Supersonic Case Research Articles

Effects of Radiative Transfer on the Observed Anisotropy in Magnetohydrodynamic Turbulent Molecular Simulations

We study the anisotropy of centroid and integrated intensity maps with synthetic observations. We perform postprocess radiative transfer including the optically thick regime that was not covered in Hernández-Padilla et al. We consider the emission in various CO molecular lines that range from optically thin to optically thick (12CO, 13CO, C18O, and C17O). The results for the velocity centroids are similar to those in the optically thin case. For instance, the anisotropy observed can be attributed to the Alfvén mode, which dominates over the slow and fast modes when the line of sight is at a high inclination with respect to the mean magnetic field. A few differences arise in the models with higher opacity, where some dependence on the sonic Mach number becomes evident. In contrast to the optically thin case, maps of integrated intensity become more anisotropic in optically thick lines. In this situation the scales probed are restricted, due to absorption, to smaller scales, which are known to be more anisotropic. We discuss how the sonic Mach number can affect the latter results, with highly supersonic cases exhibiting a lower degree of anisotropy.

Linear stability analysis of compressible boundary layer over an insulated wall using compound matrix method: Existence of multiple unstable modes for Mach number beyond 3

The linear spatial stability of a parallel two-dimensional (2D) compressible boundary layer on an adiabatic plate is investigated by considering both 2D and three-dimensional (3D) disturbances. The compound matrix method is employed here, for the first time, for compressible flows, which, unlike other conventional techniques, can efficiently eliminate the stiffness of the equations governing the spectral amplitudes. The method is first validated with published results in the literature corresponding to spatial and temporal instability of flows ranging from low subsonic to high supersonic Mach numbers (M), which shows a good match depending upon the proper choice of free-stream temperature and the wall dispersion relation. Subsequently, flow compressibility effects and the spanwise variation of disturbances are also investigated for M ranging from low subsonic to high supersonic cases (from M = 0.1 to 6). Mack (AGARD Report No. 709, 1984) reported the existence of two unstable modes for M > 3 from viscous calculations (the so-called “second mode”) that subsequently fuse to create only one unstable zone when M increases. Our calculations show a series of higher-order unstable modes for M > 3 in addition to the findings of Ma and Zhong [“Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions,” J. Fluid Mech. 488, 31–78 (2003)], where such higher-order modes for supersonic boundary layers are all noted to be spatially stable. The number and the frequency extent of the corresponding unstable zones increase with an increase in M beyond 3 while propagating downstream at a higher speed than those corresponding to incompressible, subsonic, and low supersonic (M < 2) cases.

A Numerical Analysis of the Non-Uniform Layered Ground Vibration Caused by a Moving Railway Load Using an Efficient Frequency–Wave-Number Method

The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory model is proposed to quickly obtain the numerical results without losing accuracy. The track is regarded as a composite Euler–Bernoulli beam resting on the layered ground, and the spatial heterogeneity of the ground soil is considered. The ground dynamic characteristics of an elastic, layered, non-uniform foundation are investigated, and numerical results at three typical train speeds are reported based on the developed Fortran computer programs. The results show that as the soil homogeneity coefficient increases, the peak acceleration continuously decreases in the transonic case, while it gradually increases in the supersonic case, and the ground acceleration spectrum at a far distance obviously decreases; the maximum acceleration occurs at the track edge, and a local rebound in vibration attenuation occurs in the supersonic case.

