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The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/hp stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/hp framework. We introduce revised stabilization parameters, τsupg, with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, δ: the first is described with entropy variables, and the other is the YZβ parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both L1 and L2 norms. We numerically validate the revised definitions of the stabilization parameter with Sod’s shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of 3.0 and numerically validate the shock standoff distance with results obtained from NASA Overflow 2.2 code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries.

 

In this work, we introduce a scalable and efficient GPU-accelerated methodology for volumetric particle advection and finite-time Lyapunov exponent (FTLE) calculation, focusing on the analysis of Lagrangian coherent structures (LCS) in large-scale direct numerical simulation (DNS) datasets across incompressible, supersonic, and hypersonic flow regimes. LCS play a significant role in turbulent boundary layer analysis, and our proposed methodology offers valuable insights into their behavior in various flow conditions. Our novel owning-cell locator method enables efficient constant-time cell search, and the algorithm draws inspiration from classical search algorithms and modern multi-level approaches in numerical linear algebra. The proposed method is implemented for both multi-core CPUs and Nvidia GPUs, demonstrating strong scaling up to 32,768 CPU cores and up to 62 Nvidia V100 GPUs. By decoupling particle advection from other problems, we achieve modularity and extensibility, resulting in consistent parallel efficiency across different architectures. Our methodology was applied to calculate and visualize the FTLE on four turbulent boundary layers at different Reynolds and Mach numbers, revealing that coherent structures grow more isotropic proportional to the Mach number, and their inclination angle varies along the streamwise direction. We also observed increased anisotropy and FTLE organization at lower Reynolds numbers, with structures retaining coherency along both spanwise and streamwise directions. Additionally, we demonstrated the impact of lower temporal frequency sampling by upscaling with an efficient linear upsampler, preserving general trends with only 10% of the required storage. In summary, we present a particle search scheme for particle advection workloads in the context of visualizing LCS via FTLE that exhibits strong scaling performance and efficiency at scale. Our proposed algorithm is applicable across various domains, requiring efficient search algorithms in large, structured domains. While this article focuses on the methodology and its application to LCS, an in-depth study of the physics and compressibility effects in LCS candidates will be explored in a future publication.

 

Lossy compression techniques are ubiquitous in many fields including imagery and video; however, the incursion of such lossy compression techniques in the computational fluid dynamics community has not advanced to the same extent in decades. In this work, the lossy compression of high-fidelity direct numerical simulation (DNS) is evaluated to assess the impact on various parameters of engineering interest. A Mach 2.5, spatially developing turbulent boundary layer (SDTBL) at a moderately high Reynolds number has been selected as the subject of the study. The ZFP compression scheme was chosen as the core driving algorithm for this study as it was carefully crafted for scientific, floating point data. The resilience of spectral quantities as well as two-point correlations is highlighted. Notwithstanding, we also noted that point-wise values calculated in the physical domain were prone to quantization errors at high compression ratios. Further, we have also presented the impact on higher order statistics. In summary, we have demonstrated that high fidelity results are within reach while achieving 1.45x to 9.82x reductions in required storage over single precision, IEEE 754-compliant data values. 

High-speed, spatially-evolving turbulent boundary layers are of great importance across civilian and military applications. Furthermore, compressible boundary layers present additional challenges for energy and active scalar transport. Understanding transport phenomena is critical to efficient high-speed vehicle designs. Although at any instantaneous point in time a flow field may seem random, regions within the flow can exhibit coherency across space and time. These coherent structures play a key role in momentum and energy transport within the boundary layer. The two main categories for coherent structure identification are Eulerian and Lagrangian approaches. In this video, we focus on 4D (3D+Time) Lagrangian Coherent Structure (LCS), and the effect of wall curvature/temperature on these structures. We present the finite-time Lyapunov exponent (FTLE) for three wall thermal conditions (cooling, quasi-adiabatic and heating) for a concave wall curvature that builds on the experimental study by Donovan et al. (J. Fluid Mech., 259, 1-24, 1994). The flow is subject to a strong concave curvature (δ/R ~ -0.083, R is the curvature radius) followed by a very strong convex curvature (δ/R = 0.17). A GPU-accelerated particle simulation forms the basis for the 3-D FTLE where particles are advected over flow fields obtained via Direct Numerical Simulation (DNS) with high spatial/temporal resolution. We also show the cross-correlation between Q2 events (ejections) and the FTLE. The video is available at: https://gfm.aps.org/meetings/dfd-2022/63122e0e199e4c2da9a946a0 

In this video, we show high-fidelity numerical results of supersonic spatially-developing turbulent boundary layers (SDTBL) under strong concave and concave curvatures and Mach = 2.86. The selected numerical tool is Direct Numerical Simulation (DNS) with high spatial/temporal resolution. The prescribed concave geometry is based on the experimental study by Donovan et al. (J. Fluid Mech., 259, 1-24, 1994). Turbulent inflow conditions are based on extracted data from a previous DNS over a flat plate (i.e., turbulence precursors). The comprehensive DNS information sheds important light on the transport phenomena inside turbulent boundary layers subject to strong deceleration or Adverse Pressure Gradient (APG) caused by concave walls as well as to strong acceleration or Favorable Pressure Gradient (FPG) caused by convex walls at different wall thermal conditions (i.e., cold, adiabatic and hot walls). In this opportunity, the selected scientific visualization tool is Virtual Reality (VR) by extracting vortex core iso-surfaces via the Q-criterion to convert them to a file format readable by the HTC Vive VR toolkit. The reader is invited to visit our Virtual Wind Tunnel (VWT) under a fully immersive environment for further details. The video is available at: https://gfm.aps.org/meetings/dfd-2022/6313a60c199e4c2da9a946bc 

