NUMERICAL ANALYSES IN SIMILAR CONDITONS WITH COMBUSTION CHAMBERS OF RAMJET ENGINES

JESTECH, 15(4), 163-182, (2012) JESTECH NUMERICAL ANALYSES IN SIMILAR CONDITONS WITH COMBUSTION CHAMBERS OF RAMJET ENGINES Mehmet Altug Yavuz *, Ali Kodal ** * Technical Universtiy of Eindhoven, Physics Department, Eindhoven, Netherlands ** İstanbul Technical Universtiy, Aerospace Department, Istanbul, Turkey Abstract In this study, numerical and experimental simulations are planned for methane-air jet flames and interaction with flame-holders to analyze the flow characteristics. The experimental setup built for this purpose will shed performance analysis of ramjet engine combustion chambers. Methane is delivered to the combustion zone with a thin tube and surrounded with a proper speed air flow. Combustion is established at flame-holders. The obtained visualizations at this experimental setup compared with numerical studies. At first, numerical studies have been carried out with commercial software and all the results obtained at this work were provided a base for developing a numerical program. Besides developing a new program, the flow characteristics analysis (fuel-air ratio, turbulent characteristics, flame-holder properties, etc.) had also been investigated experimentally and numerically. Recently, a lot of disciplines were focused on numerical studies. Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) methods became more important in Computational Fluid Dynamic (CFD) studies. In this work, the DNS method was preferred. Advanced computer capacities will let to obtain improved results for flow calculations. Therefore, numerical studies are still strong arguments today. A study that may enlighten subjects of combustion and fuel efficiency, turbulent flow, high speed combustion, flame-holder interaction and design, combustion chamber design are presented. The numerical studies can be classified as commercial and self constructed program studies in this thesis. Firstly, the non flame-holder conditions had been studied and compared with the commercial program. After that, the flow conditions for the different cases were solved with or without chemical reactions. The purpose of this study was to solve mixing of species and analyzing the flame for the flow characteristics with the DNS method. Another consequence of this thesis is the study of the development of the experimental setup to simulate and test the modeled ramjet engine combustion chamber. Keywords: Combustion, turbulence, flow simulation, flame-holder. 1. Introduction The combustion occurs inside an aircraft engine may be expensive to analyze by experiments. Sometimes, even the expenses had paid; there may still strict rules that hard to investigate the combustion. Therefore researches have been deepening about combustion in Computational Fluid Dynamics (CFD). In this study, a CFD analysis about a combustion chamber is developed, which includes flame-holding geometry to hold the generated flame inside the chamber. Flame-holder is a necessary component of a jet engine and it provides continual combustion. All continuously working combustion engines require a flame holding system. Flame holding systems create a low Reynolds eddy scale inside the combustion chamber and prevent the flame from explosion or dissipation. Therefore the design of the flame-holder geometry is an optimization problem to balance between drag and a stable eddy. Improved computer technologies will result in the investigation of the theoretical formulations by numerical calculations. In a turbulent flow, methods to solve N-S (Navier Stokes) equations have been studied a lot at last decades [1]. Most known methods to solve N-S equations on turbulent flows are Large Eddy Simulation (LES), Direct Numerical Simulation (DNS), Turbulent Viscosity Modeling methods and Probability Density Corresponded Author; mehmetaltugyavuz@gmail.com

