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Design of solar thermal systems utilizing pressurized hot waterstorage for industrial applications

Govind N. Kulkarni, Shireesh B. Kedare, Santanu Bandyopadhyay *

Energy Systems Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India

Received 6 June 2007; received in revised form 3 February 2008; accepted 13 February 2008Available online 7 March 2008

Communicated by: Associate Editor V. Wittwer

Abstract

A large number of industrial processes demand thermal energy in the temperature range of 80240 C. In this temperature range, solarthermal systems have a great scope of application. However, the challenge lies in the integration of a periodic, dilute and variable solarinput into a wide variety of industrial processes. Issues in the integration are selection of collectors, working fluid and sizing of compo-nents. Application specific configurations are required to be adopted and designed. Analysis presented in this paper lays an emphasis onthe component sizing. The same is done by developing a design procedure for a specific configuration. The specific configuration consistsof concentrating collectors, pressurized hot water storage and a load heat exchanger. The design procedure follows a methodology calleddesign space approach. In the design space approach a mathematical model is built for generation of the design space. In the generationof the design space, design variables of concern are collector area, storage volume, solar fraction, storage mass flow rate and heat exchan-ger size. Design space comprises of constant solar fraction curves traced on a collector area versus storage volume diagram. Results of thedesign variables study demonstrate that a higher maximum storage mass flow rates and a larger heat exchanger size are desired while

limiting storage temperature should be as low as possible. An economic optimization is carried out to design the overall system. In eco-nomic optimization, total annualized cost of the overall system has been minimized. The proposed methodology is demonstrated throughan illustrative example. It has been shown that 23% reduction in the total system cost may be achieved as compared to the existing design.The proposed design tool offers flexibility to the designer in choosing a system configuration on the basis of desired performance andeconomy. 2008 Elsevier Ltd. All rights reserved.

Keywords: Design space; Industrial applications; Pressurized hot water storage; System integration; Solar thermal; Optimization

1. Introduction

A large number of industrial processes demand thermalenergy in the temperature range of 80240 C (Proctorand Morse, 1977; Kalogirou, 2003). Solar thermal flat platecollectors are not suitable for very high temperature appli-cations. For high temperature applications, different solarconcentrators may be employed. A number of solar indus-

trial process heat systems are installed and operated on

experimental basis (ESTIF, 2004). Weiss and Rommel(2005) have reported the status of the development of med-ium temperature solar collectors for industrial applications.

The solar systems are in a developmental stage for med-ium temperature industrial applications and yet to achievea full commercialization (ESTIF, 2004). The challenge liesin the integration of a periodic, dilute and variable solarinput into a wide variety of industrial processes. Applica-tion-specific configurations are required to be adoptedand designed. Design issues in solar industrial process heatsystems involve:

0038-092X/$ - see front matter 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2008.02.011

* Corresponding author. Tel.: +91 22 25767894; fax: +91 22 25726875.E-mail address: santanu@me.iitb.ac.in (S. Bandyopadhyay).

www.elsevier.com/locate/solener

Available online at www.sciencedirect.com

Solar Energy 82 (2008) 686699

mailto:santanu@me.iitb.ac.inmailto:santanu@me.iitb.ac.in

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Nomenclature

Ac collector area, m2

A heat exchanger area, m2

Ast surface area of the storage tank, m2

Ccoll collector cost coefficient including accessoriesand piping, Rs/m2

Chx capital cost of heat exchanger, US$/kW/CCOM annual operation and maintenance cost, US$/yCF fuel price, US$/kgCpc specific heat of cold stream fluid, J/kg CCph specific heat of hot stream fluid, J/kg CCR cost function of auxiliary water heater, US$/kWCst storage system cost coefficient including piping

and insulation, US$/m2

CRFc capital recovery factor of collector and storagesystems, y1

CRFaux capital recovery factor of auxiliary heater, y1

CRFhx capital recovery factor of heat exchanger, y1(CV)F calorific value of fuel, J/kgDst average storage tank diameter, mF solar fraction over a specified time horizon, esti-

matedFs solar fraction over a specified time horizon, de-

siredFR collector heat removal factorh/d height to diameter ratio of the storage tankIbn beam normal solar radiation intensity, W/m

