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**Partner:**UNT Libraries Government Documents Department

**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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### 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 ...

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**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 ...

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**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.

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**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.

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