164 Numerical Analyses In Similar Conditons With Combustion Function (PDF). Lately, DNS method has been employed on turbulent combustion problems and improvements observed in numerical solutions [2-6]. Turbulent flow data without combustion could be analyzed with phase averaging, Proper Orthogonal Decomposition (POD) and turbulent filters [7-12]. The exact DNS solution of the instantaneous continuity and conservation equations can be robust. Averaging N-S equations, that is Reynolds and Favre averaging should employ to go beyond DNS solutions [5]. Closure problem can be passed by a proper turbulence modelling. While solving N-S equations some researchers used finite volume methods as a DNS procedure and developed a program to get results [6]. Some researchers solved equations of motion by finite difference methods with experimentally acquired polynomials to employ the closure problem [13]. Lately, the DNS method is applied to the turbulent combustion flow and many improvements have been achieved. Jakirlic and others [6] have applied DNS to the cylindrical axial rotating compressible flow and compared with experimental results. Veynante and Vervisch [5] presented a detailed numerical study on different types of turbulent models. Echekki and Chen [18] studied self flaming structure of nonhomogeneous hydrogen-air mixture. Domingo and others [19] made DNS analyses to the partially pre-mixed turbulent gaseous spray flame stabilization in hot air concentration. Hauguel and others [20] solved premixed turbulent V-flame spectral with DNS and finite difference methods. Laverdant and Thevenin [21] studied turbulent pre-mixed flames interaction with Gaussian acoustic wave. Sankaran and Menon [22] made combustion sub-grid modeling for a small reaction region in 3-D pre-mixed flamed flow. Thevenin [23] prepared three dimensional DNS analyses on diffusive turbulent methane flames. 2. Mathematical Formulation And Modelling 2.1. Governıng Equations This subsection begins with governing equations of fluid dynamics in integral form then in differential form. Firstly, the joined integral form of fluid motion equations for a single species is Here Q is the vector of conserved quantities:. (1) (2) is the inviscid flux term: (3) At the right hand side term is viscous flux term: (4) T: tensor, : normal vector, The equations of fluid motion are called Navier-Stokes equations. In that order corresponding conserved 2-D equations are:

JESTECH, 15(4), 163-182, (2012) 165 Continuity X-Momentum (5) Y-Momentum (6) Energy (7) In addition to these equations, the combustion problem includes different species of chemical mechanism. The species equation is: (8). (9) In fluid dynamics, working with dimensionless coefficients and equations will guaranty better comparison and comprehension of the problem. The way to change an equation to non-dimensional form is to exchange the entire coefficient with the dimensionless equivalents. 2.2. Numerical Method Navier-Stokes equations including chemical reaction can iteratively be solved with DNS method, using finite difference method within conservative form of the flux-vector formulation. The numerical procedure without chemical reaction for the sake of simplicity can be carried out using the below formulations. The general form of the flow equations can be represented as: Similarly, the mass fraction equations must be added when the chemical reaction mechanism wanted to be solved and then the total energy equation should be modified with chemically formed heat releases. The Flux-Vector formulation can be solved with directly using multi-step Runge Kutta time advancing method. Therefore, the partial time derivatives of the flux-vector formulation can be put on the left hand side of the equation and all the other terms to the right hand side, i.e, (10). (11) The 5 th order Runge-Kutta scheme used. In numerical analyses, the consistency, the time stepping and the mesh sizing are the parameters to pay attention when finite differencing methods applied. In this study, for the derivative calculations, the central

166 Numerical Analyses In Similar Conditons With Combustion differencing method have been chosen, because of that, special care may be needed at the boundaries. According to time step stability analyses, step sizing has to be small enough for the direct solution method. Accurate results can be obtained carefully by determining flow, heat or chemical reaction mechanism model parameters. Also viscosity, heat conduction, diffusion and energy activation parameters are the other important variables. Figure 2.1 gives a low-reynolds phase averaged Partical Image Velocimetry (PIV) data set of partially premixed CH 4 -air lifted jet for demonstration. Self developed DNS program and commercial code CFD analyses are expected to be parallel to this data set. Figure 2.1. Phase averaged partially premixed CH 4 -air lifted jet. This study represents a ramjet engine (or an afterburner mechanism) combustion chamber interior simulation and prepared model progressed during this perspective. When horizontal axis applied as x and the vertical axis y, partially premixed air fuel mixture enters from y=0. Combustion chamber width is L and the length is H and during the analyses, the ratio of L and H taken 1, ½, or 1/3 for different scenarios. Side walls are taken as solid walls and the velocities are taken zero at x=0 and x=l. Also, when the flame-holder geometry is included in the analyses, the velocities at the flame-holder boundaries are also be zero, but there may be no restriction on heat transfer through the flame-holder walls. To avoid the accumulation at the outlet, the outflow boundary conditions at the y=h are calculated by linear interpolation. In the reaction mechanism, nitrogen acts like inert and does not affects the reaction except the mixture fraction ratios will change and thus the results wil change indirectly. Fuel and air components concentrations are defined as: (12) (13). (14)

