Air purification and thermal performance of photocatalytic-Trombe wall based on multiple physical fields coupling

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Air purification and thermal performance of photocatalytic-Trombe wall based on multiple physical fields coupling Shuang-Ying Wu a, b, *, Li Xu b, Lan Xiao a, b, ** a b

Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing, 400044, China School of Energy and Power Engineering, Chongqing University, Chongqing, 400044, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 May 2019 Received in revised form 19 September 2019 Accepted 10 October 2019 Available online xxx

Photocatalytic (PC)-Trombe wall with dual functions of space heating and air purification has a promising way in solar architecture integration. In this paper, a two-dimensional numerical model on air purification and thermal performance of PC-Trombe was established based on relevant experiments in literature. The coupling relations and sequence among the low Reynolds number k-ε model, LangmuriHinshelwood kinetics, natural convection heat transfer and convection-diffusion equations were established and used to solve multiple physical fields coupling. The numerical results were in good agreement with the experimental data in related literature. The effects of environmental factors, geometric structures and operating conditions on the thermal efficiency and formaldehyde degradation rate of PC-Trombe wall were investigated. The results show that the thermal efficiency increases with increasing solar radiation and ambient temperature, but it is opposite for inlet temperature of air and ambient wind velocity. However, the thermal efficiency increases first and then decreases as the channel width increases, the maximum thermal efficiency is 52.98% when the width is 0.04 m. For the air purification rate, all factors also show the trend of increasing first and decreasing afterward, there is a maximum air purification rate of 2.91 mg/s when the channel width is 0.05 m. © 2019 Elsevier Ltd. All rights reserved.

Keywords: PC-Trombe wall Photocatalytic oxidation Multiple physical fields Air purification Thermal performance

1. Introduction In 2017, the energy used in buildings accounts for 30% of the world’s total energy consumption, and with the growing population and changing economic conditions, the proportion is increasing [1]. The use of renewable energy is a good way to meet the energy needs of buildings. Solar energy is playing an increasingly important role in the building industry, especially when the purpose of architecture, the use of regenerative energy, and climate are taken into consideration [2]. Some literatures have pointed out that investment in improving building envelopes can reduce the energy consumption [3]. Trombe wall, a kind of typical passive solar technique, is widely used in solar space heating because of

* Corresponding author. Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing, 400044, China. ** Corresponding author. Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing, 400044, China. E-mail addresses: [email protected] (S.-Y. Wu), [email protected]. cn (L. Xiao).

advantages like simple structure, high thermal efficiency, zero energy consumption and so on [4]. The blackened wall absorbs solar radiation and heats the air in the channel, which can provide heat to the room by natural convection, and some of the heat is stored in the thermal mass wall, and released into the room when there is no sunlight [5]. The air heated by Trombe wall also can be used for building’s heating, ventilating and air condition (HVAC) system, and it is an effective way to reduce the heating and the ventilation loads [6]. However, the classic Trombe wall has the disadvantages of single function, low utilization of solar energy and limited applicability. It is not suitable for dry, hot, humid or inadequately sunny areas [2]. Therefore, many new technologies and theories have been put forward in recent years to enhance its functionality and feasibility. In order to expand the range of application of Trombe wall, scholars made some improvements in accordance with different climate conditions. The easiest way to extend Trombe wall’s application may base on its existing structure. Dabaieh et al. [7] proposed a new Trombe wall structure which can be used in semiarid climates and consists of the gray paint wall with natural wool as insulation material and two roll-up wool curtains.

