Simulation of the Effect of the Freestream Turbulence Parameters on Heat Transfer in an Unsteady Boundary Layer

A variant of the two-parameter turbulence model which makes it possible continuously to calculate a flow region with laminar, transition and turbulent regimes is proposed for investigating the flow under conditions of high freestream turbulence intensity. It is shown that the properties of the thermal transition can be theoretically described using the quasi-steady turbulence model in the case of periodic freestream velocity distribution. The numerical results are compared with theoretical and experimental data. The approach proposed is developed for determining the combined effect of the parameters of harmonic fluctuations of the external velocity and freestream turbulence on the heat transfer characteristics on a flat plate with different boundary conditions for the enthalpy.     

Comparison of turbulence models for attached boundary layers relevant to aeronautics

With a single numerical method the performance of three classes of turbulence models is compared for different types of attached boundary layers, for which direct numerical simulations or experiments are available in the literature. The boundary-layer equations are solved with the following turbulence models: an algebraic model, two-equation models (k-ε andk-ω), and a differential Reynolds-stress model. The test cases are the channel flow, and boundary layers with zero, favourable and adverse streamwise pressure gradient. The differential Reynolds-stress model gives the best overall performance, whereas the performance of the algebraic model and thek-ω model is reasonably good. The performance of thek-ε model is less good for boundary layers with a non-zero streamwise pressure gradient, but it can easily be improved by an additional source term in the ε equation, which is also applied in the considered differential Reynolds-stress model.     

The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer

In the current work, the boundary layers of an unsteady incompressible stagnation-point flow with mass transfer were further investigated. Similarity transformation technique was used and the similarity equation group was solved using numerical methods. Interesting observation is that there are multiple solutions seen for negative unsteadiness parameters, β. The influences of mass transfer, unsteadiness parameter, and Prandtl numbers on velocity and temperature profiles, wall drag, and wall heat fluxes were investigated and analyzed. The asymptotic behaviors for the similarity equations in limiting situations were theoretically analyzed. It is found that solutions exist for all mass transfer parameters for β≥−1. For a certain mass transfer parameter, there are two solutions when β_c<β<0; there is one solution for (β=β_c)∪(β≥0); there is no solution for β<β_c, where β_c is a critical unsteadiness parameter dependent on mass transfer parameter.     

Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers

Formation and evolution of secondary streamwise vortices in the compressible transitional boundary layers over a flat plate are studied using a direct numerical simulation method with high-order accuracy and highly effective non-reflecting characteristic boundary conditions. Generation and development processes of the secondary streamwise vortices in the complicated transitional boundary flow are clearly analyzed based on the of numerical results, and the effects on the formation of the ring-like vortex that is vital to the boundary layer transition are explored. A new mechanism forming the ring-like vortex through the mutual effect of the primary and secondary streamwise vortices is expressed.     

Effect of the freestream turbulence scale and the leading edge shape on boundary layer laminar-turbulent transition

The effect of the leading edge shape and the turbulence scale on laminar-turbulent transition in the flat-plate boundary layer due to grid turbulence is investigated. In the experiments, the turbulence scale was changed by a factor of three and the bluntness radius of the edge by a factor of four, all other factors being fixed. It is shown that on the plate with a sharp edge the fluctuation growth rate and the laminar-turbulent transition point depend nonmonotonically on the turbulence scale. On the blunt plate transition occurs considerably earlier than on the sharp plate.     

Turbulence structure in non-equilibrium boundary layers with favorable and adverse pressure gradients

An experimental study was conducted to document the turbulence in boundary layers on smooth walls subject to a favorable pressure gradient followed by a zero pressure gradient recovery and an adverse pressure gradient. Two component velocity profiles were acquired along the spanwise centerline of the test section, and velocity fields were obtained at the same locations in streamwise wall-normal and streamwise–spanwise planes using PIV. The FPG was shown to reduce the turbulence in the outer part of the boundary layer, reducing the transport of this turbulence and the effect of sweeps toward the wall. This reduced the inclination angle of the large structures and increased their length scale, particularly in the streamwise and spanwise directions. Recovery from the FPG to a ZPG was rapid. The APG reduced the near wall shear, resulting in a reduced effect of ejections relative to sweeps. The APG had an opposite but smaller effect on the shape and size of structures compared to the FPG.     

A note on the unsteady boundary layers over a flat plate

The unsteady boundary layer over a semi-infinite flat plate was investigated in this paper. The flow involves the unsteady flow over a flat plate with leading edge accretion or ablation. The momentum boundary layer was further analyzed and it was shown that the leading edge ablation had a similar effect to the wall mass injection or upstream wall movement making the fluid blown away from the wall. The thermal boundary layer of the same flow was also studied. Results show that the leading edge accretion or ablation can greatly change the fluid motion and the heat transfer characteristics.     

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.     

逆压梯度边界层未分离情况下的湍流模式适用性研究Turbulence model applicability for boundary layer flow with adverse pressure gradient in attached case

边界层逆压梯度作用下的流动是许多工程中的一个基础问题,由于逆压梯度作用,流动形态复杂,使得数值模拟有很大的难度。基于雷诺平均纳维‐斯托克斯RANS（Reynolds Averaged Navier‐Stokes）方程对二维平板逆压梯度边界层作数值计算研究,选取6种代表性的湍流模式,得到局部摩擦系数的数值解,与实验值比较,发现k‐ω模式具有很好的精度。基于该湍流模式,给出了湍动能分布,该结果有助于认识逆压梯度边界层流动的复杂特征。     

Turbulent spots in boundary layers in a free-piston shock-tunnel flow

In this paper, experiments to detect turbulent spots in the transitional boundary layers, formed on a flat plate in a free-piston shock tunnel flow, are reported. Experiments indicate that thin-film heat-transfer gauges are suitable for identifying turbulent-spot activity and can be used to identify parameters such as the convection rate of spots and the intermittency of turbulence.     

