Stability theory applications to laminar-flow control

In order to design Laminar Flow Control (LFC) configurations, reliable methods are needed for boundary-layer transition predictions. Among the available methods, there are correlations based upon R sub e, shape factors, Goertler number and crossflow Reynolds number. The most advanced transition prediction method is based upon linear stability theory in the form of the e sup N method which has proven to be successful in predicting transition in two- and three-dimensional boundary layers. When transition occurs in a low disturbance environment, the e sup N method provides a viable design tool for transition prediction and LFC in both 2-D and 3-D subsonic/supersonic flows. This is true for transition dominated by either TS, crossflow, or Goertler instability. If Goertler/TS or crossflow/TS interaction is present, the e sup N will fail to predict transition. However, there is no evidence of such interaction at low amplitudes of Goertler and crossflow vortices

The growth of Goertler vortices in compressible boundary layers

The linear instability of Goertler vortices in compressible boundary layers is considered. Using asymptotic methods in the high wavenumber regime, it is shown that a growth rate estimate can be found by solving a sequence of linear equations. The growth rate obtained in this way takes non-parallel effects into account and can be found much more easily than by ordinary differential equation eigenvalue calculations associated with parallel flow theories

Supersonic laminar-flow control

Detailed, up to date systems studies of the application of laminar flow control (LFC) to various supersonic missions and/or vehicles, both civilian and military, are not yet available. However, various first order looks at the benefits are summarized. The bottom line is that laminar flow control may allow development of a viable second generation SST. This follows from a combination of reduced fuel, structure, and insulation weight permitting operation at higher altitudes, thereby lowering sonic boom along with improving performance. The long stage lengths associated with the emerging economic importance of the Pacific Basin are creating a serious and renewed requirement for such a vehicle. Supersonic LFC techniques are discussed

Large-Eddy Simulation of Axisymmetric Compression Corner Flow

The Wall-Modeled Large Eddy Simulation (WMLES) approach is used to study the interaction of a shock wave with a high Reynolds number turbulent boundary layer. Since the near wall region is modeled, high Reynolds number turbulent flows can be simulated at a moderate computational cost. The case considered is that of an axisymmetric Mach 2.85 turbulent boundary layer over a 30 compression corner. The Reynolds number of the boundary layer upstream of the interaction based on momentum thickness (Re theta = u sub infinity theta/v sub infinity) is ~12,000. The geometry and flow conditions match the experiments of Dunagan et al. (NASA TM 88227, 1986). The simulations were performed using equilibrium and non-equilibrium wall models. The agreement with experiment is encouraging for the finest grid with respect to the separation bubble length, unsteady shock structure and wall pressure distribution. Sensitivity ofWMLES results to grid, wall model, and blockage effects in the tunnel are reported

Experimental and theoretical investigation of boundary-layer instability mechanisms on a swept leading edge at Mach 3.5

A brief outline of the experimental and theoretical investigation of boundary layer instability mechanisms on a swept leading edge at Mach 3.5 is presented. Transition is affected by wind tunnel noise only when roughness is present. Local bar-R sub * Reynolds number and k/eta sub * are useful correlation parameters for a wide range of free stream Mach numbers. Stability theory is in good agreement with the experimental cross flow vortex wavelength. These conclusions are briefly discussed

Design and fabrication requirements for low noise supersonic/hypersonic wind tunnels

A schematic diagram of the new proposed Supersonic Low Disturbance Tunnel (SLDT) is shown. Large width two dimensional rapid expansion nozzles guarantee wide quiet test cores that are well suited for testing models at large angle of attack and for swept wings. Hence, this type of nozzle will be operated first in the new proposed large scale SLDT. Test results indicate that the surface finish of pilot nozzles is critical. The local roughness Reynolds number criteria R sub k is approx. = 10 will be used to specify allowable roughness on new pilot nozzles and the new proposed tunnel. Experimental data and calculations for M = 3.0, 3.5, and 5.0 nozzles give N-factors from 6 to 10 for transition caused by Goertler vortices. The use of N is approx. = 9.0 for the Goertler instability predicts quiet test cores in the new M = 3.5 and M = 6.0 axisymmetric long pilot nozzles that are 3 to 4 times longer than observed in the test nozzles to date. The new nozzles utilize a region of radial flow which moves the inflection point far downstream and delays the onset and amplification of the Goertler vortices

Acoustic Receptivity of Mach 4.5 Boundary Layer with Leading- Edge Bluntness

Boundary layer receptivity to two-dimensional slow and fast acoustic waves is investigated by solving Navier-Stokes equations for Mach 4.5 flow over a flat plate with a finite-thickness leading edge. Higher order spatial and temporal schemes are employed to obtain the solution whereby the flat-plate leading edge region is resolved by providing a sufficiently refined grid. The results show that the instability waves are generated in the leading edge region and that the boundary-layer is much more receptive to slow acoustic waves (by almost a factor of 20) as compared to the fast waves. Hence, this leading-edge receptivity mechanism is expected to be more relevant in the transition process for high Mach number flows where second mode instability is dominant. Computations are performed to investigate the effect of leading-edge thickness and it is found that bluntness tends to stabilize the boundary layer. Furthermore, the relative significance of fast acoustic waves is enhanced in the presence of bluntness. The effect of acoustic wave incidence angle is also studied and it is found that the receptivity of the boundary layer on the windward side (with respect to the acoustic forcing) decreases by more than a factor of 4 when the incidence angle is increased from 0 to 45 deg. However, the receptivity coefficient for the leeward side is found to vary relatively weakly with the incidence angle

Sensitivity analysis of hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudoeigenvalues are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette, trailing line vortex flow and compressible Blasius boundary layer flow. Parametric studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the non-normality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem

Analysis of Crossflow Transition Flight Experiment aboard the Pegasus Launch Vehicle

The Pegasus wing-glove flight experiment was designed to provide crossflow transition data at high Mach numbers, specifically to help validate stability based predictions for transition onset in a flight environment. This paper provides an analysis of the flight experiment, with emphasis on computational results for crossflow disturbances and the correlation of disturbance growth factors with in-flight transition locations via the e(sup N) method. Implications of the flight data for attachment line stability are also examined. Analysis of the thermocouple data reveals that transition (from turbulent to laminar flow) was first detected during the ascending flight of the rocket when the free stream Mach number exceeded about 4. Therefore, computations have been performed for flight Mach numbers of 4.13, 4.35, 4.56 and 4.99. Due to continually decreasing unit Reynolds number at higher altitudes, the entire wing-glove boundary layer became laminar at the highest flight Mach number computed above. In contrast, the boundary layer flow over the inboard tile region remained transitional up to and somewhat beyond the time of laminarization over the instrumented glove region. Linear stability predictions confirmed that the tile boundary layer is indeed more unstable to crossflow disturbances than the much colder stainless steel glove boundary layer. The transition locations based on thermocouple data from both the glove and the tile regions are found to correlate with stationary-crossflow N-factors within the range of 7 to 12.4 and with traveling mode N-factors between 7.6 and 14.1. Data from the thermocouples and hot film sensors indicates that transition from turbulent to laminar flow (i.e., laminarization) at a fixed point over the glove is generally completed within a flight time interval of 3 seconds. However, the times at which transition begins and ends as inferred from the hot film sensors are found to differ by about 2 seconds from the corresponding estimates based on the thermocouple data

Linear stability theory and three-dimensional boundary layer transition

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes