Vicinity Of Shock Waves Research Articles

Efficient Methodology with Grid Configurations for HSI Noise Prediction in Hover

Complex and unsteady flow patterns occur around rotating rotor blades owing to the generation of shock waves at the blade tip and interference between the blade and tip wake when the blade rotates at high speeds, thereby resulting in specific noise characteristics. Furthermore, these noise characteristics cause noise pollution in private areas and degrade detectability of helicopters in military applications. Therefore, it is important to accurately analyze noise characteristics around rotor blades. In this study, a novel computational methodology with a chimera wake grid was proposed to efficiently and accurately predict high-speed impulsive (HSI) noise due to the shock wave at the blade tip. The proposed method enables accurate analysis of a complex flow region by overlapping a wake grid in the vicinity of shock waves. A 1/7-scaled UH-1H rotor blade was used to compare and verify the accuracy of HSI noise prediction and computational efficiency. The chimera grid method was applied to the present simulation for considering the blade motion and moving effects. A permeable surface for wrapping the surface of the physical blade was constructed to include quadrupole noise source generated from the control volume, thickness noise source, and loading noise source. Furthermore, the permeable Ffowcs Williams and Hawkings (FW–H) equations were used with the Kirchhoff approach to realize efficient far-field noise prediction. The proposed HSI noise analysis via chimera wake grid indicated that the strength of the shock wave is more precisely predicted, thereby resulting in improved prediction of the HSI noise. The proposed chimera methodology allows efficient noise prediction using a much coarser background grid system.

A stable hybrid Roe scheme on triangular grids

AbstractNumerical shock instability is a common problem for shock‐capturing methods that try to resolve contact and shear waves with minimal diffusion. Most flux‐difference splitting and the AUSM family of schemes produce the carbuncle phenomenon on both structured and unstructured grids. The original Roe scheme is well known to generate shock anomalies and can lead to nonentropic weak solutions to the Euler equations. A simple and robust approach for healing these numerical instabilities is to apply the hybrid technique incorporated with an efficient weighting switch function to control the amount of dissipation in the vicinity of shock waves. This article proposes a simple, robust, and accurate hybrid Roe scheme (Roe+scheme) by hybridizing the Roe scheme and the modified AUSMV+scheme. A new normalized pressure/density‐based weighting switch function is proposed and applied to the scheme to minimize the numerical dissipation and maintain the robustness of the hybridization. The linearized discrete analysis is performed to evaluate the proposed scheme according to the perturbation damping mechanism of an odd–even decoupling problem. The resulting recursive equations indicate that the hybridized mechanism damps all perturbations effectively. Finally, several numerical examples demonstrated that the Roe+scheme provides an accurate, robust, and carbuncle‐free solution on both structured and unstructured triangular grids.

An adjoint-based hp-adaptive stabilized finite-element method with shock capturing for turbulent flows

In this study, an adjoint-based hp-adaptation algorithm has been developed within a Petrov–Galerkin finite-element method. The developed mesh adaptation algorithm is able to perform non-conformal mesh adaptations. To account for hanging nodes in a consistent manner, the constrained approximation method has been utilized. Hierarchical basis functions have been employed to facilitate the implementation of the constrained approximation. The methodology has been demonstrated on numerous cases using the Euler and Reynolds Average Navier–Stokes (RANS) equations, equipped with negative variant of Spalart–Allmaras (SA) turbulence model. Also, a PDE-based artificial viscosity has been added to the governing equations, to stabilize the solution in the vicinity of shock waves. For accurate representation of the geometric surfaces, high-order curved boundary meshes have been generated and the interior meshes have been deformed through the solution of a modified linear elasticity equation. Fully implicit linearization has been used to advance the solution toward a steady-state. Dirichlet boundary conditions have been imposed weakly and the functional outputs have been modified according to the weak boundary conditions in order to provide a smooth adjoint solution near the boundaries. To accelerate the error reduction in presence of singularity points, an enhanced h-refinement, based on solution’s smoothness, has been used. Numerical results illustrate consistent accuracy improvement of the functional outputs for both h- and hp-adaptation, and also capability enhancement in capturing complex viscous effects such as shock-wave/turbulent boundary layer interaction.

