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Braun, W. H.

Publications and source records attributed to Braun, W. H..

11 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Unsteady flow in a supersonic cascade with two in-passage shocks

A model for a supersonic blade row with two in-passage shock waves is developed. It accounts for three-dimensional effects in real flows by using an altered blade shape in a two-dimensional cascade. There is enough flexibility in the choice of blade shape to accommodate a desired entrance angle, exit angle, boundary-layer thickness and stage pressure ratio at a given entrance Mach number. The model divides the mean flow into regions of uniform or one-dimensional flow in which the solutions for the unsteady flow may be formed successively. The analysis makes use of previous solutions for unsteady flow in cascades and over an oscillation wedge. Six flow conditions are chosen in the range of parameters for which the two-shock model is valid for studies of flutter in torsion and bending. It is found, in keeping with previous results from a single-shock model, that in each case there is increasing instability with decreasing frequency.

Braun, W. H.↗
NASA NTRS1977

Representation of turbulent shear stress by a product of mean velocity differences

A quadratic form in the mean velocity for the turbulent shear stress is presented. It is expressed as the product of two velocity differences whose roots are the maximum velocity in the flow and a cutoff velocity below which the turbulent shear stress vanishes. Application to pipe and channel flows yields the centerline velocity as a function of pressure gradient, as well as the velocity profile. The flat plate, boundary-layer problem is solved by a system of integral equations to obtain friction coefficient, displacement thickness, and momentum-loss thickness. Comparisons are made with experiment.

Braun, W. H.↗
NASA NTRS1975

Inviscid interpenetration of two streams with unequal total pressures

A theory is proposed for analyzing the inviscid interpretation of two streams in the case when the difference in total pressure between the streams is relatively small. A stream is considered which discharges from a nozzle or reservoir into a partially moving and partially stationary environment in such a way that the flows leave the solid boundaries in a tangential direction where the two streams first interact. The problem is solved by expanding in a small parameter related to the difference in total pressure between the streams, the zeroth-order solution is obtained by classical methods, and a technique similar to that employed in thin-airfoil theory is used to transfer the first-order boundary conditions to the zeroth-order boundary. A procedure is developed to transform the problem into one that can be solved by standard techniques of the theory of sectionally analytic functions. Solutions are obtained for flows with and without free streamlines, and the general theory is applied to several specific flow configurations.

Goldstein, M. E.↗
NASA NTRS1973

Advanced methods for the solution of differential equations

This book is based on a course presented at the Lewis Research Center for engineers and scientists who were interested in increasing their knowledge of differential equations. Those results which can actually be used to solve equations are therefore emphasized; and detailed proofs of theorems are, for the most part, omitted. However, the conclusions of the theorems are stated in a precise manner, and enough references are given so that the interested reader can find the steps of the proofs.

Goldstein, M. E.↗