Compressible Flow Research Articles

Usage of multi-extruded nozzles for hydrogen fuel mixing in the double cavity flame holder in the existence of the shock generator

Improvement of the fuel mixing inside the cavity flame-holder is important for the development of this injection system in scramjet engines. This article presents significant flow results on the mixing role of multi-extruded nozzles inside dual cavity flame holders with a single shock generator. A three-dimensional model of the dual cavity with injectors located on the inclined rear wall is produced to simulate real flow physics associated with proposed jet configurations. The impression of air injection from the inclined rear wall is also examined by computational modeling of the compressible flow inside the dual cavity. Based on the achieved results, the injection of multiple extruded nozzles enhances fuel diffusion in the cavity when the shock generator is applied. Our findings disclose that the injection of the fuel from the inclined rear wall results in more efficient fuel mixing inside the dual cavity flame holder. Mixing of the annular jet is increased about 14% via backward air jet inside the cavity.

Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains

In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3D Navier–Stokes–Fourier–Poisson equations where the velocity is supposed to fulfill the full-slip boundary condition and the temperature on the boundary is given by a non-homogeneous Dirichlet condition. We establish the global-in-time weak solution to the system. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, to accommodate the non-homogeneous boundary heat flux, the concept of ballistic energy is utilized in this work.

Numerical solution of steady nonlinear differential equations for compressible flow through a spinning convergent divergent nozzle

Many projectiles tend to spin about their longitudinal axis while progressing in the forward direction. It helps in providing stability and a reference direction for guidance during their run. Many different projectiles employ a supersonic convergent-divergent nozzle to produce thrust for their forward motion; hence, the nozzle and overall whole propulsion system tend to spin about its axis of rotation. The main aim of this study is to observe the effect of spin on the nozzle. In this research, a converging bell-shaped diverging nozzle is numerically designed using a method of characteristics (MOC) for exit Mach number 3.21. Viscous simulations are performed for both two- and three-dimensional cases. The analysis is then performed with nozzle spinning about its axis of symmetry with a constant angular velocity of 10 revolutions per second. The analysis is repeated for the value of constant angular velocities to be 15 and 20 revolutions per second, and the behavior of flow with increasing angular velocity is examined. It has been observed that the exit Mach number and velocity decrease due to the radial protrusion of the boundary layer, and it has a negative impact on the performance of the nozzle. Moreover, the decrease of exit Mach number is in direct relation to increasing angular velocity.

A high-order limiter-free arbitrary Lagrangian–Eulerian discontinuous Galerkin scheme for compressible multi-material flows

In this paper, a high-order limiter-free arbitrary Lagrangian–Eulerian discontinuous Galerkin (ALE-DG) scheme is proposed for simulating one-dimensional compressible multi-material flows. The system is discretized by the DG method, and a kind of Taylor’s expansion basis functions in the general cell is used to construct the interpolation polynomials of the variables. The mesh velocity at the node recognized as the material interface is set to approximate fluid velocity, which makes our scheme can capture the material interface accurately and clearly. For controlling the oscillations and reducing the numerical dissipation, a reconstruction based on the boundary variation diminishing (BVD) algorithm and Tangent of Hyperbola for INterface Capturing (THINC) function is employed to minimize the jump between the values at the left and right sides of cell boundaries. Due to the essentially monotone and bounded properties of THINC function, the difficulties caused by solving discontinuous solutions and complexities of designing limiters can be avoided. Finally, several examples are presented to demonstrate the accuracy and good performance of our scheme such as the essentially non-oscillatory property and so on for simulating the compressible multi-material flows.

On the streamwise velocity, temperature and passive scalar fields in compressible turbulent channel flows: a viewpoint from multiphysics couplings