2

IT solar radiation intensity on tilted surface, W/m2

k thermal conductivity of storage tank insulation,

W/m Kmc cold stream mass flow rate of heat exchanger,kg/s

mh hot stream mass flow rate of heat exchanger, kg/smL desired load mass flow rate, kg/smst storage mass flow rate to heat exchanger, kg/sN number of transfer units of heat exchangern expected life of collectors and storage, ynL number of hours of load/daynaux expected life of auxiliary heater, yP cold or hot fluid temperature effectivenessPd storage tank design pressure, barPs saturation pressure corresponding to the limit-

ing storage temperature.Pmax maximum storage tank operating pressure, barqaux auxiliary energy required, WQaux auxiliary energy required over a specified time

horizon, JqL desired hot water load, WQL desired hot water load over a specified time hori-

zon, JqLs load met by solar energy or energy extracted

from the storage, WQLs load met by solar energy over a specified time

horizon, J

qs solar useful heat gain rate, WQs solar useful heat gain over a specified time hori-

zon, J

qstl storage heat losses, WR heat capacity flow rate ratio of heat exchangerRa auxiliary heater rating, WRb tilt factorr discount rate, %T time horizon of analysisTAC total annualized cost, US$Ta ambient temperature, CTci cold stream inlet temperature, CTco cold stream outlet temperature, CTco,min minimum cold stream outlet temperature re-

quired meet the entire demand, CThi hot stream inlet temperature, C

Tho hot stream outlet temperature, CTL desired process heat or load (hot water) temper-

ature, CTR make up water temperature, CTst storage temperature at any instant of time, CTsti storage temperature at the beginning of the time

step, CTstf storage temperature at the end of the time step,

Ct time step in the analysis, stins storage tank insulation thickness, mtt storage tank wall thickness, m

tca corrosion allowance for storage tank wall thick-ness, mUA heat exchanger size characterization parameter,

W/CUst storage heat loss coefficient, W/m

2C

UL collector overall heat loss coefficient, W/m2C

Vst storage volume, m3

Greek symbols

h incident anglegaux efficiency of auxiliary heatergo average optical efficiency of the concentratorq density of working fluid, kg/m3

qt density of storage tank material, kg/m3

rd design hoop stress for storage tank material,MPa

(sa) average transmittance absorptance product

Abbreviations

AUX auxiliaryHX heat exchangerISO organization for international standardsLDO light diesel oilLMTD logarithmic mean temperature differenceUS$ united states dollar

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assumed that change in the thermal energy of the storageover the time horizon (a day, a month or a year) is zero:ZT

0

qCpVstdTst

dt

dt 0 4

By varying the collector area and the storage volume, dif-

ferent feasible designs may be obtained. For illustration,a case of unity solar fraction is described. Unity solar frac-tion suggests that the entire thermal demand has to be metby the solar energy. For satisfying the entire thermal de-mand, storage tank temperature during the time of the de-mand must be greater than the desired load temperature:

Tst P TL 5

Since, water at the atmospheric pressure, is used as a work-ing fluid, the storage tank temperature has to be less than100 C:

Tst 6 100C 6

An acceptable design must satisfy these constraints. For aspecified load, all possible combinations of collector areaand storage volume that satisfy these two constraints definethe design space. Generation of the design space is demon-strated through an example.

A single day (15th April) is chosen for illustration.Monthly mean values of hourly solar radiation (Mani,1981) are adopted for this example. The time step t is3600 s and time horizon is a single day. The system param-eters are given in Table 1. Fig. 2 shows the storage temper-ature profile with a typical collector area and storagevolume combination (Ac = 90 m

2 and Vst = 3.7 m3). Limit-

ing storage temperature constraint and the hot waterdemand profile are also shown in Fig. 2. The limiting stor-age temperature constraint is 100 C while the load temper-ature constraint is 60 C. The storage temperature profile isin between these two constraints (Fig. 2). This is a feasibledesign for unity solar fraction. The combinations ofAc andVst are varied to obtain all the feasible designs for unitysolar fraction. Combination of the collector area and thestorage volume that satisfy these constraints are identifiedand illustrated in Fig. 3. The region inside these curves rep-resents all possible design combinations that satisfy theunity solar fraction. This region represents the design spacefor unity solar fraction for the example. From Fig. 3, itmay be noted that the point a represents a system withthe lowest possible storage volume requirement. Point arepresents 2.6 m3 of storage volume and 111 m2 of collectorarea. Any reduction in storage volume will result in boilingof water in the storage tank. Point m in Fig. 3 indicates a

minimum collector area design. The design occurs at a col-lector area of 76 m2 and storage volume of 28 m3. Any

decrease in the collector area from m will not meet thedesired hot water demand.It may also be noted that there exists a minimum as well

as a maximum storage volume for a given collector area.For example, a constant collector area line (Ac = 111 m

