Available online at www.sciencedirect.com
Procedia Engineering 31 (2012) 708 – 712
International Conference on Advances in Computational Modeling and Simulation
Numerical Simulation of Supersonic Combustor with Innovative Cavity Dingwu Zhanga*,Qiang Wanga a
School of Jet Propulsion, Beihang University, Beijing, 100191, China
Abstract Reynolds-Averaged Navier-Stokes simulations using k-w model are employed to explore a single cavity flameholding configuration of an analogous supersonic combustor. The flight conditions replicate those used on a typical hydrogen hypersonic air-breathing propulsion system at approximately Mach 6 and 24 km altitude. The cross-section analyzed is rectangular in shape, and selected for studying a typical scramjet flow-path as in a direct connect facility. The hypersonic inlet is assumed to condition the air past the isolator to enter the study configurations at Mach 2.0. This study focuses on the frozen performance and flow-path effects when varying the ramp angle and modifying the cavity configuration on a typical supersonic combustor. In this study, five numerical calculations are performed to find which configuration is the best one in enhancing mixing aspect. The results indicate that: firstly, The mixing effects show significant improvement when the ramp angle is positive, however, over-large ramp angle could add resistance and reduce total pressure recovery and secondly; no obvious effects are observed when the ramp angle is negative; thirdly, among the conducted numerical analysis, the model with positive 15 degree ramp angle has the best performance.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming University of Science and Technology Open access under CC BY-NC-ND license. Keywords: supersonic; innovative cavity; ramp angle; shock
1. Introduction Future space transport vehicles or even high speed aircrafts are supposed to use air breathing propulsion systems for their flight in a wide range of hypersonic Mach numbers. The great benefit of air breathing systems such as scramjets is the ability to draw the oxidizer from the surrounding atmosphere. * Corresponding author. Tel.: +86-10-82339759 ; fax: +86-10-82339759. E-mail address:
[email protected].
1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.01.1090
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Therefore, the maximum payload increases and the aircraft promises to have lower operating costs. Unfortunately, scramjet propulsion systems have many technical challenges yet to overcome. Some of the main difficulties can be traced to aeropropulsive phenomena, including transition to turbulence, shock– boundary-layer interactions, fuel injection and mixing in a short residence time environment, and their collective impact on heat load, inlet distortion, and adequate thrust generation in a practical engine. Recent advances have employed a spectrum of loosely coupled approaches, including flight tests, analytical, and simulation. Each approach has inherent strengths and limitations. For example, in the computational approach, which is the focus of this paper, the availability of 3-D steady data greatly facilitates interrogation and trend detection. The study of flow interaction with cavities is of high importance. Subsonic and supersonic cavity flows are encountered on a daily basis. A lot of research works were carried out by researchers around the world, Some notable early researchers of cavity flow include Rossiter [1], Roshko [2], and Krishnamurty [3]. Rockwell and Naudascher [4] give a thorough review of the flow driving the cavity pressure fluctuations and its many variations. The cavity has been shown to be a new effective supersonic combustion flame stabilizer, cavity flow characteristics and properties have made some progress, however, the flame stabilizer cavity research and application only through a short time, and most of the current study demonstrated the feasibility, the research model are also flat type(case 1), unfortunately, little existing research work involved in different types of cavity structure. So based on these studies this paper focuses on the frozen performance and flow-path effects when varying the ramp angle and modifying the cavity configuration on a typical supersonic combustor . In this study, five numerical calculations cases are performed to find which configuration is the best one in enhancing mixing aspect. The results indicate that: firstly, The mixing effects show significant improvement when the ramp angle is positive, however, overlarge ramp angle could add resistance and reduce total pressure recovery and secondly; no obvious effects are observed when the ramp angle is negative; thirdly, among the conducted numerical analysis, the model with positive 15 degree ramp angle has the best performance. 