Modeling the Effect of Freestream Turbulence on Unsteady Boundary Layer Flow

We present a new version of the two-equation turbulence model, which makes it possible to calculate continuously the entire flow range from laminar to turbulent, including transition, in the case of a time-periodic, high-turbulence-level freestream. The influence of the parameters characterizing the harmonic fluctuations of the external velocity and the freestream turbulence intensity and scale on the parameters of the flat-plate flow are analyzed. A comparison of the numerical solutions with the experimental and theoretical data indicates the possibility of describing the wall flow properties on the basis of a quasi-stationary turbulence model, as the Reynolds number varies from low to high values.     

Numerical modeling of laminar-turbulent transition in a boundary layer at a high freestream turbulence level

Disturbances generated by external turbulence in the boundary layer on a flat plate set suddenly in motion are determined by numerically solving the Navier-Stokes equations. The results of direct numerical simulation of isotropic homogenous turbulence are taken as initial conditions. The solution obtained models laminar-turbulent transition in the flat-plate boundary layer at a high freestream turbulence level, time measured from the onset of the motion serving as the longitudinal coordinate. The solution makes it possible to estimate the effect of different factors, such as flow unsteadiness and nonlinearity and the characteristics of the freestream velocity fluctuation spectrum, on laminar-turbulent transition in the boundary layer.     

Tollmien-Schlichting wave generation by flow turbulence

The problem of freestream-turbulence-generated instability waves in the flat-plate boundary layer is solved on the basis of a nonlinear turbulence model admitting the deviation of the speed of propagation of vortex disturbances from the flow velocity. The solution obtained well describes the experimental dependence of the laminar-turbulent transition Reynolds number on the freestream turbulence degree.     

Numerical Modeling of the Development of a Streaky Structure in a Boundary Layer at a High Freestream Turbulence Level

The disturbances generated by external turbulence in the boundary layer on a flat plate set suddenly in motion are determined. A turbulent flow calculated by direct numerical simulation is taken as the initial conditions. The solution obtained simulates the initial stage of laminar-turbulent transition in the flat-plate boundary layer at a high turbulence level in the oncoming flow. The solution makes it possible to estimate the effects of different factors, such as nonstationarity, nonlinearity, and the parameters of the freestream velocity fluctuation spectrum, on disturbance enhancement in the boundary layer.     

Experimental study on the effect of unsteadiness on boundary layer development on a linear turbine cascade

 The results from an experimental investigation of unsteady boundary layer behavior on a linear turbine cascade are presented in this paper. To perform a detailed study on unsteady cascade aerodynamics and heat transfer, a new large-scale, high-subsonic research facility for simulating the periodic unsteady flow has been developed. It is capable of sequentially generating up to four different unsteady inlet flow conditions that lead to four different passing frequencies, wake structures, and freestream turbulence intensities. For a given Reynolds number, two different unsteady wake formations are utilized. Detailed unsteady boundary layer velocity. turbulence intensity, and pressure measurements are performed along the suction and pressure surfaces of one blade. The results display the transition and development of the boundary layer, ensemble-averaged velocity, and turbulence intensity. Received: 23 September 1996/Accepted: 19 February 1997     

Bypass transition receptivity modes

The prediction of bypass transition remains an important problem in many engineering applications. This is largely because there is no suitable theoretical model for bypass transition and predictions are made using empirical models. This paper presents numerical results for the receptivity of a zero pressure gradient boundary layer subjected to simple freestream waveforms which are the constituent parts of a turbulent flow field. Significant receptivities are only obtained for a minority of freestream waveforms and these lead to two types of flow structure in the boundary layer. The first type of flow structure is essentially two dimensional in nature and consists of two rows of counter-rotating spanwise vortices and is induced by freestream waves of large normal and spanwise wavelength and streamwise wavelengths approximately equal to the boundary layer thickness. The second type of flow structure are the streamwise streaks frequently observed in flow visualisation experiments. These streaks are induced by freestream waves of long streamwise and normal wavelength and spanwise wavelengths in the range of 14.5-46 θ (1.7-5.4δ). The freestream waves can be formed of velocity components in any direction, however the boundary layer is most receptive to fluctuations that lie in a plane perpendicular to the streamwise direction. The overall receptivity to a full spectrum of waves typical of freestream turbulence is considered and is shown to have similar characteristics to those from experiments.     

Apparent transition behavior of widely-used turbulence models

The Spalart–Allmaras and the Menter k–ω SST turbulence models are shown to have the undesirable characteristic that, for fully turbulent external flow computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart–Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a freestream turbulence level higher than the threshold or by making a simple change to one of the model constants. Near the area where turbulence initiates, the SST model exhibits sensitivity to numerical resolution, but its solutions are unique on a given grid. Inconsistent apparent transition behavior with grid refinement in this case does not stem from the presence of a degenerate fixed point. A nullcline analysis is used to visualize the local behavior of the model.     

