Modeling transonic weakly underexpanded turbulent jets

The results of the calculations of model and actual turbulent jet flows with shock waves at low supersonic Mach numbers are presented. The gasdynamic flow features characterizing shock reflection from a mixing layer are analyzed. A possible version of the modified model for the turbulent viscosity is proposed; the model makes it possible to improve the prediction of the shock (rarefaction wave) intensity distribution along jet flows.     

Numerical Investigation of Multi-Jet Channel Flows

The results of a numerical simulation of the three-dimensional outflow of a system of circular supersonic turbulent jets into a cocurrent supersonic (or subsonic) air flow in a partially bounded region are given. Solutions are obtained by the splitting method using a matrix sweep of the parabolized Navier-Stokes equations. Assuming that the flow is nonseparated in the boundary layer, features of the three-dimensional structure of the jet system are investigated as functions of the pressure ratio number and the jet and cocurrent flow Mach numbers.     

Effects of the jet-to-crossflow momentum ratio on a sonic jet into a supersonic crossflow

Numerical investigation of a transverse sonic jet injected into a supersonic crossflow was carried out using large-eddy simulation for a free-stream Mach number M = 1.6 and a Reynolds number Re = 1.38 × 10⁵ based on the jet diameter. Effects of the jet-to-crossflow momentum ratio on various fundamental mechanisms dictating the intricate flow phenomena, including flow structures, turbulent characters and frequency behaviors, have been studied. The complex flow structures and the relevant flow features are discussed to exhibit the evolution of shock structures, vortical structures and jet shear layers. The strength of the bow shock increases and the sizes of the barrel shock and Mach disk also increase with increasing momentum ratio. Turbulent characters are clarified to be closely related to the flow structures. The jet penetration increases with the increase of the momentum ratio. Moreover, the dominant frequencies of the flow structures are obtained using spectral analysis. The results obtained in this letter provide physical insight in understanding the mechanisms relevant to this complex flow.     

A computational study of supersonic disk-gap-band parachutes using Large-Eddy Simulation coupled to a structural membrane

Large-scale fluid-structure interaction simulations of compressible flows over flexible supersonic disk-gap-band parachutes are compared with matching experimental results. We utilize adaptive mesh refinement, large-eddy simulation of compressible flow coupled with a thin-shell structural finite-element model. The simulations are carried out in the regime where large canopy-area oscillations are present, around and above Mach 2, where strong nonlinear coupling between the system of bow shocks, turbulent wake and canopy is observed. Comparisons of drag history and its dependence on Mach number are discussed. Furthermore, it is observed that important dynamical features of this coupled system can only be reproduced when sufficient grid resolution is used. Lack of resolution resulted in incorrect flow-physics prediction and, consequently, incorrect fluid-structure interaction coupling.     

探测器对超音速刚性盘-缝-带型降落伞系统的影响

研究了流体初始马赫数为 2.0 时, 探测器的存在与否对刚性盘-缝-带型降落伞系统气动减速性能以及流场流体结构特性的影响. 对于非定常可压缩流体的数值模拟, 流场采用了三层块结构自适应网格加密技术, 配合混合形式的TCD (tuned center difference)和WENO (weighted essentially non-oscillatory)计算格式以及基于拉伸涡亚格子模型的大涡模拟方法来处理超音速流中的激波以及大尺度湍流旋涡结构等. 结果表明: 无探测器时, 降落伞系统的流场结构稳定, 扰动较小; 有探测器存在时, 探测器后端的湍流尾迹和伞衣内部逆向运动溢出的流体与伞衣前端的弓形激波周期性的相互作用, 使得激波位置发生前移、激波倾角变小, 伞衣内部流场难以达到平衡稳定状态. 这加剧了降落伞系统的气动阻力振荡脉动变化, 降低了降落伞系统气动阻力系数, 同时也使得降落伞系统流场尾迹结构更加复杂.      

Mathematical modeling of jet interaction with a high-enthalpy flow in an expanding channel

Results of modeling the interaction of a plane supersonic jet with a supersonic turbulent high-enthalpy flow in a channel are reported. The problem is solved in a two-dimensional formulation at external flow Mach numbers M_∞ = 2.6 and 2.8 and at high values of the total temperature of the flow T ₀ = 1800–2000 K. The mathematical model includes full averaged Navier-Stokes equations supplemented with a two-equation turbulence model and an equation that describes the transportation of the injected substance. The computations are performed by using the ANSYS Fluent 12.1 software package. Verification of the computational technique is performed against available experimental results on transverse injection of nitrogen and helium jets. The computed and experimental results are demonstrated to agree well. For the examined problems, in addition to surface distributions of characteristics, fields of flow parameters are obtained, which allow one to reproduce specific features that can be hardly captured in experiments. Parametric studies show that an increase in the angle of inclination and the mass flow rate of the jet leads to an increase in the depth of jet penetration into the flow, but more intense separated flows and shock waves are observed in this case.     

