Optimizing the efficiency of a solar receiver with tubular cylindrical cavity for a solar-powered organic Rankine cycle

Energy 112 (2016) 1259e1272

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Optimizing the efficiency of a solar receiver with tubular cylindrical cavity for a solar-powered organic Rankine cycle R. Loni a, A.B. Kasaeian b, E. Askari Asli-Ardeh a, *, B. Ghobadian c a

Department of Mechanics of Biosystem Engineering, University of Mohaghegh Ardabili, Ardabil, Iran Department of Renewable Energies, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran c Department of Mechanics of Biosystem Engineering, Tarbiat Modares University, Tehran, Iran b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 March 2016 Received in revised form 21 June 2016 Accepted 22 June 2016

In this study, a solar collector was considered with a cylindrical cavity receiver. The receiver was a type of coated copper closed-tube open cylindrical cavity. Thermal oil was used as the working fluid in the cavity receiver. The affecting parameters including the concentrator shape, concentrator reflectivity, concentrator optical error, solar tracking error, receiver aperture area, receiver tube diameter, cavity receiver depth, inlet temperature and the mass flow rate of the thermal oil through the receiver were investigated. Also, R141b was considered as the working fluid of the ORC system in the condition of saturated vapor. The main focus of this study was on the thermal modeling and optimization of cylindrical cavity receiver. With the help of the ray-tracing software, SolTrace, and the receiver modeling techniques, the optimum aspect ratios are identified. It is conducted that for attaining higher collector efficiency, higher overall efficiency and higher network smaller tube diameter, optimum height of cavity and lower thermal oil inlet temperature are necessary. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Cylindrical cavity receiver Solar ORC Optimized efficiency

1. Introduction Parabolic dish concentrators can focus parallel radiation ray to a focal point for obtaining a high temperature of working fluid, so it is one of the main methods to produce heat from solar energy [1,2]. Solar receiver can be divided into tubular, volumetric and particle receivers. Avila-Ma
rın [3] considered the cavity receiver as the best alternative of the tubular receivers. Generally, cavity receivers have a higher level of efficiency compared to external receivers [4]. For a solar cavity receiver, there is an aperture on the front face of the cavity, through which concentrated sunlight was hit onto the inside surfaces of the receiver cavity. Because of the multiple reflections from the inner walls, the fraction of the incoming energy absorbed by the cavity exceeds the surface absorptance of the inner walls [5]. Meanwhile, the existence of the aperture causes unavoidable heat loss; nevertheless, if the aperture is smaller than the receiver, it reduces heat loss. So the thermal efficiency and the heat loss are the important indicators for evaluating the thermal performance of a solar cavity receiver, and the study on the thermal performance also wins much attention from researchers.

* Corresponding author. E-mail address: [email protected] (E. Askari Asli-Ardeh). http://dx.doi.org/10.1016/j.energy.2016.06.109 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

Steinfeld and Schubnell [6] described a semi-empirical method to determine the optimum aperture size and optimum operating temperature of a solar cavity-receiver for which its energy conversion efficiency was maximum. Huang et al. [7] proposed a quick process to optimize the system to provide the maximum solar energy to net heat efficiency for different optical error under typical condition. Li et al. [8] investigated an analytical function to predict the performance of a dish solar concentrator with a cavity or flat receiver. They optimized the size of receiver and rim angle of dish to maximize the annual net thermal energy which was collected at different optical errors and heat loss coefficients. Xiao et al. [9] designed and experimentally conducted a tubecavity solar receiver for obtaining high-temperature air for the micro gas turbine in a two-stage dish system. Harris and Lenz [10] analyzed the energy loss mechanisms of a parabolic dish/cavity receiver configuration. Also, the power profiles produced in the cavities with varying geometry were discussed based on the concentrators with varying rim angle. Reddy et al. [11] experimentally and theoretically analyzed the thermal performance of the fuzzy focal solar parabolic dish concentrator with modified cavity receiver for different operating conditions. It was found that the efficiency of the collector was increased with the increase of volume flow rates. Le Roux et al. [12] investigated the performance of a

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Nomenclature A C c2 cp d D F Gr h h0 h* I k m m2 m, N Nu ODP P Pr q_ Q_

area, m2 aspect ratio constant used in linear equation constant pressure specific heat, J/kg K receiver tube diameter, m receiver diameter, m view factor Grasshof number cavity depth, m heat transfer coefficient, W/m2 K enthalpy, kJ/kg direct normal solar irradiance, W/m2 thermal conductivity, W/m K coefficient slope of linear equation system mass flow rate, kg/s number of tube sections Nusselt number ozone droplet properties pressure, Pa Prandtl number heat flux density, W/m2

heat flow, W net * _ available solar heat flow at receiver Q cavity, W loss heat flow from the cavity receiver, W Q_ loss available solar heat flow at dish concentrator, W Q_ solar R thermal resistance, K/W Ra Raleigh number Re Reynolds number t thickness, m T temperature, K V velocity, m/s W power, W

rectangular cavity receiver in the solar thermal Brayton cycle where air was used as working fluid. They proposed a method for determining the receiver surface temperatures and receiver efficiencies for various cavity sizes. Their case has some benefits like simplicity, low receiver cost, and high efficiency since it operates at low pressure [12e18]. On the other hand, the ORC (Organic Rankine Cycle) is one of the most favorite technologies which has capable of generating work with fluids at different saturation temperatures. The ORC can be easily modularized and used in conjunction with various heat sources. As an efficient technology for converting heat to electricity or useful work, solar organic Rankine cycle (ORC) power plant has appeared as an attractive solution. Solar ORCs have been studied both theoretically [19,20] and experimentally [21] as early as in the 1970s. Jing et al. [22] simulated a low-temperature solar thermal ORC consisting of Compound Parabolic Concentrators (CPC) and HCFC123 as working fluid in different areas and it is concluded that the optimal ORC evaporation temperatures in most of the investigated areas are around 120
C. Delgado-Torres [23] optimized the solar-powered ORC while

