High Mach Flows Research Articles

Numerical study of shock-induced thermochemical nonequilibrium effects in a high Mach flow field

As Mach number increases, thermochemical nonequilibrium is recognized as potentially affecting the flow field structure, as well as mixing and combustion characteristics, where shock-induced thermochemical nonequilibrium is a common and crucial phenomenon in compressible flow fields. A numerical study of shock-induced thermochemical nonequilibrium effects within a high Mach flow field of the electre vehicle is conducted by employing a two-temperature model-based solver hy2foam. The validation through experimental and simulation data confirms that hy2foam coupled with Park's two-temperature model and Park's five-species mechanism correctly predicts the flow structure and nonequilibrium characteristics. Four regime cases of thermochemical equilibrium, thermal nonequilibrium, chemical nonequilibrium, and thermochemical nonequilibrium are designed for comparison. First, the mechanism of shock-induced nonequilibrium is revealed. The shock induces the thermal nonequilibrium to occur instantly, and then the equilibrium is reestablished by undergoing the relaxation process. However, chemical nonequilibrium works delayed after the shock, and the high temperature induced by the shock motivates deviation from the chemical equilibrium by turning on chemical reactions. Further comparison of the four cases reveals that thermodynamic nonequilibrium significantly affects both shock position and intensity. In contrast, chemical nonequilibrium only significantly affects the distance to the shock detachment. Furthermore, it is found that thermodynamic and chemical nonequilibria behave in a complex coupling relationship after the shock.

Influence of thermochemical non-equilibrium effects on non-uniform entrance scramjet nozzle

The high Mach number scramjet nozzle flow has prominent non-uniform characteristics and high-temperature non-equilibrium effects. Thus, the thermochemical non-equilibrium gas model was developed for simulating flows in the non-uniform and uniform entrance of a Mach 10 hydrocarbon fuel scramjet nozzle. The results show that the non-uniform entrance has a higher non-uniform degree in the flow-field compared to the uniform entrance. Additionally, the expansion degree inside the nozzle is greater and the thermal non-equilibrium effects downstream of the nozzle exit are stronger. The non-uniform entrance condition has a more intense chemical reaction near the nozzle exit but has less impact on the flow parameters. For the nozzle performance, under the influence of the non-uniform entrance, the greater gas expansion degree inside the nozzle results in a lower pressure acting on the upper wall, and then the nozzle thrust decreases by 1.68%. Hence, the structural design and performance optimization of the high Mach number scramjet nozzle must consider entrance non-uniform characteristics and thermochemical non-equilibrium effects.

Modified advection upstream splitting method: Revolutionizing accuracy and convergence speed in low-Mach flows

The vital role of the numerical scheme is becoming increasingly critical as the use of computational fluid dynamics grows. To address the unfavorable effects experienced in low-speed flows when using the AUSM+M scheme (Improved Advection Upstream Splitting Method), the present paper presents an improved approach known as Modified-AUSM+M (M-AUSM+M). This novel method offers enhanced reliability in simulating low-Mach number flows, effectively mitigating the challenges associated with low-speed symptoms encountered in the original AUSM+M scheme. The novel scheme is facilitated by the parameter-free form of the pressure diffusion term in the mass flux and the low-dissipative form of the velocity diffusion term in the pressure flux. The impacts of these critical ingredients are then thoroughly evaluated, and the different characteristics are explored in terms of robustness and accuracy using a wide range of low-Mach test cases. The proposed scheme maintains a consistent correlation between accuracy and convergence speed. In addition, the recently devised technique demonstrates superior accuracy compared to AUSM+M and AUSM+UP schemes when dealing with low-Mach flows. Furthermore, the findings indicate an incredible reduction in iteration numbers, ranging from 30% to 80%, by employing the enhanced scheme in low-Mach domains. In the investigation of high-Mach test cases, the newly developed method preserves the accuracy achieved by AUSM+M in high-Mach flows.

A computational strategy for nonlinear coupled constitutive relations of rarefied nonequilibrium flows on unstructured grids

