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Journal ArticleDOI

Modeling of supersonic combustion using point implicit finite volume method

01 Jun 2007-International Journal of Computational Methods (World Scientific Publishing Company)-Vol. 04, Iss: 02, pp 353-366
TL;DR: In this article, a numerical modeling of turbulent-reacting flow field in supersonic combustors is presented, in which the conservation equations in conjunction with chemical source terms alone are treated implicitly.
Abstract: Numerical modeling of turbulent-reacting flow field in supersonic combustors is presented. When flow field and chemical kinetics with differing time scales need to be solved simultaneously, explicit treatment of all conservation terms with reaction chemistry results in stiff equations and has a tendency to degrade the performance of numerical method. A method of preconditioning, in which the conservation equations in conjunction with chemical source terms alone is treated implicitly. Such a method has the advantage of both explicit and implicit methods. A code was developed using above method and tested successfully for a supersonic combustor configuration.
Citations
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Journal ArticleDOI
TL;DR: This review can be useful for engineers and scientists who are using numerical simulation of the thermo-gasdynamics of combustion processes for the purpose of validating the developing computer codes and kinetic models.

71 citations

Journal ArticleDOI
TL;DR: Present numerical solver is useful in simulating combustors of high speed air-breathing propulsion devices, and has been successfully validated against experimental and numerical results reported for the wall static pressure data in sonic slot injection to supersonic stream.
Abstract: Development of an Advection Upstream Splitting Method (AUSM+-up) scheme-based Unstructured Finite Volume (UFVM) solver for the simulation of two-dimensional axisymmetric/planar high speed compressible turbulent reacting shear layers is presented. The inviscid numerical flux is evaluated using AUSM+-up upwind scheme. An eight-step hydrogen–oxygen finite rate chemistry model is used to model the development of chemical species in a supersonic reacting flow field. The chemical species terms are alone solved implicitly in this explicit flow solver by rescaling the equation in time. The turbulence modeling has been done using RNG-based k–ϵ model. Three-stage Runge–Kutta method has been used for explicit time integration. The nonreacting two-dimensional Cartesian version of the same solver has been successfully validated against experimental and numerical results reported for the wall static pressure data in sonic slot injection to supersonic stream. Detailed validation studies for reacting flow solver has been done using experimental results reported for a coaxial supersonic combustor, in which species profile at various axial locations has been compared. Present numerical solver is useful in simulating combustors of high speed air-breathing propulsion devices.

6 citations

Journal ArticleDOI
TL;DR: In this article , the authors established a supersonic exhaust plume model by using the three-dimensional Reynolds-averaged Navier-Stokes (RANS) methods and realizable turbulence model.
Abstract: Heavy launch vehicles use liquid oxygen (LOX) and kerosene propellants for their high specific impulse and controlling precision. However, incomplete burnt exhaust gas reacts easily with air, which will influence the thermal environment. To investigate the afterburning effect on the plume flowfield at low altitudes, we established a supersonic exhaust plume model by using the three-dimensional Reynolds-averaged Navier–Stokes (RANS) methods and realizable turbulence model. Also, the nine-species and fourth-step chemical reactions are adopted to simulate the afterburning process. The validity of our numerical model is confirmed by the good agreement between calculation results and experiment data. On this basis, the thermal environment of the LOX/kerosene rocket between frozen and reaction flow at five typical altitudes are calculated and compared. The numerical results show that the secondary combustion reactions mainly occur in the mixing layer, with about an 11.9–18.6% increase in the peak temperature after considering the afterburning effects. The increase in range of the maximum temperature of the engine exhaust plume gradually reduces as the flight height increases. At the same altitude, the afterburning has more significant effect on flowfield for a larger distance from the nozzle exit. The results provide a vital foundation of analysis and calculation for the design of the LOX/kerosene rocket thermal protection.
References
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Journal ArticleDOI
TL;DR: In this article, a two-equation model and Reynolds stress transport model are developed for turbulent shear flows and tested for homogeneous shear flow and flow over a backward facing step.
Abstract: Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK/■) is the ratio of the turbulent to mean strain time scale. While low‐order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two‐equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