Response of the Sphere Wake to Freestream Fluctuations

Direct numerical simulations have been used to investigate the response of the wake of a sphere to freestream fluctuations. This study has been motivated by the need to understand particle-induced turbulence enhancement in particulate flows. A sequence of simulations of flow past a sphere have been carried out where the frequency and amplitude of the freestream fluctuations and the flow Reynolds number has been varied systematically. It has been suggested that turbulence enhancement is primarily caused by vortex shedding from particles (Gore and Crowe, 1989; Hetsroni, 1989). Our simulations of the forced wake indicate that turbulence enhancement may be attributed to natural vortex shedding only when the freestream fluctuation level is low and the Reynolds number is greater than about 300. In addition to natural vortex shedding, the current simulations also suggest another mechanism for turbulence enhancement. It is found that in the presence of freestream fluctuations, the wake behaves like an oscillator and returns large amounts of kinetic energy to the surrounding fluid at resonance. This mechanism is not associated with natural vortex shedding and is therefore capable of enhancing freestream turbulence even at Reynolds numbers less than 300. Simulations also indicate that when the turbulence intensity of the carrier fluid is high, this resonance mechanism might be solely responsible for turbulence enhancement. Finally, our simulations also suggest a possible explanation for the correlation between turbulence enhancement and the ratio of the particle size to the size of energy containing eddies of turbulence found by Gore and Crowe (1989). Received 5 October 1999 and accepted 14 October 1999     

Sensitivity analysis of freestream turbulence parameters on stagnation region heat transfer using a neural network

A neural network has been used to predict stagnation region heat transfer in the presence of freestream turbulence. The neural network was trained using data from an experimental study to investigate the influence of freestream turbulence on stagnation region heat transfer. The integral length scale, Reynolds number, all three components of velocity fluctuations and the vorticity field were used to characterize the freestream turbulence. The neural network is able to predict 50% of the test data within ±1%, while the maximum error of any data point is under 3%. A sensitivity analysis of the freestream turbulence parameters on stagnation region heat transfer was performed using the trained neural network. The integral length scale is found to have the least influence on the stagnation line heat transfer, while the normal and spanwise turbulence intensities have the highest influence.     

Comparison of velocity and temperature measurements with simulations in a hypersonic wake flow

A hypersonic shock-tunnel flow around an axisymmetric model of a planetary entry probe is analyzed. Planar laser-induced fluorescence is applied to measure both the velocity and the rotational temperature everywhere in the central plane of the flow field. The experimental test case is compared to simulations using the direct simulation Monte Carlo (DSMC) method. While the Mach 9.7 flow at a freestream Reynolds number based on the model diameter of 35,000 is chemically frozen, effects of thermal non-equilibrium and localized rarefaction cannot be neglected. DSMC and measurements agree well within the outer wake, but disagree close to the centerline, where in particular the measured velocity is higher than values predicted by the simulations. The experimental results indicated a shorter recirculation region and increased local fluctuations in the free shear layer upstream of the wake recompression shock when compared to the simulation. These effects are attributed to incipient transition, which is not observed in the simulations, as the simulations did not model the effects of freestream fluctuations. Furthermore, measured and simulated vorticities are compared with theoretical predictions.     

壁面温度在多参数下对平板边界层的影响研究

为了得到壁面温度在不同来流速度、不同湍流强度条件下对边界层转捩与减阻的影响规律,本文采用Transitionk-kl-ω模型对低来流速度下无压力梯度的光滑平板进行了数值模拟。结果表明,随着来流速度的升高,壁温升高所起到的减阻效果更好,即高来流速度对壁面温度更为敏感。当来流处于中高湍流强度下时,壁温升高能起到推迟转捩的作用,且随着湍流强度的升高,转捩推迟的效果越好,但减阻效果正好相反;当来流处于低湍流强度下时,壁温升高会使得转捩提前发生。壁温升高抑制了边界层内流体的脉动程度,使得层流的稳态不易被破坏,流动更加稳定;同时,壁温升高使得边界层内流体的速度梯度减小,从而降低了壁面摩擦系数,故壁温升高能起到推迟边界层转捩与减阻的作用。     

Acoustic Field Effect on Laminar Turbulent Transition on a Swept Wing in the Favorable Pressure Gradient Region

The development of disturbances in a three-dimensional boundary layer on a swept wing model is studied both under natural conditions and for artificial excitation of traveling waves by an acoustic field. It is found that steady-state streamwise structures are formed in the three-dimensional boundary layer; under natural conditions a wave packet leading to turbulence is detected. When the flow is exposed to the action of an acoustic field at a frequency from the wave packet, disturbances whose velocity along the streamwise structures is equal to 0.55 of the oncoming flow velocity are formed, while the laminar-turbulent transition is displaced upstream.     

On the receptivity of the by-pass transition to the length scale of the outer stream turbulence

The effect of length scale on flat-plate by-pass boundary layer transition under free stream turbulence conditions has been investigated. Plane grids generated a constant value of 3 percent intensity turbulent fluctuations and five values of the dissipation length parameter in the range of 2.2 mm to 33.3 mm at 5 m/s flow velocity in the plane of the leading edge of the flat plate. The investigated boundary layer corresponds to the ERCOFTAC Test Case T3A+. Distributions of integral parameters as well as the statistical characteristics of the turbulent fluctuations were measured. They document a significant effect of turbulence length scale on the onset and the end of by-pass transition. It was found that the onset of the final stage of transition comes on later in `fine-grained' turbulence than in the case of large free stream turbulence length scale. At the same time, the extent of the transition region shortens with decreasing length scale. Nevertheless, the transition process terminates sooner in a flow with a large turbulence length scale than in a flow with a small one. An attempt has been made to describe these observations quantitatively.     

