Heat transfer and fluid flow analysis of porous medium solar thermochemical reactor with quartz glass cover

International Journal of Heat and Mass Transfer 127 (2018) 61–74

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Heat transfer and fluid flow analysis of porous medium solar thermochemical reactor with quartz glass cover Bachirou Guene Lougou a, Yong Shuai a,⇑, Ruming Pan a, Gédéon Chaffa b, Heping Tan a a b

Key Laboratory of Aerospace Thermophysics of MIIT, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 15001, China Laboratory of Energetics and Applied Mechanics (LEMA), Polytechnic College of Abomey-Calavi, Abomey-Calavi University, 01 P.O. BOX 2009, Cotonou, Benin

a r t i c l e

i n f o

Article history: Received 6 February 2018 Received in revised form 27 June 2018 Accepted 29 June 2018

Keywords: Solar thermochemical Porous medium Radiative transfer Extinction coefficient Diffuse irradiance Thermal performance

a b s t r a c t In this paper, heat transfer and fluid flow of porous media solar thermochemical receiver with quartz glass cover were investigated. The Surface-to-surface radiation model and Rosseland approximation for radiation heat transfer were adopted for the transport of diffused solar irradiance and radiative transfer in the fluid phase and porous medium. An experimental test was conducted on a laboratory-scale solar thermochemical reactor. The effects of structural parameters in term of diffused irradiance intensity, the mass flow rate, heat transfer coefficient, quartz glass and inner cavity wall surface emissivity, the porosity and extinction coefficient that could affect heat transfer and fluid flow performance of the proposed solar cavity receiver were sufficiently investigated. It was found that the substantial drops in temperature were mainly attributed to the thermal losses by radiative, convective and conductive heat transfer. The numerical results are compared with the experimental data for the model validation. The thermal loss at the solar flux inlet of the receiver was obviously inevitable due to the stronger effect of heat transfer coefficient that altered the over increasing temperature and heat flux at the surface of diffuse irradiance. However, the use of optimum pore size and higher porosity material could significantly enhance the thermal performance of porous media solar thermochemical reactor. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Nowadays, the major key challenge of energy accompanied by mitigating the greenhouse effect and environmental pollution hazards rely upon developing solar energy conversion technologies to meet the ever-increasing global demands for clean transportation fuels, chemicals, and electric power. Heat derived from concentrated solar irradiation has been considered the most efficient way of producing commodities such as ammonia [1], metals [2], and fuels [2–4]. However, heat transfer and fluid flow optimization within a cavity receiver are the technical challenges in achieving higher thermal conversion efficiency [5,6]. As reported by Ijaz et al. [7], the thermal process can be improved by considering the material interaction in the presence of heat and mass transfer within a cavity receiver. Moreover, the particle density and the solid volume fraction of nanoparticles significantly affect the convective heat transfer, viscous and thermal entropy generations in the reacting medium [8,9]. Thus, the thermal performance of the solar thermochemical reacting system can be greatly improved

⇑ Corresponding author. E-mail address: [email protected] (Y. Shuai). https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.153 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

by considering the effects of the physical parameters and operating conditions of the solar cavity receiver/reactor [10,11]. The solar thermochemical process typically proceeds with high thermal reduction of raw oxide material (MOox) followed by the release of oxygen to the metal oxide containing vacant oxygen sites in the crystal lattice (MOred). This step requires a high temperature that can exceed 1600 K depending on the oxide material. However, the temperature of the process decreased when the oxidizing gas H2O/CO2 is injected into the reactor. As a result, oxygen vacancies in the reduced oxide material extract oxygen from H2O/CO2 to its initial oxide state (MOox) followed by the release of H2/CO. The solar thermochemical reacting system for converting CO2 emission into storable CO can be described as follows. More uniform and high-temperature distribution throughout the cavity receiver of solar thermochemical reactor is the limiting factor for achieving high efficiency of solar-to-fuel energy conversion. The research and development of high-temperature material processes for use as high-temperature thermochemical energy storage material and the geometry type of solar receiver able to minimize energy losses via heat transfer are the main issues addressed in the usage of concentrated solar radiation as an energy source for solar fuels production [12–15]. Among solar-driven thermochemical reactors, porous media receiver gained increasing