The effect of Reynolds number on boundary layer turbulence

A new facility for studying high Reynolds number incompressible turbulent boundary layer flows has been constructed. It consists of a moderately sized wind tunnel, completely enclosed by a pressure vessel, which can raise the ambient air pressure in and around the wind tunnel to 8 atmospheres. This results in a Reynolds number range of about 20:1, while maintaining incompressible flow. Results are presented for the zero pressure gradient flat plate boundary layer over a momentum thickness Reynolds number range 1500–15?000. Scaling issues for high Reynolds number non-equilibrium boundary layers are discussed, with data comparing the three-dimensional turbulent boundary layer flow over a swept bump at Reynolds numbers of 3800 and 8600. It is found that successful prediction of these types of flows must include length scales which do not scale on Reynolds number, but are inherent to the geometry of the flow.     

On the existence of a threshold value of the plate bluntness in the interference of an oblique shock with boundary and entropy layers

The heat transfer to sharp and slightly blunted flat plates in the zone of oblique shock incidence has been experimentally investigated. The experiments were performed at the Mach numbers M = 6, 8, and 10 and Reynolds numbers ranging from 0.2 × 10⁶ to 1.3 × 10⁶ corresponding to transitional (laminar-turbulent) flow in the shock-induced separation zone. Emphasis is placed on small values of the bluntness radius r. It is established that there exists a threshold value r _th of the radius that bounds the range of its influence on the heat transfer, namely, an increase in r to r _th leads to a sharp reduction in the maximum heat transfer coefficient in the interference zone, whereas a further increase (beyond r _th) has only a slight effect on the maximum heat transfer coefficient. The dependence of r _th on the main hypersonic flow parameters is analyzed. an explanation of the observable phenomena is given.     

Linear stability of three-dimensional boundary layers

Stability of compressible three-dimensional boundary layers on a swept wing model is studied within the framework of the linear theory. The analysis based on the approximation of local self-similarity of the mean flow was performed within the Falkner-Skan-Cooke solution extended to compressible flows. The calculated characteristics of stability for a subsonic boundary layer are found to agree well with the measured results. In the case of a supersonic boundary layer, the results calculated for a Mach number M = 2 are also in good agreement with the measured spanwise scales of nonstationary vortices of the secondary flow. The calculated growth rates of disturbances, however, are substantially different from the measured values. This difference can be attributed to a high initial amplitude of disturbances generated in the experiment, which does not allow the linear stability theory to be applied. The evolution of natural disturbances with moderate amplitudes is fairly well predicted by the theory. The effect of compressibility on crossflow instability modes is demonstrated to be insignificant. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 3–14, March–April, 2008.     

Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species

This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t~he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.     

Effect of an adverse pressure gradient on the streamwise Reynolds stress profile maxima in a turbulent boundary layer

It is widely accepted that in a turbulent boundary layer （TBL） with adverse pressure gradient （APG） an outer peak usually appears in the profile of streamwise Reynolds stress. However, the effect of APG on this outer peak is not clearly understood. In this paper, the effect of APG is analysed using the numerical and experimental results in the literature. Because the effect of upstream flow is inherent in the TBL, we first analyse this effect in TBLs with zero pressure gradient on flat plates. Under the individual effect of upstream flow, an outer peak already appears in the profile of streamwise Reynolds stress when the TBL continues developing in the streamwise direction. The APG accelerates the appearance of the outer peak, instead of being a trigger.     

Disturbed boundary layer flow with local time-dependent surface heating

Local flows in a laminar boundary layer flowing over surface heating elements are investigated. Mathematical models of disturbed flows are constructed on the basis of an asymptotic analysis and the similarity parameters are determined. The time-dependent local heating regimes ensuring control of separation and flow stability in the boundary layer are studied. The results of a numerical and analytic analysis are obtained.     

Dynamical characteristics of coherent structure in the outer region of turbulence boundary layer

In the present paper the coherent structures in the outer region of turbulent boundary layer were investigated experimentally and analytically. From the observation of the flow field over smooth wall, rough wall and sand wave wall, it was found that the direct effect of wall on the flow structure can reachy ⁺¹≈100, and both lateral and vertical vortices exist in the outer region, but the coherent structures in the outer region are mainly the formation, development and decay of the large-scale lateral vortices. By experimental and dynamical analysis, some influence factors and their relations associated with the dynamical process of lateral vortices were deduced. The project supported by the National Natural Science Foundation of China     

Receptivity of the inclined-cylinder attachment-line boundary layer to vortex perturbations

The receptivity of the boundary layer in the neighborhood of the attachment line of a cylinder inclined to the flow with respect to periodic vortex perturbations frozen into the stream is investigated. The problem considered simulates the interaction between external turbulence and the leading-edge swept wing boundary layer. It is shown that if the direction of the external perturbation vector is almost parallel to the leading edge, then the external perturbations are considerably strengthened at the outer boundary layer edge. This effect can cause laminar-turbulent transition on the attachment line at subcritical Reynolds numbers.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 72–85. Original Russian Text Copyright © 2004 by Ustinov.