Michael Hites

A note on the overlap region in turbulent boundary layers

Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number were recently completed. The experiments were performed in two facilities, the Minimum Turbulence Level (MTL) wind tunnel at Royal Institute of Technology (KTH) and the National Diagnostic Facility (NDF) wind tunnel at Illinois Institute of Technology (IIT). Both experiments utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. A collaborative study by the principals of the two experiments, aimed at understanding the characteristics of the overlap region between the inner and outer parts of the boundary layer, has just been completed. The results are summarized here, utilizing the profiles of the mean velocity, for Reynolds numbers based on the momentum thickness ranging from 2500 to 27 000. Contrary to the conclusions of some earlier publications, careful analysis of the data reveals no significant Reynolds number dependence for the parameters desc...

Problems in high speed flow prediction relevant to control

Three flow problems are discussed whose solutions suggest flow control schemes. These are 1) unsteady hypersonic flow over bodies in the Newtonian approximation, 2) a mechanism of hypersonic flow stabilization over acoustically semi-transparent walls and 3) store separation from cavities. Simplified systematic approximations based on asymptotic frameworks lead to compact computational models that elucidate the flow structure and opportunities for control. Besides generalizing the steady model of Cole, the Newtonian approximation in the unsteady context shows that unsteady body perturbations can lead to inflectional velocity profiles that can produce instabilities and boundary layer transition to enhance mixing in combustors and inlets. The absorbing wall illustrates a mechanism that can be exploited to damp 2 mode hypersonic instabilities. Simplified flow modeling based on systematic asymptotics for store separation from cavities shows the influence of the cavity shear layer on apparent mass effects that are important to damping in pitch and clearance from the parent body. Comparisons with free drop experiments are used for initial validations of the analytical models. * Senior Scientist, Fellow, AIAA f Principal Researcher, Member, AIAA * Margaret Damn Distinguished Professor, Mathematical Sciences, Fellow, AIAA § Professor ** Professor, Associate Fellow Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. 1. Unsteady Newtonian thin shock layers and hypersonic flow stability 1.11ntroduction Although the stability of high speed flows has received much attention in the recent literature, major complicating aspects have not been treated in a unified way. These features include the combined effects of the finite shock displacement on the boundary layer, the nonparallelism of the flow and the vorticity introduced by the shock curvature. The relevant structure of the shock and boundary layers has been treated in [1][9]. In [6] and [7], the aforementioned stability issues were discussed within the Hypersonic Small Disturbance approximation for the inviscid deck strongly interacting with the hypersonic boundary layer. Equations of motion for the mean and fluctuating small amplitude flows were analyzed. Because of nonparallelism in this framework, the spatial part of the waves cannot be treated by the usual Fourier decomposition and an initial value rather than eigenproblem for spatial stability is obtained. The initial value problem leads to partial rather than ordinary differential equations that require a numerical marching method for their solution. Results indicate that the specific heat ratio 7 plays a major role in the stability of flow since it controls the reflection of waves from the shock and the radiation of energy in the shock layer whose thickness scales with 7 -1. Early experiments such as those described in [2] showed that for a practically interesting class of flows, the shock layer becomes very thin compared to the boundary layer near the nose of hypersonic flat plates. This feature and the desire to further understand the shock and boundary layer structure encourage the use of the Newtonian approximation 7 —> 1. The connection with flow stability motivates the study of this approximation in an unsteady context. In this chapter, limit process expansions will be discussed relevant to unsteady viscous interactions as a prelude to the analysis of hypersonic stability and transition. The application of these limits is an unsteady extension of the steady state analysis of [3]. Although the focus here is the treatment of viscous interaction, boundary layer stability, receptivity and transition, the results derived are useful in inviscid hypersonic unsteady aerodynamic methodology and load prediction as well. 1.2 Analysis Figure 1 schematically indicates strong interaction flow near the leading edge of a hypersonic body. The viscous boundary layer which is usually thin, occupies an appreciable fraction of the distance between the shock and body that will be considered without undue loss of generality a flat plate in what follows. Accordingly F(x,f} = Q, in the notation of Fig. 1. The results in this chapter will be expressed in terms of the boundary layer thickness function A(3c,r) = 0, which in the interpretation mentioned in the Introduction could be the body shape in an inviscid context. Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. The unsteady form of the Hypersonic Small Disturbance Theory (HSDT) equations [9] are applicable and are obtained as in [7] from limit process expansions of hatted variables defined as quantities normalized by their freestream counterparts, with p,T,u,v,fJL the density, temperature, horizontal, vertical components of the velocity vector, and viscosity respectively. If the freestream density, pressure and velocity are denoted as U,p^ and p^ respectively, then a pressure coefficient used in these expansions is defined as p = (P-PJ/P-U. Fig. 1 Schematic of hypersonic strong interaction flow. With these definitions and the coordinate system in Fig. 1 as well the normalization of the Cartesian dimensional coordinates x and y to the unit reference length L and the reference time scale L/U for the time t, unbarred dimensionless normalized counterparts of these independent variables are defined. If M^ and R^ are respectively the freestream Mach and Reynolds numbers, and 5 is a characteristic flow deflection angle, then the expansions are p=a(x,y,t;H,y)+--(1.1) T=T+— p = 8p+M = l+v =• §v+• • (1.2) (1.3) (1.4) (1.5) (1.6) where y = y/(L8}. These expansions are valid in the HSDT limit x, y, t, H = M o are fixed as 8 — > 0 ,

Enhanced Performance of Airfoils at Moderate Mach Numbers Using Zero-Mass Flux Pulsed Blowing

Oscillatory wall-jets were introduced through spanwise slots along a flapped NACA 0015 airfoil to establish lift augmentation and drag reduction by the unsteady forcing of the separated flow. Pressure coefficient distributions, lift coefficients, and wake velocity profiles, to determine the drag coefficient, were measured over the test-section speed range of 25m/s between 0.01% and 0.02%, based on RMS velocity, was shown to yield substantially better performance than steady blowing with Cµ in the range 0.5% to 3.5%. In is estimated that steady blowing of at least 10% would be required to reach the same levels of lift coefficient seen with the oscillatory blowing.

Velocity and wall shear-stress measurements in high-Reynolds-number turbulent boundary layers

Velocity and wall shear stress were measured using hot-wire anemometry in two distinct turbulent boundary layers in the National Diagnostic Facility and have demonstrated some new and unique features of the high Reynolds number turbulent boundary layer. In agreement with the literature, mean velocity profiles showed that the socalled logarithmic region grew continuously for increasing Reynolds number for all of the boundary layers confirming an extended disparity between small and large scale motion. It was also observed from the mean velocity profiles that surface roughness elements of less than 2 viscous lengths caused a noticeable overshoot of the log-law line as the Reynolds number increased which indicated the importance of surface roughness at high Reynolds number even when the roughness height was within the viscous sublayer. Spectra computed from long time-series of the streamwise velocity revealed a bi-modal distribution of energy in the boundary layer close to the wall (50 viscous units) asserting that the large-scale, lowfrequency motions of the boundary layer are important in the near-wall region. Direct shear stress measurements using wire-on-wall and MEMS sensors were compared to the Clauser prediction, and it was seen that the Clauser scaling tended to mask the streamwise (Re.,) dependencies of the boundary layer quantities.

Documentation of the role of large-scale structures in the bursting process in turbulent boundary layers

The scaling of the bursting frequency with Reynolds number is investigated experimentally by means of hot-wire measurements in turbulent boundary layers over the range 1580 < ReΘ < 23 700. Bu ...