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Compared with the traditional Trombe wall, the heating load and cooling load reductions of this new structure increase by 94% and 73%, respectively and the payback time is 7 months. Taking desert climatic conditions into account, Rabani et al. [8] combined solar chimney with water spray system to design a new Trombe wall. The experimental results show that the system can reduce the indoor temperature by 8 K, increase the indoor humidity by 17%, and have better ventilation when there is no sunlight. Stazi et al. [9] studied the relationship among insulation, energy saving and thermal comfort of double glazing Trombe wall under a Mediterranean climate. Experiment and dynamic simulation results show that when using high thermal resistance material, the system’s space heating and cooling energy consumptions reduce by 47%, compared with normal Trombe wall. Kara [10] built a test room with threelayer glass plates and PCM of Trombe wall in Erzurm, Turkey, and conducted experimental research. The results show that the total daily efficiency of the room is 17%e20%, and the transmittance of the wall under solar radiation is 45%e55%. Based on the winter climate in Egypt, Abdeen et al. [11] established a mathematical model of the Trombe wall by experimental and numerical methods, which can be used to optimize the design of the Trombe wall and improve the thermal comfort of the building. In order to comprehensively consider the influences of environmental temperature, solar radiation intensity, indoor temperature, PCM melting point and thickness on the PCM-Trombe wall, Zhou et al. [12] proposed a system evaluation method of energy storage and release efficiency (ESRE) based on a Trombe wall with double-layer PCM wallboard to assess the energy-saving potential of the PCM-Trombe wall. In recent years, multi-functional Trombe walls have also become the main research objects of scholars. Ji et al. [13] proposed a Trombe wall with Photovoltaic (PV) panel, and they established the mathematical and physical models of PV-Trombe wall, to calculate the thermal and electrical performance of system. The results show that the indoor temperature of conventional Trombe wall is higher than that of PV-Trombe wall, but PV-Trombe wall can generate electricity and the electrical efficiency increases about 5% because of an air channel behind the PV panel. By the experimental and numerical analysis of the PV-Trombe room with heat storage material, it is found that the heat storage structure can significantly increase the indoor temperature, and the daily average electric efficiency of the PV panel can reach 10.4% [14]. At present, there are mainly three types of PV-Trombe wall: the PV cells attached on the glazing, the PV cells attached on the massive wall and the PV blind with Trombe wall [15]. Considering the growing indoor air pollution problem in recent years, some scholars have proposed a Trombe wall with air purification function. It can be divided into Thermal-catalytic-Trombe wall (TC-Trombe wall) and photocatalytic-Trombe (PC-Trombe) wall. Yu et al. [16] applied the thermal catalytic MnOx-CeO2 which is coated on the massive wall, and conducted a full day study of the thermodynamic properties and pollutant degradation properties of this system. The results show that the heating efficiency of the system is 41.3%, the degradation of formaldehyde is 208.4 mg/ (m2$day), and the fresh air is 249.2 m3/(m2$day). Based on the experiment, the reaction kinetics, thermodynamics and mass coupling model of the system were established, and the effects of the seasons on thermal performance and degradation performance of the system were taken into consideration. Compared the performance of thermal-catalytic-Trombe wall with that of traditional Trombe wall in the heating season, it is shown that the heat gains of the thermal-catalytic-Trombe wall reduce by 28.3%, but the total volume of clean air 8328.7 m3/m2 can be obtained [17]. Photocatalytic-Trombe wall is a promising system with the increase of building energy consumption and indoor air pollution. Combining solar photocatalytic oxidation and Trombe wall, Yu et al.

[18] proposed a novel Trombe wall which has multiple functions including degradation indoor volatile organic compounds (VOCs), space heating and ventilation. They studied the effects of concentration, ultraviolet (UV) light intensity, temperature, and humidity on the catalytic rate of the system. The results show that the system has a positive effect in winter. Later, Yu et al. [19] proposed another photocatalytic-Trombe wall, in which the catalyst film was coated on the inside of the glazing cover and the absorption plate was placed on the insulated wall. The coupling reaction kinetics, thermodynamics and mass transfer models of the PC-Trombe wall were established, and the thermal performance and formaldehyde degradation performance of the system were obtained through experiments. From literature survey, two features are identified. On the one hand, most researches are concentrated on the thermodynamic and degradation performance of PC-Trombe wall by experimental method. And the influencing parameters studied are very limited. The truth is, the PC-Trombe wall receives solar radiation and operates in a real environment, the specific structure of PC-Trome wall, environmental factors and operating conditions greatly influence the thermodynamic performance and degradation performance of the whole system. On the other hand, the numerical investigation on the performance of PC-Trombe wall is not received enough attention. In fact, there are typical flow and heat and mass transfer processes with catalytic reactions in PC-Trombe wall. It is vital and necessary to seek the mechanism of multiple physical fields coupling by numerical method. However, there are few studies on the performance of PC-Trombe wall under real thermal boundary condition. In particular, there is little research touch on the effects of multiple parameters on performance of PC-Trombe wall by numerical method. Therefore, the purpose of this study is to investigate numerically the air purification and thermal performance of PC-Trombe wall under real thermal boundary condition and to make a rigorous evaluation on the efficiency of system based on the numerical data. The effects of environmental factors, geometric structures and operating conditions on the thermal efficiency and formaldehyde degradation efficiency of PC-Trombe wall will be analyzed and discussed, which can provide scientific basis for the design and operation of PC-Trombe wall. 2. Physical and mathematical modeling As shown in Fig. 1 a Trombe wall which was experimentally researched by Yu et al. [19] is taken as the object of this study and specific structural data will be given in section 2.2. When the southfacing Trombe wall receives solar radiation, UV light and a fraction of visible light are absorbed by the high purity borosilicate glazing cover with photocatalytic layer (TiO2), and the rest of solar radiation is absorbed by absorbing plate attached on the wall. The air with formaldehyde in air channel is heated by absorbing plate and rises by buoyancy effects. Moreover, the formaldehyde in air will be degraded by the catalyst layer which absorbs UV light. So the performance evaluation of PC-Trombe wall mainly includes three physics-coupled computational models: heat transfer by natural convection, reaction kinetics and mass transport. Considering the time cost of calculation and the limited computer resources, the three-dimensional (3D) model and the two-dimensional (2D) model were calculated under the same conditions, and the results showed that the outlet temperature, wall temperature, outlet velocity and outlet concentration of the PC-Trombe wall are close to each other. Thus the 2D model is finally chosen as the numerical calculation model. The thermophysical properties of fluid are considered as the same as those of air because of low concentration of formaldehyde

