Prediction of heat transfer from laminar boundary layers, with emphasis on large free- stream velocity gradients and highly cooled walls
Prediction of heat transfer and shear stress from laminar boundary layer
HEAT TRANSFER↗
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BENDING VIBRATIONS OF A CIRCULAR CYLINDRICAL SHELL CONTAINING AN INTERNAL LIQUID WITH A FREE SURFACE.
Bending vibrations of a circular cylindrical shell containing an internal liquid with a free surface
FREE BOUNDARY↗
Effect of fluid motion on free surface shape under reduced gravity.
Velocity, Bond number and Weber number effects on liquid free surface shape and meniscus height under reduced gravity
FLOW VELOCITY↗
Response of the free surface of a cylindrically contained liquid to off-axis accelerations.
Linearized three-dimensional potential flow equations for response of liquids in cylindrical containers to slightly off-axis acceleration
FREE BOUNDARY↗
Computer program uses characteristics method for free-jet investigation
Computer program computes the free-jet boundary contours and other flow properties within the exhaust plume from highly underexpanded nozzles operating in near-vacuum conditions. The calculations are made by the method of characteristics which makes use of three-dimensional irrotational equations of flow.
Craidon, C. B.↗
A new momentum-integral method for treating MHD and simple hydrodynamic entrance flows.
Conducting fluid incompressible flow in entrance of MHD channel by momentum integral method, permitting edge stress existence at boundary layer free stream interface
Schwirian, R. E.↗
A new momentum integral method for MHD channel entrance flows
Conducting fluid incompressible flow in entrance of MHD channel by momentum integral method, permitting edge stress existence at boundary layer free steam interface
Schwirian, R. E.↗
Modes of vibration in a circular plate with three simple support points.
The analytical solutions for the vibrational modes of a thin circular flat plate that is simply supported at three points on the circumference are presented. The mode shapes and corresponding eigenvalues are obtained. Results show that the modes can be grouped into four different types depending on the manner by which they receive the pressure at the supported points. The problem is of the mixed boundary value type in that some portion of the boundary is free while the other portion is simply supported.
Chi, C.↗
Wind tunnel investigation of a Centaur standard shroud compartment vent from Mach number of 0.70 to 1.96
An experimental investigation was conducted in the Lewis Research Center 8- by 6-foot supersonic wind tunnel to determine the vent discharge coefficient for the Centaur standard shroud/liquid hydrogen tank compartment vent. The test was conducted from Mach 0.70 to 1.96 with the vent mounted in a flat plate. Full scale simulated flight hardware, such as the vent, corrugations, aft field joint ring and ice bag clip was used. Air was discharged from a plenum chamber, located on the tunnel sidewall behind the plate, through five 6.35 cm diameter vent orifices into the free stream. Boundary layer thickeners, analytically predicted displacement thickness for the vehicle nominal flight trajectory could be simulated over the Mach number range. The highest vent discharge coefficient for any given Mach number and vent pressure ratio generally occurred at the maximum displacement thickness.
Johns, A. L.↗
Free convection over a vertical porous plate with transpiration
The problem of free convection over an isothermal vertical porous plate with transpiration is studied both numerically and experimentally. Numerical solutions to the variable-property transpired free-convection boundary layer equations have been obtained using the finite difference procedure of Patankar and Spalding (1967). The effects of uniform transpiration on heat transfer and on temperature and velocity profiles are predicted. Interferometrically measured nondimensional temperature profiles for the uniform wall temperature and transpiration case agreed closely with these numerical predictions.
Parikh, P. G.↗
Calculation of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations
A numerical method is presented which is valid for integration of the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to the three-dimensional supersonic flow of a jet issuing into a supersonic free stream. Difficulties associated with the imposition of free-stream boundary conditions are noted, and a coordinate transformation, which maps the point at infinity onto a finite value, is introduced to alleviate these difficulties. Results are presented for calculations of a square jet and varying-aspect-ratio rectangular jets. The solution behavior varies from axisymmetry for the square jet to nearly two-dimensional for the high-aspect-ratio rectangle, although the computation always calculates the flow as though it were truly three-dimensional.