Greek symbols ε emissivity s StefaneBoltzmann constant, W/m2 K a the inclination angle of the wind direction in the horizontal surface,
r density, kg/m3 h efficiency Subscripts 0 initial inlet to receiver air of the air ap aperture Ave average b boiler c condenser cav for the cavity col overall for the collector conc concentrator cond due to conduction conv due to convection Dish dish concentrator f fluid forced due to forced convection inlet at the inlet ins insulation n tube section number natural due to natural convection opt optimum out at the outlet outer out of the cavity rec receiver refl due to concentrator reflectivity rad due to radiation REC for the receiver including optical efficiency s surface solar direct normal irradiance from the sun solTrace obtained by the SolTrace software t turbine ∞ environment

twelve substances are considered as working fluids of the ORC and four different models of stationary solar collectors (flat plate collectors, compound parabolic collectors and evacuated tube collectors) are investigated. Operating conditions of the solar ORC that minimizes the aperture area needed per unit of mechanical power output of the solar cycle are determined for every working fluid and every solar collector. Quoilin et al. [24] investigated the impact of the temperature glide in the collector, evaporating pressure and working conditions such as wind speed, ambient temperature and solar beam insolation on the overall efficiency of a low-cost solar ORC. According to the aforementioned literature review, the application of parabolic dish in an ORC system is a new concept. In this work, the cylindrical open-cavity receiver is coupled with the ORC at five different depths of the cavity, three diameters of inner tube and thermal oil as working fluid in the solar collector system. The utilization of thermal oil as working fluid and determination of an optimum depth and other optimum parameters of the cylindrical cavity for maximum thermal efficiency would be a new subject of interest. It shall be mentioned that the main focus of this study is thermal modeling and optimization of cylindrical cavity receiver.

R. Loni et al. / Energy 112 (2016) 1259e1272

Nevertheless, we coupled an ORC with the assumed system for the purpose of power gain in such systems. The size of the receiver aperture can be optimized by considering some factors such as heat loss and errors due to the solar dish and tracking system. It should be mentioned that the SolTrace cannot build a horizontal cylindrical as the receiver cavity. So a special method was applied for building it in the SolTrace as a new concept for the first time. The cylindrical cavity receiver was built by 16 rectangular parts around a circular top wall of the cylindrical cavity. The aim of the paper is to calculate the optimum parameters include optimum aperture size of the cavity receiver, receiver tube diameter, and optimum cavity depth for achieving high collector efficiency and ORC efficiency.

2. Model design and methodology The parabolic dish concentrator is used to reflect and concentrate the sun's rays onto the receiver aperture so that the solar heat can be absorbed by the inner walls of the receiver and be transferred to the thermal oil as the working fluid in the collector system. The layout of the components of an ORC utilizing renewable solar energy as thermal source is shown in Fig. 1. The system is composed of an evaporator (heat exchanger), a turbine expander, a condenser, and a pump. An organic working fluid flows into the evaporator in which the thermal oil from the low-temperature to medium-temperature heat source is utilized as hot fluid. The vapor of the boiling organic fluid enters the turbine expander and generates power. The exiting fluid from the turbine expander then enters the condenser in which the low-temperature cooling water is utilized to condense the fluid. Finally, a fluid pump raises the fluid pressure and feeds the fluid into the evaporator to complete the cycle. As the temperature difference between the hot source and the cold end is large enough, the cycle will continue to operate and generate power.

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2.1. Dish collector modeling The receiver presented in this work is a cylindrical open-cavity receiver constructed with a coated copper tube through which the thermal oil flows (Fig. 2). The thermal oil enters the tube at the bottom of the receiver and the heated thermal oil exits at the top. The receiver tube forms the inner wall of the open-cavity receiver. It shall be mentioned that the aperture diameter of the cavity receiver is assumed to be equal to the cylindrical cavity. According to Le Roux et al. [12], the factors contributing to the temperature profile and heat flow on the receiver wall can be divided into two components: geometry-dependent and temperature-dependent. Their research has shown that the effects of the geometry-dependent factors can be found with SolTrace (see Table 1 and Fig. 3). The temperature-dependent factors including the radiation heat loss to the environment, the re-radiation from the inner-cavity walls, the convection heat loss, and the conduction heat loss can be calculated from heat loss equations. In this study, these methods were applied to calculate the temperature profile and the heat flow on the receiver walls. The thermal modeling was done at two states in this study, first finding an optimum aperture size. After finding the optimum aperture size, stage two was included in calculating the optimum diameter of the inner tube, the optimum depth of the cavity and optimum inlet temperature of the working fluid (Fig. 4). 2.1.1. Receiver modeling The receiver modeling is shown in Fig. 5. The receiver is covered with insulation. The heat loss mechanisms from the receiver consist of convection, radiation, and conduction heat losses. For the cylindrical cavity receiver studied in this paper, five receiver depths, h, equal to 0.5D, 0.75D, 1D, 1.5D and 2D and three inner tube diameters, d, equal to 10 mm, 22 mm and 35 mm are investigated. The selected d amounts were chosen based on the availability in the market and obtaining higher working fluid outlet temperature for application of the heat gain in the ORC system. The higher working fluid outlet temperature can obtain with smaller tube diameter [12]. The interval of h is 0.5D but, for the purpose of reaching more accuracy in the lower amounts of h, 0.75D was added as well. The heat flow at the receiver tube is * Q_ net ¼ Q_  Q_ loss;cond  Q_ loss;rad  Q_ loss;conv

While the receiver efficiency is defined as

Fig. 1. The solar thermal organic Rankine cycle (ORC).