The Navier-Stokes-Fourier (NSF) equations are no longer valid in high-Knudsen and high-Mach flows, where the local thermodynamically equilibrium assumption fails, while the nonlinear coupled constitutive relations (NCCR) have been proven to be an efficient approach for rarefied non-equilibrium flows under the structured finite-volume-method computational fluid dynamic (FVM-CFD) solver. In this paper, by adding the time derivatives of non-conserved variables to the NCCR model, a computational strategy for NCCR model under the unstructured FVM-CFD framework is first proposed for further engineering applications. An upwind flux-splitting scheme with the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) implicit time-marching scheme is employed. The linear stability of one-dimensional modified NCCR model in time and space is analyzed subsequently, which indicates the modified NCCR model is unconditionally stable. The accuracy and computational performance of the proposed NCCR solution are assessed by a feat of the numerical tests for hypersonic flow over a blunt cylinder without a wake, supersonic flow past a circular cylinder with a wake, and hypersonic flow around a planetary probe. Computational results show that the newly-developed NCCR solution can get solutions in better agreement with the direct simulation Monte Carlo (DSMC) than NSF results. Moreover, the newly-developed NCCR solution has a better property of convergence than the undecomposed NCCR algorithm under the unstructured FVM-CFD framework. These superior advantages of the present computational strategy are expected to make the NCCR method a promising engineering tool for modeling rarefied non-equilibrium flows.

Numerical simulation of hypersonic thermochemical nonequilibrium flows using nonlinear coupled constitutive relations

To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect, a Nonlinear Coupled Constitutive Relations (NCCR) model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper. Three typical cases are intensively investigated for further validation, including hypersonic flows over a two-dimensional cylinder, a RAM-C II flight vehicle and a type HTV-2 flight vehicle. The results predicted by NCCR solution, such as heat flux coefficient and electron number densities, are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations, especially in the extremely nonequilibrium regions, which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects. The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.

Development of a Shock-Stable and Contact-Preserving Scheme for Multidimensional Euler Equations

The shock instability, notably the disastrous carbuncle phenomenon, has plagued many low-dissipation Godunov-type numerical schemes in calculations of high Mach flows. In the current work, two popular stability analysis tools and corresponding numerical experiments are used to investigate the root cause of shock instability of the low-dissipation Harten, Lax, and van Leer with contact (HLLC) scheme. The local linear stability analysis reveals that the HLLC flux could attenuate all perturbations in the streamwise direction but not perturbations of density and shear velocity in the transverse direction. Numerical results also indicate that the shock instability of the HLLC scheme is only related to the transverse flux. The viscosity terms of entropy wave and shear wave are introduced into the transverse flux, and the stability analysis shows that with the help of additional viscosities the shock instability of the HLLC scheme is cured. To preserve the capability of resolving contact discontinuities and shear waves, a pressure-based switching function is incorporated into the expressions of viscosity terms so that the additional viscosities are activated only when calculating the transverse flux in the shock layer. A series of numerical experiments give evidence of the robustness and accuracy of the proposed scheme, and the strategy adopted here can be easily applied to cure shock instabilities of other low-dissipation numerical schemes, e.g., the Roe scheme and the AUSM+ scheme.

Turbulent Flow Characteristics in a Model of a Solid Rocket Motor Chamber with Sidewall Mass Injection and End-Wall Disturbance

The present analytical, numerical, and experimental investigations are performed to study the flow field in acoustically simulated solid rocket motor (SRM) chamber geometry. The computational solution is carried out for a high Reynolds number and low Mach number internal flows driven by sidewall mass addition in a long chamber with end-wall disturbances. This kind of flow (transient, weakly viscous, and contains vorticity) have several features in common with a turbulent flow field. The numerical study is performed by solving the unsteady Reynolds-averaged Navier–Stokes equations along with the energy equation using the control volume approach based on a staggered grid system. The v2-f turbulence model has been implemented in the current study. A comparison of the SIMPLE and PISO algorithms showed that both algorithms provide identical results, and the computational time using the PISO algorithm is higher by about 6% than the corresponding value of the SIMPLE algorithm. A fair agreement has been obtained between the numerical, analytical, and experimental results. Moreover, the results showed that the complex turbulent internal flow patterns are induced inside the chamber due to the strong interaction of the sidewall injection with the traveling acoustic waves. Such a complex internal structure is shown to be dependent on the piston frequency and sidewall mass flux. The current study, for the first time, emphasizes the acoustic-fluid dynamics interaction mechanism and the accompanying unsteady rotational fields along with the effect of the generated turbulence on the unsteady vorticity and its impact on the real burning rate.