2. Governing Equations The three-dimensional turbulent reacting flowfields are described through the conservation equations for a multispecies chemically reactive system. The coupled governing equations of species conservation, fluid dynamics, and turbulent transport are expressed in the following conservative vector form, (1) where the conservative variable vectorQ, the convective flux vectors E,F, andG, the viscous flux vectorsEv,Fv, andGv, and the reaction source term W are defined in the previous paper [5]. The finite-volume approach is used for the spatial discretization of the governing equations. The viscous terms are expressed by the central difference method, and the convective terms are expressed as the differences in the numerical fluxes at the cell interface. The numerical fluxes containing artificial dissipation are formulated using Roe’s flux difference splitting method. The MUSCL (monotone upstream-centered schemes for conservation laws) scheme is used for the extrapolation of primitive variables at the cell interface. In addition, the Chakravarthy and Osher limiter function is used to overcome the dispersion error that is introduced by the thirdorder extrapolation and to preserve the totalvariation-diminishing property. For an analysis of unsteady supersonic reacting flow, a fully implicit, lower–upper symmetric Gauss–Seidel method is used with second-order accuracy. A Newton subiteration method is applied to reduce the error in temporal discretization and ensure second-order time accuracy
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and stability, thereby allowing a large time step. Details of the governing equations and the numerical formulation are described in previous studies [6,7,9]. 3. CFD Validation Using of FLUENT software simulate Gruber research problems [8], which conducted as a confirmatory calculations. M.R. Gruber and others used the computational fluid dynamics software, which developed by U.S. NASA Langley Air-breathing hypersonic propulsion technology research center (HAPB), to simulate cavity flow field, the VULCAN software uses the same turbulence models as FLUENT software, and the findings were compared with the U.S. Air Force Base, Wight-Patterson Air Force Research laboratory (AFRL) test results. Figure 1 shows the simulation results of this paper and literature [8], the simulation results are basically the same, to correctly reflect the cavity flow structure and pressure distribution, indicating the software used in this calculation and the choice of algorithms and computational models is appropriate. 4. Geometric model Calculated using the model of size 20mmu30mmu100mm of the rectangular main channel, the origin of Cartesian coordinate system is the main channel of the geometric center. In the lower part of the main channel, the cavity size for length 30mm, width 20mm, 6mm deep as the corresponding open cavity (case 1). Select this cavity as a reference cavity, using a different tilt angle of the ramp, to look at different ramp angles of the combustion chamber flow characteristics. Provides upward angle is positive, downward angle is negative, the ramp angle is 30°,15°,-15°,-30°, the height of the ramp to maintain a fixed value of 2mm. In this paper, numerical simulation software, FLUENT, which uses second-order upwind convective dispersion, diffusion term use of central difference discretization, turbulence model uses a compression correction and transonic modified SST k-Ȧ model. Specific combustion flow parameters P 0 = 6.78atm, P = 0.89atm, T0 = 253K, the wall no-slip adiabatic wall. 5. Numerical Analysis and Results Results are illustrated in Figures 2, 3. The cavity flame holder have a few obvious features: the mainstream separation occurs in the cavity leading edge, in the cavity low-speed air return back to form recirculation region, low back air and high-speed air flow to form the main shear layer, when shear layer downstream development or bias towards the mainstream, or bias towards the internal cavity, thus forming the leading edge of wave system, in this paper, the shear layer slightly bias towards the mainstream, so the oblique shock formed in front, until the development of the shear layer downstream at the cavity trailing edge, part of the shear layer impact the cavity back edge to form impact shock wave, the main flow through the cavity trailing edge to form a clear expansion wave.Figure 2 shows different cases of symmetry plane of the pressure field distribution, the pressure field distribution of case2,3 are significantly different with case 1, as the cavity leading edge increased upward ramp, high-speed primary air flows through the ramp formed strong oblique shock wave by compression of a stagnation, this change makes the shear layer slightly bias towards to the internal cavity when downstream development, so the expansion wave formed in front leading edge. Shear layer also could across the entire cavity and reattached to the cavity trailing edge, impact shock wave formed in the attachment, the shock wave and the reflected shock wave on the wall together to enhance the combustion chamber pressure perturbation. The flow field of case4,5 are basically the same situation as case1, the main difference is the ramp angle
