Base Pressure Control with Semi-Circular Ribs at Critical Mach Number

When better fuel-air mixing in the combustion chamber or a reduction in base drag are required in vehicles,rockets,and aeroplanes,the base pressure control is activated.Controlling the base pressure and drag is necessary in both scenarios.In this work,semi-circular ribs with varying diameters(2,4,and 6 mm)positioned at six distinct positions(0.5D,1D,1.5D,2D,3D,and 4D)inside a square duct with a side of 15 mm are proposed as an efficient way to apply the passive control technique.In-depth research is done on optimising rib size for various rib sites.According to this study,the base pressure rises as rib height increases.Furthermore,the optimal location for the semi-circular ribs with a diameter of 2 mm is at 0.5D.The 1D location appears to be optimal for the 4 mm size as well.For the 6 mm size,however,the 4D position fills this function.

Numerical Analysis of Cavity-Based Control of Base Pressure Variations at Supersonic Mach Numbers

In the present study,the base pressure variations induced by the presence of a cavity,known to have a strong influence of the behaviour of supersonic projectiles,are investigated through numerical solution of the balance equations for mass,momentum,and energy.An area ratio of four is considered and numerical simulations are carried out at Mach M=1.2,1.4,1.6,and 1.8 assuming no cavity or cavity locations 0.5D,1D,1.5D,and 2D.The inlet pressure of the nozzle is considered as a flow variable.The Taguchi method is also used,and the considered cases are then analyzed using a full factorial experimental design.The results show that the cavity is effective in increasing the base pressure for the conditions examined.For other nozzle pressure ratios,cavities do not lead to passive control due the change in the reattachment length.The distribution of wall pressure reveals that,in general,a cavity used to implement passive control of the base pressure does not adversely influence the flow pattern in the domain.

Computation of Stiffness and Damping Derivatives of an Ogive in a Limiting Case of Mach Number and Specific Heat Ratio

This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach number.Generally,the Mach number independence principle becomes effective from M=10 and above.The Ogive nose is obtained through a circular arc on the cone surface.Accordingly,the following arc slopes are consideredλ=5,10,15,−5,−10,and−15.It is found that the stability derivatives decrease due to the growth inλfrom 5 to 15 and vice versa.Forλ=5 and 10,the damping derivative declines with an increase inλfrom 5 to 10.Yet,for the damping derivatives,the minimum location remains at a pivot position,h=0.75 for large values ofλ.Hence,whenλ=−15,the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.

THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW

We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

NARX-GA-Elman Method for Mach Number Prediction of Wind Tunnel Flow Field

Mach number is a key metric in the evaluation of wind tunnel flow field performance.This complex process of wind tunnel test mainly has the problems of nonlinearity and time lag.In order to overcome the problems and control the Mach number stability,this paper proposes a new method of Mach number prediction based on a nonlinear autoregressive exogenous-genetic algorithm-Elman(NARX-GA-Elman)model,which adopts NARX as the basic framework,determines the order of the input variables by using the false nearest neighbor(FNN),and uses the dynamic nonlinear network Elman to fit the model,and finally uses the global optimization algorithm GA to optimize the weight thresholds in the model to establish the Mach number prediction model with optimal performance under single working condition.By comparing with the traditional algorithm,the prediction accuracy of the model is improved by 61.5%,and the control accuracy is improved by 55.7%,which demonstrates that the model has very high prediction accuracy and good stability performance.

