Poincare's hydrodynamic analogy in celestial mechanics
Poincare hydrodynamic analogy in celestial mechanics, relating differential equations for dynamic systems with two degrees of freedom and two and three dimensional flow
Szebehely, V.↗
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Contribution to methods for calculating the flow about thin lifting wings at transonic speeds: Analytic expressions for the far field
The problem of determining the small-disturbance flow about two-dimensional airfoils at transonic speeds has been successfully treated by the process of matching a numerical solution of the near field to analytic expressions for the far field. The three-dimensional problem, it would appear, can be treated in a similar way with the aid of algorithms adapted to high-speed and high-capacity computers. The far-field potential for both lifting and nonlifting three-dimensional wings at transonic speeds is developed herein for a subsonic free stream. This potential could be used for a three-dimensional-wing computation similar to the computation made for the two-dimensional wing.
Klunker, E. B.↗
The theoretical and experimental investigations on multiple pure tone noise, part 1
A theoretical and experimental investigation is described on multiple pure tone noise. Based on a two-dimensional and inviscid flow model, an analysis is developed to predict the generation and subsequent evolution of multiple pure tone noise from prescribed blade-to-blade nonuniformities in the rotor geometry. The results show that even small nonuniformities within manufacturing tolerances can cause a significant amount of multiple pure tone noise. Among the different kinds of nonuniformities investigated, errors in blade spacings are a weaker generator of multiple pure tone noise than errors in blade stagger or blade contours. Experimental investigations of the effects of the rotor relative Mach number, incidence angle and length of the inlet duct on the evolution of the multiple pure tone noise are conducted with a known distribution of rotor nonuniformities. The model fan is operated, in Freon 12, in a closed loop acoustical facility.
Kantola, R. A.↗
Quasi-three-dimensional calculation of velocities in turbomachine blade rows
A practical way of obtaining an approximation to a three dimensional flow is to combine several two-dimensional solutions (quasi-three-dimensional solution). Three basic types are discussed of two-dimensional solutions (meridional, blade-to-blade, and channel) and several ways of combining them. A centrifugal impeller is analyzed as an example. All recommended methods are based on available NASA general purpose computer programs.
Katsanis, T.↗
Analytical investigation of two-phase heat transfer in a porous matrix.
One-dimensional two-phase flow transpiration cooling through porous metals is studied analytically. The differential energy equations for the solid and for the liquid with temperature dependent properties are solved simultaneously with a semi-empirical pressure drop correlation. Formulation of the problem both assuming thermal equilibrium (assumes Clausius-Claperyon equation pertains) and nonequilibrium (defines a parameter representing fraction of energy transferred to mixture which contributes to evaporation) is given. Representative solutions showing the influences and significance of the controlling dimensionless parameters are presented.
Frost, W.↗
Calculation of free turbulent mixing by interaction approach.
The applicability of Bradshaw's interaction hypothesis to two-dimensional free shear flows was investigated. According to it, flows with velocity extrema may be considered to consist of several interacting layers. The hypothesis leads to a new expression for the shear stress which removes the usual restriction that shear stress vanishes at the velocity extremum. The approach is based on kinetic energy and the length scale equations. The compressible flow equations are simplified by restriction to low Mach numbers, and the range of their applicability is discussed. The empirical functions of the turbulence model are found here to be correlated with the spreading rate of the shear layer. The analysis demonstrates that the interaction hypothesis is a workable concept.
Morel, T.↗
Application of an invariant second-order closure model to compressible turbulent shear layers
A second-order closure model for two-dimensional, compressible shear flows is investigated using the invariant modeling technique developed by Donaldson. The invariant model parameters were originally selected by comparison of model predictions with critical experimental data on basic incompressible flows. Additional modeling for compressible flows has been introduced. A number of different shear flows such as the free shear layer, flat plate boundary layer and a simulation of the mixing region of a chemical laser are computed. The model is consistent with first-order closure turbulence models for equilibrium flows and is further capable of predicting nonequilibrium flows that cannot be correctly solved by eddy viscosity models. The results are in generally good agreement with experimental measurements but suggest the need for inclusion of a Mach number dependent model of the pressure diffusion terms in order to adequately represent high speed compressible flows.
Varma, A. K.↗
Quasi-three-dimensional flow solution by meridional plane analysis
A computer program has been developed to obtain subsonic or shock-free transonic, nonviscous flow analysis on the hub-shroud midchannel flow surface of a turbomachine. The analysis may be for any annular passage, with or without blades. The blades may be fixed or rotating and may be twisted and leaned. The flow may be axial, radial, or mixed. Blade surface velocities over the entire blade are approximated, based on the rate of change of angular momentum. This gives a three-dimensional flow picture based on a two-dimensional analysis. This paper discusses the method used for the program and shows examples of the type of passages and blade rows which can be analyzed. Also, some numerical examples are given to show how the program can be used for practical assistance in design of blading, annular passages, and annular diffusers.