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interests due to the higher heat transfer performance and heat transfer and heat exchanger effectiveness [16–18]. In the recent years, several works have been developed on the thermal performance of porous media receiver in order to optimize the conversion of incident solar radiation within a cavity receiver. Kasaeian et al. [19], in the review of the latest developments on nano-fluid flow and heat transfer in porous media, reported that utilizing porous media can augment the thermal efficiency by improving heat transfer rate in ducts due to the high surface area contact. However, an increase in the pressure drop ratio was observed with the decrease of Richardson number and the volume fraction of nanoparticles and the increase of nanoparticles diameter and inner cavity wall surface emissivity [20]. In order to maximize the thermal efficiency of the porous medium solar receiver, Wang et al. have developed several works on the thermal performance analysis [21,22], and thermochemical reaction performance analysis [23,24]. Milani Shirvan et al. [25] reported that the physical parameters such as Rayleigh number, Darcy number, reactor inclination angles, the thickness of porous material, inner cavity wall surface emissivity, and the surface radiation heat transfer can significantly affect heat transfer performance in a porous media solar thermal reactor. Since radiative heat transfer cannot be neglected when studying the thermal performance of porous media receiver, several researchers adopted Monte Carlo Ray Tracing (MCRT) method, Finite Volume Method (FVM), Rosseland approximation and P1 approximation for radiation heat transfer. They found that porous medium has advantages of the high fluid-solid contact surface, low-pressure drop with good heat and mass transfer performance. Also, the porosity and mean cell size significantly affected the mole fraction of H2 produced. Steinfeld et al. [26] discovered an increasing yield of H2 from their experimental studies conducted on the concentrated solar-driven porous media reactor under realistic operating conditions. Moreover, as reported by Steinfeld et al. [26], Xu et al. [27], Zhao et al. [28], Agrafiotis et al. [29], the fixed ceramic foam in the receiver can serve as the solid reactant. This can avoid the tasks of moving reactant materials by allowing both processes (endothermic and exothermic reaction) to conduct in the same reactor. Besides, Shuja et al. [30], in their study on innovative design of a solar volumetric receiver stated that aerodynamic design of the absorbing blocks could minimize the pressure drop across the receiver inlet and exit ports. Thus, increasing research development on the porous media receiver would significantly improve the solar-driven thermochemical technology for hydrogen and syngas production. Since the solar thermochemical operate at high thermal radiation, the glass cover and the structure of porous material will strongly affect the thermal efficiency, heat losses, heat transfer mechanisms and heat flux distribution within the cavity receiver. Most of the studies suggested that the porous structure greatly affects solar radiative flux distribution within the porous media absorber [31–33]. Zhao et al. [34] found that extinction coefficient is strongly dependent on the porosity and pore size. Also, Rashidi et al. [35] reported that incorporated nanoparticles into the porous materials can improve the properties of porous materials. Regarding the thermochemical reaction performance for H2O/CO2-splitting, Teknetzi et al. [36] and Lorentzou et al. [37] in their studies on NiFe2O4 mentioned that the higher the porosity and optimum pore size distribution, the higher the capability of the samples have to reversibly deliver and pick up their lattice oxygen. Thus, the oxide material can improve the thermal conductivity, heat stability, and chemical resistance of the porous media. Besides, as for the quartz glass cover, several studies have reported that adding window can enhance heat transfer in porous media [38,39]. However, Du et al. [40] demonstrated that thermal radiation loss is inevitable at the entrance of the solar receiver. Thus, taken into account the glass efficiency in the study on porous

media receiver will have relevant effects on the thermal performance of porous media solar thermochemical reactor. In this paper, heat transfer and fluid flow analysis of porous media solar thermochemical reactor with quartz glass cover were investigated. Surface-to-surface radiation model and Rosseland approximation for radiation heat transfer were adopted for predicting the thermal characteristics of both fluid phase and porous media. The reactor temperature distribution and radiation in participating media were investigated along with the effects of cooling system and mass flow rate on the heat transfer and fluid flow performance. Moreover, the effects of quartz glass and inner cavity wall surface emissivity were analyzed and the effects of porosity and extinction coefficient on the reactor thermal performance were reported. The numerical results were compared with those of experiment. 2. Methods 2.1. Physical model Fig. 1 shows the model of porous media solar thermochemical reactor used for the numerical simulation. This study used the model developed by Guene Lougou et al. [41] for advanced thermal analysis of the reactor filled with porous material. Details of the reactor physical parameters can be found in [41,42]. The solar reactor features a cavity-receiver containing fluid domain and porous media. The quartz glass is considered for the glass cover at the surface of diffused solar irradiance and porous NiFe2O4 is considered as porous material in the reacting medium. The reactor is filled with nitrogen gas (N2). The quartz glass region and hot gas outlet are cooled with water. A laboratory-scale solar thermochemical reactor was tested on seven lights solar simulator. The experiment results are shown in Fig. 2. As depicted in Fig. 2a, one light of the solar simulator is used to provide high-temperature heat flux for heating up the absorber in the inner cavity of the reactor. NiFe2O4 porous structure was heated at 5
105 kg/s of nitrogen mass flow rate and three thermocouples were used to measure the temperature variation during the thermal process. The reactor was heated for 1 h 40 min and the thermal behavior of the absorber along with the temperature distribution in the porous medium can be seen in Fig. 2b and c, respectively. The porous medium is heated up via complex coupled heat transfer and fluid flow in the inner cavity receiver. During the experiment, the heating rate of the burner was increased by increasing the light intensity as well as the flow rate from the inlet pores of the reactor. Since the front face of the reactor is heated directly by the light, the increase in the flow rate could volumetrically transport high-temperature heat flux to the porous medium. As a result, the temperature of the absorber increases as a function of time. 2.2. Governing equations The governing equation describes the numerical procedure account of the mass, momentum, and energy equations. The inner cavity of the reactor features fluid phase and porosity zone. The governing equation describing the fluid phase of the reactor is given by the following equations.

r  ðquÞ ¼ 0

ð1Þ


2 3

qðu  rÞu ¼ rP þ r  lðru þ ðruÞT Þ  lðr  uÞ qC p u  rT ¼ r  q þ Q þ Q p þ Q v d

 ð2Þ ð3Þ

B. Guene Lougou et al. / International Journal of Heat and Mass Transfer 127 (2018) 61–74

63

Fig. 1. Schematic diagram of porous media solar thermochemical reactor.

where q is the density, u is the velocity vector, P is the pressure, l is the dynamic viscosity, T is the temperature, C p is the heat capacity at constant pressure, q is the heat flux vector, Q is the heat sources, Q p is the work done by pressure changes and Q v d is the viscous dissipation.

q ¼ krT  kR rT

ð4Þ

where k is the thermal conductivity and kR is the irradiative conductivity. The laminar flow is adopted for the simulation and the viscous dissipation can be expressed as follows.