Fig. 2. A cylindrical open-cavity solar receiver.

(1)

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Table 1 SolTrace modeling assumed. The parabolic dish rim angle The optical errors The tracking error The sun-shape The half-angle width The reflectance of the cavity walls (black cobalt coating) Number of ray intersections

45
0e50 mrad 1
pillbox 4.65 mrad 15% 10000

Fig. 3. Example of analysis done in SolTrace for the solar dish receiver.

.



* _ po ðTout  Tin Þ hrec ¼ Q_ net Q_ ¼ mc

.

hoptical hrefl Q_ solar



(2)

hREC ¼ hrec $hoptical

(3)

hcol ¼ hrec $hoptical $hrefl

(4)

where

hoptical ¼

Power Absourbed by the Cavity Walls ðWÞ Total Power of Radiation Received by the Collector ðWÞ (5)

and

. Q_ solar ¼ I pD2conc 4

(6)

 Conduction heat transfer The conduction heat loss rate can be calculated with Eq. (7) by assuming an average wind speed of 2.1 m/s, an average surrounding temperature of 30
C, and atmospheric pressure of 84 kPa for Tehran. We assume that the collector orientation and the wind direction behave so that the wind direction would be parallel with

Fig. 4. The schematic of the overall path of current study for optimizing of the cylindrical cavity receiver.

the receiver top wall at any time. Note that TS;Ave is assumed as 200
C initially to calculate the heat loss from the receiver for optimization of the cavity aperture. For the receiver insulation, a mineral wool can be used while the insulation thickness of tins ¼ 2 cm and an average insulation conductivity of 0.062 W/m k at 200
C is assumed [25].

  Q_ loss;cond ¼ A Ts;Ave  T∞ Rtotal     0 ¼ Ts;Ave  T∞ 1 houter A  tins =kins A

(7)

The convection heat transfer coefficient on the outside of the insulation is determined by assuming a combination of natural convection and forced convection due to the wind. The Nusselt number for forced convection for the laminar flow (because of

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  Q_ loss;rad ¼ εsAap T4s;Ave  T4∞

(14)

The receiver tubes with emissivity assumed to be equal to 0.2. Eq. (13) was used in the first stage of the thermal modeling including optimization of the cavity aperture. The view factor is important when determining the temperature profile of the receiver tube. The receiver is built up with a stainless steel tube. When calculating the temperature profile, the radiation heat loss rate and heat gain rate at different sections of the inner wall are determined with the use of Eq. (15):

Q_ loss;rad;n ¼ An

N X

  4 4 Fnj εn sTs;n  εj sTs;j

(15)

j¼1

Fig. 5. Heat loss from the open-cavity receiver.

 Convection heat loss

Ra<5  105) over the receiver insulation on the top side of the receiver parallel with the wind direction is [26]: 1

=

Nu ¼ 0:664Re0:5 L Pr

Re < 5  105 ;

3

0:6  Pr  60

(8)

The Nusselt number for forced convection on the side of receiver is [26]: 1

=

NuD ¼ 0:193Re0:675 Pr D

3

5  103 < Re < 105 ;

Pr  0:7

(9)

The Nusselt number for natural convection on the sides of the receiver that assumed as vertical plate is [26]: 1

1

Nu ¼ 0:59 Ra4L ðcos qÞ4

q ¼ 45


(10)

It is assumed that the Nusselt number for natural convection on the upper tilted side of receiver is the same as the lower tilted sides: 1

1

Nu ¼ 0:59 Ra4L ðcos qÞ4

q ¼ 45


(11)

For the combined natural and forced convection, the Nusselt number is [26]:

1  3:5 3:5 Nucombined ¼ Nu3:5 forced þ Nunatural

(12)

h0outer ¼ h0avg ¼

1 Atotal

Hi0 Ai

h0 total ¼ h0 n þ h0 wind

(16)

where

h0wind ¼ 0:1967V 1:849

(17)

and

k h0n ¼ Nun ; Nun d

  s 1 ¼ 0:088 Gr3 ðTw =T∞ Þ0:18 ðcos4Þ2:47 Dap Lc    ¼ 1:12  0:98 Dap Lc

where s (18)

The convection heat loss rate from the open-cavity receiver surface is calculated with Eq. (19):

  Q_ loss;conv ¼ h0total Atotal Ts;Ave  T∞

For the overall convection heat transfer coefficient:

X

For convection heat loss, the available heat loss models are often limited to specific cases and temperatures. According to [26], the heat transfer in an open cylindrical cavity for mixed natural and forced convection is reported. The convection heat loss coefficient for a cavity receiver will depend on its shape, the orientation of the aperture on the wind direction and the wind speed. The convection heat loss rate from the open-cavity receiver surface is determined as followings [27]:

(19)

(13)

i

where Atotal is the summation of the surfaces of 16 side walls and one top wall. The emissivity of the mineral wool insulation is assumed to be 0.2 at normal temperatures [25]. For the purpose of this paper, the heat loss from the receiver insulation due to radiation is neglected as the surface temperature of the insulation is assumed to be close to the environment temperature. The conductivity of the copper tube at the considered temperatures is assumed to be 401 W/m K [26], and thus the thermal resistance due to conductivity through the tube wall of 2 mm thickness is neglected.  Radiation heat loss The total radiation heat loss rate from the receiver aperture can be calculated with Eq. (14):

2.1.2. Numerical methods for receiver modeling : The surface temperature (Ts,n) and the heat flow (Qnet;n ) at different elements of the tube are determined by solving Eqs. (20) and (22) using the NewtoneRaphson Method [12]:

Ts;n  Q_ net;n ¼

Pn1 i¼1

1 h0 An

Q_ net;i _ p0 mc

!

