## You limited your search to:

**Collection:**National Advisory Committee for Aeronautics Collection

### On the Instability of Methods for the Integration of Ordinary Differential Equations

**Date:**April 1, 1956

**Creator:**Rutishauser, Heinz

**Description:**Examples and a criterion for stability of integration methods is provided. The criterion is applied to well-known integration formulas.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63924/

### The Calculation of Compressible Flows with Local Regions of Supersonic Velocity

**Date:**March 1, 1947

**Creator:**Goethert, B. & Kawalki, K. H.

**Description:**This report addresses a method for the approximate calculation of compressible flows about profiles with local regions of supersonic velocity. The flow around a slender profile is treated as an example.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63851/

### Free Convection Under the Conditions of the Internal Problem

**Date:**April 1, 1958

**Creator:**Ostroumov, G. A.

**Description:**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.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63997/

### Drag Reduction by Suction of the Boundary Layer Separated Behind Shock Wave Formation at High Mach Numbers

**Date:**July 1, 1947

**Creator:**Regenscheit, B.

**Description:**With an approach of the velocity of flight of a ship to the velocity of sound, there occurs a considerable increase of the drag. The reason for this must be found in the boundary layer separation caused by formation of shock waves. It will be endeavored to reduce the drag increase by suction of the boundary layer. Experimental results showed that drag increase may be considerably reduced by this method. It was, also, observed that, by suction, the position of shock waves can be altered to a considerable extent.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63990/

### Evaporation, Heat Transfer, and Velocity Distribution in Two-Dimensional and Rotationally Symmetrical Laminar Boundary-Layer Flow

**Date:**February 1, 1958

**Creator:**Froessling, Nils

**Description:**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.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63998/

### The Turbulent Boundary Layer on a Rough Curvilinear Surface

**Date:**September 1, 1958

**Creator:**Droblenkov, V. F.

**Description:**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. The idea of making use of the basic integral momentum equation ((d delta(sup xx))/dx) + ((V' delta(sup xx))/V) (2 + H) = (tau(sub 0))/(rho V(exp 2)) proves to be fruitful also for the solution of the problems in the determination of the characteristics of the turbulent boundary layer on a rough surface.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63908/

### Temperatures and Stresses on Hollow Blades For Gas Turbines

**Date:**September 1, 1947

**Creator:**Pollmann, Erich

**Description:**The present treatise reports on theoretical investigations and test-stand measurements which were carried out in the BMW Flugmotoren GMbH in developing the hollow blade for exhaust gas turbines. As an introduction the temperature variation and the stress on a turbine blade for a gas temperature of 900 degrees and circumferential velocities of 600 meters per second are discussed. The assumptions onthe heat transfer coefficients at the blade profile are supported by tests on an electrically heated blade model. The temperature distribution in the cross section of a blade Is thoroughly investigated and the temperature field determined for a special case. A method for calculation of the thermal stresses in turbine blades for a given temperature distribution is indicated. The effect of the heat radiation on the blade temperature also is dealt with. Test-stand experiments on turbine blades are evaluated, particularly with respect to temperature distribution in the cross section; maximum and minimum temperature in the cross section are ascertained. Finally, the application of the hollow blade for a stationary gas turbine is investigated. Starting from a setup for 550 C gas temperature the improvement of the thermal efficiency and the fuel consumption are considered as well as the increase of ...

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63957/

### Gas Jets

**Date:**August 1, 1944

**Creator:**Chaplygin, S.

**Description:**A brief summary of the contents of this paper is presented here. In part I the differential equations of the problem of a gas flow in two dimensions is derived and the particular integrals by which the problem on jets is solved are given. Use is made of the same independent variables as Molenbroek used, but it is found to be more suitable to consider other functions. The stream function and velocity potential corresponding to the problem are given in the form of series. The investigation on the convergence of these series in connection with certain properties of the functions entering them forms the subject of part II. In part III the problem of the outflow of a gas from an infinite vessel with plane walls is solved. In part IV the impact of a gas jet on a plate is considered and the limiting case where the jet expands to infinity changing into a gas flow is taken up in more detail. This also solved the equivalent problem of the resistance of a gaseous medium to the motion of a plate. Finally, in part V, an approximate method is presented that permits a simpler solution of the problem of ...

