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 [4] proposed the concept of “micro heat engine” in 1997, various types of micro heat engines such as micro gas turbine engines, micro Wankel engines and micro piezoelectric devices had been developed [5-8]. Meanwhile, micro thermoelectric devices and micro TPV (thermophotovoltaic) devices were also created as direct energy conversion systems without moving parts [9].

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 [10] have investigated several factors affecting the thermal quenching phenomenon in micro-combustion devices. It was found that the quenching distance was independent of the surface characteristics at low temperatures, whereas at high temperatures, the quenching distances were strongly affected by the surface characteristics. Another factor contributing to the quenching effect is the flame speed. Ananthanarayanan et al. have developed an analytical model to predict the flame speed [11]. Their results have suggested that the net heat recirculation was the fundamental parameter which determined the flame speed in a micro channel and it could be used as a good reference to avoid the quenching phenomenon. Another challenge for micro-TPV system application is to obtain a high temperature distribution on the wall surfaces. As has been proved by researchers, porous media has a positive impact on the thermal conduction from the flame to the combustor wall and increase the wall temperature. Li et al. have studied the influence of porous media position on the micro planar combustor performance [12]. The highest emitter efficiency was achieved when the porous media was in the middle of the combustor. Chou et al. have discussed the optimal porosity of porous media to obtain the highest emitter efficiency in micro cylindrical combustors [13]. It was found that a different optimal porosity should be adopted for different fuels for the highest emitter efficiency.

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 [14]. An optimized design was achieved when the flow velocity of propane/air was at 3.9 m/s, the equivalence ratio was equal to 1.0 and the gap between the emitter outer wall and the shield inner wall was 12 mm. Federici et al. have studied the effect of heat recirculation on flame stability by computational fluid dynamics method [16]. Key results have demonstrated that heat recirculation had minimal effects on extinction mode but had profound impact on blowout mode. Yang et al. tested a micro planar combustor with heat recirculation. The temperature could be increased by 70 - 110 K and the useful radiation energy could be improved by 83% with the effect of heat recirculation [16]. Another approach to recycle the heat of exhaust gas is preheating the reactants inside a heat exchanger. By wrapping the heat exchanger in the Swill-Roll configuration, combustor heat dissipation is effectively reduced and heat transfer between the windings and the combustion in the core become integral parts of the thermal system [17]. When a swiss-roll recuperator with an effectiveness of 0.85 and pressure drop of 10%, the thermal efficiency is 19%.

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 Table 1 [18]. The impact of several key parameters such as hydrogen air equivalence ratio, outlet flow velocity and the application of heat recuperator on the temperature and emitter efficiency were judiciously investigated.

As shown in Figure 1, the experiment set up consisted of 3 sub-systems namely: fuel supply and control system, combustion system and testing system. The entire system was operated at room condition with ambient temperature spanning 295 to 300 K. Fuel supply and control system comprised of the hydrogen tank, air compressor, mass flow rate controller and pipes. Hydrogen and air were used as fuel because hydrogen has the advantages of high power density, fast flame speed and short reaction time. The hydrogen and air flow rates were controlled by two Brooks Mass Flow Controllers with an accuracy of 1% of the full scale. The combustion system included a connecting tube, 4 connectors and 4 micro combustors. Micro combustors were connected on the connectors by threaded bolts, and the 4 connectors were designed to produce a more uniform flow profile before entering the micro combustors. The testing system consisted of a high-performance RAYTEK Infrared thermometer (Model MA2SSCF, with an accuracy of ± (0.3%T + 1) K), a high precision Mitutoyo Height Gauge with an accuracy of 0.001 mm and a PC. The infrared thermometer was used to measure the wall temperature of micro combustors. The distance from the thermometer to the spots to be tested was 300 mm. The height gauge was used to control the testing position of thermometer. Taking reference from the baseline of the wall, a total of 10 temperature readings were recorded for each experiment.

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 Figure 2, a cross flow heat exchanger, performing the function of heat recuperator, has been designed to recover the heat from the exhaust gas.

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 H₂ 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 [19].

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 [20], 3) no work done by pressure and viscous forces, (4) insert wall with no surface reactions, 5) no gas radiation [21].

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 [22]. SIMPLE algorithm which is convenient to solve the coupling between pressure and velocity has been employed to discretize the governing equations. The residuals for continuity, momentum, and species are set as 1 × 10⁻³ 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/m²K. 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.