A Quasi One-dimensional Simulation of a Combustor for Micro Gas Turbine Engine Using different NGV-Ethanol Fuelled Modes

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1 AEC8 9-0 October, 0, Krabi A Quasi One-dimensional Simulation of a Combustor for Micro Gas Turbine Engine Using different NGV-Ethanol Fuelled Modes Paramust Juntarakod, * and Udomkiat Nontakaew Department of Mechanical and Aerospace Engineering, Graduate College King Mongkut s Universit of Technolog North Bangkok 58 Pibulsongkram Road, Bangsue, Bangkok Thailand 0800 Corresponding Author: paramust_kmitnb@hotmail.com * Tel: , Fax: Abstract This work is to numericall stud combustion in silo combustor tpe of micro gas turbine engine using different NGV-Ethanol fuelled modes. The simulation applied chemical equilibrium method where the fuel mixture is specified b the wa of its C-H-O-N values and curve-fit coefficients are emploed to simulate air and fuel data along with frozen composition. The stud described performance parameters, pressure and temperature profile data on the effect of mole ratio of the NGV-Ethanol-mixture (00:0, 90:0, 80:0, 70:30), equivalence ratio (0.6-.0), pressure ratio ( ), and engine speed ( RPM).In this stud, the silo combustor was simulated on the variation of the ignition length (premixed zone) 0.0, 0.5 m and burning length (primar zone) 0.0, 0.5 m. The calculated data is then showed to plot the changing performances and pressure-temperature profile. Kewords: NGV-Ethanol, equilibrium, Simulation, Thermodnamic Modeling and Olikara and Borman.. Introduction The technolog to generated power from micro gas turbine engines is new technolog and compared with the piston engines of the efficienc and cost-effective for production power. The advantages of micro gas turbine engine are smaller and more efficient, depending on the purpose of the work (electric power and heat power). Generall, it will be used as backup power onl. However, this technolog is ver expensive. Determined from Claire [], he found that pa back periods and internal rate of return (IRR) is not satisfactor in the size range of kwh as following lifetimes of the sstem, when fossil fuel prices rise and demand. So, if micro gas turbine is the common choice for cogeneration of heat and power from fossil fuel and ethanol. Instead of the one fossil fuel micro gas turbine engines ma be used. These alternatives promise a significant reduction of the cost and Possibilit of using alternate fuels. This paper aims to develop a simple, modified some empirical and accurate silo combustor simulation model without the need as great deal of computational power or knowledge

2 AEC8 9-0 October, 0, Krabi of precise silo combustor geometrical data. So, the model is based on the classical two-zone approach on primar zone, wherein parameters like heat transfer from the general combustion chamber, blowb, energ loss and heat release rate are also considered. The calculated data are performance with respect to equivalence ratios, pressure ratio, engine speed and pressuretemperature profiles with respect to combustor length respectivel.. Modeling and analsis. The Mathematical of a Silo Combustor The mathematical of a silo tpe gas turbine combustor was applicable in the same details for constant volume spark ignition engine and is based on the thermodnamic analsis of the ideal fuel-air ccle. The method is assumed that the fuels and air are supplied from a perfect sstem and mixed completel. From the first law of thermodnamics, the open sstem can be modified as following equations from Lefebvre and Lefebvre [] that shown in Fig. D U = Q W ( H ) + ( H ) () - - L a dt dm dq dv ml cpt macp, at mcv + cvt = - P - + ( ) () dl dl dl dl v v Where m is the total mass of sstem m l is the instantaneous leakage or blow-b rate and is assumed to be alwas out of the linner, m a is mass rate of air inlet passed the dilution holes, P is the average pressure,v is a constant volume in the linner and v is average gases velocit that assumed from relative engine speed and turbulent flame front speed during combustion.. Thermodnamic properties The specific heat change as the function of the length in equation () indicates the enthalp change with respect to temperature and pressure, which was obtained from curve fitted polnomial equation. Table shows the thermodnamics properties expressed as a function of length, pressure and temperature. Where, Lewis [4] has represented the thermodnamic properties of fuels and air Ferguson [3] proposed the thermodnamic properties of air and combustion products. Fig Constant volume for a silo combustor This Eq. shows the change of internal energ U of a sstem is equal to the difference between the heat Q from fuels, work generated b the sstem W, heat loss HL and the enthalp H a of the air inlet passed the dilution holes which applied to the constant volume. Taking the derivative of Eq. as the function of the length Lx ( ) ields as Table Thermodnamic properties Internal energ, volume, entrop, enthalp [3] du æ Pv ln v ö dt ææ ln v ln c v ö = dp P v dl ç è T lnt ø dl ç ç lnt ln P è è ødl dv v ln v dt v ln v dp = - dl T lnt dl P ln P dl ds æc P ö dt v ln v dp æ h ö = dl T -, ç çè ø CP dl T lnt dl ç = çè T ø P Fuels [4] c P = a0 + b0t + c0t R h b0 c0 d = a T + T + RT 3 T 0 s c0 = a0 lnt + b0t + T + e0 R Air and Combustion product [4]