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viscosity on the flow is greater than that of turbulence pulsation. At the same time, obvious heat and mass transfer phenomenon also occurs in the near-wall, so the solution of flow and heat transfer in the near-wall has a great influence on the whole calculation result. The low Re k-ε model can be used to solve the region with obvious viscous influence [27]. Thus the low Re k-ε model has been used to calculate the turbulent natural convection heat transfer of Trombe wall [28,29]. The continuity equation, the momentum equation, the energy equation are shown as follows:

vr vðrui Þ þ ¼0 vxi vt

(2)

" ! #   vðrui Þ v rui uj vP v vui vuj 2 þ ¼ þ þ ðm þ mt Þ  rkdij vt vxi vxj 3 vxj vxi vxj  rgbðT  T0 Þ (3)   vðrTÞ vðrui TÞ v l vT mt vT vP þ mi þ ¼ þ vt vxi vxi cp vxi sT vxi vxi

Fig. 1. Schematic of the 2D PC-Trombe wall.

(4)

Turbulence kinetic energy k equation: and it is considered that the formaldehyde is uniformly distributed in the air at the initial time [16,19,20]. The gas does not participate in the radiative heat transfer, and the thermophysical properties of the fluid are constant, except for the density change of the buoyancy term in the momentum equation along vertical direction, which the Boussinesq approximation is used. What’s more, the following assumptions are made: (1) Each surface is a gray diffuse surface, the back of the absorbing plate and the horizontal wall is insulated [21]. (2) The catalyst with stable chemical properties is uniformly and sufficiently covered on the inner surface of the glazing cover [20]. (3) The diffusion of formaldehyde in TiO2 layer is not considered [20]. (4) Ignore the heat transfer temperature difference of absorbing plate and glazing cover in the thickness direction, and the catalyst layer temperature is considered to be the same as the glazing cover temperature [22]. (5) Due to the low concentration of formaldehyde in this study, the reaction heat of the formaldehyde degradation process is ignored [23]. (6) The main response range of TiO2 catalyst layer is the UV part, and the absorption rate of visible light and infrared light is zero [17]. (7) Photocatalytic degradation of formaldehyde can be expressed by a single reaction equation: UV;TiO2

HCHO þ O2














!CO2 þ H2 O

(1)

On account of the low concentration of formaldehyde, the intermediate product has little effect on the whole reaction. So far, most of the literatures have only considered the main reaction when simulating the photocatalytic process [20,24e26].

2.1. Turbulent natural convection and reaction kinetics models 2.1.1. Governing equations In the flow near the PC-Trombe wall, the Re is low, the turbulence development is insufficient, and the influence of molecular

vðrkÞ vðrkui Þ v þ ¼ vt vxi vxi !2 vk1=2  2m vn





mþ



mt vk þ Gk þ Gb  rε sk vxi (5)

Specific rate of dissipation ε equation:

vðrεÞ vðrεui Þ þ ¼ vt vxi    v m vε ε þ f1 C1ε ðGk þ C3ε Gb Þ mþ t vxi k sε vxi !2 ε2 mmt v2 u þ  f2 C2ε r þ 2 k r vn2

(6)

Fluid turbulent viscosity coefficient mt:

mt ¼ Cm fm r

k2 ε

(7)

where r is fluid density, kg/m3; t is time, s; ui and uj are the components of the velocity in different directions, m/s; P is pressure, Pa; xi and xj are coordinate components, m; m is dynamic viscosity of fluid, Pa/s; g is acceleration of gravity, m2/s; b is coefficient of thermal expansion, 1/K; T0 is average temperature of fluid, K; l is thermal conductivity of fluid, W/(m$K); cp is specific heat, J/(kg$K); sT is turbulent Prandtl number; sk is the Prandtl number of turbulent energy k; sε is the Prandtl number of rate of dissipation ε; n is the normal coordinate of the wall; C1ε, C2ε, C3ε and Cm are empirical constant; f1, f2 and fm are the correction factors; Gk and Gb are the generation term of the turbulent kinetic energy k due to the average velocity gradient and the generation term of the kinetic energy k due to buoyancy respectively.

2:5 .

fm ¼ exp 50εm 1 þ rk2

! (8)

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r2 k4 f2 ¼ 1  0:3 exp  2 2 ε m

Gk ¼ mt

vui vuj þ vxj vxi

Gb ¼  g b

!

! (9)

vui vxj

(10)

mt vT sT vxj

(11)

The values of the coefficients in low Re k-ε model are given in Table 1. There is radiative heat transfer between the catalyst layer and the absorbing plate. The radiative heat transfer in Trombe wall can be calculated by surface to surface (S2S) radiation model or discrete ordinates (DO) radiation model [29,30]. Before the determination of radiation model, a trial calculation was conducted. It was shown that the S2S and the DO radiation model have little effects on the results, but the DO radiation model consumes a lot of calculation time. Therefore, the S2S radiation model is applied in this study. In S2S radiation model, the effective radiative heat transfer Ji between surface i and other surfaces is calculated as follows:

Ji ¼ εi sT 4i þ ð1  εi Þ

N X

Fij Jj

(12)

j¼1

where εi is surface emissivity of surface i; Fij is the view factor between surfaces i and j; N is the number of surfaces; s is StefanBoltzmann constant, 5.67  108 W/(m2$K4).