Hirsh, R. S.↗
Theoretical study of reactive and nonreactive turbulent coaxial jets
The hydrodynamic properties and the reaction kinetics of axisymmetric coaxial turbulent jets having steady mean quantities are investigated. From the analysis, limited to free turbulent boundary layer mixing of such jets, it is found that the two-equation model of turbulence is adequate for most nonreactive flows. For the reactive flows, where an allowance must be made for second order correlations of concentration fluctuations in the finite rate chemistry for initially inhomogeneous mixture, an equation similar to the concentration fluctuation equation of a related model is suggested. For diffusion limited reactions, the eddy breakup model based on concentration fluctuations is found satisfactory and simple to use. The theoretical results obtained from these various models are compared with some of the available experimental data.
Gupta, R. N.↗
Three-dimensional low Reynolds number flows with a free surface
The two-dimensional leveling problem (Degani, Gutfinger, 1976) is extended to three dimensions in the case where the flow Re number is very low and attention is paid to the free surface boundary condition with surface tension effects included. The no-slip boundary condition on the wall is observed. The numerical solution falls back on the Marker and Cell (MAC) method (Harlow and Welch, 1965) with the computation region divided into a finite number of stationary rectangular cells (or boxes in the 3-D case) and fluid flow traverses the cells (or boxes).
Degani, D.↗
Characteristics of laminar gas jet diffusion flames under the influence of elevated gravity
Laminar gas jet diffusion flames of hydrogen, methane, ethane, and propane, stabilized on small cylindrical burners, were studied at elevated gravity in a centrifuge to investigate the role of buoyancy in such flames. Photographic observation of the hydrocarbon flames indicated that length and carbon luminosity decreased with increasing buoyancy. These flames eventually separated from the burner rim and finally extinguished as gravity increased. Hydrogen flames, however, did not separate or extinguish up to about 31 times earth normal gravity. Length data are reported and interpreted with the aid of a simplified model which describes the flame as a heated vertical cylindrical sheet to which oxygen is supplied by a free convection boundary layer.
Altenkirch, R. A.↗
Conditions for acceleration of energetic ions greater than 30 keV associated with the earth's bow shock
A statistical analysis of particles (greater than 30 keV/charge) upstream of the earth's bow shock is conducted and shows that the rate of occurrence of upstream particle events is relative to the angle between the magnetic field and the shock normal at the shock intersection point as well as relative to the angle between the magnetic field and the radial direction (i.e., the sun-earth line). In addition, the occurrence rate of upstream particle events relative to the bow shock connection time of a field line convected with the solar wind is presented for a model bow shock. A linear dependence of the diffusion coefficient on energy per charge is apparent with the value of the mean free path of a 30-keV proton found to be about 4 earth radii, and the free escape boundary to be at about 30 earth radii in front of the bow shock.
Scholer, M.↗
Vertical slender jets
The shape of a vertical slender jet of fluid falling steadily under the force of gravity is studied. The problem is formulated as a nonlinear free boundary-value problem for the potential. Surface tension effects are neglected. The use of perturbation expansions results in a system of equations that can be solved by an efficient numerical procedure. Computations were made for jets issuing from orifices in various shapes including an ellipse, a rectangle, and an equilateral triangle. Computational results are presented illustrating the propagation of discontinuities and the formation of thin sheets of fluid.
Geer, J. F.↗
Simultaneous observations of energetic protons close to the bow shock and far upstream
Four upstream energetic proton events (30 keV-75 keV), which were simultaneously observed by the ISEE-1 and ISEE-3 satellites, are investigated. A comparison was made between the absolute flux values about 200 earth radii from the bow shock and the flux values several earth radii in front of the bow shock at two different energies. Close to the bow shock the particle distribution is more or less isotropic and indicates relatively strong scattering of these particles in the upstream wave field. At ISEE-3 between 100 and 200 earth radii upstream from the earth's bow shock, the particles move essentially scatter-free from the general bow shock direction. The proton differential intensity at ISEE-3 is a factor of about 4-15 less than at ISEE-1 at 30 keV. The spectra at ISEE-1 are steeper than the spectra at ISEE-3. Flux ratios and spectra are discussed in terms of a first order Fermi acceleration model with a diffusion coefficient increasing approximately linearly with energy and a free escape boundary at some distance upstream.
Scholer, M.↗
VNAP2: A Computer Program for Computation of Two-dimensional, Time-dependent, Compressible, Turbulent Flow
A computer program, VNAP2, for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow is presented. It solves the two dimensional, time dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing length model, a one equation model, or the Jones-Launder two equation model. The geometry may be a single or a dual flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference plane characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet powered afterbodies, airfoils, and free jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.
Cline, M. C.↗