Compressible Flow Research Articles

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

AbstractUnderstanding 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.

A Large Time Step Wave-Adding Simple Scheme for Unsteady Compressible Flows

In this paper, we construct a large time step wave-adding scheme (LTS-WA) for unsteady Euler equations in compressible flows with a much simpler strategy in the wave-adding procedure, named LTS-WAS. The new method does not need to calculate coefficients of contribution and also add the waves according to their types and families, which makes the scheme easy for coding and optimisation. The new scheme has a high speedup ratio, and its formulation is the same in scalar and system cases. The scheme is extended to 3D compressible flows using the dimension split method. Numerical experiments show that the new scheme maintains the advantages of the original LTS-WA scheme at large CFL numbers, and has a higher efficiency.

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.

Rigorous justification of the hydrostatic approximation limit of viscous compressible flows

This paper considers the asymptotic limit of small aspect ratio between vertical and horizontal spatial scales for viscous isothermal compressible flows. In particular, it is observed that fast vertical acoustic waves arise and induce an averaging mechanism of the density in the vertical variable, which at the limit leads to the hydrostatic approximation of compressible flows, i.e., the compressible primitive equations of atmospheric dynamics. We justify the hydrostatic approximation for general as well as “well-prepared” initial data. The initial data is called well-prepared when it is close to the hydrostatic balance in a strong topology. Moreover, the convergence rate is calculated in the well-prepared initial data case in terms of the aspect ratio, as the latter goes to zero.

A Bound-Preserving and Positivity-Preserving High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Compressible Multi-Medium Flows

A Bound-Preserving and Positivity-Preserving High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Compressible Multi-Medium Flows

A third-order compact finite volume scheme on unstructured grid for fluid flows

The large reconstruction stencil is one of the biggest obstacles in design and implementation of high-order finite volume schemes on unstructured grid. To tackle this problem, a third-order compact reconstruction scheme on unstructured grid is developed on the basis of compact least-squares (CLS) finite volume method. In building the reconstruction polynomial, the general boundary condition is adopted to ensure the unified third-order accuracy in both the internal and boundary cells. The reconstruction polynomial is solved in a semi-implicit sense to ensure high computational efficiency without solving the global linear algebraic equations. The theoretical accuracy order and stability limit are firstly verified by the Fourier analysis. The numerical accuracy and efficiency are then verified and validated with several incompressible and compressible flow cases. This work provides a reference to design and analysis of high-order compact finite volume schemes on unstructured grid with unified accuracy.

Vortex breakdown in the small Mach number regimes

The effect of compressibility for flow inside the cylinder with the top rotating lid (Vogel-Escudier flow) is examined. Three-dimensional Navier–Stokes equations for compressible flow in Cartesian coordinates are used to simulate the flow using open-source OpenFOAM software. The Mach number (Ma) of the flow is varied from 0.1 to 0.3, and the Reynolds number (Re) is varied from 1000 to 5000 for a fixed aspect ratio (Γ = 2.5) of the cylinder. The flow is found to have a transition from a steady axisymmetric state to a non-axisymmetric state exhibiting multiple azimuthal waves as the Mach number and the Reynolds number are varied. The flow field changes significantly with an increase in Ma for unsteady flow at higher Re. An increase in Ma increases the side wall azimuthal instability, as found in the perturbation contour plots and time series analysis. Further, we reconstruct phase portraits to show the dynamics of the flow finally becoming chaotic as the Reynolds number is increased to 5000. Finally, we support the argument with Lyapunov exponents for the higher Re samples. The Lyapunov Exponent is found to increase with Ma.

Direct numerical simulation of compressible turbulent channel flows over porous boundaries

The impact of porous boundaries on skin friction and heat transfer in compressible turbulent channel flows is explored through direct numerical simulations. Utilizing the volume-averaged Navier–Stokes equations for the porous media, we examine flows at Mach numbers Mb=0.3 and Mb=1.5, with friction Reynolds numbers ranging from 176 to 220, across three permeability levels: 0 (impermeable), 1.6×10−5, and 1.0×10−4. Our findings reveal a dual impact of porous boundaries on skin friction: a direct reduction due to averaged slip velocity at the interface and an indirect increase from amplified Reynolds shear stress due to enhanced wall-normal permeability. This permeability weakens the wall-blocking effect, leading to intensified wall-normal velocity fluctuations and consequently higher Reynolds stress. Additionally, the Mach number significantly influences flow structures, particularly at higher permeabilities, where it disrupts near-wall streaks at Mb=0.3 but has a diminished effect at Mb=1.5. Thermal analysis confirms the validity of the generalized Reynolds analogy for the mean temperature in these flows, with the turbulent Prandtl number approximating 1, in line with the strong Reynolds analogy. Moreover, a strong spatial correlation between heat flux and wall shear stress fluctuations underscores the intertwined dynamics of momentum and thermal transport at the porous–fluid interface.

