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.

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。

圆柱及切割圆柱低Mach数绕流气动声辐射

以柱体绕流声辐射为研究对象,探讨低Mach数流动气动声定量预测方法。首先,理论分析Lighthill声类比理论与基于流体动力学压力对时间求导的扰动分离模型之间内在联系。其次,利用计算流体动力学对圆柱及其尾部切割后的亚临界流态绕流进行二维数值求解,分析两种湍流模型的流场计算效果。最后,分别使用声类比理论FW-H方程及扰动分离模型进行柱体绕流气动声辐射定量预测,分析声指向性及频谱特性。数值结果表明声类比理论与扰动分离模型预测的声辐射频谱相似,但前者的幅值略高;圆柱尾部切割使尾流脉动增强,导致声辐射变大。

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 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.

Design of a continuously variable Mach-number nozzle

A design method was developed to specify the profile of the continuously variable Mach-number nozzle for the supersonic wind tunnel. The controllable contour design technique was applied to obtaining the original nozzle profile, while other Machnumbers were derived from the transformation of the original profile. A design scheme, covering a Mach-number range of3.0<Ma<4.0, was shown to illustrate the present design technique. To fully validate the present design method, computational fluid dynamics(CFD) analyses were carried out to study the flow quality in the test area of the nozzle. The computed results indicate that exit uniform flow is obtained with 1.19% of the maximal Mach-number deviation at the nozzle exit. The present design method achieves the continuously variable Mach-number flow during a wind tunnel running.

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.

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.

THEORETICAL ANALYSIS OF A HIGH-MACH-NUMBER DILUTE INELASTIC GAS IMPINGING ON A SURFACE

We consider a problem of a 2-dimensional high-Mach-number dilute inelastic gas originating from infinity impinging on an oblique surface of infinite length. By analyzing probabilities of particle-particle collisions, we derive an analytical formula for the mean force experienced by the surface when the system is dilute. We also derive conditions for the validity of our theory.

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.

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.

来流Mach数连续变化下的激波串运动特性

为了研究入射激波变化的隔离段内激波串的运动特性,设计并搭建了直连式变Mach数实验系统,捕捉了相同来流Mach数变化速率、不同背压变化速率下激波串的运动行为,揭示了入射激波与背压同时变化对激波串运动的影响机理。入射激波与背压同时变化时,共有3个方面的因素会影响激波串整体的上下游运动趋势,其一,Mach数变化,Mach数增大导致激波串向下游运动,该影响随Mach数增大逐渐减弱;其二,背景波系移动,背景激波反射点靠近激波串前缘时,可能引起激波串的突跳;其三,背压压比变化,背压压比增大时激波串向上游运动,该影响随背压压比增大逐渐增强。三方面因素共同作用下激波串表现出复杂的运动。

Modeling and Validation of Base Pressure for Aerodynamic Vehicles Based on Machine Learning Models

The application of abruptly enlarged flows to adjust the drag of aerodynamic vehicles using machine learning models has not been investigated previously.The process variables(Mach number(M),nozzle pressure ratio(η),area ratio(α),and length to diameter ratio(γ))were numerically explored to address several aspects of this process,namely base pressure(β)and base pressure with cavity(βcav).In this work,the optimal base pressure is determined using the PCA-BAS-ENN based algorithm to modify the base pressure presetting accuracy,thereby regulating the base drag required for smooth flow of aerodynamic vehicles.Based on the identical dataset,the GA-BP and PSO-BP algorithms are also compared to thePCA-BAS-ENNalgorithm.The data for training and testing the algorithmswas derived using the regression equation developed using the Box-Behnken Design(BBD).The results show that the PCA-BAS-ENN model delivered highly accurate predictions when compared to the other two models.As a result,the advantages of these results are two-fold,providing:(i)a detailed examination of the efficiency of different neural network algorithms in dealing with a genuine aerodynamic problem,and(ii)helpful insights for regulating process variables to improve technological,operational,and financial factors,simultaneously.

马赫数10条件下冲压发动机内氢气燃烧特性试验

针对高马赫数超燃冲压发动机面临的高效燃烧组织挑战,本文提出了一种凹腔后缘激波强化的高马赫数超声速燃烧组织技术,并设计了一套燃烧室采用双侧对称布置凹腔结构的三维发动机试验模型。采用OH*基化学发光光谱诊断与壁面测压相结合的试验手段,在自由活塞驱动激波风洞的名义Ma=10流场中,对凹腔上游横向氢气射流的燃烧特性进行了研究,并讨论了模拟流场的重复性,给出了氢气燃烧演化特征、火焰稳定结构及释热特性。不同车次的总压等流场参数表明试验流场具有较高的重复性,可保障氢气燃烧特性的可复现性。通过观察试验过程中OH*基动态发光特征发现,在高焓激波风洞发动机试验中采用燃料提前喷注的方法使发动机流道在空气主流到来之前充盈大量的氢气,进而在主流到达发动机内的瞬间形成所谓“激波管流动-燃烧”效应,使来流空气与氢气接触面发生自点火与剧烈燃烧,产生显著不同于发动机正常工作情况下的点火与燃烧机制,但随着主流趋于平稳,“激波管流动-燃烧”效应消失,在高总温气流的自点火效应与凹腔后缘的X型激波耦合作用下,火焰稳定在凹腔上游近壁面区的氢气射流尾迹区和凹腔后缘附近的全流场中。通过分析壁面压力分布特征发现,凹腔后缘的X型激波实现了燃烧的强化与火焰的稳定,并获得了最显著的释热压升。这些结果表明高马赫数冲压发动机可利用凹腔后缘X型激波强化燃烧和稳定火焰。

表面微沟槽对压气机叶栅气动性能的影响

为减小叶型损失,在压气机叶栅叶片表面布置沿流向的对称V形微沟槽,采用数值模拟方法研究了沟槽宽度和顶角、沟槽间隔、沟槽覆盖范围、进口湍流度以及来流马赫数对叶栅气动性能的影响。结果表明,总压损失降低主要由吸力面沟槽产生,合理匹配沟槽几何参数、覆盖范围以及来流条件,可实现较优的减损效果。对吸力面局部带沟槽结构,相同冲角下无间隔沟槽的减损效果优于有间隔沟槽的减损效果,当无间隔沟槽顶角度为60°时减损效果最优;相同沟槽结构的减损效果与冲角相关。来流湍流度增加使得相同冲角下光滑叶片和带沟槽叶片的总压损失增大,相同沟槽结构在同一冲角下的减损效果及最优减损效果对应的冲角受来流湍流度影响。冲角不变时相同沟槽结构的减损效果随来流马赫数增大整体呈下降趋势,最佳减损效果对应的无量纲沟槽宽度和具有减损效果的无量纲沟槽宽度范围不同。当保持沟槽无量纲宽度不变和沟槽其它参数不变时,不同来流马赫数条件下的最佳减损效果及其对应的冲角不同,较低来流马赫数条件下最佳减损效果更突出。微沟槽能够减小壁面平均剪切应力和湍动能,降低湍流边界层损失,同时能够推迟边界层流动分离,使得叶型损失降低。