Application of “POLIS” PIV system for measurement of velocity fields in a supersonic flow of the wind tunnels

Measurement results on the mean velocity fields and fields of velocity pulsations in the supersonic flows obtained by means of the PIV measurement set “POLIS” are presented. Experiments were carried out in the supersonic blow-down and stationary wind tunnels at the Mach numbers of 4.85 and 6. The method of flow velocity estimate in the test section of the blow-down wind tunnel was grounded by direct measurements of stagnation pressure in the setup settling chamber. The size of tracer particles introduced into the supersonic flow by a mist generator was determined; data on the structure of pulsating velocity in a track of an oblique-cut gas-dynamic whistle were obtained under the conditions of self-oscillations.     

Application of PIV to over-expanded supersonic flows: Possibilities and limits

Two-dimensional velocity distributions outside a Mach 2.0 supersonic nozzle have been investigated using a digital particle im age velocimetry (PIV). Mean velocities , vor ticity field and volume dilatation field were obtained from PIV images using 0 .33 μm titanium dioxide (TiO₂) particle. The seeding particle of larger size , 1.4 μrn Ti0₂, was also used for the experimental comparison of velocity lag downstream of shock waves. The results have been compared and analyzed with schlieren photographs for the locations of shock waves and over-expanded shock structure to inspect possibilities and limits of a PIV technique to over-expanded supersonic flows. It is found that although the quantitative velocity measurement using PIV on over-expanded supersonic flows with large velocity and pressure gradients is limited, the locations of normal shock and oblique shock waves can be resolved by the axial/radial velocity fields, and over-expanded shock structure can be predicted by vorticity field and volume dilatation field which are acquired from the spatial differential of the velocity field.     

钝锥绕流流动稳定性分析与转捩预报

研究了超音速钝锥绕流的稳定性和转捩点预报的数值计算方法,首先采用Euler方程求解钝锥绕流基本流场,用所得到的物面压力分布作为粘性边界层的外缘压力分布,给出了基本流场的初值;然后应用反迭代法与边界层渐近匹配的方法求解了钝锥边界层的稳定性方程,得到了钝锥边界层转捩数据.该方法可提高计算精度,节约计算时间.     

A coupled pressure-based computational method for incompressible/compressible flows

Pressure-based flow solvers couple continuity and linearized truncated momentum equations to derive a Poisson type pressure correction equation and use the well known SIMPLE algorithm. Momentum equations and the pressure correction equation are typically solved sequentially. In many cases this method results in slow and often difficult convergence. The current paper proposes a novel computational algorithm, solving for pressure and velocity simultaneously within a pressure-correction coupled solution approach using finite volume method on structured and unstructured meshes. The method can be applied to both incompressible and subsonic compressible flows. For subsonic compressible flows, the energy equation is also coupled with flow field and the density of fluid is obtained by equation of state. The procedure eliminates the pressure correction step, the most expensive component of the SIMPLE-like algorithms. The proposed coupled continuity-momentum-energy equation method can be used to simulate steady state or transient flow problems. The method has been tested on several CFD benchmark cases with excellent results showing dramatically improved numerical convergence and significant reduction in computational time.     

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.     

Simultaneous density and velocity measurements in a supersonic turbulent boundary layer

A novel technique for simultaneous measurements of instantaneous whole-field density and velocity fields of supersonic flows has been developed.The density measurement is performed based on the nano-tracer planar laser scattering(NPLS) technique,while the velocity measurement is carried out using particle image velocimetry(PIV).The present experimental technique has been applied to a flat-plate turbulent boundary layer at Mach 3,and the measurement accuracy of the density and velocity are discussed.Based on this new technique,the Reynolds stress distributions were also obtained,demonstrating that this is an effective means for measuring Reynolds stresses under compressible conditions.     

