solarfraction is given by