JESTECH, 15(4), 163-182, (2012) 167 The subscript F denotes fuel (methane), O is for the oxygen and N is for the nitrogen. The amount of mass produced by the chemical reaction is given by the mass action law, i.e: where, A refers to the Arrhenius coefficient and T AC is the activation temperature. For a realistic reaction mechanism A and the T AC coefficients are important parameters. In this study, these parameters are chosen for suitable temperature distribution and the analyses has shown that the chosen values do not affect the velocities very much but they affect the temperatures excessively. (15) In this perspective, the source term in equation (16) can be found using, (16), (17) here, and are the initial and the final mol coefficients of the k th species. Similarly, for the chemical reaction the amount of heat release per unit time can be calculated as,, (18) where W F is the fuel molecular weight and Q R is the fuel heating value. 3. Numerical Implementation One of the main purpose of this thesis is improving ability to develop self structured CFD program (DNS method), including chemical reaction for turbulent flow. Another purpose of this study is to gain experience in acquisition of CFD and thermodynamic relations subjects at graduate level. Finally, the presented combustion chamber study may enlighten subjects of combustion, fuel efficiency, turbulent flow, high speed combustion, flame-holder interaction and combustion chamber design. This study is based on an explicit DNS method using FORTRAN. In addition to that, the commercial CFD codes (FLUENT, STAR-CCM, etc.) has been used during the numerical analyses. The FLUENT code is preferred for the main numerical comparison tool with the developed DNS method. Before describing these cases, some numerical approaches will be given for the flow parameters. Reynolds and Mach numbers are calculated in the program. As an example, Re number was around 12000 and the Mach number around 0.28 for the case-1 at the fuel inlet. Figure 3.1 shows a not chopped triangular body inside the chamber. Here, the fuel inlet and the flame-holder is too small with respect to the chamber cross-sectional area, but the velocities are very high. Even the geometry is too small, there is high amount of turbulence to mix fuel and the air properly. However, it may be difficult to stabilize and control the flame inside combustion chamber due to small flame-holder crosssectional area. The temperatures will be high behind the flame-holder. This is a predicted and desired result for a steady solution. When a combustion chamber reaches to steady state, the combusted gases and the flame must be held behind the flame-holder. Although, there was more excessive air, the high temperature region was established behind the flame-holder, but the flame height and the length may be too long for an engine combustion chamber. This configuration was axis-symmetric calculation where fuel inlet velocity is 130 m/s. The Figure 3.2 shows comparison between the results of commercial code and the self constructed program for the non-flame holding test case. The velocity magnitudes are compared with the sparse velocity vectors of the DNS method. The velocity development process can be clearly seen in this figure. The diffusion of the species into the combustion chamber may be observed from the velocity contours. The commercial code (FLUENT) results are very detailed and demonstrate the velocity distribution precisely.

168 Numerical Analyses In Similar Conditons With Combustion a b c d e f Figure 3.1. Here as an example some preliminary calculations given; a) contours of static pressure b) velocity magnitude, c) contours of static temperature, d) mass fraction of methance, e) mass fraction of Oxygen, f) contours of turbulent kinetic energy.

JESTECH, 15(4), 163-182, (2012) 169 Frame 001 24 Feb 2009 1 V4 V2 0.8 0.6 20 18 16 14 12 10 8 6 4 2 0.4 0.2 0.2 0.4 0.6 0.8 1 V1 Frame 001 24 Feb 2009 1 V4 V2 0.8 0.6 0.4 20 18 16 14 12 10 8 6 4 2 0 0.2 0.2 0.4 0.6 0.8 1 V1 Frame 001 24 Feb 2009 1 V4 V2 0.8 0.6 0.4 20 18 16 14 12 10 8 6 4 2 0 0.2 0.2 0.4 0.6 0.8 1 V1 Figure 3.2. Comparison of the velocity magnitudes between self developed DNS program and the commercial code. Frame 001 27 Feb 2009 0.2 V4 V2 0.1 35 30 25 20 15 10 5 0-5 -10-15 -20 0.1 0.2 V1 a b Figure 3.3. Two example calculation at 0.01 seconds.

