Part 3 Stability and Transition 281
Overview T. Cebeci 1 Recent interest in the reduction of drag of underwater vehicles and aircraft components has rekindled research in the area of stability and transition. In the former case, the approal:h has been to maintain as much laminar flow on the body as possible by (a) arranging the shape so that there are extensive regions of favorable pressure gradient, (b) heating the surface, mostly in the region where flow accelerates, (c) applying suction continuously or sectionally, and (d) a combination of these three processes. Similarly, airfoils and bodies of revolution have been designed so as to locate the point of maximum thickness as far aft as possible with the result that there are extensive regions of favorable pressure gradient, and in some cases suction was applied to maintain laminar flow. In all cases, the location of transition has been estimated by the so-called en-method suggested by Smith [299] and Van Ingen [447] which is based on the Orr-Sommerfeld theory of small disturbances in a parallel shear flow; transition is assumed to occur when a modal disturbance with a critical frequency has first been amplified by a factor of en, with n being a function of freestream turbulence with a typical value of 9. The extensive consideration of airfoils and bodies of revolution has laid a foundation for extension of the methodology to three-dimensional flows including rotating disks, swept wings, and bodies of revolutions at incidence. Several computer programs allow the application of the en-method to three-dimensional incompressible and compressible flows and can be used by designers to reduce the drag of aircraft components by shaping and applying suction, as in twodimensional flows. A recent paper by Bushnell et al. [360] describes the progress in three-dimensional low and high speeds flows. The importance of transition is not limited to the design of underwater vehicles and aircraft components and Bushnell indicates in Chapter 17 the wider range and critical importance of transition-related research, including application to drag reduction, transition prediction for computational fluid dynamics, transition enhancement, for example by tripping, convective heat transfer and temperature control, and control of ancillary phenomena such as wall-pressure fluctuations, mixing in gas dynamic lasers, electron concentrations, body dynamics, inlet performance, cavitation inception in liquids, wake observables, and diffusion-controlled chemical reactions. His article contains many up-to-date ref- 1 Aerospace Engineering Deparunent, California State University, Long Beach Numerical and Physical Aspects of Aerodynamic Flows IV Editor: T. Cebeci Springer-Verlag Berlin Heidelberg 1990 283
erences on the subject and indicates the wide range of flows in which transition plays an important role. The en-method has been applied to attached flows and its first a,pplication to flows with separation was made by Nayfeh et al. [456] and Cebeci and Egan [454] who considered laminar flow over an isolated roughness element on a flat plate; they both used an interactive boundary-layer procedure to compute the velocity field needed in the Orr-Sommerfeld equation. The only application of the en-method to laminar and turbulent flows with separation was made by Cebeci [129] and Cebeci and Mcillvaine [592] in calculating flow over low Reynoldsnumber airfoils which are plagued with long separation bubbles. Cebeci and Chen, Chapter 18, present a review of this work and show that the accuracy of the en-method is better in flows with separation than that in attached flows due to the greater certainty in the value of n. In addition, they discuss the accuracy of predicting transition on an infinite swept wing and a body of revolution at incidence. The boundary-layer calculations for the infinite swept wing also used an interactive boundary-layer scheme in order to avoid the breakdown of the solutions at flow separation and those for the body of revolution used a combination of standard and characteristic box methods for a prescribed inviscid pressure distribution with a stability criterion to ensure numerical accuracy. Their eigenvalue procedure differs from those currently used (see for example, [448, 449]) in that the relationship between the two wave numbers a and {3 was determined by the saddle-point method. The results of calculations performed for a swept wing equipped with a cambered leading edge and a prolate spheroid at an incidence of 10 degrees are in good agreement with experimental data. In Chapter 19, Malik presents a linear stability theory for hypersonic flows and uses it to study the effects of a real gas in local chemical equilibrium and small nose bluntness on hypersonic boundary-layer stability. The results show. that chemical reactions have a stabilizing effect on the first mode instability and a destabilizing effect on the second mode instability and that there is a tendency for the second-mode instability to shift to lower frequencies. The effect of smallnose bluntness