A finite-difference solution to the problem of the interaction between an impinging shock wave and the laminar boundary layer on a flat plate is presented. The boundary-layer equations are used to calculate the flow with the Prandtl-Meyer formula being used to determine the pressure. Two different methods for calculating the region of separated flow are discussed. Comparisons between this theory and experimental results show good agreement. The effects of the viscosity and heat-conduction relationships on the calculated results are determined. Diagrams show the influence of the Mach number and the displacement thickness of the boundary layer at the start of the interaction on the pressure distribution. The insulated plate and the plate with given temperature are considered.

The interaction of a shock wave with a laminar boundary layer

Lift-generated vortex wakes of subsonic transport aircraft

An approximate analysis of atmospheric effects on wake vortex motion and decay is presented. The effects of density stratification, turbulence, and Reynolds number are combined in a single model so that the relative importance of different parameters can be determined. Predicted wake motion is shown to be in good agreement with limited data from both ground facility and flight test measurements taken under low turbulence conditions. Wake decay was found to depend strongly on both density stratification and turbulence. For typical levels of turbulence, wake decay was found to result from the 'Crow instability' except under strongly stratified conditions.

An approximate model of vortex decay in the atmosphere

T most severe problems of atmospheric flight at high Mach numbers are associated with viscous-inviscid interactions. Cruise vehicles for Mach numbers above four and lifting re-entry vehicles have highly complex three-dimensional configurations in which exist many regions of high compression that can cause boundary layers to separate. Although separation can result in loss of control effectiveness or flow degradation in an engine inlet, flow reattachment gives rise to heat rates that can far exceed those for an attached boundary layer. A further, and possibly far more severe viscous interaction problem is the impingement of shock waves generated by the forebody and other external components of a vehicle on aft sections resulting in local heat rates that may be many times larger than stagnation point values. Peak heating conditions may be laminar for lifting re-entry configurations, though our knowledge of boundary layertransition is far from adequate so that transitional and turbulent flows cannot be ruled out. However, Reynolds num, bers of potential high Mach number cruise vehicles are high— 10 to 10—so that viscous interactions will be predominately associated with turbulent boundary layers and their attendant higher heat rates. The high local heat rates resulting from viscous interactions cause "hot spots" that could lead to catastrophic failure. Vivid examples of damage resulting from viscous interactions are given in Figs. 1 and 2. A ventral pylon on the X-15 airplane, shown in Fig. 1, caused high^local heating of the fuselage around its root, and developed large holes near its tip due to the impingement of the shock wave from a dummy ramjet it supported, during a flight at Mach 6.7 in 1967. A study of the flowfield of the pylon-mounted dummy ramjet configuration is reported in Ref. 1. Figure 2 shows considerable damage due to interaction heating to the underside of a sled and its supporting slipper as a result of a run at 7000 fps on the 7-mile test track at Holloman Air Force Base. Unlike stagnation-point heating where the location is obvious, the problem with complex configurations is to determine "where" high heat rates are likely to occur, as well as their magnitude. It is the purpose of this paper to identify some potentially critical areas of viscous interactions associated with high Mach number vehicles and briefly review our state of knowledge in these areas with emphasis on the basic flow phenomena.

Survey of viscous interactions associated with high Mach number flight

The use of CADD has effected many changes in traditional work methods of the various interfacing disciplines at MCAIR. We have streamlined our tasks by utilizing the cost/time saving techniques presently afforded by this system, and plan to continue additional development efforts which will further improve it. As we discover more and more practical applications for CADD, new or modified software routines will be formulated to make the system as responsive and reliable as possible. Since the potential for substantial dollar savings exists, particularly in the area of manufacturing, we are consciously attempting to align our techniques to make engineering data as usable as possible by manufacturing personnel in its existing form, thus eliminating as many intermediate manual processes as possible. Our final objectives, however, cannot now be defined. CADD's utility will increase as we continue to conceive new ideas for its application. Its ultimate benefits can only be determined by the limits of our creative imagination.