170 Numerical Analyses In Similar Conditons With Combustion Figure 3.3-b shows a 64x128 grid resolution for 1 by 2 domain with sharp flame-holder edges. In Figure 3.3- a, the filleted flame-holder was demonstrated and the computation domain was a square within a 64x64 grid. Also, the jet initial velocities were different. In Figure 3.3-a, the fuel jet velocity was given 22m/s and for the Figure 3.3-b the fuel jet velocity selected 50m/s. Figure 3.3 represents the improvement by increasing the number of meshes in the self developed combustion program. The Figure 3.3-a demonstrates a 1 by 1 combustion chamber, on the other hand, the Figure 3.3-b is 1 by 2 configuration. The width and length are smaller (0.2m) than those of Figure 3.1. The chamber length is an important parameter for an effective combustion. During the numerical calculations, different styles and design conditions were studied for the length of the combustion chamber. Usually, researchers try to design the chamber as short as possible, since the every millimeter means extra cost and extra weight for an aircraft. Figure 3.4 shows the velocity distribution for the DNS method at different time intervals. This domain, in the Figure 3.4, has a 32 x 64 mesh resolution, thus the flame-holder edges were very rough for the moment. On the other hand, the velocity distributions and contours were satisfactory upon the solution. Moreover, the Figure 3.4 also demonstrates the dimensionless velocity distribution inside the combustion chamber. At this configuration, a low Re numbered results were realized for the air-fuel mixed flow. Upcoming pages will show more effective dimensionless solutions of the combustion chamber (Figure 3.5,.3.6, 3.7, 3.8). - - 1 2 - - 3 Figure 3.4. Velocity distribution after 0.4ms, 0.8ms, 1.2ms ve 1.6ms of time. 4

JESTECH, 15(4), 163-182, (2012) 171 5.00 5.00 5.00 4.50 4.50 4.50 4.00 3.50 4.00 3.50 4.00 3.50 3.00 3.00 3.00 2.50 2.00 2.50 2.00 2.50 2.00 1.50 1.50 1.50 - - - 1 2 3 5.00 5.00 5.00 4.50 4.50 4.50 4.00 3.50 4.00 3.50 4.00 3.50 3.00 3.00 3.00 2.50 2.00 2.50 2.00 2.50 2.00 1.50 1.50 1.50 - - - 4 5 Figure 3.5. Dimensionless Oxygen Fraction. 6 - - - 1 2 3 - - - 4 5 Figure 3.6. Dimensionless Fuel (CH4) Fraction. 6

Numerical Analyses In Similar Conditons With Combustion 172 Figure 3.5 and 3.6 show the dimensionless mass fraction of the oxidizer (air) and the fuel. 1.13 1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 0.99 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 0.99 1 1.19 1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 0.99 1.19 1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 0.99 - - 1-1.19 1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 0.99 6-2 - 4 3 3 4 5 Figure 3.7. Dimensionless Temperature Contours 2 1.19 1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 0.99-5 Figure 3.8. Dimensionless Velocity Magnitudes. 6