SIMULATION OF ENERGETIC PARTICLE TRANSPORT AND ACCELERATION AT SHOCK WAVES IN A FOCUSED TRANSPORT MODEL: IMPLICATIONS FOR MIXED SOLAR PARTICLE EVENTS

ABSTRACT We use numerical solutions of the focused transport equation obtained by an implicit stochastic differential equation scheme to study the evolution of the pitch-angle dependent distribution function of protons in the vicinity of shock waves. For a planar stationary parallel shock, the effects of anisotropic distribution functions, pitch-angle dependent spatial diffusion, and first-order Fermi acceleration at the shock are examined, including the timescales on which the energy spectrum approaches the predictions of diffusive shock acceleration theory. We then consider the case that a flare-accelerated population of ions is released close to the Sun simultaneously with a traveling interplanetary shock for which we assume a simplified geometry. We investigate the consequences of adiabatic focusing in the diverging magnetic field on the particle transport at the shock, and of the competing effects of acceleration at the shock and adiabatic energy losses in the expanding solar wind. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can naturally reproduce the morphologies of so-called mixed particle events in which sometimes the prompt and sometimes the shock component is more prominent, by assuming parameter values which are typically observed for scattering mean free paths of ions in the inner heliosphere and energy spectra of the flare particles which are injected simultaneously with the release of the shock.

Improved Large-Eddy Simulation Validation Methodology: Application to Supersonic Inlet/Isolator Flow

A process was demonstrated that enables more meaningful comparisons of experimental and large-eddy simulation results of the same flowfield. This approach was motivated by recent studies, which show the importance of modeling the measurement device or process when making comparisons of this nature. In the current case, a large-eddy simulation of a Mach 5 inlet/isolator flow is the subject of the validation process, a flow that was previously validated using particle image velocimetry measurements. In the present study, the particle image velocimetry measurement process is emulated by adding particles with inertia to the large-eddy simulation and using synthetic particle image velocimetry to mimic the process by which velocity data are extracted. Analysis of the particle response reveals modifications to the underlying flow consistent with the original particle image velocimetry measurements, including a drastic decrease in rms velocities in the vicinity of shockwaves and weaker velocity gradients throughout the flow. The synthetic particle image velocimetry is found to capture the sampled particle velocities quite well but does impart a significant bias error to the regions near the walls, also consistent with the experimental data. Furthermore, this process suggests improvements that could be made to any new experiment to achieve higher accuracy and thus improve the validation process.

Macrokinetics of fast reactions

Various forms of chemical reaction macrokinetics are considered taking into account the possible acceleration of processes in regions with high parameter gradients, in particular, in the vicinity of shock waves. The possibility of determining the kinetics from data of a dynamic experiment is evaluated.

Application of a third-order reconstruction scheme to hypersonic reacting flows using unstructured meshes and multigrid techniques

In this paper a high-order finite-volume method is studied to solve hypersonic steady chemically reacting flows on unstructured meshes. The quadratic polynomial reconstruction scheme is first presented as well as the monotonicity enforcement technique used to limit the oscillations in the vicinity of shock waves and regions with high gradients. The implicit time-integration procedure is based on Newton linearization and uses the GMRES algorithm. The preconditioning of the linear systems, based on an iterative inversion of a low-order Jacobian, coupled with a multigrid technique, is also discussed. Results obtained for the test case corresponding to the hypersonic flow around a double ellipse are presented.

On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite element schemes). However, it is of the first order only. (b) Pure discontinuous Galerkin finite element method of higher order combined with a technique avoiding spurious oscillations in the vicinity of shock waves.

Reynolds-Stress-Transport Modeling for Compressible Aerodynamics Applications

Progress is reported in the development of a nonlinear Reynolds-stress-transport model for compressible, turbulent flow. The focus is on a variation of a particular cublc model that does not require the usual topography-related parameters, such as normal-to-wall vectors. However, certain wall-proximity corrections that have been used in the model to replace conventional wall-reflection terms display the wrong response to shocks, which are falsoly interpreted as localized regions of strong inhomogeneity. A modified cubic variant is proposed that allows integration across the semiviscous sublayer and incorporates additional constraints to guard against unphysical response of the pressure-strain model in the vicinity of shock waves. The modified model is applied to both two- and three-dimensional compressible flows, involving shock-wave/boundary-layer interaction, and is shown to yield generally favorable results

On the Numerical Solution of Two-Dimensional, Laminar Compressible Flows With Imbedded Shock Waves

The complete, time-dependent Navier-Stokes equations are expressed in conservation form and solved by employing an explicit finite difference numerical technique which incorporates artificial viscosity terms of the form first suggested by Rusanov for numerical stability in the vicinity of shock waves. Surface boundary conditions are developed in a consistent and unique manner through the use of a physically oriented extrapolation procedure. From numerical experimentation an extended range for the explicit stability parameter is established. Also employed is an additional convergence parameter which relates incremental spatial steps. Convergence of the transient solution to a steady state flow was obtained after 400 to 500 time steps. Sample solutions are presented for supersonic flow of air over the leading edge of a slightly blunted flat plate, past a backward facing step, and in the near wake of a blunt trailing edge. Free-stream Mach numbers from 2 to 10 are included in the sample computations.