was found to be stabilizing. The critical Reynolds number for second-mode disturbances in Mach 8 flow past a blunt cone increased fifteen fold when compared with the sharp cone results, which is in agreement with the measurements of Stetson. Calculations with the en-method for transition prediction indicate that transition is delayed due to small-nose bluntness but, for a nose Reynolds number of 31,250, the increase in transition Reynolds number is only of the order of 30% compared to a fifteen-fold increase in the critical Reynolds number. Brendel and Mueller, Chapter 20, address the transition phenomena on airfoils operating at low Reynolds numbers in steady and unsteady flow and present data from several experiments concerning the transition process in the separation bubble. Low-level acoustic excitation was employed to regularize the transition process and allowed for conditional sampling techniques. Hot-wire anemometry was used to measure the spatial development of oscillations within the separated shear layer for a variety of separation bubbles. The results indicate that satura- 284
tion of the fundamental instability mode of the separated shear layer coincides with the maximum vertical displacement of the shear layer. The saturation appears to signify the beginning of the abrupt pressure rise in the aft portion of the transitional bubble and to be related to the proximity of the surface to the separated layer. In addition, the growth of disturbances was found to be sensitive to periodic, large wave-length, temporal pressure gradients in the freestream. The next three papers, Chapters 21, 22, and 23, are concerned with experiments to improve our understanding of transition in three-dimensional flows and to provide data to guide computational methods. Bippes and Mi.iller, Chapter 21, investigated the natural transition process on a swept-back flat plate in which the evolution of stationary and nonstationary disturbances was traced by means of hot-wire anemometry. The results are compared with those obtained from primary and secondary instability as well as from direct numerical simulation. It is shown that the growth of the instability modes depends on the relative size of manufacturing tolerances and freestream turbulence and on whether the stationary or the nonstationary instability mode dominates the transition process. The occurrence of both types of disturbance in the linear range of amplification is shown to be responsible for the early appearance of nonlinear effects which act over more than 50% of the transition region in the case of low freestream turbulence. The essential physical features of nonlinear phenomena are found to be well described. In Chapter 22, Saric et al. present results obtained on a swept wing placed in the Arizona State University wind tunnel using flow-visualization techniques and hot-wire anemometry. Steady and unsteady crossflow vortices were observed. Stability-code calculations were performed to map out transition behavior and yielded disturbance frequencies similar to those of the measurements. Harvey et al. report measurements of transition and the results of a stability analysis in Chapter 23 for a slotted swept laminar flow control airfoil, designated as NASA SCLFC(I)-0513F and tested in the Langley 8-Foot Transonic Pressure Tunnel at both subsonic and transonic speeds. Laminar flow control was achieved by removing a portion of the boundary-layer through the surface using discrete suction slots and this and subsequent experiments demonstrate that extensive runs of laminar flow are attainable on transport-type wings with high cruise lift coefficients and substantial reductions in drag. Finally, Amal and Juillen address leading-edge contamination on a swept wing induced by the turbulent boundary layer developing along the wind tunnel floor and detected by using hot films glued along the spanwise direction, close to the leading edge. The experiments of Chapter 24 were conducted in the Fl wind tunnel at the FAUGA-MAUZAC Center on a RA16SC1 airfoil equipped with a trailing-edge flap which was kept at an angle of attack of 10 for all the experiments. The results show that a critical Reynolds number of 245 can be used with confidence as a Reynolds number beyond which turbulent spots are self-sustaining along the leading edge. The boundary-layer structure is not, however, uniform in the spanwise direction, which means that boundary-layer calculations cannot be performed with the infinite swept-wing assumption even 285
if the pressure disuibution does not vary much along the span. The experiments also show that relaminarization is likely to occur provided the pressure gradient is steeper downstream of the attachment line than on the attachment li_ne itself. It is not clear whether or not this "relaminarization" is complete, since small turbulent packets were always observed on the upper surface of the wing. For a better understanding of this phenomenon, it is necessary to clarify the effect of the residual fluctuations on the downstream laminar boundary layer. 286