2.1.2. Kinetic model A large number of experimental studies have shown that the photocatalytic reaction process can be fitted by the LangmuirHinshelwood (L-H) kinetics equation [31]. Considering that the photocatalytic reaction is affected by UV light, the kinetic rate constant of photocatalytic reaction studied in this paper is shown as follows [19]:

r¼

kUV I nUV KLH CHCHO 1 þ KLH CHCHO

(13)

where kUV is the reaction equilibrium constant; KLH refers to the adsorption equilibrium constant; CHCHO represents the formaldehyde concentration near the TiO2 layer, mol/m3; IUV is the UV light intensity, mW/m2; n is the power law coefficient describing the reaction rate dependent on the UV light irradiance. At the same time, temperature, which mainly affects the adsorption constant and reaction constant, is also an important factor in photocatalytic reaction. The Arrhenius equation describes the relationship between temperature and these constants. The relationship among the kinetic rate constant, temperature, formaldehyde concentration, and ultraviolet light intensity is given in Ref. [19]:

Table 1 The coefficients of low Re k-ε model.

    HHCHO HCHO K CHCHO kHCHO I nUV exp  ERT exp  HCHO RTa a   r¼ HCHO CHCHO 1 þ KHCHO exp  HRT a

Based on the Arrhenius equation, kHCHO, (ppb$m)/s and KHCHO, ppb1 are the pre-exponential factors of reaction equilibrium constant and the adsorption equilibrium constant respectively. EHCHO and HHCHO are the reaction activation energy and the adsorption heat of formaldehyde, respectively, kJ/mol. These four parameters are obtained by experiment. R is the universal gas constant, J/(mol,K); Ta is the local temperature of air, K. The specific model parameters are given in section 2.3.

2.1.3. Diffusion model of formaldehyde The diffusion coefficient is an important parameter in this study. The convection-diffusion equation coupled with the velocity field is used to solve the distribution of formaldehyde in the flow channel.

vCHCHO ! þ V ,VCHCHO ¼ V,ðDVCHCHO Þ vt

Cm

C1ε

C2ε

C3ε

sT

sk

sε

1.0

0.09

1.44

1.92

1

1.0

1.0

1.3

(15)

! where V is the velocity field vector; D is the diffusion coefficient of formaldehyde in air, cm2/s. Since the diffusion coefficient is a function of temperature, the gas is non-isothermal flow in this study, so the diffusion coefficient is not constant. The semiempirical formula proposed by Gilliland is commonly used to calculate the diffusion coefficient D between two ideal gases [32]:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ

MA MB 1=3 2

435:7T 3=2

D¼ 1=3 P VA þ VB

(16)

where M is the molecular weight of gas, g/mol; P is total pressure, Pa; V is molar volumes at the normal boiling point, cm3/mol.

2.2. Boundary conditions As assumed above the temperatures of the catalyst and the glass plate are the same, the solar energy absorbed by the glazing cover and the solar energy absorbed by the heat absorbing plate are as follows:

qg;a ¼ ag I

(17)

qp;a ¼ tg ap I

(18)

In which ag is the absorptivity of glazing cover; tg is the transmittance of glazing cover; ap is the absorptivity of the absorbing plate; I is the solar radiation intensity, W/m2. Convective heat transfer loss between the glazing cover and the external environment may be written as:

  qc;g ¼ h Tg  Tamb

(19)

where Tg and Tamb are the temperatures of glazing cover and ambient respectively, K; h is convection heat transfer coefficient, W/(m2,K), whose value is related to the ambient wind velocity Vwind, m/s [33]:

h ¼ 5:7 þ 3:8Vwind

f1

(14)

(20)

The radiation heat loss between the glazing cover and the external environment is given by:

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" qrg ¼ εg C0

Tg 100

4



Tsky  100

4 #

Table 3 Model parameters of PC-Trombe wall.

(21)

where εg is emissivity of glazing cover; C0 is blackbody radiation coefficient, 5.67 W/(m2,K4); Tsky means the sky temperature and is obtained by Ref. [33]:

Tsky ¼ 0:0552Tamb

5

1:5

Types

Variables

Values

Units

Refs.

Geometry

H1 H2 W1 W2

PC-glass

ag tg

50 1000 250 50 0.1 0.75 0.85 0.25 0.2 4800 19.020 51298 13.252 0.95 0.95 1 1.18 1005 0.026 1.85  105 0.0034

mm mm mm mm e e e e e (ppb$m)/s kJ/mol ppb1 kJ/mol e e m2 kg/m3 J/(kg$K) W/(m$K) Pa/s K1

[19] [19] [19] [19] [34] [19] [34] [16] [19] [19] [19] [19] [19] [34] [34] [19] [35] [36] [19] [35] [35]

(22)

To sum up, all boundary conditions in numerical model are shown in Table 2.

Kinetics

2.3. Model parameters Absorbing plate

The geometric parameters in this model are from Ref. [19]. The parameters used in the calculations and the corresponding values are listed in Table 3. Other parameters such as solar radiation intensity, ambient temperature and inlet temperature of air, which are not given in the table, can be obtained from Ref. [19].

