Report presenting an investigation to determine the carry loads and mutual aerodynamic interference effects from high-speed wind-tunnel tests and the drop characteristics of the X-15 through the B-52 flow field from low-speed dynamic-model drop tests and six-degree-of-freedom calculations. The X-15 installation was found to increase drag at cruise conditions by approximately 15 percent.

The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics.

Turbulence was generated by using screens, and the turbulence percentage was measured by a hot-wire anemometer both in the boundary layer and the free stream. The local heat-transfer coefficient was measured at 12 locations along the plate for the cases of various turbulence levels. The transition Reynolds number from laminar to turbulent flow decreases as the main-stream turbulence level increases. In the range of laminar heat transfer the effect of turbulence in the main flow was not great, but in the range of turbulent heat transfer the heat-transfer coefficient increases according to the increase of turbulence.

Analysis is presented on the possible similarity solutions of the three-dimensional, laminar, incompressible, boundary-layer equations referred to orthogonal, curvilinear coordinate systems. Requirements of the existence of similarity solutions are obtained for the following: flow over developable surface and flow over non-developable surfaces with proportional mainstream velocity components.

The equations of shells are taken in the form of the general technical theory of shallow shells and shells of medium length. The aerodynamic forces acting on a shell are taken into account only as forces of excess pressure according to the formula proposed by A.A. Iliushin in reference 3.

A comparison of experiment with theory is made for air ejectors having cylindrical mixing sections and operating under conditions of supersonic primary flow and either mixed or supersonic regimes of mixing. The effect on ejector performance of such parameters as mixer length and cross section, terminating diffuser, primary Mach number, and primary nozzle position is presented in terms of mass flow and pressure ratio.

"A number of semiempirical approximate methods exist for determining the characteristics of the turbulent boundary layer on a curvilinear surface. At present, among these methods, the one proposed by L. G. Loitsianskii is given frequent practical application. This method is sufficiently effective and permits, in the case of wing profiles with technically smooth surfaces, calculating the basic characteristics of the boundary layer and the values of the overall drag with an accuracy which suffices for practical purposes" (p. 1).

The influence of the deflected flow caused by the fuselage (especially by unsymmetrical attitudes) on the lift and the rolling moment due to sideslip has been discussed for infinitely long fuselages with circular and elliptical cross section. The aim of this work is to add rectangular cross sections and, primarily, to give a principle by which one can get practically usable contours through simple conformal mapping. In a few examples, the velocity field in the wing region and the induced flow produced are calculated and are compared with corresponding results from elliptical and strictly rectangular cross sections.

"In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence" (p. 1).

"Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions" (p. 1).

"The increasing importance of high-speed flow leads to similar problems in various fields of research which are summarized in what follows. Typical of all cases is the conversion of high kinetic energy into extreme thermodynamic states with temperatures of several thousand degrees, frequently connected with dissociation and ionization of the gas involved. There is also a characteristic small sensitivity to the processes discussed in the case of gases of low molecular weight (light gases)" (p. 1).

Convection is called free is the stresses (including the normal pressure) to which the fluid is subjected at its boundaries do not perform mechanical work, that is, if all the boundaries of the fluid are stationary. The case where this is not true is termed forced convection. It corresponds to the action on the fluid of some mechanical suction pumping the fluid.

"We consider in this report the determination of the upper limit of critical loads in the case of simultaneous action of a compressive force, uniformly distributed over plane cross sections, and of isotropic external normal pressure on cylindrical or conical shells of circular cross section. As a starting point we use the differential equations for neutral equilibrium of conical shells which have been used for the solution of the problem of stability of conical shells under torsion and under axial compression; upon solution of the problem it is possible to satisfy all boundary conditions, in contrast to the report where no attention is paid to the fulfillment of the boundary conditions, and to the report where only part of the boundary conditions are satisfied by solution of the problem according to Galerkin's method" (p. 1).

