SIMULATION OF A THERMAL SOLAR POWER PLANT OPERATING ON MARS UNDER CLEAR SKY AND DUST STORM CONDITIONS

Acta Astronautica Vol. 49, No. 12, pp. 667–679, 2001? 2001 Elsevier Science Ltd. All rights reserved

Printed in Great Britainwww.elsevier.com/locate/actaastro PII: S0094-5765(01)00137-0 0094-5765/01/$ - see front matter

SIMULATION OF A THERMAL SOLAR POWER PLANT OPERATING ONMARS UNDER CLEAR SKY AND DUST STORM CONDITIONS

VIOREL BADESCU†,“Candida Oancea” Institute of Solar Energy, Faculty of Mechanical Engineering, Polytechnic University of

Bucharest, Spl. Independentei 313, 77206 Bucharest, Romania

GHEORGHE POPESCU,Applied Thermodynamics Department, Faculty of Mechanical Engineering, Polytechnic University of Bucharest,

Spl. Independentei 313, 77206 Bucharest, Romania

and

MICHEL FEIDTL.E.M.T.A., University “H. Poincare” of Nancy 1, UMR CNRS no 7563, 2 avenue de la Foret de Haye, 54516,

Vandoeuvres-les-Nancy, France

(Received 18 June 1999)

Abstract—The power plant analyzed in this work consists of a selective solar collector–thermalengine combination. The paper focuses on solar power plant operation under various weatherconditions during all seasons on Mars. Meteorological data measured at Viking Landers (VL) siteswere used in computations. Two strategies to collect solar radiation were analyzed: a solar horizontal(H) collector and a solar collector whose tilt and orientation are continuously adjusted to keep thereceiving surface perpendicular to Sun rays (P). Both a low and a high eDciency thermal enginewere considered. All the computations were performed for a selective solar Eat-plate collectorsimilar in size to the Mars PathFnder’s Sojourner. Results show that generally the inEuence oflatitude on performance is important. In some situations, the meteorological eHects compensatethe latitudinal eHects and the output power is quite similar at both VL1 and VL2 sites. In casea low-eDciency engine is coupled to a horizontal collector, the solar eDciency does not exceed0.13 at VL2 site. It is lower during summer and higher during winter dust storms. In case thelow-eDciency engine is coupled to a P collector, the solar eDciency increases during summer. Thesolar eDciency is as high as 0.18 in case of a horizontal collector attached to a high-eDciencyengine. If the high-eDciency thermal engine is connected to a P collector the solar eDciencyincreases signiFcantly during summer and spring but does not exceed 0.18. The power providedby a system consisting of a horizontal collector and a low-eDciency engine does not exceed 7 W.Using a high engine coupled to a horizontal collector leads to a power output up to 13 W duringspring, autumn and winter. The P collector is recommended mainly during summer and springin combination with high-eDciency engines. In this case the solar eDciency could be as high as25 W. The performance of PV cell power systems and properly designed dynamic solar powerplants operating on Mars is comparable. ? 2001 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

Among various space solar power technologies aleading role is played by the photovoltaic (PV)cells. The second rank is designated to theso-called solar-thermal (or solar dynamic) systems.They use turbogenerators, Stirling engines, thermo-

†Corresponding author. Tel.: +40-1-410-0400; fax:+40-1-410-4488.

E-mail address: [email protected] (V. Badescu).

couples and thermionic-emitter converters. In acommon solar dynamic module a concentrator isused to collect and focus the sun radiated energythrough an apperture into the receiver and thus pro-vides the heat energy input for the thermal-energyconverter.Earlier studies reported solar dynamic systems

based on thermodynamic cycles and thermionicconverters, respectively. Two systems of the for-mer type were described in [1]. One of them is a3 kW solar dynamic system of 10% overall eD-ciency consisting of a parabolic concentrator and

