Numerical discussions on complete empirical correlation in Langtry＇s transition model

Recently, introducing a transition predicting model into the Reynolds averaged Navier-Stokes （RANS） environment has been paid more and more attention. Langtry proposed a correlation-based transition model in 2006, which was built strictly on local variables. However, two core correlations in the model had not been published until 2009. In this paper, after considerable analyses and discussions of the mechanism of this transition model and a series of numerical validations in the skin friction coefficient of flat plate boundary layers, a new correlation based on free-stream turbulence intensity is developed, and the empirical correlation of the transition onset momentum thickness Reynold number aiming at the hypersonic transition is improved. Low-speed/transonic airfoils and a hypersonic double wedge fiat are tested to prove the reliability and practicability of this correlation.     

Correlation of laminar-turbulent transition data over flat plates in supersonic/hypersonic flow including leading edge bluntness effects

The paper discusses flat plate boundary layer transition in supersonic/hypersonic flow conditions. Examination of experimental infrared thermography data illustrates the importance of the leading edge thickness and (non-) uniformity to the transition process. Such observations have triggered the collection of a wide range of experimental data on supersonic/hypersonic flat plate boundary layer transition, and a number of attempts to correlate this data with characteristic parameters including leading edge thickness. Results indicate a strong dependence of the relevant transition parameters on the pressure field in the transition region, as this is determined by the combined effects of leading edge thickness and boundary layer growth/viscous interaction, and particularly on the relative importance of the two effects. In fact, two distinct correlation zones are established, depending on whether the pressure distribution at the onset of transition is dominated by leading edge bluntness effects or by boundary layer growth and viscous interaction, thus limiting the observed data scatter to reasonable levels.Received: 13 August 2002, Accepted: 7 February 2003, Published online: 28 April 2003     

Shock tunnel study of spiked aerodynamic bodies flying at hypersonic Mach numbers

A three-component accelerometer balance system is used to study the drag reduction effect of an aerodisc on large angle blunt cones flying at hypersonic Mach numbers. Measurements in a hypersonic shock tunnel at a freestream Mach number of 5.75 indicate more than 50% reduction in the drag coefficient for a 120° apex angle blunt cone with a forward facing aerospike having a flat faced aerodisc at moderate angles of attack. Enhancement of drag has been observed for higher angles of attack due to the impingement of the flow separation shock on the windward side of the cone. The flowfields around the large angle blunt cone with aerospike assembly flying at hypersonic Mach numbers are also simulated numerically using a commercial CFD code. The pressure and density levels on the model surface, which is under the aerodynamic shadow of the flat disc tipped spike, are found very low and a drag reduction of 64.34% has been deduced numerically.     

转捩位置对全动舵面热气动弹性的影响

高超声速附面层的转捩预测一直是流体力学研究中的难点,转捩前后物面的摩擦系数和传热系数会发生改变,转捩位置的不同会影响到飞行器表面热环境,进而使得飞行器的气动弹性特性发生显著变化.鉴于高超声速附面层转捩预测的不确定性,本文分析了转捩位置对高超声速全动舵面热气动弹性的影响.首先分别用层流模型和湍流模型求解N-S方程,得到气动热环境,并对气动热进行参数化;然后在不同转捩位置情况下构造出不同转捩位置的热分布模型,基于此种温度分布,结合热应力和材料属性的影响分析结构的热模态,将结构模态插值到气动网格上,采用基于CFD的当地流活塞理论进行气动弹性分析.以M=6,H=15 km的某舵面为对象进行计算,结果表明:(1)随着转捩位置向后缘移动,结构频率上升,结构颤振速度呈增大趋势,转捩位置的变化能够带来颤振临界速度最大6%的变化量;(2)当转捩位置位于舵轴附近时,结构的颤振特性变化剧烈.通过刚度特性的分解和分析发现,导致颤振特性变化的主要因素在于舵轴的刚度特性变化,舵轴的影响量占整个结构刚度特性变化量的80%以上.     

Prediction of hypersonic boundary layer transition on sharp wedge flow considering variable specific heat

When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge.     

Development of an Intermittency Equation for the Modeling of the Supersonic/Hypersonic Boundary Layer Flow Transition

An intermittency transport equation is developed in this study to model the laminar-turbulence boundary layer transition at supersonic and hypersonic conditions. The model takes into account the effects of different instability modes associated with the variations in Mach numbers. The model equation is based on the intermittency factor γ concept and couples with the well-known SST k–ω eddy-viscosity model in the solution procedures. The particular features of the present model approach are that: (1) the fluctuating kinetic energy k includes the non-turbulent, as well as turbulent fluctuations; (2) the proposed transport equation for the intermittency factor γ triggers the transition onset through a source term; (3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ, which are often cost-ineffective with the modern CFD methods; (4) in the fully turbulent region, the model retreats to SST model. This model is validated with a number of available experiments on boundary layer transition including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition with a reasonably wide range of Mach numbers.     

