Micro combustion in a porous media for thermophotovoltaic power generation

Accepted Manuscript Micro Combustion In A Porous Media For Thermophotovoltaic Power Generation Stephen Bani, Jianfeng Pan, Aikun Tang, Qingbo Lu, Yi Zhang PII: DOI: Reference:

S1359-4311(17)34225-4 https://doi.org/10.1016/j.applthermaleng.2017.10.024 ATE 11222

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

23 June 2017 4 September 2017 4 October 2017

Please cite this article as: S. Bani, J. Pan, A. Tang, Q. Lu, Y. Zhang, Micro Combustion In A Porous Media For Thermophotovoltaic Power Generation, Applied Thermal Engineering (2017), doi: https://doi.org/10.1016/ j.applthermaleng.2017.10.024

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Micro Combustion In A Porous Media For Thermophotovoltaic Power Generation Stephen Bani a, Jianfeng Pana*, Aikun Tanga , Qingbo Lua, Yi Zhanga a

School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China

*Corresponding author: Prof. Jianfeng Pan Address: School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China Tel.: +86-0511-88780210 Fax: +86-0511-88780210 E-mail address: [email protected]

Abstract This work delved into porous media combustion (PMC) TPV with H2/O2 as fuel with much focus on experiment and numerical assessment of the TPV generator. The effects of some major parameters on PMC namely flow velocity, equivalence ratio and conductivity of the solid matrix were also numerically investigated. The results indicated a reduction in combustion efficiency upon the increment in inlet velocity. It was as a result of reduction in the residence time. The average wall temperature decreased with increase in the solid matrix thermal conductivity. Increment in cell temperature decreased the forbidden band whiles the cut-off wavelength increased. Temperature variation of the PV cell also caused a 35% decline in output power of the system. For any 10 K increase in cell temperature, the cell efficiency and power output reduced by 7% and 0.14 W respectively. A projected electrical output power and power density of the complete system were 2.7 W and

0.72 Wcm-2 respectively when the cell temperature is kept at 300 K and the spacing between the radiant wall and the PVC is 1 mm. The experiment produced 1.703 W electrical power which was in consonance with what was predicted with the model.

Keywords: Thermophotovoltaic system; Power density; Porous media; Numerical simulation; Micro-combustion.

1

Highlights 

The proposed TPV device is ideal for practical applications; the experiment produced

1.703 W electrical power. 

A porous media combustor is integrated with a TPV device.



Increment in cell temperature decreased the forbidden band whiles the cut-off wavelength increased.



Temperature variation of PVC resulted in 35% decline in output power of the system.

1. Introduction Generating electricity by means of thermophotovoltaic is greatly an interdisciplinary technology. Converting thermal radiation from heat sources into electricity involves many thermo-physical phenomena connected to TPV system. TPV system as can be seen in fig.1 comprises the following: Heating system, Optical System (emitter and filter) and Photovoltaic Cell (PVC). A peculiarity of this technology is the use of any heat source in heating the emitter. The only prerequisite is that it must have a relatively high temperature for TPV conversion. This makes TPV a flexible and versatile technology. Several studies and designs for this system were suggested based on different conventional and non-conventional heating systems. They are classified under the following: Nuclear fuelled TPV, based on a radioisotope General Purpose Heat Source (GPHS) conceived for deep space emission [1]. Bio-fuelled TPV based on for instance, combustion of wood powder [2]. Concentration of solar radiation by an optical system in the case of Solar TPV [3]. Conventionally fuelled TPV system where combustion of gaseous fuels like methane, propane and natural gas or liquid fuels such as diesel and hydrocarbon fuels among others are used as the heat source [4]. For TPV application a uniform wall temperature is a must. Pan et al. [5] used a two nozzle combustor for TPV application and concluded that a swirl formation is found and this is increased when the flow rate increases. They proved by this result that under the same condition, the two nozzle combustor gives a uniform temperature. Jiaqiang, E., et al. [6] used a novel micro-combustor for non-premixed hydrogen-air combustion to study its performance. They concluded that, PMC increases the stability of the flame and attain high efficiency than free