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63958/

### Investigations on Experimental Impellers for Axial Blowers

**Date:**April 1, 1947

**Creator:**Encke, W.

**Description:**A selection of measurements obtained on experimental impellers for axial blowers will be reported. In addition to characteristic curves plotted for low and for high peripheral velocities, proportions and blade sections for six different blower models and remarks on the design of blowers will be presented.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63870/

### Stability of Cylindrical and Conical Shells of Circular Cross Section, with Simultaneous Action of Axial Compression and External Normal Pressure

**Date:**April 1, 1958

**Creator:**Mushtari, K. M. & Sachenkov, A. V.

**Description:**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. Approximate formulas are used for the determination of the critical external normal pressure with simultaneous action of longituninal compression. Let us note that the formulas suggested in reference 5 are not well founded and may lead, in a number of cases, to a substantial mistake in the magnitude of the critical load.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63878/

### Investigation of Flow in a Centrifugal Pump

**Date:**July 1, 1946

**Creator:**Fischer, Karl

**Description:**The investigation of the flow in a centrifugal pump indicated that the flow patterns in frictional fluid are fundamentally different from those in frictionless fluid. In particular, the dead air space adhering to the section side undoubtedly causes a reduction of the theoretically possible delivery head. The velocity distribution over a parallel circle is also subjected to a noticeable change as a result of the incomplete filling of the passages. The relative velocity on the pressure side of the vane, which for passages completely filled with active flow would differ little from zero even at comparatively lower than normal delivery volume, is increased, so that no rapid reverse flow occurs on the pressure side of the vane even for smaller delivery volume. It was established, further, that the flow ceases to be stationary for very small quantities of water. The inflow to the impeller can be regarded as radial for the operating range an question. The velocity triangles at the exit are subjected to a significant alteration in shape ae a result of the increased peripheral velocity, which may be of particular importance in the determination of the guide vane entrance angle.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63813/

### The Flow Through Axial Turbine Stages of Large Radial Blade Length

**Date:**April 1, 1947

**Creator:**Eckert & Korbacher

**Description:**A calulation of the flow in turbine blading is reported that includes the calculation of effect of centrifugal force. Frictional losses on the stator blades and rotor blades are allowed.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63841/

### On Possible Similarity Solutions for Three-Dimensional Incompressible Laminar Boundary-Layer Flows Over Developable Surfaces and with Proportional Mainstream Velocity Components

**Date:**September 1, 1958

**Creator:**Hansen, Arthur G.

**Description:**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.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63919/

### On the Contribution of Turbulent Boundary Layers to the Noise Inside a Fuselage

**Date:**December 1, 1956

**Creator:**Corcos, G. M. & Liepmann, H. W.

**Description:**The following report deals in preliminary fashion with the transmission through a fuselage of random noise generated on the fuselage skin by a turbulent boundary layer. The concept of attenuation is abandoned and instead the problem is formulated as a sequence of two linear couplings: the turbulent boundary layer fluctuations excite the fuselage skin in lateral vibrations and the skin vibrations induce sound inside the fuselage. The techniques used are those required to determine the response of linear systems to random forcing functions of several variables. A certain degree of idealization has been resorted to. Thus the boundary layer is assumed locally homogeneous, the fuselage skin is assumed flat, unlined and free from axial loads and the 'cabin' air is bounded only by the vibrating plate so that only outgoing waves are considered. Some of the details of the statistical description have been simplified in order to reveal the basic features of the problem. The results, strictly applicable only to the limiting case of thin boundary layers, show that the sound pressure intensity is proportional to the square of the free stream density, the square of cabin air density and inversely proportional to the first power of the damping constant ...