3 AEC8 9-0 October, 0, Krabi c P 3 4 = a + at + a3t + a4t + a5t R h a a3 a4 3 a5 4 a = a 6 lnt + T + T + T + T + RT T 0 s a3 a4 3 a5 4 = a lnt + at + T + T + T + a7 R In the primar zone, we consider the temperature in the term of unburned ( T u ) and burnt mixture ( T b ) as separate open sstems. Recalling Eq. and combining all the derivatives of thermodnamic properties will enable the pressure and temperature to be expressed as a function of length, pressure, unburned gas temperature and burned gas temperature. dp dt, b dt (3), u f( L, P, Tb, Tu) dl dl dl = Modified algorithm from Ferguson [3] as following the arbitrar heat release conditions and solving the above equations with appropriate input data enable determination of the indicated work, enthalp and heat loss throughout the sstem since indicated work, enthalp and heat loss can be expressed as a function of pressure and temperature. dp A+ B + C = dl D + E æ pb 4V ö / - h + x ( Tb- T w) b dt ç b è ø v æ b ln vb öæa + B + C ö = + ç dl vmcpb x c Pb ç lntb D E è ç ø çè + ø hu- hb édx C ù + - ( x- x ) xc ê Pb ëdl v ú û æ pb 4V ö / - h + ( - x )( Tu- T ç w) dt b u çè ø = dl vmcpb( - x) v æ u ln vu öæ A+ B + C ö + ç c Pu ç lnt u ç ç D E è øè + ø (4) (5) (6) From the derivatives of Eq. (4 6) let us defined the constant term with respect to the combination of the thermodnamic properties equations are: dv VC A ( ) m dl v é dv VC vb ln vb / Tb - Tw ù ( ) x + + dl v cpb lntb T b B= h vm vu ln vu / T ( b T - x w - ) cpu lntu T êë b úû = + (7) (8) dx ln vb hu - h é b dx ( x- x ) C ù C = - ( vb - vu) - v b - dl lntb cpbtb êdl v ë ú û é ù v æ b ln v ö b vb ln v D x b = + c Pb T ç b ç è ln T b ø P ln P êë úû é ù v æ ln ln ( u vu ö vu v E x u = - ) + c Pu T ç u ç è ln T u ø P ln P êë úû (9) (0) ().3 Chemical Equilibrium with the Fuel mixture. The basis of the equilibrium combustion products with fuel mixture model CαHβOγN δ is a solution to the atom balance equations from the chemical reaction equation of fuel and air forming and The subscript,&3 represent the One of the fuel, the fuel in the second and third respectivel. This mixture equation is given in Eq. for the condition of equivalence ratio, where n through n are mole fractions of the product species, e is the molar fuel-air ratio required to react with one mole of air. This process based on the work of modified Ferguson [3] as given below ef (- c)cαhβoγnδ + ( + a ) ef ( c) c CαHβOγNδ c 3C 3Hβ3Oγ3Nδ3 nco + nho + n3n + n4o 0.O + + n5co + n6h + n7h + n8o 0.79N + n9ohn0 NO + vn () Where c is the molar ratio of multi-fuel having the condition ( 0< c < ). c, c 3 are the fuel in the second and third which having the condition( c+ c3= ). There is the conservation of 4 atoms, C,H,O and N from mixture equation, so atom balancing can be written, C ( ) α+ α3 ( ) N (3) 3 5 H ( ) ( ) N O ( ) ( ) N N ( ) ( ) N 3 0 (4) (5) (6) Where, N is the total number of moles and is the mole fraction. Thus, the total number of mole fraction must be equal to one and this gives:

4 AEC8 9-0 October, 0, Krabi 0 i i (7) The expression for atom balance of each equation can be eliminated b dividing Eq. 4-6 b equation 3. The equation can be written as next equation d( 5) 0 (8) d( 5) 0 (9) d ( ) 0 (0) d ( ) d ( ) + 3+ ( ) α+ α3 ( ) α+ α3.58 ( ) d3 ( ) α+ α3 Eqs (7-0) have unknowns (,, 3... ), therefore in order to solve for these unknowns other 7 more equations are needed which ma be derived from the consideration of equilibrium among products. The equilibrium constant can be related to the partial pressure of the reactants and products. And the partial pressure of a component is defined relative to the total pressure and the mole faction, thus the equilibrium constant can be rewritten as Table. Table The dissociation effect P CO CO O K H O H O K / / 5 4 / / 4 6P H O OH K 9 3 / / 4 6 H H K / 7 4 / 6 O O K / 8 5 / 4 / 6 / 3 N N K O N NO K 0 7 / / 4 3 P P P Equilibrium constant in Table 3, K through K7 are curve fitted Lewis [4] and their expressions are of the from, 3 4 at a3t a4t a5t a 6 KP exp a lnt a () Through algebraic manipulations, the ten equations can be reduced into four equations with T four unknowns. The equations are nonlinear and solved b using the Newton method. Each of these ma be expanded in Talor s series f j( 3, 4, 5, 6) = 0 where j =,,3,4 (neglecting the second order and higher order) as, f j f j f j f j f + D D + D + D = 0 (3) j Functions f j are evaluated from the solution of interested functions (Eq.7 through Eq.0) the independent set of derivatives is obtained b solution of matrix equation that results from differentiating with respect to mole faction. The above can be arranged as set of linear equations in the matrix form, fi [ ][ ] [ f] 0 (4) i This set of linear equations can then be solved for 3, 4, 5, 6 and iterative procedures undertaken until the corrections are less than a specified tolerance ( ). For convenience, defining following partial derivatives and defining the constant values for a simple studied and the Jacobian of solution are given as Table 3 Table 3 constant values,the Jacobian of solution i i,,7,8,9,0, Dij j 3,4,5,6 i c c c c D D D D / / 4, / 84, / 94 / c c 4 D c D c, D, D 4 / / / 6 6 c c c D D D / / / 04, / 3 / f f = + D 03 + D3 = f f = D 4 + D4 + + D84 + D04 + D94 = D4 + D94 - dd4 4 4 f f = D 5 + = - dd5 - d 5 5 f f = D D76 + D96 = D6 + + D76 + D f3 f4 D03 D03 D3 3 3 f3 f4 D4 D4 D84 D94 D04 dd4 D04 d3d4 4 4 f3 f4 D5 dd5 d d3d5 d3 5 5 f3 f4 D6 D Eq.4 ma be solved using b Gauss elimination. The second approximation is then / / 6

5 AEC8 9-0 October, 0, Krabi 3,4,5,6. The process of forming k k k the jacobian, solving Eq.4 and calculating new values for is repeated until a stop criterion is met, results in the molar concentrations of the product species, as shown in paramust [5]..5 Model setup The combustor specification is shown in Table 4. Table 4 The specifications for Simulation Total Mass Flow Rate 0.3 kg/s Total Silo Combustor length (L) 0.45 m Silo Chamber diameter (D) 0.5 m Ignition length (premixedz, Lig) 0.0, 0.5 m. Burning length (primar, Lb) 0.0, 0.5 m. NGV-Ethanol fuel mode 00:0, 90:0, b mole faction 80:0, 70:30 Equivalence Ratio Pressure Ratio (Pin/Pambient) Engine Speed (RPM) Where, the stoichiometric fuel-air ratio b mass is F, residual fraction is f, available energ of fuel s is a c (LHV), and V is the constant volume silo combustor V LD. 4. Results and Discussions 4. Effect of Equivalence ratio on performance parameters This simulation test was run at rpm and pressure ratio 3.5. The silo combustor specifications (L ig :L b ) to be used as following 0.0:0.0, 0.0:0.5 and 0.5:0.0 while using different equivalence ratio ( f ) are 0.6, 0.7, 0.8, 0.9 and.0 respectivel. The results indicate that as the IMEP rises and thermal efficienc starts to decrease exponentiall as the equivalence ratio increases. In case, a specification of 0.0:0.0 was chosen for the following simulation since others gives a rather low performance. These are showed in Fig.. A stud of gases as models of internal combustion engines is useful for qualitativel illustrating some of the important parameters influencing combustor performances, that is, the work output wcv from fuel-air ccle. In theoretical of control volume, the combustor performances can be calculated b meaning of the indicated values which the following definitions are done b the gas. That is thermal efficienc and the indicated mean effective pressure. Thermal Efficienc) wcv [ Fs ( f )] (9) F a ( f ) s 0 The indicated mean effective pressure (IMEP) wcv [ Fs ( f )] IMEP (30) V