2)in Fig. 3 intersects the limiting curves at a and b. Pointa indicates a minimum limit on storage volume of2.6 m3,while point b indicates a maximum limit of1227.2 m3. Beyond point b, thermal losses from the storagetank will dominate resulting into a loss of solar fraction.Similarly, there exists a minimum as well as a maximumcollector area for a given storage volume. It is illustratedin Fig. 3 through points m and o. The line segment m-

a in Fig. 3 signifies the Pareto optimality curve.The region bounded by the limiting curves includes all

feasible designs of the system and is called the design space(Kulkarni et al., 2007). Similar to the above procedure, thedesign space can be identified by tracing constant solar

Table 1Solar system parameters

Location Pune, India (latitude 18.53, longitude 73.85, ground reflectance = 0.2)Load Domestic hot water for an apartment building, 4500 LPD at 60 C, Consumption pattern as per ISO 94593:1997(E)

(International Standards Organization, 1997)Collectors Flat plate collectors (single cover, selective coated, south facing Tilt = 33.53) Collector parameters FR(sa) = 0.675, FRUL = 5.656 W/m

2 K.

Storage Insulation: 0.14 m glass wool (k= 0.04 W/m K)

0

20

40

60

80

100

120

0 10 12 14 16 18 20 22 24

Time,h

Storage

temperature,

C

Limiting temperature line

Storage temperature profile for unity solar fraction

ISO

Load

profile

Load

Temp.60 C

2 4 6 8

Fig. 2. Load and storage temperature profile over a typical day.

0.1

1

10

100

1000

10000

50 75 100 125 150 175 200 225 250

Collector area,sq.m

Storagevolume,cu.m

a

b

m o

A min

Vmin

Load temperature constraint

Limiting storage temperatureline

Feasible design region(Design space)

Volumelimits fora givenarea

Area limits for a given volume

Fig. 3. Design space for F= 1.

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fraction lines for other solar fractions. Any objective func-tion involving the capital and the operating costs of the sys-tem may be chosen for optimization of the overall system.A more elaborate treatment of design space is given byKulkarni et al. (2007). Application of the design spaceapproach has been demonstrated for solar thermal system

operating up to 100 C. A large number of industrial andcommercial applications demand solar thermal energybeyond 100 C. Utility of the design space methodologyis therefore, improved and extended for systems operatingbeyond 100 C.

3. The design space for pressurized water storage

In this section, the concept of design space is improvedand extended to a solar thermal system intended for indus-trial application beyond 100 C.

3.1. System configuration

The general configuration of a solar thermal system sup-plying hot water beyond 100 C is shown in Fig. 4. Thegeneral system comprises of a concentrating collector, apressurized hot water storage tank, a load heat exchangerand an auxiliary heater.

The beam solar radiation is converted into useful heatby the concentrating collector. Water from the storage tankis circulated through the absorber tubes of the receiver.Water absorbs the heat and is returned back to the storagetank. Heat is stored in the form of pressurized hot water.When heat is demanded by the process, hot water is

pumped to the heat exchanger at a rate of mst. Hot waterat Thi from the storage tank is circulated through the heatexchanger. In the heat exchanger, heat is transferred to thecold stream. Water returns to the storage tank at a lowertemperature of Tho. The cold process stream is pumpedat a constant flow rate of mc. A minimum cold stream out-let temperature (Tco,min) is desired to meet the entiredemand. This limit can be determined on the basis of thedemand and the cold stream flow rate. Actual cold streamoutlet temperature (Tco) depends on the storage tempera-

ture Tst. Auxiliary heater is placed in the cold stream circuitin series with the heat exchanger. If Tco < Tco,min, auxiliaryheater is switched on and the cold stream is further heatedto the desired temperature.

The design variables for this generalized system are

Collector area (Ac), storage volume (Vst), solar fraction (F), maximum storage mass flow rate (mst,max), heat exchanger sizing parameter (UA) and limiting storage temperature (Tst,max).

