Vincent Wheatley

Low Reynolds number flow over a square cylinder with a splitter plate

Flows over a square cylinder of side length D with and without a splitter plate are numerically investigated at a Reynolds number of 150. The length of the splitter plate is varied systematically from L=0.5D to L=6D so the sensitivity of the flow structure to the inclusion of the splitter plate can be inspected. It is found that the splitter plate introduces a strong hydrodynamic interaction to the near wake of the cylinder and the length of the plate affects significantly the flow structure. The behavior of the flow can be grouped into three regimes. For short plate lengths (0≲L≲D), the free shear layers are convected further downstream before rolling up when the plate length is increased. For intermediate plate lengths (1.25D≲L≲4.75D), a secondary vortex is clearly visible around the trailing edge of the splitter plate and the shear layers begin to roll up closer to the trailing edge. For long plate lengths (L≳5D), a regime is observed in which the free shear layers reattach to the splitter plate. The s...

Regular shock refraction at an oblique planar density interface in magnetohydrodynamics

We consider the problem of regular refraction (where regular implies all waves meet at a single point) of a shock at an oblique planar contact discontinuity separating conducting fluids of different densities in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic (MHD) simulations indicate that the presence of a magnetic field inhibits the deposition of vorticity on the shocked contact. We show that the shock refraction process produces a system of five to seven plane waves that may include fast, intermediate, and slow MHD shocks, slow compound waves, 180 ◦ rotational discontinuities, and slow-mode expansion fans that intersect at a point. In all solutions, the shocked contact is vorticity free and hence stable. These solutions are not unique, but differ in the types of waves that participate. The set of equations governing the structure of these multiple-wave solutions is obtained in which fluid property variation is allowed only in the azimuthal direction about the wave-intersection point. Corresponding solutions are referred to as either quintuple-points, sextuple-points, or septuple-points, depending on the number of participating waves. A numerical method of solution is described and examples are compared to the results of numerical simulations for moderate magnetic field strengths. The limit of vanishing magnetic field at fixed permeability and pressure is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular structure consisting of a wedge, whose angle scales with the applied field magnitude, bounded by either two slow compound waves or two 180 ◦ rotational discontinuities, each followed by a slowmode expansion fan. These bracket the MHD contact which itself cannot support a tangential velocity jump in the presence of a non-parallel magnetic field. The magnetic field within the singular wedge is finite and the shock-induced change in tangential velocity across the wedge is supported by the expansion fans that form part of the compound waves or follow the rotational discontinuities. To verify these findings, an approximate leading-order asymptotic solution appropriate for both flow structures was computed. The full and asymptotic solutions are compared quantitatively.

Simulations of mixing in an inlet-fueled axisymmetric scramjet

An unsteady simulation of a simple axisymmetric inlet-fueled scramjet engine concept is performed using a hybrid Reynolds-averaged Navier–Stokes and large-eddy simulation approach. The freestream has a Mach number of 7.5 with Mach 8 flight enthalpy. The simulation is of a nonreacting case in which hydrogen is injected into nitrogen. The simulation is used to provide a detailed description of the structure of the flow. The simulation shows that a large-scale pair of counter-rotating vortices forms within the scramjet combustor, with rotation opposite to the rotation of the pair that forms further upstream due to the interaction of the fuel plume with the crossflow. This vortex pair is found to significantly alter the shape of the hydrogen fuel plume and increase the rate at which the hydrogen is mixing by more than a factor of 2 compared to before the vortex pair is formed. The distribution of hydrogen is examined in detail. The time-averaged and fluctuating wall pressures, the mean velocity field, and res...

The Richtmyer–Meshkov instability in magnetohydrodynamics

The Richtmyer-Meshkov instability is important in applications including inertial confinement fusion and astrophysical phenomena. In some applications, the fluids involved are plasmas and can be affected by magnetic fields. For one configuration, it has been numerically demonstrated that the growth of the instability is suppressed in the presence of a magnetic field. Here, the nature of this suppression is theoretically and numerically investigated. In ideal incompressible magnetohydrodynamics, we examine the stability of an impulsively accelerated perturbed density interface in the presence of a magnetic field initially parallel to the acceleration. This is accomplished by analytically solving the linearized initial value problem, which is a model for the Richtmyer-Meshkov instability. We find that the initial growth rate of the interface is unaffected by the magnetic field, but the interface amplitude then asymptotes to a constant value. Thus the instability is suppressed. The interface behavior from the model is compared to the results of compressible simulations. We then consider regular shock refraction at an oblique planar density interface in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic simulations indicate that the presence of the magnetic field inhibits the deposition of vorticity on the shocked contact, which leads to the suppression of the Richtmyer-Meshkov instability. We show that the shock refraction process produces a system of five to seven plane waves that intersect at a point. In all solutions, the shocked contact is vorticity free. These solutions are not unique, but differ in the type of waves that participate. The equations governing the structure of these multiple-wave solutions are obtained and a numerical method of solution is described. Solutions are compared to the results of simulations. The limit of vanishing magnetic field is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular wedge whose angle scales with the applied field magnitude. The shock-induced shear across the wedge is supported by slow-mode expansion fans within it, leaving the shocked contact vorticity free. To verify these findings, an approximate leading order asymptotic solution was computed.

