Thermal performance analysis of porous medium solar receiver with quartz window to minimize heat flux gradient

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 108 (2014) 348–359 www.elsevier.com/locate/solener

Thermal performance analysis of porous medium solar receiver with quartz window to minimize heat flux gradient Wang Fuqiang a, Tan Jianyu a,⇑, Ma Lanxin a, Shuai Yong b, Tan Heping b, Leng Yu c a

School of Automobile Engineering, Harbin Institute of Technology at Weihai, 2, West Wenhua Road, Weihai 264209, PR China School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, PR China c Department of Mechanical Engineering, University of Tulsa, 800, South Tucker Road, OK 74104, USA

b

Received 23 May 2014; received in revised form 15 July 2014; accepted 18 July 2014

Communicated by: Associate Editor Michael EPSTEIN

Abstract Exposure under concentrated solar radiation increases the temperature of volumetric receiver which can cause high thermal stress and damage the receiver. The Plano-convex quartz window is introduced with the aim to minimize heat flux gradient of porous medium receiver. Thermal performance of porous medium receiver with quartz window is numerically studied while the fluid inlet is located at the side wall which would be more practicable. The Monte Carlo ray tracing (MCRT) method is used to calculate the radiative heat transfer in the solar collector system with quartz window, and the local thermal non-equilibrium (LTNE) model with the consideration of radiative heat transfer in the porous medium receiver is used to calculate the fluid phase and solid phase temperature distribution of the porous medium receiver. The numerical results indicated that the pressure distribution and temperature distribution for the condition of fluid inlet located at the side wall is different from that for the condition of fluid inlet located at the front surface. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Volumetric receiver; Porous medium; Radiative transfer; Local thermal non-equilibrium; Quartz window; Thermal performance

1. Introduction The comprehensive utilization of solar radiation, effective conversion of solar radiation to heat and chemical energy is a subject of primary technological interest (Segal and Epstein, 2000; Jin et al., 2010). All of these routes utilize concentrated solar radiation as the energy source of high temperature process heat (Pitz-Pall et al., 1997; Hunter and Guo, 2014). The combinations of high speed fluid flow and elevated temperature encountered in concentrated solar utilization have established porous medium receiver as the primary choice (David et al., 2011). ⇑ Corresponding author. Tel.: +86 631 5687 782.

E-mail address: [email protected] (T. Jianyu). http://dx.doi.org/10.1016/j.solener.2014.07.016 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.

Porous medium has the advantages of high fluid–solid contact surface, low pressure drop with good heat and mass transfer performance, high anti-oxygenic properties, excellent thermal shock resistance and mechanical strength (Fend et al., 2004; Bai, 2011). Silicon carbide (SiC) porous medium demonstrates superior thermo-mechanical performance and can be coated with catalyst layer for thermochemical reaction. Due to its naturally black color and high conductivity, the porous medium receiver or reactor made of SiC enables the high performance of concentrated solar radiation collection (Fend et al., 2004). With the advantage of high efficiency and low cost, volumetric porous medium receiver had been put forth through the SOLAIR project to promote its installation in the next generation European solar

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Nomenclature cp dp Esun hv ka ke ks n p R Rr Red T u v x y

specific heat, J/(kg K) particle diameter, mm solar irradiance, W/m2 volumetric heat transfer coefficient, W/(m3 K) absorption coefficient extinction coefficient scattering coefficient Refractivity pressure, pa radius, m random number Reynolds number temperature, K velocity in x direction, m/s velocity in y direction, m/s coordinates in x region, m coordinates iny region, m

a l asf k e r x s n

absorptivity dynamic viscosity, kg/(m s) surface area per unit volume, 1/m conductivity, W/(m K) emissivity Stefan–Boltzmann constant albedo coefficient transmissivity characteristic parameter

Subscripts e effective f fluid phase r radiative heat transfer s solid phase w wall

