Layer Interaction Problem Research Articles

Experimental Investigation on the Control of Hypersonic Shock Wave/Boundary Layer Interaction Using Surface Arc Plasma Actuators at Double Compression Corner

Compression corner shock wave/boundary layer interaction (SWBLI) is a typical shock wave/boundary layer interaction (SWBLI) problem in supersonic/hypersonic flows. In previous studies, the separation flow is usually caused by a single shock wave. However, in the actual aircraft surface configuration, two-stage compression or even multistage compression will produce more complex SWBLI problems. The multi-channel shock structure makes the flow field structure more complicated and also puts forward higher requirements for the flow control scheme. In order to explore a flow control method for the double compression corner shock wave/boundary layer interaction problem, an experimental study is carried out to control the double compression corner shock wave/boundary layer interaction with a high-energy flow pulsed arc discharge array under the condition that the incoming flow velocity Ma 6.0 has both noise flow fields and quiet flow fields. The results show that when UDC = 0.5 kV actuation is applied, the influence range of the hot gas mass flow direction is about 65 mm, which can weaken the shock wave intensity to a certain extent. When UDC = 1 kV actuation is applied, the influence range of the hot gas mass flow direction extends to 85 mm, and the actuation has a significant control effect on the flow field. Through spatio-temporal evolution analysis and spatial gradient threshold processing of high-speed schlieren images of actuated flow fields, the feasibility of controlling the hypersonic double compression corner shock wave/boundary layer interaction by using a high-energy flow pulsed arc discharge array is verified. The control law of a high-energy flow pulsed arc discharge array acting on the double compression corner shock wave/boundary layer interaction is revealed.

Surrogate-based optimization on bump for shock wave/boundary layer interaction control

Supersonic and hypersonic vehicles have complex shock wave/boundary layer interaction problems during flight, and it adversely affect the aerodynamic performance of the vehicle. In this paper, the bump passive control approach is introduced to control the shock wave/boundary layer interaction, and its configuration is optimized with the minimum separation area and the maximum total pressure recovery coefficient. The Kriging model is established by means of the Latin hypercube experimental design approach to obtain the sample points. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) algorithm is utilized to optimize the parameters of the bump configuration, and the flow field structures of the uncontrolled condition, the special basic condition and the optimized condition are compared and analyzed. The obtained results show that the surrogate-based optimized model shows better performances than the basic condition. In the parameter setting range considered in this study, the optimized Case 3c with the middle position in the optimization front owns a larger total pressure recovery coefficient and a smaller separation area, with its separation area and total pressure recovery coefficient being 0.80 mm2 and 67.39% respectively.

Multi-fidelity parametric sensitivity estimation for large eddy simulation with the Spalart–Allmaras model

ABSTRACT A computationally affordable approach to estimate parametric sensitivities of engineering relevant quantities of interest for a large eddy simulation (LES) is explored. The method is based on defining a Reynolds-averaged Navier–Stokes (RANS) problem that is constrained to reproduce the LES mean flow field. The proposed method is described and assessed for a shock/boundary layer interaction problem, where the shock angle and wall temperature are considered variable or uncertain. In the current work, we show that the proposed method offers improved sensitivity predictions for certain flow features as compared to standalone RANS simulations, while using a fraction of the LES cost.

Swept shock wave/boundary layer interaction control based on surface arc plasma

Swept shock wave/boundary layer interactions occur widely in the internal and external flows of supersonic and hypersonic aircraft, which can seriously affect aircraft stability and engine intake efficiency. Based on the conventional S–A turbulence model, this study investigates surface arc plasma actuation for regulating swept shock wave/boundary layer interactions at Mach 2.95 to explore the ability and the three-dimensional shock wave/boundary layer interactions control method of plasma actuation. First, the flow control effect is explored in terms of indirect control by applying actuation in the upstream boundary layer or in front of the separation line, and in terms of direct control by applying actuation in the separation region. These three methods all achieve clear control effects. Control results show that the first method is more effective in regulating the wall pressure and friction coefficient and can improve the friction and heat transfer of the wall in a wide range of flow direction and cone direction. The second method is more effective in regulating separated shock waves. The third aspect is more effective in regulating the reattachment region. The associated control mechanisms are then refined. The control effects of the first control method depend on the transmission of vortices, those of the second are based on the virtual surface generated by actuation, and those of the third rely on energy injection. Finally, the application scenarios of the different control methods are determined according to the flow control requirements of aircraft and the corresponding control mechanisms. This study provides a reference method for solving more complex three-dimensional shock boundary layer interaction problems.

