is there a need for a rock bed store? simulation and optimization of solar air heating systems for...

Solar Energy Vol. 36, No. 2, pp. 99-114, 1986 0038-092X/86 $3.00 + .00 Printed in the U.S.A. © 1986 Pergamon Press Ltd.

IS THERE A NEED FOR A ROCK BED STORE? SIMULATION AND OPTIMIZATION OF SOLAR AIR HEATING SYSTEMS FOR OFFICES WITH LARGE

THERMAL CAPACITY WALLS

ELIZABETH MICHELSON and AVRAHAM SHITZER+

Department of Mechanical Engineering, Technion-lsrael Institute of Technology, Haifa, Israel 32000

(Received 28 July 1983, revision received and accepted 31 May 1985)

Abstraet--A solar air heating system is designed for a floor of 120 m 2 offices, with large thermal capacity walls, in Israel. A constant air volume system is chosen for its operational simplicity. Rep- resentative winter hourly weather data are used to calculate the heating load. The building behavior is modeled in detail with dynamic wall and room temperatures which are linked to the heat input. The heat losses are found to be primarily (70-75%) due to storage in the walls for two different values of wall heat capacity and for two design temperatures ( 19 ° and 20°C). The paper deals with the operational details, seasonal performance and economics of the system. Multivariate optimization is carried out using the Simplex method. Optimum collector area, store volume and air flow rate of 30 m 2, 2-3 m 3 and 0.5 kg s - i respectively, are not affected by economic predictions. A comparison of this system with one which omits the rock bed store and uses only the building material as storage is also made. Results show that for the higher design temperaturre of 20°C, the rock bed store improves system performance, but the same solar fraction can be achieved by increasing the collector area from 30 to 50 m 2 in the system without active storage. For the lower design temperature of 19°C the improvement in performance made by the addition of the rock bed store is small, and can be obtained by increasing the collector area from 30 to 40 m 2, obviating the need for the store system. In buildings with a high heat capacity, operated during daytime only, the no-active-store system is recommended for its ease of operation and suitability for retrofitting.

INTRODUCTION

The majority of active solar air heating systems include a specialized heat storage facility, e.g. a rock bed. In certain cases, the thermal inertia of the building itself has also been used for storage, in warm temperature climates[I] as well as in cold ones[2, 3]. The oldest example of the type of system designed to use the building mass as storage, is the Lefever (residential) House in Pennsylvania, built in 195414]. Space heating of nonresidential buildings by this method was recommended by Lawand et al.[3] for its good performance and simplicity, on the basis of tests on their installation in Canada. The Trombe-Michel system also uses the wall as storage[4]. Some encouraging theoretical and prac- tical results on the use of building elements as passive systems for collection and storage were obtained by Hoffman et al.[5] for the Israeli climate.

In this work, we use a computer simulation to compare an active solar heating system with a rock bed store against one, termed a "no active storage" system, in which the building mass alone performs as the storage. In the latter case, the rooms are heated by available solar energy even when the building is not occupied. The building for which the system is to be designed is an upper floor of offices

t Correspondence should be sent to Professor A. Shitzer.

at the Department of Mechanical Engineering, which is of heavy masonry construction. Modeling of the dynamic heating load of this building has been performed recently by Levy and Shitzer[6]. Details of modeling equations are, therefore, not included in this article.

The space heating system chosen for the present study is of the constant air volume (CAV) type, e.g. [18]. It employs solar air heating collectors, air ducts and fans and suitable controls. A thermal storage system, i.e. a rock bed store, is included as an option. A schematic diagram of this system is shown in Fig. 1.

This study had a twofold purpose. The first was to design and optimize a solar air heating system for a floor of offices. By their very nature, offices are representative of public buildings which oper- rate during daytime only. These hours coincide with the hours of sunshine on bright days. Thus, in principle, available solar energy may be supplied directly to the heated space, minimizing, or even obviating, the need for thermal storage. The second purpose of this study was therefore to compare the performance of two solar air heating systems. One system included an active rock bed store while the other system did not. In both systems, however, heat stored in the building elements has been considered. The spectific building used for this study is a heavy masonry one, a fact which bears significantly on the comparative result.

99

lO0 E. MICHELSON and A. SHITZER

(OPTIONAL) ,

"~" I , I EXHAUST I I q _ . m

l / \ \ r - - " " - - ' I ROCK" BEe I

(OPTIO.A'): STORE I

I I I I I I I FAN

DUCT " ' - -

BACKUP HEATER + FAN

II TO ROOMS

- - - - "]CONTROL I CONNECTION

I I I

OUTDOOR AIR

FROM ROOMS

Fig. 1. Flow circuit diagram of solar air heating system with and without rock bed store.

This article contains a general description of the heat load calculation procedure and of the system components ' modeling equations. The solar heating system is optimized with respect to certain variables. Finally a comparison is made between the performance of the system with the active thermal storage facility against the one which does not include this facility.

CALCULATION OF BUILDING HEATING LOAD

The office space for which the heating system is to be built consists of ten rooms on the top floor of the Energy Laboratory of the Department of Me- chanical Engineering, Technion, Israel Institute of Technology. By their function, offices are charac- terized by a heating requirement during the daytime only for five to six days of the week. A floor plan

of the offices is shown in Fig. 2. Seven of the offices are identical (type D in Fig. 2).

The building behavior is modeled in detail, with dynamic wall and room temperatures which are linked to the heat input. The normal design temperature is 19°C. Due to the apparent function of the walls as heat storage media, which exchange heat directly with room air, each wall was repre- sented by a one-dimensional finite difference model with seven subdivisions[7]. Complete details of the heat load program are given in Ref. [6]. The corridor temperature is taken to be the average of the room and outside temperatures as the staircase has louvre windows to the outside which do not close tightly. The temperatures of all adjoining rooms, including those on the floor below, are assumed to be equal to the design temperature during working hours.

