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Experimental and numerical analysis of radiation effects in heat re-circulating combustors

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Experimental and numerical analysis of radiation effects in heat re-circulating combustors

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Content EXPERIMENTAL AND NUMERICAL ANALYSIS OF RADIATION EFFECTS IN HEAT RE-CIRCULATING COMBUSTORS by Sandeep Gowdagiri A Thesis Presented to the FACULTY OF THE USC VITERBI SCHOOL OF ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (MECHANICAL ENGINEERING) August 2010 Copyright 2010 Sandeep Gowdagiri ii Acknowledgements At University of Southern California (USC), I have had many opportunities to learn from renowned scholars, both from academia and industry. I would like to extend my gratitude to all of them for their motivation and encouragement; in particular I would like to thank Professor Paul Ronney for boosting my interest in the thermal sciences, especially in combustion and radiation heat transfer. This master‟s thesis was completed at the Combustion Physics Laboratory in the Aerospace and Mechanical Engineering Department (AME), under the auspices of supervising committee composed of Professor Paul Ronney (Mechanical Engineering Department), Professor Satwindar Sadhal (Aerospace & Mechanical Engineering Department), and Professor Hai Wang (Aerospace and Mechanical Engineering Department). I would like to extend my gratitude to all of the thesis committee members for the support I enjoyed during this work, and especially for their cooperation and inspiration. I would like to specially thank Professor Paul Ronney for providing the necessary computational resources to conduct my research work. Without his generous advice and contributions, this work would have not been accomplished. I would also like to thank Chien-Hua Chen, for the numerous discussions, technical advice and help with all the experimental apparatus during the course of my research. This work is supported by the U.S. Defense Threat Reduction Agency (DTRA) Joint Science and Technology Office iii under contracts HDTRA1-07-C-0092. Finally, I am everlastingly grateful to my parents for their continuing understanding, patience and encouragement. iv Table of Contents Acknowledgements ii List of Figures v List of Tables vii Nomenclature ix Abstract x CHAPTER ONE: INTRODUCTION 1 1.1 Role of radiation heat transfer 2 1.2 Objective of Research 5 CHAPTER TWO: EXPERIMENTAL SETUP 6 CHAPTER THREE: NUMERICAL MODELING 9 3.1 Grid Generation and Properties 9 3.2 Virtual Thermocouples 16 3.3 Third Dimension Heat Loss 17 CHAPTER FOUR: RESULTS AND DISCUSSION 21 4.1 Φ – Experimental vs. Numerical 21 4.2 Temperatures – Experimental vs. Numerical 25 4.3 Effect of Third Dimension Heat Loss on Thermocouple Accuracy 31 4.4 Heat Re-circulation and Radiation 35 CHAPTER FIVE: CONCLUSIONS 37 Bibliography 39 v List of Figures Figure 1: Geometry of “Swiss Roll” Heat Re-circulating Combustor 2 Figure 2: Extinction limit obtained using full model, full model without radiation (heat loss included) and full model without heat loss (radiaton included) 4 Figure 3: Identical titanium alloy and gold coated Swiss Roll combustors 7 Figure 4: Experimental Apparatus and Setup 8 Figure 5: Two-dimensional numerical model along with virtual thermocouple locations 9 Figure 6: Close-up of numerical model virtual thermocouple 16 Figure 7: Schematic of third dimensional heat loss model 18 Figure 8: Corresponding electrical network for third dimension heat loss 18 Figure 9: Equivalence ratio (Φ) at extinction Limit vs. Re 22 Figure 10: Gold coated combustor after degradation of walls 25 Figure 11: Temperature at Extinction vs. Re for TC 1 26 Figure 12: Temperature at Extinction vs. Re for TC 2 26 Figure 13: Temperature at Extinction vs. Re for TC 3 27 Figure 14: Temperature at Extinction vs. Re for TC 4 27 vi Figure 15: Temperature comparison between titanium and gold combustors during combustion 31 Figure 16: 2D and 3D Virtual Thermocouple Models 32 vii List of Tables Table 1 – Experimental results for Re vs. Φ for titanium combustor 23 Table 2 – Experimental results for Re vs. Φ for gold plated combustor 23 Table 3 – Numerical simulation results for Re vs. Φ for ε = 0.8 24 Table 4 – Numerical simulation results for Re vs. Φ for ε = 0.4 24 Table 5 – Numerical simulation results for Re vs. Φ for ε = 0.1 24 Table 6 - Temperature data for titanium combustor, v = 20 cm/s; Re ≈ 64 28 Table 7 - Temperature data for gold combustor, v = 20 cm/s; Re ≈ 64 28 Table 8 - Temperature data for titanium combustor, v = 33 cm/s; Re ≈ 104 29 Table 9 - Temperature data for gold combustor, v = 33 cm/s; Re ≈ 104 29 Table 10 - Temperature data for titanium combustor, v = 67 cm/s; Re ≈ 210 30 Table 11 - Temperature data for gold combustor, v = 67 cm/s; Re ≈ 210 30 Table 12 – 2D simulation with and without UDF 32 Table 13 - 3D simulation with insulated and const. temperatures boundary conditions 33 Table 14 – Calculation of heat transfer coefficient h for convective heat loss 34 viii Table 15 – Individual heat transfer contributions (in bold) by convection, radiation and conduction, respectively 35 ix Nomenclature Re Reynolds Number [Dimensionless] ε Emissivity [Dimensionless] Φ Equivalence Ratio [Dimensionless] Nu Nusselt Number [Dimensionless] σ Stefan-Boltzmann constant [W/m 2 K 4 ] Pr Prandtl Number [Dimensionless] RTE Radiative Transfer Equation RSM Reynolds Stress Model DO Discrete Ordinates x Abstract Prior studies have shown that surface-to-surface radiation transfer within heat re- circulating combustors significantly affect their performance, especially at low Reynolds number (Re). With this as motivation, a comparison of standard titanium and gold-plated combustors was performed. Corresponding numerical simulations were performed on