Model for Asymmetry of Shock/Boundary Layer Interactions in Nozzle Flows

The reason for the asymmetry phenomenon of shock/boundary layer interactions(SBLI)in a completely symmetric nozzle with symmetric flow conditions is still an open question.A model for the asymmetry of nozzle flows was proposed based on the properties of fluid entrainment in the mixing layer and momentum conservation.The asymmetry model is deduced based on the nozzle flow with restricted shock separation,and is still applicable for free shock separation.Flow deflection angle at nozzle exit is deduced from this model.Steady numerical simulations are conducted to model the asymmetry of the SBLIs in a planar convergent-divergent nozzle tested by previous researchers.The obtained values of deflection angle based on the numerical results of forced symmetric nozzle flows can judge the asymmetry of flows in a nozzle at some operations.It shows that the entrainment of shear layer on the separation induced by SBLTs is one of the reasons for the asymmetry in the confined SBLIs.

Parallelization strategies for resolved simulations of fluid-structure-particle interactions

Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary(IB)method developed in our previous work.For the moving structure modeled using the sharp interface IB method,a recursive box method is developed for efficiently classifying the background grid nodes.For the particles modeled using the diffuse interface IB method,a‘master-slave’approach is adopted.For the particle-particle interaction(PPI)and particle-structure interaction(PSI),a fast algorithm for classifying the active and inactive Lagrangian points,which discretize the particle surface,is developed for the‘dry’contact approach.The results show that the proposed recursive box method can reduce the classifying time from 52seconds to 0.3 seconds.Acceptable parallel efficiency is obtained for cases with different particle concentrations.Furthermore,the lubrication model is utilized when a particle approaches a wall,enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem.At last,the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls.

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the practicability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disintegrates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17 % occurs with a triangular shape, while the maximum increase in aerodynamic efficiency（lift-to-drag ratio）of around 10 % happens with a rectangular shape at an angle of attack of 2.26？.

Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

HEATING CHARACTERISTICS OF BLUNT SWEPT FIN-INDUCED SHOCK WAVE TURBULENT BOUNDARY LAYER INTERACTION

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0.similar to 4.7) x 10(7)/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30 degrees for a sweepback angle of 67.6 degrees. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10 degrees and secondary separation were detected at deflection of theta greater than or equal to 20 degrees. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements at M greater than or equal to 6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers.

Numerical Simulation of Interaction Between Laminar Flow and Elastic Sheet

A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.

Gao's interacting shear flows( ISF) theory and its inferences and their applications

Gao＇s viscous/in-viscid interacting shear flows （ISF） theory, proposed by professor Gao Zhi in Institute of Mechanics, China Academy of Science, and its inferences and their applications in computational fluid dynamics （CFD） are reviewed and some subjects worthy to be studied are pro- posed in this paper. The flow-field and motion law of ISF, mathematics definition of strong viscous shear layer flow in ISF, ISF equations, wall-surface compatibility criteria （Gao＇s criteria ）, space scale variety law of strong viscous shear layer reveals flow mechanism and local space small scale triggered by strong interaction that cause some abnormal severe local pneumatic heating phenomenon in hypersonic flow. Gao＇s ISF theory was used in near wall flow, free ISF flow simulation and design of computing grids, Gao＇s wall-surface criteria were used to verify calculation reliability and accuracy of near wall flows, ISF theory approximate analytical result of shock waves-boundary layer interac- tion and ISF equations were used to obtain the numerical exact solution of local area flow （ such as stationary point flow）. Some new subjects, such as, improving near-wall turbulent models according to the turbulent flow simulation satisfying the wall-criteria and illustrating relation between grid-con- vergence based on the wall criteria and other convergence tactics, are suggested. The necessity of applying Gao＇s ISF theory and wall criteria is revealed. Difficulties and importance of hypersonic vis- cous/in-viscid interaction phenomenon were also emphasized.