þ 2m_1: c

!  Tinlet;0 !

(20)

p0

* Q_ net;n ¼ Q_ n  Q_ loss;rad;n  Q_ loss;con;n  Q_ loss;cond;n

(21)

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Q_ net;n

 

N     X 4 4 þ An ¼ Q_ n  An εn s Ts;n Fnj εj s Ts;n

rf ¼ 1071:76  0:72 Tf

*



kg m3

(26)

j¼1



4 An εn sFn∞ T∞

   An   An m2 Ts;n þ c2  Ts;n  T∞ Rcond

 7:7127 Pr ¼ 6:73899  1021 Tf

(27)

(22) The receiver surface temperature at different elements of the tube and the heat flow depend on the receiver aperture size, the cavity receiver depth, the mass flow rate of the solar working fluid, the receiver tube diameter, and the working fluid inlet temperature. The optical parameters including the dish reflectivity, DNI (direct solar radiation) and the reflector surface optical error are the other parameters which effect on the thermal efficiency of the system. Thus, a dish concentrator diameter of 1.8 m with 84% reflectivity, 650 W/m2 of direct solar radiation and 10 mrad as the optical error were chosen and optimum parameters of the cavity were determined. The mass flow rate of the thermal oil in the range of 0.002 kg/s to 0.06 kg/s, the thermal oil inlet temperatures of 70
C, 100
C and 150
C, three inner tube diameters of 10 mm, 22 mm and 35 mm and five cavity depths of 0.5a, 0.75a, 1a, 1.5a and 2a were investigated. The view factors for different tube sections are determined from the view factor relations available at [26]. Note that, for the analysis, the receiver tube of the cylindrical cavity is divided into a number of sections as determined by Eq. (23):



h D þ N¼ d 2d

(23)

It shall be noted that in the numerical modeling of the cylindrical cavity receiver, each circular round of the inner tube is defined as an element (grid) in the numerical analysis, which are shown as E1 to E21 in Fig. 6. While the output properties of the working fluid at the outlet of each element would be same as the inlet properties of the latter element. The thermal Behran oil is taken as the solar working fluid while the thermal characteristics of the thermal Behran oil are obtained by the following correlations [28]:

  kf ¼ 0:1882  8:304  105 Tf

cp;f

  ¼ 0:8132 þ 3:706  103 Tf



W mK





kJ kgK

2.2. Organic Rankine cycle modeling The corresponding T-s diagram of the solar Rankine process is shown in Fig. 7. The thermodynamic properties were calculated using the REFPROP.8 developed by NIST [29]. The analysis was focused on the ORC efficiency. The ORC system consists of an evaporator, turbine, condenser, and pump. The pressures drop in the heat exchangers and the pipelines have been neglected, besides the heat losses from the pipelines. The mechanical power produced by the turbine, the thermal power is given by the vapor generator, the mechanical power required by the pump, the thermal power generated by the condenser and the net power output are provided by the following equations:

  _ t ¼ m_ h*  h* W f 3 4

(28)

  Q_ b ¼ m_ f h*3  h*2

(29)

  _ PUMP ¼ m_ h*  h* W f 2 1

(30)

  Q_ c ¼ m_ f h*4  h*1

(31)

_ t W _ PUMP _ net ¼ W W

(32)

The procedure to calculate the enthalpy is depicted in Fig. 8. The ORC efficiency is defined as the net power output to the thermal power given by the vapor generator:

(24)

hORC



    _ PUMP m_ f h*3  h*4  m_ f h*2  h*1 _ net W _ t W W   ¼ ¼ ¼ Q_ b Q_ b m_ f h*  h* 3

(25)

2

(33) where

Fig. 6. A detailed drawing of the cylindrical cavity receiver that was indicating the numerical grid at h ¼ D and d ¼ 10 mm.

R. Loni et al. / Energy 112 (2016) 1259e1272

1265

Fig. 7. The schematic T-s diagram of the solar ORC for R141b.

application but also adequate chemical stability at the desired working temperature. The R141b as an isentropic fluid must qualify for a superior environmental benefit exemption as it has a small ODP of 0.120 and short half-life of 9.3 years [30]. Referring to the aforementioned advantages, the R141b was chosen as the organic fluid in this paper. Fixing the additional physical parameters is necessary to perform the Rankine cycle simulations. The simulation conditions of the ORC system is listed in Table 2. 3. Results and discussions 3.1. Optimum aspect ratio In the first stage of the study, by assuming an average receiver surface temperature of 200
C, the heat losses from the receiver due to the conduction, radiation and convection were determined, and the overall receiver efficiency (Eq. (3)) was calculated. Eq. (36) shows the aspect ratio, C, where N is the number of the receiver walls, equal 16 side walls, and one top wall:

.

C¼

m_ oil cp ðTout  Tin Þ   h*3  h*2

hOverall ¼ hcol $hORC

Atotal;receiver

wall

¼ PN

pD2Dish 4

(36)

i¼1 Ai;receiver wall

Figs. 9e13 show the overall receiver efficiency as a function of the aspect ratio C. These graphs are depicted for a tracking error of 1
at five levels of the optical errors (5, 10, 15, 20 and 35 mrad) and five cavity receiver depths (h ¼ 0.5D, h ¼ 0.75D, h ¼ 1D, h ¼ 1.5D, and h ¼ 2D). It can be concluded from Figs. 9e13 that the overall receiver efficiency increases to an optimum point because of the smaller optical efficiency at the higher C values, but decreases at

Fig. 8. Enthalpy calculation procedure in a superheated vapor basic ORC.

m_ f ¼

ADish;ap

Table 2 Simulation conditions of the ORC system.

