Simulation Of Compressible Flows Research Articles

Multiscale modeling and simulation of turbulent flows in porous media

Numerical simulation is an important tool for understanding the physics of flows in porous media and for making predictions. The state of the art of multiscale modeling and simulation of turbulent flows in porous media is reviewed in this paper. Numerical simulations of flows in porous media can be classified as microscopic simulations, in which both macroscopic and pore-scale flows are directly resolved, and macroscopic simulations, in which the pore-scale motions are modeled while the volume-averaged equations are solved. Studies in the past few years have shown that microscopic simulations improve the understanding of turbulent flows in porous media considerably; this motivates the development of more efficient and more accurate turbulence models for macroscopic simulations. On the basis of this review, we believe that simulation of flows with higher Reynolds numbers, understanding the transport of macroscopic turbulence, modeling of turbulent flows in inhomogeneous and anisotropic porous media, simulation of compressible and multiphase turbulent flows in porous media, and fluid–structure interaction in deformable porous matrices are important topics to be studied in the future.

Restraining vocal fold vertical motion reduces source-filter interaction in a two-mass model.

Previous experimental studies suggested that restraining the vocal fold vertical motion may reduce the coupling strength between the voice source and vocal tract. In this study, the effects of vocal fold vertical motion on source-filter interaction were systematically examined in a two-dimensional two-mass model coupled to a compressible flow simulation. The results showed that when allowed to move vertically, the vocal folds exhibited subharmonic vibration due to entrainment to the first vocal tract acoustic resonance. Restraining the vertical motion suppressed this entrainment. This indicates that the vertical mobility of the vocal folds may play a role in regulating source-filter interaction.

A high-efficiency adaptive TENO scheme with optimal accuracy order for compressible flow simulation

In this paper, we propose a new adaptive cut-off function and develop a fifth-order targeted ENO scheme that achieves optimal accuracy at any order of critical points, which performs excellently in conventional compressible gas dynamics. The cut-off value CT is crucial for controlling the dissipation in TENO schemes. Adjusting CT can improve shock capture and increase dissipation for small-scale features. To address this issue, Fu et al. [27] and Peng et al. [28] developed the TENO-A and TENO-LAD schemes, respectively, with adaptive cut-off values CT. However, these adaptive cutoffs CT are computationally expensive due to additional free parameters and complexity. Furthermore, all TENO schemes, including the adaptive versions, can suffer from loss of accuracy at higher-order critical points. In this paper, a new adaptive cut-off function is proposed that uses a global smoothness indicator correction so that it can be automatically tuned between 0 and a given positive constant λd, ensuring that the new TENO scheme achieves optimal accuracy in smooth regions and good shock-capturing in the less smooth parts. A series of benchmark simulations demonstrate that the presented scheme provides optimal accuracy, better robustness, resolution, and numerical stability, and higher resolution than existing TENO schemes while improving computational efficiency. Due to the simplicity of the new cut-off structure, it can be easily extended to improve other TENO schemes.Program files associated to this article may be found at https://github.com/fourhairs/cfd.

High‐order gas kinetic flux solver for viscous compressible flow simulations

AbstractAlthough the gas kinetic schemes (GKS) have emerged as one of the powerful tools for simulating compressible flows, they exhibit several shortcomings. Since the local solution of continuous Boltzmann equation with the Maxwellian distribution function is used to calculate the numerical fluxes at the cell interface, the flux expression in GKS is usually more complicated. In this paper, a high‐order simplified gas kinetic flux solver (GKFS) is presented for simulating two‐dimensional compressible flows. Circular function‐based GKFS (C‐GKFS), which simplifies the Maxwellian distribution function into the circular function, combined with an improved weighted essentially non‐oscillatory (WENO‐Z) scheme is applied to capture more details of the flow fields with fewer grids. As a result, a simple high‐order accurate C‐GKFS is obtained, which improves the computing efficiency and reduce its complexity to facilitate the practical application of engineering. A series of benchmark‐test problems are simulated and good agreement can be obtained compared with the references, which demonstrate that the high‐order C‐GKFS can achieve the desired accuracy.

