Numerical simulation of stabilization of the boundary layer on a surface with a porous coating in a supersonic separated flow

Stability of a supersonic (M _∞ = 5.373) boundary layer with local separation in a compression corner with a passive porous coating partly absorbing flow perturbations is considered by solving two-dimensional Navier-Stokes equations numerically. The second mode of disturbances of a supersonic boundary layer is demonstrated to be the most important one behind the boundary-layer reattachment point. The possibility of effective stabilization of these disturbances behind the reattachment point with the use of porous coatings is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 39–47, March–April, 2007.     

超音速混合层稳定性分析及增强混合的研究

利用流动稳定性提高超音速混合层的混合效率,对于提高超音速流的高效混合是一个有效途径。研究结果表明,有展向曲率的三维混合层中,三维扰动的增长率很大,且法向的掺混能力也较强,可以有效地增强混合。对于高马赫数来流的超音速混合层,这一特性依然存在,这将有利于提高高超音速混合层的混合能力。     

用格子Boltzmann方法数值模拟混合层中旋涡的合并过程

用格子Boltzmann方法计算混合层中的流动问题。在流场的入口处加不同频率、振幅和相位的小扰动,观察混合层中旋涡的演进机理,模拟二维混合层中旋涡合并现象。在基本扰动波的基础上,又加入频率为基本波频率一半的亚谐波,得到了两个涡合并的计算结果,当加入的亚谐波频率为基本波频率的三分之一时,得到了三个涡合并的计算结果。这些计算结果与已有文献的结果基本一致,显示用格子Boltzmann方法模拟混合层问题是可行的。     

Numerical modeling of perturbation propagation in a supersonic boundary layer

The growth of two-dimensional disturbances generated in a supersonic (M = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the second-mode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 33–44. Original Russian Text Copyright © 2004 by Egorov, Sudakov, Fedorov.     

Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Direct numerical simulations of the evolution of disturbances in a viscous shock layer on a flat plate are performed for a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵. Unsteady Navier-Stokes equations are solved by a high-order shock-capturing scheme. Processes of receptivity and instability development in a shock layer excited by external acoustic waves are considered. Direct numerical simulations are demonstrated to agree well with results obtained by the locally parallel linear stability theory (with allowance for the shock-wave effect) and with experimental measurements in a hypersonic wind tunnel. Mechanisms of conversion of external disturbances to instability waves in a hypersonic shock layer are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 84–91, May–June, 2007.     

Wavelet analysis of coherent structures in a three-dimensional mixing layer

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists. The project supported by the Research Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation for Outstanding Youth of China (19925210)     

Eulerian-Lagranigan simulation of aerosol evolution in turbulent mixing layer

The formation and evolution of aerosol in turbulent flows are ubiquitous in both industrial processes and nature. The intricate interaction of turbulent mixing and aerosol evolution in a canonical turbulent mixing layer was investigated by a direct numerical simulation (DNS) in a recent study (Zhou, K., Attili, A., Alshaarawi, A., and Bisetti, F. Simulation of aerosol nucleation and growth in a turbulent mixing layer. Physics of Fluids, 26, 065106 (2014)). In this work, Monte Carlo (MC) simulation of aerosol evolution is carried out along Lagrangian trajectories obtained in the previous simulation, in order to quantify the error of the moment method used in the previous simulation. Moreover, the particle size distribution (PSD), not available in the previous works, is also investigated. Along a fluid parcel moving through the turbulent flow, temperature and vapor concentration exhibit complex fluctuations, triggering complicate aerosol processes and rendering complex PSD. However, the mean PSD is found to be bi-modal in most of the mixing layer except that a tri-modal distribution is found in the turbulent transition region. The simulated PSDs agree with the experiment observations available in the literature. A different explanation on the formation of such PSDs is provided.     

Vortex structure simulation for supersonic mixing layers using nonlinear PSE method

The method of nonlinear parabolized stability equations (PSE) is applied in the simulation of vortex structures in compressible mixing layer. The spatially-evolving unstable waves, which dominate the vortex structure, are investigated through spatial marching method. The instantaneous flow field is obtained by adding the harmonic waves to basic flow. The results show that T-S waves do not keep growing exponentially as the linear evolution, the energy transfer to high order harmonic modes, and that finally all harmonic modes get saturated due to nonlinear interaction. The mean flow distortion induced by the nonlinear interaction between the harmonic modes and their conjugate harmonic ones, makes great change of the average flow and increases the thickness of mixing layer. PSE methods can well capture the two- and three-dimensional large scale nonlinear vortex structures in mixing layers such as vortex roll-up, vortex pairing, and Λ vortex.     

Numerical modeling of the receptivity of a supersonic boundary layer to acoustic disturbances

The receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate to acoustic disturbances is investigated on the basis of a numerical solution of the 2D Navier-Stokes equations. Numerical results obtained for fast and slow acoustic waves impinging on the plate at zero angle agree qualitatively with asymptotic theory. Calculations carried out for other angles of incidence of the acoustic waves reveal new features of the perturbation field in the neighborhood of the leading edge of the plate. It is shown that, due to visco-inviscid interaction, the shock formed near the leading edge may significantly affect the acoustic field and the receptivity.     

空间模式下可压缩气固两相混合层流动特性研究

采用Euler-Lagrange颗粒-轨道双向耦合模型对空间模式下含有固粒的二维可压缩混合层流场进行了研究。气相流场采用具有空间三阶精度的WNND格式进行数值模拟,固相方程采用单边三点差分离散。在考虑流场对固粒作用的同时,也计及了固粒对流场的反作用。在对流马赫数为0.5时,研究了颗粒相对密度、颗粒尺寸、Stokes数等因素对粒子运动和流场结构的影响。研究结果表明:在可压缩空间模式混合层中,固粒的Stokes数仍然是主要影响参数之一;相同Stokes数下不同密度的固粒对流场的干扰不同,轻固粒对流场的干扰明显要小。     

超声速平面混合层小激波的形成与演变

为了揭示超声速混合层中小激波形成机理及其与涡相互作用的演变过程,本文基于大涡模拟（LES）方法,结合五阶精度混合TCD／WENO格式,对超声速平面混合层在对流马赫数为Mc=0．65条件下的流场结构进行了数值模拟,数值结果详细描述了超声速混合层中小激波的形成过程。研究了小激波形成后,随涡运动而产生的变形、脱落及发展过程。同时,对混合层双涡合并过程中,小激波与相邻涡相互作用所产生的变形与演变过程进行了讨论。     

Numerical prediction of isothermally reacting mixing layer using vortex‐in‐cell and filtered density function

A large eddy simulation based on the filtered vorticity transport equation and the filtered density function (FDF) transport equation developed in an earlier study is extended to predict a chemically reacting flow with no heat release. The filtered vorticity transport equation is solved using the vortex‐in‐cell scheme in conjunction with the dynamic eddy viscosity subgrid‐scale models. The transport equation for FDF is solved using the Lagrangian Monte‐Carlo method. The methodology is tested on a chemically reacting spatially growing mixing layer with no heat release. The effects of Damköhler number (Da) on the concentration structure of the reacting mixing layer, the mean reactant and product concentrations and on the reactant FDF are investigated. It is shown that mixing has a greater effect on scalar field within the vortex structure as compared with the braid regions. Also for high Da, the reaction zones are mainly limited to the thin reacting interfacial zones, i.e. the contact zone between the reactants, whereas for low Da, the reacting zones are spread as reacting pockets within the vortex structure. The effects of Da on mean reactant and product concentrations, root‐mean‐square concentration fluctuations and probability density are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re_ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity (u_k), and decreases to 1.2u_k, which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length (η) and :β:γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.     

Numerical modeling of the stabilization of a supersonic flat-plate boundary layer by a porous coating

On the basis of a numerical solution of the two-dimensional Navier-Stokes equations, the stability and the receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate with a passive porous coating partially absorbing flow disturbances is studied. The results of direct numerical simulation are in good agreement with the data of the linear stability theory. The studies confirm the possibility of effectively stabilizing the second mode of the supersonic boundary layer using porous coatings.     

Numerical research on the coherent structure in the viscoelastic second-order mixing layers

I.IntroductionViscoelastict'olwsareprevalentinstiring,mixingandchemicalreactionofdilutepolymersolutions.SinceTomsdiscoveredthedragreducingeffectofpolylllerudditivesontul.bulent11owsin1948,1llilnystudiesonitsmechanisms11acebeendoneinviewofitsenormouspr'tcticillalld[lleorcticill\'al[Ics.UPtodata,1ilorcasonilbicilltcrl,rclilti')lls,II()wcvcr,ill'cstillun'lvtlilabjedLlctotiledilllcultiesillfoeviscoelasticdyllalnicsalldthetLlrbulellcetllcory.Al'cwpolymericadditiveshavinglittleeffectonthesolvent…     

Numerical simulation of gap effect in supersonic flows

The gap effect is a key factor in the design of the heat sealing in supersonic vehicles subjected to an aerodynamic heat load. Built on S-A turbulence model and Roe discrete format, the aerodynamic environment around a gap on the surface of a supersonic aircraft was simulated by the finite volume method. As the presented results indicate, the gap effect depends not only on the attack angle, but also on the Mach number.     

二维超声速混压式进气道的数值模拟

本文采用TVD格式求解二维可压非定常Euler方程组,对二维超声速混压式进气道进行了数值计算,首先模拟了后部压力对进气道的影响过程,当进气道的后部压力与入口压力的比值逐渐增加时,进气道内的正激波逐渐往前移动,当比值达到一个临界值,进气道将不起动.其次.通过对R52.1和R54.5两种进气道模型进行计算,对它们的总压恢复进行了对比.通过计算得到了喉道处曲线弧的曲率越大,进气道的总压损失越大,进气道也越难起动.     

可压缩气固混合层中离散相与连续相的相互作用研究

尽管已有许多文献采用数值模拟方法研究两相流问题,但主要是集中不可压流动方面.本文采用Eul-er-Lagrange颗粒-轨道双向耦合模型对时间模式下含有固粒的二维可压缩混合层流动进行了研究.气相流场采用非定常全Navier-Stokes方程描述,并应用具有空间三阶精度的WNND(Weighted Non-Oscillatory, Contai-ning No Free Parameters and Dissipative)格式进行数值高散.固相方程采用二阶单边三点差分离散.在考虑流场对固粒作用的同时,也计及颗粒对流场的反作用.主要研究混合层大尺度涡对颗粒扩散特性的影响及颗粒对流场结构的影响问题.在对流马赫数为0.5时,研究不同Stokes数颗粒在连续流场中的扩散特性,而在对流马赫数为0.8时研究了不同Stokes数颗粒对流场小激波结构的影响.     

Effect of suspended solid particles on unstability of two-dimension mixing layer

I.Intr0ducti0nThereexistsalargenumberofmixinglayernowswithsuspendedparticlesinindustryandagriculture,suchasintheburningcourseofc0alpowderandpowderyfuelandinthemixingcourseofpowderymaterials.Bytheoriticalandexperimenta1researches,wecanlearntheinteractionbe…