Improvement and application of wall function boundary condition for high-speed compressible flows

In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simulation for the skin friction and heat flux,a research was performed to improve the compressible wall function boundary condition proposed by Nichols.Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation.Besides,the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately.Whereafter,the application study of the modified wall function was carried out.The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux,and profiles of velocity,temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y+<400,and that the modifications to the original wall function can obviously improve the simulation precision.As for the application of separation flows,it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression corner that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall region inside the separation flows,which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows,while for the region near separation and reattachment points,the wall function gives results with a relatively large error,because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real velocity profiles near the separation and reattachment points.

A numerical study of turbulent combustion characteristics in a combustion chamber of a scramjet engine

3D numerical simulation of flow fields in a combustion chamber of a scramjet engine using an SST turbulence model with an explicit compressibility correction was performed and the results were compared to the experimental results.The characteristics of the turbulent combustion flow fields were analyzed via the numerical results and presented.In order to identify the mechanisms of turbulent combustion in supersonic flows,the evolutions of governing dimensionless parameters in the flow fields were investigated based on the theory of combustion and the available numerical results.It was found that the supersonic combustion takes place in the region of fully developed turbulence and that the strongest effects of turbulence and combustion processes appear in the vicinity of the injector.The unsteady effects and the local flame extinction phenomenon induced by turbulent flows were found to be negligibly small,and the steady flamelet approximation will hold for practical applications.

Numerical research on mixing characteristics of different injection schemes for supersonic transverse jet

A numerical method using AUSMDV scheme and k-ω SST turbulence model with an explicit compressibility correction was developed,and a 3-D numerical simulation of a supersonic flow field with a vertical sonic jet of hydrogen was performed.Good agreement between numerical results and experimental data validated the reliability of the numerical method.Whereafter,two parameters,mass-weighted average total pressure and mixing efficiency,were defined to evaluate the mixing performance of different injection schemes.Based on the numerical method and evaluation criterion,the mixing characteristics of different injection schemes were studied in detail.It was found that for the mixing field of supersonic transverse jet,the near-field mixing is controlled by convection transport while the far-field mixing is controlled by mass diffusion;the circular-hole injection causes a loss of total pressure comparable to the slot injection,but can induce a much higher mixing efficiency because of its 3-D flow characteristic;the variation of injection angle under circular-hole injection mainly affects the near-field mixing degree,and among the five injection angles studied in the present paper,angle 120° is the optimal one;with the increase of the ratio between injector space and diameter,the induced mixing efficiency increases while the caused loss of total pressure can grow greatly;the two-stage injection method designed through reducing the injector area to keep the same hydrogen mass flowrate can induce a much higher mixing efficiency while only a bit larger loss of total pressure when compared to the single-stage injection,and hence the two-stage injection is superior to the single-stage injection.The research results can direct the design of the fuel injection method in the combustor of scramjet engine.

A flamelet model for turbulent diffusion combustion in supersonic flow

In order to develop a turbulent diffusion combustion model for supersonic flow, the physical argument of the extension of the flamelet model to supersonic flow was presented, and the flow field of a hydrogen/air diffusion combustion generated by axisymmetric supersonic jets was numerically simulated by employing the flamelet model. Using the experimental data, value of the model coefficient of scalar dissipation in the flamelet model was revised specifically for supersonic flow. The computational results of the modified flamelet model were compared with the experimental results, and it was indicated that the precision of the modified flamelet model was satisfying. Based on the numerical results and flamelet theory, the influence mechanisms of turbulence fluctuation on the average state equation and chemical reaction rate were studied for the first time. It was found that the fluctuation correlation of species mass fractions and temperature has little effect on the averaged gas state equation; the temperature fluctuation decreases the product of H2O, but its effect is small; the fluctuation of species mass fractions increases the product of H2O in the region close to oxidizer while decreases the product of H2O in other regions; the fluctuation correlation of species mass fractions and temperature largely decreases the product of H2O.

A Favré averaged transition prediction model for hypersonic flows

Transition prediction is crucial for aerothermodynamic and thermal protection system design of hypersonic vehicles.The compressible form of laminar kinetic energy equation is derived based on Favréaverage formality in the present paper.A closure of the equation is deduced and simplified under certain hypotheses and scaling analysis.A laminar-to-turbulent transition prediction procedure is proposed for high Mach number flows based on the modeled Favré-averaged laminar kinetic energy equation,in conjunction with the Favré-averaged Navier-Stokes equations.The proposed model,with and without associated explicit compressibility terms,is then applied to simulate flows over flared-cones with a free-stream Mach number of 5.91,and the onset locations of the boundary layer transition under different wall conditions are estimated.The computed onset locations are compared with those obtained by the model based on a compressibility correction deduced from the reference-temperature concept,together with experimental data.It is revealed that the present model gives a more favorable transition prediction for hypersonic flows.

