Compressible Flow Research Articles

Well-posedness and blow-up criterion for strong solutions of a class of compressible MHD equations

In this paper, we consider the initial boundary value problem of a class of one-dimensional magnetohydrodynamics (MHD) with viscous, compressible, and non-Newtonian flow. We prove the existence of the solution in the presence of the resistivity coefficient, obtain the convergence rate in L2-norm, and establish the blow-up criterion of the local strong solution in the presence of the resistivity coefficient. Moreover, the initial vacuum is allowed.

Simplified weighting formulations of weighted compact nonlinear schemes for compressible flows

Simplified weighting formulations of weighted compact nonlinear schemes for compressible flows

Assessment of particle image velocimetry applied to high-speed organic vapor flows

Compressible flows of fluids whose thermophysical properties are related by complex equations are quantitatively and can be qualitatively different from high-speed flows of ideal gases. Nonideal compressible fluid dynamics (NICFD) is concerned with these fluid flows, which are relevant in many processes and power and propulsion systems. Typically, NICFD effects occur if the fluid is an organic compound and its vapor state is close to the vapor–liquid critical point, at high-reduced temperature and pressure (even supercritical). Current design and analysis of devices operating in the nonideal compressible regime demand for validated simulation software, characterized in terms of uncertainty. Moreover, experiments are needed to further validate related theory. Experimental data are limited as generating and measuring these flows is challenging given their high pressure or temperature or both. In addition, flows of organic compounds can be flammable, can thermally decompose, and sealing may demand for special materials. Recently, more research has been devoted to the measurement of these flows using both intrusive and less intrusive techniques relying on optical access and lasers. The transparency and refractive properties of these dense vapors pose additional problems. The ORCHID (organic Rankine cycle hybrid integrated device) at the Aerospace Propulsion and Power Laboratory of Delft University of Technology is a closed-loop facility, used to generate a continuous nonideal supersonic flow of siloxane MM with the vapor at 4bar\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ extrm{bar}}}$$\\end{document} and 220 °C at the inlet of the test section. Within this work, we have employed particle image velocimetry for the first time to obtain the velocity field in a de Laval nozzle in such flows. Measured velocity fields (expanded uncertainty within 1.1% of the maximum velocity) have been compared with those resulting from a CFD simulation. The comparison between experimental and simulated data is satisfactory, with deviation ranging from 0.1 to 10 % from the throat to the outlet, respectively. This discrepancy is attributed to hardware limitations, which will be overcome in the future experiments. The feasibility of PIV with uncontrolled but fixed seeding density to measure high-speed vapors of organic vapors has been demonstrated, and future experimental campaigns will target flows for which nonideal effects are more pronounced, other paradigmatic configurations, and improvements to the measurement techniques.

Physics-aware recurrent convolutional neural networks for modeling multiphase compressible flows

Multiphase compressible flow systems can exhibit unsteady and fast-transient dynamics, marked by sharp gradients and discontinuities, and material boundaries that interact with the evolving flow. The transient nature of the dynamics presents challenges to employing artificial intelligence (AI) and data-driven models for predicting flow behaviors. In this study, we explore the potential of physics-aware recurrent convolutional neural networks (PARC) to model the spatiotemporal dynamics of multiphase flows in the presence of shocks and reaction fronts. PARC is a neural network model that incorporates the generic form of the diffusion–advection–reaction equation in its network architecture, which mimics the process of solving the governing equations of fluid flows. In contrast to physics-informed machine learning approaches such as physics-informed neural networks (PINNs) where models are trained to directly minimize the residual of governing equations, PARC takes a dynamical systems viewpoint and does not seek to minimize potentially nonconvex and nonlinear loss terms. To assess the ability of PARC to accurately learn and simulate the physics of multiphase flows, we train and test PARC on various flow simulation problems, including the Burgers’ equation, fluid flow behind a cylindrical cross-section, and unsteady shock interactions with a particle at varying Mach numbers. We analyze PARC’s performance and examine sources of error in its prediction, in terms of differentiation and integration schemes and different weighting strategies for the model update. Based on our observations, we discuss PARC’s capabilities and limitations in multiphase flow applications and propose future research directions.

