Numerical solution of laminar jet mixing with and without free stream
Systematic numerical analysis of two dimensional and axisymmetric laminar jet of incompressible fluid with and without free stream
Hsieh, T. Y.↗
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Measurement of flow magnitude and direction by hot wire anemometer
Hot-wire anemometer measurements of incompressible fluid flow direction and velocity in pipes
Fox, R. W.↗
A phenomenological theory of streaming birefringence
Streaming birefringence theory, discussing incompressible fluids, shear and Couette flows, fading memory, deformations
Coleman, B. D.↗
Stability and transient motion of a vertical three-lobe bearing system
Stability characteristics and general transient motion of vertical finite width three lobe journal bearing, assuming incompressible fluid with cavitation
Falkenhagen, G. L.↗
Numerical solution of laminar jet mixing with and without free stream.
Systematic numerical solutions of two-dimensional and axisymmetrical laminar jet of an incompressible fluid with and without free stream have been obtained. For the case without free stream, the exact numerical solutions have been obtained for different initial velocity profiles and compared with experimental results and similarity solutions. For the case with free stream, the numerical solutions have been compared with the linearized analytical solutions. An approximate numerical solution for the axial velocity distribution of the three-dimensional laminar jet is proposed. The accuracy of the method has been determined from the exact solutions of the two limiting cases of three-dimensional jets, i.e., the two-dimensional and axisymmetric cases.
Pai, S. I.↗
Multiple element airfoils optimized for maximum lift coefficient.
Optimum airfoils in the sense of maximum lift coefficient are obtained for incompressible fluid flow at large Reynolds number. The maximum lift coefficient is achieved by requiring that the turbulent skin friction be zero in the pressure rise region on the airfoil upper surface. Under this constraint, the pressure distribution is optimized. The optimum pressure distribution is a function of Reynolds number and the trailing edge velocity. Geometries of those airfoils which will generate these optimum pressure distributions are obtained using a direct-iterative method which is developed in this study. This method can be used to design airfoils consisting of any number of elements. Numerical examples of one- and two-element airfoils are given. The maximum lift coefficients obtained range from 2 to 2.5.
Ormsbee, A. I.↗
Thermocapillary convection in weightless condition
Results are presented of studies on thermocapillary instability of a liquid in a spherical layer with free surface and convection in a rectangular channel with horizontal temperature gradient. It is shown that in vessels partly filled with a viscous incompressible fluid and under essentially weightless conditions free convection may arise due to the surface tension temperature dependence.
Babskiy, V. G.↗
A theoretical method for the analysis and design of axisymmetric bodies
A theoretical method is presented for the computation of the flow field about an axisymmetric body operating in a viscous, incompressible fluid. A potential flow method was used to determine the inviscid flow field and to yield the boundary conditions for the boundary layer solutions. Boundary layer effects in the forces of displacement thickness and empirically modeled separation streamlines are accounted for in subsequent potential flow solutions. This procedure is repeated until the solutions converge. An empirical method was used to determine base drag allowing configuration drag to be computed.
Beatty, T. D.↗
The NASTRAN SRB slapdown water impact analysis
A computer analysis was made of the hydroelastic interaction between a shell structure representing the space shuttle solid rocket motor case and an incompressible fluid during the slapdown phase of water impact. The large motions and hydroelastic response of the system were obtained by numerical integration of the combined hydrodynamics and structural equations of motion and are analyzed for a selected interval after the initial nozzle impact. The computerization of the slapdown hydroelastic capability was incorporated into the general purpose NASTRAN computer code. The development of the theoretical basis, a guide to the program's usage, results of correlation and parameter studies, and a detailed description of the computer code are also included.
Herting, D. N.↗
Starting vortex, separation bubbles and stall - A numerical study of laminar unsteady flow around an airfoil
The stalling characteristics of an airfoil in a laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behavior of the forces at large times are studied. Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behavior of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles.