A multi-physics correction of the shear-stress transport turbulence model for supersonic flows

Though the k–ω shear-stress transport (SST) turbulence model is widely used, it is developed based on incompressible flow and the analysis of simple flow characteristics such as boundary layer and free shear flows. Due to the lack of comprehensive consideration of important flow structures, such as shock wave and highly compressible zones, the k–ω SST turbulence model has inherent limitations in describing supersonic flows. A multi-physics improvement strategy is proposed to improve the prediction accuracy of the k–ω SST model for supersonic flows. This strategy leverages shock/turbulent boundary layer and shock/compressibility functions to accurately recognize areas with significant structures, enabling targeted improvement of the turbulence model. Five supersonic flow cases are tested and analyzed, and the results show that while the single-physics turbulence model can improve the prediction accuracy of flows with a single flow structure corresponding to the correction, its prediction ability is insufficient in other flows with different flow structures. In contrast, the multi-physics turbulence model exhibits good ability in flows with multiple flow structures, while also maintaining the performance of the single-physics turbulence model. The multi-physics turbulence model has higher accuracy and stronger universality, making it advantageous for modeling complex supersonic flows.

CPU–GPU heterogeneous code acceleration of a finite volume Computational Fluid Dynamics solver

This research focuses on accelerating the finite-volume Computational Fluid Dynamics (CFD) solver, SENSEI, through concurrent CPU–GPU heterogeneous computing, leveraging multiple CPUs and GPUs. An overview of SENSEI, its discretization, and the heterogeneous computing workflow utilizing MPI and OpenACC are provided. A performance model for CPU–GPU heterogeneous computing, incorporating ghost cell exchange usually applied in stencil computations, is introduced to estimate the performance. This work explores the scaling performance of CPU–GPU heterogeneous computing in comparison to a pure multi-CPU/GPU setup using a supersonic inlet test case. The results emphasize the advantages of leveraging both CPU and GPU computational power concurrently. Highlighting the collaborative synergy of CPUs and GPUs as co-workers, this work shows improved performance over exclusive use of pure CPUs or GPUs, with the proposed performance model ensuring a fair estimation of these advantages. This work concludes by offering suggestions for application users interested in accelerating scientific computing simulations and providing feedback for hardware architects designing improved CPU–GPU heterogeneous systems for heterogeneous computing.

Gas Dynamical Friction on Accreting Objects

The drag force experienced by astronomical objects moving through gaseous media (gas dynamical friction) plays a crucial role in their orbital evolution. Ostriker derived a formula for gas dynamical friction by linear analysis, and its validity has been confirmed through subsequent numerical simulations. However, the effect of gas accretion onto the objects on the dynamical friction is yet to be understood. In this study, we investigate the Mach number dependence of dynamical friction considering gas accretion through three-dimensional nested-grid simulations. We find that the net frictional force, determined by the sum of the gravitational force exerted by surrounding gas and momentum flux transferred by accreting gas, is independent of the resolution of simulations. Only the gas outside the Bondi–Hoyle–Lyttleton radius contributes to dynamical friction, because the gas inside this radius is eventually absorbed by the central object and returns the momentum obtained through the gravitational interaction with it. In the subsonic case, the front–back asymmetry induced by gas accretion leads to larger dynamical friction than predicted by the linear theory. Conversely, in the slightly supersonic case with a Mach number between 1 and 1.5, the nonlinear effect leads to a modification of the density distribution in a way that reduces the dynamical friction, compared with the linear theory. At a higher Mach number, the modification becomes insignificant and the dynamical friction can be estimated with the linear theory. We also provide a fitting formula for dynamical friction based on our simulations, which can be used in a variety of applications.

The existence and nonlinear stability of stationary solutions to outflow problem for a reduced gravity two and a half layer model

The main concern of this paper is to study large-time behavior of solutions for an outflow problem to the reduced gravity two and a half layer model in a half space. We establish the existence of stationary solutions and further obtain the large time asymptotic stability of small-amplitude stationary solutions provided that the initial perturbation is sufficiently small. Moreover, we obtain the convergence rate of the solution toward the stationary solution in some weighted Sobolev spaces only for the supersonic case. The proof is based on the basic energy method. A key point for the proof of convergence rates is to capture the positivity of the temporal energy dissipation functional and boundary terms with suitable space weight functions either algebraic or exponential depending on whether or not the incoming far-field velocity satisfy some additional conditions.