Employing the Akbari Ganji Method (AGM) to conduct a semi-analytical analysis of transient Eyring-Powell compressible flow in a tensile Surface under the influence of a magnetic field

This study explores the transfer of mass and heat within unstable two-dimensional flows of non-Newtonian material under conditions involving radiation generation, absorption, and thermal radiation. Additionally, it investigates the impact of magnetic hydromagnetic joule (MHD) heating on these processes. The researchers converted the partial differential equations into ordinary ones through appropriate transformations. Subsequently, a new idea was considered, involving coupling fractional differential equations using the AGM method, with an order of 0.5 < a <0.8 and the initial condition x (0) = x0. A new technique is introduced to find the exact solution of fractional differential equations by solving the correct order differential equations. The primary aim of this paper is to explore the impact of parameter variations on velocity, temperature, local skin friction coefficient, and local Nusselt and Sherwood numbers. This article investigates the effect of multi-parameter changes on local skin friction coefficient and Schmidt number. In most fluid heat transfer problems, especially in non-Newtonian fluids, fractional differential equations are widely used in liquids. The obtained results indicate that the Lorentz force, influenced by the magnetic field parameter (Ha), diminishes the velocity distribution. Additionally, it is observed that the temperature profile decreases as the radiation parameter (R) increases.

Compressible Flow Through Flat Valve Seals at Microscale Displacements

Abstract Existing analytical flow models for predicting flow rates at microscale seal displacements are limited to two separate domains. The first assumes a small channel length to height aspect ratio at relatively large seal displacements. The second assumes a large channel length to height aspect ratio at relatively small seal displacements. A piecewise analytical model for compressible flow is developed here to enable predicting flow rates in valves with fluid pathways of any aspect ratio. The new model is validated by numerical studies and experiment. The results are applicable to flat valve seals having a cylindrical seal boss feature with fluid passage length to height aspect ratios ranging from 3.3 to 800. The new model is particularly useful for the design of microvalves and macroscale valves with small actuator displacements.

Effect of grain orientation angles and compressive parameters on the deformation characteristics and corrosion property of 6061 Al alloy

The influence of grain orientation angle and processing parameters on the compressive flow stress and corrosion behaviour of 6061-T6 Al alloy was investigated in this study by altering the grain orientation angles in relation to the compressive direction. At relatively low processing temperatures (≤ 300 °C), an increase in the grain orientation angle from 0° to 90°reduced flow stress at low strain ranges (< 0.1) due to the facilitated slip of Al grains. As strain and processing temperature increased, changes in orientation angles had a negligible effect on the flow stress, attributed to the enhanced contribution of intermetallic particles (IMPs) and the occurrence of recrystallisation. Microstructural analysis revealed that higher processing temperatures resulted in a diverse range of IMPs, including Mg2Si (β phase) and Al15(Fe,Mn)3Si2 phases. When the Al alloy was compressed at a high strain rate (25 s−1) and processed at 500 °C, submicron-scale β”, β’, and β phases coexisted. Corrosion tests indicated that a wider distribution of Al15(Fe,Mn)3Si2 phases reduced the corrosion resistance of the Al alloy. This led to the formation of connected corrosion sites in specimens compressed at 500 °C, where a larger corrosion area and enhanced charge transfer ability were confirmed by equivalent circuit fitting. However, no significant variation in corrosion resistance was observed for Al alloys with various grain orientation angles, due to similar grain structure and precipitation behaviour at similar processing temperatures.