The doors and windows are considered to have

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D ROOMS

L ' ~ W I N D O W

T 4"40

26"25

J---- ' , ,J-- O C

.,,-.-2"90--,, ,---3"00--,.

i I I I

B

',--- 2 .70- , , "

Fig. 2. Floor plan for heated offices. Dimensions are in meters.

i 1 .5

3"65

1

Is there a need for a rock bed store?

Table 1. Summary of weather data[10]*

I01

Monthly Total global radiation, MJ m-2 No. of average air horizontal 45 ° tilted

Month degree-days temp. C surface surface

November 81 - - - - - - December 171 12.8 305 470 January 215 l 1.2 328 506 February 191 11.4 372 513 March 151 14.1 560 648 April 89 - - - - - - Total 898 1565 2137

Latitude of location (Haifa) 32 ° 48' N Longitude of location (Haifa) 34 ° 59' E Altitude of location 220 m

* Air temperatures are I°C below those in [10]. November and April are not included in the heating season.

negligible heat capacity, and the heat losses are modeled simply with constant loss coefficients. The losses due to doors being opened, which is quite infrequent, are not taken into account. The solar heat gain due to radiation through the windows is taken as a safety factor, since the windows are fac- ing north and receive only reflected radiation from another building. It is also assumed that since the air is circulated by a fan, its pressure in the rooms is maintained slightly above outside pressure, thus causing exfiltration and suppressing infiltration of outdoor air. Outside working hours, with the fan turned off, it is assumed that the rate of outdoor air infiltration is one-third that of the mechanical ventilation rate during working hours, i.e. 0.0047 m3/ s - ~[8].

In the load calculation, positive heat gains are assumed from one occupant per office (100 W) and from the lights (215 W) during working hours (08:00-18:00 Sun. -Thurs . and 08:00-13:00 on Fri- days). It is also assumed that the design temperature (19°C) is reached after the first half hour of operation of the heating system.

The weather data used in this study, consisting of hourly averages of global and diffuse radiation and air temperatures, were adapted from[9, 10]. Table 1 summarizes the data for six months, No- vember through April. It can be seen that the number of degree-days for November and April, and thus the heating load, is much lower than that of the other winter months. Therefore the heating season for the present simulation was taken to be 1 December to 31 March. The day to night temperature swings in this locality, are small to moderate ranging from 5-15°C, the high values corresponding to sunny days. In preliminary heating load calculations[11] January was taken as the design month.

Calculation of the heating loads is performed in 15 rain time intervals. The heat supplied by the heating system is taken to be constant over this time step. Within this time step, the heat balance of the room is calculated at ten sub-time steps, ~o hr each. From the heat losses and input in the 1 hr period,

and the relationship of the individual room temperatures to the design value, the required load for the subsequent time step is estimated. The aim of the heating control is to steer the room temperatures towards the design value whenever they diverge. This must be achieved sufficiently fast to avoid unnecessary use of the backup and store, at the same time avoiding rapid fluctuations in room temperatures. The maximum allowable rate of change of room temperature was stipulated to be 0.4°C per ~ hr[8]. The calculated total load is supplied in the next ~ hr period, with equal quantities to each room. Because of this, and the time step lag, the room temperatures will not be precisely 19°C (see below). The heat balance in the rooms continued to be calculated overnight, and during the weekend, to give the correct room and wall temperatures at the next day start-up time.

The monthly summaries of the nominal heating loads are shown in Table 2. Values in this table do not include the heat input from the occupants and from the lights. Details are given for three cases:

(a) Standard case for which the room design temperature was 19°C and wall densities were taken at their nominal values[6].

(b) Room design temperature assumed to be I°C higher, i.e. 20°C with wall densities taken at their nominal values.

(c) Wall densities assumed to be half their nominal values with room design temperature maintained at 19°C.

Referring to Table 2, it can be seen that some 75% of the energy losses go to storage in the walls, for both rooms A and D. The storage losses can be divided into their major components as follows. One-quarter (of the 75%) is due to the ceiling, and one-sixth to the floor, in both room types. An ad- ditional one-quarter is due to the partition walls in room type D, and one-fifth to the outer walls in room A. The other walls make up the remainder of the storage losses. Conduction losses, which are defined as the portion which passes through the

102 E. MICHELSON and A. SHITZER

Table 2. Summary of monthly loads. The standard case has a design temperature of 19°C and wall densities given in the Appendix; the case with design temperature 20°C has the standard wall densities; the case with walls at half the

standard density has a design temperature of 19°C

Total load, MJ per m 2 floor area (Standard case) Total load, all rooms, GJ

Room type DESIGN WALLS AT STANDARD TEMP HALF-

Month A B C D CASE 20°C DENSITY

December 38 41 30 23 3.33 4.37 3.06 January 57 63 45 34 5.02 6.06 4.32 February 52 57 41 31 4.51 5.43 3.93 March 30 32 24 18 2.63 3.41 2.47

Season total 177 193 140 106 15.49 19.27 13.78

% Heat losses for room types A and D, during working hours, due to various load components (standard case):

Load component Walls Windows Doors Ventilation

Room type A D A D A D A D

CO* SO** CO* SO**

December 18 74 14 75 2 2 1 2 5 7 January 15 73 11 74 3 3 2 2 7 9 February 14 73 11 74 3 3 2 2 8 9 March 19 74 15 76 2 2 1 1 5 6

* CONDUCTION ** STORAGE

wall at each time step, make up 14-19% of the total in room A, with the ceiling and outer walls contributing most, and in essentially equal amounts. For room type D, conduction losses are 11-15%, with the ceiling contributing more than twice that of the outer walls.