FLUENT 12.1, including gas-phase conduction and convection, solid-phase conduction, chemical reaction as well as surface-to-surface radiation heat transfer. It is found both experimentally and numerically that reducing surface-to-surface radiation heat transfer by reducing wall emissivity can significantly extend extinction limits at low Re where heat loss dominates the extinction behavior. Temperature distributions inside the combustor are measured by physical thermocouples as well as numerical “virtual” thermocouples for both combustors, i.e., standard titanium and gold-plated ones. 1 CHAPTER ONE: INTRODUCTION Interest in heat re-circulating “excess enthalpy” combustors which were first studied over 30 years ago (S.A. Lloyd et al) has been renewed due to efforts in micro- scale combustion and power generation. Such work is motivated by the fact that hydrocarbon fuels contain 100 times more energy per unit mass than lithium-ion batteries, thus devices that convert fuel to electricity at better than 1% efficiency represent improvements in portable electronic devices and other battery-powered equipment (A.C Fernandez-Pello). However, at small scales, heat and friction losses become more significant due to increased surface area to volume ratio, thus devices based on existing macro-scale designs such as internal combustion engines may be impractical. Consequently, many groups have considered heat re-circulation using a counter-current heat exchanger for thermal management. By transferring thermal energy from the combustion products to the reactants without mass transfer (thus dilution of reactants), the total reactant enthalpy (sum of thermal and chemical enthalpy) is higher than in the incoming cold reactants and therefore can sustain combustion under conditions (lean mixtures, small heating value fuels, large heat losses, etc.) that would otherwise lead to the flame being extinguished, without re-circulation (Fig. 1). With the heat re-circulated to the reactant, the combustion can sustain in either much leaner or richer conditions than conventional flame. Also, the heat loss is minimized by re-circulating the heat, which diffuses from the hottest location of the combustor, back to the reaction zone. Although there is more surface area to conduct heat 2 in the third dimension, the heat lost / re-distributed due to conduction relative to heat produced by combustion, is probably minimal. Consequently, this combustor probably is most efficient from a thermal management viewpoint in small size application. It has been found, according to numerical models that the surface-to-surface radiation heat transfer, plays an important role in reducing extinction limits during combustion, more so than gas-phase radiation heat transfer, especially at lower Re (J. Ahn et al, F.J.Weinberg). Fig. 1 - Geometry of “Swiss Roll” Heat Re-circulating Combustor 1.1) Role of radiation heat transfer Prior studies (P.D. Ronney) have shown that straight-channel combustors without counter-flow, in which stream-wise heat conduction along the channel wall, is the only means to recycle heat. This configuration, which relies primarily on conduction across 3 the wall dividing products from reactants for which stream-wise conduction (along as opposed to across the dividing wall) is fundamentally different from counter-current combustors and is almost always detrimental; consequently the performance of counter- current heat re-circulating combustors exceeds straight-channel combustors. In the counter-current combustors, for zero wall thermal conductivity, no heat recirculation via conduction across the wall is possible. For high thermal conductivity, some thermal energy is transferred away from the combustion region, re-deposited into the gas, and then lost to ambient. Thus an optimum thermal conductivity causing the widest extinction limits has to exist (C.H. Kuo et al). Computations have shown that wall-to-wall radiation heat transfer acts similar to stream-wise wall conduction in heat re-circulating combustors, since this type of radiative transfer would also increase heat transfer within the solid phase and out of the central reaction zone without a corresponding increase in heat exchange with the gas (C.H. Kuo et al). Fig. 2 shows the comparisons between a full model with laminar flow, full model without surface-to-surface radiation within the combustor and full model without convective / radiative heat transfer to ambient air. As can be seen, at higher Re, all three extinction limits merge due to the chemical enthalpy flux (and therefore, the heat release) being much greater than conductive heat loss or heat transport by radiation, and the extinction limits behavior is dominated by blow off mechanism (insufficient residence time, as compared to chemical time scales, determine extinction conditions). At lower Re, heat losses dominate extinction behavior due to similar order of radiative and conductive heat loss with chemical enthalpy heat release. 4 At lower Re, where convection does not dominate, heat losses dominate extinction behavior due to longer residence times and smaller chemical enthalpy fluxes (A.R. Jones et al, D.G. Norton et al, T.T Leach et al). It has also been found that suppressing the surface-to-surface radiation has a similar effect to suppressing heat loss. One might expect the surface-to-surface radiation to increase heat re-circulation by radiating to the gas within the combustor. However, since the gases can be considered essentially transparent given the small scale of the channel width, the effect of gas-phase radiation is minimal and the radiation transfers heat directly between walls. This has, qualitatively, the same effect as stream-wise conduction along the walls, which is detrimental to heat re-circulation as explained above. As a result, the extinction limits are likely to become narrower with wall-to-wall radiation heat transfer. Fig. 2 – Extinction limit obtained using full model, full model without radiation (heat loss included) and full model without heat loss (radiation included) (C.H. Kuo et al) 5 1.2) Objective of Research The set outline for the research is as follows: a) Compare the extinction limits during combustion within the “Swiss Roll” heat re- circulating combustors having high emissivity (standard titanium) and low emissivity (gold coated) walls. b) Compare the experimental data obtained (such as equivalence ratio at extinction limit Φ, thermocouple temperatures at extinction, etc.) to numerical predictions carried out on computational fluid dynamics (CFD) software FLUENT 12.1. c) Through an understanding of the underlying processes taking place within the combustor, seek to propose an explanation for the results obtained. 