(34)

(35)

The choice of the working fluid for the ORC is crucial since the fluid must have not only thermo-physical properties that match the

Term

R141b

Environment temperature (
C ) Environment pressure (MPa) Turbine inlet pressure (MPa) Turbine isentropic efficiency (%) Pump isentropic efficiency (%) Temperature of condenser (
C)

30 84 2 100 100 35

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R. Loni et al. / Energy 112 (2016) 1259e1272

smaller C values because of the higher thermal losses. This means that an optimum C can be defined. Table 3 shows the results of the overall receiver efficiency for different depth cavity and different cavity aperture diameters at tracking error of 1
and optical error of 10 mrad. Base on Table 3, the optimum values of Ch¼0.5D z 54.32, Ch¼0.75D z 40.74, Ch¼D z 32.59, Ch¼1.5D z 23.28 and Ch¼2D z 18.11 are identified for the cavity depths at a tracking error of 1
and optical error of 10 mrad. Also, it can be seen that for all cavity depths, the optimum aperture diameter of 14.1 mm was calculated as the optimum aperture diameter with different overall thermal efficiency. This shows the optimum cavity aperture is independent of the height of the cavity. The optical efficiencies at the optimum aperture size were 89%, 92%, 93%, 95% and 96% at the cavity depths of 0.5D, 0.75D, 1D, 1.5D and 2D, respectively. It can be seen that the optical efficiency increases with increasing the cavity depth because of increasing of the receiver surface area and increased the chance of absorbing the inlet solar heat flux. On the other side, the overall receiver efficiency shows an optimum at the value of h between 2D and 0.5D. Because, at higher cavity depths, the thermal loss increase whereas at the lower cavity depths, the optical efficiency is increased; hence an optimum cavity depth can be defined (Fig. 14). It can be seen from Fig. 14, the receiver efficiency is higher at the smaller depth of the cavity in the higher C than C 0 . This is clear the effect of the lower heat loss in the smaller depth of the cavity is higher ́ of the optical efficiency. While in the C lower
than the effect than C , this is vice versa. The found optimum ratio is valid for all sizes of the dish concentrators. For validation of the obtained results of this paper [12], A was defined as the to the ́ aperture areá of the cavity receiver ́ aperture. So, Eq. (32) was described for translating C to A value. A in ́ ́ this study will be equal to 0.0061, and it can be compared with the 0 optimum ratios of A z0.0035 in Ref. [12]. While A in this study is larger because of the insulation of the cavity is taken thinner than that of [12] and its conductivity is larger than that reference.


¼ A

1

Fig. 10. The overall receiver efficiency for a tracking error of 1
, cavity depth of “0.75D” and receiver surface emissivity of 0.2.

Fig. 11. The overall receiver efficiency for a tracking error of 1
, cavity depth of “1D” and receiver surface emissivity of 0.2.

(37)

0

4C ð0:25 þ mÞ

where m is a coefficient equal to 0.75, 1, 1.5 and 2 for the receiver depth of 0.75D, 1D, 1.5D, and 2D, respectively. 3.2. Receiver solar heat flux profile

Fig. 12. The overall receiver efficiency for a tracking error of 1
, cavity depth of “1.5D” and receiver surface emissivity of 0.2.

In the previous section, the results showed that the optimum amounts of Ch¼0.5D z 54.32, Ch¼0.75D z 40.74, Ch¼D z 32.59, Ch¼1.5D z 23.28 and Ch¼2D z 18.11 were identified for the five cavity depths. Following diagrams and calculations always use the ́

́ ́

́

́ Fig. 13. The overall receiver efficiency for a tracking error of 1
, cavity depth of “2D” and receiver surface emissivity of 0.2.

Fig. 9. The overall receiver efficiency for a tracking error of 1
, cavity depth of “0.5D” and receiver surface emissivity of 0.2.

optimum C0 values. For these optimum aspect ratios at tracking error of 1
and optical error of 10 mrad, the solar heat flux density at different parts of different receiver walls at d ¼ 10 mm, 22 mm and

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1267

Table 3 Results of receiver efficiency according to D, h, and C, at optical error ¼ 10 mrad, tracking error ¼ 1
. D (mm)

3.10 4.47 9.49 12.20 14.10 16.70 20.00 49.00

h ¼ 0.5D

h ¼ 0.75D

h ¼ 1D

h ¼ 1.5D

h ¼ 2D

h (mm)

C

hREC

h (mm)

C

hREC

h (mm)

C

hREC

h (mm)

C

hREC

h (mm)

C

hREC

1.55 2.24 4.75 6.10 7.05 8.35 10.00 24.50

1123.83 540.52 119.92 72.56 54.32 38.72 27.00 4.50

0.01 0.09 0.60 0.81 0.86 0.85 0.84 0.50

2.33 3.35 7.12 9.15 10.58 12.53 15.00 36.75

842.87 405.39 89.94 54.42 40.74 29.04 20.25 3.37

0.03 0.09 0.62 0.82 0.87 0.87 0.85 0.41

3.10 4.47 9.49 12.20 14.10 16.70 20.00 49.00

674.30 324.31 71.95 43.54 32.59 23.23 16.20 2.70

0.04 0.09 0.64 0.83 0.88 0.87 0.84 0.31

4.65 6.71 14.24 18.30 21.15 25.05 30.00 73.50

481.64 231.65 51.39 31.10 23.28 16.60 11.57 1.93

0.04 0.09 0.63 0.83 0.88 0.87 0.82 0.09

6.20 8.94 18.98 24.40 28.20 33.40 40.00 98.00

374.61 180.17 39.97 24.19 18.11 12.91 9.00 1.50

0.04 0.10 0.63 0.82 0.87 0.85 0.78 0.00

Fig. 14. The overall receiver efficiency for a tracking error 1
, optical error of 10 mrad and the receiver surface emissivity of 0.2 at different cavity depths.