Greek symbols q density, kg/m3; reflectivity / porosity

thermal power plant (STPP) (Fend et al., 2004). Besides, the porous medium solar thermochemical reactor coated with catalyst was adopted for thermochemical reaction by both the CNRS-PROMES laboratory (Villafa´nVidales et al., 2011) and CETRH/CPERI laboratory (Agrafiotis et al., 2007). Many numerical researches of porous medium receiver under concentrated solar radiation have been conducted, and the numerical studies can be useful for porous medium receiver design and operation improvement. The steady state heat and mass transfer characteristics of porous medium receiver for the tower type STPP were numerically investigated by Xu et al. (2011), and the fluid entrance surface was subjected to a uniform solar radiation during the numerical simulation. The MCRT and Finite Volume Method (FVM) coupling method was developed by Wang et al. (2013, 2014) to research the thermal performance of porous medium solar receiver, and the MCRT method was used to calculate the concentrated solar radiation distribution on the fluid entrance surface. Villafa´nVidales et al. (2011) had investigated the temperature distribution of porous medium solar thermochemical reactor under Gaussian heat flux distribution, and the fluid entrance surface was irradiated by concentrated solar radiation during the numerical simulations. A coupled numerical model for volumetric porous medium receiver was developed by Wu et al. (2011), and several cases of heat flux distribution change on the fluid entrance surface were conducted. Wang et al. (2014) had developed a heat and mass transfer model coupled with radiative heat transfer

and thermochemical reaction kinetics for the volumetric porous medium solar thermochemical reactor, and the fluid inlet surface under Gaussian heat flux distribution was adopted to study the thermal performance and hydrogen production performance. Fig. 1 shows the volumetric solar receiver designed and manufactured by ETH Zurich (Chueh et al., 2010) and German Aerospace Center (DLR) respectively (Ro¨ger et al., 2006). As seen from this figure, a quartz window with high transmissivity was assembled on the front surface of volumetric solar receiver or reactor with the aim to decrease heat losses, maintain operating pressure (above or below atmospheric) and isolate the receiver from the ambient to prevent undesired reactions (Cui et al., 2013). According to the literature survey, it can be seen that most pervious numerical analyses of volumetric porous medium receiver or thermochemical reactor were conducted with fluid entrance located on the front surface of volumetric porous medium receiver. Exposure under concentrated solar radiation increases the temperature of volumetric receiver or thermochemical reactor up to 1500 K or even higher (Fend et al., 2004). The highly non-uniform heat flux distribution across the solar receiver during operation induces thermal stress which can cause the mechanical failure of solar receiver (Khanna et al., 2014). Therefore, an operational design that can minimize the development of thermal stress is very essential. In this study, thermal performance of porous medium receiver with quartz window is numerically studied and

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(a) Manufactured by ETH

(b) Manufactured by DLR

Fig. 1. Volumetric solar receiver designed and manufactured by ETH and DLR respectively.

the fluid entrance is assembled at the side wall which would be more practical. The MCRT method is used to calculate the radiative heat transfer in the solar collector system with quartz window. The LTNE model with the consideration of radiative heat transfer in the porous strut is solved by commercial software Fluent to calculate the fluid phase and solid phase temperature distribution. The concentrated solar radiation calculated by the MCRT method is imported to the thermal performance analysis of porous medium receiver by fitting curve method. The re-radiation from the porous medium and its absorption and heating in the window is neglected. Besides, the Plano-convex quartz window is introduced with the aim to reduce the radiative heat flux distribution gradient and thus also reduce thermal stress. The pressure distribution and temperature distribution of porous medium receiver model with fluid inlet located at the side wall is compared with that fluid inlet located at the front surface. 2. Model assumptions As shown in Fig. 2, the porous medium receiver is placed vertically on the focal plane of solar dish collector. Parabolic solar dish collector concentrates the incoming solar radiation on the fluid inlet surface of porous medium receiver. The front surface of porous medium receiver absorbs the concentrated solar radiation. Heat is conducted and irradiated along the whole porous strut. When air flows through the porous medium, heat is transferred from porous strut to air by conduction and convection coupled transfer (Xu et al., 2011). The flow and heat transfer can be simplified to two dimensions. As the air is transparent, the radiative heat transfer in the fluid phase is not considered.

z

Porous media receiver Quartz window

y

O

Dish concentrator

x Fig. 2. Schematic diagram of the porous medium receiver with solar dish collector system.