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

Evaluating the sensitivity of direct shear testing of soils for rheological characterization of masonry mortars

The present work evaluated the applicability of the direct shear test of soils (ASTM D 3080) as an alternative for the rheological characterization of masonry mortars. The sensitivity analysis of the method for mortars was carried out by varying the particle size distribution of the sand and the water/dry material ratio, generating twelve different mixtures. In addition to a basic characterization, the shear test results were compared with those of the squeeze-flow test (ABNT NBR15839). For squeeze-flow, 24 tests were carried out with two speeds (0.1 and 3mm/s), and for direct shear, 48 tests were carried out with 4 normal stresses (13.5, 25, 50, and 100 KPa). It is concluded that the direct shear test, using cohesion and friction angle parameters, demonstrated the ability to adequately characterize the complex behavior of plastic mortars and the sensitivity to variations in the mixture. A linear correlation was found between the friction angle (shear test) and the consistency index (flow table), with R2 = 0,87. Furthermore, for high plasticity mortars, was found a non-linear correlation between compression flow (squeeze flow) and cohesion (direct shear test), with R2 = 0,67.

Validity of Stokes' hypothesis for near-continuum hypersonic flows

The alternative interpretation of Stokes' hypothesis provided by Buresti [Acta Mech. 226, 3555–3559 (2015)] is investigated by an analysis of a near-continuum, hypersonic flow of oxygen over a double cone obtained from a large-scale direct simulation Monte Carlo computation. We show that for molecular oxygen, which has comparable bulk and shear viscosity coefficients, the difference between mechanical and thermodynamic pressure is negligible throughout most of the flow. This result justifies neglecting viscous stresses in the normal stress tensor associated with fluid particle dilatation, as is often done in continuum descriptions of compressible flows. The violation of the revisited Stokes' hypothesis was only observed in highly nonequilibrium regions of the flow (shocks and strong expansions) and wherever non-continuum effects become significant. For nonequilibrium flows of gases with large bulk viscosity relative to their shear viscosity, the revisited Stokes' assumption may still breakdown and requires further investigation.

Numerical study of shock wave boundary layer interaction flows using a novel turbulence model

This study proposes a novel partial average fluctuation velocity (PAFV) turbulence based on the PAFV and the average strain rate tensor, which is used to calculate the shock wave boundary layer interaction flows, including cascade flow and transonic compressor flow. In order to illustrate the adequacy, the calculation results of several other turbulence models were also compared with PAFV, including k-ω, shear stress transport, SA-neg (negative Spalart-Allmaras), and stress-BSL (ω-based Reynolds stress model). The suitability of the PAFV turbulence model was initially tested by calculating the transonic flow in the L030-4 cascade. Subsequently, numerical computations were performed for the 3D (three-dimensional) National Aeronautics and Space Administration Rotor 67 transonic compressor rotor. In the numerical simulation, the flow control equations were transformed in a general curvilinear coordinate system for precision enhancement, and the spatial discretization of control equations was executed using the finite difference method. The convection term was processed using the Steger–Warming flux vector splitting method, the diffusion term was discretized using a second-order central difference scheme, and the time derivative term was discretized using the third-order Runge–Kutta method. A parallel computing strategy with multi-block partitioning was employed to speed up the calculations and facilitate faster convergence alongside a local time step method. All numerical computation procedures were written in Python, revealing the following: (1) The PAFV turbulence model aptly simulates the transonic flow within the cascade channel. The shock wave pattern in the cascade channel aligns well with the experimental schlieren images. (2) During the Rotor 67 transonic compressor rotor calculation, the flow–pressure ratio, flow efficiency, and inlet and outlet total temperatures and pressures align well with the experimental data. Furthermore, the resolution of the flow field structure related to the interaction between the tip leakage vortex and channel shock wave is high. (3) The turbulence model uses PAFV as the turbulence velocity scale, thereby suppressing the fluctuation velocity and turbulence viscosity near shock wave areas, preventing excessive turbulence viscosity. Moreover, PAFV inherently exhibits transport properties and anisotropic characteristics, making it well-suited for handling transonic compressor flows.