2

flame. Chou et al. [7] researched into PMC for TPV system applications and summed up that useful radiation energy from a micro combustor with a porous media (PM) inserted is higher by 81.2% than TPV without PM. Yang et al.[8] used cylindrical combustor with two different configurations and concluded that combustor with backward facing step achieve uniform and high temperature. Pan et al. [9] investigated the effect of major parameters on micro-combustion for TPV conversion. They summed it up that; their new design was able to increase wall temperature by 150 K. Porous materials are vast in nature and practically all solids and semisolids to some enormous degree are porous materials, exceptions to these are metals, dense rocks and some plastics. The porous structure is composed of the pore size (d) and porosity  with varying range of values [10]. The pore ranges from molecular size, to the order of centimeters for pebbles and debris and larger. The porosity ranges from 0.02-0.07 for concrete to 0.88-0.98 for fiber glass and metallic foams [11]. The occurrence of flow in PM is in many engineering and scientific applications. These are enhanced oil reservoir recovery, fluidized bed combustion, packed bed chromatography , underground spreading of chemical waste, enhanced combustion within porous matrix, salt water intrusion into coastal aquifers, dehumidifying and transpiration cooling [12]. PMC began from the thought of circulation of energy from reaction zone into the approaching reagents in order to attain high temperatures and efficiencies. Weinberg [13] conducted theoretical analysis on the merits of recirculating the heat to incoming mixtures. Takeno et al. [14] brought forth the thought of inserting conducive porous materials during combustion to actualize Weinberg’s conception . An intriguing feature of PMC is that there exist combustion and thermal waves that creates super adiabatic temperatures [15, 16]. On the same premises, [17, 18] suggested modification to the Peclet number,  Pe  SL d f cf f  when we have reactors with two sections having porous materials whose properties are different. This modification is that, flame propagation is attained if Pe  65 but inhibited if Pe  65 . PMC extends fuel combustibility limit because of excellent heat transport properties due to the porous materials [19, 20]. This is viewed as chemical energy harvesting converted to heat and has triggered studies for its application for volatile organic compounds (VOC) destruction in regeneratic burners (RB) [21, 22]. An interesting application of VOC oxidation through PMC is using generated heat for conversion into electricity employing thermoelectric modules (TEM). 3

Chua et al. [23] used numerical simulation to investigate the consequence of employing PM in micro combustion and concluded that higher fuel/oxidizer ratio gives high wall temperature. Pan et al. [24] studied the effects of PM materials, hydrogen to oxygen ratio, porosity and mixture flow rate on combustion with PM and selected SiC as suitable PM material. Li, J., et al. [25] conducted numerical studies on recirculation of heat in premixed H2/air filtration combustion using micro planar combustor. They concluded among others that, porosity and thermal conductivity of solid matrix have an influence on the wall temperature and flame position. Micro combustors are desirable for TPV applications due to their high surface-to-volume ratio and also they yield high power density. In this paper, we study PM combustion based TPV and the effects of some parameters on PMC and finally assess how the device will work in practice.

Fig. 1 Schematic of a TPV unit

2. Porous media TPV generator The generator comprises four components namely, PMC, half adiabatic layer, two PVC arrays and a cooling layer. Fig.2 outlays the schematic diagram of the TPV generator. Combustion starts by letting premixed fuel, H2/O2 flow into combustion chamber via a rectangular inlet located at one end of combustor. The burnt gas is expelled through the outlet. The generated power is dependent on the radiation energy from the combustor. As the size of combustors reduce, the heat flux via the wall increases. There is transfer of thermal energy to the emitter during combustion and when the emitter attains high temperature, it emits photons to the surrounding. PVC’s are designated with bandgaps, that is GaSb ( 72 eV ) or GaInAsSb ( 55 eV ) 4

and photons whose energy are more than the bandgap of the PVC’s will stir up free electrons. Using P-N junction principle, electrical power will be generated.