Behavior of multiple jet interactions in a hypersonic boundary layer

The fundamental flow physics of the interaction between an array of fuel jets and a hypersonic boundary layer is investigated. Hydrogen is injected at jet-to-freestream dynamic pressure ratios ranging from 0.350 to 0.875 on a flat plate into a Mach 4.5 crossflow. The injection array consists of four streamwise-aligned flush circular portholes. Both the streamwise spacing and jet-to-freestream dynamic pressure ratio are varied in a parametric study. The injection was performed completely within the boundary layer, with the intention of application to film-cooling drag reduction and boundary-layer combustion. Numerical simulations of four streamwise-aligned transverse sonic injectors in a fully turbulent hypersonic boundary layer revealed a very complex jet interaction flowfield. Variation of the streamwise injector port spacing, along with the jet-to-freestream dynamic pressure ratio, induced a variety of flow structures in the cases investigated. For all downstream interactions, the associated flow behavi...

The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics

The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers.

Hypersonic Turbulent Boundary-Layer Fuel Injection and Combustion: Skin-Friction Reduction Mechanisms

Drag reduction is important to improving the performance of scramjet engines operating at high Mach numbers. One demonstrated method for reducing skin-friction drag on a surface exposed to hypersonic flow is the injection and combustion of hydrogen fuel in the boundary layer. However, there are other fuels of interest in scramjet applications, and the underlying mechanisms that drive the reduction of skin friction are not well understood. An existing analytical model for boundary-layer combustion of hydrogen is rederived for a general fueling condition and then extended to allow investigation of the underlying flow physics in this model. Applying this theory to ethylene fueling indicates that skin-friction reduction through boundary-layer combustion is possible with fuels other than hydrogen. Analysis of the modeled boundary-layer profiles demonstrates that skin-friction reduction is accomplished through several coupled mechanisms: a change in near-wall viscosity, density changes and combustion act to red...

On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics

It has been claimed that the particular numerical flux used in Runge-Kutta Discontinuous Galerkin (RKDG) methods does not have a significant effect on the results of high-order simulations. We investigate this claim for the case of compressible ideal magnetohydrodynamics (MHD). We also address the role of limiting in RKDG methods. For smooth nonlinear solutions, we find that the use of a more accurate Riemann solver in third-order simulations results in lower errors and more rapid convergence. However, in the corresponding fourth-order simulations we find that varying the Riemann solver has a negligible effect on the solutions. In the vicinity of discontinuities, we find that high-order RKDG methods behave in a similar manner to the second-order method due to the use of a piecewise linear limiter. Thus, for solutions dominated by discontinuities, the choice of Riemann solver in a high-order method has similar significance to that in a second-order method. Our analysis of second-order methods indicates that the choice of Riemann solver is highly significant, with the more accurate Riemann solvers having the lowest computational effort required to obtain a given accuracy. This allows the error in fourth-order simulations of a discontinuous solution to be mitigated through the use of a more accurate Riemann solver. We demonstrate the minmod limiter is unsuitable for use in a high-order RKDG method. It tends to restrict the polynomial order of the trial space, and hence the order of accuracy of the method, even when this is not needed to maintain the TVD property of the scheme.

Rarefied, superorbital flows in an expansion tube

This paper describes a free‐piston driven expansion tube and its instrumentation. The facility is used to generate rarefied flows at speeds of approximately 10 km/s. Although the flow in the tube itself is in the continuum regime, rarefied flow conditions are achieved by allowing the test gas to further expand as a free jet into the facilitys test section. The test flow is surveyed to provide bar‐gauge pressure measurements. Numerical simulation is then used to describe more fully the test flow properties. The flows produced are suitable for the aerodynamic testing of small models at superorbital speeds and should provide data that are suitable for the calibration of Direct Simulation Monte‐Carlo codes.

Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer-Meshkov instability

The effects of seed magnetic fields on the Richtmyer-Meshkov instability driven by converging cylindrical and spherical implosions in ideal magnetohydrodynamics are investigated. Two different seed field configurations at various strengths are applied over a cylindrical or spherical density interface which has a single-dominant-mode perturbation. The shocks that excite the instability are generated with appropriate Riemann problems in a numerical formulation and the effect of the seed field on the growth rate and symmetry of the perturbations on the density interface is examined. We find reduced perturbation growth for both field configurations and all tested strengths. The extent of growth suppression increases with seed field strength but varies with the angle of the field to interface. The seed field configuration does not significantly affect extent of suppression of the instability, allowing it to be chosen to minimize its effect on implosion distortion. However, stronger seed fields are required in three dimensions to suppress the instability effectively.