Compressive properties of Min-mod-type limiters in modelling shockwave-containing flows

The long-ignored compressive properties of Min-mod-type limiter is investigated in this manuscript by demonstrating its potential in numerically modelling shockwave-containing flows, especially in shock wave/boundary layer interaction (SWBLI) problems. Theoretical studies were firstly performed based on Sweby’s total variation diminishing (TVD) limiter region and Spekreijse’s monotonicity-preserving limiter region to indicate Min-mod-type limiters’ compressive properties. The influence of limiters on the solution accuracy was evaluated using a hybrid-order analysis method based on the grid-independent study in three typical shockwave-containing flows. The conclusions are that, Min-mod-type limiter can be utilized as a dissipative and/or compressive limiter, but depending on the reasonable value of the compression parameter. The compressive Min-mod limiter tends to be more attractive in modelling shockwave-containing flows as compared to other commonly preferred limiters because of its stable computational process and its high-resolution predictions. However, the compressive Min-mod limiter may suffer from its slightly poor convergence, as that observed in other commonly accepted smooth limiters in modelling SWBLI problems.

A new genuinely two-dimensional Riemann solver for multidimensional Euler and Navier–Stokes Equations

A novel two-dimensional flux splitting Riemann solver called ME-AUSMPW (Multi-dimension E-AUSMPW) is proposed. By borrowing the Balsara’s idea, it is built upon the Zha–Bilgen splitting procedure and considers both the waves orthogonal to the cell interfaces and the waves transverse to the cell interfaces. Systematic numerical cases, including the one dimensional Sod shock tube case, the double Mach reflection of a strong shock case, the two-dimensional Riemann problem, the hypersonic viscous flows over the two-dimensional Double-ellipsoid case, and the shock wave/laminar boundary layer interaction problem, are carried out. Results show that the ME-AUSMPW scheme proposed in this manuscript is with a higher resolution than conventional one-dimension Riemann solvers in simulating not only inviscid complex flows, but also viscous flows. Therefore, it is promising to be widely used in both scholar and engineering areas.

Lattice Boltzmann simulation for high-speed compressible viscous flows with a boundary layer

• A coupled DDF-LB model was used to simulate high-speed compressible viscous flows. • NND and second-order upwind difference schemes were compared in simulations. • The DDF-LB model could simulate a compressible boundary layer up to Ma = 6. • Local high pressure appeared with the shock wave due to LBM’s mesoscopic feature. • High potential of LBM was shown for the shock boundary layer interaction problem. In this study, the lattice Boltzmann method is employed for simulating high-speed compressible viscous flows with a boundary layer. The coupled double-distribution-function lattice Boltzmann method proposed by Li et al. (2007) is employed because of its good numerical stability and non-free-parameter feature. The non-uniform mesh construction near the wall boundary in fine grids is combined with an appropriate wall boundary treatment for the finite difference method in order to obtain accurate spatial resolution in the boundary layer problem. Three typical problems in high-speed viscous flows are solved in the lattice Boltzmann simulation, i.e., the compressible boundary layer problem, shock wave problem, and shock boundary layer interaction problem. In addition, in-depth comparisons are made with the non-oscillatory and non-free-parameter dissipation (NND) scheme and second order upwind scheme in the present lattice Boltzmann model. Our simulation results indicate the great potential of the lattice Boltzmann method for simulating high-speed compressible viscous flows with a boundary layer. Further research is needed (e.g., better numerical models and appropriate finite difference schemes) because the lattice Boltzmann method is still immature for high-speed compressible viscous flow applications.