The porous medium is assumed to be SiC with isotropic properties. Generally, the ceramic is often deposited with catalyst layer for thermochemical reactor. The lateral walls are assumed to be well insulated without any heat losses. Homogeneous properties of the gas and solid phase are used, and the thermophysical properties of air vary with temperature. It is important to note that the pore size of porous medium receiver is much larger than the mean free path of the gas molecules, therefore diffusion can be modeled using continuum theory. Two porous medium receiver models shown in Fig. 3 are adopted for numerical study: model with fluid inlet located at the front surface of receiver and model with fluid inlet located at the side wall of

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351

L=176 mm y

Insulation

Outlet

R=70 mm

Concentrated Solar Energy

Porous medium CFD domain

x

(a) Fluid inlet located at the front surface of receiver Inlet

y Insulation

Concentrated Solar Energy

Porous Medium CFD domain

Outlet

(b) Fluid inlet located at the side wall of receiver

x

Fig. 3. Two porous medium receiver models used for the numerical analyses.

receiver. The dimensions of the length and height are the same for the two porous medium receiver models. The geometrical and physical parameters of parabolic dish collector and porous medium solar thermochemical reactor are listed in Table 1. 3. Mechanism of MCRT method The methodology of MCRT method in solar concentration and transmission problems is the stochastic trajectories of a huge number of rays (Mao et al., 2014). When the Table 1 Geometrical and physical parameters of parabolic dish collector and porous medium solar thermochemical reactor. Parabolic dish concentrator and porous medium reactor Value Focal length of dish concentrator Aperture radius of dish concentrator Length of receiver Radius of receiver Emissivity of porous medium Conductivity of porous medium Specific heat of porous medium Density of porous medium Distance between window and top surface of porous Transmissivity of quartz window

3.5 m 2.25 m 0.176 m 0.07 m 0.9 118 W/(m K) 11,500 J/(kg K) 3200 kg/m3 10 mm 0.95

solar rays intersecting with components, the fate of each ray is determined by emissive, reflective, and absorptive characteristics on the surface described by series statistical relationships, and the reflection direction of each ray follows the Fresnel optics rule (Cheng et al., 2011; Dai et al., 2014). When the reflectivity of an opaque surface (no transmitted rays) is q, the fate of each ray is fitted with the following correlations Rr 6 q; reflection Rr > q; absorption where Rr is a random number which is uniformly distributed between zero and one. As a semitransparent surface, such as quartz window, the transmissivity, reflectivity, and absorptivity follow the expression of a + q + s = 1. For semi-transparent medium (i.e. quartz window), an equivalent method is proposed by the authors to calculate the radiative transfer in semitransparent medium with high transmissivity (larger than 0.90) (Wang et al., 2013): the interaction of ray and the quartz window is equivalent to the interaction of ray and two surfaces. Two semitransparent interfaces with refraction ability are served as a substitute for the semi-transparent media:

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Rr 6 ae ; absorbed ae < Rr 6 ae þ qe ; reflected Rr > ae þ qe ; refracted where Rr is a random number which is uniformly distributed between 0 and 1, ae is the equivalent absorptivity, qe is the equivalent reflectivity, and se is the equivalent tansmissivity. As shown in Fig. 4, the relationship between the equivalent properties (ae,qe,se) and the total properties (a,q,s) of the quartz window can be expressed as Meng et al. (2014):   q ¼ qe þ s2e qe þ s2e q3e þ    ¼ qe þ s2e qe = 1  q2e ð2Þ a ¼ ae þ ae se þ a e se qe þ ae se q2e þ ae se q3e þ    ¼ ae þ ae s e =ð 1  q e Þ