εg εTiO2 n kHCHO EHCHO KHCHO HHCHO

ap εp A

Fluid

r0 cP

l m b

2.4. Mesh sensitivity and validation The three physical fields of natural convection heat transfer, dilute species transport and chemical reaction are coupled. In this paper, finite element method is used to solve the problem of multiple physical fields coupling by commercial CFD software COMSOL multiphysics 5.3a. The SARDISO direct linear solver was used to solve the two-dimensional unsteady state flow and heat and mass transfer with photocatalytic reaction, and the backward difference formula method was used to discretize the governing equation and the diffusion equation. The minimum convergence criteria for all variables are 108. Time step size is 0.1s, and number of time steps is 2000. However, in order to reflect the final performance of PC-Trombe wall, this paper only gives the steady state results. Since natural convection and chemical reactions occur in the air channel of PC-Trombe wall, the temperature gradient, velocity gradient and concentration gradient near the solid wall are large, thus the mesh near the wall is refined [26]. All surfaces were assumed to be no slip boundary. Quadrangle elements were used to divide the computational region. The dimensionless distances to the wall and the glazing cover are taken as yþ<1. In order to select suitable meshes for computation, detailed mesh independence verification is needed. Six kinds of meshes 2780, 4570, 5310, 7100, 18375, 47507 were tested for mesh independence, and the outlet concentration CHCHO,out and fluid outlet temperature Tout and outlet velocity Vout were monitored. According to the experimental data in Ref. [19], the mesh independence is checked under the conditions of solar radiation intensity I ¼ 749 W/ m2, inlet temperature of air Tin ¼ 295.16 K, ambient temperature Tamb ¼ 295.56 K, ultraviolet light intensity IUV ¼ 31.68 W/m2, inlet concentration of formaldehyde CHCHO,in ¼ 3.649  105 mol/m3, ambient wind velocity Vwind ¼ 1 m/s. The mesh independence test results are shown in Table 4. The results show that the maximum

Table 2 Boundary conditions in numerical model. Boundary

Conditions

Inlet Outlet Glazing cover Absorbing plate Other boundary

Pressure inlet (101.3 kPa) Open border qg,a-qc,g-qr,g qp,a Adiabatic

discrepancy of Tout, CHCHO, outt and Vout are less than 1% when the mesh number is more than 2780. By comparison, it is found that 4570 quadrilateral meshes are sufficient to meet the condition of mesh independence verification. At this time, the thickness of the first layer boundary layer is 0.0004 m, the growth rate is 1.1, the number of boundary layers is 16, and the average mesh quality is 0.9764, meshes of PC-Trombe wall is shown in Fig. 2. 2.5. Model verification 2.5.1. Flow model verification In Section 2.1.1, referring to relevant literatures, the low Re k-ε model was adopted as a flow model. Due to the great influence of air flow on the heat transfer and formaldehyde diffusion, the flow model is verified before multi-physics coupling verification. Herein the standard k-ε, realizable k-ε, low Re k-ε and laminar model were selected to verify the experiment in Ref. [16], and the results of outlet velocity Vout, outlet temperature Tout, inner wall temperature Tw are shown in Fig. 3. Fig. 3(a) illustrates the outlet velocity Vout obtained respectively by the simulation and experiment. It can be observed that the results obtained by different flow models vary greatly, and the calculation result by the low Re k-ε model is consistent with the experimental data. Fig. 3(b) shows that the outlet temperature Tout obtained by different flow models has little difference and all the numerical results are not far from the experimental results. The calculation results of wall temperature Tw with different flow models are shown in Fig. 3(c), and results of laminar flow model and the low Re k-ε model agree with the experimental data. Taking all the factors mentioned above into account, the low Re k-ε model is selected in this study. 2.5.2. Verification of multiple physical fields coupling model The error between the simulated value and the experimental value can be analyzed by the root mean square deviation (RSMD) and is expressed as follows:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 P  Xsim;i  Xexp;i Xexp;i RSMD ¼ n

(23)

According to the experimental results of Yu et al. [19] on PCTrombe wall, the mathematical models of multiple physical fields

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Table 4 Numerical results for different mesh numbers. Mesh numbers

Tout (K)

CHCHO,out (mol/m3)

Vout (m/s)

Running time (min)

2780 4570 5310 7100 18375 47507

310.916 311.285 311.434 311.181 310.978 311.047

2.451  105 2.492  105 2.488  105 2.479  105 2.481  105 2.482  105

0.226 0.230 0.229 0.231 0.228 0.230

2 5 7 12 27 141

hth ¼

ma ca ðTout  Tin Þ IA

  mHCHO ¼ QMHCHO CHCHO;in  CHCHO;out

(24) (25)

where ma is the mass flow rate of air, kg/s; ca is the heat capacity of air, J/(kg$K); Tout and Tin are outlet temperature and inlet temperature of air respectively, K; A is the absorbing plate area, m2; I is the solar radiation intensity, W/m2; MHCHO is molar mass of formaldehyde, mg/mol; Q is volume flow rate of air, m3/s. 3.1. Effects of environmental and operating parameters