A pressure-based Mach-uniform method for viscous fluid flows

ABSTRACTA pressure-based, Mach-uniform method is developed by combining the SLAU2 numerical scheme and the higher temporal order pressure-based algorithm. This hybrid combination compensates the limitation of the SLAU2 numerical scheme in the low-Mach number regime and deficiencies of the pressure-based method in the high-Mach number regime. A momentum interpolation method is proposed to replace the Rhie-Chow interpolation for accurate shock-capturing and to alleviate the carbuncle phenomena. The momentum interpolation method is consistent in addition to preserving pressure–velocity coupling in the incompressible limit . The postulated pressure equation allows the algorithm to compute the subsonic flows without empirical scaling of numerical dissipation at low-Mach number computation. Several test cases involving a broad range of Mach number regimes are presented. The numerical results demonstrate that the present algorithm is remarkable for the calculation of viscous fluid flows at arbitrary Mach number including shock wave/laminar boundary layer interaction and aerodynamics heating problem.

Improvement of weighted compact scheme with multi-step strategy for supersonic compressible flow

With shock capturing capability and spectral like resolution, weighted compact schemes are good choices for supersonic turbulent flow simulation. However, because of the implicit nature of compact schemes, accuracy decrease at one point would contaminate the overall solution. The recently proposed compact-reconstructed WENO (CRWENO) scheme (Ghosh and Baeder, 2012) is an efficient weighted compact scheme. Analysis shows that the accuracy of the CRWENO scheme is only second order for points near discontinuities. In this paper, a multi-step strategy is proposed to increase the accuracy of the CRWENO scheme near discontinuities. Instead of constructing the fifth order compact scheme directly from three third order compact schemes, two fourth order compact schemes are first constructed. The final fifth order scheme is then obtained by these two fourth order schemes. In this way, the accuracy of the CRWENO scheme is increased to third order for points near discontinuities. The dissipation and dispersion properties of the new scheme are analyzed by employing the modified wave number method. Several examples, including linear advection cases, three one-dimensional shock tube problems, two-dimensional isentropic vortex convection, double Mach reflection, and shock/mixing layer interaction problems, are considered to assess the present method. Numerical results show that the present multi-step CRWENO scheme has lower dissipation and higher resolution in both smooth and discontinuous regions compared with the original scheme.

Parallel Navier–Stokes simulations for high speed compressible flow past arbitrary geometries using FLASH

We report extensions to the FLASH code to enable high-speed compressible viscous flow simulation past arbitrary two- and three-dimensional stationary bodies. The body shape is embedded in a block-structured Cartesian adaptive mesh refinement grid by implementing appropriate computer graphics algorithms. A high mesh refinement level is required for an accurate body shape representation which results in large grid sizes especially for three-dimensional simulations. Simulations are done in parallel on IBM Blue Gene/Q computing system on which the code performance has been assessed in both pure MPI and hybrid MPI-OpenMP modes. We also implement appropriate wall boundary conditions in FLASH to model viscous-wall effects. Navier–Stokes (NS) solutions for various two-dimensional test cases like a shock–boundary layer interaction problem as well as for hypersonic flow past blunted cone–cylinder–flare and double-cone geometries are shown. Three dimensional NS simulations of micro vortex generators employed in hypersonic flow control have also been carried out and the computed results have been found to be consistent with experimental results.

보정한 Bleed 모델을 이용한 초음속 흡입구 버즈 제어

Database of a bleed model has been corrected and numerical simulations have been performed to control buzz using the corrected bleed model. The existing bleed model, which was developed as a part of a boundary condition model for porous bleed walls, underestimates bleed flow rate because flow accelerations near the bleed regions are ignored. Also, it overpredicts the sonic flow coefficient when the bleed plenum pressure ratio is high. To correct these problems, and to enhance the performance of the bleed model, the database has been corrected using CFD simulations to compensate for the flow acceleration near the bleed region. Futhermore, the database of the bleed model is extended with the second order extrapolation. The corrected bleed model is validated with numerical simulations of a shock-boundary layer interaction problem over a solid wall with a bleed region. Using the corrected bleed model, numerical simulations of supersonic inlet buzz are performed to find the deterrent effects of bleed on buzz. The results reveal that bleed is effective to prevent buzz and to enhance the inlet performance.