35 mm were obtained by the SolTrace. It should be mentioned that the SolTrace cannot build a horizontal cylindrical as the receiver cavity. So a special method was applied for building it in the SolTrace. The cylindrical cavity receiver was built by 16 rectangular vertical parts around a circular top wall of the cylindrical cavity as the polygonal shape of the model is shown in Fig. 15. The heat flux distribution of the side wall tubular element was obtained for all of the 16 side wall parts. Finally, an average heat flux of the 16 parts of the side wall was assumed for each tube element on the side wall. On whereas, an average heat flux on the top wall was obtained by the SolTrace for the tube element on the top wall of the cylindrical cavity. The found data were utilized in the program for calculating the net received heat and the surface temperatures. The calculations were carried out for five cavity depths, but typically the result of h ¼ 2D at d ¼ 10 mm is reported in Fig. 16. It is mentioned that the “Distance of Tubes” in the Figures can be defined as the distance of each tube element from the aperture of the cavity at the side walls. Note that these solar heat flux densities were for a parabolic concentrator rim angle of 45
and a solar beam irradiance of I ¼ 650 W/m2. The absorbed heat rate at different parts of the inner cavity can be determined by the following equation:

Q_ n ¼ q_ n;SolTrace An hrefl

In Fig. 16, the non-same trends of the heat flux density at different side walls were because of the tracking error assumed to be equal to 1
. We can see that when the tracking error was reached to 0
, the same trends of heat distribution can happen. This case could be observed in Fig. 18a and b that were found with SolTrace software. This was mentioned for a rectangular cavity receiver in Ref. [12].

(38)

where Q_ n (W) is the absorbed heat rate at the element number n, q_ n; SolTrace is the total heat flux rate obtained by SolTrace at the element number n (W/m2) and An ¼ dinner tube$pD (m2). Also, it shall be mentioned that the roughness trend of the heat flux density in decreases as the diameter of the inner tube increases; the heat flux density for the inner tube diameter is equal to 35 mm (Figs. 16 and 17).

Fig. 15. A schematic for illustrating the polygonal shape of cylindrical cavity receiver.

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Also, it has to mention that the flux map can obtain with the SolTrace software but for only one surface. While the cylindrical cavity was built by 16 rectangular parts around its circular top wall. So we cannot show the flux map for all of the cylindrical cavity

parts at the same time in the manuscript. Fig. 19 shows a sample of the Flux intensity chart of one side wall among 16 side walls. Fig. 20 show a comparison of the average heat flux of different elements at the tube diameter of 10 mm and five cavity depths for

Fig. 16. The heat flux density at a different position of the different receiver inner walls for h ¼ 2D at d ¼ 10 mm, optical error ¼ 10 mrad and tracking error ¼ 1
.

Fig. 17. The heat flux density at a different position of the different receiver inner walls for h ¼ 2D at d ¼ 35 mm, optical error ¼ 10 mrad and tracking error ¼ 1
.

Fig. 18. Heat flux on different side walls at tracking errors equal to a) 0
and b) 1
.

R. Loni et al. / Energy 112 (2016) 1259e1272

1269

the side walls. It can be observed that there is no significant difference between the peaks of the heat flux of side wall for different cavity depths. Also, the higher cavity depth show larger heat flux densities at the bottom parts of each side wall of the receiver. Whereas, there is a significant difference between the average heat flux intensity of the top wall for different cavity depths. While at the lower depth of the cavity the intensity of the heat flux on the top wall is larger. Such that, the average heat flux intensity of the top wall equal to 63608, 48944, 38968, 24476 and 16709 (W/m2) for h ¼ 0.5D, h ¼ 0.75D, h ¼ 1D, h ¼ 1.5D and h ¼ 2D, respectively. 3.3. Temperature profile and the heat flow of the receiver tube The results shown in Figs. 21e23 present the element tube surface temperature, the heat flow and the thermal oil temperature for five cavity depths, respectively. It may be observed from Figs. 21 and 22 that the maximum surface temperature and the heat flow are increased in the smaller cavity depth because the maximum heat flux density is increased at the smaller cavity depth. Also, it can be shown from Fig. 21 there is a jump on the curves. This is because of the intensity of the heat flux on the top wall is larger than the intensity of the heat flux on the side wall, especially in the smaller depth of the cavity. From Fig. 22 can be observed there are firstly increasing on the curves of top wall that reason was mentioned. After rising in the curves, there is a decreasing on the curves because of the area of the tube element on the top wall decreasing as near to the center of the cylindrical cavity consequently net absorber power on this smaller tube element will be lower. From Fig. 23, it is evident that the temperature of the outlet oil has a peak at nearly h ¼ D which will be discussed in later sections. The collector efficiencies were calculated as 47.2%, 49.99%, 49.5%, 49.1% and 46.48% for the cavity depths of 0.5D, 0.75D, 1D, 1.5D and 2D, respectively.

Fig. 20. The heat flux densities at a different position of the side wall for different cavity depths at d ¼ 10 mm, optical error ¼ 10 mrad and tracking error ¼ 1
.

Fig. 21. Surface temperatures for five cavity depths at tube diameter of 0.01 m, the inlet temperature of 150
C, the mass flow of 0.006 kg/s with tacking error of 1
and optical error of 10 mrad.