Improved SST turbulence model for supersonic flows with APG/separation

A goal in modeling the turbulent flows in computational fluid dynamics is to find an empirical yet universal model to address the complex scenarios. Menter's Shear Stress Transfer (SST) [1] is a Reynolds-Averaged Navier-Stokes (RANS) based two-equation turbulence model and has been one of the most widely used turbulence models for numerical simulation of viscous flows. However, in some practical cases on supersonic, the standard SST model shows unsatisfactory prediction of flow separation and the often underestimation of Reynolds stress. The error mainly comes from the inappropriate use of Bradshaw's assumption which is proposed under turbulent kinetic energy (TKE) equilibrium flow conditions. This paper proposes an improved SST turbulence model which combines the structural parameter with the ratio of the turbulence generation term to the dissipation term and imposes a mixing function to correct the logarithmic and wake parts of the region. Several supersonic test cases are carried out to verify the new model. The calculation results show that the new model exhibits better performance in capturing the separation zones than the baseline model (BSL) and the standard SST model.

A new rapid deflagration-to-detonation transition in a short smooth tube

A new rapid deflagration-to-detonation transition in a short smooth tube

Investigation of a Near-Field Cylinder Wake in the Subsonic, Transonic, and Supersonic Regimes

The near wake of a circular cylinder in a high-Reynolds-number regime is investigated using the particle image velocimetry technique for an inflow Mach number spanning 0.3 to 2. The mean flow and turbulent kinetic energy field for different Mach number cases are presented. Furthermore, the influence of the Reynolds and Mach number effects is examined based on the mean separation point along the cylinder surface, which is extracted from complementary schlieren visualization measurements, and the literature. The wake width for the supersonic inflow case is found to be an order of magnitude smaller physically than the subsonic case with an identical cylinder diameter. Additionally, the swirl strength criterion is used to identify the eddies present within the wake, and the eddy size and convection velocity are characterized based on the spatiotemporal correlations. The result suggests that the mean wake features for the subsonic and supersonic cases are very different. Moreover, the interaction of eddies generated at the cylinder’s top and bottom shear layers leads to the large-scale features present in the wake, and the differing paths followed by the eddies between the subsonic and supersonic cases are responsible for the variation in the observed wake width.

The Effect of Conduit Walls Roughness on Volcanic Jets and Their Seismo‐Acoustic Radiation: An Experimental Investigation

AbstractTo explore the effect of conduit roughness on volcanic jet dynamics and on the related seismo‐acoustic radiation we performed a series of shock‐tube experiments using pipes with variable inner surface fractal dimension D. Variable starting pressure produced subsonic to supersonic jets visualized using high‐speed shadowgraph and recorded with an array of accelerometers and microphones. At all starting pressures, increasing D increases the energy transfer from the gas to the conduit walls, decreasing the jet exit velocity (Mach number) and, for supersonic cases, the related shock‐cell spacing, and increasing the seismic to acoustic radiation amplitude ratio. The roughness‐induced changes in jet velocity and turbulence affect the dominant sources of the jet noise and modulates the spectral properties of the acoustic signals. From our study we show that conduit wall roughness is an important and yet largely neglected factor in the dynamics of explosive volcanic eruptions and their monitored geophysical signals.

Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport

The solution of conservation laws with parametrised shock waves presents challenges for both high-order numerical methods and model reduction techniques. We introduce an r-adaptivity scheme based on optimal transport and apply it to develop reduced order models for compressible flows. The optimal transport theory allows us to compute high-order r-adaptive meshes from a starting reference mesh by solving the Monge–Ampère equation. A high-order discretization of the conservation laws enables high-order solutions to be computed on the resulting r-adaptive meshes. Furthermore, the Monge–Ampère solutions contain mappings that are used to reduce the spatial locality of the resulting solutions and make them more amenable to model reduction. We use a non-intrusive model reduction method to construct reduced order models of both the mesh and the solution. The procedure is demonstrated on three supersonic and hypersonic test cases, with the hybridisable discontinuous Galerkin method being used as the full order model.