6 AEC8 9-0 October, 0, Krabi Fig Thermal efficienc, IMEP-Equivalence ratio 4. Effect of Pressure ratio on Performance Parameters This simulation test was run at rpm and equivalence ratio 0.8. The silo combustor specifications (L ig :L b ) to be used as following 0.0:0.0, 0.0:0.5 and 0.5:0.0 while using different pressure ratio (Pratio) are 3.00, 3.5,3.50,3.75 and 4.00 respectivel. The results indicate that as the IMEP rises and thermal efficienc starts to increases exponentiall as the pressure ratio increases. In case, these IEMP curves are almost the same values of NGVethanol fueled and 0.0:0.0 was chosen for high performances. These are showed in Fig. 3. Fig 3 Thermal efficienc,imep-pressure ratio 4.3 Effect of Engine Speed on Performance Parameters This simulation test was run at equivalence ratio 0.8 and pressure ratio 3.5. The silo combustor specifications (L ig :L b ) to be used as following 0.0:0.0, 0.0:0.5 and 0.5:0.0 while using different engine speed (RPM) are 40000, 60000, 80000, and 0000 respectivel. The results indicate that as the IMEP and thermal efficienc starts to decrease exponentiall as the engine speed increases. In case, these IEMP are almost the same values and 0.0:0.0 was chosen for high performances as showed in Fig. 4.

7 AEC8 9-0 October, 0, Krabi Fig 4 Thermal efficienc,imep-engine Speed 4.4 Effect of Equivalence ratio on pressuretemperature profiles This simulation test was run at engine speed RPM and pressure ratio 3.5. The silo combustor specifications (L ig :L b ) to be used in the simulation as following 0.0:0.0, 0.0:0.5 and 0.5:0.5 respectivel. The results indicate that as the equivalence ratio increases, pressures and temperature gives the value that is not the appropriate design predictions. These are lowpressure and high temperature. These are showed in Fig. 5. Fig 5 Pressure-Temperature-Equivalence Ratio 4.5 Effect of Pressure ratio on pressuretemperature profiles This simulation test was run at equivalence ratio 0.8 and engine speed RPM. The silo combustor specifications (L ig :L b ) to be used in the simulation as following 0.0:0.0, 0.0:0.5 and 0.5:0.5 respectivel. The results indicate that as the pressure rises as the pressure ratio increases, but, temperatures are almost the same values. In case, high pressure ratio was chosen for the appropriate design predictions. These are showed in Fig. 6.

8 AEC8 9-0 October, 0, Krabi Fig 6 Pressure-Temperature-Pressure ratio 4.6 Effect of Engine speed on pressuretemperature profiles This simulation test was run at equivalence ratio 0.8 and pressure 3.5. The silo combustor specifications (L ig :L b ) to be used in the simulation as following 0.0:0.0, 0.0:0.5 and 0.5:0.5 respectivel. In case, these pressures and temperatures are almost the same values as showed in Fig. 7. These results indicate that as the engine speed does not affect to design predictions of pressures and temperatures Fig 7 Pressure-Temperature-engine speed 5. Conclusion The present work achieves its goal b being a simple, fast and silo combustor model. Based on the Olikara-Borman method [3,4], a subroutine for equilibrium combustion [3,4] product was developed and obtained. The results obtained can be used as a first-degree approximation and is useful in numerous engineering applications including general design predictions and easil adapt to an combustion chamber shape for a micro gas turbine. Due to its

9 simplicit and computational efficienc, the model can also be used as a preliminar test on a wide range of alternate fuels. 6. Acknowledgement The author would like to acknowledge with appreciation, Department of Mechanical and Aerospace Engineering, Graduate College and Department of Mechanical and Aerospace (KMUTNB) 7. References [] Claire Soares, P.E. (007), Microturbines: Applications For Distributed Energ Sstems, Elsevier Inc. [] Lefebvre, A.H. (00) Gas Turbine Combustion, nd edition, Talor & Francis, Philadephia. [3] Colin. R. F, (986) Internal Combustion Engines, Applied Thermosciences, John Wile and Sons, New York. [4] Lewis, G. N. and Randall, M. (96). Thermodnamics, McGraw-Hill, New York. [5] Paramust, J. and Veera, C. (008). Analsis of Water Injection into Mixture of Combustion Products in a Clinder of Spark Ignition Engine, Master thesis, Graduate College, King Mongkut s Institute of Technolog North Bangkok. AEC8 9-0 October, 0, Krabi

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