6 CHAPTER TWO: EXPERIMENTAL SETUP Two identical 3.5 turns “Swiss Roll” heat re-circulating combustors were used (Fig. 3). One of them was constructed with titanium alloy (Ti-8Al-1Mo-1V) and the other was a titanium alloy with a layer of polyurethane electro-plated gold on the walls. Coating the walls of the titanium combustor with a lower emissivity material reduced the surface-to- surface radiation heat transfer within the combustor. The combustors were of dimensions 90 mm X 90 mm X 50 mm, with channel width 5 mm and wall thickness 0.5 mm. These combustors were constructed and experiments carried out earlier at USC (Jeongmin Ahn et al). K-type thermocouples were placed along one half of the diagonal of the combustor and a centrally placed heating wire was used to begin the combustion reaction. During the experiments, each of the combustors had, above and below them, two sets of ceramic fiber blankets, sealed with ceramic based glue. This was done in order to minimize heat losses as well as to prevent gas leakage. The research entailed comparing the gold plated combustor and the bare walled titanium combustor under identical experimental conditions with regard to temperature distribution and extinction limits, thus confirming the surface-to-surface radiation effects. 7 Fig. 3 – Identical titanium alloy and gold coated Swiss Roll combustors A predetermined ratio of air-fuel mixture, with pre-set velocity, was made to flow through the flow controllers and into the Swiss-Roll combustor (Fig. 4) A nichrome heating wire, connected to an external power source, was used to „ignite‟ the combustion reaction within the combustor. A value of 40 W was used as input power for all experiments. The thermocouples placed inside the combustor detected temperatures during the combustion reaction. A suitable program on LabVIEW was used to display the thermocouple temperature readings within the combustor, and to also control the ratio of air-fuel mixture flowing into the combustor. Once combustion occurred, the external power source, and hence the heating wire, was „switched off‟. The reaction then becomes a self sustaining one, due to heat recirculation, under steady conditions (no change in flow velocity or air-fuel mixture). To obtain equivalence ratios at extinction, either the air-fuel ratio or flow velocity (depending on experimental conditions) was gradually lowered over a period of time 8 where successive steady conditions are reached at each stage. Through this experimental process, one can obtain the fuel percentage at extinction limit, and hence the equivalence ratio as well as thermocouple temperatures at extinction. Fig 4. – Experimental Apparatus and Setup 9 CHAPTER THREE: NUMERICAL MODELING The Swiss-roll combustor geometry was chosen to match experiments on propane-air combustion in a 3.5-turn square inconel spiral heat exchanger (Fig. 5). The channel width, wall thickness and overall dimensions are 5 mm, 0.5 mm and 90 x 90 mm, respectively. 3.1) Grid Generation and Properties Fig. 5 – Two-dimensional numerical model along with virtual thermocouple locations During the simulation, FLUENT solved the conservation equations for mass and momentum, energy conservation and species conservation were also solved. Furthermore, transport equations were solved for turbulent flow and radiation heat transfer. 10 The equation for conservation of mass, or the continuity equation, is solved as follows: (1) Eq. (1) is the general form of the mass conservation equation and is valid for compressible and incompressible flows. ρ denotes density of fluid, v denotes velocity of fluid and S m denotes the source term. The equation for the conservation of momentum in an inertial reference frame is described by: (2) In eq. (2), t denotes time, p denotes static pressure, v denotes velocity of fluid, ρg represents gravitational body force and F denotes external body forces, as well as other model dependent source terms such as user-defined sources, porous media, etc. The stress tensor in eq. (2) is given by: (3) where μ is the molecular viscosity of the gas, and I is the unit tensor. The energy equation is solved in the form: (4) 11 where k eff is the effective conductivity (k + k t , where k t is the turbulent thermal conductivity, defined according to the turbulence model being used), and J j is the diffusion flux of species j. The first three terms on the RHS of eq. (4) represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively. The viscous dissipation term was neglected during the simulations as a low Mach number model approximation was used in FLUENT. S h includes the heat of chemical reaction, and other volumetric heat sources. The energy E, on the LHS of eq. (4), is given by: (5) where h is the enthalpy defined for the gas, p is the pressure, ρ is the density, and v is the velocity of the fluid (gas). However, the kinetic energy term (V 2 /2) in eq. (5) is neglected since the simulations in FLUENT used low Mach number model approximation. h