JESTECH, 15(4), 163-182, (2012) 173 The results given in Figures 3.5-3.8 were solved for lower velocities than realistic ramjet conditions. It was assumed a 3/5 ratio between the air and the fuel velocities and the Re number was lower than the main cases which will be given on coming sections. The reaction mechanism parameters and the velocity ratio studies had been realized during these solutions. Lower temperature and lower Re number analyses allow testing different circumstances of the combustion chamber dimensions and the geometry. By this way, the high gradients were not been formed and the solution did converged much more easily. The trials had been also done for the high Re numbers at low resolved domains. The activation energy and the high Mach number analyses were much closer to divergence. According to the numerical theory of grid construction in CFD analyses, the mesh elements should be more then the number of Re 4/3 number and that means extra time to solve the problem in computers while increasing the number of mesh elements. As a result of this, the parameters, which effect the Re number, were sometimes changed such like the viscosity of fluids. At higher viscosity values, the Re number will decrease, therefore, the number of mesh elements will be proportional to the Re 4/3 and the calculations will not diverge because of the mesh resolution. In Figure 3.9, the temperature distributions are represented for various time intervals, for the fuel inlet velocity of 100 m/s and the air inlet velocity of 10 m/s inside the combustion chamber. The reference temperature was taken as 300 K. In this figure, there are three flame-holder geometries applied to the numerical domain and solved in this condition. More flame-holder geometries were studied for the same amount of cross-sectional area blocking. This is an important parameter to compare with the other configurations, because, when the blockage area was changed, the characteristic of the channel flow would change. Therefore, the ratio between the cross-sectional area of channel and the flame-holders were fixed to the 40 % of the chamber s overall cross-sectional area. The purpose of increasing the number of flameholders is to increase the turbulence in the flow and to locate more flames in the chamber by preparing more circulation zones behind the bluff bodies. 1 2 3 4 5 6 Figure 3.9. Temperature contours inside the combustion chamber at 100 m/s fuelvelocity and 10 m/s air velocity.

174 Numerical Analyses In Similar Conditons With Combustion 1 2 3 4 5 6 Figure 3.10. Methane mass fraction contours inside the combustion chamber. The mass fraction of the methane has a reference value as 100 % concentration at the jet inlet with the velocity of 100 m/s. Figure 3.10 demonstrates the fuel mass fraction distribution with respect to time progression. The reaction starts at the entrance of the combustion chamber, as a result, the fuel mass fraction decreases immediately during the process. The fuel concentration will rapidly decrease behind the flameholders. The amount of turbulence intensity values is suitable so that the reaction environment is seen to combust efficiently. In the Figure 3.11, the velocity magnitudes can be seen inside the domain. The Mach wave s effects in the flow domain can be clearly seen even at the beginning of the flow. Just before the fuel or the flow reaches the flame-holders, Mach waves impact the channel. This figure also demonstrates the velocity gradient effects inside the domain and this effect can be better understood by comparing with the other figures such like the temperature distribution given in Figure 3.10. Figure 3.11 shows the dimensionless velocity magnitudes for three flame-holder condition.

JESTECH, 15(4), 163-182, (2012) 175 1 2 3 4 5 6 Figure 3.11. Velocity magnitude contours inside the combustion chamber. 3.1 Implementation of DNS program In this section, two cases are considered in detail. These cases are considered realistic as possible to a real ramjet engine combustion chamber and it may be thought also as an afterburner mechanism for the jet engines. The characteristic flow parameters and the conditions employed for the DNS method had been decided from the previous analyses which were already described in the Chapter 2. The main properties used in these two cases are summarized in Table 4.4 comparatively with those of taken in FLUENT. Table 3.1. The chosen parameters for the FLUENT and the DNS method. DNS FLUENT Jet inlet velocity (fuel-ch4) (m/s) [case-1] 100 100 Air inlet velocity (m/s) [case-1] 10 10 Jet inlet velocity (fuel-ch4) (m/s) [case-2] 140 -- Air inlet velocity (m/s) [case-2] 84 -- Characteristic Length (m) Dynamic viscosity (Kg/ms) 1.45e-5 1.45e-5 Time step 01 01 D, diffusion coef. 2e-5 2e-5 k, heat conduction coef. (W/m.K) 0.026 0.026 Cp, specific heat(j/kgk) 1005 1005 Excess Air %20 %20 Air Temperature (K) 300 300 Case-1 In Case-1, only one flame-holder at relatively low Re number is considered for the analysis. This part of the study represents a dimensionless self constructed DNS program outputs about a ramjet combustion chamber (or an afterburner mechanism) simulation. The selected parameters used in Case-1 are shown in Table 4.5. The width of the combustion chamber is taken as the characteristic length which is m. The parameter, RD in the Table 4.5 refers to the fuel inlet length ratio with respect to the characteristic length, RL. The