On the outflow conditions for spectral solution of the viscous blunt-body problem

The purpose of this paper is to study and identify suitable outflow boundary conditions for the numerical simulation of viscous supersonic/hypersonic flow over blunt bodies, governed by the compressible Navier–Stokes equations, with an emphasis motivated primarily by the use of spectral methods without any filtering. The subsonic/supersonic composition of the outflow boundary requires a dual boundary treatment for well-posedness. All compatibility relations, modified to undertake the hyperbolic/parabolic behaviour of the governing equations, are used for the supersonic part of the outflow. Regarding the unknown downstream information in the subsonic region, different subsonic outflow conditions in the sense of the viscous blunt-body problem are examined. A verification procedure is conducted to make out the distinctive effect of each outflow condition on the solution. Detailed comparisons are performed to examine the accuracy and performance of the outflow conditions considered for two model geometries of different surface curvature variations. Numerical simulations indicate a noticeable influence of pressure from subsonic portion to supersonic portion of the boundary layer. It is demonstrated that two approaches for imposing subsonic outflow conditions namely (1) extrapolating all flow variables and (2) extrapolation of pressure along with using proper compatibility relations are more suitable than the others for accurate numerical simulation of viscous high-speed flows over blunt bodies using spectral collocation methods.     

A quadrature-based LES/transported probability density function approach for modeling supersonic combustion

The joint-scalar probability density function (PDF) approach provides a comprehensive framework for large eddy simulation (LES) based combustion modeling. However, currently available stochastic approaches for solving the high-dimensional PDF transport equation can be error prone and numerically unstable in highly compressible shock-containing flows. In this work, a novel Eulerian approach called the direct quadrature method of moments (DQMOM) is developed for evolving the PDF-based supersonic combustion model. The DQMOM technique uses a set of scalar transport equations with specific source terms to recover the PDF. The new technique is coupled to a compressible LES solver through the energy equation. The DQMOM approach is then used to simulate two practical flow configurations: a supersonic reacting jet and a cavity-stabilized supersonic combustor. Comparisons with experimental data demonstrate the predictive accuracy of the method.     

Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the height of the free boundary on the density of the fluid. Self-similar continuous and discontinuous solutions are obtained for a system on a slope, and a solution is found to the initial discontinuity decay problem in this case.     

Supersonic flows with small perturbations in the presence of external effects in the flow. Part 1: “Thin body of revolution”

Axisymmetric supersonic flow about a thin body of revolution with an external energy supply and an external force localized near the body surface is considered in the linear approximation. An analytic theory is constructed for calculating spatial fields of flow parameters in this case for an arbitrary dependence of external effects on the longitudinal coordinate. Formulas are derived for the pressure ratio on the surface of the thin body of revolution. The results of calculations based on the analytic theory are in good agreement with numerical data obtained from the solution of hydrodynamic equations in the Euler approximation.     

A improved incompressible lattice Boltzmann model for time-independent flows

It is well known that the lattice Boltzmann equation method (LBE) can model the incompressible Navier-Stokes (NS) equations in the limit where density goes to a constant. In a LBE simulation, however, the density cannot be constant because pressure is equal to density times the square of sound speed, hence a compressibility error seems inevitable for the LBE to model incompressible flows. This work uses a modified equilibrium distribution and a modified velocity to construct an LBE which models time-independent (steady) incompressible flows with significantly reduced compressibility error. Computational results in 2D cavity flow and in a 2D flow with an exact solution are reported.     

基于格子Boltzmann方法的超声速非平衡流模拟

基于D1Q4可压缩格子Boltzmann模型,按照流通矢量分裂方法的思路,采用坐标旋转技术构造求解三维带化学反应Navier-Stokes方程对流通量求解器.结合有限体积法求解三维化学非平衡流Navier-Stokes方程,采用时间算子分裂算法解决化学反应刚性问题,数值模拟超声速化学非平衡流的三个经典算例.数值结果表明:在高马赫数下,采用D1Q4可压缩格子Boltzmann模型构造的三维对流通量求解器数值模拟中没有出现非物理解,同时在超声速化学非平衡流场中正确分辨激波、燃烧波等物理现象,精度和分辨率均较高,验证了本文构造的三维对流通量求解器的可靠性,拓宽了D1Q4可压缩格子Boltzmann模型的应用范围,为计算超声速化学非平衡流提供一种新方法.     