is given by the formula: (6) where Y j is the mass fraction of species j and h j is: (7) Eq. (7) represents the sensible enthalpy of the gas, and h j 0 denotes the enthalpy of formation of species j, and the reference temperature T ref, j ≈ 298 K. 12 The term S h in eq. (4) which represents the source of energy due to chemical reactions was calculated by: (8) where, R j is the volumetric rate of creation of species j. S h can also include user-defined sources, radiative surface-to-surface heat transfer, etc., which are explained below. As with the momentum equation, the species transport equation is solved by FLUENT in the following form: (9) where ρ is the density of fluid, v is the velocity of fluid flow, Y i is the local mass fraction of each species i, R i is the net rate of production of species i by chemical reaction and S i is the rate of creation by addition of species plus any user-defined sources. Grid-independence was verified by refining the grid until solutions no longer varied with further increase in grid points as shown below. Grid independency: 1. Grid amount: 27531 Re = 500 Extinction limit = 0.72% T max at extinction limit = 1419 K T avg at extinction limit = 799 K 13 2. Grid amount: 110124 Re = 500 Extinction limit = 0.72% T max at extinction limit = 1414 K T avg at extinction limit = 797 K The combustor height (in the z-direction) is incorporated via specification of heat loss coefficients described below (section 3.3). Since preliminary studies [7, 9-11] showed that radiation heat transfer within the heat exchanger is important, surface-to- surface radiation was modeled via Discrete Ordinate (DO) method. The general form of the radiative transfer equation (RTE) is given in the following form: (10) where, σ s = scattering coefficient 14 Since the numerical simulations in FLUENT were carried out for incompressible (since ρ changes due to heat release), steady-state flow, eqs. (1), (2), (4), and (9) simplify to the following: (11) (12) (13) (14) All gas- and solid-phase thermodynamic and transport properties are modeled as temperature-dependent using handbook values. Turbulent transfer of heat, mass and momentum are modeled using the Reynolds Stress Model (RSM). Propane-air reaction was modeled using a one-step mechanism. 1-step Reaction Model: Reaction Mechanism: C 3 H 8 + 5 O 2 → 3CO 2 + 4H 2 O 15 Rate Equations: Parameters used were: A = 4.836E+9 [m-sec-kmole]; E a = 1.254E+8 J/kmole = 30 kcal/mole; m = 0.1; n = 1.65 With the Reynolds Stress Model in FLUENT, the turbulent heat transport is modeled using the concept of Reynolds‟ analogy to turbulent momentum transfer. The equation is given by: (15) where E is given by eq. (5), c p denotes specific heat of the fluid, μ t the viscosity, and the deviatoric stress tensor is represented by the formula: (16) The default value of the turbulent Prandtl number (Pr t ) is 0.85. The turbulent mass transfer equation is treated similarly, with a turbulent Schmidt number as 0.7. The inlet boundary condition is a specified velocity with ambient (300K) temperature reactants. The outlet condition is ambient pressure. The combustor external surfaces (in the x-y plane) experience heat loss via natural convection with heat transfer coefficient 10 W/m 2 K and radiation transfer. Computations were started with mixtures away from 16 extinction limits. The initial conditions were high (≈1500K) [7] center temperatures tapering to the ambient at the outer boundary. This was sufficient to “ignite” reaction and converge to steady solutions. Converged solutions were used as initial conditions for subsequent computations in which the inlet composition or velocity was changed slightly, and then new converged solutions were obtained. This process was repeated until extinction was observed, in which case the center temperature would decrease continuously to ambient during the iterations. As in experiments, this extinction process was found to be abrupt and well-defined. 3.2) Virtual Thermocouples Fig. 6 – Close-up of numerical model virtual thermocouple 17 In order for correct numerical values to be obtained through simulation, “virtual thermocouples” were modeled (Fig. 6) within the two-dimensional Swiss Roll combustor model. This served two purposes – a) The virtual thermocouple itself was made part of the calculations, which implied that the radiation heat transfer to/from the thermocouple, as well as conductive and convective heat transfer along the thermocouple surface played a part in calculating accurate temperatures. b) It served as a means of assessing temperature measurement errors of the real “physical” thermocouples via the phenomena explained above. The virtual thermocouples were modeled by placing solid objects at the required locations, with numerical properties such as conductivity, initial temperature, heat transfer co-efficient, etc. being assigned. The cells at the boundaries of the solid objects were packed closer together in order to obtain results with a greater accuracy. 