The heat load calculations were repeated for a building identical in every way except the density of the wall materials, which were decreased to one- half of their nominal values [case (c)]. The heat capacity of the walls is thus reduced to one-half. A test case, for a few days of weather data, was carried out where the room temperatures were held at 19°C exactly. The heat losses to storage in the walls did in fact decrease by about 16% with respect to those for the nominal density. When room temperatures were allowed to fluctuate around the design value, the situation was further complicated. For the case of the lower density material, the losses of the inner D type rooms, which are due mainly to storage in the partition walls, are lower relative to the losses in the outer rooms A and B. Since all rooms are equally heated, rooms D will be warmer in the case of the higher density walls. The higher room temperatures, in turn, increase the storage losses to offset the effect of the lower density. The percentage of heat losses to storage in the walls decreases from 74% to 70% for the two coldest

months January and February, and the seasonal load decreases from 15.5 to 13.8 GJ, when the density of the wall material is halved. In summary, decreasing the wall material heat capacity by one-half, case (c), serves to decrease the heating load by 11% (Table 2). Raising the design temperature from 19 to 20°C, case (b), increases the heating load by 25%.

The heating control algorithm specifies that the fluctuations in room temperature during working hours, must not exceed 0.4°C in any ¼ hour time step. In fact the number of time steps in which the temperatures change by 0.3-0.4°C is small, i.e. eight times only in the entire heating season. The peak-to-peak range of variation of an individual room temperature was found to be up to 1.5°C over the whole day, for days of high heating load, and otherwise less than I°C. The rate of change and peak to peak variation agree well with the values recommended in [8]. Since all the rooms are equally heated, and their loads differ (Table 2), details of their temperatures were investigated for the coldest day, and the day of highest load in the season, 11 and 14 February, respectively[10]. On these days, room temperatures could diverge by up to I°C from the design value, e.g. room A at 18-19°C, and rooms B or D at 19-20°C. On days of lower load, all room temperatures were found to be within +-0.4°C of 19°C.


SOLAR AIR HEATING SYSTEM

WITH ACTIVE THERMAL STORAGE

Concurrently with the calculation of the building heating load, the potential contributions from solar energy were also estimated in each time step. The controller was called upon to consider the possi- bilities and make the decision on how to supply the load. Eight modes of operation were employed and are shown in Table 3.

The features of the control strategy are as follows:

1. To avoid unnecessary switching of the heating system, there has to be some threshold below which the loads are not supplied. A value of ~ kW for the threshold was found to be suitable as it did not affect room temperature stability, and decreased the seasonal supplied load with respect to the case where all loads are supplied, by only 0.2%. The system is not completely off though, when the load is in the range 0-~ kW, as ventilation air must be supplied throughout the working day. When backup is required, however, loads smaller than the threshold value are also supplied.

2. In addition to the above threshold load, whenever the expected rise in supply air temperature was equal to or less than 4°C, the load is supplied by backup energy. This is done to avoid using the long collector- store duct circuit and to protect the store from wasteful depletion at low heating loads.

3. The collectors (or store) are not used at all, even in conjunction with the backup for higher loads, if their output is less than 1 kW. This is to avoid unproductive use of the large fan(s) which may consume up to 400 W.

4. When either the collector or the store alone supply the load, modes 3 or 5, respectively,

5.

6.

103

their output energy may be in excess of the load. In these cases the supply energy is controlled by mixing with outdoor air and venting out the excess energy. For charging the store, the collector output temperature must be at least 4°C above the mean rock bed temperature. The latter is representative of the energy content of the rock bed store. Hence the store will not be- come destratified by air from the collectors unless there are definite energy gains to be made. It should be noted that in a number of solar air heating installations, the temperature of the cold end of the storage facility is often used for making the decision of whether or not the store should be charged. In this study the main considera- tion was to maintain a well stratified store. Thus the average store temperature, rather than the temperature of the cold end, was used. The collectors charge the store while the backup supplies the load (mode 8 in Table 3), if the collector power output is more than a number X times the load. The search for a suitable values for X is described sub- sequently. The solar collectors are modeled by the Hottel-Whillier-Bliss equation[12], which was modified to include heat capacity. Constant values for the plate efficiency factor and loss coefficient were used for each flow rate. In the absence of sufficient tests on propsective collectors, for various air flow rates, parameter values listed in the Appendix were adapted from [13]. This source, which refer to the collectors in- stalled in the CS Solar House II, was selected since it gave some manufacturer 's data on the variation of plate efficiency factor with flow rate. As the collector area is varied in the parametric analysis and optimization, it is assumed that the collectors are

Table 3. Modes of operation of the systems with and without active storage. Modes 3, 4, 7 in the no-active-store system apply to working hours only

Description

Mode No. Active-store System No-active-store system

No. of decisions in control strategy

No load, system off No load, collectors charge store Charge rooms out of working hrs

Collectors alone supply load Collectors and back-up supply load

Store alone supplies load Store and back up supply load

Backup alone supplies load Backup supplies load while

collectors charge store

19 10

104 E. MICHELSON

connected in series, so that their flow rate dependent parameters may be taken as constant for different areas.

The heat transfer through the rock bed store is computed with a one-dimensional finite-difference model based on the work of Mumma and Mar- vin[14]. The modification made to this model is that the time-dependent differential equations, one for each layer, are solved analytically. This was necessary because we introduced heat losses from the top and bottom surfaces of the store whereas only side losses are considered in [14]. The high losses from the top and bottom layers of the store make the finite difference solution for the time-dependent equation unstable. The assumption made for the analytical solution is that the heat input to a layer from neighboring layers, is constant over one time step. The time step for the rock bed simulation was taken to be & hr, that is 10 iterations per system time step. The pressure drop across the store is calculated according to [15].

The air ducts are modeled for their heat losses and pressure drops. Two duct systems are considered. One is the collector-store circuit which would be located on the roof; the other is the room distribution circuit. The latter will be located mostly in the rooms and so its energy losses were neg- lected.

ECONOMICS AND OPTIMIZATION

The criterion by which the system is to be judged enters the calculations as the objective function, i.e. the function which is minimized, such a payback time, or ma dmized, such as energy output. Two other essential requirements are a choice of variable parameters and the method of optimization. The method used here is the Simplex method[16] which, as a direct search optimization method, is very robust and is recommended for functions with discontinuities. Such discontinous functions appear as a result of calculations with hourly weather data[17]. The method is, however, not sufficiently accurate for more than ten variables, which is not a drawback in the present application.