Q v d ¼ s : ru

ð5Þ

where s is the viscous tensor. The governing equations describing the porous media filled with fluid is given by the following equations.

r  ðqp up Þ ¼ 0 1

ep

qp ðup  rÞup

ð6Þ 1

ep


  2 1 1 ¼ rP þ r  l rup þ ðrup ÞT  l ðr  up Þ 3 ep ep    lj1 þ bF jup j up ð7Þ

qp C pp up  rT ¼ r  qp þ Q þ Q v d

ð8Þ

where qp is the density of porous matrix, up is the velocity within the pores, ep is the porosity, j is the permeability tensor in the porous media, bF is the Forchheimer drag option, C pp is the specific heat

capacity of porous matrix and qp is the heat flux vector in the porous medium. The velocity within the pores and the heat flux vector is defined as:

up ¼ u=ð1  hp Þ qp ¼ keff rT  kR rT

ð9Þ ð10Þ

where u is the velocity computed from the fluid flow, hp is the volume fraction and keff is the effective thermal conductivity. By considering the thermal conductivity of porous matrix kp and the volume fraction, the effective thermal conductivity can be expressed as follows [43].

keff ¼ hp kp þ ð1  hp Þk

ð11Þ

The radiative source term r  qr is calculated from the radiation intensity considering surface-to-surface radiation heat transfer model. Accordingly, diffuse irradiance intensity at the diffuse surface is given by the following equations [44].

n  q ¼ eðG  eb ðTÞÞ

ð12Þ

J ¼ ð1  eÞG þ eeb ðTÞ

ð13Þ

where n is the transparent media refractive index, e is the surface emissivity, G is irradiation, eb ðTÞ is the blackbody hemispherical total emissive power and J is the surface radiosity. At a given point, the irradiation is split into three contributions as follows.

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(a)

1000

(c) Temperature (oC)

800 600 Temperature distribution in porous medium

400 200

0

20

40

60

80

100

Time (min)

(b) Fig. 2. Experiment setup of porous media solar thermochemical system: (a) solar thermochemical coupled to the solar simulator; (b) porous medium behavior at high temperature; (c) temperature distribution in the porous medium during the heating phase.

ð16Þ

where ja is the absorption coefficient and Ib is the Blackbody intensity. Considering the radiative intensity IðX; sÞ at a given position s following the direction X, G and the heat flux qr in the gray media can be defined by the following expressions:

ð17Þ

G¼

G ¼ Gm ðJÞ þ Gamb þ Gext

ð14Þ

Gamb ¼ F amb eb ðT amb Þ

ð15Þ

Gext ¼ Gext

Dir

þ Gext

Diff

eb ðTÞ ¼ n2 rT 4

where Gm is the mutual irradiation coming from other boundaries in the system, Gamb is the ambient radiation source, F amb is an ambient view factor, T amb is the assumed far-away temperature in the directions included F amb , Gext is the irradiation from external radiation sources, n is the refractive index, and r is the Stefan-Boltzmann constant equal to 5.67
108 W/(m2 K4). By combining Eqs. (13) and (14), the radiosity at the diffuse surface can be given as follows.

J ¼ ð1  eÞGm ðJÞ þ Gamb þ Gext þ en2 rT 4

ð18Þ

The porous media is considered not completely transparent. Thus, it is assumed that the radiation rays may interact with the medium and the system will compute and add the radiative heat source term Q r given by the following equation.

Q r ¼ r  qr ¼ ja ðG  4pIb ðTÞÞ

ð19Þ

Z

4p

Z qr ¼

4p

IðXÞdX

ð20Þ

IðXÞXdX

ð21Þ

By taking account the radiation absorbed and scattering, the radiative transfer equation can be given as follows [45].

X  rIðX; sÞ ¼ ja Ib ðTÞ  bIðX; sÞ þ

rs 4p

Z 4p

IðX; sÞ/ðX0 ; XÞdX0

ð22Þ

0

where IðX; sÞ is the radiation intensity at the position s in the X direction; Ib ðTÞ is the blackbody radiation intensity; ja is the absorption coefficient; b is the extinction coefficient; rs is the scattering coefficient; /ðX0 ; XÞ is the scattering phase function. The blackbody radiation intensity Ib ðTÞ is defined as:

Ib ðTÞ ¼

n2 rT4

p

ð23Þ

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In this paper, among of the approximation methods for solving the radiative transfer equation, Rosseland approximation is adopted as discretization method for radiation in participating media [46]. Accordingly, the radiative heat flux is approximated as follows.

qr ¼ 

4r rðn2 T 4 Þ 3b

ð24Þ

The numerical simulation is carried out considering constant refractive index. In this case, the radiative heat flux can be simplified as follows.

qr ¼ kR rT

ð25Þ

where the thermal conductivity kR is modified as follows.

kR ¼

16n2r rT 3 3b

ð26Þ

firstly described by the fluid phase governing equations while heat transfer and fluid flow in the burner region is described by the porous medium governing equations. The flow balance between fluid zone and porous region is attributed to the volume fraction of the absorber. Afterward, the exhaust hot flux from the porous medium is described by the fluid phase governing equations. Besides, the radiation models, including S2S and Rosseland approximation for radiation heat transfer model is used for describing the thermal characteristics of the fluid phase and porous medium, respectively. A no-slip condition is considered for the inner cavity wall and Laminar flow conditions (Re << 150) are assumed for all the domains. The initial temperature throughout the reactor including gas and reactor cavity wall temperature is set at 293.15 K and the diffuse irradiance is considered as a heat source. The convergence criterion was 105 for all the equations. The results obtained are postprocessed for further analyze.

The extinction coefficient is evaluated as the sum of absorption and scattering coefficients as follows [47].

2.5. Model validation

b ¼ ja þ rs

The model validation was made by comparing the measured temperature with that of the numerical simulation results. The numerical simulation was carried out considering 50 kW/m2 of diffuse irradiance at the surface of concentrated solar flux inlet region of the receiver, at 1 atm, and 1
105 kg/s of mass flow rate. The temperature changes along the centerline of the reactor were considered during the experiment. The temperature at the locations, including the front region (0.014 m), porous medium (0.085 m), and the back region (0.15 m) were selected. The experimental measurement temperature compared to that of the numerical result is depicted in Fig. 3. As indicated in Fig. 3, a temperature difference of 47.79 K, 35.59 K, and 52.19 K was observed in the front region, porous medium, and back region, respectively. The predicted temperature distributions in both fluid phase and porous region are close to the measured temperature. Thus, the numerical results agree well with the experimental data. The agreement observed indicates the accuracy of this model for analyzing the thermal performance of solar thermochemical reactor.