分区拼接网格算法数值模拟超声速复杂流场

以分区拼接网格数值模拟方法为研究对象,对二阶Godunov方法在拼接网格中流场的数值模拟进行了研究,发展了适用于Godunov格式的通量守恒型算法,结合二阶Godunov有限体积法离散非定常Euler方程,数值模拟了捆绑火箭及航天飞机的超声速流场,计算结果正确描述了流场中的激波相交、反射等干扰特性.     

Explicit algebraic Reynolds stress model for compressible flow turbulence

Algebraic Reynolds stress model (ARSM) is often employed in practical turbulent flow simulations. Most of previous works on ARSM have been carried out for incompressible flows. In the present paper, a new ARSM model is suggested for compressible flows. The model adopts a compressibility factor function involving the turbulent Mach number and the gradient Mach number. Compared to incompressible flow, explicit solution for ARSM for compressible flow can hardly be obtained due to dilatation terms. We propose approximate representations for these dilatation-related terms to obtain an explicit procedure for compressible flow turbulence. The model is applied to compressible mixing layer, supersonic flat-plate boundary and planar supersonic wake flow. It is found that the model works very well yielding results that are in good agreement with the DNS and the experimental data.     

The art and science of flow control – case studies using flow visualization methods

Active flow control (AFC) has been the focus of significant research in the last decade. This is mainly due to the potentially substantial benefits it affords. AFC applications range from the subsonic to the supersonic (and beyond) regime for both internal and external flows. These applications are wide and varied, such as controlling flow transition and separation over various external components of the aircraft to active management of separation and flow distortion in engine components and over turbine and compressor blades. High-speed AFC applications include control of flow oscillations in cavity flows, supersonic jet screech, impinging jets, and jet-noise control. In this paper we review some of our recent applications of AFC through a number of case studies that illustrate the typical benefits as well as limitations of present AFC methods. The case studies include subsonic and supersonic canonical flowfields such as separation control over airfoils, control of supersonic cavity flows and impinging jets. In addition, properties of zero-net mass-flux (ZNMF) actuators are also discussed as they represent one of the most widely studied actuators used for AFC. In keeping with the theme of this special issue, the flowfield properties and their response to actuation are examined through the use of various qualitative and quantitative flow visualization methods, such as smoke, shadowgraph, schlieren, planar-laser scattering, and Particle image velocimetry (PIV). The results presented here clearly illustrate the merits of using flow visualization to gain significant insight into the flow and its response to AFC.     

Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixtures

Unstructured adaptive grid flow simulation is applied to the calculation of high-speed compressible flows of inert and reactive gas mixtures. In the present case, the flowfield is simulated using the 2-D Euler equations, which are discretized in a cell-centered finite volume procedure on unstructured triangular meshes. Interface fluxes are calculated by a Liou flux vector splitting scheme which has been adapted to an unstructured grid context by the authors. Physicochemical properties are functions of the local mixture composition, temperature, and pressure, which are computed using the CHEMKIN-II subroutines. Computational results are presented for the case of premixed hydrogen–air supersonic flow over a 2-D wedge. In such a configuration, combustion may be triggered behind the oblique shock wave and transition to an oblique detonation wave is eventually obtained. It is shown that the solution adaptive procedure implemented is able to correctly define the important wave fronts. A parametric analysis of the influence of the adaptation parameters on the computed solution is performed.     