An incoming canonical spatially developing turbulent boundary layer (SDTBL) over a 2-D curved hill is numerically investigated via the Reynolds-averaged Navier–Stokes (RANS) equations plus two eddy-viscosity models: the K−ω SST (henceforth SST) and the Spalart–Allmaras (henceforth SA) turbulence models. A spatially evolving thermal boundary layer has also been included, assuming temperature as a passive scalar (Pr = 0.71) and a turbulent Prandtl number, Prt, of 0.90 for wall-normal turbulent heat flux modeling. The complex flow with a combined strong adverse/favorable streamline curvature-driven pressure gradient caused by concave/convex surface curvatures has been replicated from wind-tunnel experiments from the literature, and the measured velocity and pressure fields have been used for validation purposes (the thermal field was not experimentally measured). Furthermore, direct numerical simulation (DNS) databases from the literature were also employed for the incoming turbulent flow assessment. Concerning first-order statistics, the SA model demonstrated a better agreement with experiments where the turbulent boundary layer remained attached, for instance, in Cp, Cf, and Us predictions. Conversely, the SST model has shown a slightly better match with experiments over the flow separation zone (in terms of Cp and Cf) and in Us profiles just upstream of the bubble. The Reynolds analogy, based on the St/(Cf/2) ratio, holds in zero-pressure gradient (ZPG) zones; however, it is significantly deteriorated by the presence of streamline curvature-driven pressure gradient, particularly due to concave wall curvature or adverse-pressure gradient (APG). In terms of second-order statistics, the SST model has better captured the positively correlated characteristics of u′ and v′ or positive Reynolds shear stresses ( > 0) inside the recirculating zone. Very strong APG induced outer secondary peaks in and turbulence production as well as an evident negative slope on the constant shear layer. 

The interaction of a turbulent, spatially developing crossflow with a transverse jet possesses several engineering and technological applications such as film cooling of turbine blades, exhaust plumes, thrust vector control, fuel injection, etc. Direct Numerical Simulation (DNS) of a jet in a crossflow under different streamwise pressure gradients (zero and favorable pressure gradient) is carried out. The purpose is to study the physics behind the transport phenomena and coherent structure dynamics in turbulent crossflow jets at different streamwise pressure gradients and low/high-velocity ratios (0.5 and 1). The temperature was regarded as a passive scalar with a molecular Prandtl number of 0.71. The analysis is performed by prescribing accurate turbulent information (instantaneous velocity and temperature) at the inlet of a computational domain. The upward motion of low-momentum fluid created by the “legs” of the counter-rotating vortex pair (CVP) encounters the downward inviscid flow coming from outside of the turbulent boundary layer, inducing a stagnation point and a shear layer. This layer is characterized by high levels of turbulent mixing, turbulence production, turbulent kinetic energy (TKE) and thermal fluctuations. The formation and development of the above-mentioned shear layer are more evident at higher velocity ratios. 

We employ numerically implicit subgrid-scale modeling provided by the well-known streamlined upwind/Petrov–Galerkin stabilization for the finite element discretization of advection–diffusion problems in a Large Eddy Simulation (LES) approach. Whereas its original purpose was to provide sufficient algorithmic dissipation for a stable and convergent numerical method, more recently, it has been utilized as a subgrid-scale (SGS) model to account for the effect of small scales, unresolvable by the discretization. The freestream Mach number is 2.5, and direct comparison with a DNS database from our research group, as well as with experiments from the literature of adiabatic supersonic spatially turbulent boundary layers, is performed. Turbulent inflow conditions are generated via our dynamic rescaling–recycling approach, recently extended to high-speed flows. Focus is given to the assessment of the resolved Reynolds stresses. In addition, flow visualization is performed to obtain a much better insight into the physics of the flow. A weak compressibility effect is observed on thermal turbulent structures based on two-point correlations (IC vs. supersonic). The Reynolds analogy (u′ vs. t′) approximately holds for the supersonic regime, but to a lesser extent than previously observed in incompressible (IC) turbulent boundary layers, where temperature was assumed as a passive scalar. A much longer power law behavior of the mean streamwise velocity is computed in the outer region when compared to the log law at Mach 2.5. Implicit LES has shown very good performance in Mach 2.5 adiabatic flat plates in terms of the mean flow (i.e., Cf and UVD+). iLES significantly overpredicts the peak values of u′, and consequently Reynolds shear stress peaks, in the buffer layer. However, excellent agreement between the turbulence intensities and Reynolds shear stresses is accomplished in the outer region by the present iLES with respect to the external DNS database at similar Reynolds numbers.