The objective function for the optimization was taken to be the payback time defined for assumed fuel inflation and interest rates. The payback time is obtained by equating the savings over this time to the capital cost C,

C = ( L - L s ) f 1 + is)/(1 + id • (1) n = |

Summing the geometrical series and taking loga- rithms of both sides yields an explicit expression for the payback time, N ,

N = log 1 + f( l +~)( -L ---Ls)

~1 + is~ log [ l - "~ idJ " (2)

and A. SHITZER

An alternative form used for the objective function was the simple payback time.

C N - f ( L - L s ) ' (3)

which is identical to eqn (1) when the fuel inflation and interest rates are equal. It was thought important to have results for the simple payback time for comparison, as it requires no predictions for the economic situation in the future. Besides, for the simple payback time, the position of the optimum, i.e. the set of optimum system parameters, is independent of the auxiliary fuel cost and the absolute component costs. Specifically, the simple payback time depends only on the relative component costs and system performance[17].

A parametric analysis was carried out for the following variables: (1) collector area, (2) total air mass flow rate, (3) store volume, (4) the store- charging criterion X, and (5) the collector tilt angle. Nominal values of these variables and those of the fixed parameters are listed in the Appendix.

The Simplex method in the CERN minimization package MINUITS, was used for multivariate optimization of the system with active storage, as described in [17]. As a first step and in order to make the optimization procedure feasible in terms of CPU time it was necessary to write the calculated heating load onto a file. This is done because the load calculations consume most of the CPU time. Thus a file containing bhourly totals of load and average room temperatures was generated for the entire season. The optimization program can then read the load and temperatures as data, taking only 27 seconds (on an IBM 370/168 machine) for a season's silmulation instead of the 420 seconds required when the heating load is also being calculated.

The three variables in the optimization of the thermal performance of the air heating system were collector area A, store volume V and total air flow rate m. The bounds on these variables were selected to be 10-60 m 2, 1-20 m 3 and 0.1-1.0 kg s -1, respectively. A fourth variable, the store-charging criterion X, was also included in some test cases. However, when X is present together with store volume, there are two variables for which the shape of the objective function (payback time) is very shallow. This refers to the range V > 5 m 3 and X > 4. The results with the four variates were therefore not sufficiently accurante, and X was fixed at 4. After the optimization routine had converged onto a minimum, a one-dimensional search was un- dertaken for each variable in turn, while the remaining variables retained their values at the minimum, until the function increases by a preset e%. This gives the "range" of each variable, indicating the breadth of the minimum. The variables are searched in step sizes of 2 m 2, 2 m 3 and 0.1 kg s 1 for A, V and m, respectively. During the optimization process the variables are allowed to change continuously. The value used for e was 3, chosen

Is there a need for a rock bed store? 105

Table 4. Results of optimization. The ranges of each variable refer to an increase of not more than 3% in the payback time

Values of variables at optimum, and Function range value at optimal Total air

Objective point, Collector Store flow rate, Function years A r e a , m 2 V o l u m e , m 3 kg s-

Payback time with i s = 8% ia = 4 %

Simple Payback time

23 2.2 0,5 21 (18-32) (2-4) (0.4-0.6)

24 2.2 0.45 34 (20-30) (2-4) (0,4-0,5)

to represent an increase in the payback time of 6 months to a year.

The results of the 3-variate optimization, apply- ing to the entire heating season December-March , are shown in Table 4. The number of iterations required to reach the optimum, was 35-40. The total CPU time, including searching the area of the minimum after the optimization routine had converged, was 1100-1200 sec on the IBM 37/168 machine. The convergence criterion was set to 0.1, i.e. convergence is attained when the values of the objective function at the Simplex points differ by less than 0.1 years.

The most important point that emerges from Table 4 is that the optimum system sizes, as indi- cated by both objective functions, are virtually the same. These are, a collector area of 23-24 m 2, a store volume of 2.2 m 3, operated at a flow rate of 0.45-0.5 kg s-1. Even though the actual values of the payback times cannot be taken too seriously due to the uncertainty in the economic parameters, the optimum system sizes appear to be reliable and are virtually independent of economic predictions.

COMPARISON OF SOLAR AIR HEATING SYSTEMS

WITH AND WITHOUT ACTIVE THERMAL

STORAGE FACILITY

It is recalled that the second purpose of the present study is to compare the performance of two solar air heating systems. One system, which in- cludes an active thermal storage facility, termed here active-store system (AS), was described in the foregoing. In the other system, termed here a no- active-store (NAS) system, the storage facility is eliminated (optional scheme in Fig. 1).

The principle of operation of the NAS system is that the collectors supply part or all of the load during working hours, and heat the rooms outside working hours, so that the rooms are preheated by the time the working day begins. In practice this means that the rooms are charged at the weekends (Friday afternoon through Saturday) and between 07:00 and 08:00 hrs Sunday through Friday on

sunny days. The early morning heating does occur quite frequently even in January and February as dawn is between 6:11 and 6:42 AM. Outside working hours the collectors discharge all available energy into the rooms as long as the mean room temperature is below 26°C during the weekend, or 19°C before 08:00 hrs on a working day. 26°C was chosen as a maximum tolerable temperature should some- one enter the rooms during the weekend. The modes of operation of this system, together with those of the active storage system, are shown in Table 3. The control strategy, the building behavior, the collectors and the air ducts are modeled in the same way as in the AS system, and have the same parameters.

In the case of the no-active-storage system, it was not possible to carry out the multivariate optimization as for the active-store system. The load calculations must be performed together with those for the heating system, and thus the CPU time cannot be reduced as in the case of the active-store system. This is because the extent of preheating of the rooms during the weekend or early morning, and the consequent heating load during working hours, depend upon the system parameters. For example, the larger the collector area, the lower the required heating load. However, there are only two major variables, i.e. collector area and air flow rate, and a parametric analysis is therefore considered adequate.