667

668 V. Badescu et al.

a turbo-generator unit which uses mercury as theworking Euid in a Rankine cycle. The other one isa 15 kW system for space vehicle applications. Itsworking Euid is rubidium while the overall elec-trical eDciency was 21.7%. The solar–thermionicsystem was designed to provide 135 W at Mars dis-tance from the Sun with a system weighing about14 kg [1]. More recent Russian studies are usingpermanent gases (mainly mixtures of xenon and he-lium) as working Euid in Brayton cycles. They havean output power of 3–5 kW, speciFc weights up to40–45 kg=kW and an overall eDciency of 31.2%[2–4]. SigniFcant eHorts to develop solar dynamicpower systems (25 kW) for application to a lowEarth orbit space station have been conducted byNASA Lewis Research Center (LeRC) as an inte-gral part of the US space station development pro-gram from 1984 through 1990. The culmination ofthe LeRC program demonstration was a full systemtest in a thermal=vacuum tank of a Space StationFreedom type solar dynamic system of 2 kW sizein February 1995 [5]. Related reports can be foundin [6,7]. Typical values, which were derived fromthe Space Station Freedom design and technologystatus show the sun-to-user eDciency is 5.7–6.8%for PV-based systems and 18.7–19.8% for dynamicsystems. If one includes the storage subsystem intoconsideration, the solar dynamic system becomeseven more attractive, mainly because the eDciencyof the latent heat storage is higher compared to theNi–Cd batteries of the photovoltaic system [6].Spacecraft exploration of Mars started in the

1960s. Since then diHerent missions took place withvarious scientiFc goals such as the determinationof the internal structure of the planet, the chem-ical and mineralogical analyses of Martian rocksand soils and the study of atmospheric circulationand weather patterns. On Mars, PV cells were al-most exclusively envisaged as the main source ofenergy. They were proposed to power small rovers[8], long-endurance, remotely piloted aircraft ca-pable of Eying within the Martian environment [9]and to ensure the life support for a 40-day mannedMars surface scientiFc expedition [10]. More re-cently, the Sojourner of the PathFnder mission wasalso powered by PV cells (see e.g. [11]).A model of dynamic solar power plant oper-

ating on the surface of Mars was proposed in[12]. The most important question we put thereis: are properly designed dynamic systems operat-ing on Mars comparable in performance with thePV-based power systems? Some of the referenceswe already cited here seem to indicate an aDrma-tive answer but they all refer to systems operatingin the interplanetary space. A surface-based solar

power system has to take into consideration, how-ever, one very important feature of the Martianweather. The period between the areocentric lon-gitude Ls = 161–326

◦ has been referred to as the“dust storm season”. This period is nearly centeredon perihelion, which is the time of maximum inso-lation on Mars [13,14]. The dust storm periods arecharacterized by an almost vanishing direct solarradiation (see e.g. [15] and references therein). Inthis case the solar (diHuse) radiation cannot beconcentrated and �at plate solar collectors haveto be used. But common Earth practice provedthat very low eDciency is associated with solarpower generation using Eat plate (blackbody-like)collectors. The model we developed in [12] isbased on Eat-plate selective solar collectors thatoperate at higher eDciency. To provide upperlimits for the performance of an actual thermalconverter (based for instance on Brayton, Rankineand Stirling cycles) a Carnot endoreversible enginewas used. This has, on the one hand, the advantageof generality and, on the other hand, it takes intoaccount the irreversibilities associated with theheat transfer at the hot and cold parts of the engine.The optimization procedure developed in [12] isbased on Fnite-time thermodynamics methods.This paper focuses on solar power plant opera-tion under various weather conditions during allseasons on Mars.

2. SOLAR POWER PLANT MODEL

We are using here the solar power plant modeldeveloped in [12]. This section summarizes its mainfeatures. A solar Eat-plate collector is coupled to aheat engine operating on an endoreversible Carnotcycle. One denotes by TC and Ta the collector andambient temperatures, respectively.

2.1. Solar collector model

We shall consider a selective Eat-plate solar col-lector (Fig. 1). Its main components are the ab-sorber plate (1) containing pipes for the workingEuid and the transparent cover (3) of thicknessa. The gap between (1) and (3) (thickness s) isFlled with carbon dioxide at the Martian atmo-spheric pressure (carbon dioxide represents 95% ofthe Martian atmosphere; its pressure oscillates be-tween 6 and 10 hPa at Viking Landers latitude).The bottom thermal insulation (4) has a thicknessb. The collector tilt angle is �. Seven temperaturescan be associated with various parts of the solarcollector (see Table 1 of [12]). The collector oper-ation was studied by using the thermal resistancemethod in [12].

