Effects of step height on wall temperature of a ... - CiteSeerX

INSTITUTE OF PHYSICS PUBLISHING

JOURNAL OF MICROMECHANICS AND MICROENGINEERING

J. Micromech. Microeng. 15 (2005) 207–212

doi:10.1088/0960-1317/15/1/029

Effects of step height on wall temperature of a microcombustor Z W Li1 , S K Chou, C Shu and W M Yang Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117576, Singapore E-mail: [email protected]

Received 6 May 2004, in final form 10 September 2004 Published 29 October 2004 Online at stacks.iop.org/JMM/15/207 Abstract We investigate the effects of step height of a cylindrical microcombustor on the premixed flame and external wall temperature. A simulation study is carried out employing a hydrogen–air fuel mixture and the detailed reaction mechanism. The external wall temperature increases drastically with decreasing step height, while the flame temperature is nearly independent of step height. Experimental investigations have been conducted on microcombustor tubes to explore the effects of step height and compare the results with those obtained by simulation. A stable flame is obtained in microcombustors having step heights of 1 mm, 2 mm and 3 mm. Good agreement between the simulated and measured external wall temperature has been achieved. When the inlet velocity and fuel–air ratio are constant, the emissive power of the microcombustor wall increases with decreasing step height. (Some figures in this article are in colour only in the electronic version)

1. Introduction The proliferation of micro devices creates a strong demand for small-scale power sources. These power sources commonly convert chemical energy stored in fuels into electrical and mechanical power by combustion in sub-centimeter packages [1]. One such power source is a micro thermophotovoltaic (TPV) system [2]. The micro TPV system consists of three main parts, namely, a heat source, an emitter and a photovoltaic cell array. The emitter, which is the wall of a microcombustor, converts heat from combustion into radiation, while the photovoltaic cell converts radiation energy into electricity. However, only those radiated photons having energy greater than the band gap (e.g. for GaSb cells, it is 0.72 eV, corresponding to a wavelength of 1.7 µm) of the photovoltaic cell can be converted into electricity. In other words, those photons with a wavelength longer than 1.7 µm cannot generate free electrons to produce electricity when impinging on the photovoltaic cell. An increase in the temperature of the emitter not only enhances the emissive power drastically, but also improves the spectral distribution 1

Address for correspondence: SSLS, National University of Singapore, 5 Research Link, 117603, Singapore.

0960-1317/05/010207+06$30.00

so that a large portion of photons has energy greater than 0.72 eV. Therefore, it is of great importance to ensure a high and uniform temperature along the external wall of the microcombustor. Besides the emitter material, its internal radius, shape and wall thickness, the fuel used, fuel–air ratio and fuel– air mixture flow rate and the height of a sudden expansion step of the microcombustor chamber also affect the external wall temperature and emissive power. An earlier study [2] has shown that a sudden expansion step is advantageous for the application of the micro TPV system. However, the effects of step height on the external wall temperature of the microcombustor have not been well understood. The objective of the present paper is to investigate the effects of step height on the external wall temperature and the emissive power of a microcombustor. For simplicity, we consider a premixed laminar flame in a cylindrical microcombustor. Numerical simulation of a premixed hydrogen–air flame has been carried out in microcombustors having different step heights. The detailed reaction mechanism is used in the simulation. Experiments on the microcombustors with different step heights have been conducted to compare the results with those obtained by simulation.

© 2005 IOP Publishing Ltd Printed in the UK

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Flow

r 1

2

3

2

2

1 x

x

2 x

where µ is the viscosity and p is the pressure. And the r momentum may be written as ∂(ρuv) 1 ∂(ρvvr) + = ∂x r ∂r ∂ ∂p ∂u 1 ∂ 2rµ ∂u + − µ − ∂r ∂x ∂r r ∂r 3 ∂x ∂v 1 ∂ 4rµ ∂v 1 ∂ 2 ∂ µ + − µv . (3) + ∂x ∂x r ∂r 3 ∂r r ∂r 3 Taking an energy balance of the flame, we write 1 ∂ ∂ ∂T 1 ∂ ∂T ∂ (ρuh) + (ρvhr) = r + q, k + k ∂x r ∂r ∂x ∂x r ∂r ∂r (4)