3. Results and discussion

3.1.1. Effect of solar radiation intensity During the experiment, when the UV light intensity is greater than 1.5 mW/cm2, the UV light intensity has little effect on the reaction rate [37]. Therefore, the effect of UV light intensity on the reaction is not considered in this paper. And based on the experimental condition in Ref. [19], i.e. Tin ¼ 295.16 K, ambient temperature Tamb ¼ 295.56 K, the ambient wind velocity Vwind ¼ 1 m/s, and inlet formaldehyde concentration CHCHO,in ¼ 3.649  105 mol/m3 (1094.7 mg/m3), Fig. 5 displays the effect of solar radiation intensity varying from 100 W/m2 to 1000 W/m2 on thermal efficiency hth and air purification rate mHCHO. It can be seen that the thermal efficiency hth of the PC-Trombe wall increases with the solar radiation intensity. It is due to that the air temperature and mass flow increase with the solar radiation intensity. However, the air purification rate has different trends with increasing solar radiation intensity. From Eq. (14), the main factor affecting the photocatalytic reaction rate is air temperature, and the air velocity is another important aspect in surface photocatalytic degradation. In general, the air velocity increases with the solar radiation intensity. The faster the air flows, the less pollutant be absorbed by the catalyst layer and the less the amount of pollutant degradation. From Fig. 5, there is a maximum air purification rate when the solar radiation intensity is 600 W/m2. That is, in PC-Trombe wall, due to the coupling of the temperature field and the velocity field, there is an optimal solar radiation intensity to maximize the degradation rate.

Based on the physical and mathematical models established in the above section, the effects of environmental factors (ambient temperature, ambient wind velocity and solar light intensity), geometric factor (width of air channel) and operating parameter (inlet temperature of air) on the performance of PC-Trombe wall are analyzed. Understanding the effects of environmental, geometric and operating parameters on all aspects of the PC-Trombe wall can provide better design and reasonable operating conditions for PCTrombe wall, thereby improving the thermal efficiency and air purification rate. For this purpose, two performance evaluation indexes of PC-Trome wall are introduced, i.e. the thermal efficiency hth and air purification rate mHCHO, mg/s [16].

3.1.2. Effect of inlet air temperature According to section 3.1.1, the optimal solar radiation intensity is 600 W/m2. Thus the environmental parameters in this case are selected as follows: I ¼ 600 W/m2, Tamb ¼ 283.15 K, Vwind ¼ 1 m/s and CHCHO,in ¼ 3.649  105 mol/m3 (1094.7 mg/m3). Fig. 6 displays the effect of inlet temperature on thermal efficiency hth and air purification rate mHCHO. It can be seen that hth of PC-Trombe wall decreases with inlet temperature varying from 278.15 K to 303.15 K. On the other hand, the air purification rate presents a parabolic trend, which means the inlet temperature of air has an optimal value. This also indicates that there is an optimal reaction temperature for the photocatalytic degradation of formaldehyde. When

Fig. 2. Meshes of PC-Trombe wall.

coupling in this study are verified. The comparison between the numerical simulation and the experimental results is shown in Fig. 4. It can be seen that the simulation results have the same trend with the experimental values as the intensity of sunlight changes. The RSMD of CHCHO,out and Tout are 8% and 4.8%, respectively. Therefore, the established mathematical model and related numerical simulation methods are reliable and can be confidently used to further study the performance of PC-Trombe wall.

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Fig. 4. Results comparison between numerical simulation and experiment by Yu et al. [19].

Fig. 5. Variations of ƞth and mHCHO with solar radiation intensity.

Fig. 3. Comparison between numerical results by different flow models and experimental results. Fig. 6. Variations of hth and mHCHO with inlet temperature of air.

inlet temperature or the indoor temperature is too high, the space heating efficiency and degradation efficiency of the PC-Trombe wall both reduce.

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3.1.3. Effect of ambient temperature Ambient temperature is another important external parameter affecting the performance of PC-Trombe wall. Since the photocatalytic reaction occurs on the inside of the glazing cover, the temperature change of the glazing cover has a great influence on the photocatalytic reaction. According to Eqs. (21) and (22), the surface heat loss of glazing cover is affected by ambient temperature Tamb, which indicates that Tamb has a great influence on the temperature of glazing cover. The effect of ambient temperature on the thermal efficiency hth and air purification rate mHCHO of PCTrombe wall is shown in Fig. 6 under Tin ¼ 293.15 K, I ¼ 600 W/ m2, Vwind ¼ 1 m/s, CHCHO,in ¼ 3.649  105 mol/m3 (1094.7 mg/m3). Considering the wide variation range of outdoor temperature, the ambient temperature varies from 273.15 K to 303.15 K. It can be seen from Fig. 7 that the hth of PC-Trombe wall monotonically increases with the ambient temperature, but the degradation rate increases first then decreases, which indicates there is an optimum ambient temperature (about 288.15 K) maximizing the air purification rate.

Fig. 8. Variations of hth and mHCHO with ambient wind velocity.