Characterization of the three-dimensional supersonic flow for the MHD generator

A numerical procedure based on a five-wave MHD model associated with non-ideal,low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations,in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode,where the local adverse pressure gradient is large,and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases,and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction,all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section,which,in turn,induces the corner eddy current at the corner. A numerical parametric study was also performed,and the computed performance parameters for the MHD generator suggest that,in order to enhance the performance of MHD generator,the magnetic interaction parameter should be elevated.

Direct numerical simulation of the turbulent MHD channel flow at low magnetic Reynolds number for electric correlation characteristics

Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption.The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations.The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner.The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations.The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model.The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation,while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation.

Influence of Hall effects on characteristics of magnetohydrodynamic converging channel

Influences of Hall effects on the flow characteristics and performance of the magnetohydrodyanmic (MHD) converging channel as an MHD generator are studied numerically in the present study. The numerical algorithm used is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of the electric field. It is found that Hall effects may lead to distortions in both the flow field and electric field in the MHD converging channel. The electric current lines are distorted and induce eddy currents, which will be mitigated by Hall effects. Comparisons of parameters characterizing the performance of the MHD generator for different geometry also reveal that the Hall effects may deteriorate the performance of MHD generator, especially for converging channel.

Numerical investigation of compressibility effects in turbulent channel flows using large eddy simulation

The large eddy simulation (LES) of compressible turbulent channel flows at three different Mach numbers is performed in the present work,by extending the dynamic mixed subgrid-scale (SGS) model to compressible flows.The turbulent statistics agree well with those from the existing direct numerical simulation (DNS) results,indicating that the LES method established in the present work is reliable.The analysis of the turbulent fluctuations computed by the present LES reveals that the flows considered in this work follow the Morkovin's hypothesis.Thus,the compressibility effects are dominated by the mean field properties,and the relevant statistical ratios are invariant to the variation of Mach number.The near-wall streamwise streaks are more coherent and the spacing between streaks is wider as the Mach number increases.This can be regarded as a direct feature characterized by the compressibility effects.The restrained influences of compressibility effects on the production and dissipation of the turbulence kinetic energy are also identified based on the present LES results.

An implicit algorithm based on iterative modified approximate factorization method coupling with characteristic boundary conditions for solving subsonic viscous flows

An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.

Simulation of three-dimensional nonideal MHD flow at low magnetic Reynolds number

A numerical procedure based on a five-wave model associated with non-ideal,low magnetic Reynolds number magnetohydrodynamic(MHD)flows was developed.It is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations,in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of flow field.To validate the developed procedure,two different test cases were used which included MHD Rayleigh problem and MHD Hartmann problem.The simulations were performed under the assumption of low magnetic Reynolds number.The simulated results were found to be in good agreement with the closed form analytical solutions deduced in the present study,showing that the present algorithm could simulate engineering MHD flow at low magnetic Reynolds number effectively.In the end,a flow field between a pair of segmented electrodes in a three dimensional MHD channel was simulated using the present algorithm with and without including Hall effects.Without the introduction of Hall effects,no distortion was observed in the current and potential lines.By taking the Hall effects into account,the potential lines distorted and clustered at the upstream and downstream edges of the cathode and anode,respectively.

Numerical investigation on jet interaction with a compression ramp

A numerical investigation on jet interaction in supersonic laminar flow with a compres- sion ramp is performed utilizing the AUSMDV scheme and a parallel solver. Several parameters dominating the interference flowfield are studied after defining the relative increment of normal force and the jet amplification factor as the evaluation criterion of jet control performance. The computational results show that most features of the interaction flowfield between the transverse jet and the ramp are similar to those between a jet and a flat plate, except that the flow structures are more complicated and the low-pressure region behind the jet is less extensive. The relative force increment and the jet amplification factor both increase with the distance between the jet and the ramp shortening till quintuple jet diameters. Inconspicuous difference is observed between the jet-before-ramp and jet-on-ramp cases. The variation of the injection angle changes the extent of the separation region, the plateau pressure, and the peak pressure near the jet. In the present computational conditions, 120 is indicated relatively optimal among all the injection angles studied. For cold gas simulations, although little influence of the jet temperature on the pressure distribution near the jet is observed under the computation model and the flow parameters studied, reducing jet temperature somehow benefits the improvement of the normal force and the jet efficiency. When the pressure ratio of jet to freestream is fixed, the relative force increment varies little when increasing the freestream Mach number, while the jet amplification factor increases.