Turbulence simulations with an improved interior penalty discontinuous Galerkin method and SST k-ω model

The feasibility of high-precision interior penalty discontinuous Galerkin (IPDG) method is still questionable when SST k-ω model and its compressibility correction are adopted. To this end, turbulence simulations with an improved IPDG method and SST k-ω model have been conducted in the present study. In detail, the improved IPDG method was first introduced to eliminate the fourth-order homogeneity tensor connecting the viscous terms and variable gradients. The numerical accuracy has been systematically validated with several canonical cases. To overcome the numerical instability problem coming along with turbulence model simulation, a hybrid approach was implemented. Actually, finite volume method was utilized here for SST k-ω model. Then, the accuracy and reliability of the improved IPDG method have been analyzed in accompany with SST k-ω model and its compressibility correction. Actually, simulations of subsonic, transonic and supersonic cases have been conducted, including plate/airfoil boundary layers and shear layers. The accuracy has been comprehensively validated through quantitative comparison with experimental data, while the superiority of the compressibility correction could be observed at high Mach number.

Axisymmetric slender magnetic cavities

The pressure at the boundary of a slender body of revolution immersed in a subsonic or supersonic flow may be found by classical asymptotic analysis. The inverse problem, to find the shape of the cavity knowing the pressure, is a physically relevant question as applied to the study of magnetic cavities. The equation determining this shape turns out to be a nonlinear one involving a convolution term. While this equation is extremely difficult to solve, estimates may be found that constrain the functional form of the inner magnetic field in order for the cavity to exist. Also the study of the Fourier transform of the convolution term yields some light on the behavior of the solution; for the supersonic case an approximation may be found by solving a sequence of ordinary differential equations.

Numerical investigation of the influence of the nozzle bump on nozzle flow

Fluid Mechanics is the study of liquid or gas performance in motion or at rest. Many of the engineering disciplines apply fluid mechanics principles and concepts. With the development of technology, computer is involved in the field, which leads to computational fluid dynamics. In this paper, nozzles with various shapes of bump are used as the research object to investigate the influence of the bump on the nozzle flow via small disturbance approximation. Specifically, triangular, parabolic, irregular and combined shapes are utilized. Two different situations are also included in this paper, which are subsonic and supersonic case. The experimental results demonstrated that within reasonable parameters as the variable increases, the change becomes clearer. When area decreases in the same shape, the streamlines become fluctuant more extremely, especially the one near the boundary. The assumption that the fluid flows disorderly near the bottom is also verified by the simulation.

On the application of gradient based reconstruction for flow simulations on generalized curvilinear and dynamic mesh domains

Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and α-damping schemes introduced by Chamarthi (2022) for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservation property. In the first part of this paper, the algorithms are detailed within the generalized curvilinear coordinate framework, with a focus on demonstration through stationary and dynamic mesh test cases. It has been shown both theoretically and through the use of test cases that the conservative metrics, including their interpolation to cell interfaces, must be numerically computed using a central scheme that is consistent with the inviscid flux algorithm to achieve the freestream preservation property. The second part of the paper illustrates the efficacy of the algorithm in simulating supersonic jet screech by displaying its capability to capture the screech tones and accurately characterize the unsteady lateral flapping mode of a Mach 1.35 under-expanded supersonic jet, in contrast to the WENO-Z scheme which fails to do so at the same grid resolution. In the final part of the paper, the parallelizability of the schemes on GPU architectures is demonstrated and performance metrics are evaluated. A significant speedup of over 200× (compared to a single core CPU) and a reduction in simulation completion time to 34.5 h per simulation were achieved for the supersonic jet noise case at a grid resolution of 13 million cells.