176 Numerical Analyses In Similar Conditons With Combustion parameter Uinf, shows the reference velocity for the analysis and taken equal to the fuel inlet velocity. Similarly, the symbol W shows molecular weights of the species. In Figure 4.23, the dimensions of the combustion chamber given as a blue print. In Table 3.3, the list of Re numbers at different locations of the flow are given for Case-1. The average Mach number is also given in Table 3.3. Table 3.2. The selected parameters used in Case-1. RL m RD RL/32 A 1.e8 Delta_t 1e-5 s Uinf 100 m/s V_co-flow 10 m/s Woxygen 32 V_fuel 100 m/s Wfuel 16 Viscosity 1.45e-5 WN 28 Tac 800 Table 3.3. Mach and Re numbers in Case-1. Step in space 0.166667 Re_1 11929 at fuel inlet Re_2 190862 at outlet Re_3 101793 at flame-holder M 0.28 at domain (average) Case-2 In Case-2, the effects of more than one flame-holder are investigated. Therefore, in Case-2, three flameholders in the combustion chamber at relatively higher Reynolds are considered. Similar to Case-1, the analysis is carried out by the DNS method and this time the flow conditions will represents more realistic situations for a ramjet combustion chamber. The air inlet velocity is higher than Case-1. The other parameters are taken same with Case-1. The increase of flame-holder number will lead to produce more turbulence inside the chamber. The ratio between the cross-sectional areas of the chamber and the flame-holders was not changed to provide controlled analysis. The selected parameters used in Case-2 are shown in Table 3.4. In Table 3.5, the list of Re numbers at different locations of the flow are given for Case-2. The values shown in the Table 3.5 are very close to a real ramjet engine case with the Mach number of around 0.4. Table 3.4. The selected parameters used in Case-2. RL m RD RL/32 A 1.e10 Tref 300 K Uinf 140 m/s rho 1.23 Tac 800 D 2e-5 Woxygen 32 Delta_t 1e-5 s Wfuel 16 V_co-flow 84 m/s WN 28 V_fuel 140 m/s R 287 Viscosity 1.45e-5 Table 3.5. Mach and Re numbers in Case-2. Step in space 0.166667 Re_1 32473 at fuel inlet Re_2 534414 at outlet Re_3 368152 at flame-holder Re_4 122717 at one flame-holder M 324 at domain (average)

JESTECH, 15(4), 163-182, (2012) 177 The progressions of the density and the oxidizer mass fraction distributions are presented in Figures 3.13 and 3.12, respectively. In this case, the turbulence and the mixing of species is relatively higher with respect to the previous case, therefore, the fuel diminishes in a short period of time. At the starting of the flow, the combustion region is assumed to be filled by the air. Consequently, the chamber is unicolor in the first frames. After the fuel enters to the chamber, the ambient density is increasing inside the domain. The oxygen mass fraction, on the other hand, decreases as the reaction progress. The reaction and the entrance of the fuel affect the oxygen mass fraction and the density distribution together. 1 2 3 4 5 6 7 8 Figure 3.12. Dimensionless Velocity magnitudes for Case-2 (first 8 ms).

178 Numerical Analyses In Similar Conditons With Combustion 1 2 3 4 5 6 7 8 9 Figure 3.13. Dimensionless density distribution for Case-2 (first 8 ms).