3.3) Third Dimension Heat Loss In order to minimize computational time and complexity, a 2D Swill Roll model was built, and a third dimension heat loss model (for the out-of-plane loss) was needed. Hence, heat loss in the z-direction (Fig. 7) was modeled via a volumetric sink term in the energy equation that matched the experimental configuration as closely as possible. This term simulates conduction through the thermocouple (in the solid-phase) or convection 18 (in the gas-phase) to insulating blankets and aluminum plates on the top/bottom of the Swiss-roll, conduction through the blankets/plates, and natural convection and radiation to ambient air. Fig. 7 – Schematic of third dimensional heat loss model Fig. 8 – Corresponding electrical network for third dimension heat loss 19 In order to simulate heat loss in the third dimension, the values of R1s (resistance due to solid wall), R1g (resistance due to gas), R2, R3r and R3c (thermal resistance of gases – radiation and convection), T2 and T3 were obtained. This was carried out by calculating the resistances R1s and R1g, and the combined parallel resistance R1t (not shown in figure). The heat loss was calculated using the formula: (17) where, Q = heat loss (W/ m 2 ) H = convective heat transfer coefficient (W/m 2 K) ΔT= temperature gradient (K) ΣR = effective thermal resistance (K/W) ΔL = length (m) Once R1t was known and R2 already known, an iterative process beginning with a guess value for T2 was carried out and through successive stages, an estimated optimum value for T2 was obtained. Since the resistance R1t has a very low value, it was assumed that temperature for insulation is (T1+T3)/2 instead of (T2+T3)/2 to avoid two uncertain variables (T2 and T3) in the iterative process. Essentially, a slight amount of accuracy was sacrificed to obtain T3 by this process. The values of R3r and R3c were then calculated by using formulae in standard thermodynamic handbooks. 20 The heat loss was then obtained for different values of T1, and plotted against temperature to obtain a curve displaying heat loss characteristics. The curve was fitted to a third degree polynomial function and the individual coefficients were included in a C program written to account for heat loss in the third dimension. This program was interpreted by FLUENT, thus helping to simulate out-of-plane heat loss in the 2D grid generated. 21 CHAPTER FOUR: RESULTS AND DISCUSSION 4.1) Φ – Experimental vs. Numerical Fig. 10 shows the effect of coating the surface of the Swiss Roll combustor with gold, thus reducing wall emissivity. As can be seen, the experimental equivalence ratios at extinction limit were lower for the gold combustor as compared to the titanium combustor. This implies more effective heat re-circulation within the gold combustor. The numerical results showed a similar trend, matching experimental data. With lesser wall emissivity, the extinction limits could be significantly extended. Fig. 9 shows curves for emissivity values ε = 0.8 (assumed upper-bound emissivity for titanium), 0.4 (intermediate value of emissivity chosen during simulation in FLUENT to show effect of reducing wall emissivity) and 0.1 (assumed emissivity for gold). However, ε = 0.1 showed much leaner-than-expected extinction limits than experimental data. The equivalence ratio (Φ) is plotted against Re in Fig. 10, as displayed below. Re is calculated by the formula: (18) where V = inlet fluid velocity, L = characteristic length (channel width), and ν = kinematic viscosity of air at room temperature. 22 Fig. 9 –Equivalence ratio (Φ) at extinction limit vs. Re (The solid lines connecting the experimental data are drawn to guide the eye) The values obtained for experimental titanium and gold combustors were first at low Re, and then subsequently increased. From Fig. 9, we can see that for there is good agreement between the experimental gold curve and the numerical ε = 0.4 curve, but only at lower Re. The experimental gold curve shifts after Re ≈ 70, possibly due to the degradation of the gold coating on the walls of the combustor (Fig. 10), which occurred after about 2-3 weeks of testing (around 4-5 tests at different Re values: 40<Re<70). 23 However, the experimental titanium curve agrees well with the ε = 0.8 curve, even at higher Re. Tables 1 and 2 below, show the experimental equivalence ratios (Φ) and Re for the titanium and gold plated combustors, and Tables 3-5, the numerical simulation results for ε = 0.8, 0.4 and 0.1 respectively. Velocity (cm/s) Fuel % at ext. limit Re Ф 15 1.5 47.199 0.375 16 1.45 50.346 0.3625 20 1.25 62.933 0.3125 25 1.14 78.666 0.285 30 1.05 94.399 0.2625 33 1.03 103.839 0.2575 50 0.94 157.332 0.235 67 0.88 210.824 0.22 80 0.85 251.731 0.2125 160 0.76 503.461 0.19 Table 1 – Experimental results for Re vs. Φ for titanium combustor Velocity (cm/s) Fuel % at ext. limit Re Ф 13 1.33 40.906 0.3325 15 1.25 47.199 0.3125 20 1.05 62.933 0.2625 33 0.98 103.839 0.245 50 0.9 157.332 0.225 67 0.83 210.824 0.2075 Table 2 – Experimental results for Re vs. Φ for gold plated combustor 24 Velocity (cm/s) Fuel % at ext. limit Re Ф 20 1.52 62.933 0.38 40 1.12 125.865 0.28 67 0.92 210.824 0.23 80 0.86 251.731 0.215 160 0.72 503.461 0.18 Table 3 – Numerical simulation results for Re vs. Φ for ε = 0.8 Velocity (cm/s) Fuel % at ext. limit Re Ф 20 0.82 62.933 0.205 40 0.59 125.865 0.1475 80 0.49 251.731 0.1225 160 0.53 503.461 0.1325 Table 4 – Numerical simulation results for Re vs. Φ for ε = 0.4 Velocity (cm/s) Fuel % at ext. limit Re Ф 20 1.05 62.933 0.2625 40 0.72 125.865 0.18 80 0.59 251.731 0.1475 160 0.53 503.461 0.1325 Table 5 – Numerical simulation results for Re vs. Φ for ε = 0.1 25 Fig. 10 – Gold coated combustor after degradation of walls 4.2) Temperatures – Experimental vs. Numerical During combustion, the experimental temperature data (tables 6-11) show that the thermocouples in the gold coated combustor were at similar or slightly higher temperatures to their corresponding standard titanium combustors under the same conditions (inlet velocities and air-fuel mixture). The temperature values in the tables are shown for Re ≈ 64, 104, and 210. Fig. 15 shows us a graphical representation of the same. At extinction, the temperatures in the gold coated combustor were similar to that of the titanium combustor as well. This was matched by the numerical results which predicted similar temperatures at extinction limits for both Swiss Roll combustors. Figs. 11-14 26 show the experimental and simulation temperature values at extinction for the thermocouples (TC) 1-4. Fig. 11 – Temperature at Extinction vs. Re for TC 1 (The solid lines connecting the experimental data are drawn to guide the eye) Fig. 12 – Temperature at