A ghost-cell immersed boundary method for large-eddy simulations of compressible turbulent flows

A methodology to perform a ghost-cell-based immersed boundary method (GCIBM) is presented for simulating compressible turbulent flows around complex geometries. In this method, the boundary condition on the immersed boundary is enforced through the use of ‘ghost cells’ that are located inside the solid body. The computations of variables on these ghost cells are achieved using linear interpolation schemes. The validity and applicability of the proposed method is verified using a three-dimensional (3D) flow over a circular cylinder, and a large-eddy simulation of fully developed 3D turbulent flow in a channel with a wavy surface. The results agree well with the previous numerical and experimental results, given that the grid resolution is reasonably fine. To demonstrate the capability of the method for higher Mach numbers, supersonic turbulent flow over a circular cylinder is presented. While more work still needs to be done to demonstrate higher robustness and accuracy, the present work provides interesting insights using the GCIBM for the compressible flows.     

Effects of Compressibility and Shock-Wave Interactions on Turbulent Shear Flows

Compressibility effects are present in many practical turbulent flows, ranging from shock-wave/boundary-layer interactions on the wings of aircraft operating in the transonic flight regime to supersonic and hypersonic engine intake flows. Besides shock wave interactions, compressible flows have additional dilatational effects and, due to the finite sound speed, pressure fluctuations are localized and modified relative to incompressible turbulent flows. Such changes can be highly significant, for example the growth rates of mixing layers and turbulent spots are reduced by factors of more than three at high Mach number. The present contribution contains a combination of review and original material. We first review some of the basic effects of compressibility on canonical turbulent flows and attempt to rationalise the differing effects of Mach number in different flows using a flow instability concept. We then turn our attention to shock-wave/boundary-layer interactions, reviewing recent progress for cases where strong interactions lead to separated flow zones and where a simplified spanwise-homogeneous problem is amenable to numerical simulation. This has led to improved understanding, in particular of the origin of low-frequency behaviour of the shock wave and shown how this is coupled to the separation bubble. Finally, we consider a class of problems including side walls that is becoming amenable to simulation. Direct effects of shock waves, due to their penetration into the outer part of the boundary layer, are observed, as well as indirect effects due to the high convective Mach number of the shock-induced separation zone. It is noted in particular how shock-induced turning of the detached shear layer results in strong localized damping of turbulence kinetic energy.     

Nonlinear Instability in the Region of Laminar-Turbulent Transition in Supersonic Three-Dimensional Flow over a Flat Plate

Direct numerical simulation is applied to obtain laminar-turbulent transition in supersonic flow over a flat plate. It is shown that, due to the nonlinear instability, Tollmien–Schlichting waves generated in the boundary layer lead to the formation of oblique disturbances in the flow. These represent a combination of compression and expansion waves, whose intensities can be two orders higher than that of external harmonic disturbances. The patterns of the three-dimensional flow over the plate are presented and the structures of the turbulent flat-plate boundary layers are described for the freestream Mach numbers M = 2 and 4.     

Shock structure in separated nozzle flows

In the case of high overexpansion, the exhaust jet of the supersonic nozzle of rocket engines separates from nozzle wall because of the large adverse pressure gradient. Correspondingly, to match the pressure of the separated flow region, an oblique shock is generated which evolves through the supersonic jet starting approximately at the separation point. This shock reflects on the nozzle axis with a Mach reflection. Thus, a peculiar Mach reflection takes place whose features depend on the upstream flow conditions, which are usually not uniform. The expected features of Mach reflection may become much difficult to predict, depending on the nozzle shape and the position of the separation point along the divergent section of the nozzle.      

Direct numerical simulation of the transition to turbulence in a supersonic boundary layer on smooth and rough surfaces

Direct numerical simulations of instability development and transition to turbulence in a supersonic boundary layer on a flat plate are performed. The computations are carried out for moderate supersonic (free-stream Mach number M = 2) and hypersonic (M = 6) velocities. The boundary layer development is simulated, which includes the stages of linear growth of disturbances, their nonlinear interaction, stochastization, and turbulent flow formation. A laminar–turbulent transition initiated by distributed roughness of the plate surface at the Mach number M = 2 is also considered.     