3.4. Optimum cavity depth Fig. 24a, b and c show the changes of the absorbed net heat versus five cavity depths at the inlet temperature of 70
C, 100
C and 150
C, respectively. The concentrator dish diameter of 1.8 m and optimum diameter of the aperture size of receiver cavity equal to 0.141 m were assumed for all investigations. It can be concluded that the absorbed net heat is increased at the smaller tube diameter and lower temperature of the working fluid. This is because, in the same mass flow rate, the Reynolds number and Nusselt number of

Fig. 22. Heat flows for five cavity depths at tube diameter of 0.01 m, inlet temperature of 150
C, mass flow of 0.006 kg/s with tacking error of 1
and optical error of 10 mrad.

Fig. 19. The Flux Intensity chart of wall 15 of the side walls at h ¼ 2D, optical error ¼ 10 mrad and tracking error ¼ 1
.

Fig. 23. Oil temperatures for five cavity depths at tube diameter of 0.01 m, inlet temperature of 150
C, mass flow of 0.006 kg/s with tacking error of 1
and optical error of 10 mrad.

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R. Loni et al. / Energy 112 (2016) 1259e1272

Fig. 24. The distribution of the absorbed net heat at five cavity depths and three tube diameters, optical error ¼ 10 mrad and tracking error ¼ 1
at three working fluid inlet temperatures of 70
C (a), 100
C (b) and 150
C (c).

Table 4 Average collector efficiency of the cavity receiver at different receiver diameter and different diameter of the inner tube. T inlet (
C)

70

100

150

d

10 mm

22 mm

35 mm

10 mm

22 mm

35 mm

10 mm

22 mm

35 mm

0.5 D 0.75 D h¼D h ¼ 1.5 D h¼2D

58.38 62.45 65.13 65.80 66.01

52.34 57.62 61.46 61.75 62.27

46.79 51.31 53.97 55.84 55.81

55.79 59.41 60.90 61.19 60.44

49.78 54.38 57.92 57.31 56.95

44.38 48.40 50.76 51.74 50.86

52.19 54.24 55.00 54.00 51.54

45.48 48.95 51.98 49.86 47.97

40.36 43.54 45.39 44.88 42.55

Table 5 Average overall efficiency of the cavity receiver at different receiver diameter and different diameter of inner tube. T

inlet

(
C)

d h h h h h

¼ ¼ ¼ ¼ ¼

0.5 D 0.75 D D 1.5 D 2D

70

100

150

10 mm

22 mm

35 mm

10 mm

22 mm

35 mm

10 mm

22 mm

35 mm

0.14 0.15 0.15 0.15 0.15

0.12 0.14 0.14 0.14 0.14

0.11 0.12 0.13 0.13 0.13

0.13 0.14 0.14 0.14 0.14

0.12 0.13 0.14 0.13 0.13

0.10 0.11 0.12 0.12 0.12

0.12 0.13 0.13 0.13 0.12

0.11 0.11 0.12 0.12 0.11

0.09 0.10 0.11 0.11 0.10

the solar working fluid in the inner tube of the cavity receiver are increased at the smaller tube diameter. Hence, better heat transfer to fluid and subsequently lower tube surface temperature and lower radiation heat loss would happen. But we can see that there is a peak of the absorbed net heat nearly at h ¼ D. This is because of increasing the thermal losses at higher cavity depths and decreasing the optical efficiencies in the lower cavity depths.

Of course, it can be shown that in the lower inlet temperature, the net power in the larger cavity depth of h ¼ D is the same or little larger than the net power in h ¼ D. But it should be mentioned that in the larger depth of the cavity, the shadow of the cavity on the dish receiver will be larger. Consequently, received heat flux in the cavity receiver will be smaller, so h ¼ D is an optimum depth of the cylindrical cavity.

R. Loni et al. / Energy 112 (2016) 1259e1272

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Table 6 Average network of the cavity receiver at different receiver diameter and different diameter of the inner tube. T

inlet

(
C)

d h h h h h

¼ ¼ ¼ ¼ ¼

0.5 D 0.75 D D 1.5 D 2D

70

100

150

10 mm

22 mm

35 mm

10 mm

22 mm

35 mm

10 mm

22 mm

35 mm

0.23 0.24 0.25 0.26 0.26

0.20 0.22 0.24 0.24 0.24

0.18 0.20 0.21 0.22 0.22

0.22 0.23 0.23 0.24 0.23

0.19 0.21 0.22 0.22 0.22

0.17 0.19 0.20 0.20 0.20

0.20 0.21 0.21 0.21 0.20

0.18 0.19 0.20 0.19 0.19

0.16 0.17 0.18 0.17 0.16

3.5. Cycle efficiency It may be concluded that all the collector efficiencies and overall efficiencies are increased by smaller inner tube diameter and lower working fluid inlet temperature according to Tables 4 and 5, respectively. The reason was mentioned in the previous section. This result is verified by the literature [12,31,32]. Also from Table 6, it is evident that the network is increased by the smaller tube diameter and lower inlet temperature of the thermal oil. This reason was obtaining higher heat solar power by the cylindrical cavity receiver in the smaller tube diameter and lower inlet temperature. It should be mentioned that in smaller tube diameter, all the efficiency is increased while the pressure drop is increased (Tables 7e11); consequently, the pump size and the strength of the equipment have to be increased for the higher pressure differences, so the cost of installation is increased. All of the efficiencies can be improved by altering inlet temperature of the thermal oil, the cavity depth, and the tube diameter. Therefore, the optimum structure of the solar ORC includes an optimum cavity depth nearby 1D, small tube diameter, and low inlet temperature. Also, the pressure drop is increased by decreasing the tube diameter. The collector efficiency can be compared with the receiver efficiency of hrec z 0.66 [12]. Fig. 25 shows a comparison between our modeling results with the experimental result of [33] for the cylindrical cavity. Good agreement is observed between our modeling and the experimentally reported data of [33].