3.1.4. Effect of ambient wind velocity In the real environment, the heat loss of the Trombe wall, which is generally installed on the south facing wall, is affected by the ambient wind velocity. From this perspective, the ambient wind affects the thermal and degradation performance of PC-Trombe wall. Fig. 8 provides the variations of thermal efficiency hth and air purification rate mHCHO with ambient wind velocity varying from 0 to 6 m/s, Tin ¼ 293.15 K, Tamb ¼ 288.15 K, I ¼ 600 W/m2, CHCHO,in ¼ 3.649  105 mol/m3 (1094.7 mg/m3). The results show that hth of PC-Trombe wall decreases with the ambient wind velocity. When the ambient wind velocity increases, the convection heat transfer between the glazing cover and the external environment is enhanced, resulting in a decrease of temperature in the channel and temperature of glazing cover. Therefore, the heat loss of PC-Trombe wall increases and the thermal efficiency decreases with the increase of ambient wind. For the air purification rate, similar to the influence of ambient temperature, inlet temperature and solar radiation intensity, there is also an optimal ambient wind velocity maximizing the air purification rate. Owing to the fact that the temperature of glazing cover is equal to that of the catalyst layer, the ambient wind has the same effect on the temperatures of the catalyst layer and the glazing cover. Therefore, the photocatalytic reaction in PC-Trombe wall has an optimum reaction

When designing a PC-Trombe wall, the distance between the glazing cover and external wall must be considered. Therefore, it is necessary to study the influence of channel width on the performance of PC-Trombe wall. Fig. 9 shows the effect of channel width on thermal efficiency hth and air purification rate mHCHO under I ¼ 749 W/m2, Tin ¼ 295.6 K, Tamb ¼ 295.56 K, Vwind ¼ 1 m/s, CHCHO,in ¼ 3.649  105 mol/m3 (1094.7 mg/m3). It should be pointed out that, when the channel width changes, the length of outlet W1 remains unchanged and the height of outlet H1 is consistent with the channel width W2. The change in width of the channel is reflected by the aspect ratio W2/H2. Herein the aspect ratios are taken as 1:50, 1:40, 1:30, 1:25, 1:20, 1:10 and the corresponding channel widths are 0.02 m, 0.025 m, 0.033 m, 0.04 m, 0.05 m, 0.0667 m, 0.1 m, respectively. As shown in Fig. 9, as the width of channel increases, both hth and mHCHO increase first and then decrease. The maximum thermal efficiency 52.98% occurs at W2 ¼ 0.04 m, while the maximum air purification rate 2.91 mg/s occurs at W2 ¼ 0.05 m. It can be concluded that the performance of

Fig. 7. Variations of hth and mHCHO with ambient temperature.

Fig. 9. Variations of hth and mHCHO with width of channel.

temperature when the ambient wind velocity is optimal. 3.2. Effect of geometric factor

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PC-Trombe is largely related to channel width. Fig. 10 shows the velocity fields for four different channel widths, i.e., 0.02 m, 0.04 m, 0.05 m and 0.1 m. It can be seen from the vortex appearing in the four width channels that the size of the vortex increases with increasing channel width. Meanwhile, there exists flow separation at the top vent. The flow separation bubbles rise from the heating wall to the top vent, reducing the effective cross-sectional area of the vent at outlet. Fig. 11 clearly shows that the relative size of the vortex at the vertical corner decreases as the width increases, which leads to different velocity distributions under the four widths. Also from the velocity fields, the velocity gradient near the glazing cover increases with the width. As the channel width increases, the frictional resistance loss decreases, i.e., the flow resistance decreases, and the mass flow rate increases. When the channel width increases to a certain value, the airflow state changes from finite space flow to infinite space flow, and the temperature difference at inlet and outlet of channel is reduced, meanwhile the reflux at the outlet is very obvious. Fig. 12 reports the temperature fields for four different channel widths, namely 0.02 m, 0.04 m, 0.05 m and 0.1 m. Obviously, when the channel width is 0.02 m, the average temperature at outlet is the highest, while the thermal efficiency is not high due to the small cross-sectional area. In addition, the average outlet temperature decreases as channel width increases. When channel width is 0.02 m, the temperature distribution at the inner corner of the channel vent is significantly different, compared with temperature distributions at the same area under other widths. The reason for such difference is as follows: when the flow channel width is 0.02 m, the air velocity and heat transfer coefficient are larger due to the larger proportion of the vortex at the corner; meanwhile the proportion of the vortex decreases as the channel width increases. Fig. 13 shows the formaldehyde concentration fields for four different channel widths namely 0.02 m, 0.04 m, 0.05 m and 0.1 m. Generally speaking, the temperature of the gas in the narrow channel is higher than that in wide channel, which increases the average kinetic energy of the formaldehyde molecule and makes it easy to diffuse in the channel and reach the catalyst layer, the higher average velocity of the fluid in the narrow channel leads to

Fig. 11. Streamlines of corner at outlet for four widths of channel.

Fig. 12. Temperature fields (unit: K) for four widths.

Fig. 13. Concentration fields (unit: mol/m3) for four widths. Fig. 10. Velocity fields (unit: m/s) for four widths.