Mechanism of three-dimensional boundary-layer receptivity

Boundary-layer receptivity is always a hot issue in laminar-turbulent transition. Most actual laminar-turbulent transitions belong to three-dimensional flows. An infinite back-swept flat-plate boundary layer is a typical three-dimensional flow. Study of its receptivity is important both in theory and applications. In this paper, a freestream turbulence model is established. A modified fourth-order Runge-Kutta scheme is used for time marching, and compact finite difference schemes are used for space discretization. On these bases, whether unsteady cross-flow vortices can be excited in the three-dimensional boundary layer(the infinite back-swept flat-plate boundary layer) by free-stream turbulence is studied numerically. If so, effects of the level and the direction of free-stream turbulence on the three-dimensional boundary-layer receptivity are further studied. Differences of the three-dimensional boundary-layer receptivity are then discussed by considering the non-parallel effect, influence of the leading-edge stagnation point of the flat plate, and variation of the back-swept angle separately. Intensive studies on the three-dimensional boundary-layer receptivity will benefit the development of the hydrodynamic stability theory, and provide a theoretical basis for prediction and control of laminar-turbulent transition.     

Stability of a spanwise nonuniform boundary layer flow

The linear stability of a boundary layer flow with a spanwise-periodic nonuniformity in the velocity profile is investigated. This flow can be considered as a model of a streaky structure occurring in the boundary layer at a high freestream turbulence level. It is shown that for a small nonuniformity amplitude symmetric modes similar to Tollmien-Schlichting waves are the most unstable. At higher nonuniformity amplitudes, antisymmetric modes, qualitatively different from Tollmien-Schlichting waves and having a larger phase velocity, are the most amplified. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 54–63, November–December, 1998. The study was carried out with the support of the International Scientific and Technical Center (project No. 199-95) and the Russian Foundation for Basic Research (project No. 95-01-01201a).     

Toward low‐noise synthetic turbulent inflow conditions for aeroacoustic calculations

The accuracy of boundary conditions for computational aeroacoustics is a well‐known challenge, due in part to the necessity of truncating the flow domain and replacing the analytical boundary conditions at infinity with numerical boundary conditions. In particular, the inflow boundary condition involving turbulent velocity or scalar fields is likely to introduce spurious waves into the domain, therefore degrading the flow behavior and deteriorating the physical acoustic waves. In this work, a method to generate low‐noise, divergence‐free, synthetic turbulence for inflow boundary conditions is proposed. It relies on the classical view of turbulence as a superposition of random eddies convected with the mean flow. Within the proposed model, the vector potential and the requirement that the individual eddies must satisfy the linearized momentum equations about the mean flow are used. The model is tested using isolated eddies convected through the inflow boundary and an experimental benchmark data for spatially decaying isotropic turbulence. Copyright © 2013 John Wiley & Sons, Ltd.     

Experience Gained Using Second-Moment Closure Modeling for Transitional Flows Due to Boundary Layer Separation

This paper presents detailed information on the experience gained during the attempts to model a set of transitional flows due to boundary layer separation. These flows are developed on a flat plate with a semi-circular leading edge and they have been coded by the ERCOFTAC Special Interest Group on Transition, as T3L flows. Different freestream velocities and turbulence intensities configure these transitional flows and, by consequence, govern the transition mechanism, resulting in larger or smaller transitional regions. The modeling of the T3L flows has been performed by adopting a low-Reynolds number second-moment closure turbulence model. The results showed satisfactory agreement with the experimental measurements, although some difficulties regarding successful convergence have been faced. The final conclusion is that turbulence modeling can present quite accurate results for transitional flows without any additional use of ad-hoc modifications or additional equations based on various transition models and intermittency transport modeling.     

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time-stepping scheme with a stability-bound local time step, while the turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. Low-Reynolds-number modifications to the original two-equation model are incorporated in a manner which results in well-behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.     

Correlations for modeling transitional boundary layers under influences of freestream turbulence and pressure gradient

This paper presents mathematical expressions for two significant parameters which control the onset location and length of transition in the γ–Re_θ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. In: ERCOFTAC International Symposium on Engineering Turbulence Modelling and Measurements]. The expressions are formulated and calibrated by means of numerical experiments for predicting transitional boundary layers under the influences of freestream turbulence and pressure gradient. It was also found that the correlation for transition momentum thickness Reynolds number needs only to be expressed in terms of local turbulence intensity, so that the more complex form that includes pressure gradient effects is unnecessary. Transitional boundary layers on a flat plate both with and without pressure gradients are employed to assess the performance of these two expressions for predicting the transition. The results show that the proposed expressions can work well with the model of Menter et al. (2005).