where h is the specific enthalpy, T is the flame temperature, k is the gas thermal conductivity and q is the heat generation rate per unit volume. The enthalpy h is defined as h = -7 0 20 i mi hi , where hi is the specific enthalpy of species i, mi is the mass fraction of species i. For each species i, the mass Figure 1. Sketch of the microcombustors. balance may be written as ∂(ρumi ) 1 ∂(ρvrmi ) + ∂x r ∂r 2. Modeling the microcombustor ∂ ∂(ρmi ) ∂(ρmi ) 1 ∂ = (5) Di + Di r + ωi , ∂x ∂x r ∂r ∂r A sketch of the microcombustor is shown in figure 1. The combustor chamber is made of stainless steel and has a constant where Di is the mass diffusivity of the specifies i and ωi is cross-sectional area. The length L and wall thickness b of the the species mass generation rate per unit volume. Taking an combustor are 20 mm and 1 mm, respectively. At the inlet energy balance of the wall enclosing the flame, we have plane of the combustor chamber, there is a sudden expansion 1 ∂ ∂ ∂Tw ∂Tw kw + kw r = 0, (6) step and an inlet orifice. The inlet orifice has a radius of 1 mm. ∂x ∂x r ∂r ∂r The step heights, s, are 1 mm, 2 mm and 3 mm, and the internal where k is the conductivity of the wall, and T is the wall w w radii of the combustor chamber, r0 = 1 + s, are 2 mm, 3 mm temperature. and 4 mm. In our present study, we assume that the wall material The governing equations describing the flame and flow of the microcombustor is stainless steel, and use kw = are written in a cylindrical coordinate system (x, r), where 20 W m−1 K−1 [7]. Equations (1) to (6) are valid for the x-axis is chosen to lie along the centerline of the tube; the following boundary conditions. At the inlet plane of positive in the flow direction. We choose x = 0 at the inlet the computational domain x = −7 mm, the temperature of of the microcombustor chamber. The velocity components u the unburned gas mixture is equal to 300 K, the fuel–air and v are in the x and r directions, respectively. The following equivalence ratio is 0.5, and the average velocity of the assumptions are applied to the flow and flame: (i) no Dufour unburned gas mixture is U = 4 m s−1. In our experimental effects [3]; (ii) no gas radiation; (iii) no work done by pressure set-up, there is a straight tube of 2 mm internal diameter with and viscous forces; (iv) no kinetic energy change in the flame a length of 80 mm upstream of the microcombustor. The ratio zone; (v) homogeneous chemical reaction; (vi) steady state; of the length to diameter is 40. The entrance length, Le, given (vii) the detailed reaction mechanism applies [4–6]; (viii) by White [8], is approximately Le = 0.06d Re, where Re is the chemically inert internal wall surface and (ix) body forces Reynolds number, and d is the tube internal diameter. In our present study, Re = U d/ν = 4 × 2 × 10−3 /1.8 × 10−5 = 444 are neglected. With the above assumptions, the governing equations for and Le = 27d. Therefore, we impose a fully developed velocity profile at the inlet plane of the computational domain x = the premixed flame are written as follows. For the overall mass −7 mm. At the inlet plane of x = −7 mm and the exit plane balance, we write x = 20 mm, a heat flux of 0 is specified [9, 10] for the solid wall cross sections. Downstream of the microcombustor a ∂(ρu) 1 ∂(ρvr) + = 0, (1) far-field pressure condition is specified. At the internal wall, ∂x r ∂r a no-slip boundary condition applies, and non-permeable and where ρ is the density and r is the radial coordinate. The x no-species mass flux normal to the wall surface are specified. momentum may be written as Finally, at the external wall r = r1 , the heat flux from the external wall to the surroundings is qw = h1 (Two − T0 ) + 4 ∂(ρuu) 1 ∂(ρuvr) ∂p ∂ 4 ∂u 1 ∂ ∂u εσ Two − T04 W m−2, where h1 is the natural convective heat + =− + µ + rµ ∂x r ∂r ∂x ∂x 3 ∂x r ∂r ∂r transfer coefficient from the external wall to the surroundings. ∂ 2µ ∂(vr) 1 ∂ ∂v For a vertical cylindrical microcombustor considered in − + rµ , (2) ∂x 3r ∂r r ∂r ∂x our present study, h1 = 1.42 [(Two − T0)/L]0.25 [11], Two 208

Effects of step height on microcombustor wall temperature

Table 1. Gas-phase reaction mechanism for hydrogen–air a [4–6]. Reactions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

