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Micro-combustion research works are motivated by development of portable, autonomous power generators such as the micro TPV with improvement in energy density over batteries. Heat recuperation is a technique which contributes to better energy efficiency performance by recovering heat from the exhaust gas. In this paper, a numerical simulation is carried out to study the impact of incorporating recuperation on the performance of micro modular combustor system. The simulation results have been validated by experiments; achieving close agreement between simulated and experi-mental data. It was observed that the mean wall temperature, radiation power and emitter efficiency markedly improved with the incorporation of a heat recuperator. In addition, 25.8% enhancement of total radiation power and 30.6% emitter efficiency could be realized when the hydrogen air equivalence ratio was 0.9.

With the continuous development of MEMS (micro electro-mechanical system) devices, much attention has been focused towards the design of light weight power sources with high power density. For a long time, chemical batteries have played a dominant role as the power source for MEMS and mobile electronic devices. However, there exist some major limitations such as negative environmental impacts, low power density and short usage time [1-3]. To overcome these limitations, there is an exacting need to develop an alternative and environmental friendly energy source with a higher power density. Ever since Epstein and Senturia [

Micro-TPV power generator is a typical micro power generation system which converts thermal radiation into electrical power. It consists of series of micro combustors, emitters, filters and photovoltaic cells. There are many challenges to improve the performance of the micro-TPV system. Firstly, the heat loss caused by the large surface to volume ratio brings thermal quenching to the micro combustion process. A number of studies have been carried out to stabilize the flame in the micro scale combustion process. Kim and Lee [

Besides the positive impact of integrating porous media to the micro combustor’s performance, another method which can be utilized to increase the wall temperature and emitter efficiency of micro TPV system is to recycle the heat of exhaust gas. In previous works, the hot exhaust gas is used to reheat the outer surface of the combustor. Park et al. have developed several micro cylindrical emitters with annular-type shield for heat recirculation [

In this work, a numerical model has been detailed and formulated to study the combustion of premixed hydrogen and air in planar combustors with and without heat recuperator. The significance of this work includes the detailed fundamental study of new generation of micro combustors incorporating heat recuperation with the chief aim of markedly improving the combustor’s temperature distribution as well as energy efficiency. The originality of this work stems from studying the effects of incorporating heat recuperation in a modular mirco combustor design as well as its energy efficiency performance. Combing through available literature, we would like to emphasis that such a study has not been conducted before. In developing the numerical model, the combustion process was modeled as species transport based on the detailed mechanism with 9 species and 19 reactions as shown in

As shown in

Between the combustors and connectors, stainless steel wire meshes were employed. The holes on the mesh were small enough to prevent the back flow of the hydrogen flame. The error associated with each experimental measurement was computed to be 5%.

As shown in

For a complete combustion of hydrogen in air, the overall chemical reaction can be written as

This stoichiometric relation is based on the assumption that the simplified composition for air is 21% and 79% by volume. The stoichiometric hydrogen-air ratio can be expressed as:

In which, is expressed as:

The flow rates of H_{2} and air can be determined by considering the conservation of mass within the plenum. At the combustor inlet, it can be observed that:

By applying ideal gas law and with the assumption of constant pressure and temperature in the plenum,

The mass flow rates equations for and air can be written as:

The heat transfer between exhaust gas and intake gas is calculated by NTU method for cross flow heat exchanger. In the calculation of NTU, fouling factor is ignored in calculating the heat transfer coefficient:

A simple calculation reveals that the thickness of the centre tube has little effect on the overall heat transfer of the recuperator.

The outlet temperature of heat recuperator can be determined:

The heat transfer coefficient is determined by Dittus Boelter equation which is applicable to premixed gas inside tube [

The planar combustor employed in this study has internal dimensions of 10 mm × 1 mm × 17 mm with 0.5 mm wall thickness. The heat recuperator has a shell diameter of 10 mm and tube diameter of 5 mm. The exhaust gas flows through the shell side while the fresh gas flows through the tube. A 3-D model was built up.