Thermal solar power plant 669

Fig. 1. Solar collector. (i) Longitudinal section; (ii)transversal section; (iii) lateral view. 1—absorberplate; 2—carbon dioxide layer; 3—transparent cover;

4—bottom thermal insulation.

Direct beam (b), diHuse (d) and ground reEected(r) Euxes of solar energy are incident on the col-lector. They depend upon collector’s tilt and orien-tation. Generally, the incident and absorbed solarenergy density Euxes (’inc and ’abs, respectively)are given by

’inc =Gb + Gd + Gr ; (1)

’abs = �mC( �)bGb + ( �)d(Gd + Gr): (2)

Here G’s denote solar irradiances at collector levelwhile ( �) are eHective transmittance–absorptanceproducts.

2.2. Thermal engine model

The largest and smallest working Euid tem-peratures are denoted by T ′ and T ′′, respectively(Fig. 2). Generally, TC¿T ′ and T ′′¿Ta. Hence,both

X ≡ TC − T ′ and Y ≡ T ′′ − Ta (3)

are positive quantities.

Table 1. The number of complete records used during simulation of solar power plant operation

Viking VikingLander 1 Lander 2

Sol Number of Sol Number ofnumbers complete records numbers complete records

Spring — — — —Year Summer 6–155 22 6–111 371 Autumn 168–306 108 120–257 77

Winter 307–350 56 269–415 55

Spring — — 416–608 147Year Summer — — 610–784 582 Autumn — — 792–872 25

Winter — — — —

The solar energy density Eux incident on collec-tor is ’inc while ’abs is the absorbed energy densityEux.Consequently, the Eux of solar energy �abs ab-

sorbed by the collector is

�abs =’abs AC; (4)

where AC is the collector surface area. Part of thisEux is transferred to the working Euid (QC), whilethe other part constitutes the Eux of thermal lossesto the ambient (QL). Then, the solar collectorsteady-state energy balance is

�abs − QC − QL = 0: (5)

The heat Euxes QC and QL can be written as

QC = hC ACX and QL =ULAC(TC − Ta);(6)

where hC and UL are appropriately deFned overallheat transfer coeDcients between the solar collectorand the working Euid and ambient, respectively.The Carnot engine partially converts the Eux QC

into power. Thus

QC = W + Qa ; (7)

where W is the output power and Qa is the ther-mal energy Eux Fnally reaching the surroundings.There is no further increase of entropy during workproduction. Consequently,

QCT ′ +

QaT ′′ =0: (8)

The heat Eux Qa can be written as

Qa = haAaY; (9)

where Aa and ha are appropriately deFnedheat transfer area and overall heat transfer co-eDcient between working Euid and ambient,respectively.


Fig. 2. Temperature–entropy diagram for an endo-reversible Carnot cycle (for notations see text).

2.3. Performance indicators

Two performance indicators are considered inthis work. First, there is the output power W , eval-uated from:

W = hCACX − haAaY: (10)

Here we used eqns (6), (7) and (9).Second, there is the solar (or sun-to-user) eD-

ciency, deFned as

�solar ≡ W’incAC

: (11)

Other indicators (as the Carnot engine eDciency)could also be used.

2.4. Optimization

A procedure to maximize the output power Wwas developed in [12]. The Lagrange method withtwo constraints (namely, eqns (5) and (8)) wasused. In addition, the weight of the space powerplant was kept at minimum. The procedure led to anequations system with six unknowns among whichare the collector’s surface area and temperature.Table 6 from [12] shows the solution. In a two-stepcalculation procedure one can derive subsequentlythe maximum power and the optimum solar eD-ciency (for details see [12]).

3. RESULTS AND DISCUSSIONS

During the application we used as input datavalues of atmospheric pressure and temperature,wind speed and atmospheric optical depth mea-sured at Viking Lander 1 (VL1) (22:3◦N; 47:9◦W)and Viking Lander 2 (VL2) (47:7◦N; 225:7◦W)sites. The data were taken from the Viking LanderMeteorology and Atmospheric Opacity Data Set

Archive from the Planetary Data System databasemade publicly available on a compact disc [16]. Inall cases the numbering of the Martian solar days(sols) started at day 0 when each Lander toucheddown. Details about preparing the data can befound in [17].Atmospheric pressure values are missing for

eleven records. In these cases the following proce-dure was adopted:

(i) in case of the record VL2, year 1, are-ocentric longitude=229:808 (autumn),sol = 200; hour = 11:41, we used the arith-metic mean of the pressure values corre-sponding to sol = 199, hour = 13:87 andsol = 201; hour = 11:42, respectively.

(ii) in case of the record VL2, year 2, areocen-tric longitude=19:228 (spring); sol = 454,hour = 9:62, we used the arithmetic meanof the pressure values corresponding tosol = 453, hour = 17:33 and sol = 454; hour =17:25, respectively.

(iii) in case of VL2, year 2, the Frst nine recordsduring summer (areocentric longitudes be-tween 93.363 and 100.510) we used thepressure value corresponding to the tenthrecord (areocentric longitude=101:697,sol = 634; hour = 6:98).

A set of complete records was Fnally obtained.Each complete record associates to a given sol num-ber and a local solar time value, a set of four me-teorological values, namely optical depth and at-mospheric temperature Ta, atmospheric pressurepaand wind speed w. The number of complete recordsis rather small (Table 1).The optical depth values were used to evaluate

the incoming Euxes of solar radiation. The threecomponents of global radiation Eux (namely direct,diHuse and ground reEected) were computed for allthe complete records of Table 1 by using the proce-dure we previously proposed in [15]. The resultingFle of solar energy data was used as input duringthe simulation of solar heat engine operation.One of the goals of this study is to perform

a rough comparison between the performance ofPV cell power systems and dynamic solar powerplants. In case of PV cell systems we had in mindthe PathFnder’s Sojourner. Sojourner is a small(11:5 kg), six-wheel robotic vehicle built at JetPropulsion Laboratories. Sojourner was landed onMars aboard the PathFnder spacecraft on July 4,1997. In the same sol, she began to traverse theMartian terrain, perform science and technologyexperiments, and transmit images and data backto the Lander space craft. Sojourner’s equipment


(computers, motors, radio modem) was mainlypowered by a light weight 0:34 kg solar array withreceiving surface area 0:22 m2. The PV cell systemwas designed to provide Sojourner with around16 W of electric power at noon on Mars. Thelanding place was in Ares Vallis at 19:17◦N and33:21◦W on the US Geological Survey (USGS)cartographic network [11]. PathFnder landedin late northern summer (areocentric longitudeLs = 143

◦) and operated for 83 sols.To allow comparison with Sojourner perfor-

mance a dynamic power plant equipped with aEat-plate selective solar collector is analyzed here.The distance between VL 1 and PathFnder Landeris around 815 km. Thus, one expects quite similarmeteorological and actinometric features in bothplaces.Four strategies for collecting solar energy were

considered in a preliminary test [18]. The followingtwo strategies will be used in this study: (i) hori-zontal collector—strategy H; (ii) the collector tiltand orientation are continuously adjusted to keepthe receiving surface perpendicular to Sun’s rays—strategy P (or P collector, for short). Strategy His easier to use while strategy P gives the higherpower output most time of the year.A number of assumptions were accepted during

model application. First, a simple relation is usedfor both eHective transmittance–absorptance prod-ucts

( �)b = ( �)d = cs�ps; (12)

where cs and �ps are the transparent cover transmit-tance and absorber absorptance, respectively, bothof them for short (solar) wavelengths.The dynamic solar power plant performance

depends signiFcantly on the heat transfer co-eDcients hC and ha. Preliminary tests allowedto emphasize two sets of values which couldbe associated with a low- and high-eDciencyengine, respectively: (a) hC = ha = 10 W=m2=K(low-eDciency engine); (b) hC =50 W=m2=K andha = 500 W=m2=K (high-eDciency engine). Prac-tical situations should normally lie between theseextreme cases. The cases (a) and (b) above will beused to provide lower and upper bounds for actualperformance.Details about solar collector design are given in

Table 2. The collector’s transparent cover is madeup of crystal (light Eint glasses). Its thermal con-ductivity lies between 0:691 W=m=K at −100◦Cand 1:025 W=m=K at +100◦C [19]. Preliminarytests [18] were performed to determine an optimumcollector area AC;opt close to Sojourner PV cell sur-face area (0:22 m2). Finally, a total heat exchange

surface area (i.e. solar collector plus engine’s ra-diator) Atot = 0:23 m2 was used in computations.As a consequence the optimum solar collector areaAC;opt varies during sol 301 VL 1 between 0.172and 0:182 m2 in case (a) above and between 0.219and 0:221 m2 in case (b) [18].

3.1. Performance dependence on atmospheric opticaldepth

To test the performance of the thermal engine–solar collector combination we simulated its op-eration at both VL1 and VL2 sites. At VL1 sitewe used meteorological data from summer, autumnand winter, year 1. Some results are shown in Fig.3 in case of the already deFned high-eDciency en-gine. All available data were used to simulate theoperation at VL2 site. Some results are shown inFig. 4 (for solar eDciency) and Fig. 5 (for outputpower). We analyzed a horizontal collector (strat-egy H) and a collector orientated perpendicularlyon sun’s rays (strategy P), respectively, and the al-ready deFned low- and high-eDciency engines.The inEuence of latitude on performance is ob-

vious. When the collector is horizontal, the solareDciency is generally smaller at VL1 site as com-pared to VL2 site (see Figs. 3a and 4c, respec-tively). When a P collector is considered, the eD-ciency increases (at small ’s) but it is still smallerat VL1 site than at VL2 site (see Figs. 3b and 4d,respectively).The maximum power provided by a horizontal

collector at VL1 site shows some interesting fea-tures (Fig. 3c). Generally, it is smaller than in caseof VL2 site (see Figs. 3c and 5c, respectively).However, there are some situations (for ≈ 1)when the meteorological eHects compensate the lat-itudinal eHects and the output power is quite similarfor both VL1 and VL2. If a P collector is used, thepower increases for small ’s but slighter at VL1site (Fig. 3d) than at VL2 site (Fig. 5d).In case the low-eDciency engine is coupled to a

horizontal collector, the eDciency does not exceed0.13 at VL2 site (Fig. 4a). Generally, it is lowerduring summer when the horizontal orientation issurely a good option [15]. It is higher during win-ter, when the optical depth is higher, indicating duststorms occurence. During dust storms the incidentsolar radiation is mainly diHuse and the horizontalorientation is the best strategy for radiation collec-tion [15].In case a low-eDciency engine is coupled to a P

collector, the maximum eDciency values lie around0.13 (Fig. 4b). The eDciency increases at smalloptical depth values, which generally correspondto summer. The center of the output data cloud is


Table 2. Details about selective Eat-plate solar collector design (see [12])

Quantity Notation ValueUsed in [12]

Concentration ratio C 1Number of transparent covers N 1Transparent cover thickness a 0:003 mDistance between transparent cover and absorber plate s 0:045 mBottom thermal insulation thickness b 0:1 mShort-wavelengths transparent cover transmittance cs 0:82Short-wavelength absorber plate absorptance �ps 0:90Long-wavelengths (IR) absorber plate emittance �1 0:10Long-wavelengths (IR) transparent cover emittance �2 0:88Thermal conductivity of bottom insulation (polyurethane) �b 0.02

W=m=K

Fig. 3. Dependence of solar eDciency �solar;opt and output power Wmax on the atmospheric optical depth at VL1site. (a) �solar;opt in case of a horizontal solar collector; (b) �solar;opt in case of a P solar collector; (c) Wmax in caseof a horizontal solar collector; (d) Wmax in case of a P solar collector. Meteorological data for summer, autumn andwinter year 1 were used. A high-eDciency engine was considered (ha = 500 W=m2=K, hC = 50 W=m2=K). Table 2

shows design data for the selective Eat-plate solar collector.

placed around 0.09–0.10. The P strategy does notdiminish the performance at larger optical depth.For a horizontal collector attached to a

high-eDciency engine, the solar eDciency is

as high as 0.18 (Fig. 4c). The qualitative fea-tures pointed out in Fig. 4a maintain. The lowersun-to-user eDciency corresponds to lower opticaldepth.


Fig. 4. Dependence of solar eDciency �solar;opt on the atmospheric optical depth at VL2 site. (a) Low-eDciencyengine and horizontal collector; (b) low-eDciency engine and P solar collector; (c) high-eDciency engine andhorizontal solar collector; (d) high-eDciency engine and P solar collector. All the available meteorological datafor VL2 site were used (years 1 and 2). The low eDciency engine is deFned by ha = hC = 50 W=m2=K, while thehigh-eDciency engine is characterized by ha = 500 W=m2=K; hC = 50 W=m2=K. Table 2 shows design data for the

selective Eat-plate solar collector.

If a P collector is considered, the solar eDciencyincreases during summer and spring (Fig. 4d) butdoes not signiFcantly exceed 0.18. The center ofthe output data cloud is placed around 0.15, higherthan in the case of Fig. 4c. Again, the P strategydoes not diminish the performance. This strategykeeps constant the solar eDciency at higher opticaldepths but improves the performance as comparedto the H strategy at smaller optical depths.The power provided by a system consisting of

a horizontal collector and a low eDciency enginedoes not exceed 7 W (Fig. 5a). Generally, it islower for small optical depth. Indeed, the Eux of di-rect solar energy is higher at smaller optical depth

and the horizontal orientation is not recommendedin this case. At higher optical depth direct solar ra-diation diminishes and diHuse radiation increases.As a result, the horizontal orientation is close tooptimum. This explains the higher values of Wmax

around =1. For further increase of the diHuseradiation Eux diminishes. Consequently, Wmax de-creases in this case.If a P collector is considered, the solar eDciency

is obviously higher during summer and spring,when the optical depth is small (Fig. 5b). Gener-ally, the eDciency increases as compared to the Hstrategy. At high optical depth the solar eDciencyis comparable for both H and P strategies.


Fig. 5. Same as Fig. 4 in case of the maximum output power Wmax.

Using a better engine with a horizontal collectorleads to output power up to 13 W for around1 (during sols of spring, autumn and winter)(Fig. 5c). For small values of the output poweris smaller, as shown in Fig. 5a.The P strategy is recommended in combination

with high-eDciency engines (Fig. 5d). In this casethe sun-to-user eDciency during sols with smalloptical depth increases strongly, exceeding 25 W.The center of the output data cloud is placed around13 W. The P strategy can be used at high opticaldepth, too.

3.2. Performance dependence on the level of solarirradiance

The dependence of solar eDciency on the level ofglobal irradiance incident on a horizontal surface

is shown in Figs. 6 and 7. The two types of engines(low and high eDciency) and the two strategies ofcollecting solar radiation (H and P) were analyzedagain.Figure 6 refers to VL2 site. All available mete-

orological data were used in calculations. In caseof a horizontal collector, a slightly non-linear re-lationship exists between solar eDciency and in-cident global irradiance for both the low- and thehigh-eDciency engines (Figs. 6a and c, respec-tively). When the P collector is considered, the de-pendence is more complicated (see Figs. 6b and d).When a combination of low-eDciency engine–

horizontal collector is considered, the eDciency ishigher (whatever the incident irradiance is) duringautumn and winter and lower during summer (Fig6a). This is rather a surprising fact which is validfor the P collector, too (Fig. 6c). It is probably due


Fig. 6. Dependence of solar eDciency �solar;opt on the level of solar global irradiance incident on a horizontal surfaceat VL2 site. (a) Low-eDciency engine and horizontal solar collector; (b) low-eDciency engine and P solar collector;(c) high-eDciency engine and horizontal solar collector; (d) high-eDciency engine and P solar collector. All theavailable meteorological data for VL2 site were used (years 1 and 2). The low-eDciency engine is deFned byha = hC = 50 W=m2=K, while the high-eDciency engine is characterized by ha = 500 W=m2=K, hC = 50 W=m2=K.

Table 2 shows design data for the selective Eat-plate solar collector.

to the inEuence of the ambient temperature, whichis lower during autumn and winter. The situation isdiHerent in case of the high-eDciency engine. Then,the solar eDciency is higher during summer, evenif it corresponds to lower incident irradiance (seeFig. 6d for the horizontal collector). This remark iseven more obvious when a P collector is considered(Fig. 6d). A more uniform solar eDciency valuesdistribution can be seen in this case.In case of a horizontal collector, the eDciency

increases by increasing the irradiance level, what-ever be the type of engine (Figs. 6a and c). For theP collector, the eDciency depends on the irradi-ance level in a more interesting manner. Thus, the

lower bound of the eDciency increases with the ir-radiance level, but the upper bound practically doesnot depend on the irradiance level. This is valid forboth the low- and high-eDciency engines (Figs. 6band d, respectively).Figure 7 shows the solar eDciency at VL1 site.

Meteorological data from year 1 were used. Duringautumn and winter the dependence of �solar on thelevel of incident global irradiance is nearly similarfor both the horizontal and the P collector (cf. Figs.7a and b). Important diHerences exist during sum-mer. The P collector is more eHective, as expected.The inEuence of irradiance on solar eDciency de-creases drastically beyond a certain threshold value


Fig. 7. Dependence of solar eDciency �solar;opt on at-mospheric optical depth at VL1 site. (a) Horizon-tal solar collector; (b) P solar collector; meteoro-logical data for summer, autumn and winter year 1were used. A high-eDciency engine was considered(ha = 500 W=m2=K, hC = 50 W=m2=K). Table 2 showsdesign data for the selective Eat-plate solar collector.

(about 300 W=m2). This applies to both types ofsolar collectors.Figure 8 shows the power output at VL1 site. Me-

teorological data from year 1 were used. In case ofa horizontal collector the dependence of the maxi-mum output power on the level of global irradianceis not diHerentiated upon season (Fig. 8a). Whena P collector is considered, the same incident ir-radiance value leads to an output power obviouslyhigher during summer (Fig. 8b). For a horizontalcollector the output power increases when the inputirradiance increases (Fig. 8a). This remark main-tains for the P collector except for summer results(Fig. 8b).

Fig. 8. Dependence of maximum output power Wmax

on atmospheric optical depth at VL1 site. (a) Hori-zontal solar collector; (b) P solar collector. Meteoro-logical data for summer, autumn and winter year 1were used. A high-eDciency engine was considered(ha = 500 W=m2=K, hC = 50 W=m2=K). Table 2 showsdesign data for the selective Eat-plate solar collector.

The power provided by a system based on ahorizontal collector increases at VL2 site withthe level of solar irradiance, as expected (Fig.9). The increase is almost proportional in caseof the low-eDciency engine (Fig. 9a) and slightlynon-linear for the high-eDciency engine (Fig. 9c).Generally, there is no obvious dependence on sea-son. In case of the P collector, the output powerobviously depends on season, with a maximumduring spring and summer and a minimum dur-ing autumn and winter. This is true for both thelow- and high-eDciency engines (Figs. 9b and d,respectively).The seasonal inEuence is similar for both so-

lar eDciency and output power in case of a low


Fig. 9. Dependence of the maximum output power Wmax on the level of solar global irradiance incident on a horizontalsurface at VL2 site. (a) Low-eDciency engine and horizontal solar collector; (b) low-eDciency engine and P solarcollector; (c) high-eDciency engine and horizontal solar collector; (d) high-eDciency engine and P solar collector.All the available meteorological data for VL2 site were used (years 1 and 2). The low-eDciency engine is deFned byha = hC = 50 W=m2=K, while the high-eDciency engine is characterized by ha = 500 W=m2=K; hC = 50 W=m2=K.