O2 + H = OH + O H2 + O = OH + H H2 + OH = H2O + H OH + OH = H2O + O H2 + O2 = OH + OH H + OH + M = H2O + Mb O2 + M = O + O + M H2 + M = H + H + M c H + O2 + M = HO2 + Md H + O2 + O2 = HO2 + O2 H + O2 + N2 = HO2 + N2 HO2 + H = H2 + O2 HO2 + H = OH + OH HO2 + O = OH + O2 HO2 + OH = H2O + O2 HO2 + HO2 = H2O2 + O2 H2O2 + M = OH + OH + M H2O2 + H = H2 + HO2 H2O2 + OH = H2O + HO2

Ak (m, kmol, s) 5.10 × 1013 1.80 × 107 1.20 × 106 6.00 × 106 1.70 × 1010 7.50 × 1017 1.90 × 108 2.20 × 109 2.10 × 1012 6.70 × 1013 6.70 × 1013 2.50 × 1010 2.50 × 1011 4.80 × 1010 5.00 × 1010 2.00 × 109 1.20 × 1014 1.70 × 109 1.0 × 1010

βk

Ek (J kmol−1)

−0.82 1.00 1.30 1.30 0.00 −2.60 0.50 0.50 −1.00 −1.42 −1.42 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

6.91 × 107 3.70 × 107 1.52 × 107 0.00 2.0 × 108 0.00 4.001 × 108 3.877 × 108 0.00 0.00 0.00 2.90 × 106 7.90 × 106 4.20 × 106 4.20 × 106 0.00 1.905 × 108 1.57 × 107 7.50 × 106

Rate constants are given in the form k = Ak T βk exp(−Ek /RT ). Enhancement factors: H2O = 20.0. c Enhancement factors: H2O = 6.0, H = 2.0, H2 = 3.0. d Enhancement factors: H2O = 21.0, H2 = 3.3, O2 = 0.0, N2 = 0.0. a

b

is the temperature of the external wall, T0 is the ambient temperature, ε is the wall emissivity, and σ is the Stefan– Boltzmann constant. We use T0 = 300 K and ε = 0.5 in our present study. The gas density is calculated using the ideal gas law. The gas viscosity, specific heat and thermal conductivity are calculated from a mass fraction weighted average of the species properties. The specific heat of each species is calculated using a piecewise polynomial fit of temperature given in Fluent [12]. We use hydrogen as fuel and simulate a premixed hydrogen–air flame in the vertical cylindrical microcombustor. The detailed hydrogen–air reaction mechanism [4–6] is used in the present study, which involves nine species and 19 elementary reactions. The nine species are H2, O2, H2O, H, O, OH, HO2, H2O2 and N2. The three parameters Ak, βk and Ek for each of the 19 reactions are shown in table 1 [4–6].

3. Numerical simulation Given the above information, the governing equations can be solved by using a segregated solution solver with an underrelaxation method [12]. The momentum equations are solved, then the continuity equation, before the pressure and mass flow rate are updated. The energy and species equations are subsequently solved. Iterations are monitored and checked until a converged solution is obtained. Figure 2 plots the temperature contour for the microcombustors with different step heights. The flame is stabilized at the step and the flame front presents a ‘V’ shape. The curved flame front could be caused by the viscous drag within the fluid shear layers, which becomes more important as the tube diameter decreases. A high velocity of the fuel–air mixture at the centerline near the step may also cause the nonflat flame front. The higher the mixture velocity, the greater will be the effects. However, the maximum temperature for

different step heights is the same, and the flame cores have a similar shape. Figure 3 shows the axial temperature distribution at different step heights. The axial flame temperature distribution is nearly identical for different step heights. Starting from the inlet plane of the microcombustor chamber, the flame temperature is at the initial condition of 300 K. A short distance downstream, it can be seen that the flame temperature rises suddenly and reaches a maximum temperature. This is attributed to the liberation of heat from combustion. Then, the flame temperature decreases gradually due to heat loss to the wall. The results shown in figures 2 and 3 suggest that the flame temperature is independent of step height. The external wall temperature distribution in the axial direction is shown in figure 4. It is seen that the external wall temperature increases with decreasing step height. In figure 2, we observe that the relatively hotter flame plume attaches to the wall earlier as the step decreases. In addition, the temperature distribution along the external wall tends to become uniform with decreasing step height.