Study of effect of a smooth hump on hypersonic boundary layer instability

Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier–Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.     

高超声速稀薄流中横向喷流干扰特性实验研究

喷流干扰是高超声速飞行高精度控制的一种有效手段,研究者们以往大部分都主要集中于连续流条件下喷流干扰效应的机理研究,并给出了喷流干扰流场的典型结构,而稀薄流条件下喷流干扰特性的实验数据还十分匮乏.本文利用JFX爆轰激波风洞产生高超声速稀薄自由流,基于平板模型开展不同喷流压力和自由来流参数对横向喷流干扰特性影响的实验研究,采用高速纹影成像及图像处理技术,获得稀薄流条件下喷流干扰流场演化过程及流场结构的变化规律.相比于无喷流条件形成的流场,横向喷流与稀薄自由流相互作用形成的流场结构更为复杂,喷流压力由于受到稀薄来流的扰动,斜激波会短暂穿透喷流干扰流场并延伸至楔形体上部.喷流干扰流场内桶状激波的影响范围随着喷流压力的升高而逐渐变宽,位于三波点上游的斜激波空间位置不会随喷流压力的变化而改变,而位于三波点下游的弓形激波则向上游移动,当喷流压力过低时,桶状激波不会与其他两种激波交汇形成三波点.高超声速稀薄来流压力的降低同样会使桶状激波的影响范围变宽,弓形激波同样也会向上游移动,但基本不会对斜激波空间位置产生任何影响.     

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.     

k-ω-γ模式对转捩影响因素的预测性能研究

高超声速边界层转捩的准确预测对飞行器的防热、减阻至关重要,而影响高超声速边界层转捩的因素众多.从模式角度出发研究边界层转捩的影响因素,采用k-ω-γ 转捩模式对5°圆锥的边界层转捩进行了数值分析,计算了不同头部钝度、来流雷诺数和湍流度情况下的边界层转捩,并与实验结果进行了对比. 研究结果表明:k-ω-γ 转捩模式基本能够反映头部钝度、来流雷诺数、来流湍流度对高超声速圆锥边界层转捩的影响规律,但对转捩后的热流峰值预测不准;从模式构造角度分析发现,雷诺数越高或头部钝度越小,层流区边界层越薄,k-ω-γ 转捩模式中第一、第二模态时间尺度增大,因此转捩起始位置提前;来流湍流度越大,等效脉动动能初值越大,导致层流区发展过程中等效脉动动能越大,因此转捩易于发生.      

Numerical Calculation of the Hypersonic Rarefied Transverse Flow Past a Cold Flat Plate

The hypersonic rarefied transverse flow past a flat plate is considered over a wide Knudsen number range. The problem is formulated for a model kinetic equation and solved using an implicit finite-difference second-order method. The results presented demonstrate the Knudsen and Mach number effect on the aerodynamic characteristics of the plate and the flow pattern.     

宽速域下神经网络对雷诺应力各向异性张量的预测

基于Pope修正的有效黏度假设,张量基神经网络(tensor based neural network,TBNN)构建了从雷诺平均方程湍流模型(RANS)的平均应变率张量和平均旋转率张量到高精度数值解的雷诺应力各向异性张量的映射.将高精度数值解用于TBNN的训练,从而使TBNN根据RANS求解的湍动能、湍流耗散率和速度...     

Experimental study of compressible boundary layer on a cone at angles of attack

Experimental study was conducted for boundarylayers on a sharp 5° half-angle cone of 400mm length at angles of attack. The model was tested in the T-326 hypersonic wind tunnel （ITAM） at freestream Mach number M = 5.95. Mean and fluctuation wall characteristics of the boundary layer are measured at 0°, 2°, 3° and 4° angles of attack for different stagnation pressures. Pulsation measurements are carried out by means of ALTP sensor. Pressure and temperature distributions along the model are obtained, and transition beginning and end locations have been found. Boundary layer stabilization with the increase of angle of attack and the decrease of stagnation pressure is observed. High frequency pulsations inherent to hypersonic boundary layer （second mode） have been detected.     

Numerical investigation of drag and heat reduction in hypersonic spiked blunt bodies

In this investigation, the effects of spike as retractable drag and aerodynamic heating reduction into the reentry Earth’s atmosphere for hemispherical body flying at hypersonic flow have been numerically studied. This numerical solution has been carried out for different length, shapes and nose configuration of spike. Additional modifications to the tip of the spike are investigated in order to obtain different bow shocks, including no spike, conical, flat and hemispherical aerodisk mounted. Unsteady compressible 3-D Navier–Stokes equations are solved with k ? ω (SST) turbulence model for a flow over a forward facing spike attached to a heat shield for a free stream Mach number of 6. The obtained numerical results are compared with the experimental ones, and the results shows acceptable verification. This analysis shows that the aerodisk is more effective than aerospike. The designs produced 60 and 15 % reduction in drag and wall temperature responses, respectively.     