ð3Þ   2 2 2 2 4 2 6 2 2 4 s ¼ se þ se qe þ se qe þ se qe þ    ¼ se 1 þ qe þ qe þ      ð4Þ ¼ s2e = 1  q2e As the MCRT method is a stochastic method, the calculation accuracy of the MCRT method is highly related to the number of dispatched solar rays and randomness performance of the pseudorandom number generator (Cheng et al., 2014). With the increasing of solar-ray density (emitted rays per square meter), the calculation precision of the MCRT method increases but the calculation efficiency decreases. A number of ray-sampling studies are also performed for the physical model to ensure the essential physics independent of the ray-sampling number. In this study, the solar-ray density is set to 107 W/m2 in this study (Wang et al., 2013). Since quartz is nearly transparent for wavelengths over the solar spectrum (0.3–3 lm, 97% energy of solar energy in this wavelength range), the spectral effects of the quartz window transmission is not considered for simplification. As known, the transmissivity of quartz window is generally larger than 0.95 (0.95 is used in this study), very little energy is absorbed by the window. Therefore, the quartz window can be not overheated or failure due to thermal stress. The concentrated solar radiation calculated by the MCRT method is imported to the thermal performance

analysis of porous medium receiver by fitting curve method. Compared to using constant value (Rolda´n et al., 2013), the fitting curve method can effectively illustrate the real heat flux distribution on the receiver surface with very small interpolating error (Mwesigyea et al., 2014; Wang et al., 2012).

4. Governing equations 4.1. Continuity equation @ ðuqf Þ @ ðvqf Þ þ ¼0 @x @y

ð5Þ

In the above correlation, the symbol qf is the density of fluid phase and the symbol u and v delegates the fluid velocity. 4.2. Momentum equation The momentum equation for the porous medium solar receiver is expressed by Brinkman–Forchheimer Extended Darcy equation:         qf @u @u @P @ @u @ @u l qf F / ffiffiffi u u ¼ þ þ  fþ p u þv lf;e lf;e / k @x @y @x @x @x @y @y k         qf @v @v @P @ @v @ @v lf qf F / ¼ þ þ  u þv lf;e lf;e þ pffiffiffi v v / k @x @y @y @x @x @y @y k

ð6Þ ð7Þ

In the above two equations, / represents the porosity of porous medium receiver, lf,eff is the effective dynamic viscosity of the fluid (lf,eff = lf//). The permeability of the porous medium k and the geometric function F can be represented as Alazmi and Vafai (2000):

2 k ¼ d 2p /3 = 150ð1  /Þ pffiffiffiffiffiffiffiffi

F ¼ d 2p /3 = 150/3=2

Fig. 4. Schematic of the relationship between equivalent properties and total properties of quartz window.

ð8Þ ð9Þ

W. Fuqiang et al. / Solar Energy 108 (2014) 348–359

where dp is the average particle parameter of porous medium receiver, and the boundary conditions for the momentum equations are: Fluid inlet surface: u = u0, v = 0 Fluid outlet surface: ou/ox = ou/oy = ov/ox = ov/oy = 0

4.3. Energy equation The local thermal non-equilibrium condition is considered which can provide more temperature information of the fluid phase and solid phase (Xu et al., 2011). The energy equation for the fluid phase is expressed by         @ qf cp T f @ q f cp T f @ @T f @ @T f u þv ¼ kf;e kf;e þ @x @y @x @y @x @y þ hv ðT s  T f Þ And the energy equation for the solid phase is     @ @T s @ @T s kf;e kf;e þ ¼ hv ð T s  T f Þ þ r  qr @x @y @x @y

ð10Þ

ð11Þ

where the symbols Tf and Ts delegate the fluid phase temperature and solid phase temperature respectively. The symbol hv denotes the volumetric convective heat transfer coefficient between the fluid phase and the solid phase. The symbols kf;e and ks;e are the effective thermal conductivity of the fluid and solid phase respectively. The kf;e and ks,e can be estimated from the following correlations kf;e ¼ /kf ks;e ¼ ð1  /Þks

ð12Þ ð13Þ

The volumetric convective heat transfer coefficient hv can be expressed as hv ¼ hsf asf

ð14Þ

where hsf is the heat transfer coefficient between the fluid phase and solid phase in [W/m2 K] and asf is the specific surface area of per unit volume in [1/m]. Hwang et al. (1995) had put forward correlations of heat transfer coefficient for porous channel and the correlations were compared by Xu et al. (2011) with experimental results for porous foam receiver with good agreements. The correlations of heat transfer coefficient at different Reynolds number variation range are expressed by: hsf ¼ 0:004ðd v =d p Þðkf =d p ÞPr0:33 Re1:35 for Red 6 75 d