Fig. 2 Schematic diagram of the TPV generator

3. Micro combustor and experimental set up The micro combustor designed for this study is shown in Fig. 3.The combustor has dimensions of 15 mm in length, 10 mm in width and 1 mm in height with 0.5 mm being the wall thickness. The material for the wall was 316L stainless steel due to its ability to stand high temperatures without physical degradation. The fuel used was H2/O2 and equivalence ratio was 1.0 and 0.8. The combustor was filled with mesh made of stainless steel (SS) with a porosity of 0.9. The inserted PM is made by cutting the SS mesh into one ply. The porosity is calculated by:

  1  Vs V  1   m  N W  L  ss W  H  L  1  m ss  N H

(1)

Where Vs represents volume of solid phase, V the total volume,  m and ss the areal density of SS mesh (  0.5275 g/cm2 ) and density of SS 316L (  7.98 g/cm3 ) respectively. N is number of plies, W and L the width and length of PM respectively, H is width of combustor (10 mm) so it gives N  1and   0.9.

5

The combustor and flow connector were made of SS 316L. The emissivity of the wall was 0.8 and the solid matrix properties were as follows: emissivity 0.8 and conductivity 16.27 W/mK. Fig. 4 depicts the schematics of the experiment. Pure hydrogen and oxygen, both of more than 99.9% purity were supplied from two pressurized tanks. The outlet pressure of 0.15 Mpa was set for fuel and oxidizer. The ambient temperature was 293 K with a relative humidity of 76%. The mass flow controller, a product of MKS Company of America, was used to set inlet velocity and calculate the equivalence ratio of hydrogen and oxygen. It is used in many situations when it requires high repeatability and has an accuracy of about ±1% with a response time less than 1 second. The wall temperature was measured using the infrared thermal imager. Its model is the Thermovision A40, and has a least focal length of 4

mm . It detects temperature change between -40ᵒC to 2000ᵒCand has a measurement accuracy of

.

For a complete H2/O2 combustion, the chemical equation is given as:

2H2 +O2  2H2O

(2)

 mH 2  f a,stoichiometric =   2  2 1.00794 2 15.9994  0.126   mO2 stoichiometric

(3)

 mH 2  f a,actual =     f a,stoichiometric  0.126   mO2 actual

(4)

Considering the law of conservation of mass at inlet of combustor, VH2 +VO2 =Vmixture

(5)

Using the ideal gas law, equation (5) is written as follow: mH 2 mO2   u in Ain  H 2  O2

Where, u in denotes mixture flow velocity,

(6)

 m/s 

and Ain is area of the combustor  m 2  .

Combining equations (4) and (6), mass flow rate of H 2 and O 2 is:

 1  1 mH 2 = u in Ain      H 2 0.126 O2 

(7)

6

 0.126 1  mO2  u in Ain     O2    H2

(8)

Fig. 3 (a) Photograph of the micro combustor, (b) design feature of the planar micro combustor and flow connector.

Fig. 4 Schematic of the experimental set-up.

7

4. Numerical models and simulation approach Accessing the small space of the combustor with measuring devices is somewhat difficult. For this reason, we employ numerical approach to study H2/O2 premixed flame to obtain detailed information in the combustor. Macroscopic dimensions give micro combustors unique features. Of these, large surface to volume ratios are the most important because comparatively large heat and mass transfer rates are attainable. A 3D simulation is performed and Table 1 lists some important parameters for the computational model. On each wall, a nonslip boundary condition was imposed. The initial temperature for the chamber, the solid wall and the surrounding temperature of the chamber were all specified as 300 K . In predicting heat transfer and combustion phenomena in the combustor, we developed a 3D uniform grid at three different mesh densities. Centerline gas temperature profiles for the different meshes were checked to decide the grid size, as shown in Fig. 5. The mesh with 0.1 mm density in all three directions and 330,000 cells in total was chosen after comparing the three.