Extinction vs. Re for TC 2 (The solid lines connecting the experimental data are drawn to guide the eye) 27 Fig. 13 – Temperature at Extinction vs. Re for TC 3 (The solid lines connecting the experimental data are drawn to guide the eye) Fig. 14 – Temperature at Extinction vs. Re for TC 4 (The solid lines connecting the experimental data are drawn to guide the eye) 28 Titanium Combustor: Fuel percentage Thermocouple readings (°C) 1 2 3 4 5 6 1.5 470 469 328 285 202 174 1.45 501 496 346 304 213 182 1.4 519 511 365 321 226 193 1.35 535 523 376 333 238 204 1.34 539 527 384 340 248 212 1.33 543 530 390 345 254 218 1.32 547 534 395 352 262 225 1.31 549 535 397 355 266 228 1.3 551 538 400 357 269 231 1.29 554 538 401 357 269 232 1.27 559 539 401 357 270 234 1.26 563 539 400 356 270 234 1.25 566 538 396 354 269 232 1.24 EXTINCT!! Table 6 – Temperature data for titanium combustor, v = 20 cm/s; Re ≈ 63 Gold Combustor: Fuel Percentage Temperature readings (deg. C) 1 2 3 4 5 6 1.18 638 618 559 504 354 279 1.16 647 609 547 485 342 269 1.14 649 602 540 470 332 262 1.12 676 624 550 472 331 259 1.1 707 644 559 477 331 257 1.08 702 636 547 471 326 254 1.06 697 625 536 461 321 251 1.05 688 600 516 448 315 246 1.04 EXTINCT!! Table 7 – Temperature data for gold combustor, v = 20 cm/s; Re ≈ 63 29 Titanium Combustor: Fuel Percentage (%) Thermocouple readings (°C) 1 2 3 4 5 6 1.7 615 630 475 589 278 255 1.6 637 669 548 536 334 309 1.5 658 684 576 555 374 347 1.4 670 684 580 560 397 368 1.3 674 669 570 553 308 378 1.25 671 665 560 539 409 378 1.2 671 660 555 530 410 378 1.15 669 681 542 512 403 370 1.1 672 687 536 505 399 366 1.05 678 691 532 488 386 354 1.02 EXTINCT!! Table 8 – Temperature readings for titanium combustor, v = 33 cm/s; Re ≈ 104 Gold Combustor: Fuel Percentage Temperature readings (°C) 1 2 3 4 5 6 1.4 676 622 492 438 213 180 1.3 719 765 660 612 353 275 1.2 746 720 654 605 408 321 1.2 759 733 674 620 439 349 1.1 767 734 677 615 458 366 1 810 749 674 609 463 370 0.97 EXTINCT!! Table 9 - Temperature readings for gold combustor, v = 33 cm/s; Re ≈ 104 30 Titanium Combustor: Fuel Percentage (%) Thermocouple readings (°C) 1 2 3 4 5 6 1.2 855 875 1020 792 622 585 1.1 860 857 736 746 567 550 1 846 865 709 714 545 527 0.95 896 909 672 700 510 500 0.9 882 895 650 665 490 475 0.87 EXTINCT! Table 10 – Temperature readings for titanium combustor, v = 67 cm/s; Re ≈ 210 Gold Combustor: Fuel Percentage (%) Temperature readings (°C) 1 2 3 4 5 6 1.4 867 860 730 706 502 436 1.3 900 900 832 803 685 602 1.2 910 892 821 795 690 615 1.1 899 875 802 773 670 605 1 902 858 773 736 636 574 0.95 889 845 752 715 611 552 0.9 893 831 729 688 580 523 0.83 EXTINCT! Table 11 – Temperature readings for gold combustor, v = 67 cm/s; Re ≈ 210 Fig. 15 below shows us a graphical representation of the temperatures within the titanium and gold-plated combustors during combustion. Data shown is for velocities v = 20 cm/s, 33 cm/s and 67 cm/s and equivalence ratios, Φ = 0.325, 0.3 and 0.2375, and as can be 31 seen, the temperatures in the gold plated combustor is similar or slightly higher than the corresponding titanium combustor. Fig. 15 – Temperature comparison between titanium and gold combustors during combustion 4.3) Effect of Third Dimension Heat Loss on Thermocouple Accuracy To determine the effect of heat loss in the third dimension, i.e. heat loss by conduction along the thermocouple, virtual thermocouple tests were conducted in which the 2D simulation included a user-defined function to account for third dimension heat flow, and compared to results obtained using a 3D straight duct (10 cm x 5 mm x 5 cm) with virtual 32 TC and the same geometry, boundary conditions, and mesh 2D case, with the top and bottom insulated. Fig. 16 – 2D and 3D Virtual Thermocouple Models The results obtained through these simulations were as follows: Inlet V (m/s) Inlet T (K) Side Wall UDF TC (K) Real gas T 0.25 1000 H = 10 No 389 393 0.25 1000 H = 10 Yes 384 393 1 1000 H = 10 No 626 652 1 1000 H = 10 Yes 620 652 8 1000 H = 10 No 897 942 8 1500 1300 No 1359 1420 8 2000 1300 No 1462 1643 Table 12 - 2D Simulation with and without UDF 33 Inlet V (m/s) Inlet T (K) Side Wall TC bottom TC (K) real gas T 0.25 1000 H = 10 insulated 390 397 0.25 1000 H = 10 300 K 389 397 1 1000 H = 10 insulated 629 657 1 1000 H = 10 300 K 629 657 8 1500 1300 insulated 1358 1421 8 1500 1300 300 K 1358 1421 Table 13 – 3D simulation with insulated and constant temperatures boundary conditions As can be seen, comparison between the 2D and 3D cases for all inlet velocities show that having no user-defined function to simulate heat loss through the thermocouple displays the same temperature as having an insulated boundary condition at the end of the thermocouple (implying no heat flow through it). Again, comparing the 2D and 3D cases having a user-defined function with a constant temperature boundary condition (room temperature, implying heat flow through the thermocouple) shows that the UDF in the 2D case over-estimates the effect of heat loss compared to the 3D case. It can be concluded thus, that the effect of heat loss by conduction through the thermocouple is minimal for temperature measurements, and hence can be neglected. An energy balance by textbook formulae analysis further reinforces the minimal effect of heat loss due to conductive transfer along the thermocouple. For calculation purposes, the heat transfer coefficient H was calculated by first computing Re and Nu for flow past a cylinder (thermocouple), using empirical formulae 34 from standard thermodynamic handbooks. In the table below, the convective heat transfer coefficient H was calculated based on different inlet velocities (v = 1m/s and 8 m/s). Q conv was then obtained, as were Q rad and Q cond based on formulae presented by eqs. (19), (20) and (21). V (m/s) D (m) ν (m 2 /s) Re C m Nu K gas (W/mK) H (W/m 2 K) 1 0.0005 2.25e- 04 2.22E+00 0.989 0.33 1.143 0.086 196.5761 8 0.00005 2.25e- 04 1.78E+00 0.683 0.466 0.793 0.086 1363.823 Table 14 – Calculation of heat transfer coefficient h for convective heat loss Q conv = H*A*(T 2 – T 1 ) (19) Q rad = ε*A*σ*(T 2 4 – T 1 4 ) (20) Q cond =k*A*(T 1 -300)/L (21) where, ε = 0.8 A = 3.93e-5 m 2 (for convective and radiative transfer – across thermocouple) A = 1.9625e-7 m 2 (for conduction – across cross section of thermocouple) σ = 5.67*10 −8 W/m 2 K 4 k = 11 W/mK L = 0.025 m Table 15 presented below shows the individual contributions to heat loss by convection, radiation and conduction across the thermocouple respectively, and as can be seen, convective and radiative heat transfer contribute much more to heat loss than conduction. 