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63891/

### Application of the Method of Coordinate Perturbation to Unsteady Duct Flow

**Date:**September 1, 1958

**Creator:**Himmel, Seymour C.

**Description:**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.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63897/

### Gas-Dynamic Investigations of the Pulse-Jet Tube, Parts 1 and 2

**Date:**February 1, 1947

**Creator:**Shultz-Grunow, F.

**Description:**Based upon a simplified representation of the mode of operation of the pulse-jet tube, the effect of the influences mentioned in the title were investigated and it will be shown that, for a jet tube with a fccmndesigned to be aerodynamically favorable, the ability to operate is at least questionable. By taking into account the course of the development of pressure by combustion, a new insight has been obtained into the processes of motion within the jet tube, an insight that explains a number of empirical observations, namely: certain particulars of the sequence of pressure variations; the existence of an optimum valve-opening ratio; the occurrence of an intrusion of air; and the existence of a flight speed above lrhichthe jet tube ceases to operate. At too great an opening ratio or at too great a flight s-peed, the continuous flow through the tube is too predominant over the oscilla~ory process to perinitthe occurrence of an explosion powerful enough to maintain continuous operation. Certain possible means of making the operation of the jet tube more independent of the flight speed and of reducing the flow losses were proposed and discussed.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63972/

### Some Basic Laws of Isotropic Turbulent Flow

**Date:**September 1, 1945

**Creator:**Loitsianskii, L. G.

**Description:**An Investigation is made of the diffusion of artificially produced turbulence behind screens or other turbulence producers. The method is based on the author's concept of disturbance moment as a certain theoretically well-founded measure of turbulent disturbances.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63978/

### Theory of Wings in Nonstationary Flow

**Date:**June 1, 1947

**Creator:**Nekrasov, A. I.

**Description:**This paper gives an overview of equations for vibration and flutter affecting airplane wings in nonstationary flow.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63973/

### Possibilities of Reducing the Length of Axial Superchargers for Aircraft Motors

**Date:**January 1, 1947

**Creator:**Eckert, B.

**Description:**Axial blowers are gaining importance as aircraft engine superchargers. However, the pressure head obtainable per stage is small. Due to the necessary great number of stages, the physical length of the blower becomes too great for an airworthy device. This report discusses several types of construction that permit a reduction in the length of the blower.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63881/

### Dornier "Superwal" commercial seaplane with : two Rolls-Royce "Condor" 600 HP. engines

**Date:**February 1, 1927

**Creator:**unknown

**Description:**In November 1926, an exhibition flight of the Dornier giant flying boat was made for 3/4 of an hour. It was a larger version of the Dornier Wal, with a stepped hull, and wing stubs for lateral stability. It has a range of 1200 miles and is outfitted for baggage and 8 passengers.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63001/

### Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

**Date:**July 1, 1958

**Creator:**Frenkiel, Francois N.

**Description:**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. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63983/

### Wind-Tunnel Measurements on the Henschel Missile "Zitterrochen" in Subsonic and Supersonic Velocities

**Date:**April 1, 1948

**Creator:**Weber & Kehl

**Description:**At the request of the Henschel Aircraft Works. A. G. Berlin. three models of the missile "Zitterrochen" were investigated at subsonic velocities.(open jet 215-millimeter diameter) and at supersonic velocities (open jet 110 by 130 millimeters) in order to determine the effect of various wing forms on the air forces and moments. Three-component measurements were taken, and one model was also investigated with deflected control plates.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc63980/

### Investigation of turbulent flow in a two-dimensional channel

**Date:**January 1, 1951

**Creator:**Laufer, John

**Description:**A detailed exploration of the field of mean and fluctuating quantities in a two-dimensional turbulent channel flow is presented. The measurements were repeated at three Reynolds numbers, 12,300, 30,800, and 61,600, based on the half width of the channel and the maximum mean velocity. A channel of 5-inch width and 12:1 aspect ratio was used for the investigation. Mean-speed and axial-fluctuation measurements were made well within the laminar sublayer. The semitheoretical predictions concerning the extent of the laminar sublayer were confirmed. The distribution of the velocity fluctuations in the direction of mean flow u' shows that the influence of the viscosity extends farther from the wall than indicated by the mean velocity profile, the region of influence being approximately four times as wide.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc60399/

### On the theory of oscillating airfoils of finite span in subsonic compressible flow

**Date:**January 1, 1950

**Creator:**Reissner, Eric

**Description:**The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results.

**Contributing Partner:**UNT Libraries Government Documents Department

**Permallink:**digital.library.unt.edu/ark:/67531/metadc60341/