2000

165000 cells (0.20, 0.10, 0.10) 330000 cells (0.10, 0.10, 0.10) 660000 cells (0.10, 0.10, 0.05)

Centerline Temperature (K)

1800 1600 1400 1200 1000 800 600 400 0

2

4

6

8

10

12

14

Distance from inlet (mm)

Fig. 5 Distribution of the centerline temperature in the channel with different grid sizes under inlet velocity of 1.0 m s . 8

Table1: Important parameters of the computational model Parameters

Methods

Flow

RNG k–e turbulence

Reaction

Finite-rate (mechanism with 8 species and 19 reversible reactions)

Discretization First-order upwind Pressure–

SIMPLE algorithm

velocity coupling Solver

Fluent

Mixture

Density: incompressible-ideal-gas law

physical

Specific heat: mixing-law

properties

Thermal conductivity: mass-weighted-mixing law Viscosity: mass-weighted-mixing law Mass diffusivity: kinetic-theory

Species

Specific heat: a piecewise polynomial fitting of temperature

physical

Thermal conductivity: kinetic-theory

properties

Viscosity: kinetic-theory

Boundary

Inlet: velocity-inlet

conditions

Exit face: outflow External wall: mixed thermal conditions Velocity: 1 m/s Hydrogen-Oxygen equivalent ratio: 1.0, 0.8

The equations governing momentum, species, continuity and energy in PM are written for the micro combustor. Continuity:

   u   0

(9)

9

Momentum:



 

T   u u   p      u   u   2 3   uI      D  u   p 2 u c  u     

(10)

Energy:

  u  pEf  p     keff T  

  hJ     u  u 

T

i

i



 2   uI   u   Sfh 3   (11)

Where keff   k f  1    ks and S hf is the fluid enthalpy source term.

Species:

   uYi     J i  Ri  Si

(12)

Where Ri is rate at which species i is produced by chemical reaction, Si corresponds to rate of creation as a result of adding from the dispersed phase, and J i , the diffusion flux of species i which is specified as:

J i    DimYi

(13)

The wall energy equation is written as:

   kw T   0

(14)

The heat loss from the external wall to the surrounding is specified as: qw  h Tw  To    w Tw4  To4 

Where

(15)

denotes heat transfer coefficient from the external wall to the surrounding with a value

of 10 W m2 K . Reynolds number for flow in PM is defined by Dybbs and Edwards as:

Red 

 up d 

(16)

Where: Red denotes Reynolds number at pore scale,  is density of fluid, u p is mean pore velocity (m/s), d is characteristic length scale of the pore (m) and  is viscosity of fluid ( Pa  s ).

10

After careful examination of velocity distribution via a hexagonal arrangement of spheres [26] opined that, there are four distinct flow regimes they described namely: 1. Darcy or creeping flow regime, where Red  1; 2. Inertia flow regime 1 to 10  Red  150; 3. Unsteady laminar flow regime 150  Red 300; 4. Unsteady and chaotic flow regime Red  300. The average pore velocity is calculated by up  uin  . Kuwahara et al. suggested a clear distinction between the turbulence characteristics in PM and that of clear fluid flow, that is, high turbulence intensity usually occurs in PM. They therefore suggested the use of turbulence effect when Reynolds number is larger than 80. In our work, we employed the RNG k-e turbulence model. EDC model was employed in simulating the turbulence flow with complex chemical reaction mechanism. The following were applied in our work: 1. Radiation of inner PM – DO radiation model 2. Combustor walls – mixed thermo boundary conditions 3. Velocity set at inlet; mass fraction and flow rate also specified. 4. The mixture had a uniform temperature of 300 K at the inlet. 5. Outflow boundary condition specified at the exit. 6.

Fluid area; porous zone boundary condition.

Permeability of PM,  and inertial resistance coefficients C2 are given by Ergun equation:



3 150 1   2

(17)

3.5 1    Dp  3

(18)

C2 

Dp2

Where Dp is the average diameter of particles and  is the porosity of PM.