It is generally believed that the velocity and passive scalar fields share many similarities and differences in wall-bounded turbulence. In the present study, we conduct a series of direct numerical simulations of compressible channel flows with passive scalars and employ the two-dimensional spectral linear stochastic estimation and the correlation function as diagnostic tools to shed light on these aspects. Particular attention is paid to the relevant multiphysics couplings in the spectral domain, i.e. the velocity–temperature ( $u-T$ ), scalar–temperature ( $g-T$ ) and velocity–scalar ( $u-g$ ) couplings. These couplings are found to be utterly different at a given wall-normal position in the logarithmic and outer regions. Specifically, in the logarithmic region, the $u-T$ and $u-g$ couplings are tight at the scales that correspond to the attached eddies and the very large-scale motions (VLSMs), whereas the $g-T$ coupling is robust in the whole spectral domain. In the outer region, $u-T$ and $u-g$ couplings are only active at the scales corresponding to the VLSMs, whereas the $g-T$ coupling is diminished but still strong at all scales. Further analysis indicates that although the temperature field in the vast majority of zones in a channel can be roughly treated as a passive scalar, its physical properties gradually deviate from those of a pure passive scalar as the wall-normal height increases due to the enhancement of the acoustic mode. Furthermore, the deep involvement of the pressure field in the self-sustaining process of energy-containing motions also drives the streamwise velocity fluctuation away from a passive scalar. The current work is an extension of our previous study (Cheng & Fu, J. Fluid Mech., vol. 964, 2023, A15), and further uncovers the details of the multiphysics couplings in compressible wall turbulence.

Turbophoresis and preferential accumulation of inertial particles in compressible turbulent channel flow: Effect of Mach number

Turbophoresis and preferential accumulation of inertial particles in compressible turbulent channel flow: Effect of Mach number

Variations in gas temperature and average velocity during laminar-turbulent transition in high-speed gas flow through microtubes

The primary objective of this study is to investigate variations in gas temperature and average velocity during the laminar-turbulent transition of compressible flow. This investigation encompasses an exploration of the effect of Mach number on transitional Reynolds number. Experiments were conducted utilizing a pair of adiabatic stainless steel microtubes with a diameter (D) of 131.6 μm. The first microtube was dedicated to measuring local pressure to obtain friction factor, local Mach number, and bulk temperature. The second microtube was employed for measuring local wall temperature. Additionally, a stainless steel microtube with a diameter (D) of 124 μm and a rectangular microchannel with a hydraulic diameter (Dh) of 99.36 μm were incorporated in the study. Friction factor, Mach number, and bulk temperature were determined by measuring mass flow rate and local pressure near the outlet. The measured mass flow rate exhibited a slight increase that plateaued during the laminar-turbulent transition as the Reynolds number increased. In laminar flow, an increase in the Reynolds number resulted in an increase of the Mach number and a reduction in bulk temperature. Conversely, during the laminar-turbulent transition, the Mach number either remained constant or decreased, and the bulk temperature increased due to the conversion of kinetic energy to thermal energy. Experimental validation of this phenomenon was achieved by measuring the wall temperature of an adiabatic microtube.

Strong solutions to the 3D full compressible magnetohydrodynamic flows

In this paper, we deal with the strong solutions to the full compressible magnetohydrodynamic flows in a domain Ω⊆R3. We prove the local existence and unique of strong solution under three different types of boundary conditions provided that the initial data satisfies a natural compatibility condition. The initial density of such a strong solution is allowed to contain vacuum states. Compared to the classical compressible MHD, the key issue in the limit passage is to obtain the a priori estimates of the absolute temperature, some new estimate ideas are introduced to estimate these results.

Eulerian discrete kinetic framework in comoving reference frame for hypersonic flows

Flow physics vary in different regimes across the full Mach number range, with our knowledge being particularly poor about the hypersonic regime. An Eulerian realization of the particles on demand method, a kinetic model formulated in the comoving reference frame, is proposed to simulate hypersonic compressible flows. The present model allows for flux evaluation in different reference frames, in this case rescaled and shifted by local macroscopic quantities, i.e. fluid speed and temperature. The resulting system of coupled hyperbolic equations is discretized in physical space with a finite volume scheme ensuring exact conservation properties. Regularization via Grad expansion is introduced to implement distribution function and flux transformation between different reference frames. It is shown that the proposed method possesses Galilean invariance at a Mach number up to $100$ . Different benchmarks including both inviscid and viscous flows are reproduced with the Mach number up to $198$ and pressure ratio up to $10^5$ . Finally, the new model is demonstrated to be capable of simulating hypersonic reactive flows, including one-dimensional and two-dimensional detonations. The developed methodology opens up possibilities for the simulation of the full range of compressible flows, without or with chemical reactions, from the subsonic to hypersonic regimes, leading to enhanced understanding of flow behaviours across the full Mach number range.