JESTECH, 15(4), 163-182, (2012) 179 4. Discussions Figure 3.14. Dimensionless oxygen mass fraction for Case-2 (first 8 ms). Overall evaluation of the numerical studies described in this chapter will be given in this section. The self constructed program studies were carried out parallel to the commercial code analyses. The aim was to control the conditions, geometries and configurations inside the numerical domain, such as, the flame-holder geometry. The flame-holder shape, its position and the number of the flame-holders were found during these

180 Numerical Analyses In Similar Conditons With Combustion analyses. When the analysis about the geometry and the boundary conditions were finished, another study has been started about controlling the behaviour of the numerical method. Also, the non-dimensional studies were employed with the DNS method. There was also another analysis ran for the flame-let prediction. The flame-let results will be compared with the experimental study in the next chapter. The purpose of this study is to compare the commercial and the self constructed program to get realistic results for the problem in consideration. Therefore, two different cases had been prepared to demonstrate and establish the situation inside the combustion chamber. These main cases were described in detail and a lot of frames of the solution given in section 3. Before getting the appropriate the results demonstrated in this chapter, a lot of different test cases and grid resolutions had been investigated. As a result of these investigations, a 192x576 grid resolution had been selected for the main case studies in order to prevent 5 % difference from the FLUENT solutions. The lower resolutions for the grid domain may bring out higher differences between the commercial code and the self constructed program (around 17 % for 64x128 and around 9 % for 128x256). The other resolutions studied in this thesis were given in preliminary studies section. Increasing the grid resolution decreases the difference, as expected. The flame-holder geometry designed and employed inside the chamber is like a triangle and blocks 40 % of the combustion chamber cross-sectional area in order to stabilize the flame behind the flame-holder. The flow inside the chamber was increased to very high velocities for the un-chopped triangular flame-holder case. This was more chaotic for the flow characteristics and it may threaten flame stabilization. Different flameholder geometries, for example, dugout triangular geometry have been analyzed and the results were discussed. But, for the simplicity, only some important results were presented in this study. Finally, the chopped triangular flame-holder studies were carried out. This kind of a flame-holder is usual in the literature studies [15]. The numerical studies in this chapter can give an opinion about the reaction inside the combustion chamber. The turbulence intensity was directly proportional to the geometrical design. The performance would be improved by the suitable flame-holder geometry modifications. The turbulence can affect the reaction mechanism as a result of preparing the environment inside the combustion chamber. This environment conditioning was the subject of this thesis and the results obtained may be used for the optimization studies of a ramjet engine combustion chamber. The flame-let modelling results were included in the design of the combustion chamber constructed for the experimental setup. 5. Conclusion The comparison of numerical and experimental results is one of the indispensable methods in scientific researches. Mostly, the experimental results found are more reliable than the numerical results. Researchers will be able to observe the real situation in the experiments. This fact did not stop the numerical studies since they are much cheaper than the experimental studies. The time consumption may be smaller than the experimental works. Furthermore, the numerical methods were improved a lot and developed rapidly at last decades. As a result of these, this thesis presents an experimental and numerical mixed study. The numerical studies can be classified as commercial and self constructed program studies in this thesis. The commercial studies carried out in this study presented some initial values and ideas for the numerical program developed. The preliminary studies with the commercial code constituted a feasibility study before the self constructed DNS program. When the developed DNS program has reached to some level, the commercial analyses were stopped and the DNS studies were continued. The Direct Numerical Simulation (DNS) of N-S equations have been studied with chemical reaction. The N- S equations are solved with proper initial and boundary conditions. The purpose of this study was to solve mixing of species and analyzing the flame for the flow characteristics. Firstly, the non flame-holder conditions had been studied and compared with the commercial program. After that, the flow conditions for the different cases were solved with or without chemical reactions. Another issue was the number of flameholders inside the combustion chamber. One and three flame-holder configurations were presented in Chapter 4. The comparison of the results between the commercial and self constructed program for different cases was given. Same boundary and initial condition values had been employed for both methods. The results were in good agreement with each other. The developed program was seen that it can give better results with larger grid domain.