ð27Þ

ja ¼

3eð1  ep Þ 2ds

ð28Þ

rs ¼

3ð2  eÞð1  ep Þ 2ds

ð29Þ

where ds is the mean cell size. 2.3. Boundary conditions Where h is heat transfer coefficient, Idiff is the diffuse irradiance applied at the quartz glass surface and the negative normal direction is selected for the radiation direction. The reference pressure and temperature are 1 atm and 293.15 K, respectively. The prescribed fluid temperature of 293.15 K is given at the fluid inlet surface, and zero temperature gradient is given at the fluid outlet surface (see Table 1).

3. Results and discussion

The numerical simulation is performed using COMSOL Multiphysics [46]. As indicated in Fig. 1, the fluid domain including the front region of the reactor cavity, the inlets, and the outlet region are modeled as fluid domains and assumed to be a nonparticipating media for radiation. The reactor internal field consisting of the reacting medium is modeled as a porous domain filled with fluid and assumed to be a participating media for radiation. Moreover, the inner cavity of the reactor is set up by selecting the thermodynamic and thermophysical properties of the materials used. The fluid flow inside the reactor is assumed as weakly compressible and transparent to radiation. According to this arrangement, a stationary study is considered and the physic interfaces, including heat transfer in porous media, laminar flow, and non-isothermal flow are coupled for describing the thermal performance analysis of the reactor. The front region of the reactor is Table 1 Boundary conditions and initial conditions. Boundary fields

Temperature

Velocity

Inlet Quartz glass

293.15 K Idiff ðW=m2 Þ 293.15 K 293.15 K q0 ¼ h  ðT amb  TÞ @T=@n ¼ 0

Mass flow rate (kg/s) 0

Wall Initial values External boundary Outlet

@u=@n ¼ 0 0 0 Pressure-Outlet

3.1. Reactor temperature distribution and radiation in participating media The temperature distribution along the flow direction of the reactor and radiative flux at the participating media was evaluated by considering diffuse solar irradiance intensity as shown in Fig. 4. As indicated in Fig. 4a and b, the inner cavity of the reactor is more

Experiment result Simulation result

1800 1600

Temperature (K)

2.4. Numerical solution method

1400 1200 1000 0.00

0.03

0.06

0.09

0.12

0.15

Axial length (m) Fig. 3. Measured temperature compared to the predicted temperature distribution along the axial direction of the reactor.

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1600

2

Radiation flux (W/m )

1800

Temperature (K)

70000

2

20 kW/m 2 30 kW/m 2 40 kW/m 2 50 kW/m 2 60 kW/m 2 70 kW/m

2000

1400 1200 1000 800 (a) 0.00

0.03

0.06

0.09

0.12

(b)

60000 50000 40000 30000 20000 10000

0 0.05 0.06 0.07 0.08 0.09 0.10 0.11

0.15

Axial direction (m) 48000 2

Radiation losses (W/m )

1600

Temperature (K)

Axial direction (m)

Reactor temperature difference T_in media T_out media

1800

1400 1200 1000 800 (c)

600 20

30

40

50

60

2

20 KW/m 2 30 KW/m 2 40 KW/m 2 50 KW/m 2 60 KW/m 2 70 KW/m

Radiation loss at the down front media Radiation difference in the media

42000 36000 30000

(d)

24000 18000 12000 6000

70

20

30

40

50

60

70

2

Diffuse irradiance intensity (kW/m )

2

Diffuse irradiance intensity (kW/m )

Fig. 4. Temperature distribution along the flow direction of the reactor and radiation flux in the participating media at 1
105 kg/s of mass flow rate and 1 atm: (a) reactor temperature distribution at different diffuse solar irradiance intensities; (b) radiation in the participating media; (c) and (d) effect of diffuse solar irradiance intensity on the reactor thermal performance. T_in: Temperature of heat transfer fluid entering the porous media; T_out: Temperature of heat transfer fluid leaving the porous media.

1100

1360 Temperature drop at reactor outlet Temperature predicted at the media outlet

1080

1800 1750 1700 1650

(a)

1060

1320

1040

1300

1020

1280

1000

1260

980

1240

960 (b)

1600 100

200

300

400

500

600

700

1340

100

800

2

Temperature (K)

Temperature drop at radiation inlet Temperature drop at media inlet

Temperature (K)

Temperature (K)

1850

1220 200

300

400

500

600

700

800

2

Heat transfer coefficient (W/(m .K))

Heat transfer coefficient (W/(m .K)) 12000

2

2

Irradiance flux (W/m )

10000

48000

Irradiance flux (W/m )

50000

8000

46000 Radiation flux at the media Radiation loss at the media

44000

6000 4000

42000

2000

40000

(c) 38000

0

0

100 200 300 400 500 600 700 800 2

Heat transfer coefficient (W/(m .K)) Fig. 5. Temperature drop and radiation losses due to the effect of heat transfer coefficient at the surface of the cooling system: (a) effect of the cooling system at the diffuse irradiance interface; (b) effect of cooling system at the outlet of the reactor; (c) effect of cooling systems and external boundary condition on the radiation in the participating media.

B. Guene Lougou et al. / International Journal of Heat and Mass Transfer 127 (2018) 61–74

heated when the diffuse solar irradiance was increased from 20 to 70 kW/m2. The higher temperature observed in the front region of the reactor is obvious due to the higher emitted radiative heat flux because the solar irradiance is diffused directly at this part [40]. According to the literature related to the technologies of solar thermochemical for hydrogen and syngas production [48,49], different values of temperature predicted and radiative flux distribution obtained could response on the thermal energy required for carrying out the chemical reaction. Moreover, the boundary temperature distribution and radiation losses are depicted in Fig. 4c and d. The reactor temperature difference increases as the solar irradi-

67

ance increases as well. The temperature difference of the internal field of the reactor increased to 45.7–54.3% and 47.6–52.4% when the solar irradiance was increased from 20 to 40 kW/m2 and 40 to 60 kW/m2, respectively. As a result, both temperatures of heat transfer fluid entering the porous media and those leaving the porous media increased when the inner cavity of the reactor was heated up [40]. This can also be observed in the participating media where it can be seen the radiative flux difference increased with increasing irradiance intensity. However, radiative heat losses gradually increase as the solar irradiance increases. An increase in the radiative heat loss of 11.34–19.15% is obtained when the dif-

Fig. 6. Qualitative temperature distribution due to the effect of cooling system at 50 kW/m2, 1 atm, 200 W/(m2 K) of heat transfer coefficient, and 1
105 kg/s of mass flow rate: (a) surface of diffuse irradiance; (b) reactor body; (c) surface of the cavity of the reactor; (d) Slice cut of the inner cavity of the reactor.