Robustness of the hybrid DRP‐WENO scheme for shock flow computations

SUMMARYThis paper describes a new variant of hybrid scheme that is constructed by a wave‐capturing scheme and a nonoscillatory scheme for flow computations in the presence of shocks. The improved fifth‐order upwind weighted essentially nonoscillatory scheme is chosen to be conjugated with the seven‐point dispersion‐relation‐preserving scheme by means of an adaptive switch function of grid‐point type. The new hybrid scheme can achieve a better resolution than the hybrid scheme which is based on the classical weighted essentially scheme. Ami Harten's multiresolution analysis algorithm is applied to density field for detecting discontinuities and setting point values of the switch function adaptively. Moreover, the tenth‐order central filter is applied in smooth part of the flow field for damping dispersion errors. This scheme can promote overall computational efficiency and yield oscillation‐free results in shock flows. The resolution properties and robustness of the new hybrid scheme are tested in both 1D and 2D linear and nonlinear cases. It performs well for computing flow problems with rich structures of weak/strong shocks and large/small vortices, such as the shock‐boundary layer interaction problem in a shock tube, which illustrates that it is very robust and accurate for direct numerical simulation of gas‐dynamics flows. Copyright © 2011 John Wiley & Sons, Ltd.

Generalized finite compact difference scheme for shock/complex flowfield interaction

A class of generalized high order finite compact difference schemes is proposed for shock/vortex, shock/boundary layer interaction problems. The finite compact difference scheme takes the region between two shocks as a compact stencil. The high order WENO fluxes on shock stencils are used as the internal boundary fluxes for the compact scheme. A lemma based on the property of smoothness estimators on a 5-points stencil is given to detect the shock position. There is no free parameter introduced to switch the compact scheme and the WENO scheme. Some numerical experiments are given and they demonstrate that the present scheme has low dissipation due to the compact central differencing scheme used in the smooth regions.

Spatially adaptive PIV interrogation based on data ensemble

This paper proposes a specific application of the approach recently proposed by the authors to achieve an autonomous and robust adaptive interrogation method for PIV data sets with the focus on the determination of mean velocity fields. Under circumstances such as suboptimal flow seeding distribution and large variations in the velocity field properties, neither multigrid techniques nor adaptive interrogation with criteria based on instantaneous conditions offer enough robustness for the flow field analysis. A method based on the data ensemble to select the adaptive interrogation parameters, namely, the window size, aspect ratio, orientation, and overlap factor is followed in this study. Interrogation windows are sized, shaped and spatially distributed on the basis of the average seeding density and the gradient of the velocity vector field. Compared to the instantaneous approach, the ensemble-based criterion adapts the windows in a more robust way especially for the implementation of non-isotropic windows (stretching and orientation), which yields a higher spatial resolution. If the procedure is applied recursively, the number of correlation samples can be optimized to satisfy a prescribed level of window overlap ratio. The relevance and applicability of the method are illustrated by an application to a shock-wave-boundary layer interaction problem. Furthermore, the application to a transonic airfoil wake verifies by means of a dual-resolution experiment that the spatial resolution in the wake can be increased by using non-isotropic interrogation windows.