4. Experiments Figure 5 shows the microcombustion experimental rig. The rig [13] consists of: (i) a cylindrical microcombustor; (ii) a connection tube with four 0.2 mm diameter orifices distributed equally around the perimeter through which high pressure hydrogen is injected into an air stream to obtain a mixture; (iii) a plenum filled with hydrogen at a uniformly high pressure and (iv) two sets of electronic mass flow controllers, one for hydrogen with a capacity of 10−3 m3 s−1 and the other for air with a capacity of 5 × 10−3 m3 s−1. The controllers are capable of controlling flow rates accurate to 1% of the full scale. The experimental rig illustrated in figure 5 not only provides good mixing of hydrogen with air but also prevents the flame from flashing back into the plenum. 209

Z W Li et al 1.42e+03 1.36e+03 1.31e+03 1.25e+03 1.20e+03 1.14e+03 1.08e+03

(a) 1mm

1.03e+03 9.72e+02 9.16e+02 8.60e+02 8.04e+02 7.48e+02 6.92e+02 6.36e+02 5.80e+02 5.24e+02 4.68e+02 4.12e+02 3.56e+02 3.00e+02

Aug 31, 2004 FLUENT 6.1 (axi, dp, segregated, sep 9, I am)

Contours of Static Temperature (k)

1.42e+03 1.37e+03 1.31e+03 1.26e+03 1.20e+03 1.14e+03 1.09e+03

(b) 2mm

1.03e+03 9.75e+02 9.19e+02 8.62e+02 8.06e+02 7.50e+02 6.94e+02 6.37e+02 5.81e+02 5.25e+02 4.69e+02 4.12e+02 3.56e+02 3.00e+02


1.42e+03 1.36e+03 1.31e+03 1.25e+03 1.20e+03 1.14e+03 1.08e+03 1.03e+03 9.72e+02 9.16e+02 8.60e+02 8.04e+02 7.48e+02 6.92e+02 6.36e+02 5.80e+02 5.24e+02 4.68e+02 4.12e+02 3.56e+02 3.00e+02


(c) 3 mm



Figure 2. Simulated temperature contours for different step heights.

The microcombustor, the connection tube and the plenum are made of stainless steel. At the inlet of the microcombustor chamber, a sudden expansion step is designed for flame stabilization. Earlier studies [14–17] indicate that a sudden expansion step is able to facilitate recirculation of the combustion mixture near the wall, thereby enhancing the mixing process of combustion around the rim of the tube (normal scale) and ensuring a complete and stable combustion. Therefore, we employ the sudden expansion step in the design 210

of the cylindrical microcombustor. In our present study, the step heights are 1 mm, 2 mm and 3 mm, respectively. Experiments have been conducted using the vertical cylindrical microcombustors having the same geometry, the same inlet velocity and the same fuel–air ratio as the numerical simulation. Hydrogen is chosen as fuel because of its high heating value, rapid rate of vaporization, fast diffusion velocity, short reaction time and high flame speed [1]. The mixture is ignited at the exit plane of the microcombustor. A stable

Effects of step height on microcombustor wall temperature 6.8

1500

6.7

1300 Power (W)

Temperature (K)

6.6

1100

1 mm 2 mm 3 mm

900

6.5 6.4 6.3

700

6.2 6.1 0.5

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1

1.5

2

2.5

3

3.5

s/r 0

300 0

0.2

0.4

0.6

0.8

1

x/L

Figure 3. Simulated axial flame temperature distributions for different step heights. 810

Temperature (K)

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710 Simulated 1 mm Simulated 2 mm Simulated 3mm Measured 1mm Measured 2mm Measured 3mm

660

610

560 0

0.2

0.4

0.6

0.8

1

x/L

Figure 4. Simulated and measured external wall temperature for different step heights.

Microcombustor

Hydrogen controller

Figure 6. Measured emissive power at different step heights s/r0

measured by K-type thermocouples. The microcombustor is easily dismantled and replaced. The whole system is exposed to air and is not insulated. The use of a microcombustor with a high aspect ratio is intended to eliminate the radiative heat transfer between the thermocouple wire and the wall. A large surface area of contact between the thermocouple junction and external wall surface also helps us to reduce the uncertainty. Compared with the results obtained by thermomelt crayons (produced by Markal Company, USA) having an accuracy of 1%, the uncertainty of the wall temperature measurement is approximately ±2%. Figure 4 shows the measured external wall temperature distribution in the axial direction at the average inlet velocity of 4 m s−1 and the fuel–air ratio of 0.5. The simulation results are also plotted on this figure for comparison. Both experiment and simulation show that the external wall temperature increases with decreasing step height. The maximum difference between the measured and simulated external wall temperature is about 4%. Given the measured external wall temperature distribution, the emissive power can be predicted. Figure 6 shows the calculated emissive power for different step heights. The emissive power decreases with increasing step height. An increase in step height increases the external wall surface area, but it decreases drastically the external wall temperature of the microcombustor. As a result, the emissive power decreases.