35 H (W/m 2 K) T 2 (K) T 1 (K) Q conv (W) T 1 (K) T wall (K) Q rad (W) T 1 (K) Q cond (W) 196.6 650 626 0.185 626 500 0.162 626 0.028 177 1000 650 2.432 650 500 0.207 650 0.030 177 1000 700 2.084 700 500 0.316 700 0.035 177 1000 750 1.737 750 500 0.452 750 0.039 421 1642 1463 2.958 1463 1300 3.071 1463 0.100 177 1700 1329 2.577 1329 1000 3.774 1329 0.089 1363 1700 1546 8.239 1546 1000 8.390 1546 0.108 177 1078 938 0.973 938 650 1.060 938 0.055 1363 1078 1043 1.872 1043 650 1.789 1043 0.064 Table 15 – Individual heat transfer contributions (in bold) by convection, radiation and conduction, respectively 4.4) Heat Re-circulation and Radiation It is known that at constant Re, the residence time of the air-fuel mixture, and thus the reaction rate to avoid extinction regardless of amount of mixture needed, is constant. The high activation energy to get the combustion reaction started, and thus the reaction rates are mostly dependent on the temperatures in the surrounding region. With high thermal conductivity walls, as explained earlier, stream-wise conduction transfers away thermal energy from the combustion region, re-deposits into the gas, which is then lost to ambient air. This decreases the temperatures in the central combustion zone. Since radiative heat is transferred directly between walls (due to a non-zero view factor across wall faces), it 36 qualitatively has the same effect as stream-wise conduction along the combustor wall surface. In order to minimize the surface-to-surface radiation effect, the walls are coated with gold – a lower emissivity material. When the wall-to-wall radiation is minimized, the central temperature in the combustion zone may be higher, implying efficient combustion, and lesser heat loss, leading to wider extinction limits. The explanation provided accounts for both lower Φ (equivalence ratio) and similar temperatures at extinction limits in the titanium alloy Swiss Roll combustor and the gold coated one. 37 CHAPTER FIVE: CONCLUSIONS The following conclusions can be drawn through the results obtained from the research conducted. a) The numerical simulations conducted showed good agreement with the experimental data with regard to temperatures during combustion, temperatures at extinction as well as extinction limits (up to Re ≈ 70) and confirmed the effects of surface-to-surface radiation inferred from the experiments. b) The surface-to-surface radiation decreased with lower emissivity walls, which in turn increased the heat exchanger performance by decreasing the equivalence ratio (Φ) at extinction, thus widening the limits. c) The degradation of gold plated surface in the Swiss Roll combustor during experiments decreased performance because of an increased emissivity (ε), as seen by an increased flame extinction equivalence ratio (Φ) and temperatures at extinction limits. d) The effects of gold coating are less pronounced at high Reynolds number because radiative heat transfer is less significant as compared to convective heat transfer due to possible transitioning to turbulent flow, and hence larger chemical enthalpy release rate as compared to heat loss. It is also possible that, due to the degradation of the gold coating after repeated usage, the experimental and numerical simulations showed lesser agreement. 38 e) The effect of heat loss in the third dimension (i.e. conduction along the thermocouple) on temperature measurements in the apparatus used can be neglected as its effect is minimal compared to radiation and convective heat transfer. 39 Bibliography 1 J. Ahn, K. Borer, O. Deutchman, K. Maruta, P.D. Ronney, L. Sitzki, K. Takeda, Twenty-Ninth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 2002, pp 957–963. 2 Jeongmin Ahn, Craig Eastwood, Lars Sitzki, P.D. Ronney, “Gas-phase and catalytic combustion in heat re-circulating combustors”, Proceedings of the Combustion Institute 30 (2005) 2463-2472. 3 A.C. Fernandez-Pello, “Micropower generation using combustion: Issues and approaches”, Proc. Combust. Inst. 29 (2002) 883-899 4 A.R. Jones, S.A. Lloyd, F.J. Weinberg, “Combustion in heat exchangers”, Proc. Roy. Soc. (London) A360 (1978) 97-115 5 C.H Kuo, P.D. Ronney, “Numerical Modeling of Heat Re-circulating Combustors”, Proceedings of the Combustion Institute, Vol. 31, pp. 3277-3284 (2007). 6 T.T. Leach, C.P. Cadou “The role of structural heat exchange and heat loss in the design of efficient silicon micro-combustors”, 7., Proc. Combust. Inst. 30 (2005) 2437-2444. 7 S.A. Lloyd, F.J. Weinberg “A combustor for mixtures of very low heat content”, Nature 251 (1974) 47–49. 8 S.A. Lloyd & F.J. Weinberg, “Limits to energy release and utilization from chemical fuels”, Nature Vol. 257, October 2 1975, 367–370. 9 D.G. Norton, D.G. Vlachos “A CFD study of propane/air microflame stability”, Combust. Flame 138 (2004) 97-107. 10 P.D. Ronney “Analysis of non-adiabatic heat re-circulating combustors”, Combustion and Flame 135 (2003) 421-439 11 F.J. Weinberg “Advanced combustion methods” Ch.3. “Combustion in heat re- circulating combustors”, Academic Press, London and New York, (1986).