Mach Number Prediction for a Wind Tunnel Based on the CNN-LSTM-Attention Method

The test section’s Mach number in wind tunnel testing is a significant metric for evaluating system performance.The quality of the flow field in the wind tunnel is contingent upon the system's capacity to maintain stability across various working conditions.The process flow in wind tunnel testing is inherently complex,resulting in a system characterized by nonlinearity,time lag,and multiple working conditions.To implement the predictive control algorithm,a precise Mach number prediction model must be created.Therefore,this report studies the method for Mach number prediction modelling in wind tunnel flow fields with various working conditions.Firstly,this paper introduces a continuous transonic wind tunnel.The key physical quantities affecting the flow field of the wind tunnel are determined by analyzing its structure and blowing process.Secondly,considering the nonlinear and time-lag characteristics of the wind tunnel system,a CNN-LSTM model is employed to establish the Mach number prediction model by combining the 1D-CNN algorithm with the LSTM model,which has long and short-term memory functions.Then,the attention mechanism is incorporated into the CNN-LSTM prediction model to enable the model to focus more on data with greater information importance,thereby enhancing the model's training effectiveness.The application results ultimately demonstrate the efficacy of the proposed approach.

A NOVEL SLIGHTLY COMPRESSIBLE MODEL FOR LOW MACH NUMBER PERFECT GAS FLOW CALCULATION

By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

Numerical Simulation of Shock Bubble Interaction with Different Mach Numbers

The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method （PPM）, in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers （Ma）. The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 （2007） 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.

LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL

In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.

Influences of attack angle and mach number on aerodynamic characters of typical sections of extra-long blade in a steam turbine

On super-sonic or trans-sonic planar cascade wind tunnel of free jet intermittent type, wind blowing experiments were performed on the typical sections of stator and rotor blades in the last stage of ultra-ultra-critical steam turbine with extra-long blade of 1200mm. The influences of attack angle and Mach number on the aerodynamic performances of these sections of the blade profiles were verified, and their operating ranges were also specified.

A Conservative Pressure-Correction Method on Collocated Grid for Low Mach Number Flows

A novel extension to SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor—corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to satisfy the continuity equation at each time step. The proposed algorithm has second order centrally differenced convective fluxes with upwinding based on Cell Peclet number while diffusive flux are viscous fourth order accurate. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straight forward extension to curvilinear coordinate systems. The algorithm is kinetic energy preserving. Further in this paper robustness and accuracy are demonstrated by performing test on channel flow with non-Boussinesq condition on different temperature ratios.

The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.

Effects of Freestream Turbulence,Reynolds Number and Mach Number on the Boundary Layer in a Low Pressure Turbine

In order to investigate the aerodynamics of a high speed low pressure turbine works in high Mach number and low Reynold number environment,the effect of freestream turbulence(FST)on the boundary layer development on the high speed low pressure turbine under different Reynolds numbers(Re)is numerically investigated.Large eddy simulation is adopted here with a subgrid scale model of Wall Adapting Local Eddy viscosity(WALE).Cases with Re ranging from 100000 to 400000 under an exit Mach number(Ma)of 0.87 have been considered at low and high FST levels.A low Ma case(0.17)under very low Re has also been studied under both low and high FST.It is found that higher Re or FST level leads to earlier transition.Re has a greater effect than FST on the development of boundary layer.The effect of FST on the boundary layer depends on the Re.The boundary layer development shows totally different behaviors under different Ma.A separation bubble could be formed under low Ma while no attachment could be detected under high Ma.The FST has a stronger effect on the separated boundary layer under low Ma,which could eliminate the separation in the present study.For all the cases under low FST,the Kelvin-Helmholtz instability is the dominate mechanism in the transition process.For the low Ma case with high FST,the streamwise streaks play a dominant role in the transition process.For the high Ma cases with high FST,both the streamwise streaks and Kelvin-Helmholtz instability work in the transition process.The streamwise streaks play a more important role when the Re increased.