11

5. Model validation The experimental results were compared with the numerical simulation results in order to ascertain the validity of the model. We compared the wall temperature of the outer wall as shown in fig. 6 at a velocity of 1 m/s. From fig.6, there is a clear agreement between the experimental results and simulation as the maximum deviation recorded were 2.7% for equivalence ratio of 1.0 and 2.4% of equivalence ratio of 0.8. This point to the fact that, the calculated results are reliable.

1250

Simulation (phi=1.0, u=1 m/s) Experiment (phi=1.0, u=1 m/s) Simulation (phi=0.8, u=1 m/s) Experiment (phi=0.8, u=1 m/s)

Wall temperature (K)

1200 1150 1100 1050 1000 950 900 0

2

4

6

8

10

12

14

Distance from inlet (mm)

Fig. 6 Comparison of the external wall temperature distributions between the simulation results and experimental data.

6. TPV System Performance This is obtained base on estimation from the temperature predictions. The TPV cell used is the Gallium Antimonide (GaSb). The distance between the TPV cell and combustor was set to 5 mm and a cooling system attached behind the TPV cell to keep temperature at 300 K. The total efficiency of the system is calculated by:

TPV  RS RH PV

(19)

Where TPV denotes total efficiency of the system,  RS is combustion radiation efficiency, RH is the radiation heat transfer efficiency and PV is the PVC conversion efficiency. For MTPV 12

system, increasing the external wall temperature is ideal to improve the output power and energy conversion efficiency. The radiation efficiency is the ratio of the radiant energy output from the external wall of the combustor to the total chemical energy input. The three efficiencies are defined as follows:

Net radiation of the side wall Chemical energy of fuel

(20)

RH 

The usable radiation arrived at the PVC Net radiation of the side wall

(21)

PV 

The electric Power output The usable radiation arrived at the PVC

(22)

RS 

The incident radiation of wall, Pin is given by [27]: 

Pin   j 1 A  j     Eb  j d  n

(23)

0

Where A  j  , area of each element’s surface, Eb  j  , spectral allocation of emissive power and

 , emissivity. Useful radiation Pen is cell energy band gap wavelength. It is derived as follows: g

Pen   j 1 A  j   C  j     Eb  j d  n

(24)

0

Here C  j  , radiation angle factor between element surface and PVC. Electric power Pel is given by:

Pel  Voc  FF  J sc  Acell

(25)

Where Voc is open circuit voltage, FF is fill factor, J sc is short circuit current density and Acell is area of the PVC. Short circuit current density is calculated by:

J sc   j 1 n

A  j   C  j   g Eb QEext q0 d 0 Acell hc

(26)

Where QEext is external quantum efficiency, q0 is elementary charge, h is planks constant and

C is speed of light. 13

The Voc is determined by Shockley formulation as:

J  Voc   Tc In  sc  1  J0 

(27)

Where  is Boltzmann constant, Tc is cell temperature and J 0 is saturation current density. The saturation current is estimated by ref.

 Eq  J 0  1.84 103  Tc3  exp   g 0   kTc 

(28)

Where Eg is energy bandgap, 0.72 eV for GaSb PVC. Fill factor is calculated as:

FF 

v  In  v  0.72  v 1

Where

(29)

is normalized Voc calculated as:

v  Voc q0 kTc

(30)

7. Results and Discussions 7.1 Effect of equivalence ratio The location of the peak temperature is affected by the equivalence ratio as shown in fig. 7. The mean values of the wall temperatures are 880.70 K, 1031.59 K and 1071.37 K for equivalence ratios 0.6, 0.8 and 1.0 respectively. There is increase in phi leading to increase in flame temperature towards the inlet as shown in fig.8. Similar results were obtained by Pan et al.[24] . Phi signifies fuel available for combustion and a higher value indicates more H2 available for reaction leading to more energy being released. However, an observation to the effect that, the highest emitter efficiency with PM occurred at phi=0.8 as shown in fig. 9 even though the highest wall temperature was recorded at phi=1, fig 8. This occurrence is explained by the fact that, there was a shift in the core of the flame further from the inlet but close to the combustor wall at the condition when phi=1. This means, great sum of heat is dissipated by the wall, fewer than that which will be used to preheat and ignite the incoming fuels. Therefore the combustor wall may not be able to absorb the same 14

proportion of heat. This clarifies why the highest emitter efficiency occurred at phi = 0.8, though the temperature is not the highest. Fig. 9 shows total efficiency of the system ( TPV ), PVC conversion efficiency ( PVC ), combustion efficiency (  RS ) and radiation heat transfer efficiency (RH ) of the PM TPV device for premixed H2/O2 flames of equivalence ratios 0.6, 0.8 and 1.0.