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fuse irradiance intensity was increased from 20 to 40 kW/m2. In contrast to the diffuse irradiance lower than 40 kW/m2, increasing the irradiance intensity to 60 kW/m2 led to a gradual decrease in the heat loss to 19.15–16%. Besides, the higher radiation heat loss in the participating media was obtained at higher irradiance flux [32].

Qualitative temperature distribution in the presence of cooling system and weighted average temperature predicted at the boundary fields of the reactor are depicted in Figs. 6 and 7. The effect of local convective heat exchange between the reactor external body and ambient air was taken into account by considering 10 W/(m2 K) of local convective heat transfer coefficient. As shown in Fig. 6, the external heat source can significantly affect the reactor thermal

3.2. Effect of heat transfer coefficient on the surface of the cooling system of the reactor The drop of temperature and radiative flux losses due to the effect of the cooling system was evaluated by considering constant convective heat transfer coefficients at the irradiated side and hot fluid outlet surface of the reactor [12] as shown in Fig. 5. A cooling system is applied to the reactor at the diffuse irradiance region and the exhaust gas region in order to protect the quartz glass window against unexpected increasing temperature and lower down the product gas temperature to fit the product gas analysis equipment, respectively. As can be seen in Fig. 5a and b, increasing heat transfer coefficient altered the temperature predicted at both radiation inlet and the reactor outlet regions. As a result, significant drops in temperature were observed at the porosity media which consists of the reacting medium. The temperature at the quartz glass area and reacting medium can be altered to 67.66 K and 75.45 K, respectively by varying heat transfer coefficient from 100–400 W/(m2 K). Further increased heat transfer coefficient from 100 to 800 W/(m2 K) led to a considerable decrease in the temperature of 99.52 K and 105.65 K at the quartz glass area and reacting medium, respectively. Increasing the heat transfer coefficient results in a stronger convective cooling of the diffuse surface, as well as the outlet surface of the solar receiver [12]. Moreover, as shown in Fig. 5c, significant drops in the temperature at the reacting medium can be associated to the higher attenuation of radiative heat flux followed by the increase in the radiation losses with increasing heat transfer coefficient. Furler [50] experimentally observed that the water-cooling system can lower the radiative power input through the aperture by up to 15%. Thus, both surface temperature and heat flux can be altered by changing heat transfer coefficient.

1800 1757.68 1733.14 1683.57

(a): 0.5x10-5 kg/s

(b): 1x10-5 kg/s

(c): 3x10-5 kg/s

(d): 5x10-5 kg/s

1500 1200 903.06

900 600

501.09

305.59

300 0

bhs1

bhs2

bhs3

hf1

(e)

1800

517.36

hf2

hf3

294.62

Inflow Outflow

Boundary fields bhs = boundary heat source; hf = heat flux; Inflow = gas flow inlet; Outflow = Outlet flow Fig. 7. Weighted average temperature distribution at the boundary fields of the reactor at 50 kW/m2, 1 atm, 200 W/(m2 K) of heat transfer coefficient, and 1
105 kg/s of mass flow rate: bhs1: temperature predicted at the surface of diffuse irradiance; bhs2: temperature predicted at the cavity receiver; bhs3: temperature predicted at the aperture; hf1: temperature at the cooling system surface; hf2: temperature at the reactor external body; hf3: temperature at the outlet cooling system surface; Inflow: temperature of inlet gas flow; Outflow: temperature of outlet gas flow.

Temperature drop (K)

Temperature (K)

Weighted average temperature (K)

1700

0.5M 1M 2M 3M 4M 5M

1600 1500 1400 1300 0.00

0.01

0.02

0.03

0.04

Axial length (m)

M = 10-5 kg/s Fig. 8. Fluid flow temperature drop due to the effect of the mass flow rate of inlet gas at 50 kW/m2 and 1 atm: (a, b, c and d) qualitative temperature distribution; (e) quantitative temperature distribution.

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performance by cooling down unexpected increasing boundary field temperature. It seems that energy can be transferred from solid to the fluid by conduction in the bottom of thermal boundary [40]. Thus, providing the cooling system can protect the reactor against high concentrated solar thermal temperature. However, the desired reaction temperature would depend on the amount of heat flux applied to the reactor along with the capacity of the cooling system since energy required for heating active material inside the reactor can be reduced by thermal losses. For instance, the results indicate that low-temperature drop could be obtained for lower heat losses and more uniform distribution of absorbed incoming radiation. 3.3. Effect of mass flow rate on heat transfer and fluid flow performance The flow and temperature changes due to the effect of mass flow rate of inlet gas are shown in Fig. 8. Increasing the rate of fresh feeding gas significantly affected the fluid flow and temperature

distribution in the inner cavity of the reactor [24,32]. As depicted in Fig. 8e, increasing drop in temperature from 17.82 to 259.43 K was observed when the mass flow rate was increased to 0.5
105 to 3
105 kg/s. Moreover, further increased the mass flow rate led to a remarkable drop in temperature reported to 423.48 K in the region of the jet. Thus, the flow rate of feeding gas could significantly influence the energy efficiency of the system, as well as the chemical reaction [24,42,49] since a large amount of energy would be consumed to heat the gas up to the desired reaction temperatures. Moreover, as the chemical reaction rate is highly controlled by fluid phase temperature and mass transport, the species conversion efficiency will decrease with increasing the gas velocity [23]. Therefore, the design of solar thermochemical reacting system should take into account the configuration of injection nozzles in order to avoid considerable drops in temperature due to the increased thermal radiation loss in the reacting medium. As shown in Fig. 9a, notably, the gas flow once entered in the reactor was rapidly heated up to the reactor temperature. Conse-