Mach数和壁面温度对HyTRV边界层转捩的影响

典型的高超声速飞行器流场存在着复杂的转捩现象,其对飞行器的性能有着显著的影响。针对HyTRV这款接近真实高超声速飞行器的升力体模型,采用数值模拟方法,研究Mach数和壁面温度对HyTRV转捩的影响规律。采用课题组自研软件开展数值计算,Mach数的范围为3~8,壁面温度的范围为150~900 K。首先对■转捩模型和SST湍流模型进行了高超声速修正:将压力梯度系数修正、高速横流修正引入到■转捩模型,并对SST湍流模型闭合系数β~*和β进行可压缩修正;然后开展了网格无关性验证,通过与实验结果对比,确认了修正后的数值方法和软件平台;最终开展Mach数和壁面温度对HyTRV边界层转捩规律的影响研究。计算结果表明,转捩区域主要集中在上表面两侧、下表面中心线两侧;增大来流Mach数,上下表面转捩起始位置均大幅后移,湍流区大幅缩小,但仍会存在,同时上表面层流区摩阻系数不断增大,下表面湍流区摩阻系数不断减小;升高壁面温度,上下表面转捩起始位置先前移,然后快速后移,最终湍流区先后几乎消失。

A low-diffusion robust flux splitting scheme towards wide-ranging Mach number flows

This paper develops a low-diffusion robust flux splitting scheme termed TVAP to achieve the simulation of wide-ranging Mach number flows.Based on Toro-Vazquez splitting approach,the new scheme splits inviscid flux into convective system and pressure system.This method introduces Mach number splitting function and numerical sound speed to evaluate advection system.Meanwhile,pressure diffusion term,pressure momentum flux,interface pressure and interface velocity are constructed to measure pressure system.Then,typical test problems are utilized to systematically assess the robustness and accuracy of the resulting scheme.Matrix stability analysis and a series of numerical cases,such as double shear-layer problem and hypersonic viscous flow over blunt cone,demonstrate that TVAP scheme achieves excellent low diffusion,shock stability,contact discontinuity and low-speed resolution,and is potentially a good candidate for wide-ranging Mach number flows.

Airfoil Aeroelastic Flutter Analysis Based on Modified Leishman-Beddoes Model at Low Mach Number

Based on modified Leishman-Beddoes （L-B） state space model at low Mach number （lower than 0.3）, the airfoil aeroelastic system is presented in this paper. The main modifications for L-B model include a new dynamic stall criterion and revisions of normal force and pitching moment coefficient. The bifurcation diagrams, the limit cycle oscillation （LCO） phase plane plots and the time domain response figures are applied to investigating the stall flutter bifurcation behavior of airfoil aeroelastic systems with symmetry or asymmetry. It is shown that the symmetric periodical oscillation happens after subcritical bifurcation caused by dynamic stall, and the asymmetric periodical oscillation, which is caused by the interaction of dynamic stall and static divergence, only happens in the airfoil aeroelastic system with asymmetry. Validations of the modified L-B model and the airfoil aeroelastic system are presented with the experimental airload data of NACA0012 and OA207 and experimental stall flutter data of NACA0012 respectively. Results demonstrate that the airfoil aeroelastic system presented in this paper is effective and accurate, which can be applied to the investigation of airfoil stall flutter at low Mach number.

Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows

We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis of several Roe-type schemes is carried out.This analysis approach allows to propose a simple and effective modification to eliminate shock instability of the Roe method for hypersonic flows.A desirable feature of this modification is that it does not resort to any additional numerical dissipation on linear degenerate waves to suppress the shock instability.With an all Mach correction strategy,the modified Roe-type scheme is further extended to solve flow problems at all Mach numbers.Numerical results that are obtained for various test cases indicate that the new scheme has a good performance in terms of accuracy and robustness.

All Speed Scheme for the Low Mach Number Limit of the Isentropic Euler Equations

An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficultyin the low Mach regime. The key idea of our all speed scheme is the special semiimplicit time discretization, in which the low Mach number stiff term is divided intotwo parts, one being treated explicitly and the other one implicitly. Moreover, the fluxof the density equation is also treated implicitly and an elliptic type equation is derivedto obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared withprevious semi-implicit methods [11,13,29], firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs tobe solved implicitly which reduces much computational cost. We develop this semiimplicit time discretization in the framework of a first order Local Lax-Friedrichs (orRusanov) scheme and numerical tests are displayed to demonstrate its performances.