Rapid Scanning, Three-Dimensional Hot-Wire AnemometerSurveys of Wing-Tip Vortices

A method has been developed for estimating the nonlinear aerodynamic characteristics of missile wing and control surfaces. The method is based on the assumption that if a fin on a body has the same normal-force coefficient as a wing alone composed of two of the same fins joined together at their root chords, then the other force and moment coefficients of the fin and the wing alone are the same, including the nonlinearities. The method can be used for deflected fins at arbitrary bank angles and at high angles of attack. In this paper a full derivation of the method is given, its accuracy is demonstrated, and its use in extending missile data bases is shown.

Equivalent angle-of-attack method for estimating nonlinear aerodynamics of missile fins

Theme A integral boundary-layer method is extended to calculation of separated turbulent boundary layers by treating the pressure as a dependent variable and prescribing the wall shear variation. The boundary-layer method and a suitable potential flow method are used in an iterative procedure to produce a method for predicting the characteristics of separated flows. The interaction between the boundary layer and the inviscid flow is accounted for by augmenting the physical surface by the boundary-layer displacement thickness. Good comparisons are shown between the theory and data for a separated turbulent boundary layer on the wall of a transonic wind tunnel.

Prediction of Turbulent Separated Boundary Layers

Recent experimental results show that the control effectiveness of a missile fin in supersonic flow at moderate to high angles of attack is a strong nonlinear function of freestream Mach number, body incidence angle, fin bank angle, and fin deflection angle. Analysis of the experimental results using an Euler finite-difference computer code with flow separation, together with the equivalent angle-of-attack concept, indicates that the observed nonlinearities are due to the variation of local dynamic pressure and local Mach number around the missile body alone. The nonlinearities are shown to be a strong source of control cross-coupling for high Mach number, high angle-ofattack combinations. The analysis suggests a relatively simple yet comprehensive approach for accurately accounting for these nonlinear effects. The impact of the results on missile aeroprediction methods is discussed.

Extension of equivalent angle-of-attack method for nonlinear flowfields

A model of a trailing vortex pair behind an aircraft is presented which is thought to represent a case of extreme vortex persistency and which therefore is relevant from the safety point of view. Three stages are considered in the analysis: a rolling-up stage directly behind the aircraft, a second stage in which the vortices act independently as constant strength equilibrium turbulent vortices, and a third stage where the vortices physically interact and decay in strength. An overall theory is presented encompassing all three stages and aimed at obtaining equilibrium solutions. Calculative examples are presented for all stages.

Decay of a Vortex Pair behind an Aircraft

: A alculative method is presented for determining separated, laminar, boundary-layer characteristics from in front of the separation point to the reattachment point under the influence of 'free interaction' between the main flow and the boundary layer The analysis covers supersonic flow over two-dimensional and axisymmetric configurations with adiabatic or nonadiabatic wall conditions For nonadiabatic wall conditions, theories based on first-order coupling and second-order coupling between velocity and total temperature profiles were presented The theory based on first-order coupling was included in a machine calculation program with options for two-dimensional or axisymmetric flow and adiabatic or nonadiabatic wall conditions Extensive systematic calculations were made to determine the range of possible separated flows over a two-dimensional configuration as a function of separation point location and wall temperatures Comparison between experiment and theory for separation pressure distributions on two -dimensional or axisymmetric adiabatic configurations shows generally good agreement (Author)

Calculation of laminar separation with free interaction by the method of integral relations. part ii. two-dimensional supersonic nonadiabatic flow and axisymmetric supersonic adiabatic and nonadiabatic flows.

Jack N. Nielsen

Papers

Equivalent angle-of-attack method for estimating nonlinear aerodynamics of missile fins

Prediction of Turbulent Separated Boundary Layers

Extension of equivalent angle-of-attack method for nonlinear flowfields

Decay of a Vortex Pair behind an Aircraft

Calculation of laminar separation with free interaction by the method of integral relations. part ii. two-dimensional supersonic nonadiabatic flow and axisymmetric supersonic adiabatic and nonadiabatic flows.