An efficient discrete unified gas-kinetic scheme for compressible thermal flows

In this paper, an efficient discrete unified gas-kinetic scheme (DUGKS) is developed for compressible thermal flows based on the total energy kinetic model for natural convection with a large relative temperature difference. A double distribution function model is designed with the second distribution representing the total energy. This efficient DUGKS enables the simulation of compressible thermal flows, governed by the compressible Navier–Stokes–Fourier system, using only a seventh-order, off-lattice Gauss–Hermite quadrature (GHQ) D3V27A7 combined with a fifth-order GHQ D3V13A5. The external force is included by truncated Hermite expansions. Based on the Chapman–Enskog approximation and Hermite projection, we propose a systematic approach to derive the discrete kinetic boundary conditions for the density and total energy distribution functions. The discrete kinetic boundary treatments are provided for the no-slip boundary condition, Dirichlet boundary condition and Neumann boundary condition. To validate our scheme, we perform simulations of steady natural convection (Ra=103−106) in two- and three-dimensional cavities with differentially heated sidewalls and a large temperature difference (ε=0.6), where the Oberbeck–Boussinesq approximation is invalid. The results demonstrate that the current efficient DUGKS is robust and accurate for thermal compressible flow simulations. With the D3V27A7 and D3V13A5 off-lattice discrete particle velocity model, the computational efficiency of the DUGKS is improved by a factor of 3.09 when compared to the previous partial energy kinetic model requiring the ninth-order Gauss–Hermite quadrature.

Absolute atomic nitrogen density spatial mapping in three MHCD configurations

In this work, nanosecond two-photon absorption laser induced fluorescence (TALIF) is used to perform spatial mappings of the absolute density of nitrogen atoms generated in a micro-hollow cathode discharge (MHCD). The MHCD is operated in the normal regime, with a DC discharge current of 1.6 mA and the plasma is ignited in a 20% Ar/ 80% N2 gas mixture. A 1-inch diameter aluminum substrate, acting as a third electrode (second anode), is placed further away from the MHCD to emulate a deposition substrate. The spatial profile of the N atoms is measured in three MHCD configurations. First, we study a MHCD having the same pressure (50 mbar) on both sides of the anode/cathode electrodes and the N atoms simply diffuse in three dimensions from the MHCD. The recorded N atoms density profile in this case satisfies our expectations, i.e. the maximal density is found at the axis of the hole, close to the MHCD. However, when we introduce a pressure differential, thus creating a plasma jet, an unexpected N atoms distribution is measured with maximum densities away from the jet axis. This behavior cannot be simply explained by the TALIF measurements. Then, as a first simplified approach in this work, we turn our attention to the role of the gas flow pattern. Compressible gas flow simulations show a correlation between the jet width and the radial distribution of the N atoms at different axial distances from the gap. Finally, a DC positive voltage is applied to the third electrode (second anode), which ignites a micro cathode sustained discharge (MCSD). The presence of the pressure differential unveils two stable working regimes depending on the current repartition between the two anodes. The MCSD enables an homogenization of the density profile along the surface of the substrate, which is suitable for nitride deposition applications.

The effect of basis polynomial degree on the performance of compressible flow simulations employing a split-form DG method

High order methods have garnered significant interest recently for simulating compressible flows due to their low dissipation nature. In this regard, the use of discontinuous Galerkin method has been actively pursued due to the advantages ensuing from its compact interpolation. However, these methods generally require employing a limiter for stable computation of supersonic compressible flows that contain shocks. Many limiters are designed to incorporate ideas from robust second order implementations of the Finite Volume Method for shock capturing. It is therefore prudent to examine the effectiveness of high order discontinuous Galerkin solutions when simulating flows containing discontinuities. To this end, the present work investigates the variation of accuracy per degrees of freedom as the basis polynomial degree is changed. Several standard one-dimensional and two-dimensional compressible flow cases are simulated for multiple basis polynomial degrees while employing different meshes to keep the degrees of freedom fixed. It is found that high order solutions are more efficient than second order solution as regards the accuracy per degrees of freedom. The improvement in this metric with increasing basis polynomial degree plateaus at cubic basis degree for cases containing strong discontinuities (shock Mach numbers greater than 3), and shifts to a further higher basis in simpler problems. However, in problems containing slowly moving shocks and or weak discontinuities, high order solutions generate increased numerical oscillations, suggesting the need for improvement in anti-aliasing techniques.

Consistent Coupling of Compressibility Effects in Manifold-Based Models for Supersonic Combustion

Manifold-based models are an efficient modeling framework for turbulent combustion but, in their basic formulation, do not account for the compressibility effects of high-speed flows. To include the effects of compressibility, ad hoc corrections have been proposed but result in an inconsistent thermodynamic state between the manifold and flow simulation. In this work, an iterative algorithm to consistently incorporate compressibility effects into manifold-based models is developed. The manifold inputs (fuel and oxidizer temperatures and pressure) are determined iteratively to reflect the nonnegligible variations in thermodynamic state (expressed in terms of density and internal energy in flow simulations) that are characteristic of supersonic combustion. The algorithm is demonstrated on data from simulations of high-speed reacting mixing layers and is significantly more accurate than established approaches that only partially couple the manifold in compressible flow simulations. The proposed approach eliminates partial coupling approximation errors in excess of 10 and 20% for temperature and water source term.