再入体头部粘性流场高分辨率格式数值模拟

TVD格式是目前数值研究以激波为主要特征之一的超声速、高超声速流场的最先进的算法之一。本文用二阶迎风TVD格式,对三种烧蚀外形的轴对称粘性流场和10°钝锥有攻角三维粘性流场进行了数值模拟,得到了高质量的头部脱体激波和与实验结果及直线推进法计算一致的物面压力分布,表明了TVD格式在再入体粘性绕流计算中的独特优势。     

Study of density field measurement based on NPLS technique in supersonic flow

Due to the influence of shock wave and turbulence, supersonic density field exhibits strongly inhomogeneous and unsteady characteristics. Applying traditional density field measurement techniques to supersonic flows yields three problems: low spatiotemporal resolution, limitation of measuring 3D density field, and low signal to noise ratio (SNR). A new method based on Nano-based Planar Laser Scattering (NPLS) technique is proposed in this paper to measure supersonic density field. This method measures planar transient density field in 3D supersonic flow by calibrating the relationship between density and concentration of tracer particles, which would display the density fluctuation due to the influence of shock waves and vortexes. The application of this new method to density field measurement of supersonic optical bow cap is introduced in this paper, and the results reveal shock wave, turbulent boundary layer in the flow with the spatial resolution of 93.2 μm/pixel. By analyzing the results at interval of 5 μs, temporal evolution of density field can be observed. Supported by the National Natural Science Foundation of China (Grant No. 10672178)     

强梯度复杂流场中的粒子动力学响应试验研究

示踪粒子在(高)超声速流场中的动力学响应是粒子成像测速等粒子示踪测量技术的关键问题之一.现有文献对粒子动力学响应的试验测量往往是通过单个斜激波响应的测量方法.然而,当示踪粒子用于测量高速飞行器发动机内部复杂的激波串流场时,粒子将经历由多道激波导致的速度、压力、黏性等剧烈变化.本文结合目前(高)超声速飞行器的研究热潮,重点关注示踪粒子在应用于发动机内部具有连续激波的复杂流场测量中存在的跟随性评估方面,开展了一系列的相关试验研究.包括测量超声速风洞的喷管出口速度分布以验证测试系统的性能,在马赫4.2和3.0流场中测量了粒子对二维10°和15°单斜劈绕流中的斜激波动力响应,并测量了模拟发动机内部连续梯度的双斜劈粒子斜激波动力响应.结合粒子动力学的理论模型,得到了各状态的粒子弛豫时间、弛豫距离、Stokes数.基于图像方法、统计学规律分析了激波非定常抖动对测量结果的影响,并对测量结果进行了修正.结果显示,相同斜劈角度下,马赫数越高,粒子的弛豫时间、弛豫距离就越大.但是在相同的来流马赫数下,斜劈角度越大,粒子的弛豫时间、弛豫距离反而减小.在强梯度之后由于流场的雷诺数和黏性系数变化剧烈,粒子的跟随性降低了大约5.7%,stokes数增加了约1%.虽然在本文条件下Stokes数仍满足超声速流场对粒子跟随性的要求,但粒子响应的降低无疑是值得关注的,尤其是当其被应用于具有更多连续梯度的复杂流场测量中.     

A multislope MUSCL method on unstructured meshes applied to compressible Euler equations for axisymmetric swirling flows

A finite volume method for the numerical solution of axisymmetric inviscid swirling flows is presented. The governing equations of the flow are the axisymmetric compressible Euler equations including swirl (or tangential) velocity. A first-order scheme is introduced where the convective fluxes at cell interfaces are evaluated by the Rusanov or the HLLC numerical flux while the geometric source terms are discretizated to provide a well-balanced scheme i.e. the steady-state solutions with null velocity are preserved. Extension to the second-order space approximation using a multislope MUSCL method is then derived. To test the numerical scheme, a stationary solution of the fluid flow following the radial direction has been established with a zero and nonzero tangential velocity. Numerical and exact solutions are compared for classical Riemann problems where we employ different limiters and effectiveness of the multislope MUSCL scheme is demonstrated for strongly shocked axially symmetric flows like in spherical bubble compression problem. Two other tests with axisymmetric geometries are performed: the supersonic flow in a tube with a cone and the axisymmetric blunt body with a free stream.