TSTO并联分离激波/边界层干扰流动特性分析

针对两级入轨飞行器的缩比模型,通过试验与数值模拟相结合的方式,在马赫数6条件下开展典型级间距状态的激波/边界层干扰流场研究,详细分析干扰区壁面及空间的流动结构与特性。结果表明:试验中模型壁面边界层在激波入射之前为层流状态,在强激波干扰后迅速转捩为湍流状态,因此试验结果在第一道激波作用结束之前与层流计算结果吻合,而在第一道激波作用结束之后与湍流计算结果一致;激波/边界层干扰呈现复杂的三维流动特征和明显的开放结构,强激波在壁面形成的高压区呈弧状向下游展开,轨道级头部产生的入射激波在级间来回反射,强度依次递减;同时,干扰区内存在展向弯曲的主分离线与再附线、沿流向排列的二次分离线与再附线、流动剪切形成的旋涡结构以及包括鞍点、结点、焦点在内的临界点;层流边界层受到激波作用形成的分离区明显大于湍流边界层,同时开放特征更为显著。

A TIME DOMAIN BOUNDARY ELEMENT METHOD FOR WATER-SOLID IMPACT ANALYSIS

A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones.

激波/湍流边界层干扰中的自适应控制技术

从激波/湍流边界层干扰机理以及流动控制的迫切需求入手,从自适应涡流发生器、自适应鼓包、自适应微射流以及自适应次流循环四个方面对激波/湍流边界层干扰中的自适应控制技术研究进展进行了总结。分析认为,结合AI技术发展自适应流动控制技术,加速控制方式智能化,可作为新一代高超声速飞行器宽速域飞行的重要技术手段。具体来说,就是通过调节外加激励对高超声速飞行器不同区域实现局部流动加/减速、气动热防护、气动控制等功能,根据流场参数建立控制反馈回路,自适应调整局部流场结构,以满足工程实际需求。

Numerical analysis on shock-cylinder interaction using immersed boundary method

The problem of shock interaction with a rigid circular cylinder has been investigated using a compressible immersed boundary method coupled with high-order weighted-essentially non-oscillatory(WENO) scheme.First,the accuracy of the developed code is validated.Then,influences of the incident shock Mach number on the flow-field structure and dynamic drag coefficient,as well as time evolution of the flow field are studied.For different shock Mach number,the flow structure shows very different features.At a given dimensionless time,both the normalized shock detachment distance and the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder decreases with increasing shock Mach number.However,location of the upper triple point varies non-monotonically with shock Mach number.For a case with given shock Mach number,the trajectory of the upper triple point and the time evolution of the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder can both be predicted by linear correlation.Nevertheless,the time evolution of the normalized shock detachment distance is biased to be non-linear.Meanwhile,time evolution of force exerted on the cylinder is quite unsteady for a case with given shock Mach number and given cylinder diameter.For small shock Mach number,there exists a negative valley,and it disappears when the incident shock Mach number increases to a large value,e.g.,1.7.Furthermore,correlations to predict the occurrence of the peak drag and its value under different shock Mach numbers have been proposed.

Analysis of the Oscillatory Flows of Multiple Shock Waves in a Constant Area Duct

The oscillatory response of multiple shock waves to downstream perturbations in a supersonic flow is studied numerically in a rectangular duct.Multiple shock waves are formed inside the duct at a shock Mach number of 1.75.The duct has an exit height of H,and the effect of duct resonance on multiple shock oscillations is investigated by attaching exit ducts of lengths 0H,50H,and 150H.The downstream disturbance frequency varied from 10 Hz to 200 Hz to explore the oscillation characteristics of the multiple shock waves.The oscillatory response of shock waves under self-excited and forced oscillation conditions are analyzed in terms of wall static pressure,shock train leading-edge location,shock train length,and the size of the separation bubble.The extent of the initial shock location increases with an increase in exit duct length for the self-excited oscillation condition.The analysis of the shock train leading edge and the spectral analysis of wall static pressure variations are conducted.The variation in the shock train length is analyzed using the pressure ratio method for self-excited as well as forced oscillations.The RMS amplitude of the normalized shock train length(ζ_(ST))increases with an increase in the exit duct length for the self-excited oscillation condition.When the downstream perturbation frequency is increased,ζ_(ST)is decreased for exit duct configurations.For all exit duct designs and downstream forcing frequencies,the size of the separation bubble grows and shrinks during the shock oscillations,demonstrating the dependence on duct resonance and forced oscillations.