1250 1200 1150

Phi = 0.6 Phi = 0.8 Phi = 1.0

Wall Temperature (K)

1100 1050 1000 950 900 850 800 750 700 0

2

4

6

8

10

12

14

Distance from inlet (mm)

Fig. 7 - Temperature distributions along the external wall of micro combustor different for equivalence ratio.

15

1400

Centerline Temperature (K)

1200

Phi = 0.6 Phi = 0.8 Phi = 1.0

1000

800

600

400

200 0

2

4

6

8

10

12

14

Distance from inlet (mm)

Fig. 8 - Distribution of the centerline temperature in the combustor for different equivalence ratio.

26 24

TPV

22

pvc

Efficiency (%)

20 18

rs

16

rh

14 12 10 8 6 4 2 0 0.6

0.8

1.0

H2-O2 Equivalence Ratio

Fig. 9 -  ,  PV ,  rs and  rh of the PM TPV device for premixed H2/O2 flames of Equivalence Ratio 0.6, 0.8 and 1.0 16

7.2 Effect of Solid Matrix Thermal Conductivity Heat is transferred by convection and conduction during combustion via the solid matrix and in ascertaining which transport medium dominates, we compute as follows [23]:

 d      u  d    Pe  2

d

s

 uin 

in

 s 

 s 

f

(31)

Where: d denotes characteristic length scale of the pore,  s is thermal diffusivity of solid matrix, = ks sCp,s  m2 /s  ,  f is thermal diffusivity of fluid  m2 /s  ,  is the porosity, uin is the inlet velocity and Pe is Peclet number. Chua et al.[23] opined that the mechanism which dominates the thermal transport process within PM is conduction. The effect of ks on TPV performance is studied with uin  1 m s , phi = 0.8 and

ks  5, 25,50,100 W/mK. The mean temperature distribution from fig.10 along the walls are 988.93 K, 994.28 K, 1005.50 K and 1020.75 K for ks  5, 25,50,100 W/mK respectively. The peak temperatures from fig.12 for ks  5, 25,50,100 W/mK are 2072.93 K, 1742.97 K, 1652.26 K and 1573.3 K respectively. From Fig.11, the high temperature is restricted to a small portion for ks  5 W/mK. The reason for this occurrence is clarified by thermal diffusivity, which relates to the rate at which heat is propagated. In a porous media, the thermal diffusivity of the solid matrix is lower than that of the wall. The rate of movement of heat is faster from the inner surface of the combustor to the outer surface than it is conducted downstream. This explains why the distribution of temperature down the wall is steep. Also, the rate at which heat is released via combustion is faster than the rate at which heat is being lost and this explains why heat is contained in that small region. Fig.12 shows the comparison of the various system efficiencies, that is, overall efficiency, combustion radiation efficiency, the radiation heat transfer efficiency and the PVC conversion efficiency. It can be observed that, the highest overall efficiency of the system, 0.322% is recorded when k s = 50 W/mK.

17

1500 1400

Wall Temperature (K)

1300

5 W/mK 25 W/mK 50 W/mK 100 W/mK

1200 1100 1000 900 800 700 0

2

4

6

8

10

12

14

Distance from inlet (mm)

Fig. 10 - Temperature profile along the centerline of the wall.

2200 2000

5 W/mK 25 W/mK 50 W/mK 100 W/mK

Wall Temperature (K)

1800 1600 1400 1200 1000 800 600 400 200 0

2

4

6

8

10

12

14

Distance from inlet (mm)

Fig. 11 - Temperature profile along the center axis for different ks .