A study of streamline geometries in subsonic and supersonic regions of compressible flow fields

The geometrical properties of streamlines, such as the curvatures, directions and positions, are studied in steady inviscid compressible flow fields via differential geometry theories and conservation laws. The influences of the streamline geometries on the flow speeds and pressures are also identified and discussed. By transforming the streamlines to fill the domain and satisfy the boundary conditions, a unified geometry-based solver, the streamline transformation method, is proposed for both subsonic and supersonic regions. The governing equations and boundary conditions along streamlines and shock waves are also derived. This method is verified by numerical results of three typical flow fields, including the subsonic channel flow, the supersonic downstream of attached shock waves and especially the subsonic/supersonic downstream of detached bow shock waves. Both two-dimensional planar and axisymmetric flow fields are considered. Compared with the results from computational fluid dynamics, good agreements are achieved by this method, while fewer computational resources, by an order of magnitude, are consumed. Features of these flow fields are also analysed from a geometrical perspective, such as flow speeds and pressures deviated by the wall curvatures, and three-dimensional effects in the after-shock flow fields. For a hyperbolic-shaped bow shock wave, the stand-off distances and the transitions from subsonic to supersonic regions are also discussed. As indicated by the accuracy, efficiency and applicability in a wide range of flow speeds, the streamline transformation method would be a potential candidate for the theoretical analysis and inverse design of high-speed flow fields, especially where the subsonic regions exist downstream of strong shock waves.

Implication of injection angle and jet-to-cross flow ratio on the combustion characteristics of a scramjet combustor

The present work deals with the implication of injection angle and jet-to-cross flow ratio on the combustor performance of a cavity-based scramjet combustor. Unsteady, two-dimensional compressible flow through the scramjet combustor is considered to comprehend the effects of Mach number (Ma), jet-to-cross flow ratio ([Formula: see text]) and injection angle (α) on the combustion characteristics. Results are presented for the following range of parameters: 2.0 ≤ Ma ≤ 2.7; 15° ≤ α ≤ 60° and 0.5 ≤ [Formula: see text] ≤ 1.2. Intense recirculation zone is observed at θ = 45° irrespective of inlet Mach number which are quintessential for proper mixing. Further, the size of the recirculation zone is the largest when jet-to-cross flow ratio is equal to 0.8 acting as a precursor for enhanced mixing performance. Moreover, static pressure reaches an optimum value at injection angle of 45° beyond which further increase would result in thermal choking. Our study reveals that mixing is improved with an increase in Mach number (Ma). It is observed that the size of the recirculation zone is strongly dependent on the jet-to-cross flow pressure ratio along with the injection angle. To put it in a nutshell, the injection angle of 45° along with a jet-to-cross flow pressure ratio of 0.8 is conducive the optimal performance in scramjet combustor.

The role of annular 2-lobe nozzle in a strut injection system on the mechanism of fuel distribution at a scramjet engine

The strut injection system is a conventional technique for the injection of the fuel in combustor in hypersonic vehicles. The present article investigates the usage of the annular 2-lobe injector to improve the fuel jet behind the strut. Computational studies have been employed for the modeling of fuel jets released from 2-lobe injectors at the supersonic free stream of the combustion chamber. Simulation of the compressible flow is done by solving Reynolds-Averaged Navier-Stokes (RANS) equations with the turbulence model of SST. The roles of the proposed injection configuration on the flow and fuel jet penetration are disclosed in this work. The shape of fuel jet plume behind the injector is also investigated to explain the mechanism of fuel jet distribution in this technique. Presented data disclosed that the usage of the annular 2-lobe nozzle instead of a single circular jet improves fuel mixing by about 50 % behind the strut model.

A systematic analysis of three-dimensional Riemann problems for verification of compressible-flow solvers

Numerical simulation is a well-established way of analyzing compressible flows. Due to high computational demands of solvers for such flow problems, their verification is typically limited to two-dimensional (2D) cases. However, 2D simulations suppress fundamental three-dimensional (3D) aspects of the flow evolution in (compressible) turbulent flows or shock-bubble and shock-drop interactions. With increase of computational power, 3D simulations become more feasible for routine analyses. The verification of 3D simulation frameworks is often limited to transformations of lower dimensional test cases in the 3D space. There is a lack of strictly 3D reference test cases for gas dynamics. In this work, we present a set of genuine 3D Riemann problems in order to validate and verify numerical solvers for compressible flows. The problems are designed such that each octant’s constant initial data connects two neighboring states by an elementary wave only. The problem design is inspired by well-established 2D Riemann problems most prominently posted by Lax and Liu (1998). In contrast to the twenty published 2D cases, more than 300 distinct combinations can be found in 3D. We provide example solutions for the particularly interesting ones of these case combinations and show how the cases help to expose shortcomings of numerical solvers. We provide reference data from computations with an open-source compressible multiresolution flow solver. For the reference solutions, we employ the Harten-Lax-van Leer contact (HLLC) Riemann solver and a weighted essentially non-oscillatory (WENO) reconstruction stencil of fifth order. The reference solutions use an effective resolution of one billion cells. We additionally make the full compute pipeline of this work publicly available, so interested researchers may reproduce and extend the current work.

Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

Method for scalable and performant GPU-accelerated simulation of multiphase compressible flow

Multiphase compressible flows are often characterized by a broad range of space and time scales, entailing large grids and small time steps. Simulations of these flows on CPU-based clusters can thus take several wall-clock days. Offloading the compute kernels to GPUs appears attractive but is memory-bound for many finite-volume and -difference methods, damping speedups. Even when realized, GPU-based kernels lead to more intrusive communication and I/O times owing to lower computation costs. We present a strategy for GPU acceleration of multiphase compressible flow solvers that addresses these challenges and obtains large speedups at scale. We use OpenACC for directive-based offloading of all compute kernels while maintaining low-level control when needed. An established Fortran preprocessor and metaprogramming tool, Fypp, enables otherwise hidden compile-time optimizations. This strategy exposes compile-time optimizations and high memory reuse while retaining readable, maintainable, and compact code. Remote direct memory access realized via CUDA-aware MPI and GPUDirect reduces halo-exchange communication time. We implement this approach in the open-source solver MFC [1]. Metaprogramming results in an 8-times speedup of the most expensive kernels compared to a statically compiled program, reaching 46% of peak FLOPs on modern NVIDIA GPUs and high arithmetic intensity (about 10 FLOPs/byte). In representative simulations, a single NVIDIA A100 GPU is 7-times faster compared to an Intel Xeon Cascade Lake (6248) CPU die, or about 300-times faster compared to a single such CPU core. At the same time, near-ideal (97%) weak scaling is observed for at least 13824 GPUs on OLCF Summit. A strong scaling efficiency of 84% is retained for an 8-times increase in GPU count. Collective I/O, implemented via MPI3, helps ensure the negligible contribution of data transfers (<1% of the wall time for a typical, large simulation). Large many-GPU simulations of compressible (solid-)liquid-gas flows demonstrate the practical utility of this strategy.

An improved Baldwin–Lomax algebraic wall model for high-speed canonical turbulent boundary layers using established scalings

In this work, we employ well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity (TV) relation, to systematically improve the algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient air boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semilocal scalings. Three targeted modifications are made. First, we employ a total-stress-based transformation (Griffin et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 34, 2021, e2111144118) to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, we utilize the van Driest transformation in the outer layer based on the compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, we design a two-layer strategy and use the TV relation to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4 % in the logarithmic wall-normal coordinate and 3.4 % in the outer coordinate, around one-third of those in the baseline model.

A general multi-objective Bayesian optimization framework for the design of hybrid schemes towards adaptive complex flow simulations

Achieving accuracy with underresolved simulation of complex compressible flows with multiscale flow structures is a challenge. Either the numerical dissipation or the resolution and thereby the numerical cost is impractically high. Also, in the design of numerical solvers, the application of a solver for specific flow classes is balanced by robustness allowing the study of a broad range of flows. In this study, we propose a hybrid fifth-order targeted essentially non-oscillatory (TENO5)-based scheme tailored to optimally simulate compressible flows with underresolved dilatational and vortical multiscale structures. For optimal design, three data-driven objectives are defined. A novel objective that derives from the numerical dissipation rate analysis is a key element to deal with underresolved complex flows in practical applications. The optimization process employs a multi-objective Bayesian optimization framework with an expected hypervolume improvement and three flow configurations representative for a broad range of two- and three-dimensional flows with genuine and non-genuine subgrid scales. The optimized hybrid scheme is validated by comparing with shock-capturing schemes of the weighted essentially non-oscillatory (WENO)- and TENO- families with flows of complex shock interactions, Kelvin-Helmholtz instabilities, shock-vortex interactions, vortical and turbulent flows