4

5.0x10

(a) 2

1600 1400 0.5M 1M 2M 3M 4M 5M

1200 1000 0.00

0.03

0.06

(b)

4

4

4.0x10

4

3.5x10

4

3.0x10

4

2.5x10

4

2.0x10

4

1.5x10

4

1.0x10

0.09

0.12

0.05

0.15

0.06

3.5x10

4

3.0x10

4

2.5x10

4

2.0x10

4

1.5x10

4

1.0x10

4

5.0x10

3

0.08

0.9 Radiation losses radiation flux shifted

0.09

0.10

0.11

-5

0.5x10 kg/s -5 1x10 kg/s -5 2x10 kg/s -5 3x10 kg/s -5 4x10 kg/s -5 5x10 kg/s

0.6

Velocity (m/s)

2

Radiation flux (W/m )

4

0.07

Participating media (m)

Flow direction (m)

4.0x10

-5

0.5x10 kg/s -5 1x10 kg/s -5 2x10 kg/s -5 3x10 kg/s -5 4x10 kg/s -5 5x10 kg/s

4.5x10

Radiation flux (W/m )

Temperature (K)

1800

0.3 0.0 -0.3 -0.6

(c)

(d)

0.0

0

1

2

3

4

5

0.00

0.02

Mass flow rate (kg/s)

0.04

0.06

0.08

0.10

Flow direction (m)

8 7

Velocity (m/s)

6 5 4

0.5M 1M 2M 3M 4M 5M

(e)

3 2 1 0 0.1 1

0.1 2

0.13

0.14

0.15

Flow direction (m) Fig. 9. Effect of mass flow rate on the heat transfer and fluid flow performance at 50 kW/m2 and 1 atm: (a) temperature distribution; (b) radiation heat flux; (c) Effect of mass flow rate in the participating media; (d) velocity of the flow in fluid phase and porous media; (e) velocity of outflow.

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3.4. Effect of quartz glass and inner cavity wall surface emissivity on the reactor thermal performance Fig. 10 describes the effect of quartz glass window by considering typical values (0.41–0.95) of quartz glass emissivity under high thermal temperature. The effect of glass emissivity on the reactor thermal performance was highly observed at the fluid phase where the thermal diffusivity, fluid phase temperature, and the internal energy decreased with increasing the glass emissivity as shown in Fig. 10a, b, and d. The decrease in the internal energy resulted in the drop in temperature which can be ascribed to the rate of high flux thermal diffusion towards the flow direction of the reactor [38]. Afterward, the porosity media exhibited a very close temperature and internal energy changes with increasing the glass emissivity. As the porous media is quite far from the glass window,

1800 (b)

(a) 3.12 3.09

gl gl

3.06

gl gl

3.03

gl

0.00

Temperature (K)

-4

the pore cell sizes since the outflow velocity was very higher than that of the inflow. Thus, heat transfer between the fluid phase and the solid phase could increase by increasing the mass flow rate [32].

3.15

2

Thermal diffusivity (x10 m /s)

quently, the temperature distribution in the porous medium and reactor outlet region increases due to the convective heat transfer correlation and the thermal conductivity of the heat transfer fluid in the medium [40]. Also, this phenomenon can be associated with the increase in the thickness of thermal nonequilibrium. During the experiment, it was found that the heating rate of porous medium could be increased by increasing the flow rate. However, Fig. 9b and c indicated significant radiation losses with increasing the mass flow rate in the participating media. The radiative heat flux is highly shifted towards the fluid direction of the reactor since the hot flow velocity was highly increased with increasing the mass flow rate as shown in Fig. 9d and e. Therefore, larger velocity is beneficial for the enhancement of the convective heat transfer in contrast to radiative heat transfer. Besides, higher velocity of fluid flow was observed in the fluid zone while lower and more uniform fluid flow velocity was obtained in the porosity zone. Thus, the porous skeleton has great influence on the fluid flow [40]. Therefore, a significant decrease in the fluid flow velocity can be attributed to the volume fraction of the burner. Fig. 9e indicated that the fluid flow velocity is strongly dependent on the mass flow rate and

= 0.41 = 0.68 = 0.75 = 0.8

1780 1760

= 0.68

gl

= 0.75

gl

1740

= 0.8

gl

= 0.95

gl

= 0.95

0.01

= 0.41

gl

0.02

0.03

0.04

1720 0.00

0.01

Fluid phase length (m)

gl

Temperature (K)

gl

1600

gl gl

1500

gl

= 0.68 = 0.75 = 0.8 = 0.95

1400 1300 0.05 0.06 0.07 0.08 0.09 0.10 0.11

(d)

920 912 904 gl

896

gl

888

gl gl

880

gl

0.00

Internal energy (KJ/kg)

gl gl gl gl

800

= 75 =8 = 0.95

0.02

0.03

0.04

Fluid phase length (m)

860

820

= 0.41 = 0.68

0.01

Porous media length (m)

840

0.04

928

= 0.41

(c)

0.03

Fluid phase length (m)

Internal energy (KJ/kg)

1700

0.02

gl

= 0.41 = 0.68 = 0.75 = 0.8 = 0.95

780 760 740

(e)

0.05 0.06 0.07 0.08 0.09 0.10 0.11

Porous media length (m) Fig. 10. Effect of quartz glass surface emissivity at 50 kW/m2, 1 atm, and 1
105 kg/s of mass flow rate: (a) thermal diffusivity in fluid phase; (b) and (c) fluid phase and porous media temperature distribution, respectively; (d) and (e) fluid phase and porous media internal energy changes, respectively.