ð15Þ

for Red P 350 hsf ¼ 1:064ðkf =d p ÞPr0:33 Re0:59 d

ð16Þ

For 75 < Red < 350, the heat transfer coefficient is calculated from the interpolation of Eqs. (15) and (16). asf ¼ 20:346ð1  /Þ/2 =d p

ð17Þ

d v ¼ 4/=asf up ¼ u0 =/

ð18Þ ð19Þ

353

where Pr is the fluid Prandtl number and Red ¼ /qf~ u=lf (Xu et al., 2011). It should be noted that there are many correlations of the permeability, geometric function and volumetric convection heat transfer coefficient for porous medium. Take the correlations of volumetric heat transfer coefficient as an example: Hwang et al. (1995),Achenbach (1995), Dixon and Cresswell (1979) as well as Wu et al. (2011) have put forward different models. Many investigators have used the permeability, geometric function put forward by Ergun (1952) and correlations of volumetric convection heat transfer coefficient put forward by Hwang et al. (1995) simultaneously to study the heat transfer performance of porous medium (Xu et al., 2011; Alazmi and Vafai, 2000). The correlations of permeability, geometric function and volumetric convection heat transfer coefficient for porous medium used in this study are the same as those in Ref. (Xu et al., 2011; Alazmi and Vafai, 2000). In the solid phase energy equation, the source term $  qr is the volumetric heat source term due to radiative heat transfer. Due to the characteristics of strongly absorbing solar radiation, the porous medium is large optically thickness with a short radiation transport mean free path, radiation travels only a short distance before being scattered or absorbed, the local intensity is the result of radiation from only nearby locations (Zhao, 2012). Generally, the optical thickness of porous medium is much larger than five (Wang et al., 2014; Wang et al., 2012). Therefore, Rosseland approximation method is used in this study due to the simplicity and providing fairly good predictions in comparison with experimental results. Invoking the Rosseland approximation for radiative heat transfer (Modest, 2013) yields qr ¼ 

4rn2 dT 4 3k e dx

ð20Þ

where ke is the extinction coefficient of porous medium, ke = ka + ks. By assuming geometrical optics approximation, the extinction coefficient can be calculated by Tseng and Kuo (2002): 3eð1  /Þ 2d p 3ð2  eÞð1  /Þ ks ¼ 2d p 3ð1  /Þ ke ¼ ka þ ks ¼ dp

ka ¼

ð21Þ ð22Þ ð23Þ

Generally, the Reynolds number in the porous medium is low. However, the characteristic of laminar turbulent transition in the porous medium is different from that in the tube or pipe. The research conducted by Kuwahara et al. (2006) indicates that the turbulent effects need to be considered when the Reynolds number is higher than 160.

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z

k equation   @ ðuqf k Þ @ ðvqf k Þ @ lt @k þ ¼ lþ @x @y @x rk @x   @ lt @k lþ þ þ Gk  qe @y rk @y

y O Quartz window

ð24Þ

x

e equation  l @e lþ t re @x   @ l @e lþ t þ @y rk @y  e þ c1 Gk  c2 qf e k

@ ðuqf eÞ @ ðvqf eÞ @ þ ¼ @x @y @x



Concentrated solar energy Fig. 5. Schematic of the Plano-convex quartz window in the local coordinate.

ð25Þ

where the symbol lt is the turbulent viscosity, rk and re are the Prandtl numbers of the turbulent kinetic energy and turbulent dissipation rate respectively, the symbols c1 and c2 are constant values. The front surface of porous medium receiver is subjected to concentrated solar radiation collected by a parabolic dish concentrator. Prescribed fluid temperature is given at the fluid inlet surface, and zero temperature gradient is given at the fluid outlet surface: Inlet: Tf = 300 K Outlet: oTf/ox = oTf/oy = oTs/ox = oTs/oy = 0 As the maximum fluid phase temperature is as high as 1500 K or higher, the air properties variation with temperature needs to be considered. The correlation of fluid heat capacity change with temperature is (Mulholland, 1995) cp ¼ 1:06  103  0:449T f þ 1:14  103 T 2f  8  107 T 3f þ 1:93  1010 T 4f