Large eddy simulations of sheet-to-cloud cavitation transitions with special emphasis on the simultaneous existence of the re-entrant jet and shock waves

Sheet-to-cloud cavitation transitions are very complex owing to the simultaneous appearance of the re-entrant jet and shock waves. The objective of this paper is to investigate the physics of compressible cavitating flows with emphasis on the simultaneous existence of the re-entrant jet and shock waves. A compressible cavitating solver, which considers the compressibility effects of both the liquid and the vapour, was used to account for the different shedding characteristics induced by the re-entrant jet mechanism (RJM), the shock wave mechanism (SWM), and both the re-entrant jet and the shock waves (RJM-SMW). The solver used Large Eddy Simulations (LES) and the Schnerr-Sauer cavitation model. The numerical results are first compared with available experimental data [1] which showed satisfactory agreement for various aspects of the flow, including the pressure distribution, cavity shapes, condensation front speed, and shedding frequency. The results first show three different cavity shedding processes induced by the re-entrant jet and the shock waves. Frequency analyses show that the shock waves produce a wider frequency distribution which indicates that shock waves induce more shedding than the re-entrant jet. The quasi-periodic characteristics of the transitions between the various cavity shedding characteristics are mainly induced by the variations of the pressure, residual cavity volume and medium compressibility. Further analyses show that the different pressure, residual cavity volume and medium compressibility amplitudes determine the cavity shedding characteristics in the subsequent shedding cycle. When the conditions favour both the re-entrant jets and the shock wave effects, both the re-entrant jet and the shock waves impact the cavity shedding.

A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics (MD) simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is—at present—no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method and has been introduced recently for the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469: 111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argon-methane mixtures in several space dimensions. To our knowledge, such compressible two-phase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

Performance Comparison of CFD Microbenchmarks on Diverse HPC Architectures

OpenFOAM is a CFD software widely used in both industry and academia. The exaFOAM project aims at enhancing the HPC scalability of OpenFOAM, while identifying its current bottlenecks and proposing ways to overcome them. For the assessment of the software components and the code profiling during the code development, lightweight but significant benchmarks should be used. The answer was to develop microbenchmarks, with a small memory footprint and short runtime. The name microbenchmark does not mean that they have been prepared to be the smallest possible test cases, as they have been developed to fit in a compute node, which usually has dozens of compute cores. The microbenchmarks cover a broad band of applications: incompressible and compressible flow, combustion, viscoelastic flow and adjoint optimization. All benchmarks are part of the OpenFOAM HPC Technical Committee repository and are fully accessible. The performance using HPC systems with Intel and AMD processors (x86_64 architecture) and Arm processors (aarch64 architecture) have been benchmarked. For the workloads in this study, the mean performance with the AMD CPU is 62% higher than with Arm and 42% higher than with Intel. The AMD processor seems particularly suited resulting in an overall shorter time-to-solution.

Predicting compressor mass flow rate using various machine learning approaches

Abstract A major focus of the present study is to construct high-fidelity models for predicting corrected mass flow rates based on the collected compressor map data. Both traditional machine learning research and modern deep learning techniques have been employed to obtain well-fitted regression models of compressor mass flow rate. As traditional machine learning methods, Multiple Linear Regression and Random Forest, are conducted on compressor maps for prediction of corrected mass flow rate. The time series-based deep learning models are able to capture the overall trend of a given input for specific map data. Therefore, a time series-based deep learning technique, namely Gated Recurrent Unit has been employed to improve regression results. Besides, the prediction capabilities of the models, results also show that the proposed models can be used for the development of dynamic aero-thermal mathematical models of gas turbine engines and mass flow rate models created for dynamic compressors in other disciplines.

Implementation of IDEAL algorithm based on Delaunay triangular mesh for 2D-compressible flows

PurposeTo present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.Design/methodology/approachProgramming completely in C++.FindingsFive compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.Originality/valueThe detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.