71

12 9 6

Fluid phase Inlet of porous media Outlet of porous media

3 0.2

0.4

0.6

0.8

1.0

10 (c)

0.020 0.015 0.010 0.005 0.000

(b) 0.2

0.4

8 6 Fluid phase Porous media

4 2 0

0.2

0.4

0.6

0.8

1.0

Inner surface emissivity

0.6

0.8

1.0

Inner surface emissivity 93

Porous media Blackbody radiation Radiation loss at porous media

2

Internal energy drop (KJ/kg)

Inner surface emissivity

Fluid phase Porous media

0.025

90

6000 5500

87 84

5000 (d)

4500

81 78

Radiation loss

-4

15

Blackbody radiation (kW/(m sr))

Temperature drop (K)

(a)

0

0.030

2

18

Thermal diffusivity drop (x10 m /s)

B. Guene Lougou et al. / International Journal of Heat and Mass Transfer 127 (2018) 61–74

4000 3500 0.2

0.4

0.6

0.8

1.0

Inner surface emissivity

Fig. 11. Effect of inner cavity wall surface emissivity: (a) temperature drop; (b) thermal diffusivity drop; (c) the drop in internal energy; (d) Blackbody radiation and radiation losses in the porous media.

the less effect of glass emissivity observed can be associated with the decrease in the glass thermal efficiency with increasing the centerline of the reactor. However, the use of glass with low emissivity could improve the thermal performance of solar thermochemical reactor [38]. In addition to the glass emissivity, the emissivity of inner cavity wall of the reactor significantly affects both fluid phase and porous media thermal performances [21,39]. As shown in Fig. 11a and b, the drop in temperature in both phases’ increases as the drop in the rate of diffused thermal energy increases with increasing emissivity of inner cavity wall of the reactor. As a result, the drop in the internal energy increases. The radiation heat transfer is significantly affected by emissivity of inner surface. Thus, the use of ceramic materials with higher surface emissivity in the design of solar thermochemical reactor could result in significant drops in thermal energy necessary to drive the chemical reaction. This can be quite a bit observed in Fig. 11d where the decrease in Blackbody radiation with increasing the surface emissivity led to considerable losses of radiation heat flux. Therefore, the higher drop in the temperature in porous media could be ascribed to the radiation losses since the heat loss caused by radiation is very sensitive to the inner surface temperature [40]. 3.5. Effects of porosity and extinction coefficient on the reactor thermal performance Heat transfer characteristics of porous media solar thermochemical reactor were evaluated by considering the variation of porosity from 0.5 to 0.95 as shown in Fig. 12. The increase in the porosity greatly affected the temperature distribution throughout the inner cavity of the reactor [12,31,32]. As depicted in Fig. 12a, higher temperature distribution was obtained in the porous media with increasing the porosity of the media to 0.5–0.7. Moreover, the temperature distribution gradually increases and becomes closer as the porosity further increases to 0.95. Thus, the temperature

of porous media and thickness of thermal equilibrium increases with the medium porosity [21]. In contrast to porous media, an increase in the temperature was observed in the phase downstream of the porous media with decreasing the porosity to 0.5. This phenomenon can be attributed to the accumulated heat flux leading to the increase in the thickness of thermal equilibrium in the fluid phase. Moreover, the thermal characteristic of the reactor regarding the heat transfer mechanism can be seen in Fig. 12(b)– (e). Higher convective heat flux was obtained in both fluid phases as shown in Fig. 12b and d. However, porosity does not any effect on the convective heat flux in the phase downstream of the porous media as shown in Fig. 12b while significant increases in the convective heat flux were observed in the fluid zone in the back phase of porous media with increasing the porosity of the medium as shown in Fig. 12d. Thus, as shown in Fig. 12c, increasing the porosity of the media considerably enhanced heat and mass transfer in porous media solar thermochemical reactor via convective heat transfer [31,32]. Besides, as indicated in Fig. 12e, the effect of conductive heat transfer cannot be neglected in the thermal performance of porous media solar thermochemical reactor. As reported by DU [40] high thermal conductivity could ensure the uniformity of temperature distribution inside the porous skeleton. As shown in Fig. 12f, significant heat losses of conductive flux can occur as a function of the porosity of the medium [31]. Increased the porosity of the medium led to the increase in the conductive heat loss at the inlet of the porous media while the conductive heat loss decreases at the outer surface of the porous media with the porosity. In contrast to conductive heat loss, as shown in Fig. 12g, the radiative heat loss, convective heat loss, as well as total heat flux loss can be decreased by increasing the porosity of the medium [35]. Compared to the convective flux, heat transfer by thermal conductivity has little impact on the temperature distribution in the porous media receiver [22]. Thus, the thermal efficiency of ceramic foam absorbers depends on their porosity [12]. Also, Steinfeld [17] and Teknetzi [36] reported that the reacting

B. Guene Lougou et al. / International Journal of Heat and Mass Transfer 127 (2018) 61–74

(a)

1600 1500 1400 1300 0.02

0.04

0.06

0.08

15000 10000 5000 0

0.10

(b)

0.00

0.01

2

Convective heat flow (W/m )

2

Convective heat flux (W/m )

5500

5000

4500 (c) 4000

0.06

0.08

0.02

0.03

0.04

0.05

Flow direction (m)

Axial length (m) 250000 200000 150000 100000 50000

(d) 0 0.11

0.10

0.12

0.13

0.14

2

Conductive heat loss (W/m )

(e)

2

Conductive heat flux (W/m )

1500 1200 900 600 300 0 0.00

0.03

0.06

0.09

0.12

0.15

180 500 150 400

Inlet porous media Pourous media outer surface

300

60

100 0

120 90

200

30 (f) 0.5

0.6

0.7

0.8

0.9

0

Porousity

Flow direction (m) +2

300

Radiative heat loss (x10 ) Convective heat loss Total heat flux loss

250

2

Heat flux (W/m )

0.15

Flow direction (m)