ð26Þ

and the fluid conductivity variation with temperature is (Mulholland, 1995) k ¼ 3:93  103 þ 1:02  104 T f  4:86  108 T 2f þ 1:52  1011 T 3f

ð27Þ

Eqs. (26) and (27) are calculated from polynomial curve fits to a data set for 100–1600 K in book (Mulholland, 1995). Besides, the viscosity variation with temperature is computed by the Sutherland Law and the density is treated to ideal gas during the numerical calculation. 5. Results and discussion 5.1. Heat flux distribution on the front surface of receiver Quartz window is placed 10 mm in front of the front surface of porous medium receiver to minimize heat losses. The Plano-convex quartz window put forward by Shuai et al. is introduced in this study to decrease the peak temperature and temperature gradient on the front surface of porous medium receiver, which in turn can increase the

reliability of porous medium receiver (Shuai et al., 2011). As shown in Fig. 5, the bottom surface of the Plano-convex quartz window is a plane and the top surface of the Planoconvex quartz window is a convex surface. The equation of convex surface for the Plano-convex quartz window in the local coordinate system is expressed by x2 þ y 2 þ z2 þ n  z ¼ 0

ð28Þ

In the above equation, the symbol n denotes the characteristic parameter of equation. The curvature of convex surface changes with the variation of n. Fig. 6 shows the heat flux distribution on the front surface of porous medium receiver concentrated by a parabolic dish collector, where the solar irradiance is 400 W/m2 for suitable porous medium receiver working temperature. As seen from this figure, the image radius on the front surface of porous medium receiver is about 30 mm with the peak heat flux magnitude value of 5.19 MW/m2 for the plane quartz window condition. With the introducing of Planoconvex quartz window, the peak heat flux magnitude on the front surface of porous medium receiver decreases. The peak heat flux magnitude on the front surface of porous medium receiver decreases with the increasing of characteristic parameter n. However, the image radius enlarges with the increasing of characteristic parameter n to keep the total energy equilibrium. When the value of characteristic parameter n is 320, the peak heat flux magnitude on the front surface of porous medium receiver is 3.90 MW/m2, and this value decreases to 1.75 MW/m2 when the value of characteristic parameter n is 240. In order to avoid the image radius to be larger than the aperture radius of receiver and working temperature of porous media receiver to be over high, the Plano-convex quartz window with n = 280 is used for the thermal performance analysis of porous medium receiver. Compared to the plane window condition, the peak heat flux magnitude on the front surface of porous medium receiver can be decreased to 47%, whereas the image radius increases about 50%. 5.2. Pressure distribution with different receiver models Fig. 7 presents the pressure distribution contours of the porous medium receiver. Two receiver models are

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(a) Plane window

(b) ξ=320

(c) ξ=280

(d) ξ=240

Fig. 6. Heat flux distribution on the front surface of porous medium receiver calculated by MCRT method (Solar irradiance is 400 W/m2).

considered, the fluid inlet located at the front surface of porous medium receiver and the fluid inlet located at the side wall of porous medium receiver, while the mass flow rate (m = 0.1 kg/s) and porosity (/ = 0.60) for the two models are the same. As seen from this figure, the pressure distribution is nearly 1D in the axial direction for the condition of fluid inlet located at the front surface of receiver and the total pressure decreases gradually from 0 Pa to 127,063 Pa along the fluid flow direction. For the condition of fluid inlet located at the side wall of receiver condition, the pressure distribution is very different from that for the condition of fluid inlet located at the front surface of receiver, the pressure at the fluid inlet surface is 53235.8 Pa and it decreases to 163,777 Pa at the fluid outlet surface. 5.3. Temperature distribution with different receiver models In order to compare the temperature distribution between the condition of fluid inlet located at the front