Simulation of fluid‐structure interaction using the boundary data immersion method with adaptive mesh refinement

SummaryThe fluid‐structure interaction is simulated using the boundary data immersion method. As the fluid‐structure interface is smeared in the smoothing region, deviations are incurred in fluid simulations. For compressible flow, high order difference schemes with more mesh cells for the stencils are usually employed to achieve high overall accuracy, but near interfaces it requires wider smoothing region of several mesh cells for computational stability and hence lowers its accuracy significantly. To address this issue, the proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss. Implemented with Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI), the algorithm shows notable improvement in the overall accuracy and efficiency in cases such as channel flow and flow past a cylinder. The algorithm is used to simulate the shock wave past a fixed or free cylinder with Ma and Re , which reveals the relaxation process and the temporal evolution of the drag coefficient, it goes through a valley and maintains at relatively high value for the fixed cylinder, while that of the free cylinder tends to decrease in fluctuation which is found to be caused by the interaction between the forward moving cylinder and vortexes in the unsteady wake.

A cluster analysis-based shock wave pattern recognition method for two-dimensional inviscid compressible flows

Compressible flows typically exhibit multiple shock waves which interact with each other, making the detection of these shock waves crucial for various aspects of flow studies including construction of high-order numerical schemes (e.g., shock-fitting), adaptive grid refinement, and flow visualization. This study aims to effectively identify and localize multiple shock waves and their interaction points in two-dimensional inviscid steady and unsteady flows. A novel shock wave pattern recognition method based on cluster analysis is proposed, including three processes. First, a series of grid-cells located at the transition zones of captured shock waves are extracted using a shock wave detection approach based on local flow variation. Subsequently, these grid-cells are grouped into numerous clusters using the classical K-means clustering algorithm, with categorization based on nearest neighbor features. Finally, a strategy is introduced to merge relevant adjacent clusters and further localize the points where shock waves interact. The Bézier curve fitting technique is then employed to obtain the high-quality shock-lines. Several numerical cases demonstrate that this method achieves high localization accuracy for shock-lines while being minimally affected by grid type and scale variations. Moreover, it enables clear and effective identification of the shock interaction patterns in both steady and unsteady flows, providing an effective visualization means for analyzing the motion and evolution of shock wave configurations.

Existence and Stability of Dissipative Measure-Valued Solutions to the Full Compressible Magnetohydrodynamic Flows

Existence and Stability of Dissipative Measure-Valued Solutions to the Full Compressible Magnetohydrodynamic Flows

Experimental and numerical study on the high-speed gas-solid nozzle erosion of choke manifold material in high pressure and high production gas well

High pressure difference, high flow rate, and high sand content in throttling manifolds of high-pressure and high-production gas wells make the problems of high-speed gas-solid erosion wear especially prominent. The failure of the throttling manifold is frequent, which is easy to induce overflow, kick, and blowout accidents, aggravates well-controlled risks, and brings safety risks. Therefore, according to ASTM G76–2013, this paper adopts the gas-solid nozzle erosion test method and air jet erosion test rig. The high speed (107 m/s-49 m/s) gas-solid nozzle erosion test of 30CrMo alloy steel was carried out under different inlet pressures (0.06 MPa–0.15 MPa) and impact Angle (15°-90°), and the erosion rate of 30CrMo alloy steel under different experimental conditions was obtained. The erosion rate equation of 30CrMo alloy steel suitable for high-speed solid particle impact is established. Based on the results of erosion experiments, the optimal particle motion model for high-speed compressible flow is constructed. Combined with the discrete phase model (DPM) and gas-solid two-phase coupling calculation method, a three-dimensional CFD erosion model of the “reduced-tuber-nozzle-erosion cavity” was established. The erosion simulation of the gas-solid nozzle of 30CrMo alloy steel, a throttling manifold material, was carried out at different impact angles (15°-90°) and inlet pressure (0.06 MPa–0.15 MPa), and the distribution characteristics of the flow field, particle movement trajectory, impact velocity distribution, and slip characteristics were revealed. The accuracy and reliability of the CFD erosion model and simulation results have been validated by test data.