On investigating the detailed operation throughout the day, it was found that the active-store system may operate continuously in any one mode for periods of ¼ hr (one time step) up to 5 hrs. Occa- sional switching of modes from one time step to the next does occur. In the NAS system switching between modes occurs much less frequently, as there are only four modes available during working hours compared to eight modes in the AS system. The NAS system is often in mode 2 (charging rooms out of working hours) from 07:00-08:00 hrs on a working day.

The calculated system pressure drops were 260 and 310 Pa, leading to fan powers of 160 and 190 W, for collector areas of 30 and 40 m z, respectively, at a flow rate of 0.5 kg s i. These values apply to both

106

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0'~

~.0"2 !

0.1

E. MiCr~ELSON and A. SmTZER

/ / / 5 I0

Saturday

l e f t # |to,re |v l l lm A , 3 0 m I

V • Sm| (CubiC:) • , 0 ' 5 kg s "l

/ / /

15 ~0

Day in Jonu4ry

~ J~Cktip From W~'e From Wiled:tore

/

25 30

N

S

Ooy in Februory

:.5;

Fig. 3. Detailed breakdowns of load supply by the system with active storage in the coldest winter days.

systems as the pressure drop across the collectors is larger than that across the store.

Figure 3 shows the daily totals of load, and its supply by the active-storage system for the coldest period of the season, 1 January-20 February. An interesting point to note is the peak load on the first day of the working week. The store contribution in January and February is about 45% of the energy supplied to the rooms directly from the collectors, the main use of the store being on the first day of the working week when it has been charging over

the weekend. The store plays a part at mid-week days (6, 14, 15, 26-28 January), only when it has had an opportunity to recharge on the previous day. The function of the store shows up well on 18 Jan- uary when it is utilized on a cloudy day following a sunny one. It appears to provide storage for one or two days (see also results for 3 February). for the rest of the season, when the heating load is lower, the store contributes throughout the week, and almost as much as the energy coming directly from the collectors. Throughout the season some

Table 5. Seasonal summaries for both systems ~

Item

ACTIVE NO-ACTIVE- NO-ACTIVE- STORE SYSTEM STORE SYSTEM, STORE SYSTEM,

A = 30 m 2 A = 30 m 2 A = 40 m 2

Reference Load, GJ (2) 15.46 15.46 Supplied Load (working hrs), GJ 15.46 13.51 Mean room temp. Dec-Feb. C 19.28 19.32

(working hrs) (3) Solar fraction .74 .67 Fraction supplied by collectors, .47 .55

(working hrs) Fraction Supplied by store (4) .27 .12 Fraction Store losses, (4) .06 - - Fraction Net energy left in store .01 - -

at end of season (4) Fraction Duct losses (4) .04 .03. Fraction Excess energy (4) .42 .36 Collected Energy fraction 1.27 .93 Peak backup, kW 21.5 21.2 Hours of operation of main fan 735 740 Hours of operation of backup 450 250

fan Capital cost, $ 8440 7530 Annual savings, $ 244 221 Payback time, yrs. (5) 21.9 21.6

15.46 12.97 19.34

.73

.57

.16

.03

.57 1.17

21.1 740 250

8740 240

22.6

(1) Design temperature 19°C and standard wall density. (2) The reference load in row 1 does not include duct losses. (3) March temperatures are 0.5-0.6°C higher due to higher outdoor temperatures. (4) Refers to working hours. (5) Payback time is for is = 8% and id = 4%.

Is there a need for a rock bed store'? 107

0..I

~ 0.2

0.I

No active store Svltem A.3Oml m . 0 5 I~1 s-'

[ ~ S.mlied by ~ l t~w Supl~ied by collectors

m

5 IO 15 20 25

I I _ ~ 7 ;

Z Z Z z ~:f:~ Z

~ t u r ~ y Ooy inJa~ary ~ y

Fig. 4. Detailed breakdowns of load supply by the system without active storage days.

m l //

/ /

z ~ z I0 15

in Fd~'uar y

in the coldest winter

20

15

( u

I0

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+--+ Outdoor air temperature .... Average room temperature

Mode of operation 03 System off

(~ Charge rooms out of working hours

(~) Supply load with collectors alone

Average room T for active store system

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\ . , t I+

\ I

24 4 8

Feb 14

Fig. 5. Average room temperature on the weekend of 12-14 February for the system without active storage.

108 E. MICHELSON

(40%) of the collected energy has to be vented out as it is in excess of the requirements, Table 5. This " exces s " energy cannot be fed into the rooms during working hours because later in the day, when the backup might be called upon, it would be necessary to use higher levels of backup to avoid un- acceptable swings in room temperature.

Calculations were repeated for the system without active store. Results for the coldest months, as for the AS system, are shown in Fig. 4. The peak loads at the beginning of the working week, seen in Fig. 3, disappear due to charging of the rooms during the weekend. The decrease in load with respect to the system with active storage, is quite dra- matic on Sundays. The effect persists, though to a smaller extent on Mondays, whereas for the rest of the week the loads for the two systems are virtually the same.

On 14 February, the day of the highest non-solar heating load, the charging of the rooms over the weekend in the no-active-store system reduces the peak of the total daily load from 36.7 kW to 25.6 kW. The daily totals are reduced from 0.4 GJ to 0.27 GJ (Figs. 3 and 4). The operation of the no- active-store system over the preceding weekend (13.00 hrs 12 Feburary to 08:00 hrs 14 February) is shown in Fig. 5. The average room temperature reaches 19-20°C. The temperature drops through the afternoon and night, and with some heating from 07:00-08:00 hrs on the morning of Sunday, 14

and A. SmTZER

February, its value at the beginning of the working day is 12.5°C. This is almost 3.5°C above the average room temperature in the AS system. Thus both the peak heating load and the daily total are decreased by about ~ when no active storage is employed.