18

26 24

TPV

Efficiency (%)

22 20

pvc

18

rs

16

rh

14 12 10 8 6 4 2 0 5 W/mK

25 W/mK

50 W/mK

100 W/mK

Solid matrix conductivity (W/mK)

Fig. 12  ,  PV ,  rs and  rh of the PM TPV device for premixed H2/O2 flames for varying solid matrix conductivity.

7.3 Effect of mixture flow velocity Another condition which affects the residence time and the location of the flame center is the mixture flow velocity. The effect of mixture flow velocity on distribution of temperature along the combustor walls was investigated under the conditions where phi=0.8 and ks  50

W/mK. A higher mean wall temperature was observed when the flow velocity increased from 1 to 4 m/s as depicted in fig.15. At v= 4 m/s the highest temperature along the combustor wall is 1501.36 K . A decrease was observed in temperature when the flow velocity reduced to 1 m/s and a mean temperature of 1203.85 K was recorded. Increasing flow velocity improves heat transfer rate between combustion product and walls of the combustor. This leads to the attainment of high temperature. It is observed that, the increase in mean wall temperature becomes smaller as the flow velocity gets larger. When the flow velocity is high more fuel participates in the combustion leading to a higher mean wall temperature. A drawback to this is that, it carries along with it a shorter residence time and before combustion would have been completed, a chunk of the heat would have been conducted away. The main issue with micro combustors is the 19

limitation posed to the residence time as a result of the small length scale of the combustor. The inlet velocity is inversely proportional to residence time and how to sustain the flame inside the combustor is of paramount concern if the inlet velocity increases beyond a certain value. We achieved the highest emitter efficiency when the inlet velocity was 3 m/s, which was 29.1375% as shown in fig. 16. The range for the occurrence of the maximum efficiency is between 1-3 m/s. The Nusselt number for flow in PM is found to increase linearly as the Reynolds number increases, giving room for heat to be convected from the flame to end of combustor. The optimized configuration of the entire system is listed in table 2.

1650 1600

Mean wall temperature (K)

1550 1500 1450 1400 1350 1300 1250 1200 1.0

1.5

2.0

2.5

3.0

3.5

4.0

Inlet velocity (m/s)

Fig. 13 - Mean wall temperature under different inlet velocities

20

30

 pv

25

rs rh

Efficiency (%)

20

15

10

5

0 1

2

3

4

Inlet velocity (m/s)

Fig. 14  ,  PV ,  rs and  rh of the PM TPV device for premixed H2/O2 flames for varying inlet velocity.

Table 2. Optimized Configuration and performance of the PM TPV device Performance parameter

values

materials

Emitter: steel PVC: GaSb

Solid matrix conductivity

50 W/mK

Inlet velocity

3 m/s

Equivalence ratio

0.8

Emitter efficiency

29.1375%

Electrical power output

2.7 W

7.4 Experimental performance assessment of the TPV system A prototype porous media generator was built. It mainly consisted of the planar PM combustor and two GaSb PVC. Fig 15 depicts the circuit of the GaSb cell. The test conditions were same as that described in the experimental set up. The combustor size was 15 10 1 mm3 with a wall thickness of 0.5 mm . The hydrogen flow rate was 600 mL/min and the hydrogen to 21

oxygen ratio was 2:1. The wall and the PVC had a distance of 1 mm separating them. In real time operation, the PV cells become hot and therefore cooling fin was attached at the back of the PVC to bring the temperature down. An electrical power of 1.703 W was obtained. The opencircuit electrical voltage and short-circuit current were 0.491 V and 4.857 amp respectively.