Integrating Nonlinear Controllability into a Multidisciplinary Design Process

Even in multidisciplinary aircraft design, most aspects of nonlinear controllability are only considered in later design phases. Hence, control considerations are not used to inform the overall design of the airframe. This paper presents a control-aware controller-agnostic design optimization framework that integrates nonlinear controllability constraints, which are informed by the solutions to optimal control problems, into the multidisciplinary design process. To implement the optimization, procedures to evaluate the sensitivity of the controllability constraint to variations in the design variables are defined. A supersonic aircraft case study illustrates the methodology and the steps involved in the process. The proposed approach enables the integration of control-related constraints into gradient-based design optimization.

Skin-friction drag reduction by local porous uniform blowing in spatially developing compressible turbulent boundary layers

This paper investigates the effects of local porous uniform blowing on the skin-friction drag reduction in the spatially developing compressible turbulent boundary layers through direct numerical simulations. Under the influence of uniform blowing, the skin-friction drag decreases drastically within the controlled regions, and the effect extends downstream. The drag reduction rate exceeds 10% for the uniform blowing velocities considered herein. The intrinsic mechanism of decreased skin-friction drag is further explored, in terms of the various contributions to this quantity, the Reynolds shear stress budget, and the multi-scale distributions and transfer of enhanced turbulent motions. The numerical results for the identity of Renard and Deck [“A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer,” J. Fluid Mech. 790, 339–367 (2016)] indicate that the decreased skin-friction drag is reflected in a negative contribution in the streamwise developing direction. The enhanced turbulent motion is investigated through the Reynolds shear stress budget, and uniform blowing is found to strengthen the magnitudes of all budget terms. We conclude that uniform blowing promotes the energy cascade process in the near-wall region, promoting the appearance of smaller turbulent structures and the formation of large outer scales. Similar skin-friction drag reduction in the subsonic case is also observed in a supersonic case. The upstream transition process is delayed, which leads to a relatively larger skin-friction drag reduction rate in a supersonic case. Finally, we investigate the porosity effects on the skin-friction drag and conclude that the blowing flux is a decisive factor.

An Investigation of Scale-Resolving Turbulence Models for Supersonic Retropropulsion Flows

Characterization of unsteady loads is critical for the development of control systems for next-generation air vehicles. Both Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) methods are prohibitively expensive, and existing Reynolds-Averaged Navier-Stokes (RANS) approaches have been shown to be inadequate in predicting both mean and unsteady loads. In recent years, scale-resolving methods, such as Partially Averaged Navier-Stokes (PANS) and Detached Eddy Simulation (DES), have been gaining acceptance and filling the gap between RANS and LES. In this study, we focus on a new variant of the PANS method, namely blended PANS or BPANS, which was shown to perform well in the incompressible regime for both wall-bounded and free shear flows. In this paper, we extend BPANS to compressible supersonic flows by adding a compressibility correction, leading to a new model called BPANS CC. The new model is tested using a well-known supersonic mixing layer case, and the results show good agreement with experimental data. The model is then used on a complex supersonic retropropulsion case and the results are in good agreement with experimental data.

On the Rossiter-Heller frequency of resonant cavities

The goal of this paper is to revise the Rossiter-Heller formula of cavity resonance frequencies for rectangular cavities in subsonic and supersonic flow conditions. Two modifications are proposed; the first one consists in using a second-order polynomial fit of literature experimental data for the non-dimensional time lag coefficient as a function of the cavity aspect ratio. The second modification consists in taking into account the reversed flow convective effects in the calculation of the backward acoustic propagation time, by including the reversed flow Mach number in the formula, expressed as a function of the free-stream Mach number and cavity aspect ratio. A second-order polynomial fit of scale-resolving flow simulation results of the reversed flow Mach number is used to derive the final resonance frequency formula. The effects of the two modifications are investigated for three values of the aspect ratio in the range 5 to 10, and four values of the free-stream Mach number in the range 0.6 to 1.35. It is concluded that taking into account both modifications yields globally more accurate predictions of the resonance frequencies. Finally, an attempt is made to identify the nature of additional tones observed for the deep supersonic case around the fourth and fifth Rossiter-Heller resonance modes.