The variation of solar fraction and payback time with collector area A is shown in Fig. 6 for both systems, AS and NAS. From Table 5 it can be seen that the AS system with 30 m 2 of collectors, and the NAS system with 40 m 2, are roughly equivalent in cost and solar fraction. An interesting feature to note in Fig. 6 is that the solar fraction of the AS system seems to essentially saturate at collector areas above 40 m 2, whereas the NAS system shows no such signs of saturation, and the solar fractions of both systems at 60 m 2 are very close. This is because the 5 m 3 rock bed store in the AS system has a heat capacity of 7 MJ C - ~, whereas the storage in the NAS system, which consists of the walls only, has a heat capacity of about 120 MJ C -1. The large wall heat capacity is of course also present in the AS system, but here it serves only to dampen the room temperature fluctuations rather than to function as and replace the rock bed store.

The performance of the two systems is further compared for the cases of I°C higher indoor design temperature, Fig. 7, and 50% heat capacity walls, Fig. 8. In Fig. 7 the gap between the NAS and AS systems curves for solar fraction vs. collector area

8O

7O

6O

# g 50

4o

30

2O

IO

\ / / / y

x \ I / /

- System with active store (Sin s)

/ • S:;:;frac/~io:Ctive store

x Payback time l l I I I I

- 3 0

- 2 5

- 20

15 0 I0 20 30 40 50 6O

Collector area, m =

Fig. 6. Solar fraction and payback time vs. collector area for standard case (19°C design temperature and nominal wall densities.)

IfJ

O

E

U O / n

O n

ls there a need for a rock bed store? 109

8 0

7 0

6 0

50 0 . 1 4- ¢)

P 4 0

3o

2 0

I0

\ \ X \

\ /

A

//

I0

. / /

/

/

/

/ • ,.,...-

\ 1 t \ x . . ~ i

~ . . . . . . . . . . X ~ ' ' ' "

System with active store • Solar fraction System w/o active store x Poybock time

I I I I I 20 30 40 50 60

Collector area, m !

- 3O

- 2 5 O 0

E ow

I,I

It - 2 o g'

Q.

IS

Fig. 7. Solar fraction and payback time vs. collector area for a design temperature of 20°C, and nominal wall densities.

8 0 - . ~ ~"

/ , I " - 3 5 /

7 0 - /

- 3 0 ~

. l

- ~ X ~ x ~ X / / / / x/ " U O

.10 - / ~

0

/ j \ \ //x - 2 5 a.

// . .~ 20 ~ / . "------a ~''" ~-

IC System with active store • Solar fraction S y s t e m w/o a c t i v e s t o r e x P o y l ~ c k t i m e

1 I I I I I .~0 O0 I0 20 30 40 50 60

Collector a r e a , m 2

Fig. 8. Solar fraction and payback time vs. collector area for low heat capacity walls, and 19°C design temperature.

50 =- 0

4 o

"~ 3C

LIO

150(

= I00(

Q.

o 5 0 C - C

0

E. MICHELSON and A. SHrrZER

• Peak backup

- x Total fan operating time

m m With active store

W/O active store

i I I i" i i I0 20 3 0 4 0 50 6 0

Collector area, m=

Fig. 9. Peak backup and fan operating times vs. collector area.

4 0

v

30 E

O"

U 0

2 0 .a

0 lID Q.

I0

~s considerably greater than for the lower design temperature, Fig. 6. The curves for payback time even show a reversal, indicating that, for the economic factors in these calculations the AS system may be more economic. However, solar fraction of the AS system with 30 m 2 collector area can be achieved by 50 m 2 in the NAS system, and the operational simplicity of the NAS system may still weigh in its favor. The effect of halving the wall density, and hence heat capacity, with respect to the standard case can be seen in Fig. 8. In this case the system with active store has a clear advantage as the walls do not provide as much heat storage capacity.

The peak backup requirements, which dictate the size of the backup installation, and the total fan operating times, are shown in Fig. 9 for different collector areas. A non-solar heating system, indi- cated by the intersection with the ordinate, requires a backup installation of about 38 kW, and the introduction of a solar heating system with collector area greater than or equal to 30 m 2, reduces the size to around 22 kW. This reduction in the required size of the backup installation, which has not been taken into account in the economic calculations, serves to decrease the relative cost and the payback times of the solar heating systems. It is also interesting to note in Fig. 9 that the NAS system total fan operating times remain at about the same value (950- 1000 hrs) as in a non-solar air heating system. The AS system fan times are 200 hrs greater, these hours relating to the backup fan (Table 5).

Figure 10 shows the variation in solar fraction and payback time with total air flow rate, for both systems and two collector areas. The solar fraction decreases with increasing flow rate above 0.6 kg s - ' , because the collector output is at lower temperatures. High flow rates also lead to higher pressure drops and operating costs. At the low flow rate (0.25 kg s - ' ) the collector efficiency is lower. For both systems and collector areas, the optimum flow rate is around 0.5 kg s - ' . Another important con- sideration is the air velocity in the rooms, a recommended value for which is 0.2 m s - ' [8 ] . A flow rate much above 0.5 kg s - ' , with reasonable duct dimensions, might appear as a draught to the occupants.

The parametric analysis described below, for the store parameters and the collector tilt angle were obviously carried out for the AS system only. Fig- ure 11 shows the slight increase of solar fraction with store volumes in the range 1-5 m 3, which saturates for volumes above 5 m 3. The payback time increases as the store volume decreases below 3 m 3, because of the higher pressure drops for smaller stores at a given total air flow rate[15]. The payback time increases slowly with volumes above 5 m 3, for the costs used in this simulation.