Abstract (if available)

Abstract Prior studies have shown that surface-to-surface radiation transfer within heat re-circulating combustors significantly affect their performance, especially at low Reynolds number (Re). With this as motivation, a comparison of standard titanium and gold-plated combustors was performed. Corresponding numerical simulations were performed on FLUENT 12.1, including gas-phase conduction and convection, solid-phase conduction, chemical reaction as well as surface-to-surface radiation heat transfer. It is found both experimentally and numerically that reducing surface-to-surface radiation heat transfer by reducing wall emissivity can significantly extend extinction limits at low Re where heat loss dominates the extinction behavior. Temperature distributions inside the combustor are measured by physical thermocouples as well as numerical “virtual” thermocouples for both combustors, i.e., standard titanium and gold-plated ones.

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Asset Metadata

Creator Gowdagiri, Sandeep (author)

Core Title Experimental and numerical analysis of radiation effects in heat re-circulating combustors

School Viterbi School of Engineering

Degree Master of Science

Degree Program Mechanical Engineering

Publication Date 08/05/2010

Defense Date 07/01/2010

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag heat re-circulation,heat transfer,OAI-PMH Harvest,Radiation,Swiss Roll burner

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ronney, Paul D. (committee chair), Sadhal, Satwindar S. (committee member), Wang, Hai (committee member)

Creator Email gowdagir@usc.edu,sandeep.gowdagiri@hotmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3286

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Document Type Thesis

Rights Gowdagiri, Sandeep

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu