Simulation Of Compressible Flows Research Articles

Perspectives of computational fluid dynamics methods in the study of membrane processes

In the mathematical modeling of membrane processes, the study of the structural features of the membranes used and the significant limitation of information in the formal description of their separation properties led to the development of physical models that take into account not only the structural features of real membranes, but also their functioning features. When compiling physical models of membrane processes, it is impossible to objectively carry out a quantitative accounting of most factors due to their great diversity and variability, which distances the mathematical model far from the real process. This is why CFD methods reliably and efficiently perform calculations for all physical models and types, including steady or transient flow, incompressible or compressible flow (from small subsonic to hypersonic), laminar or turbulent flow simulations, Newtonian or non-Newtonian fluids, ideal or real gas . The authors analyzed the possibility of using CFD to calculate the hydrodynamics of flows in a membrane bioreactor based on hollow fibers. Safarov R.R. etc., an electronic geometric model of the installation was built, mesh geometry with different densities was selected to optimize the calculation time and solution accuracy for a specific case, the kinetic dependence of cell growth was calculated, the flow rates of the nutrient medium into the intrafiber and interfiber spaces of the bioreactor were determined, and the hydrodynamic conditions were analyzed. All of the above confirms the prospects for using CFD methods for modeling membrane processes complicated by culturing cells on the surface of membranes.

A new open-source library based on novel high-resolution structure-preserving convection schemes

This work develops a new finite volume convection scheme and open-source library for convection-dominated problems on unstructured grids. The formulated reconstruction operators can realize high-resolution and structure-preserving properties by adjusting numerical dissipation and anti-dissipation errors in a unified normalized-variable diagram. Then, this work develops a new open-source library based on the devised schemes within one of the most widely used general-purpose open-source software whose solution quality is intrinsically limited by the low accuracy of the conventional total variation diminishing schemes. The performance of the new library is first verified by some fundamental problems including pure advection and inviscid Euler equations. The numerical results of the accuracy tests show that the developed interpolation library can significantly reduce numerical errors with a minor increased computational cost compared with the conventional second-order schemes. The complex profile advection test demonstrates that the new library can offer an improved structure-preserving property that gives essentially oscillation-free solutions and preserves the structures of the passive transported scalar. Furthermore, the robustness of the new library is validated by compressible high-speed flow simulations with irregular geometries. Thus, this work presents a new library of high-resolution structure-preserving schemes for the accurate and efficient discretization of the convection term which plays an essential role in a wide range of computational fluid dynamics. The source code of the new scheme and library are released via DOI:10.5281/zenodo.8399000.

Advancing high-speed flow simulations: SAUSM – an innovative hybrid numerical scheme for shock stability and accuracy

This paper introduces a novel hybrid numerical method, SAUSM, designed for accurate and robust simulation of compressible flows governed by the Euler equations. While the AUSM[Formula: see text] scheme provides proper resolution of smooth flow features, it is susceptible to anomalies, particularly the carbuncle phenomenon near strong shock discontinuities. Conversely, the AUFS scheme offers inherent stability in capturing shocks; however, it lacks the accuracy of AUSM[Formula: see text] in smooth regions. The proposed SAUSM method combines AUSM[Formula: see text] and AUFS through an adaptive weighting function, facilitating a seamless transition between the schemes. This approach preserves the accuracy of AUSM[Formula: see text] in smooth regions while ensuring robust shock-capturing capabilities near discontinuities. The effectiveness of the SAUSM method is rigorously demonstrated through a comprehensive suite of progressively complex test cases. Numerical experiments demonstrate SAUSM’s proficiency in resolving intense shock patterns and discontinuities without introducing anomalies. In the selected test cases, SAUSM agrees with reference solutions and effectively mitigates anomalies observed in AUSM[Formula: see text], including kinked Mach stems. In the challenging test case involving hypersonic blunt body flow over a cylinder, SAUSM adapts dissipation effectively by utilizing its adaptive weighting function to generate smooth pressure distributions, thereby eliminating the carbuncle instability linked to AUSM[Formula: see text] when applied to a high aspect ratio grid. The consistent formulation of flux splitting and the adaptive weighting in SAUSM prevent excessive dissipation away from discontinuities, thus preserving accuracy comparable to that of exact Riemann solvers. Consequently, SAUSM emerges as a promising and innovative approach to accurately and robustly simulate a wide range of compressible Euler flows. The comprehensive results obtained from the validation tests firmly establish SAUSM as a highly effective general-purpose technique for computational fluid dynamics in academic research.

Numerical simulation of compressible gas flow in flat channels in the narrow channel approximation

In this paper, numerical simulation of a compressible gas in plane channels of constant and variable cross-section is performed within the framework of two-dimensional parabolized Navier-Stokes equations. The "narrow channel approximation" model is used for the numerical solution of the uranation system.A number of transformations are described in detail, such as de-dimensioning the equation system, reducing the considered area to a square, as well as thickening the calculated points in large gradients of gas dynamic parameters. Flow conservation conditions are used to determine the pressure gradient.An effective method is given for simultaneously determining the pressure gradient and the longitudinal velocity, then other gas dynamic parameters stable for subsonic and supersonic flows, as well as a method for determining the critical flow rate for solving Laval nozzle problems.The results of methodical calculations are presented, with the aim of verifying the effectiveness of the developed calculation methodology, as well as confirming the reliability of the results obtained by comparing them with data from other authors

A new high-fidelity Total Variation Diminishing scheme based on the Boundary Variation Diminishing principle for compressible flows

High-accuracy and stable simulations of compressible flows have been highly demanded in many engineering situations. However, it remains a challenging task due to the complicated fluid structures in compressible flows, which include both continuous and discontinuous solutions. The total variation diminishing (TVD) scheme is a mainstream numerical method because it has second-order accuracy for the smooth solution and suppresses numerical oscillations near the discontinuous solution. The properties of the TVD scheme depend on the design of the second-order slope-limiter function, Φ(r), for which minmod, superbee, and van Leer types are commonly adopted. However, the limiter function that provides both superior numerical accuracy and stability has not yet been established. In this paper, we provide an adaptive model for determining the suitable limiter function in the second-order TVD range, unlike the conventional methods, which use one type of limiter function for the entire calculation region. To designate the suitable limiter value, we use the boundary variation diminishing (BVD) principle, which suggests the most appropriate reconstruction method within the specific candidates. The numerical results of benchmark tests show that the proposed scheme has fewer numerical dissipation errors and provides a suitable limiter value that ensures both accuracy and stability.

Lagrangian Voronoï meshes and particle dynamics with shocks

We present a new first order particle method on lagrangian and moving Voronoï meshes for the numerical simulation of compressible flows with shocks and internal interfaces between different gas. The method is based on the closed form formula of the partial derivative of the volume of Voronoï cells with respect to the generators. The mathematical proof of the formula seems original with respect to the literature. A corollary is that the volume of Voronoï cells is generically of class C1 with respect to the generators. The final scheme is conservative in local mass, total momentum and total energy, and it is endowed with an entropy inequality which insures the correctness of shocks calculations. Numerical illustrations in dimension d=2 are displayed for basic problems on coarse meshes. The implementation developed to obtain the numerical illustrations uses a freely available library for the generation of the Voronoï cells at all time steps.

On the coupling between wall-modeled LES and immersed boundary method towards applicative compressible flow simulations

The current work presents an innovative numerical technique for high-Reynolds/high-Mach number compressible flow simulations in complex configurations. In particular, the research combines a novel wall-modeled large-eddy simulation technique with a sharp-interface immersed boundary method in the framework of high-order numerical schemes. The proposed approach enables the best from wall modeling and the immersed boundary. The first is concerned with accurately dealing with wall flows while avoiding direct control of near-wall resolution; the second is related to efficiently treating arbitrarily complex geometries in Cartesian grids. In particular, the paper extends a well-established wall model already presented by the research group to arbitrarily-shaped bounds. The method yields a minimally invasive technique that switches between wall-resolved and wall-modeled large-eddy simulations according to the local near-wall resolution. Thus, easily fitting aerodynamic simulation needs. After discussing the numerical procedure, the paper provides several benchmarks to demonstrate the validity of the proposed approach. In particular, literature-available direct numerical datasets are mined to compare acquired outcomes. The results’ accuracy is found to be remarkable from low-Mach-channel and -pipe flow configurations up highly-compressible flows concerning the spatial deployment of the boundary layer over a flat plate and the shock-wave/boundary-layer interaction over a compression ramp. Thus, the proposed method appears to be a promising framework for dealing with engineering-relevant flow simulations along with the efficient path of Cartesian meshes combined with massively parallel GPU-accelerated architectures.

Kinetic-energy- and pressure-equilibrium-preserving schemes for real-gas turbulence in the transcritical regime

Numerical simulations of compressible turbulent flows governed by real-gas equations of state, such as high-pressure transcritical flows, are strongly susceptible to instabilities. In addition to the inherent multi-scale nature of the flow, the presence of a pseudo-interface can generate spurious pressure oscillations when conventional schemes are utilized. This study proposes a general framework to derive and analyze discretization methods that are able to preserve kinetic energy by convection, and simultaneously maintain pressure equilibrium in discontinuity-free compressible real-gas flows. The formal analysis reveals that the discrete pressure-equilibrium condition can be fulfilled at most to second-order accuracy, as it requires the spatial differential operator to satisfy a discrete chain rule when total or internal energy are directly discretized. A novel class of schemes based on the solution of a pressure equation is thus proposed, which preserves mass, momentum, kinetic energy and pressure equilibrium, but not total energy. Extensive numerical tests of increasing complexity confirm the theoretical predictions, and show that the proposed scheme is capable of providing non-dissipative, stable and oscillation-free simulations, unlike existing methods tailored for the transcritical regime.

Efficient solution of bimaterial Riemann problems for compressible multi-material flow simulations

When solving compressible multi-material flow problems, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular idea in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. The work presented in this paper aims to accelerate the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed, including (1) a change of integration variable through rarefaction fans, (2) storing and reusing integration trajectory data, (3) step size adaptation, and (4) constructing an R-tree on the fly to generate initial guesses. The performance of these acceleration methods is assessed using four example problems in underwater explosion, laser-induced cavitation, and hypervelocity impact. These problems exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the acceleration methods are able to significantly reduce the computational cost without affecting solver robustness or solution accuracy. In different cases, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times.

Compressible multicomponent flow simulations and data-driven modeling of high-speed liquid droplet impingement

Accurate prediction of the force exerted on a droplet during high-speed liquid droplet impingement (LDI) is challenging yet important for the safety management of nuclear/fossil power plants. This paper describes compressible multicomponent flow simulations and data-driven modeling of high-speed LDI. The compressible multicomponent flow simulations are conducted for various impact Mach numbers ranging from Ma = 0.045 to 0.077. Whereas the peak force associated with the water hammer shock exhibits dependency on the impact Mach number, a self-similar structure for the pressure field within the small region about the impact plane is observed during high-speed LDI. An important observation is that the nondimensional mass-averaged droplet velocity does not vary with the impact Mach number. Finally, a data-driven LPP approach is presented to obtain fast and highly realistic simulations of high-speed LDI.

Evolution behavior of cavitation bubble in pure Sn liquid medium with narrow gap under low-amplitude ultrasound

In this study, a numerical model of cavitation bubble in the narrow-gap pure Sn liquid medium was established by two-dimensional compressible multiphase flow simulation. The effects of the pressure amplitude and the gap size on the shape, size and position of the cavitation bubble were investigated. The calculation results showed that the cavitation bubble in the narrow-gap soldering seam could exist stably after experiencing two stages of the nonlinear oscillation and the near-wall oscillation with the low-amplitude ultrasound and moved directionally on the metal substrate surface. When the pressure amplitude increased or the gap size decreased, the directional motion rate of the cavitation bubble increased and the shape of the bubble was elliptical due to the confinement effect of the substrate wall. The ultrasonic degassing mechanism of the narrow-gap soldering seam under the action of exponential decay ultrasonic vibration was analyzed by comparing the fluid pressure and velocity field variations. The flow field in the center of the soldering seam vibrated stronger than that of the peripheral regions, which could promote the outward motion of the cavitation bubble. Within the calculation time of 0.002 s, the maximum horizontal motion distance of bubble in the narrow-gap soldering seam was 1.13 mm.

A deep reinforcement learning framework for dynamic optimization of numerical schemes for compressible flow simulations

Marginal or under-resolved simulations of compressible flow configurations that often occur in practical applications classically are enabled by administering sufficient numerical dissipation to keep the simulation stable. Such measures, however, often are physically inconsistent due to non-selectively altering of dynamics across scales. Sustaining physically consistent large scale dynamics requires the numerical solution to effectively model non-resolved small scale dynamics. In this work, we propose a general deep-reinforcement-learning framework for devising an agent to interact with high-resolution scheme in order to balance dissipation and dispersion such that physically consistent modeling of non-resolved scales is achieved. A densely distributed reward function without involving labeled data is defined. The agent is trained on low-resolution uniform grids that capture the dominant flow structures. We demonstrate that it can be applied directly to high-resolution simulations without the need for retraining or fine-tuning, thereby, demonstrating significantly improved modeling performance compared to empirically designed high-resolution schemes. The proposed methodology opens a new path for self-adaptive numerical solutions whose truncation errors act as physically consistent model for unresolved scales of widely differing flow configurations.

Numerical study of liquid jet and shock wave induced by two-bubble collapse in open field

The shock waves and high-speed jets induced by the violent collapse of bubbles can cause serious damage to nearby structures. To fully understand the shock wave and jet characteristics induced by bubble-bubble interaction, we developed a diffuse-interface method for the simulation of compressible two-phase flow, which combined interface compression technique with interface sharpening technique to keep the sharpness of the shock wave and phase interface. The thermodynamically consistent five-equation model was improved using interface compression technique to maintain a constant thickness of the phase interface. To further suppress numerical dissipation, the high-order scheme WENO (Weighted Essentially Non-Oscillatory) and interface sharpening function THINC (Tangent of Hyperbola for INterface Capturing) were used for the flux reconstruction at the grid boundary to ensure that the total variation at the cell boundary was minimized (Boundary Variation Diminishing, BVD), thus the spatial reconstruction scheme, named WENO-THINC-BVD, was developed. Moreover, we extended the present method to a block-structured adaptive mesh refinement framework to improve grid resolution and save computing resources. Numerical results of several benchmark tests fully demonstrated the advantages of the present method in simulating complex compressible flows containing shock-shock and shock-interface interactions. Based on the present high-fidelity numerical methods, we investigated the shock wave and liquid jet induced by the two-bubble interaction in an open space. A phase diagram of the liquid jet propagation direction as a function of the initial bubble pressure and the inter-bubble distance was summarized. Finally, according to the bubble-bubble interaction process, an empirical formula for the collapse strength and another for the attenuation of shock waves were developed.

Моделирование турбулентных сжимаемых течений в программном комплексе FlowVision

Моделирование турбулентных сжимаемых течений в программном комплексе FlowVision

DetonationFoam: An open-source solver for simulation of gaseous detonation based on OpenFOAM

Detonation has promising applications in advanced propulsion systems, and numerical simulation is widely used to gain insights into the complex interaction between the hydrodynamic flow and chemical reactions involved in detonation. In this work, detonationFoam, an open-source solver for accurate and efficient simulation of compressible reactive flow and detonation are developed based on OpenFOAM. detonationFoam can simulate compressible, multi-component, reactive flow and it can accurately evaluate the detailed transport coefficients using the mixture-averaged transport model. Compared to rhoCentralFoam, the improved HLLC-P approximate Riemann solver is used in detonationFoam and it helps to accurately resolve shock waves appearing in detonation. Besides, the adaptive mesh refinement and dynamic load balancing algorithms are used in detonationFoam, which greatly improves the computational efficiency. Validation tests including homogenous ignition, unsteady diffusion, shock tube problem, premixed flame, planar detonation, double Mach reflection, detonation cellular structure and oblique detonation wave are conducted. These tests demonstrate that detonationFoam can be used to accurately and efficiently to simulate the compressible, multi-component reactive flow and detonation processes. Program summaryProgram Title: detonationFoamCPC Library link to program files:https://doi.org/10.17632/x45zh4nz28.1Developer's repository link:https://github.com/JieSun-pku/detonationFoamLicensing provisions: GPLv3Programming language: C++Nature of problem: Gaseous detonation involves different length scales and complicated chemistry. To accurately and efficiently simulate the gaseous detonation, adaptive mesh refinement needs to be conducted and detailed chemistry should be considered. Besides, the severe load imbalance caused by the chemical source term evaluation may greatly reduce the computation efficiency.Solution method: An open-source solver, detonationFoam is developed based on OpenFOAM. The species equations considering detailed chemistry are solved in detonationFoam and thereby detonation in a compressible, multi-component, reactive flow can be simulated. The adaptive mesh refinement technique and the dynamic load balancing algorithm are incorporated into detonationFoam. It is demonstrated that detonationFoam can accurately and efficiently simulate gaseous detonation.