Dingwu Zhang and Qiang Wang / Procedia Engineering 31 (2012) 708 – 712
becomes smaller, the intensity of the oblique shock wave becomes weaker.Figure 3 shows the Mach number and shock formation for the full configuration, there can be seen the formed vortices filled with the whole cavity, the vortex center position near the cavity trailing edge, as the ramp angle changes from positive 30 degrees to negative 30 degrees, the vortex size changes from large to small, which is not conducive to the stability of the flame.Combustor drag including differential pressure between leading edge and trailing edge, also contain the solid surface and shear layer friction. Cavity differential pressure drag can produce two parts: firstly, the leading edge of the cavity pressure may be lower than the free stream pressure, which leads to the x-direction drag, if the leading edge of the cavity pressure is higher than the free stream pressure, which leads to thrust. Secondly, the shear layer re-attached to the trailing edge form a high pressure region, resulting in an x-direction force, which acting on the cavity back wall to form drag. Differential pressure drag is the main part of drag in the combustion chamber, so in this paper only considered the differential pressure drag. Table 1. Various types of cavity drag coefficient and total pressure recovery coefficient Numerical examples
Drag coefficient
Total pressure recovery coefficient˄%˅
Case 1
0.067
92.6
Case 2
0.094
85.0
Case 3
0.080
91.3
Case 4
0.072
92.5
Case 5
0.074
92.3
As shown in Table 1 when the ramp upward, the cavity drag coefficient much larger than the reference cavity(case 1), as a strong shock wave formed when the main flow through the ramp, leading to increased drag. When upward ramp angle becomes smaller, the strength of shock becomes weaker, so the drag coefficient is reduced accordingly. When the ramp angle downward, there is no significant change. 6. Conclusions Firstly, The mixing effects show significant improvement when the ramp angle is positive, however, over-large ramp angle could add resistance and reduce total pressure recovery and secondly; no obvious effects are observed when the ramp angle is negative; thirdly, among the conducted numerical analysis, the model with positive 15 degree ramp angle has the best performance. 7. Author Artwork
Fig.1. (a) the flow chart of literature [8]; (b) the flow chart in this paper; (c) wall pressure distribution
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Fig.2. pressure contour of different cases, full configuration
Fig.3 mach number contour of different cases, full configuration
References [1] J. Rossiter, “Wind-Tunnel Experiments on the Flow Over Rectangular Cavities at Subsonic and Transonic Speeds,” Aeronautical Research Council, Reports and Memoranda No. 3438, 1964. [2] A. Roshko, “Some Measurements of Flow in a Rectangular Cutout,” NACA, TN 3488, 1955. [3] K. Krishnamurty, “Acoustic Radiation from Two-Dimensional Rectangular Cutouts in Aerodynamic Surfaces,” NACA, TN 3487, 1955. [4] D. Rockwell and E. Naudascher, “Review: Self Sustaining Oscillations of Flow Past Cavities,” Journal of Fluids Engineering, vol. 100, pp. 152-165, Jun. 1978. [5] Won, S.-H., Jeung, I.-S., Shin, J.-R., Cho, D.-R., and Choi, J.-Y., “Three-Dimensional Dynamic Characteristics of Transverse Fuel Injection into a Supersonic Crossflow,” AIAA Paper 2008-2515, 2008. [6] Choi, J.-Y., Yang, V., and Ma., F., “Combustion Oscillations in a Scramjet Engine Combustor with Transverse Fuel Injection,” Proceedings of the Combustion Institute, Vol. 30, No. 2, 2005, pp. 2851–2858. [7] Choi, J.-Y., Ma, F., and Yang, V., “Dynamics Combustion Characteristics in Scramjet Combustors withTransverse Fuel Injection,”AIAA Paper 2005-4428, 2005. [8] M. R. GruberˈR. A. Baurle and T. Mathur Fundamental Studies of Cavity-Based Flameholder Concepts of Supersonic Combustors. Journal of Propulsion and Power Vo.17ˈNo.1 January-Feburayrˈ2001 [9] Choi, J.-Y., Jeung, I.-S., and Yoon,Y., “Computational Fluid Dynamics Algorithms for Unsteady Shock-Induced Combustion, Part 1:Validation,” AIAA Journal, Vol. 38, No. 7, 2000, pp. 1179–1187.