surface of receiver and the condition of fluid inlet located at the side wall of receiver, the fluid phase temperature distribution and solid phase temperature distribution contours of porous medium receiver are presented in Fig. 8. For the condition of fluid inlet located at the front surface of receiver, the maximum fluid phase temperature is 1253.4 K which locates at the centerline of porous medium receiver and about 0.005 m from the front surface of porous medium receiver. However, for the condition of fluid inlet located at the side wall of receiver, the maximum fluid phase temperature is 1981.8 K which locates at the center point of the front surface of porous medium receiver. For the condition of fluid inlet located at the front surface of receiver, the fluid phase temperature distribution is highly non-uniform from the front surface to x = 0.065 m. From x = 0.065 m to the fluid outlet surface, the fluid phase temperature almost has no variation along the fluid flow direction. The maximum solid phase temperature has a 760.5 K difference when the receiver model shifted from the condition of fluid inlet located at the front surface of receiver to

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(a) Fluid inlet located at the front surface

(b) Fluid inlet located at the side wall Fig. 7. Pressure (in unit of Pa) distribution contours of the porous medium receiver with the Plano-convex quartz window (n = 280, m = 0.1 kg/s, / = 0.60).

the condition of fluid inlet located at the side wall: the maximum solid phase temperature of porous medium receiver is 1386.4 K for the condition of fluid inlet located at the front surface of receiver whereas it increased to 2013.9 K when the fluid inlet located at the side wall. The fluid phase temperature stabilization region locates from L = 0.1 m to the fluid outlet surface for the condition of fluid inlet located at the side wall of receiver. Fig. 9 illustrates the solid phase temperature and fluid phase temperature distributions along the centerline of the porous medium receiver for the two receiver model conditions. As seen from this figure, there is little temperature differences between the solid phase temperature and fluid phase temperature for the condition of fluid inlet located at the side wall. However, there is a non-equilibrium region for the condition of fluid inlet located at the front surface: the fluid phase temperature is 300 K and the solid phase temperature is 1386.4 K at the front surface, the solid phase temperature and fluid phase temperature reaches the thermal equilibrium at x = 10 mm. However, the solid phase temperature and fluid phase temperature at the fluid outlet surface for the condition of fluid inlet located at the side wall are the same as those for the condition of fluid inlet located at the front surface to keep the total energy balance. Due to the high solid phase temperature and mass flow rate, the convective heat transfer coefficient and convective heat transfer is very high, the thermal equilibrium

(a) Tf―Fluid inlet located at the front surface

(c) Tf―Fluid inlet located at the side wall

(b) Ts―Fluid inlet located at the front surface

(d) Ts―Fluid inlet located at the side wall

Fig. 8. Temperature (in unit of K) distribution contours of the two porous medium receiver models with the Plano-convex quartz window (n = 280, m = 0.1 kg/s, / = 0.60).

W. Fuqiang et al. / Solar Energy 108 (2014) 348–359

According to the above analyses, it can be seen that the temperature distribution for the condition of fluid inlet located at the side wall is very different from that for the condition of fluid inlet located at the front surface.

2100

T, ( Κ)

1800

Τs , Front

1500

Τf , Front

1200

Τf , Biliteral

Τs , Biliteral

5.4. Effects of fluid mass flow rate on temperature distribution

900 600 300 0

30

60

90

x, (mm)

120

150

Fig. 9. Comparisons of temperature distribution along the centerline of porous medium receiver with the Plano-convex quartz window between two receiver models (n = 280,m = 0.1 kg/s, / = 0.60).

point is reached with a small flow length. The solid phase temperature and fluid phase temperature stabilized at x =150 mm along the length direction. The solid phase temperature distributions on the front surface for both the condition of fluid inlet located at the front surface of receiver and the condition of fluid inlet located at the side wall of receiver are presented in Fig. 10. As seen from this figure, the solid phase temperature decreases sharply from the centerline to the side wall for the two receiver model conditions. The solid phase temperature at the side wall is 361.1 K for the condition of fluid inlet located at the side wall, whereas it increases to 546.5 K when fluid inlet is fixed at the front surface. The temperature gradient at the front wall for the condition of fluid inlet located at the side wall is much higher than that for the condition of fluid inlet located at the front surface.