The fluid medium can be regarded as to be in continuum as the Knudsen number is less than unity. That is the characteristic lengths of the models used are sufficiently large compared to the mean free path of air or hydrogen molecules. After the chemical energy is released in the combustor, an energy balance is achieved between the combustor and the environment. As a result, a steady-state model is employed. As the gas flowing through the combustor at a constant speed, the temperature effect caused by mass gradient can be neglected. Based on these, the following assumptions were made: 1) steady-state combustion, 2) no Dufour effects [

For continuity conservation:

For momentum conservation:

For energy conservation:

where and is the fluid enthalpy source term.

For species conservation:

where is the net rate of production of species I by chemical reaction, is the rate of creation by addition from the dispersed phase, and is the diffusion flux of species I which is given by

A detailed hydrogen-air reaction mechanism with 9 species and 19 reactions is employed to simulate the hydrogen combustion. Based on the governing equations listed above, the 3-D model is solved by Fluent Release 14.0 [^{−3} for the criteria of convergence. 1 × 10^{−6} is set as the energy convergence criterion. A massfractionweighted average method is utilized to compute the viscosity, constant pressure specific heat and thermal conductivity of the hydrogen and air mixture. A piecewise polynomial fitting method is employed to calculate the specific heat of each species. A mesh independence study is performed to get better accuracies as well as to reduce the computational time. The calculation error can be neglected as the mesh size is 0.1.

The pressure drop in heat exchanger is defined as

where f is the streamwise pressure drop coefficient which is expressed as

where is the entrance loss coefficient, is the exit loss coefficient, is the core friction factor, is the specific volume at the exit, is the specific volume at the inlet, is the mean specific volume.

The wall thermal conductivity is taken to be 20 W/m^{2}K. At the inlet plane, the mixture enters the combustor with a uniform temperature 300 K. Heat loss from the noninsulated wall to the ambient are given by

where the convective heat transfer and the wall emissivity are taken to be 5 and 0.78, respectively.

The efficiency of micro combustor is defined as the ratio of the net radiation power emitted by emitter to the chemical energy input flow. Planck’s distribution shows the emissive power of a blackbody as a function of wavelength, , at different temperatures.

where and

By Stefan-Boltzmann law, the total emissive power per unit surface area of a black body can be determined from

where

The efficiency of the micro combustor is defined as

where is the mass flow rate of the hydrogen, corresponds to the emissive surface area of micro combustor that will be utilized to emit photon for PV cell and is the wall emissivity.

Adopting the various assumptions to simplify the complexity of the model, we expect an acceptable degree of variance between the numerical results and experimental results. From the comparison of the mean wall temperature between the numerical result and experimental result, (

It is noteworthy that the numerical temperature data are higher than experimental results for all equivalence ratios. This observation may be attributed to the assumptions made in the computational methods and involving deviation from the real condition.

Micro combustors with single and double inlet pipes are employed in the experiment. The hydrogen/air mixture flows through the inlet pipe and enters the combustors for burning. Figures 4 and 5 show the temperature distributions of the micro modular combustors with single inlet pipe for both simulation and experiment. Symmetric distributions are obtained in both numerical and experimental results. It is apparent that the temperature distribution is non-uniform where the two central combustors have comparatively higher temperature than the two combustors located at the sides. This fact indicates that the design with single inlet pipe is not suitable for the micro modular TPV system application. An obvious temperature gradient can be observed between the top and the bottom of the connector. The temperature gradient on the connectors may be attributed to the thermal conduction from high temperature zone to the ambient temperature zone through the wall. A more combustors uniform distribution can be observed among the four with double inlet pipes as shown in Figures 6 and 7 which is caused by the equally supplied hydrogen/air mixture. There exist marginal differences between numerical and experimental results. This is due to the oxidizing of wire meshes between combustors and connectors in the experiment. After a long combustion duration, the meshes potentially become oxidized and may block the flow at certain region. This can account for the differences between numerical and experimental results.