压缩拐角强激波边界层干扰直接数值模拟研究

激波/湍流边界层干扰是高超声速飞行中常见的流动现象,平板-压缩拐角存在于飞行器进气道、翼舵等,是研究激波/湍流边界层干扰的标准构型。采用直接数值模拟方法研究了马赫数6.0、40°压缩拐角的高超声速强激波/湍流边界层干扰问题。在上游湍流边界层内,近壁流动以高低速条带结构为主;当流动进入干扰区后,流向条带消失,同时形成具有三维特征的流动结构。在强激波作用下,分离长度超过10个边界层厚度。流动再附后,壁面摩阻、压力及其脉动峰值分别达到上游湍流边界层的8.9、36和124倍。干扰区内湍动能强度显著增加,其峰值是边界层峰值的6.4倍。研究发现激波运动、分离剪切层是湍动能强度增加的主要原因。

基于膨胀波效应的高超声速进气道肩部流动分离控制研究

为改善高超声速进气道唇口激波/附面层干扰诱导的肩部流动分离,从膨胀波及激波理论出发,推导出了膨胀波效应影响下的斜激波附面层干扰理论公式,获得了影响斜激波诱导分离的主要因素:膨胀角梯度、激波角及波前马赫数。在此基础上,开展了膨胀波效应影响下的流动分离控制研究,给出了膨胀波效应影响下斜激波诱导分离的判别及预测方法。结果表明:增大激波入射点处膨胀角梯度,可以显著减小甚至消除肩部流动分离;随着激波角增大,激波强度及逆压力梯度增加,分离区尺寸显著增大。而波前马赫数对分离区尺寸的影响不显著;在进口马赫数3.57~5.18,唇罩角度6°~10°范围内,当激波入射点处逆压比梯度小于250 m^(-1)时,斜激波诱导的流动分离消失,可为改善超声速/高超声速进气道内流道流动分离提供技术支撑。

Numerical Simulation of Low Reynolds Number Fluid-Structure Interaction with Immersed Boundary Method

This article introduces a numerical scheme on the basis of semi-implicit method for pressure-linked equations （SIMPLE） algorithm to simulate incompressible unsteady flows with fluid-structure interaction. The Navier-Stokes equation is discretized spatially with collocated finite volume method and Eulerian implicit method in time domain. The hybrid method that combines immersed boundary method （IBM） and volume of fluid （VOF） method is used to deal with rigid body motion in fluid domain. The details of movement of immersed boundary （IB） and calculation of VOF are also described. This method can be easily applied to any existing finite-volume-based computational fluid dynamics （CFD） solver without complex operation, with which fluid flow interaction of arbitrarily complex geometry can be realized on a fixed mesh. The method is verified by low Reynolds number flows passing both stationary and oscillating cylinders. The drag and lift coefficients acquired by the study well accord with other published results, which indicate the reasonability of the proposed method.

Scaling of interaction lengths for hypersonic shock wave/turbulent boundary layer interactions

The interaction length induced by Shock Wave/Turbulent Boundary-Layer Interactions(SWTBLIs)in the hypersonic flow was investigated using a scaling analysis,in which the interaction length normalized by the displacement thickness of boundary layer was correlated with a corrected non-dimensional separation criterion across the interaction after accounting for the wall temperature effects.A large number of hypersonic SWTBLIs were compiled to examine the scaling analysis over a wide range of Mach numbers,Reynolds numbers,and wall temperatures.The results indicate that the hypersonic SWTBLIs with low Reynolds numbers collapse on the supersonic SWTBLIs,while the hypersonic cases with high Reynolds numbers show a more rapid growth of the interaction length than that with low Reynolds numbers.Thus,two scaling relationships are identified according to different Reynolds numbers for the hypersonic SWTBLIs.The scaling analysis provides valuable guidelines for engineering prediction of the interaction length,and thus,enriches the knowledge of hypersonic SWTBLIs.

Strong interactions of incident shock wave with boundary layer along compression corner

The coherent structure and instability of the interaction of incident shock wave with boundary layer developing on a compression corner are experimentally studied.The experiments are carried out in a supersonic wind tunnel of Mach number 2.Particular attention is paid to shock patterns and unsteady shock motions induced by the separation bubble.The high-speed schlieren is used to visualize the flowfield evolution and to characterize the instability.The snapshot proper orthogonal decomposition of schlieren sequences is applied to investigate the primary coherent structure in the flowfield.Fast Fourier transform and continuous wavelet transformation are applied to characterize the instability.The results show that there are large-scale low-frequency oscillations of the shock waves and small-scale high-frequency pulsations in the separation region.The peak frequency of shock oscillation is mainly concentrated in the range of 100–1000 Hz.The pulsation of the small flow structure in the separation bubble is mainly concentrated above 12.5 k Hz.Based on the results of experimental analysis,the preliminary mechanism of the largescale instability of such interaction is obtained.

NATURE OF THE SURFACE HEAT TRANSFER FLUCTUATION IN A HYPERSONIC SEPARATED TURBULENT FLOW

This paper presents the results of an experimental study of the unsteady nature of a hypersonic sepa- rated turbulent flow.The nominal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5x10^7/m.The separated flow was generated using finite span forward facing steps.An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make mul- ti-channel measurements of the fluctuating surface heat trtansfer within the separated flow.Conditional sampling ana- lysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness.The compression waves con- verge into a single leading shock beyond the boundary layer.The shock structure is unsteady and undergoes large-scale motion in the streamwise direction.The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave.There exists a wide band of frequency of oscillations of the shock system.Most of the frequencies are in the range of 1-3 kHz.The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave.This inter mittent phenomenon is considered as the consequence of the large-scale shock system oscillations.Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed.

Passage shock wave/boundary layer interaction control for transonic compressors using bumps

Flow separation due to shock wave/boundary layer interaction is dominated in blade passage with supersonic relative incoming flow,which always accompanies aerodynamic performance penalties.A loss reduction method for smearing the passage shock foot via Shock Control Bump(SCB)located on transonic compressor rotor blade suction side is implemented to shrink the region of boundary layer separation.The curved windward section of SCB with constant adverse pressure gradient is constructed ahead of passage shock-impingement point at design rotor speed of Rotor 37 to get the improved model.Numerical investigations on both two models have been conducted employing Reynolds-Averaged Navier-Stokes(RANS)method to reveal flow physics of SCB.Comparisons and analyses on simulation results have also been carried out,showing that passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot for moderate adverse pressure gradient as well as suppression of boundary layer separations and secondary flow of low-momentum fluid within boundary layer.It is found that adiabatic efficiency and total pressure ratio of improved blade exceeds those of baseline at 95%-100%design rotor speed,and then slightly worsens with decrease of rotatory speed till both equal below 60%rated speed.The investigated conclusion implies a potential promise for future practical applications of SCB in both transonic and supersonic compressors.

左行运动激波主导的管内流动特性研究

为了分析左行运动激波主导的管内流动特征,本文采用非定常数值仿真方法,对亚声速进口条件下等直管道内左行运动激波传播与演化特性、左行运动激波/边界层干扰特征开展研究。研究结果表明:在出口周期性强压力脉动干扰下管内存在连续的左行运动激波,该左行运动激波传播特征具有相似性,激波强度、传播速度按幂函数规律衰减。气流经过左行运动激波后总压、总温、静压阶跃式升高,随后受膨胀波影响气流总压、总温、静压下降;左行运动激波/边界层干扰诱发形成翼型回流区,该回流区随运动激波强度衰减逐渐减小。理论与数值分析表明存在左行运动激波后速度为零和运动激波两侧总压相等的两个临界状态。波前马赫数低于临界值或左行运动激波强度高于临界值时,左行运动激波后为倒流、波后总压高于波前。