Assessment of Uncertainties in Modeling of Laminar to Turbulent Transition for Transonic Flows

The effect of physical variability and uncertainty in model correlations on laminar-turbulent transition in transonic flows is computed using two different Stochastic Collocation methods. Physical variability in the boundary conditions is first investigated for a flow over a flat plate with and without pressure gradient to quantify the uncertainties on the skin friction distribution along the plate surface. Since the laboratory conditions for the flat plate test cases are well defined and the applied transition model has been tuned for these cases, good agreement with experiments is achieved and the variability in the output is low. The second investigated cases exhibit boundary layer transition on the surface of a highly loaded turbine guide vane under transonic flow conditions. Comparisons between the predicted and measured wall heat transfer are used to quantify uncertainties in the free stream turbulence and the model correlations that accounts for compressibility effects on the onset and extension of the bypass transition. The computational results show that the uncertainties have a significant impact on the transition location for the turbine guide vane simulations and, consequently, on the reliability of the predictions for compressible flows. The output uncertainty accounts to a large extent for the difference between the deterministic simulation and the experiments. The results from the Simplex Stochastic Collocation method are computationally more efficient than those of the Stochastic Collocation based on Clenshaw–Curtis quadrature.     

Non-intrusive generation of instability waves in a planar hypersonic boundary layer

The aim of this work is to show the possibility of non-intrusively exciting second-mode instability waves with arbitrary frequency and amplitude in a hypersonic, planar boundary layer, by means of optical methods. Surface heat flux sensors were used to measure natural and artificially excited instability waves on a flat plate at zero angle of attack. The measurements were made using a stream-wise array of flush-mounted high-frequency heat flux sensors. In addition, surface pressure sensors were applied and show the instability waves, as well. The possibility to generate such waves by locally heating the model surface is shown.     

平屋盖风压分布的数值模拟

基于Reynolds时均N-S方程和RSM模型对平屋面的风压分布进行了数值模拟,在此基础上系统研究了风向角、跨高比、地面粗糙度、风速等因素对屋面风压分布的影响,探讨了结构周围流场的绕流特性,最后根据屋面的结构形式及风压分布特点将屋面进行分区,给出了屋面在不同风向角下的分区风载体型系数以供工程设计参考。     

Critical transition Reynolds number for plane channel flow

The determination of the critical transition Reynolds number is of practical importance for some engineering problems. However, it is not available with the current theoretical method, and has to rely on experiments. For supersonic/hypersonic boundary layer flows, the experimental method for determination is not feasible either. Therefore,in this paper, a numerical method for the determination of the critical transition Reynolds number for an incompressible plane channel flow is proposed. It is basically aimed to test the feasibility of the method. The proposed method is extended to determine the critical Reynolds number of the supersonic/hypersonic boundary layer flow in the subsequent papers.     

Effect of glow discharge on hypersonic flat plate boundary layer

Glow discharge is introduced as an artificial disturbance to investigate the evolution of first-and second-mode instabilities in a hypersonic flat plate boundary layer.Experiments are conducted in a Mach 6.5 quiet wind tunnel using Rayleigh scattering visualization and particle image velocimetry(PIV). Detailed analysis of the experimental observations is provided. It is found that the artificially introduced 17 kHz disturbance,which belongs to the first-mode frequency band, can effectively enhance first-mode waves.Moreover, it can enhance second-mode waves even more intensely. Possible mechanisms to explain this phenomenon are discussed.     

Analysis and modelling of the relation between the shear rate and Reynolds stress tensors in transitional boundary layers

A non-linear eddy-viscosity transition model is presented, tuned by a large experimental data set describing transitional boundary layers. Data have been acquired by TR-PIV on a flat plate placed in a 2D converging-diverging channel with variable opening angle, allowing variation of the adverse pressure gradient, the free-stream turbulence intensity and the flow Reynolds number. Overall, 48 different combinations of these flow parameters encompass different modes of transition from bypass to separated-flow mechanisms, thus allowing fine tuning of the model, spanning significantly different conditions. The model is tuned locally as a function of the turbulent kinetic energy, a Reynolds number based on the wall distance and the ℓ₂-norm of the shear rate tensor. A first correlation determines the rotation for alignment of the principal axes of the shear and stress tensors. By a second correlation, the eigenvalues of the stress tensor are obtained. The non-linear eddy-viscosity relation reproduces the anisotropy of the turbulence field observed for both bypass and separated-flow transitional cases. The relation has been applied to another experimental data set that did not participate to the fitting of the model and that is characterized by a different range of Reynolds number and turbulence intensity and a significantly stronger adverse pressure gradient with respect to the tuning dataset. Such application further strengthens the capability of the proposed correlations, that can easily be implemented in existing CFD solvers.