Development of three-dimensional rotated lattice Boltzmann flux solver for the simulation of high-speed compressible flows

A three-dimensional (3D) Rotated Lattice Boltzmann Flux Solver (RLBFS) is proposed and analyzed with matrix-based linear stability theory for simulating compressible flows in a wide range of Mach numbers. The 3D RLBFS applies the finite volume method to discrete the Navier-Stokes equations and evaluates its fluxes at each cell interface. To improve numerical stability, the convective fluxes are obtained in a hybrid way by using the D1Q4 lattice Boltzmann model in two perpendicular directions decomposed by the outer normal vector of each cell interface. The viscous fluxes are computed in a conventional way using the second-order central scheme. The stability performance and order accuracy of the proposed 3D RLBFS are examined by using the matrix-based stability theory and L2 errors on different meshes respectively. It is shown that the 3D RLBFS is stable even at high Mach number and has the second-order accuracy in space. The reliability and capability of the proposed method is further evaluated by simulating several challenging compressible flow problems, including subsonic flow over the DLR-F4, transonic flow over the ONERA M6 wing, supersonic flow around NACA0012 wing, hypersonic flow over the Viking lander capsule, hypersonic flow over a hemisphere and hypersonic flow around a blunt nose double cone. The obtained numerical results are in good agreement with experimental and/or numerical data published in the literature, indicating that the present method provides a reliable and effective tool for simulating practical three-dimensional compressible flow problems in aeronautics and astronautics.

Analysis of Discrete Velocity Models for Lattice Boltzmann Simulations of Compressible Flows at Arbitrary Specific Heat Ratio

This paper is devoted to the comparison of discrete velocity models used for simulation of compressible flows with arbitrary specific heat ratios in the lattice Boltzmann method. The stability of the governing equations is analyzed for the steady flow regime. A technique for the construction of stability domains in parametric space based on the analysis of eigenvalues is proposed. A comparison of stability domains for different models is performed. It is demonstrated that the maximum value of macrovelocity, which defines instability initiation, is dependent on the values of relaxation time, and plots of this dependence are constructed. For double-distribution-function models, it is demonstrated that the value of the Prantdl number does not seriously affect stability. The off-lattice parametric finite-difference scheme is proposed for the practical realization of the considered kinetic models. The Riemann problems and the problem of Kelvin–Helmholtz instability simulation are numerically solved. It is demonstrated that different models lead to close numerical results. The proposed technique of stability investigation can be used as an effective tool for the theoretical comparison of different kinetic models used in applications of the lattice Boltzmann method.

Further Development of Eddy Dissipation Model for Turbulent Non-Premixed Combustion Simulation

In view of the application limits of the modified eddy dissipation model (MEDM) in simulations of weakly turbulent flow, compressible flow, and internal flow, an improved eddy dissipation model (IEDM) is proposed. The IEDM model uses the dissociation reactions to obtain the correct combustion temperature instead of the specific heat compensation used in the MEDM model. This extends the application in compressible flow simulation. The simulation accuracy of the IEDM model for weakly turbulent flow is improved by using the accurate transport property and model. The maximum ε/k is limited to give a reasonable reaction rate near walls, and the expression for the model parameter A is also updated. Nine turbulent flames including seven jet flames and two opposed jet flames are simulated with the improved model. Compared with the experimental data of the jet flames, the peak temperature differences with the MEDM model and the IEDM model are 189 and 161 K, respectively, indicating the minor accuracy improvement of the IEDM model. Compared with the experimental data of the opposed flames, the peak temperature differences with the MEDM model and the IEDM model are 131 and 7 K, respectively, indicating the significant accuracy improvement of the IEDM model.

Detecting Under-Resolved Flow Physics Using Supervised Machine Learning

The accuracy of flow simulations is a major concern in computational fluid dynamics (CFD) applications. A possible outcome of inaccuracy in CFD results is missing a major feature in the flowfield. Many methods have been proposed to reduce numerical errors and increase overall accuracy, but these are not always efficient or even feasible. In this study, the principal component analysis (PCA) has been performed on compressible flow simulations around an airfoil to map the high-dimensional CFD data to a lower-dimensional PCA subspace. A machine learning classifier based on the extracted principal components has been developed to detect the simulations that miss the separation bubble behind the airfoil. The evaluative measures indicate that the model is able to detect most of the simulations where the separation region is poorly resolved. Moreover, a single mode responsible for the missing flow separation was uncovered that could be the subject of future studies. The results demonstrate that a machine learning model based on the principal components of the dataset is a promising tool for detecting possible missing flow features in CFD.

Achieving high performance and portable parallel GMRES algorithm for compressible flow simulations on unstructured grids

Achieving high performance and portable parallel GMRES algorithm for compressible flow simulations on unstructured grids