A centered limited finite volume approximation of the momentum convection operator for low‐order nonconforming face‐centered discretizations

AbstractWe propose in this article a discretization of the momentum convection operator for fluid flow simulations on quadrangular or generalized hexahedral meshes. The space discretization is performed by the low‐order nonconforming Rannacher–Turek finite element: the scalar unknowns are associated with the cells of the mesh while the velocities unknowns are associated with the edges or faces. The momentum convection operator is of finite volume type, and its expression is derived, as in MUSCL schemes, by a two‐step technique: computation of a tentative flux, here, with a centered approximation of the velocity, and limitation of this flux using monotonicity arguments. The limitation procedure is of algebraic type, in the sense that its does not invoke any slope reconstruction, and is independent from the geometry of the cells. The derived discrete convection operator applies both to constant or variable density flows and may thus be implemented in a scheme for incompressible or compressible flows. To achieve this goal, we derive a discrete analogue of the computation (with the velocity, one of its component, the density, and assuming that the mass balance holds) and discuss two applications of this result: first, we obtain stability results for a semi‐implicit in time scheme for incompressible and barotropic compressible flows; second, we build a consistent, semi‐implicit in time scheme that is based on the discretization of the internal energy balance rather than the total energy. The performance of the proposed discrete convection operator is assessed by numerical tests on the incompressible Navier–Stokes equations, the barotropic and the full compressible Navier–Stokes equations and the compressible Euler equations.

Implementation and assessment of a low-dissipative OpenFOAM solver for compressible multi-species flows

An ever-increasing number of engineering problems regard the numerical simulation of fluid flows with high-density ratio, shock wave onset, and different chemical species. In such conditions, obtaining reliable results depends on the ability of the numerical algorithm to offer a stable and robust time and space discretization of the governing equations while simultaneously limiting the numerical diffusivity.This work presents the extension and the assessment of a low-dissipative Navier–Stokes solver for compressible, multi-specie flows. We first studied the Richtmyer–Meshkov instability to test the code on fluid flows involving shock waves and species interactions for ideal gas. Then, we simulated a benchmark case regarding a cryogenic coaxial injector often used in rocket engines to explore the solver’s capability in representing high-Reynolds-number supercritical flows of multi-species real gases with large density gradients. Finally, we studied the flow in complex geometries like a high-pressure gasoline injector for propulsion application. The results demonstrate the capability of the present approach in the cases investigated.

Numerical simulation of transpiration cooling in porous nose cone under hypersonic conditions

Transpiration cooling in a two-dimensional porous nose cone under hypersonic flow have been numerically investigated. The numerical model intricately captures the interaction between compressible and incompressible flows in the boundary layer and the phase change of coolant within porous region. The validation of numerical method is performed by comparing the simulation results with experimental data. The simulation results are in reasonable agreement with the experimental data. The results show that the increase of blowing ratio can effectively improve the cooling efficiency of transpiration cooling，where the blowing ratio represents the mass flow rate ratio between the coolant of porous region and the mainstream free flow. Such as, the average cooling efficiency rises from 0.33 to 0.86 when the blowing ratio increases from 0.0459% to 0.2753%. Although the porous resistance force increases as the particle diameter and porosity decrease, the effect of these parameters and solid material of porous region on the cooling efficiency are marginal.

FLEW: A DNS Solver for Compressible Flows in Generalized Curvilinear Coordinates

AbstractWe present FLEW, an in-house high-fidelity solver for direct numerical simulation (DNS) of turbulent compressible flows over arbitrary shaped geometries. FLEW solves the Navier–Stokes equations written in a generalized curvilinear coordinate system, in which the surface coordinates are non-orthogonal, whereas the third axis is normal to the surface. Spatial discretization relies on high-order finite-difference schemes. The convective terms are discretized using an hybrid approach, combining the near-zero numerical dissipation provided by central approximations with the robustness of weighted essentially non-oscillatory (WENO) schemes, required to capture shock waves. Central schemes are stabilized using a skew-symmetric-like splitting of convective derivatives, endowing the solver with the energy-preserving property in the inviscid limit. The maximum order of accuracy is eighth for central schemes (also used for viscous terms discretization) and seventh for WENO. The code is oriented to modern high-performance computing (HPC) platforms thanks to message passing interface (MPI) parallelization and the ability to run on graphics processing unit (GPU) architectures. Reliability, accuracy and robustness of the code are assessed in the low-subsonic, transonic and supersonic regimes. We present the results of several benchmarks, namely the inviscid Taylor–Green vortex, turbulent curved channel flow, transonic laminar flow over a NACA 0012 airfoil and turbulent supersonic ramp flow. The results for all configurations proved to be in excellent agreement with previous studies.