Fluid flow direction (m)

2

0.00

20000

Conductive heat loss (W/m )

Temperature (K)

1700

2

1800

Convective heat flux (W/m )

72

200 150 100 50 (g) 0

0.5

0.6

0.7

0.8

0.9

1.0

Porosity Fig. 12. Effect of porosity on the reactor thermal performance: (a) temperature distribution; (b) convective heat flux in the phase downstream of the porous media; (c) convective heat flux in the porous media; (d) convective heat flux in the back phase of porous media; (e) conductive heat flux; (f) conductive heat losses; (g) effect of porosity on heat transfer.

medium has the highest capability of lattice oxygen exchanges when it is characterized by highest porosity and optimum pore size distribution. Therefore, the choice of highest possible porosity materials for solar cavity receiver could enhance heat and mass transport within the reactor thereby improving the reactivity of chemical species involved. The effects of extinction coefficients in term of absorptivity and scattering on the reactor thermal performance was evaluated by varying the mean cell size (ds) form 1 to 2.25 mm as shown in Fig. 13. The effects of absorptivity and scattering were observed

in both fluid phase and porous media. As shown in Fig. 13a, increasing the extinction coefficients by increasing both absorptivity and scattering led to the increase in the temperature distribution in the fluid phase. Thus, volumetric heat transfer coefficient increases as the mean cell size decrease in the fluid phase [23,31]. However, increasing the mean cell size resulted in the increase in temperature in the participating media due to the increase in the permeability that enhanced the convective heat transfer. The extinction coefficient decreased with the increase in the pore size [34]. Considering the value of extinction coefficient

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B. Guene Lougou et al. / International Journal of Heat and Mass Transfer 127 (2018) 61–74

1800

(a)

1700

s

= 67.5;

1500

= 73.33 = 82.5 s

= 77.14; = 90;

1400

= 108;

1300 0.00

= 135;

0.02

s

= 94.28

= 110 s s s

= 132

1600 1500 1400

= 165

0.04

= 300 = 208.33 = 225.33

1300 0.06

0.08

0.10

0.00

140000

s

s

= 77.14;

120000

= 108; = 135;

100000

= 135;

0.04

0.06

0.08

0.10

s

= 82.5 s

= 94.28

= 110 s s s

= 132 = 165 = 73.33

80000 60000

20

120

= 73.33

= 75.5; = 90;

0.02

Flow direction (m)

Temperature drop (K)

= 60;

2

Blackbody radiative flux (W/m sr)

Flow direction (m)

2

= 60;

Fluid flow Porosity zone Porous media radiation loss

100

16

80

12

60 8

40 20

(d)

4

(c) 0.05 0.06 0.07 0.08 0.09 0.10 0.11

0

Flow direction (m)

20

25

30

35

Media radiative heat loss (kW/m )

1600

(b)

1700

Temperature (K)

Temperature (K)

1800

40

45

0

Optical thickness

Fig. 13. Effects of extinction coefficients and optical efficiency evaluation: (a) and (b) effect of extinction coefficients on temperature distribution; (c) effect of extinction coefficients on Blackbody radiation distribution; (d) optical efficiency evaluation.

resulted in higher temperature distribution in the fluid phase, as shown in Fig. 13b, lowering the extinction coefficient by decreasing the scattering resulted in the increase in temperature distribution in the porous media. Thus, the drop in the temperature in porous media solar thermochemical reactor can be attributed to the higher radiation scattering [17,51]. Moreover, higher attenuation in the Blackbody radiative flux was observed with increasing the extinction coefficients as shown in Fig. 13c. This also reflects the higher drops in the temperature with absorptivity and scattering in the porous media. Besides, as can be seen in Fig. 13d, increased the optical thickness could result in considerable losses of radiative flux and the drops in temperature as well. The decrease in the fluid phase temperature with optical thickness indicated that moderate optically thick medium could result in effective volumetric absorption of solar radiation [17,18]. The increasing drop in radiative flux with the increase in optical thickness can be associated with the decrease in the permeability which may increase the scattering in the porous medium [17,33]. Thus, the solar thermochemical reactor can be optimized by taking into account the optical efficiency which, however, can be optimized for efficient radiative penetration and volumetric absorption by rearranging the pore size and porosity.

(2)

(3)

(4)

(5)

the diffuse surface of the reactor that altered both surface temperature and heat flux. The increase in the mass flow rate resulted in significant drops of fluid phase temperature and radiation losses in the participating media. The emissivity of inner cavity wall of the reactor significantly affected both fluid phase and porous media thermal performances. Moreover, the use of glass cover with low emissivity could improve the thermal performance of the solar thermochemical reactor. A higher drop of temperature in the porous media could be ascribed to heat loss caused by radiation. Heat transfer and fluid flow were considerably enhanced by increasing the porosity of the medium. In contrast to fluid phase domain, the increase in the mean cell size resulted in the increase in the temperature in the participating media. Heat losses by radiative and convective, as well as total heat flux loss can be reduced by increasing the porosity of the medium. However, the conductive heat transfer cannot be neglected in the thermal performance of porous media solar thermochemical reactor. Optimum pore size and higher porosity could favor efficient penetration and volumetric absorption of radiative heat flux in porous media solar thermochemical reactor.

4. Conclusion This study analyzed heat transfer and fluid flow of porous media solar thermochemical receiver with quartz glass cover. The Surface-to-surface radiation model was adopted in the fluid domain while Rosseland approximation for radiation heat transfer was considered for the radiation in the participating media. The porous media consists of porous NiF2O4 filled with nitrogen (N2) fluid. Experimental validation of numerical results was provided. The following conclusions have been drawn: (1) The thermal loss is obvious inevitable at the surface of diffuse irradiance due to the stronger convective cooling of

Conflict of interest No conflict of interest exists in the submission of this manuscript, and the manuscript is approved by authors for publication.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 51522601, 51436009) – China and the Fok Ying-Tong Education Foundation of China (No. 141055) – China.

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