4. Conclusion The optimization parameters of a proposed cylindrical closedtube open-cavity solar receiver made of copper are numerically investigated. Thermal oil was used as the solar working fluid while a dish collector with the reflectance of 0.84 and diameter of 1.8 m were assumed for the numerical modeling. This cavity receiver was coupled with an organic Rankine cycle by R141b as the working fluid at the saturated vapor condition. The optimization of the cavity based on the thermal performance was done in two stages. The first stage includes the determination of the optimum aperture size of the cavity receiver. While the second stage involves the identification of the optimum inlet temperature of the working fluid, the optimum inner diameter, and the optimum cavity depths. Also, it should be mentioned that the main focus of this study is the detailed thermal modeling of the solar collector system and a summary on the ORC modeling. The results are extracted as followings:  It can be conducted that the overall receiver efficiency increases to an optimum point because of the smaller optical efficiency at the higher C values, but decreases at the smaller C values because of the higher thermal losses. This means that an optimum C can be defined. For a concentrator with 45
rim angle, 10 mrad optical error and 1
tracking error, Ch¼0.5D z 54.32, Ch¼0.75D z 40.74, Ch¼D z 32.59, Ch¼1.5D z 23.28 and

Table 7 ORC efficiency and pressure drop of the cavity receiver with h ¼ 0.5D. Mass flow (kg/s)

Tinlet (
C)

d 10 mm

22 mm

35 mm

0.002e0.06 0.002e0.06 0.002e0.06

70 100 150

0.096e20.734 0.096e21.145 0.096e21.876

0.003e0.417 0.003e0.425 0.003e0.439

0.0005e0.048 0.0005e0.049 0.0005e0.050

Table 8 ORC efficiency and pressure drop of the cavity receiver with h ¼ 0.75D. Mass flow (kg/s)

Tinlet (
C)

d 10 mm

22 mm

35 mm

0.002e0.06 0.002e0.06 0.002e0.06

70 100 150

0.118e25.497 0.118e26.002 0.118e26.900

0.005e0.561 0.005e0.571 0.005e0.590

0.0007e0.060 0.0007e0.061 0.0007e0.063

Table 9 ORC efficiency and pressure drop of the cavity receiver with h ¼ D. Mass flow (kg/s)

0.002e0.06 0.002e0.06 0.002e0.06

Tinlet (
C)

70 100 150

d 10 mm

22 mm

35 mm

0.147e31.847 0.147e32.478 0.147e33.599

0.006e0.704 0.006e0.718 0.006e0.742

0.0008e0.072 0.0008e0.074 0.0008e0.076

Table 10 ORC efficiency and pressure drop of the cavity receiver with h ¼ 1.5D. Mass flow (kg/s)

Tinlet (
C)

d 10 mm

22 mm

35 mm

0.002e0.06 0.002e0.06 0.002e0.06

70 100 150

0.199e42.959 0.199e43.810 0.199e45.323

0.008e0.920 0.008e0.938 0.008e0.969

0.001e0.097 0.001e0.098 0.001e0.102

Table 11 ORC efficiency and pressure drop of the cavity receiver with h ¼ 2D. Mass flow (kg/s)

0.002e0.06 0.002e0.06 0.002e0.06

Tinlet (
C)

70 100 150

d 10 mm

22 mm

35 mm

0.25e54.071 0.25e55.142 0.25e57.047

0.009e1.136 0.009e1.157 0.009e1.196

0.001e0.121 0.001e0.123 0.001e0.127

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R. Loni et al. / Energy 112 (2016) 1259e1272

Fig. 25. Comparison between the obtained modeling results (for 10 mm inner tube diameter) and the experimental result of [33] for cylindrical cavity (for 12.7 mm inner tube diameter).













Ch¼2D z 18.11 are identified for five cavities with h ¼ 0.5D, h ¼ 0.75D, h ¼ 1D, h ¼ 1.5D and h ¼ 2D where the accompanying optical efficiencies are 89%, 92%, 94%, 96% and 96%, respectively. It can be seen that the optical efficiency increases with increasing the cavity depths. For these optimum aspect ratios at the tracking error of 1
and optical error of 10 mrad, the solar heat flux density at different parts of different receiver walls at d ¼ 10 mm, 22 mm and 35 mm were obtained by the SolTrace in a special method. It can be observed that there is no significant difference between the peaks of the heat flux of side wall for different cavity depths. Also, the higher cavity depth shows larger heat flux density at the bottom parts of each side of the receiver. Whereas, there is significant difference between the average heat flux intensity of the top wall for different cavity depths. While at the lower depth of the cavity, the intensity of the heat flux on the top wall is larger. It may be resulted that the maximum surface temperature and the heat flow are increased in the smaller cavity depth because the maximum heat flux density is increased at the smaller cavity depth. But there is an optimum outlet temperature of the thermal oil in the special depth of the cavity between 0.5D to 2D. It can be concluded that the absorbed net heat is increased at the smaller tube diameter and lower temperature of the working fluid. The reason is that in the same mass flow rate, the Reynolds ́ number and Nusselt number of the solar working fluid in the inner tube of the cavity receiver are increased at the smaller tube diameter. Hence, better heat transfer to fluid and subsequently lower tube surface temperature and lower radiation heat loss would happen. An optimum cavity depth of h ¼ 1D absorbs the maximum net heat rate. This is because of increasing the thermal losses at higher cavity depths and decreasing the optical efficiencies in the lower cavity depths. The collector efficiency and overall efficiency are increased by smaller inner tube diameter and lower working fluid inlet temperature. It should be mentioned that in the smaller tube diameter, all the efficiency is increased besides increasing the pressure drop. Consequently, the pump size and the required power of the equipment have to be increased for the higher pressure differences, so the cost of installation is increased.

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