High‐resolution mapping type WENO‐Z schemes for solving compressible flow

SummaryThis paper presents a new WENO‐Z scheme (WENO‐MZ) that incorporates a mapping function to enhance the weights of the less smooth sub‐stencils. The mapping function uses an innovative approach to modify the weight ratio of the less smooth sub‐stencil to the smooth stencil. In addition, we present the WENO‐MD scheme, which is a further development of the WENO‐MZ scheme that incorporates a modifier function. The WENO‐MD scheme shows improvements over the WENO‐MZ scheme by achieving an improved optimal order at critical points in higher orders and by increasing the proportion of less smooth sub‐stencils. Theoretical and numerical experiments have shown that the newly developed methods have improved shock capture capabilities and resolution compared to WENO‐JS, WENO‐Z, WENO‐M, WENO‐D, and WENO‐AIM, and also lead to significant computational time savings compared to WENO‐M and WENO‐AIM.

An averaged mass correction scheme for the simulation of high subsonic turbulent internal flows using a lattice Boltzmann method

This paper addresses the simulation of internal high-speed turbulent compressible flows using lattice Boltzmann method (LBM) when it is coupled with the immersed boundary method for non-body-fitted meshes. The focus is made here on the mass leakage issue. The recent LBM pressure-based algorithm [Farag et al. Phys. Fluids 32, 066106 (2020)] has shown its superiority on classical density-based algorithm to simulate high-speed compressible flows. Following our previous theoretical work on incompressible flows [Xu et al. Phys. Fluids 34, 065113 (2022)], we propose an averaged mass correction technique to mitigate mass leakage when simulating high-Mach-number compressible flows. It is adapted to deal here with a density, which is decoupled from the zero-moment definition. The simulations focus on two generic but canonical configurations of more complex industrial devices, the straight channel at different angles of inclination at Mach numbers (Ma) ranging from 0.2 to 0.8, and the National Aeronautics and Space Administration Glenn S-duct at Ma = 0.6. The present results show that mass leakage can be a critical issue for the accuracy of the solution and that the proposed correction technique effectively mitigates it and leads to significant improvements in the prediction of the solution.

Enhancing accuracy and efficiency: A novel implicit–explicit approach for fluid dynamics simulation

This study presents an innovative implicit–explicit time-stepping algorithm based on a first-order temporal accuracy method, addressing challenges in simulating all-regimes of fluid flows. The algorithm's primary focus is on mitigating stiffness inherent in the density-based “Roe” method, pivotal in finite volume approaches employing unstructured meshes. The objective is to comprehensively evaluate the method's efficiency and robustness, contrasting it with the explicit fourth-order Runge–Kutta method. This evaluation encompasses simulations across a broad spectrum of Mach numbers, including scenarios of incompressible and compressible flow. The scenarios investigated include the Sod Riemann problem to simulate compressible Euler equations, revealing the algorithm's versatility, and the low Mach number Riemann problem to analyze system stiffness in incompressible flow. Additionally, Navier–Stokes equations are employed to study viscous and unsteady flow patterns around stationary cylinders. The study scrutinizes two time-stepping algorithms, emphasizing accuracy, stability, and computational efficiency. The results demonstrate the implicit–explicit Runge–Kutta algorithm's superior accuracy in predicting flow discontinuities in compressible flow. This advantage arises from the semi-implicit nature of the equations, reducing numerical errors. The algorithm significantly enhances accuracy and stability for low Mach number Riemann problems, addressing increasing stiffness as Mach numbers decrease. Notably, the algorithm optimizes computational efficiency for both low Mach number Riemann problems and viscous flows around cylinders, reducing computational costs by 38%–68%. The investigation extends to a two dimensional hypersonic inviscid flow over cylinder and double Mach reflection case, showcasing the method's proficiency in capturing complex and hypersonic flow behavior. Overall, this research advances the understanding of time discretization techniques in computational fluid dynamics, offering an effective approach for handling a wide range of Mach numbers while improving accuracy and efficiency.