As seen from Fig. 9, the temperature differences between the fluid phase and solid phase (TsTf) is very small for the condition of fluid inlet located at the side wall. Besides, the mass flow rate influences on the temperature distribution as well as (TsTf) for the condition of fluid inlet located at the front surface were widely investigated by previous researches (Wang et al., 2014; Wu et al., 2011). Therefore, only the effects of fluid mass flow rate on the solid phase temperature distribution for the condition of fluid inlet located at the side wall are considered in this study. The solid phase temperature distribution is plotted as functions of distance along the length direction which is presented in Fig. 11. Three mass flow rates values, m = 0.10, 0.20 and 0.30 kg/s are examined. The remaining parameters are kept unchanged from those from Fig. 9. Qualitatively similar trends as those shown in Fig. 9 are presented: the solid phase temperature decreases along the length direction. In the same position, the solid phase temperature decreases with the increasing of fluid mass flow rate. For example: the maximum solid phase temperature is 2013.9 K when the mass flow rate is 0.1 kg/s, whereas it decreases to 1427.4 K when the mass flow rate increases to 0.3 kg/s. 5.5. Effects of porosity on temperature distribution The effects of porosity on the temperature distribution for the condition of fluid inlet located at the side wall are presented in Fig. 12, in which the solid phase temperature distribution is plotted as functions of distance along the

2100

2100

Τs , Bileteral Τs , Front

1800

Τs , v=0.1 kg/s Τs , v=0.2 kg/s Τs , v=0.3 kg/s

1800

1500

1500

T, ( Κ)

T, ( Κ)

357

1200 900

1200

900

600 600 300 0

10

20

30

40

50

60

70

y, (mm) Fig. 10. Comparisons of temperature distribution on the front surface of porous medium receiver with the Plano-convex quartz window between two receiver models (n = 280,m = 0.1 kg/s, / = 0.60).

0

30

60

90

120

150

x, (mm) Fig. 11. Effects of fluid mass flow rate on the solid phase temperature distribution for the condition of fluid inlet located at the side wall with the Plano-convex quartz window (n = 280, / = 0.60).

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2100

Τs , φ =0.5 Τs , φ =0.55 Τs , φ =0.60 Τs , φ =0.65

T, ( Κ)

1800

1500

1200

900

Acknowledgements This work was supported by Supported by the National Natural Science Foundation of China (No. 51336002), Program for New Century Excellent Talents in University (NCET-12-0152), Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2011110, HIT.NSRIF. 2015117) and the Foundation for Guide Scientific and Technological Achievements of Qingdao (No. 14-2-4-43-jch). References

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x, (mm) Fig. 12. Effects of porosity on the solid phase temperature distribution for the condition of fluid inlet located at the side wall with the Plano-convex quartz window (n = 280,m = 0.1 kg/s).

length direction. Four porosities, / = 0.50, 0.55, 0.60 and 0.65 are examined. The remaining parameters are kept unchanged from those from Fig. 9. Similar trends of the solid phase temperature distribution along the length direction as those reported in Fig. 9 are observed. As the flow mass rate is kept unchanged, the solid phase temperature increases with porosity increasing. For example, the solid phase temperature is 1797.2 K for / = 0.50, whereas it increases to 2154.6 K when the porosity is increased to 0.65. However, the solid phase temperature at the fluid outlet surface has little variation with the increasing of porosity. 6. Conclusions The heat transfer performance of porous medium receiver with quartz window is numerically studied. With the aim to be more consistent with application, the temperature distribution of porous medium receiver model with fluid inlet located at the side wall is compared with the condition of fluid inlet located at the front surface. The Planoconvex quartz window is introduced with the aim to minimize the thermal stress of porous medium receiver. The following conclusions have been drawn. (1) With the introducing of Plano-convex quartz window, the peak heat flux magnitude on the front surface of porous medium receiver decreases and the image radius increases to keep energy balance. (2) The pressure distribution as well as the temperature distribution for the condition of fluid inlet located at the side wall is very different from that for the condition of fluid inlet located at the front surface. (3) As the flow mass rate is kept unchanged, the solid phase temperature of the porous medium receiver increases with porosity increasing in the same position.

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