The near-field aerodynamic characteristics of hot high-speed jets

Abstract

Research on Parameters Optimization of High Voltage Circuit Breaker Nozzle Based on Image Recognition and Deep Learning

Traditional modeling and optimization methods for high voltage equipment, specially, circuit breaker components and nozzles, require manual testing and improvement of a large number of parameters, and the efficiency is relatively low. The strong processing power of artificial intelligence technology in the identification and prediction of complex systems is an effective solution in such case. This paper presents the optimization approach of image recognition combined with deep learning for circuit breaker nozzle. The nozzle model was conducted using the high Mach flow model in a commercial software (COMSOL Multiphysics 5.4) to study the gas flow state and behavior during cold flow, and obtains Shock wave image recognition model of the nozzle chamber based on the convolutional neural network (CNN) method of multiscale layered features. On the basis of effective image recognition, combined with deep learning Convolutional Recurrent Neural Network (CRNN), the image sequence under different parameters is sent to the convolutional layer for feature extraction, and then the feature map is input into the loop. The prediction sequence is obtained through the layer, and finally the relationship between the kinematic parameters of the nozzle and the internal gas flow state is predicted through the prediction layer. Results indicated, according to the prediction of CRNN, the range of the throat length should be between 7 and 13 mm and the angle should be between 8 ∼ 15°. The presented method could be also used for similar materials and components, with certain universality. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

An accurate and shock-stable genuinely multidimensional scheme for solving the Euler equations

In numerical simulations of multidimensional high Mach flows, the conventional low-diffusion upwind schemes built on the dimensional splitting method will encounter the shock instability which is mainly manifested as the infamous carbuncle phenomena. A linear stability analysis reveals that the shock instability is triggered by the unattenuated perturbations in the transverse direction of the flow field. In the present work, an accurate and shock-stable genuinely multidimensional numerical scheme based on the Toro-Vázquez splitting method is presented. Different from the conventional one-dimensional upwind schemes that just consider the waves propagating along the direction normal to an interface, the proposed multidimensional scheme whose multidimensional properties are achieved by calculating multidimensional numerical fluxes at each corner of an interface also takes into account the waves traveling along the transverse direction. For obtaining these multidimensional numerical fluxes at the corner, a simple multidimensional upwind method is used to solve the weakly hyperbolic convection subsystem and the pressure subsystem whose flux Jacobian has a complete set of linearly independent eigenvectors is calculated by a multidimensional HLLEM scheme. Based on Balsara’s framework for constructing multidimensional schemes, the total numerical flux across an interface is obtained by using the Simpson’s rule to assemble the conventional one-dimensional numerical flux with the multidimensional numerical fluxes at the corner. A series of benchmark test problems validate the accuracy, robustness and efficiency of the proposed multidimensional scheme.

Analytical method of nonlinear coupled constitutive relations for rarefied non-equilibrium flows

It is well known that Navier-Stokes equations are not valid for those high-Knudsen and high-Mach flows, in which the local thermodynamically non-equilibrium effects are dominant. To extend the non-equilibrium describing the ability of macroscopic equations, Nonlinear Coupled Constitutive Relation (NCCR) model was developed from Eu’s generalized hydrodynamic equations to substitute linear Newton’s law of viscosity and Fourier’s law of heat conduction in conservation laws. In the NCCR model, how to solve the decomposed constitutive equations with reasonable computational cost is a key ingredient of this scheme. In this paper, an analytic method is proposed firstly. Compared to the iterative procedure in the conventional NCCR model, the analytic method not only obtains exact roots of the decomposed constitutive polynomials, but also preserves the nonlinear constitutive relations in the original framework of NCCR methods. Numerical tests to assess the efficiency and accuracy of the proposed method are conducted for argon shock structures, Couette flows, two-dimensional hypersonic flows over a cylinder and three-dimensional supersonic flows over a three-dimensional sphere. These superior advantages of the current method are expected to render itself a powerful tool for simulating the hypersonic rarefied flows and microscale flows of high Knudsen number for engineering applications.

Drag-based aerodynamic braking system for the Hyperloop: a numerical study

The Hyperloop promises to revolutionize the transport infrastructure of the 21st century by reducing travel time and allowing people to reach transonic speed on land. It carries with it the hope of a sustainable transportation system during an era of global energy crisis. Overall passenger safety in a high-speed pod necessitates a reliable braking system. This paper introduces the possibility of utilizing aerodynamic drag in the Hyperloop, anticipated to operate at high Mach and low Reynolds flow regime, to attenuate the speed of the pod. Numerical analysis was conducted to investigate the effect of incorporating an aerodynamic brake at different pod velocities (100, 135, and 150 m/s) and deployment angles (30°, 45°, 60°, and 90°). A detailed comparison between the proposed aerodynamic braking system (AeBS) and existing braking systems for the Hyperloop has been presented in this paper. The results demonstrate an increase in drag value of the pod by 3.4 times using a single 0.15 m2brake plate. When the brake plate was fully deployed at a pod velocity in excess of 112 m/s, the aerodynamic drag-based braking systems was shown to be more effective than the contemporary eddy current braking system.