Large-eddy Simulation of Film Cooling Flows with Variable Density Jets

The present paper investigates the impact of the velocity and density ratio on the turbulent mixing process in gas turbine blade film cooling. A cooling fluid is injected from an inclined pipe at α=30° into a turbulent boundary layer profile at a freestream Reynolds number of Re_∞ = 400,000. This jet-in-a-crossflow (JICF) problem is investigated using large-eddy simulations (LES). The governing equations comprise the Navier–Stokes equations plus additional transport equations for several species to simulate a non-reacting gas mixture. A variation of the density ratio is simulated by the heat-mass transfer analogy, i.e., gases of different density are effused into an air crossflow at a constant temperature. An efficient large-eddy simulation method for low subsonic flows based on an implicit dual time-stepping scheme combined with low Mach number preconditioning is applied. The numerical results and experimental velocity data measured using two-component particle-image velocimetry (PIV) are in excellent agreement. The results show the dynamics of the flow field in the vicinity of the jet hole, i.e., the recirculation region and the inclination of the shear layers, to be mainly determined by the velocity ratio. However, evaluating the cooling efficiency downstream of the jet hole the mass flux ratio proves to be the dominant similarity parameter, i.e., the density ratio between the fluids and the velocity ratio have to be considered.     

Visual observations of supersonic transverse jets

We present experimental results on penetration of round sonic and supersonic jets normal to a supersonic cross flow. It is found that penetration is strongly dependent on momentum ratio, weakly dependent on free-stream Mach number, and practically independent of jet Mach number, pressure ratio, and density ratio. The overall scaling of penetration is not very different from that established for subsonic jets. The flow is very unsteady, with propagating pressure waves seen emanating from the orifice of helium jets.     

Effect of flow nonparallelism on instability of the Taylor-Görtler waves in supersonic axisymmetric jets

Within the framework of the linear theory of hydrodynamic stability, the characteristics of the Taylor-Görtler waves are numerically simulated at the initial section of a supersonic axisymmetric jet taking into account the effects of flow nonparallelism and expansion. The special features of the streamwise dynamics of the growth rates of various wave components for turbulent. weakly nonisobaric, and laminar jets are studied. It is shown that the growth rates depend strongly on the quantity on which their determination is based, the position of the point where it is measured, and the flow regime. Some experimental results are discussed, and a method for determining the growth rates is proposed.     

Numerical simulation of fully-developed compressible flows over wavy surfaces

Rough surfaces are common on high-speed vehicles, for example on heat shields, but compressibility is not usually taken into account in the flow modelling other than through the mean density. In the present study, supersonic fully-developed turbulent rough wall channel flows are simulated using direct numerical simulation to investigate whether strong compressibility effects significantly alter the mean flow and turbulence properties across the channel. The simulations were run for three different Mach numbers M = 0.3, 1.5 and 3.0 over a range of wall amplitude-to-wavelength ratios from 0.01 to 0.08, corresponding to transitionally and fully rough cases respectively. The velocity deficit values are found to decrease with increasing Mach number. It is also found that at Mach 3.0 significant differences occur in the mean flow and turbulence statistics throughout the channel and not just in a roughness sublayer. These differences are found to be due to the presence of strong shock waves created by the peaks of the roughness elements.     

Direct Numerical Simulation of a Supersonic Base Flow Behind a Circular Cylinder

A supersonic flow in the near wake behind a cylinder is considered. Base pressure distributions behind a circular cylinder for various Mach numbers M_∞ are obtained and analyzed by means of direct numerical simulation based on high-order approximation algorithms. For M_∞ = 2.46, the results obtained in the present study are compared with available experimental and numerical data. Generation of turbulent kinetic energy is calculated for various Mach numbers.     

Analysis of the nozzle exit flow parameter effect on the turbulence characteristics and the noise level in jets issuing from nozzles of different types

The flow, turbulence, and noise parameters of cold and hot jets flowing out of nozzles of different types at subsonic and supersonic velocities are calculated using the high-resolution RANS/ILES method. The effect of the Mach number and the temperature at the nozzle exit on the flow features, the turbulent fluctuations of the velocity, the static pressure, and the temperature, together with the overall noise level is analyzed for all the jets considered. The accuracy of the calculations is confirmed by means of comparing with the available experimental data concerning certain parameters.     

基于扰动方程的超音速轴对称射流马赫波辐射研究

超音速不稳定波是导致剪切流失稳和转捩的主要不稳定模态,这种模态以马赫波的形式辐射到远场,从而产生强烈的声场。采用线性稳定性理论和非线性扰动方程(NLDE)分析,计算超音速轴对称射流不稳定波的扰动演化(Ma=2.1),对马赫波辐射进行研究,包括马赫波辐射方向、辐射源位置,以及随斯特劳哈尔数的变化情况。研究结果表明,在超音速轴对称射流中,马赫波沿固定方向辐射向远方,不稳定波相位沿另一方向传播,这两个方向相互正交;马赫波辐射源位置位于不稳定波压力幅值最大处;斯特劳哈尔数St越大,马赫波辐射的能力越强,辐射区域越集中。