The limiting storage temperature determines the maxi-mum operating pressure of the system and the thicknessof the storage tank. For simplification, it is assumed thatthe type of heat exchanger and its size may be characterizedand selected on the basis of UA product. UA product rep-resents the output of a heat exchanger for a unit logarith-

mic temperature difference (LMTD). Design procedureproposed here uses UA product as a heat exchanger sizingparameter. A mathematical model of the system is devel-oped in the following section.

3.2. Mathematical model of the system

Energy balance of a well mixed storage tank can beexpressed as

qCpVstdTst

dt qs qLs qstl 7

where the storage losses (qstl) are estimated to beqstl UstAstTst Ta 8

Solar useful heat gain rate (Duffie and Beckman, 1991) isestimated using the following equation:

qs AcITFRgo FRULTst Ta 9

where + sign indicates, hot water from the collectorenters the tank only when solar useful heat gain becomespositive. It may be noted that Eq. (9) represents a linear

Solar

Concentrator

mc

Cold stream pump

Tci

Tco

Load

pump

Thi

Pump

Tho

HX Load

Pressurized

hot water

Storage

Tst = Thi

mst AUX

Fig. 4. Schematic of a solar industrial process heat configuration.

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characteristic equation for a solar collector. For high tem-perature applications and for concentrating collectors, thismay not always be suitable. For such systems, a second orhigher order characteristic equation may be more suitable.For more accurate results, a non-linear characteristic equa-tion should be used instead of(9). The proposed methodol-

ogy is independent of the nature of the characteristicequation. However, for the system, for which the method-ology is demonstrated, it has been observed that an accu-rate non-linear characteristic equation does not improvethe system sizing significantly (Kulkarni, 2008).

Solar flux incident on the aperture of a tracking concen-trator is calculated as

IT Ibn cos h 10

Combining Eqs. (8) and (9) with Eq. (7), energy balance ofthe tank can be expressed as

qCpVstdTst

dt

AcITFRgo FRULTst Ta

qLs UstAstTst Ta 11

Load met by solar energy is given by

qLs mstCphTst Tho 12

To determine the solar contribution of load (qLs), hotstream outlet temperature (Tho) and storage mass flow rate(mst) must be known. For calculating Tho,heat exchangerparameters such as number of transfer units (N), heatcapacity flow rate ratio (R) and cold or hot fluid tempera-ture effectiveness (P), have to be considered. In this case,hot stream flow rate mh is the storage flow rate mst and

hot stream temperature Thi is the storage temperature Tst.Number of transfer units (N), heat capacity flow rate ratio(R) and cold or hot fluid temperature effectiveness (P) aredefined as follows:

N UA

mstCph13

R mstCph

mcCpc14

P Tst Tho

Tst Tci15

Computation begins with the assumption of initial storage

temperature (Tsti), storage flow rate (mst) and heat exchan-ger sizing parameter (UA). With these parameters known,values of N and R can be calculated using Eqs. (13) and(14). For simplicity, a counter flow heat exchanger is as-sumed. The relation between N, R, and P on the basis ofhot stream is used (Shenoy, 1995):

P expNR 1 1

expNR 1 Rfor R 6 1 16a

P N

N 1for R 1 16b

With hot stream effectiveness P known, hot stream outlet

temperature Tho can be calculated:

Tho Tst PTst Tci 17

With known P and R, the cold process stream outlet tem-perature can also be determined:

Tco Tci PRTst Tci 18

The minimum cold process stream outlet temperature

(Tco,min) needed to fulfill the complete demand can bedetermined as

Tco;min Tci QL

nLtmcCpc19

By knowing the hot stream outlet temperature, solar con-tribution to the load during a time step may be determined.In Eq. (19), desired load (QL) over a time horizon (a day)and duration of load in nL time steps (number of hours)is specified. The load is assumed to be uniformly distrib-uted over the time steps. Cold stream mass flow rate ( mc)and inlet temperature (Tci) are assumed to be constant in

this analysis. No auxiliary energy will be required ifTcoP Tco,min. In all the cases, hot stream flow rate is con-trolled in such away that cold stream outlet temperaturedoes not exceed Tco,min. This ensures effective utilizationof the solar energy. Auxiliary energy is required if Tco