Reynolds Stresses in a Hypersonic Boundary Layer with Streamline Curvature-Driven Favorable Pressure Gradients

Author(s):  
Nathan Tichenor ◽  
Raymond Humble ◽  
Rodney Bowersox
2014 ◽  
Vol 742 ◽  
pp. 466-494 ◽  
Author(s):  
Somnath Ghosh ◽  
Rainer Friedrich

AbstractDirect numerical simulation (DNS), based on high-order numerical schemes, is used to study the effects of distributed pressure gradients on the redistribution of fluctuating kinetic energy in supersonic nozzle and diffuser flow with incoming fully developed turbulent pipe flow. Axisymmetric geometries and flow parameters have been selected such that shock waves are avoided and streamline curvature remains unimportant. Although mean extra rates of strain are quite small, strong changes in Reynolds stresses and their production/redistribution mechanisms are observed, in agreement with findings of Bradshaw (J. Fluid Mech., vol. 63, 1974, pp. 449–464). The central role of pressure–strain correlations in changing the Reynolds stress anisotropy is highlighted. A Green’s function-based analysis of pressure–strain correlations is presented, showing remarkable agreement with DNS data.


Volume 1 ◽  
2004 ◽  
Author(s):  
Francesco Soranna ◽  
Yi-Chih Chow ◽  
Oguz Uzol ◽  
Joseph Katz

This paper presents results of an experimental investigation on the response of a rotor boundary layer to an impinging Inlet Guide Vane (IGV) wake. High resolution two-dimensional Particle Image Velocimetry (PIV) measurements are conducted in a refractive index matched facility that provides an unobstructed view of the entire flow field. Data obtained at four different rotor phases, as the wake is chopped and passes by the rotor blade, allows us to examine the response of the rotor boundary layer to the mean flow and turbulence associated with the impinging wake. We focus on the suction side boundary layer in regions with adverse pressure gradients, from mid chord to the trailing edge. The phase-averaged velocity profiles are used for calculating the momentum and displacement thicknesses of the boundary layer, and for estimating the pressure gradients along the wall. Distributions of Reynolds stresses are also provided. The phase-averaged velocity profiles in the rotor boundary layer vary significantly with phase. During wake impingement the boundary layer becomes significantly thinner and more stable compared to other phases at the same location. Analysis of the possible causes for this trend suggests that the dominant contributors are unsteady, phase-dependent variation in pressure gradients along the wall.


2017 ◽  
Vol 820 ◽  
pp. 693-735 ◽  
Author(s):  
Xi Chen ◽  
Yiding Zhu ◽  
Cunbiao Lee

The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Görtler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Görtler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.


Author(s):  
Landon D. Owen ◽  
Tao Xing ◽  
Donald M. McEligot ◽  
John C. Crepeau ◽  
Ralph S. Budwig

Minimizing entropy generation is important to improve the efficiency of any system. The objective of this study is to use computational fluid dynamics (CFD) to elucidate the effects of pressure gradients on entropy generation rates in laminar and transitional boundary layers. The commercial CFD software, ANSYS FLUENT, is employed. The favorable and adverse pressure gradients are generated using various curved slip top walls. Bypass transition is simulated using the mean inlet velocity and Reynolds stresses from the direct numerical simulation (DNS) conducted by Nolan and Zaki [1]. Various turbulence and transitional models are employed and the results are compared to the DNS data. The factor of safety method is used to evaluate numerical error and grid uncertainties. Three systematically refined meshes are used to evaluate grid convergence. Monotonic convergence is achieved for all simulations with small grid uncertainties. The boundary layer correlation function, F(λ), the shear stress correlation, S(λ), and the dissipation coefficient, Cd, are calculated for the laminar CFD results. The dissipation coefficient, Cd and the intermittency, γ, are also calculated for the bypass transition CFD results. The laminar CFD results show better agreement with the correlation developed by McEligot than with the Thwaites correlation for F(λ) and S(λ). Overall, the percentage differences between the CFD results and the correlations increase as the magnitude of the pressure gradient variable, β, increases. The solvers and turbulence models in the transitional simulations are similar to the study by Ghasemi et al [2]. However, this study uses a much finer grid and improved boundary conditions for the inlet. These changes show an improvement for most turbulence models by comparison with the DNS results, especially for the location of transition.


1985 ◽  
Vol 157 ◽  
pp. 305-326 ◽  
Author(s):  
B. E. Thompson ◽  
J. H. Whitelaw

Experimental techniques, including flying-hot-wire anemometry, have been used to determine the pressure and velocity characteristics of a flow designed to simulate the trailing-edge region of an airfoil at high angle of attack. Emphasis is placed on the region of recirculating flow and on the downstream wake. It is shown that the effect of this recirculation is large even though the details of the flow within it may be unimportant. Normal stresses and cross-stream pressure gradients are important immediately upstream and downstream of the recirculating flow and are associated with strong streamline curvature. The relative importance of the terms in the transport equations for mean momentum and turbulence energy are quantified and the implications for procedures which solve potential-flow and boundary-layer equations and for alternative calculation methods are discussed.


2001 ◽  
Vol 123 (3) ◽  
pp. 551-558 ◽  
Author(s):  
InSub Lee ◽  
Hong Sun Ryou ◽  
Seong Hyuk Lee ◽  
Ki Bae Hong ◽  
Soo Chae

It is the aim of this article to investigate numerically the effects of spanwise pressure gradient on an embedded streamwise vortex in a turbulent boundary layer. The governing equations were discretized by the finite volume method and SIMPLE algorithm was used to couple between pressure and velocity. The LRR model for Reynolds stresses was utilized to predict the anisotropy of turbulence effectively. The validation was done for two cases: one is the development of a streamwise vortex embedded in a pressure-driven, three-dimensional turbulent boundary layer. The other involves streamwise vortex pairs embedded in a turbulent boundary layer without the spanwise pressure gradient. In the case of the former, the predicted results were compared with Shizawa and Eaton’s experimental data. In the latter case, the calculated results were compared against the experimental data of Pauley and Eaton. We performed numerical simulations for three cases with different values of spanwise pressure gradient. As a result, the primary streamwise vortex with spanwise pressure gradients decays more rapidly than the case with no pressure gradients, as the spanwise pressure gradient increases. This indicates that the spanwise pressure gradient may play an important role on mean and turbulent structures. In particular, it can be seen that the increase of pressure gradient enhances a level of turbulent normal stresses.


AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 464-470 ◽  
Author(s):  
Glen P. Doggett ◽  
Ndaona Chokani ◽  
Stephen P. Wilkinson

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