A reproduction of the technical papers presented by staff members of the NACA Laboratories at the NACA Conference on High-Speed Aerodynamics at the Ames Aeronautical Laboratory during March 18-20, 1958. The primary purpose of the conference was to convey to military services and contractors the results of recent research and to provide an opportunity to discuss the results.

"Ideally, the reflection of a shock from the closed end of a shock tube provides, for laboratory study, a quantity of stationary gas at extremely high temperature. Because of the action of viscosity, however, the flow in the real case is not one-dimensional, and a boundary layer grows in the fluid following the initial shock wave. In this paper simplifying assumptions are made to allow an analysis of the interaction of the shock reflected from the closed end with the boundary layer of the initial shock afterflow. The analysis predicts that interactions of several different types will exist in different ranges of initial shock Mach number" (p. 1).

"Autocorrelation and frequency analyses of a series of aperiodic time events, in particular, filtered noises and sibilant sounds, were made. The position and band width of the frequency ranges are best obtained from the frequency analysis, but the energies contained in the several bands are most easily obtained from the autocorrelation function. The mean number of zero crossings of the time function was determined from the curvature of the latter function in the vicinity of the zero crossing, and also with the aid of a decimal counter. The second method was found to be more exact" (p. 1).

The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.

"Upon impact of a solid body on the plane surface of a fluid, there occurs on the vetted surface of the body an abrupt pressure rise which propagates into both media with the speed of sound. Below, we assume the case where the speed of propagation of sound in the body which falls on the surface of the fluid may be regarded as infinitely large in comparison with the speed of propagation of sound in the fluid; that is, we shall assume that the falling body is absolutely rigid. IN this case, the entire relative speed of the motion which takes place at the beginning of the impact is absorbed by the fluid" (p. 1).

A study is made of the spectrum of isotropic turbulence with the aid of the customary method of Fourier analysis. The spectrum of the turbulent motion is derived to the smallest wave lengths, that is, into the laminar region, and correlation functions and pressure fluctuations are calculated. A comparison with experimental results is included. Finally, an attempt is made to derive the numerical value of a constant characteristic of the energy dissipation in isotropic turbulence.

In the investigation of stability of a two-dimensional laminar flow with respect to small disturbances, a disturbance of the stream function moving downstream (in the direction of the x-axis) by the "partial wave formula" is described.

"The literature on turbulent heat transfer has in the course of years attained a considerable volume. Since this very complicated problem has not as yet found a complete solution, further studies in this field may be expected. The heat engineer must therefore accommodate himself to a constantly increasing number of theories and formulas. Since the theories generally start from hypothetical assumptions, and since they contain true and false assertions, verified knowledge and pure suppositions often being intermingled in a manner difficult to tell them apart, the specialist had difficulty in forming a correct evaluation of the individual studies" (p. 1).

"The unsteady aerodynamic forces, [based on two-dimensional incompressible flow considerations], are determined for an unstaggered cascade, the blades of which are vibrating in phase in an approach flow parallel to the blades" (p. 1).

"The plastic flow during deformation of real polycrystalline metals has specific characteristics which distinguish the plastic deformation of metals from the deformation of ordinary isotropic bodies. One of these characteristics is the marked micro-nonuniformity of the plastic deformation of metals. P.O. Pashkov demonstrated the presence of a considerable micro-nonuniformity of the plastic deformation of coarse-grained steel wit medium or low carbon content" (p. 1).

"The presence of sound waves in one or the other of the fluid regions on either side of a shock wave is made apparent, in the region under superpressure, by acoustic waves (reflected or refracted according to whether the incident waves lie in the region of superpressure or of subpressure) and by thermal waves. The characteristics of these waves are calculated for a plane, progressive, and uniform incident wave. In the case of refraction, the refracted acoustic wave can, according to the incidence, be plane, progressive, and uniform or take the form of an 'accompanying wave' which remains attached to the front of the shock while sliding parallel to it" (p. 1).