In order to make fuller use of the rock bed store it is evidently worthwhile to be able to charge the store during working hours as well as during the weekend. The best opportunities during working hours are offered by periods of no or little load. During these hours we have to specify a criterion

8 0 -

7 0 -

6 0 -

5 o -

40 t, "3 O3

3 0 -

2 0 -

I 0 -

0


• f ~ . . . . ~ " - e . . . --.. - - . /40

- -'-/3o

2 // ~'/ Collector orea,m / ~./

/ / 7 x / / S ~ ' ~ \ 30 / ~ //-/?7 \30 40 40 - - -

- - ~ A c t i v e s t o r e s y s t e m (AS) • S o l a r f r a c t i o n

, No active store system (NAS)

x Payback time AS + Payback time NAS

1 . I I I 0.25 0.5 0-75 I '0

Total air flow rate, kg s -~

Fig. 10. Solar fraction and payback time vs, total air mass flow rate,

30

25

- 2 0

t.. 0 Q)

6 E

O 0 JO

0 11.

II

80

70

6O ,<

50 "6 o "" 40

0 O9

3O

2 0 -

I0 o

m

J r ~ " - - - - - . ~ _ J r . ~ Jr _ ~ - - Jr - ' - - ' - - - - - - ~ Jr - - - ' - -

- - - - - 40 mZ~ 30 m= j, Collector area

• Solar fraction + Payback time

1 .... I , I 2 4 6

S t o r e v o l u m e , m ~

- 3 0

¢;

-25 "., O .~_

U O

0 n - 2 0

I I0 (Cubic stores)

Fig. 11. Solar fraction and payback t ime vs. store volume.


Solar fraction: D m Collector area 4 0 m = ~ Contribution from collectors a

Collector area 3 0 m = + Contribution from collectors • Poybock time 3 0 m = x Contribution from store

8 0 ~ , % . . . . . R . . . " ~ ~ . - - - R ~ ~ - - R . . . . - - I 1 - ~

I \ ~-""" ~ * - - - - - - - - - * - - - - - * - - ,op 6 o ~ - ° ~ - - - ' - - - - - - - - ~ ~ _ _

-~ 50

8 3 0

2Q

I0

a . ~ ÷ ~ "t - - + " "

X ~ x - - - - x

I I 1 I 2 3; 4 5 6

Store charging criterion x

Fig. 12. Solar fraction and payback time vs. store charging criterion X.

store

2 5

o Q

Q

E

O o

o r l

15

by which a decision that the load is small enough to be supplied by backup while the collectors charge the store is made (mode 8 in Table 3). Thus the system will operate in mode 8 if the ratio of collector output to load is greater than X. The relative contribution of the store to the solar supplied energy will decrease as X increases as is seen in Fig. 12. At X = 2 the store and collector contributions over the season are roughly equal. The solar fraction increases significantly from X -- 1 to X = 4, from 62% to 79% for a collector area of 40 m 2, and saturates for values of X above 4. The performance therefore improves with increasing X, im- plying that it is more viable to make use of collected energy directly, even if the excess with respect to the load has to be wasted, than to charge and discharge the store. For the current study the standard value of X was chosen to be 4.

The solar fraction was found to vary slightly with collector tilt angle. It increases from 72% to 79% at A = 30 m 2 as the tilt increases from 10 ° to 40 °. A shallow optimum exists around 30 ° to 60 °. This conforms with previous experience[2] which sug- gests that collectors for space heating be tilted at the local latitude plus 10 °.

CONCLUSIONS

The heating load of an upper floor of offices located in Haifa, Israel is calculated for the entire heating season. This load is dominated by storage in the walls for two different wall heat capacities and for the two design temperatures of 19 ° and 20°C. The heat losses to storage in the walls comprise 70-

75% of the total heat losses. Decreasing the wall material density and hence heat capacity by 50%, serves to decrease the seasonal heating load by 11%, and increasing the design temperature from 19 to 20°C, while retaining the nominal wall densities, leads to an increase in the load of 25%.

The Simplex optimization procedure has been used on a simulation of a solar air heating system for the above installation. The optimum values of the system parameters collector area, store volume and air mass flow rate of 30 m 2, 2-3 m 3 and 0.5 kg s - ] , respectively, were found to be essentially independent of predicted inflation rates. The solar air heating system can be simplified a great deal by discarding the active energy store. For a design temperature of 19°C, a no-active-store system with a collector area of 40 m 2 yields the same solar fraction, and a similar payback time, as does the 30 m 2 system with a rock bed store. The optimum air flow rate for this case is also in the range 0.4-0.5 kg s - i. For the design temperature of 20°C, the no-active- store system requires a collector area of 50 m 2 to perform as well as the rock bed store system with 30 m 2 of collectors. The no-active-store system does not compete with the system with active store when the building heat capacity is halved.

The reasons for the excellent performance of the no-active-store system lie in the climate and the properties of the heavy masonry building considered in this study. The high heat capacity concrete is commonly used in construction in Israel and else- where. The moderate-to-high day to night temperature swings, and the high building heat capacity, cause most of the room heat losses to be due to

ls there a need for a rock

storage in the building material. Whereas the outer walls, acting as storage, lose a lot of heat to the outside, the rock bed store also wastes heat in charging and discharging when placed outside the heated space. Besides, the collectors operate more efficiently charging the rooms than charging the store since in the former case the air temperatures at the collector inlet usually are lower. An excep- tion to this would occur only when a relatively "cold" store is being charged with air outlet temperatures being essentially equal to room temperatures. The walls constitute storage that is much larger in capacity and therefore at lower temperatures, than the rock bed store. In the present case the combined heat capacity of the walls is 120 MJ C-J compared to only 7 MJ C-1 for a 5 m 3 rock bed store.

The specific application considered here is the heating of a public building. The potential of the no-active-store system for residential buildings, and for situations where storage losses are less dominant, should also be investigated. In general, infiltration losses can be cut down relatively easily by weatherproofing, double glazing, etc. while the remaining storage losses are more difficult to re- duce, involving measures such as insulating the walls, preferably on the inside surfaces[6].

The payback times were found to be lower for the higher design room temperature as it serves to increase both the reference heating load and the savings due to the solar heating system.

The no-active-store system has the following advantage s:

(a) The control strategy is simple. (b) The system with active store generally re-

quires two large fans, unless the duct system is made more complex. The no-active-store system always takes only one large fan.