Compact high-order gas-kinetic scheme for direct numerical simulation of compressible turbulent flows

In this paper, the three-dimensional fully compact high-order gas-kinetic scheme (HGKS) is proposed for the direct numerical simulation of compressible turbulent flows. Because of the high-order gas evolution model, the numerical fluxes as well as the point-wise conservative variables can be evaluated from the time-accurate gas distribution function at the cell interface. As a result, both the cell-averaged variables and their cell-averaged gradients can be updated inside each cell. Based on the cell averaged values and their gradients, the compact Hermite weighted essentially non-oscillatory (HWENO) scheme is developed, in which the dimension-by-dimension reconstruction is used for three-dimensional turbulences. In both normal and tangential directions, the fifth-order HWENO reconstruction is adopted. Compared with the classical WENO scheme, the stencil for the HWENO scheme only contains 33 cells for each cell. To achieve the temporal accuracy, the two-stage fourth-order temporal discretization is used. For the evaluation of point-wise variables, the simplified third-order gas-kinetic solver is used. Several classical benchmark problems are simulated, which validate the accuracy, resolution, and robustness of compact HGKS. As a comparison, the numerical results of HGKS using non-compact WENO reconstruction are also provided. Due to the compact stencil, the compact HGKS has a favorable performance for turbulence simulation in resolving the multi-scale structures.

A high-order simulation method for compressible multiphase flows with condensed-phase explosive detonation in underwater explosions

This study introduces an efficient method designed for the simulation of compressible multiphase flows associated with explosive detonation, primarily in the context of underwater explosions. The proposed approach integrates three core components: the compressible Euler equations, the level-set equation, and the program burn model. Spatial terms of the compressible Euler equations undergo discretization using a fifth-order accuracy weighted essentially non-oscillation reconstruction, while the third-order total variation diminishing Runge–Kutta scheme manages the temporal terms. The level-set method ensures accurate tracking of the multiphase interface. To detail the transition from solid, non-reactive explosives to gaseous detonation products in the condensed charge's detonation reaction zone, the program burn model based on Zeldovich, von Neumann, Doering theory. The efficacy and accuracy of the incorporated program burn model and the multiphase interface capture method are employed through four benchmark tests, exhibiting excellent agreement with previously published data from alternative numerical methods or commercial software. In conclusion, applying the proposed method to four distinct engineering scenarios facilitates a comprehensive understanding of the inherent dynamics associated with detonation and shock wave generation and propagation.

High-Resolution and High-Precision Weighted Essentially Non-Oscillatory Scheme for Compressible Flow Simulations

High-Resolution and High-Precision Weighted Essentially Non-Oscillatory Scheme for Compressible Flow Simulations

Equivalent diffusion ratio distribution in the UGT15000 low pressure compressor

With spatial and temporal periodicity approach the results of steady state CFD simulation of compressible air flow in each blade-to-blade row of low pressure compressor (LPC) of the UGT15000 gas turbine engine (Ukrainian SSR constr. and prod.) are presented. Near the nominal rotation speed compressor map and adiabatic efficiency of each stage and the flow angles at leading and trailing blade edges are predicted and calculated. At the average radius stage flow and stage load coefficients are determined. It has been established that the reason of the low efficiency of the last stage is associated with the low stage reaction (≈0.5) leading to high airflow swirling at outlet. For LPC optimization a calculation of the radial distributions of the equivalent diffuser coefficient was performed. It is shown that the greatest total pressure losses are in the stator rows of stages 9, 8, 5 and in the rotor rows of stage 9. High losses are also shown on the upper half of the 4th, 3rd, 2nd stator blades and the lower half of the 1st rotor blades. The identified potential for increasing the efficiency of the LPC is up to 2% without significant construction changes.