Finite element methods for multicomponent convection-diffusion

Abstract We develop finite element methods for coupling the steady-state Onsager–Stefan–Maxwell (OSM) equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Developing a variational formulation for discretizing these equations is challenging: the formulation must balance physical relevance of the variables and boundary data, regularity assumptions, tractability of the analysis, enforcement of thermodynamic constraints, ease of discretization and extensibility to the transient, anisothermal and nonideal settings. To resolve these competing goals, we employ two augmentations: the first enforces the definition of mass-average velocity in the OSM equations, while its dual modifies the Stokes momentum equation to enforce symmetry. Remarkably, with these augmentations we achieve a Picard linearization of symmetric saddle point type, despite the equations not possessing a Lagrangian structure. Exploiting structure mandated by linear irreversible thermodynamics, we prove the inf-sup condition for this linearization, and identify finite element function spaces that automatically inherit well-posedness. We verify our error estimates with a numerical example, and illustrate the application of the method to nonideal fluids with a simulation of the microfluidic mixing of hydrocarbons.

Numerical simulation of vapor explosion bubbles in the presence of a non-condensable gas and a phase change

The complex dynamics of two flow problems of vapor explosion bubbles near a free surface and between two parallel plates are simulated by a compressible three-phase flow code. Firstly, a coupled high-order monotonicity-preserving (MP) interface capturing scheme is developed for the numerical computation of compressible three-phase flows, which is followed by validation with previous numerical and experimental data. Phase changes are taken into consideration and the empirical condensation coefficient is calibrated with the experimental data. For both two flow problems, good agreement between the numerical results and reference data is obtained. Most physical phenomena, including the free surface spike, the liquid jet before the impact and the complex interface deformations during multiple expanding and collapsing oscillations, are reasonably well reproduced. Afterwards, the effects of the initial vapor pressure and the non-condensable gas volume fraction in the surrounding water on the behavior of vapor bubbles are analyzed and discussed. It is found that both the initial vapor pressure and the non-condensable gas volume fraction have a substantial influence on the behavior of the bubble. Higher initial vapor pressure does indeed tend to result in larger bubbles. The presence of non-condensable gases tends to hinder the transfer of heat, slowing down condensation and potentially resulting in larger bubbles. When the initial vapor pressure is in the range of 10 to 20 atmospheres and the gas volume fraction is in the range of 0 to 0.2, the maximum vapor bubble volume is found to increase linearly with an increase of the amount of non-condensable gas.

Exploring nanoscale metallic multilayer Ta/Cu films: Structure and some insights on deformation and strengthening mechanisms

Nanoscale metallic multilayer (NMM) films are systems offering insight into the role of interfaces in metal plasticity, deformation, and strengthening mechanisms. Magnetron sputtering was used to fabricate the Ta/Cu NMM films with a periodicity (equal Ta and Cu layer thickness) from 6 to 80 nm, and with the structure exhibiting immiscible tetragonal β-Ta and face-centred cubic Cu phases. Transmission electron microscopy and X-ray diffraction analyses revealed that, irrespective of the period, all films manifested a polycrystalline structure. The growth direction of both Cu and Ta layers was found to be along 〈001〉 β-Ta || 〈111〉 Cu directions, with the crystallite size constrained by the layer thickness. The studies showed that the Ta/Cu NMMs exhibited compressive residual macro-stress and flow strength, and enhanced elastic recovery at the periodicity of ≤12 nm. Activation volume V⁎ value of 11 to 20 b3 as determined from the indentation creep test under a constant load, may indicate a mixed deformation mechanism. This mechanism likely involves the emission of dislocations from the incoherent Ta/Cu interfaces, as well as the formation of screw dislocations within Cu grains. The high-load indentation test, TEM studies, and the rCLS model collectively demonstrate that all NMM films predominantly undergo plastic deformation. This plastic deformation primarily occurs within the soft Cu layer, while the propagation of dislocations across the incoherent interface is largely excluded.

The stability of simple plane-symmetric shock formation for three-dimensional compressible Euler flow with vorticity and entropy

The stability of simple plane-symmetric shock formation for three-dimensional compressible Euler flow with vorticity and entropy

Compressible Flow Through Flat Valve Seals at Microscale Displacements

Abstract Existing analytical flow models for predicting flow rate 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 macro-scale valves with small actuator displacements.