(c) If it is not convenient to place the store at ground level, as in a retrofit installation, the weight loading on the roof due to the store may be too great. Even if ten extra m 2 of collector are used in lieu of the store, these weigh much less than 2-3 m s of rocks (3400- 5000 kg).

The no-active-store system may therefore be recommended for its ease of operation and suitability for retrofitting on buildings which are used during daytime only and which have a high heat capacity and low heating load.

Acknowledgements--This work was supported in part by a grant from the Caesarea foundation. The first named au- thor received a travel grant from the Royal Society (U. K.). The manuscript was types by Mrs. M. Schreier.

NOMENCLATURE

A Collector area, m 2 AS System with active storage C Capital cost, $ C s Heat capacity of fluid (air), J kg- ~ C-

e Range of variable increase around a minimal point

f if ia L

Ls

m N

NAS V X

bed store? 113

Auxiliary (electricity) fuel cost, $ GJ - Fuel inflation rate, above general inflation Discount or interest rate, above general inflation Season's heating load, GJ Season's backup requirement with solar heating system, GJ Total air mass flow rate, kg s- Payback time, yrs System without active storage Store volume, m 3

Store charging criterion. The collectors charge the store while the backup supplies the load if the ratio of collector output to current load is greater than X

REFERENCES

1. J. J. Greenland, The thermal inertia of buildings, in Solar energy applications in the design of buildings. (Edited by H. J. Cowan). Applied Science, London (1979).

2. S. V. Szokolay, World Solar Architecture. The Ar- chitectural Press, London (1980).

3. T. A. Lawand, J. Le Norman, A. Skelton and N. Pa- padopoli, Development of solar wall collectors using forced ventilation. Solar World Forum, Proceedings oflSES Conference, Vol. 1, p. 433. Brighton, U.K. (1981).

4. P. R. Sabady, The Solar House. Newnes-Butter- worths, London (1978).

5. M. Hoffman, K. Rodan, M. Feldman and D. S. Sa- posnik, Solar heating using common building elements as passive systems. Solar Energy 30, 275-287 (1983).

6. M. Levy and A. Shitzer, Dynamic simulation of of- rices coupled with measured occupancy distribution. ASHRAE Trans. 90, Part 1,226-244 (1984).

7. A. J, Chapman, Heat Transfer, 2nd ed. Macmillan, New York (1967).

8. Handbook of Fundamentals. American Society of Heating, Refrigerating and Air Conditioning Engi- neers, Atlanta, Georgia (1981).

9. S. Schweitzer, A possible average weather year for Israel's coastal plain for solar system simulations. Solar Energy 21, 511-515 (1978).

10. S. Schweitzer, A representative average weather year for Israel's coastal plain based on 1967-1976 data at Bet-Dagan, Agricultural Research Organisation (Is- rael), Report No. 3-78 (March 1978).

11. E. Michelson, M. Levy, A. Shitzer and Y. Zvirin, Simulation of a solar office heating system with air collectors and a rock bed store, Proc. of the Inter- national Institute of Refrigeration Meeting on Utili- zation of Solar Energy for Air Conditioning, pp. 283- 284, Jerusalem (1982).

12. J. A. Duffle and W. A. Beckman, Solar Energy Ther- mal Processes. Wiley-Interscience, New York (1974).

13. R. C. Winn, C. B. Winn, Optimal control of mass flow rates in flat plate solar collectors, Trans. ASME, J. Solar Energy Engng. 103, 113-118 (1981).

14. S. A. Mumma and W. C. Marvin, A method of sim- ulating the performance of a pebble bed thermal energy storage and recovery system, ASME paper 76- HT-73 (1976).

15. S. Ergun, Fluid flow through packed columns, (?hem. Engng. Prog. 48, 89-94 (1952).

16. L. C. W. Dixon, Non-Linear Optimization. English Universities Press, London (1972).

17. E. Michelson, Multivariate Optimisation of a solar water heating system using the Simplex method. Solar Energy 29, 89-99 (1982).

18. D. S. Ward, G. O. G. Lof, C. C. Smith and L, L. Shaw, Design of a solar heating and cooling system for CSU Solar House II. Solar Energy 19, 79-85 (1977).


APPENDIX: DATA FOR STANDARD SYSTEM

Collector area, m 2 30 tilt angle, deg. from horizontal 45 orientation South plate absorptivity[i 3] 0.9 heat capacity, J C- i m 2 5000 glazing transmissivity at normal incidence[ 13] 0.86 plate efficiency factor[13] 0.9"[1 - exp (-5.6m)] loss coefficient 4.0 for m ~< 0.5

4.0 + 2(m - 0.5) for m > 0.5 pressure drop, Pa m -2 5.0

ground albedo 0.3 Total air mass flow rate, kg s - 1 0.5 Rock bed store

volume, m 3 5 shape cubic layer thickness, m[14] 0.1 rock effective diameter, m 0.05 void fraction 0.3 rock heat capacity, J kg- 1 C- i 837 rock material density, kg m -3 2400 total heat capacity, MJ m -3 C- i 1.41

insulation thickness, m, on top, 0.3 bottom and side 0.15

insulation conductivity, W m- t C- J 0.04 Ducts in collector--store circuit

loss coefficient, per m 2 surface area of duct, W m 2C 1. 0.2

average inner surface roughness, m 0.001 length, m 40 cross section dimensions, m 0.3*0.3

Ducts in room circuit pressure drop, Pa 60

Costs collectors (panels only), $ m -2 100 store (rock bed itself,) $ m -3 40 installation (size independent), $ 1700 installation (collector-area dependent), $ m 2 5 installation (store-volume dependent), $ m-3 80 ducts (size independent), $ 2000 ducts (collector-area dependent), $ m-2 10 each fan, $ kW-1 2000 backup electricity, $ G J - i 22

is there a need for a rock bed store? simulation and optimization of solar air heating systems for...

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