5. Analysis Connection tube Plenum

Air controller

Figure 5. Schematic diagram of test rig.

flame can be established inside the tube by adjusting the flow rate or fuel–air ratio. The existence of combustion inside the microcombustor is detected by the thermocouples placed at the external wall surface and the exit plane, and indicated by the glow of the tube. The flame and wall temperatures are

The results from the simulations and experiments have shown that the external wall temperature increases with decreasing step height. This trend can be explained by analyzing the heat transfer from the flame to the surroundings. The heat transfer from the flame to the internal wall, Q, over a length of L for the above cylindrical microcombustors may be written as Q/L = 2πr0 h0 (T − Twi ),

(7)

where h0 is the convective heat transfer coefficient from the flame to the internal wall surface. This yields Q 1 . (8) T − Twi = 2π r0 h0 L where Twi is the internal wall temperature. The heat transfer from internal wall to external wall over a length of L for the 211

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above cylindrical microcombustor may be expressed as dTw . (9) Q/L = −2πrkw dr Rearranging and integrating equation (9) from r0 to r1 yields r1 Q 1 ln . (10) Twi − Two = 2π kw L r0 Combining equations (8) and (10), we obtain Q 1 r0 + b Q 1 + ln T − Two = . (11) 2π r0 h0 L 2π kw L r0 The heat transfer from the external wall surface of the vertical cylindrical microcombustor to its surrounding is 4 − T04 r1 εσ L, (12) Q = 2π(Two − T0 )r1 h1 L + 2π Two 3 by using the total heat transfer coefficient ht = h1 + σ ε Two + 2 T0 + Two T02 + T03 , we have Two Q 1 . (13) Two − T0 = 2π r1 ht L Eliminating Q by combining equations (11) and (13) and noting r0 = 1 + s, we obtain T − Two 1 . (14) = 1 − (1+s+b)ht (1+s+b)ht T − T0 + k ln 1+s+b +1 (1+s)h 1+s 0

w

Simulation results described above have shown that the flame temperature is independent of step height. Keeping the wall thickness and the inlet orifice radius constant, taking respect to step the derivative of Two with height, s, and 2 using ∂ht /∂s = εσ 3Two + 2Two T0 + T02 + 1.02L−1 (h1 )−3 (∂Two /∂s), we obtain ∂Two = ∂s

−

T − T0 (Two − T0 )2

+(

r1 r0 h0

+

ht bht ht r1 r0 h0 − kw r0 + kw ln r0 r1 r1 2 σ ε 3Two + 2Two T0 kw ln r0

)[ (

+ T02 ) + 1.02 ] Lh3

,

1

(15) where h0 = k Nu/2r0, and Nu is the Nusselt number. For a premixed laminar flame in a narrow tube or duct, Mayer and Drysdale [18, 19] recommended Nu = 3.65. Taking the Nusselt number as 3.65, we have h0 = 1.825k/r0 . Generally, k kw and b < r0 . Therefore, we have b bht ht ht r0 − − = > 0. r0 h0 kw r0 r0 1.825k kw Applying these relationships to equation (15), we obtain ∂Two /∂s < 0. This means that the external wall temperature increases with decreasing step height. The maximum external wall temperature will occur at zero step height. Therefore, there is no peak value of Two for a step with nonzero height. The external wall temperature is critical to the micro TPV system. To achieve a desired external temperature, the step size should be as small as possible. However, without the step the flame position is hard to control [2]. Therefore, in choosing step height, there is a trade off between the flame position and the wall temperature.

6. Conclusion The effects of step height on the flame and external wall temperature have been simulated using the detailed hydrogen– air reaction mechanism. The simulation results show that the external wall temperature increases drastically with decreasing 212

step height. However, the axial flame temperature is unaffected. An experimental study has been carried out employing hydrogen as fuel. Good agreement between the simulated and measured external wall temperature has been obtained. Using the external wall temperature measured at the constant inlet velocity and fuel–air ratio, we are able to show that emissive power increases with decreasing step height. At an average inlet velocity of 4 m s−1 and a fuel–air ratio of 0.5, the emissive power of 6.2 W, 6.4 W and 6.6 W can be achieved for the microcombustors having step heights of 1 mm, 2 mm and 3 mm, respectively. A simplified heat transfer analysis has helped us to show that the external wall temperature increases with decreasing step height.

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