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the rapid flow of the gas through the catalyst layer, and the short contact time between the molecule and the catalyst layer makes it difficult to be adsorbed and degraded by the catalyst. On the other hand, a vortex forms at the corner of the exit. It is the presence of the vortex at the outer corner of the channel outlet that can prolong residence time of pollutants in the channel, more formaldehyde molecules are absorbed and degraded, and the formaldehyde near the glazing cover can be effectively degraded. From Fig. 13, it can be found that the outlet concentration is the lowest when the width is 0.02 m, but the air purification rate is still very small because of relatively low flow rate. However, when the width is 0.1 m, the temperature, velocity and vortex at the corner of the channel are small, so the air purification rate is low. Therefore, the width of the PC-Trombe wall can affect the relationship among the flow velocity, temperature, and vortex structure, thereby affecting the adsorption degradation of formaldehyde molecules. There is an optimal width of 0.04 m, which enables the PC-Trombe wall to have the maximum purification efficiency. 4. Conclusions The effects of environmental factors, geometric structures and operating conditions on the thermal efficiency and air purification rate of PC-Trombe wall were analyzed and discussed. The following conclusions can be drawn. (1) With the increase of solar radiation intensity, the thermal efficiency of PC-Trombe wall increases, but the air purification rate first increases and then decreases. (2) The thermal efficiency of PC-Trombe wall decreases with the inlet temperature of fluid. When the inlet temperature varies from 278.15 K to 303.15 K, the air purification rate firstly increases slowly and then decreases rapidly, and reaches the maximum value at 293.15 K. When Tamb ¼ 288.15 K, the PCTrombe wall has the maximum air purification rate. The thermal efficiency and air purification rate of PC-Trombe wall vary little under different ambient wind velocity. (3) When the width is 0.02 m, the vortex structure in the channel has a great influence on the velocity, temperature and concentration distributions. From the perspective of optimal width, the PC-Trombe wall has the maximum thermal efficiency 52.98% when the width is 0.04 m, and the highest air purification rate 2.91 mg/s is reached at the width of 0.05 m. Acknowledgments This work is funded by Project of Technological Innovation and Application Development of Chongqing (No. cstc2019jscxmsxmX0213) and the Fundamental Research Funds for the Central Universities of China (No. 2018CDXYDL0001). References [1] International Energy Agency, Energy Efficiency 2018dAnalysis and Outlooks to 2040, 2018. [2] O. Saadatian, K. Sopian, C.H. Lim, N. Asim, M.Y. Sulaiman, Trombe walls: a review of opportunities and challenges in research and development, Renew. Sustain. Energy Rev. 16 (8) (2012) 6340e6351. [3] N. Monghasemi, A. Vadiee, A review of solar chimney integrated systems for space heating and cooling application, Renew. Sustain. Energy Rev. 81 (2018) 2714e2730. [4] Z. Hu, W. He, J. Ji, S. Zhang, A review on the application of Trombe wall system in buildings, Renew. Sustain. Energy Rev. 70 (2017) 976e987. [5] S. Jaber, S. Ajib, Optimum design of Trombe wall system in mediterranean region, Sol. Energy 85 (9) (2011) 1891e1898. [6] S. Corasaniti, L. Manni, F. Russo, F. Gori, Numerical simulation of modified Trombe-Michel Walls with exergy and energy analysis, Int. Commun. Heat

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T: temperature, K V: velocity, m/s; molar volume, cm3/mol W1: length of vent, m W2: width of channel, m

Nomenclature

Greeks

A: area, m2 C: concentration, mol/m3 C1ε, C2ε, C3ε, Cm: empirical coefficients C0: blackbody radiation coefficient, W/(m2,K4) c: specific heat capacity, J/(kg$K) D: diffusion coefficient, cm2/s E: reaction activation energy, kJ/mol F: view factor f1, f2, fm: correction factors G: the generation term of the turbulent kinetic energy k H: adsorption heat of formaldehyde, kJ/mol H1: height of vent, m H2: height of glazing cover, m h: heat transfer coefficient, W/(m2 K) I: solar radiation intensity, W/m2 K: pre-exponential factor of adsorption equilibrium ppb1; adsorption equilibrium constant k: pre-exponential factor of reaction equilibrium, (ppb$m)/s; reaction equilibrium constant M: molar weight, g/mol m: mass flow rate, kg/s; air purification rate, mg/s P: pressure, Pa Q: volumetric flow rate, m3/s q: heat flux, W/m2 R: universal gas constant, J/(mol$K)

a: absorptivity b: volumetric thermal expansion coefficient, (K1) t: transmissivity h: efficiency

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ε: emissivity l: thermal conductivity, (W/K) s: Stefan-Boltzmann constant, 5.67  108 W/(m2$K4) m: dynamic viscosity, (Pa/s) r: density (kg/m3) Subscripts out: outlet g: glazing cover a: air th: thermal wind: wind HCHO: formaldehyde in: inlet sim: simulation data exp: experiment data amb: ambient ppb: parts per billion sky: sky

Please cite this article as: S.-Y. Wu et al., Air purification and thermal performance of photocatalytic-Trombe wall based on multiple physical fields coupling, Renewable Energy, https://doi.org/10.1016/j.renene.2019.10.039