Katsanis, T.↗
Aerodynamic Analyses Requiring Advanced Computers, part 2
This compilation consists of papers presented at a conference on Aerodynamic Analyses Requiring Advanced Computers held at the NASA Langley Research Center on March 4-6, 1975. The purpose of the conference was to present results of recent theoretical research on aerodynamic flow problems requiring the use of advanced computers. The conference was divided into the following sessions: (1) Viscous Flows, (2) Internal Flows, (3) Two-Dimensional Configurations, and (4) Three-Dimensional Configurations. Papers were presented by members of NASA Centers, Universities, and Industry.
Langley Research Center↗
A general algorithm using finite element method for aerodynamic configurations at low speeds
A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.
Balasubramanian, R.↗
Effect of anisotropy and rotation on turbulence production
The dynamical equations for the Reynolds stresses in a form which is suitable for incompressible homogeneous flows are used as a starting point in the investigation. It is assumed that the mean flow is two-dimensional. The equation for the rate of change of the kinetic energy of turbulence is derived. If the turbulence is isotropic, there is no turbulence production. However, the isotropic condition is not stable. The production mechanism is found to be autocatalytic. Rotation always inhibits production because it reduces anisotropy.
Ferziger, J. H.↗
Calculation of transonic potential flowfields about complex, three-dimensional configurations
Methods for extending iterative, finite-difference calculations of transonic potential flowfields to complex three-dimensional configurations are discussed. One particularly attractive approach is to use relatively simple conformal mappings in combination with shearing transformations to generate computational domains that are nearly-conformally mapped from the physical space in one family of coordinate surfaces, and which map the complex boundaries to grid surfaces. The application of such a method to a general wing-body combination or to a multi-bladed fan is discussed. A transformation to map the wing-fuselage or fan-hub combination to a convenient computational domain is proposed. The transformation is useful in its own right for treating the two-dimensional problems of flow past a profile in a wind tunnel or through a cascade. Some results of preliminary calculations are presented.
Caughey, D. A.↗
Transonic airfoil analysis and design
TRANDES program provides aircraft engineer with accurate and efficient tool for analysis of steady, irrotational, transonic flow over specified two dimensional airfoil in free air. Program is used to design airfoils having prescribed pressure distribution, including effects of weak viscous interaction. TRANDES yield accurate solutions efficiently for biconvex, conventional, and aftcambered airfoils.
Carlson, L. A.↗
A study of viscous cross-flow effects on circular cylinders at high Reynolds numbers
Results of experimental studies on viscous cross-flow over circular cylinders for Reynolds numbers from 0.15 x 10 to the 6th to 10.9 x 10 to the 6th at Mach numbers of less than 0.3 are presented and compared with previous work where possible. Results presented include the variation of static cross-flow drag coefficients with both Reynolds number and ratio of surface roughness to model diameter, the variation of Strouhal number with Reynolds number and the dynamic variation of surface static pressure coefficients with both angular position around the cylinder and Reynolds number. The effects of end-plates on flow around two-dimensional bluff-bodies and of tunnel blockage on drag measurements are also discussed.
James, W. D.↗
Approximate and exact numerical integration of the gas dynamic equations
A highly accurate approximation and a rapidly convergent numerical procedure are developed for two dimensional steady supersonic flow over an airfoil. Examples are given for a symmetric airfoil over a range of Mach numbers. Several interesting features are found in the calculation of the tail shock and the flow behind the airfoil.
Lewis, T. S.↗
Simple turbulence models and their application to boundary layer separation
Measurements in the boundary layer and wake of a stalled airfoil are presented in two coordinate systems, one aligned with the airfoil chord, the other being conventional boundary layer coordinates. The NACA 4412 airfoil is studied at a single angle of attack corresponding to maximum lift, the Reynolds number based on chord being 1.5 x 10 to the 6th power. Turbulent boundary layer separation occurred at the 85 percent chord position. The two-dimensionality of the flow was documented and the momentum integral equation studied to illustrate the importance of turbulence contributions as separation is approached. The assumptions of simple eddy-viscosity and mixing-length turbulence models are checked directly against experiment. Curvature effects are found to be important as separation is approached.
Wadcock, A. J.↗
Laminar free convection boundary layer heat transfer over non-isothermal surface
Accurate heat transfer results are provided for the case of nonisothermal objects. A steady, laminar, free convection boundary layer flow over two-dimensional or rotationally symmetrical bodies of nonuniform surface temperature situated in an ambient fluid of undisturbed temperature is considered analytically. The surface heat flux is given in terms of the Nusselt number and wall derivatives of universal functions for Prandtl numbers of 0.72 and 100 are provided. The method is shown to be valid up to a temperature/radius ratio of 130 deg.
Lin, F. N.↗
Conjugated heat transfer in a laminar boundary layer with heat source at the wall
This work presents the solution of the temperature field in a two-dimensional laminar incompressible flow over a conducting solid plate with a line heat source located at the fluid-solid interface perpendicular to the flow direction. A numerical scheme was used to obtain the temperature profiles as a function of the source strength, and of the properties of the fluid and the solid. The heat conduction and forced convection in the fluid and the heat conduction in the solid were solved for the case of moderate temperature rise, where the assumption of constant properties applies. The model enables the improvement of an instrument for the detection of boundary layer separation. It was found that for the actual parameters of the separation detector, a distance of 4 to 24 mm between the sensors gives an indication of 70 percent of the maximum temperature difference.
Brosh, A.↗