A quasi-one-dimensional model for an outwardly opening poppet-type direct gas injector for internal combustion engines

Direct injection of compressed natural gas in internal combustion engines is a promising technology to achieve high indicated thermal efficiency and, at the same time, reduce harmful exhaust gas emissions using relatively low-cost fuel. However, the design and analysis of direct injection–compressed natural gas systems are challenging due to small injector geometries and high-speed gas flows including shocks and discontinuities. The injector design typically involves either a multi-hole configuration with inwardly opening needle or an outwardly opening poppet-type valve with small geometries, which make accessing the near-nozzle-flow field difficult in experiments. Therefore, predictive simulations can be helpful in the design and development processes. Simulations of the gas injection process are, however, computationally very expensive, as gas passages of the order of micrometers combined with a high Mach number compressible gas flow result in very small simulation time steps of the order of nanoseconds, increasing the overall computational wall time. With substantial differences between in-nozzle and in-cylinder length and velocity scales, simultaneous simulation of both regions becomes computationally expensive. Therefore, in this work, a quasi-one-dimensional nozzle-flow model for an outwardly opening poppet-type injector is developed. The model is validated by comparison with high-fidelity large-eddy simulation results for different nozzle pressure ratios. The quasi-one-dimensional nozzle-flow model is dynamically coupled to a three-dimensional flow solver through source terms in the governing equations, named as dynamically coupled source model. The dynamically coupled source model is then applied to a temporal gas jet evolution case and a cold flow engine case. The results show that the dynamically coupled source model can reasonably predict the gas jet behavior in both cases. All simulations using the new model led to reductions of computational wall time by a factor of 5 or higher.

CFD analysis of the aerodynamic characteristics of biconvex airfoil at compressible and high Mach numbers flow

In the present study, numerical investigation of the turbulent flow over a biconvex airfoil at compressible and high Mach numbers flow is done using computational fluid dynamics (CFD). The flow is considered as turbulent, two-dimensional, steady and compressible. For this purpose, three Reynolds number of 2.4 × 107, 2.9 × 107 and 3.3 × 107 are considered. The simulations are implemented using the commercial software Ansys Fluent 16. The results are obtained with Reynolds-averaged Navier–Stokes (RANS), and for simulating the flow turbulence, SST k–ω turbulence model is carried out. The results show that the lift coefficient (CL) and drag coefficient (CD) increase by the increment of the angle of attack (α). The lift-to-drag ratio (CL/CD) is improved by increasing the Mach number (Ma) and cause to delay the boundary layer separation. Increasing the Mach number affects the stall angle which causes to increase it from α = 22° to α = 30° from Ma = 1 to Ma = 1.4.

A High-performance and Portable All-Mach Regime Flow Solver Code with Well-balanced Gravity. Application to Compressible Convection

Abstract Convection is an important physical process in astrophysics well-studied using numerical simulations under the Boussinesq and/or anelastic approximations. However, these approaches reach their limits when compressible effects are important in the high-Mach flow regime, e.g., in stellar atmospheres or in the presence of accretion shocks. In order to tackle these issues, we propose a new high-performance and portable code called “ARK” with a numerical solver well suited for the stratified compressible Navier–Stokes equations. We take a finite-volume approach with machine precision conservation of mass, transverse momentum, and total energy. Based on previous works in applied mathematics, we propose the use of a low-Mach correction to achieve a good precision in both low and high-Mach regimes. The gravity source term is discretized using a well-balanced scheme in order to reach machine precision hydrostatic balance. This new solver is implemented using the Kokkos library in order to achieve high-performance computing and portability across different architectures (e.g., multi-core, many-core, and GP-GPU). We show that the low-Mach correction allows to reach the low-Mach regime with a much better accuracy than a standard Godunov-type approach. The combined well-balanced property and the low-Mach correction allowed us to trigger Rayleigh–Bénard convective modes close to the critical Rayleigh number. Furthermore, we present 3D turbulent Rayleigh–Bénard convection with low diffusion using the low-Mach correction leading to a higher kinetic energy power spectrum. These results are very promising for future studies of high Mach and highly stratified convective problems in astrophysics.

A kinetic BGK edge-based scheme including vibrational and electronic energy modes for high-Mach flows

A first principles formulation for the calorically imperfect behavior of gases is here proposed within a Boltzmann-type discretisation of the Navier–Stokes equations. The formulation is intended to enhance the consistency of gas kinetic schemes (GKS) with the physics of supersonic and hypersonic regimes where vibrational and electronic energy modes are activated before any thermal nonequilibrium or chemical activity takes place. The so-called node-pair BGK scheme, an edge-based implementation of the GKS, is considered in the present work for the implementation of a thermodynamic model where the calorically imperfect behavior is obtained from a modification of the way the different moments of the particle distribution function are computed and eventually used to determine the fluxes of conserved quantities across the boundary of each control volume. The method is validated on a series of canonical test cases for supersonic and hypersonic flows.