SOD2D: A GPU-enabled Spectral Finite Elements Method for compressible scale-resolving simulations

As new supercomputer architectures become more heavily focused on using hardware accelerators, in particular general-purpose graphical processors, it is therefore relevant that algorithms for computational fluid dynamics, especially those targeting scale-resolving simulations, be designed in such a way as to make efficient use of such hardware.In this paper, we propose one such hardware-accelerated Continuous Galerkin Finite Elements model, aimed at handling simulations of turbulent compressible flows over complex geometries. As this model is intended for use in Large-Eddy and Direct Numerical simulations, it is necessary that the resulting scheme introduces only small amounts of artificial (numerical) diffusion for stabilization purposes. We achieve this through a combination of Spectral Finite Elements, operator splittings on the convective term, and the use of the Entropy Viscosity stabilization model adapted to spectral elements scheme.The paper will present the resulting algorithm, how it is made to work efficiently on the accelerators, and results obtained that demonstrate its high-accuracy capabilities.

High speed flows with particles on demand: Boundary conditions

The particles on demand (PonD) method is a new kinetic theory model that allows for simulation of high speed compressible flows. While the standard lattice-Boltzmann method is limited by a fixed reference frame, significantly reducing the range of Mach numbers, PonD takes advantage of adaptive reference frames to get rid of the restrictions of standard LB and is able to simulate flows at high speeds and with large temperature variation. Previously, PonD has been shown to be a viable alternative for simulation of flows with strong discontinuities and for detonation modelling. However, treatment of flows with complex boundaries has been lacking. Here, we present PonD augmented with a non-equilibrium extrapolation based boundary condition. We present several compressible test cases such as shock-vortex interaction in the Schardin’s problem and supersonic flow over a two-dimensional cylinder at Mach numbers up to 5. We observe that the results agree well with literature, paving the way for a kinetic theory based approach for simulating compressible flows in realistic scenarios.

Computational Fluid Dynamics Simulation of Internal Compressible Flow in Transfer Lines and Structural Optimization

Computational Fluid Dynamics Simulation of Internal Compressible Flow in Transfer Lines and Structural Optimization

Temporal discretization for improving kinetic-energy and entropy preservation properties in KEEP schemes

A temporal discretization for improving kinetic-energy and entropy preservation on compressible flow simulations is proposed. The key of the proposed scheme is to introduce the auxiliary velocity, density, and internal energy to the temporal discretization and derive the quantities that satisfy the analytical relations of temporal-derivative terms in the kinetic-energy and entropy equations at the discrete level by utilizing the Maclaurin expansion and truncating high-order terms. The numerical fluxes in the kinetic-energy and entropy preserving (KEEP) schemes proposed by Kuya et al. (2018) are also evaluated by the auxiliary quantities to enhance kinetic-energy and entropy preservation in both spatial and temporal discretizations. The numerical experiments of the inviscid Taylor–Green vortex demonstrate that the proposed scheme significantly improves the kinetic energy and entropy preservation and achieves stable and non-dissipative compressible flow simulations at CFL ≈1.0, at which the temporal-discretization errors for the kinetic-energy and entropy preservation are not negligible when the widely used fourth-order four-step Runge–Kutta scheme is employed.

Exponential distribution functions for positivity-preserving lattice Boltzmann schemes: Application to 2D compressible flow simulations

A family of positivity-preserving lattice Boltzmann methods (LBMs) is proposed for compressible flow simulations in the continuum regime. It relies on the efficient collide-and-stream algorithm with a collision step based on exponential distribution functions. The latter serves as a generalization of Grad's post-collision distribution functions for which here (1) the linearized non-equilibrium contributions are replaced by their exponential forms and (2) the number of these contributions can be chosen arbitrary. In practice, post-collision moments of our exponential formulation are enforced through an iterative moment-matching approach to recover any macroscopic physics of interest, with or without external forces. This methodology directly flows from the extended framework on numerical equilibria [J. Latt et al., Philos. Trans. R. Soc. A 378, 20190559 (2020)] and goes one step further by allowing for the independent relaxation of hydrodynamic and high-order modes in a given moment space, notably, making the Prandtl number freely adjustable. The model is supplemented by a shock-capturing technique, based on the deviation of non-equilibrium moments from their equilibrium counterparts, to ensure good numerical properties of the model in inviscid and under-resolved conditions. A second exponential distribution accounts for extra degrees of freedom of molecules and allows for the simulation of polyatomic gases. To validate this novel approach and to quantify the accuracy of different lattices and moment closures, several 2D benchmark tests of increasing complexity are considered: double shear layer, linear wave decay, Poiseuille flow, Riemann problem, compressible Blasius flow over a flat plate, and supersonic flow past an airfoil. Corresponding results confirm the accuracy and stability properties of our approach for the simulation of compressible flows with LBMs. Eventually, the performance analysis further highlights its efficiency on general purpose graphical processing units.

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.