Table 2 shows design data for the selective Eat-plate solar collector.

eDciency engine-horizontal collector combination(Figs. 6a and 9a). This is still valid when the collec-tor is connected to a high eDciency engine. How-ever, in this case the power values have a largerdispersion, which increases slightly with increasingthe irradiance (cf. Figs. 9c and 6c).In case of a low-eDciency engine and a P col-

lector, the inEuence of the season is stronger onpower than on solar eDciency (cf. Figs. 9b and 6b).This is even more obvious if one connects a P col-lector to a high-eDciency engine (cf. Figs. 9d and6d). The high solar eDciency values during springand autumn at smaller irradiance values (Fig. 6d)

are not the main cause of the higher output power(which is obtained in summer (Fig. 9d)).Let us compare Figs. 9a and b in case of a

low-eDciency engine. Then, a P collector is rec-ommended mainly during summer and spring(which are dust storm-free seasons). Figure 9bshows higher output power values as comparedto the case when a horizontal collector is used. Ifthe summer and spring values would be neglected,one can see that choosing a P instead of a H col-lector leads to a relatively small increase in powerduring the other two seasons (autumn and winter).This is valid for the high-eDciency engine, too


(cf. Figs. 9c and d). However, the increase inpower by using a P collector during seasons with-out dust storms is more spectacular. Compare thepower values as high as 20 W obtained at lower in-put irradiance by using a P collector (Fig. 9d) withthe power values of at most 12–13 W obtainedat high irradiance values by using a horizontalcollector (Fig. 9c).

4. CONCLUSIONS

A solar thermal power plant operating on Marssurface is analyzed in this work. The power plantmodel is based on Eat-plate selective solar collec-tors that operates at relatively high-eDciency (fordetails see [12]). A Carnot endoreversible enginemodel was used in order to provide upper limitsfor the performance of actual power plants. Theoptimization procedure developed in [12] is basedon the Fnite-time thermodynamics methods. Thispaper focuses on solar power plant operation un-der various weather conditions during all seasonson Mars. In computations we used as input datavalues of atmospheric pressure and temperature,wind speed and atmospheric optical depth mea-sured at Viking Landers (VL) sites. Two strategieswere used to collect solar radiation, namely a solarhorizontal collector (which is easier to built anduse) and a solar collector whose tilt and orientationare continuously adjusted to keep the receivingsurface perpendicular on Sun’s rays (this strategyprovides higher collected solar energy most timeof the year). A low- and a high-eDciency thermalengines were analyzed. Practical situations shouldnormally lie between these two cases. All thecomputations were performed for a selective solarEat-plate collector whose design data are shown inTable 2 (collector area 0:22 m2).The main results of this work are:

(1) The inEuence of latitude on performance isobvious. Generally, the solar eDciency is smallerat VL1 site as compared to VL2 site for both strate-gies of collecting solar radiation. In most cases themaximum power provided by a horizontal collectorat VL1 site is smaller than at VL2 site. However,in some situations the meteorological eHects com-pensate the latitudinal eHects and the output poweris quite similar at both VL1 and VL2 sites.(2) In case a low-eDciency engine is coupled to

a horizontal collector, the solar eDciency does notexceed 0.13 at VL2 site. Generally, it is lower dur-ing summer and higher during winter’s dust storms.In case the low-eDciency engine is coupled to aP collector, the solar eDciency increases duringsummer.

(3) The solar eDciency is as high as 0.18in case of a horizontal collector attached to ahigh-eDciency engine. If the high-eDciency ther-mal engine is connected to a P collector the solareDciency increases signiFcantly during summerand spring but does not exceed 0.18.(4) The power provided by a system consisting

of a horizontal collector and a low eDciency en-gine does not exceed 7 W. Using a high-eDciencycoupled to a horizontal collector leads to a out-put power up to 13 W during spring, autumn andwinter.(5) The P strategy is recommended mainly

during summer and spring in combination withhigh-eDciency engines. In this case the solar eD-ciency could be as high as 25 W.(6) Our results show a comparable performance

for both PV cell power systems and properly de-signed dynamic solar power plants operating onMars.

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SIMULATION OF A THERMAL SOLAR POWER PLANT OPERATING ON MARS UNDER CLEAR SKY AND DUST STORM CONDITIONS