Mehta, U. B.↗
An analytical study of reduced-gravity flow dynamics
Addition of surface tension forces to a marker-and-cell code and the performance of four incompressible fluid simulations in reduced gravity, were studied. This marker-and-cell code has a variable grid capability with arbitrary curved boundaries and time dependent acceleration fields. The surface tension logic includes a spline fit of surface marker particles as well as contact angle logic for straight and curved wall boundaries. Three types of flow motion were simulated with the improved code: impulsive settling in a model Centaur LH2 tank, continuous settling in a model and full scale Centaur LO2 tank and mixing in a Centaur LH2 tank. The impulsive settling case confirmed a drop tower analysis which indicated more orderly fluid collection flow patterns with this method providing a potential savings in settling propellants. In the LO2 tank, fluid collection and flow simulation into the thrust barrel were achieved. The mixing simulation produced good results indicating both the development of the flow field and fluid interface behavior.
Bradshaw, R. D.↗
Some new results on the statistics of radio wave scintillation. I - Empirical evidence for Gaussian statistics
This paper presents an analysis of ionospheric scintillation data which shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact, it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure, it is found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus, the signal is modeled by a Gaussian, but highly non-Rician process. From simultaneous UHF and VHF data, only a weak dependence of this statistical structure on changes in the Fresnel radius is deduced. The signal variance is found to have a nonquadratic wavelength dependence. It is hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov (1941) in his early studies of incompressible fluid turbulence.
Rino, C. L.↗
An analytical study of noise generation by subsonic flows in the presence of rigid surfaces
A general analytical method is developed for determination of the radiated noise field from highly sheared, subsonic flows in the presence of rigid surfaces. The method is specifically formulated to use measurable flow field properties as the basis input data for calculations. The governing equations of a viscous, incompressible fluid are employed to determine approximately the so-called shear noise source strength distribution in the flow. Mean rates of strain and fluctuating velocity covariances are the fundamental input data for calculations. The method is applied to the wall jet region of a circular jet impinging at 45 deg to an infinite plane surface. Velocity field measurements of Foss are used to describe the required flow properties. Comparisons of calculated results with measured surface pressures and sound pressure levels are given and discussed.
Wooley, J. P.↗
A three-dimensional, time-dependent model of Mobile Bay
A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.
Pitts, F. H.↗
A numerical study of flow phenomena within a vortex sink rate sensor
A numerical investigation of a viscous incompressible fluid with constant properties within a vortex sink rate sensor is undertaken. A computer program was developed, for obtaining the numerical solution of the Navier-Stokes equations, assuming laminar flow, having general prescribed inlet conditions and axisymmetric boundary conditions. Computational results for various viscous flows and assorted boundary conditions have been obtained. In the vortex chamber, the radial momentum is conserved, whereas the axial momentum is negligible. In the sink region, the radial and tangential velocities, as well as the tangential vorticities, have significantly high values. In the sink tube, the radial momentum is negligible. The radial momentum within the vortex chamber is converted to the axial momentum in the sink tube. A change in the flow rate had an appreciable effect within the sensor and particularly near the sink tube entrance. As the flow rate was increased, both the tangential velocity and tangential vorticity increased rapidly. At the higher flow rates, vortices were produced at the corner of the entrance section of the sink tube.
Patel, D. K.↗
On the large-scale structure in turbulent free shear flows
The interaction between the large-scale structure and the disparately fine-grained turbulence in a free turbulent shear flow, in particular, the mixing region is considered. New results pertaining to the spatial problem are presented. An incompressible fluid is considered. An energy integral description is discussed, giving attention to shape assumptions, the interaction problem, energy transfer mechanisms, the spectral dependence of the interaction, and the control of the large-scale structure.
Liu, J. T. C.↗
Navier-Stokes solution for the laminar and turbulent supersonic flow near the trailing edge of a flat plate
The present paper deals with problems of two-dimensional laminar and turbulent flow of a viscous incompressible fluid near the trailing edge of a thin flat plate. The complete system of Navier-Stokes equations is solved by means of MacCormack's finite-difference scheme. In the laminar case, the results are compared with the triple deck solution of Daniels (1973). The comparisons indicate that the asymptotic triple deck theory for supersonic trailing-edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clausner algebraic eddy viscosity model is used, showing that the region of upstream influence is roughly of the order of the boundary layer thickness.
Hussaini, M. Y.↗
A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations
Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.
Kurtz, L. A.↗