A Robust Low Diffusive Kinetic Scheme for the Navier–Stokes/Euler Equations

A new kinetic scheme based on the equilibrium flux method (EFM) and modified using Osher intermediate states is proposed. This new scheme called EFMO combines the robustness of the equilibrium flux method and the accuracy of flux-difference splitting schemes. The original EFM scheme is expressed in terms of simple wave decomposition in which only the linearly degenerate subpath is calculated from Osher numerical flux while nonlinear waves are still evaluated from the regular EFM splitting. Owing to its capability of withstanding intense nonlinear waves and yet exactly resolving contact discontinuities, EFMO is particularly well suited for the resolution of the Navier–Stokes equations as demonstrated by a series of severe test cases including the high-speed viscous flow around a cone, a shock-boundary layer interaction problem, a vacuum apparition problem, the hypersonic flow around a circular cylinder at Mach 100, and the forward-facing step at Mach 3.

Numerical studies of real-gas effects on two-dimensional hypersonic shock-wave/boundary-layer interaction

Nonequilibrium real-gas effects on surface heating rates, skin friction, and flow field unsteadiness of two-dimensional hypersonic shock-wave/boundary-layer interaction were studied by numerical simulations. The unsteady Navier–Stokes equations with nonequilibrium vibrational and chemical models for five-species air were solved by a finite-volume second-order TVD scheme together with a third-order semi-implicit Runge–Kutta scheme. Two cases of high-enthalpy shock/boundary layer interaction problems were studied in this paper. The freestream enthalpy was high enough to produce vibrational excitation and dissociation/recombination chemistry behind the shock. The first case was a steady two-dimensional shock/boundary layer interaction on a flat plate with a mixture of N2 and O2 in the freestream. It was found that the real gas effects reduce the size of the shock induced separation bubble and the magnitude of the surface heating rates. The second case was a self-sustained unsteady type IV shock–shock interference heating of a pure N2 flow over a cylinder. The results showed that type IV shock–shock interference heating flows with real-gas effects are inherently unsteady. Vortices are generated and shed off near the jet impingement point. This periodic shedding of the vortices contributes to the self-sustained oscillations of both the jet and other parts of the flow fields. In addition, the real-gas effects reduce the level of peak surface heating and peak surface pressure due to endothermic real-gas effects.

Grid adaptation using chimera composite overlapping meshes

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Investigation of flux formulae in transonic shock wave/turbulent boundary layer interaction

AbstractThe aim of the present study is to examine the accuracy and improvement of various numerical methods in the solution of the transonic shock/turbulent boundary layer interaction problem and to show that a significant source of numerical inaccuracies in turbulent flows is not only the inadequacy of the turbulence model but also the numerical discretization. Comparisons between a Riemann solver and a flux‐vector‐splitting method as well as between various numerical high‐order extrapolation schemes with corresponding experimental results are presented.

Compressible Boundary Layer-Inviscid Flow Interactions in Entrance Region of Internal Flows

The coupling between the inviscid flow and the compressible boundary layer in the developing entrance region for internal flows is analyzed by solving the particular inviscid flow-boundary layer interaction problem. The interaction problem is solved by postulating certain series forms of solutions for the inviscid region and the boundary layer. The boundary-layer equations and inviscid-flow equations are perturbed to third order and each generated equation is solved numerically. In order to preserve the universality of each of the perturbed boundary-layer equations, the perturbation parameter is described by an integral equation which is also solved in series form. The final results describing the interaction problem are then constructed for any given conditions by forming the three series to a consistent order of magnitude. This technique of coordinate perturbation is generalized to show how it may be applied to the entrance regions of pipe flows, including mass injection or suction, and also to the laminar boundary layers in shock tube flows. It demonstrates analytically the manner in which the boundary layer and inviscid flow interact and create a streamwise pressure gradient. In particular, the interaction problem which occurs in shock tube flows is solved in detail by the use of this generalized method, as an example.

Estimation of the critical viscous sublayer in heat transfer problems

Imagining a disturbance made on a compressible boundary layer with the help of a heat source, the critical viscous sublayer, through which the skin friction at any point on a surface is connected with the heat transferred from a heated element embedded in it, has been estimated. Under similar conditions of external flow (Ray1)) the ratio of the critical viscous sublayer to the undisturbed boundary layer thickness is about one-tenth in the laminar case and one hundredth in the turbulent case. These results are similar to those (cf.1)) found in shock wave boundary layer interaction problems.