Fig. 15 Circuit of GaSb cell

7.5 Effect of temperature change of PVC The temperature of the PVC has an important effect on the cell’s characteristics and performance. The temperature of the PVC was varied from 290 K to 340 K to examine the temperature effect on the performance of the PVC. Fig. 16-18 illustrates the effect of varying the cell temperature on the GaSb bandgap, cut-off wavelength, saturation current density, open circuit voltage and the fill factor. As the temperature increase from 290 K to 340 K, the forbidden band width decreased slightly whiles the cut-off wavelength witnessed a slight increment. This in effect causes the short circuit current to observe a slight increase whiles the open circuit voltage decreases. Variation of temperature from 290 K to 340 K recorded a 35% decline in the output power of the system. Similarly, there is obvious increase in the fill factor as the temperature increases. The efficiency and the power density of the PVC therefore show a tendency to decrease gradually as the cell temperature increases. When the cell temperature changes and the other conditions remain the same, the systems efficiencies change as well. Fig. 19 shows the variation of the cell efficiency and output power

22

when the mixture flow rate is 1800 mL/min. From fig. 19, when the cell temperature increases, the cell efficiency and output power show a gradual decline linearly. For any 10 K increase in cell temperature, the cell efficiency and power output reduce by 7% and 0.14 W respectively. The impact of the PVC surface temperature is great as can be seen from the simulated results. The cooling of the PVC is very important in every micro thermal energy conversion system as the PVC becomes hot in operation. It is therefore important to attach cooling fins at the back of the PVC. Incorporating a filter in the system will not impact the photoelectric energy conversion process but to a large extent reduce the cooling burden of the PVC.

0.725 1.78

0.720

Bandgap (eV)

1.76

0.710 1.74

0.705

0.700

Cut-off wavelenght (µm)

0.715

1.72

0.695 290

300

310

320

330

340

Cell Temperature (K)

Fig.16, Variation of forbidden band and cutoff wavelength at different cell temperature.

23

32.0 0.36

2

Short Circuit current density (A/m )

31.5 31.0 30.5

0.32 30.0 0.30

29.5 29.0

0.28

Open circuit voltage (V)

0.34

28.5 0.26 28.0 290

300

310

320

330

340

Cell Temperature (K)

Fig.17 Variation of short circuit current density and open circuit voltage at different cell temperature.

24

0.74

0.72

Fill factor

0.70

0.68

0.66

0.64 290

300

310

320

330

340

Cell Temperature (K)

Fig.18 Variation of fill factor at different cell temperature

3.0 22 21

2.8

2.6

19 18

2.4 17 16

Output Power (W)

Cell efficiency (%)

20

2.2

15 14

2.0 290

300

310

320

330

340

Cell Temperature (K)

Fig.19 Variation of cell efficiency and electricity output at different cell temperature.

25

Conclusions The possibility of connecting a TPV device to a porous media combustor inserted with SS mesh, both experimentally and numerically was investigated. The system was designed and fabricated and the following key parameters were measured; the overall efficiency, the radiant surface temperature distribution, emitter efficiency and output power. The conclusions are as follows: 1. The combustion efficiency increases when inlet velocity increase from 1 to 3 m/s and then decreases when inlet velocity is 4 m/s. 2. Oxygen rich mixing ratio results in highest emitter efficiency. 3. A high wall thermal conductivity produces more uniform temperature. The lowest mean wall temperature was recorded at ks = 5 W/mK, whereas the highest was recorded at ks = 100 W/mK 4. The projected output power is 2.7 W corresponding to a power density of 0.72 W/cm2, when the PVC temperature is kept at 300 K and the spacing between the radiant wall and the PVC is 1 mm. An output electric power of 1.703 W can be obtained with a micro-combustor of 15 × 10 × 1

mm3 , two PVCs of 187 mm2 each and a distance of 5 mm between the PVC and the radiator. Acknowledgements The authors acknowledge research grant from National Science Foundation of China (No. 51376082 and 51676088) and Project Funded by Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions..

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Highlights 

The proposed TPV device is ideal for practical applications; the experiment produced

1.703 W electrical power. 

A porous media combustor is integrated with a TPV device.



Increment in cell temperature decreased the forbidden band whiles the cut-off wavelength increased.



Temperature variation of PVC resulted in 35% decline in output power of the system.

29