Study of Parameters Affecting Separation Bubble Size in High Speed Flows using k-ω Turbulence Model

Shock waves generated at different parts of vehicle interact with the boundary layer over the surface at high Mach flows. The adverse pressure gradient across strong shock wave causes the flow to separate and peak loads are generated at separation and reattachment points. The size of separation bubble in the shock boundary layer interaction flows depends on various parameters. Reynolds-averaged Navier-Stokes equations using the standard two-equation k-ω turbulence model is used in simulations for hypersonic flows over compression corner. Different deflection angles, including q ranging from 15o to 38o, are simulated at Mach 9.22 to study its effect on separated flow. This is followed by a variation in the Reynolds number based on the boundary layer thickness, Red from 1x105 to 4x105. Simulations at different constant wall conditions Tw of cool, adiabatic, and hot are also performed. Finally, the effect of free stream Mach numbers M∞, ranging from 5 to 9, on interaction region is studied. It is observed that an increase in parameters, q, Red, and Tw results in an increase in the separation bubble length, Ls, and an increase in M∞ results in the decrease in Ls.

Direct numerical simulations of supersonic turbulent channel flows of dense gases

The influence of dense-gas effects on compressible wall-bounded turbulence is investigated by means of direct numerical simulations of supersonic turbulent channel flows. Results are obtained for PP11, a heavy fluorocarbon representative of dense gases, the thermophysics properties of which are described by using a fifth-order virial equation of state and advanced models for the transport properties. In the dense-gas regime, the speed of sound varies non-monotonically in small perturbations and the dependency of the transport properties on the fluid density (in addition to the temperature) is no longer negligible. A parametric study is carried out by varying the bulk Mach and Reynolds numbers, and results are compared to those obtained for a perfect gas, namely air. Dense-gas flow exhibits almost negligible friction heating effects, since the high specific heat of the fluids leads to a loose coupling between thermal and kinetic fields, even at high Mach numbers. Despite negligible temperature variations across the channel, the mean viscosity tends to decrease from the channel walls to the centreline (liquid-like behaviour), due to its complex dependency on fluid density. On the other hand, strong density fluctuations are present, but due to the non-standard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, i.e. in the viscous sublayer instead of the buffer layer like in perfect gases. As a consequence, these fluctuations do not alter the turbulence structure significantly, and Morkovin’s hypothesis is well respected at any Mach number considered in the study. The preceding features make high Mach wall-bounded flows of dense gases similar to incompressible flows with variable properties, despite the significant fluctuations of density and speed of sound. Indeed, the semi-local scaling of Patelet al.(Phys. Fluids, vol. 27 (9), 2015, 095101) or Trettel & Larsson (Phys. Fluids, vol. 28 (2), 2016, 026102) is shown to be well adapted to compare results from existing surveys and with the well-documented incompressible limit. Additionally, for a dense gas the isothermal channel flow is also almost adiabatic, and the Van Driest transformation also performs reasonably well. The present observations open the way to the development of suitable models for dense-gas turbulent flows.

Numerical analysis of high Mach flow and flow reversal in the experimental advanced superconducting tokamak divertor

The B2-Eirene (SOLPS 4.0) code package is used to investigate the plasma parallel flow, i.e., the scrape-off layer (SOL) flow, in the experimental advanced superconducting tokamak (EAST) divertor. Simulation results show that the SOL flow in the divertor region can exhibit complex behaviour, such as a high Mach flow and flow reversal in different plasma regimes. When the divertor plasma is in the detachment state, the high Mach flow with approaching or exceeding sonic speed is observed away from the target plate in our simulation. When the divertor plasma is in the high recycling state, the flow reversal with a small Mach number (|M| < 0.2) is observed near the X-point along the separatrix region. The driving mechanisms for the high Mach flow and the reversed flow are analysed theoretically through momentum and continuity equations, respectively. The profile of the ionization sources is shown to be a possible formation condition causing the complex behaviour of the SOL flow. In addition, the effects of the high Mach flow and the flow reversal on the impurity transport are also discussed in this paper.

S055034 高マッハ数チャネル乱流における摩擦抵抗低減制御の直接数値シミュレーション([S05503]流れの抵抗低減(3))

S055034 高マッハ数チャネル乱流における摩擦抵抗低減制御の直接数値シミュレーション([S05503]流れの抵抗低減(3))