JESTECH, 15(4), 163-182, (2012) 181 Another consequence of this thesis is the study of the development of the experimental setup to simulate and test the modelled ramjet engine combustion chamber. This experimental setup was designed to visualize the reaction and flames through a window and control the flow parameters accordingly during the process. All these missions were accomplished successfully and described in detail at appropriate chapters. Recommendations For Future Works One of the future works may be modelling with CHEMKIN flame-let code. The experimental setup can be modelled in 3-D by CAD programs and a numerical analysis may be carried out by FLUENT or self developed programs. Therefore, the comparison of the experimental and the numerical results will be more consistent. The DNS method may be improved by so many different ways. As an example, a more complicated multistep reaction mechanism can be added to the DNS program as a simple way to improve the numerical study. In addition to these, the boundary conditions can be changed to investigate different cases for a ramjet combustion chamber. The grid resolution and the mesh distribution can also be changed and a structural mesh may apply to the domain. Also the flow conditions, such like the temperature, pressure, etc, can be found at this circumstances and analyzed with the DNS method. For the experimental studies, different types of flame-holding geometries and different types of fuels can be studied. Also, a study can be carried out by changing the flow conditions, such like the temperature, pressure, etc, with already available experimental setup. Data acquisition instruments such like PIV, infrared thermometers, etc, can be used to understand and obtain valuable experimental data about the behaviour of the flame and combustion inside a ramjet engine combustion chamber. References 1. Pope S. B. Turbulent Flows, Cambridge University Press, 2003. 2. Huh K. Y., Sreedhara S., Conditional statistics of nonreacting and reactining sprays in turbulent flows by direct numerical simulation, Proc. of the Combustion Ins., 31, 2335-2342, 2007. 3. Domingo P, Vervisch L, DNS of partially premixed flame propagating in a turbulent rotating flow, Proc. of the Combustion Ins., 31, 1657-1664,2007. 4. Domingo P., Vervisch L., Two recent developments in numerical simulation of premixed and partially premixed turbulent flames, C. R. Mecanique, 334, 523-530, 2006. 5. Veynante D, Vervisch L., Turbulent Combustion modelling, Progress in Energy and Combustion Science, 28, 193-266, 2002. 6. Jakirlic S., Volkert J., Pascal H., Hanjalic K., Tropea C., DNS, experimental and modelling study of axially compressed in-cylinder swirling flow, International J. of Heat and Fluid Flow 21, 627-639, 2000. 7. Kodal A., Watson K. A., Roberts W. L. and Lyons K. M. Turbulence filter and POD analysis for velocity fields in lifted CH 4 -Air diffusion flames, Flow, Turbulence and Combustion, 70, 21-41, 2003. 8. Yilmaz T., and Kodal A., An Analysis On Coaxial Jet Flows Using Different Decomposition Techniques, Journal of Fluids and Structures, 14, 3, 359-373, 2000 9. Yilmaz T., and Kodal A., An Investigation Of Forced Structures In Turbulent Jet Flows, Experiments in Fluids, 29, 6, 564-572, 2000 10. Brereton G. J. and Kodal A., An Adaptive Turbulence Filter for Decomposition of Organized Turbulent Flows, Physics of Fluids 6 (5), 1775-1786, 1994 11. Kodal A. A New Orthogonal Decomposition Method for Turbulent Flows, Doktora tezi, The University of Michigan, Ann Arbor, Michigan, USA, May 1993 12. Brereton G. J. and Kodal A., A Frequency Domain Filtering Technique for Triple Decomposition of Unsteady Turbulent Flow Journal of Fluid Engineering, Vol. 114, 45-51, March, 1992 13. Hilbert R., Thevenin D., Influence of differential diffusion on maximum flame temperature in turbulent nonpremixed hydrogen/air flames, Combustion and Flame 138, 175-187, 2004. 14. HILL P. G., PETERSON C. R., 1992: Mechanics and Termodynamics of Propulsion, 2. baskı, Addison- Wesley yayınları, Menlo Park, Califronia, USA 15. AGARD, (Advisory Group for Aerospace Research & Development), 1993: Research and Development of Ram/Scramjets and Turboremjets in Russia, kurum North Atlantic Treaty Organization. 16. Veynante D., Large Eddy Simulations of Turbulent Combustion, Conference on Turbulence and Interactions TI2006, Laboratoire E.M2.C. CNRS et Ecole Centrale Paris, 92295 Châtenay-Malabry,

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