2,347 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of unmixedness on reaction in turbulent flow were investigated using a parabolic marching simulation of a super-sonic air stream with a finite-rate chemistry system.
Abstract: Good agreement has been obtained between published profiles of composition and pitot pressure with the calculated results from a computer program in which finite rate chemistry was used. Significant differences are noted between results calculated using 7 species and 8 reactions and those calculated using 12 species and 25 reactions. Differences are also found between results in which the effect of unmixedness on reaction in turbulent flow is applied or is not applied. ULTI-REACTION finite-rate chemistry has been used for many years in computer simulation of complex flowfields, and results have been good in laminar flows. Mixing of fuel and air is faster in turbulent flows than in laminar flows, but in turbulent flows the folding together of large volumes of fluid alternately rich in either fuel or oxygen produces the phenomenon of "unmixedness" in which the time-averaged temperature and composition at a point do not represent correctly the degree to which fuel and air are mixed on a molecular scale. Thus, the use of time-averaged values of temperatures and concentrations in the finite-rate chemistry equations is incorrect and can lead to serious errors in calculated results. This by no means rules out the use of time- averaged values, since the effects of unmixedness may be small for many turbulent, reacting flows. One purpose of this paper is to demonstrate that this is so by calculating some results with and without the effects of unmixedness. Another purpose of the paper is to report improvement in the ability of a computer program to simulate burning of H 2 in a super- sonic air stream when an eddy breakup chemistry model is replaced with one in which finite reaction rates, corrected for unmixedness, are used. In a prior investigation,1 the usefulness of a parabolic marching computer program was evaluated by comparing computed results with data from five experimental test cases. Mixing of fuel and oxidant was computed for parallel in- jection of H2 using a two-equation turbulence model, and the extent of chemical reaction was deduced by comparing the data with results obtained from three different assumptions: 1) no reaction, corresponding to zero combustion efficiency; 2) complete burning of all fuel mixed with oxygen, corresponding to combustion efficiency = 1; and 3) finite-rate burning based on the rate of decay of large turbulent eddies into small ones. The last of these assumptions, the eddy- breakup (EBU) model,2 provided a means for obtaining combustion efficiency values intermediate between 0 and 1 and is believed to be useful as a tool to account for the effects of unmixedness on chemical reaction in turbulent flows if chemical reaction rates are large enough so that the production of combustion products is limited by the mixing rate. In this paper three of the experimental test cases used in the previous computer program evaluation are reanalyzed using the same program but with a finite-rate chemistry system reported by Spiegler. 3 In this chemistry system the effect of unmixedness on individual reactions is modeled by decreasing any rate for which one or more of the species involved goes negative during fluctuation of its concentration about the average value. (Temperature fluctuations are not considered.) In addition to calculations using Spiegler's system of 7 species and 8 reactions, calculations were also made using 12 species and 25 reactions. The latter system required the solution of twice as many differential equations for chemical species, but this was judged to be necessary in order to examine the effect of the added equations on the generation rates of radicals such as H, O, and OH. The elemental reactions by means of which H2 and O2 are transformed into H2O provide multiple paths between the reactants and the product, most of which depend on the presence of high concentrations of radicals. The relative importance of the paths changes as conditions in the flow change, and it is important not to neglect any path which might be a large source or sink for one or more of the radicals, since such a path might be critical for prediction of ignition.

301 citations

Journal ArticleDOI
TL;DR: In this article, a technique d'acceleration basee sur le preconditionnement des equations de conservation is proposed, based on the integration numerique des equations d'Euler and Navier-Stokes.
Abstract: Integration numerique des equations d'Euler et Navier-Stokes. On developpe une technique d'acceleration basee sur le preconditionnement des equations de conservation

216 citations

Journal ArticleDOI
TL;DR: In this article, the authors describe the numerical investigations concerning the combustion enhancement when a cavity is used for the hydrogen fuel injection through a transverse slot nozzle into a supersonic hot air stream.

196 citations

Journal ArticleDOI
TL;DR: In this article, a two-equation turbulence model based on a kappa-omega formulation, a PDF that yields Favre averages, and relaxes the gradient diffusion assumption is presented.
Abstract: Recent calculations of turbulent supersonic reacting shear flows using an assumed multivariate beta probability density function (PDF) resulted in reduced production rates and a delay in the onset of combustion. This result is not consistent with available measurements. Earlier work was based on a one-equation turbulence model that required a specification of the length scale, PDFs that did not yield Favre-averaged quantities, and the gradient diffusion assumption. The present work incorporates a two-equation turbulence model based on a kappa-omega formulation, a PDF that yields Favre averages, and relaxes the gradient diffusion assumption. Results suggest that the form of the assumed multivariate PDF and the gradient diffusion assumption are the main causes of the discrepancy. 15 refs.

29 citations