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A program called RAXBOD is presented for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. The method solves the exact equation for the disturbance velocity potential function and applies the exact surface boundary condition. Instructions on program usage and listings of the program and sample cases are given.
An experimental investigation has been conducted to determine the physical process of the noise production from the trailing edge of an isolated two-dimensional airfoil embedded in a low turbulence uniform mean flow. The Reynolds number of the airfoil based on chord was greater than 1,000,000 and that the boundary layer was fully turbulent at the trailing edge. Smoke injection technique and spark shadowgraphy were used to study the structural features of the boundary layer. Two point joint statistical analyses were made on the surface pressure, the radiated sound and the relationship between the two quantities. Operating conditions included two free stream velocities and two angles of attack for both a naturally developed and an artificially tripped boundary layer. Flow visualizations revealed the existence of large scale coherent motions in the outer region of the boundary layer. The observed coherent motions had scales of the order of boundary layer thickness and a convection velocity near the free stream velocity. The production process of the airfoil trailing edge noise was determined to be the convection of the large scale coherent eddies over the trailing edge of the airfoil. The noise field so generated was found to be rather coherent and dipole-like.
The objective of this work has been to evaluate whether or not Marangoni flow could be suppressed in molten metals by the presence of very thin oxide films. Experimental work has been carried out on molten Sn under UHV conditions. A disk floating zone arrangement was developed to allow in situ Auger examination of molten surfaces. An electron energy loss technique was developed which allows detection of continuous tin oxide films of 6 A or greater. Experiments were planned to detect the effects of oxide formation upon Marangoni flow by measuring: (1) temperature profiles, (2) solid liquid interface shapes, (3) macrosegregation, and (4) the onset of oscillatory Marangoni flow by detecting oscillating temperature variations. Work on (4) showed that oscillatory temperature variations of frequency or = 10 Hz were not present in the disk float zone geometry under conditions of Ma = 4300 with an oxide free molten surface. The disk float zone geometry was modeled with a finite element analysis and temperature and velocity profiles were determined.
A ground-based experiment has validated the effectiveness of a noncontaminating method developed to reduce Marangoni (thermal capillary) convection in float-zone processing of corrosive materials in space microgravity. A drop of silicone oil 1.5 mm high was enclosed in a transparent box, and the small size of the drop was shown to suppress the 1-g thermal-buoyant convection. A vertical jet of air was blown tangentially over a vertical free surface, producing a viscous shear drag which opposes the Marangoni surface shear. A 66 percent reduction in Marangoni velocities was found in the lowest one-third of the drop, corresponding to the resolidification surface in a float-zone melt.
A FORTRAN 4 computer program has been developed that obtains a subsonic or shock-free transonic flow solution on the hub-shroud mid-channel flow surface of a turbomachine. The blade row may be fixed or rotating, and may be twisted and leaned. Flow may be axial or mixed, up to 45 deg from axial. Upstream and downstream flow variables may vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the flow surface; and approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference stream-function solution. Transonic solutions are obtained by a velocity-gradient method, using information from a finite-difference stream-function solution at a reduced mass flow.
A method for measurement of temperature in the earth's lower thermosphere from a high-velocity probes is described. An undisturbed atmospheric sample is admitted to the instrument by means of a free molecular flow inlet system of skimmers which avoids surface collisions of the molecules prior to detection. Measurement of the time-of-flight distribution of an initially well-localized group of nitrogen metastable molecular states produced in an open, crossed electron-molecular beam source, yields information on the atmospheric temperature. It is shown that for high vehicle velocities, the time-of-flight distribution of the metastable flux is a sensitive indicator of atmospheric temperature. The temperature measurement precision should be greater than 94% at the 99% confidence level over the range of altitudes from 120-170 km. These precision and altitude range estimates are based on the statistical consideration of the counting rates achieved with a multichannel analyzer using realistic values for system parameters.
A FORTRAN 4 computer program was developed that obtains a detailed subsonic or shock-free transonic flow solution on the hub-shroud midchannel stream surface of a turbomachine. The blade row may be fixed or rotating, and the blades may be twisted and leaned. Flow may be axial, mixed, or radial. Upstream and downstream flow variables may vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the stream surface as well as approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference, stream-function solution. Transonic solutions are obtained by a velocity-gradient method that uses information from a finite-difference, stream-function solution at a reduced mass flow.
A FORTRAN IV computer program has been developed that obtains a detailed subsonic or shock free transonic flow solution on the hub-shroud midchannel stream surface of a turbomachine. The blade row may be fixed or rotating, and the blades may be twisted and leaned. Flow may be axial, mixed, or radial. Upstream and downstream flow variables may vary from hub to shroud, and provisions are made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the stream surface and approximate blade surface velocities.
The most important factors determining solar coronal activity are believed to be the availability of magnetic free energy and the constraint of magnetic helicity conservation. Direct measurements of the helicity and magnetic free energy in the coronal volume are difficult, but their values may be estimated from measurements of the helicity and free energy transport rates through the photosphere. We examine these transport rates for a topologically open system such as the corona, in which the magnetic fields have a nonzero normal component at the boundaries, and derive a new formula for the helicity transport rate at the boundaries. In addition, we derive new expressions for helicity transport due to flux emergence/submergence versus photospheric horizontal motions. The key feature o four formulas is that they are manifestly gauge invariant. Our results are somewhat counterintuitive in that only the lamellar electric field produced by the surface potential transports helicity across boundaries, and the solenoidal electric field produced by a surface stream function does not contribute to the helicity transport. We discuss the physical interpretation of this result. Furthermore, we derive an expression for the free energy transport rate and show that a necessary condition for free energy transport across a boundary is the presence of a closed magnetic field at the surface, indicating that there are current systems within the volume. We discuss the implications of these results for using photospheric vector magnetic and velocity field measurements to derive the solar coronal helicity and magnetic free energy, which can then be used to constrain and drive models for coronal activity.
In the two papers on the 'Theory of Blade Design for Large Deflections' published in 1984, a new inverse design technique was presented for designing the shape of turbomachinery blades in three-dimensional flow. The technique involves the determination of the blade profile from the specification of a distribution of the product of the radius and the pitched averaged tangential velocity (i.e., r bar-V(sub theta), the mean swirl schedule) within the bladed region. This is in contrast to the conventional inverse design technique for turbomachinery blading in two dimensional flow in which the blade surface pressure or velocity distribution is specified and the blade profile determined as a result; this is feasible in two-dimensional flow because the streamlines along the blade surfaces are known a priori. However, in three-dimensional flow, the stream surface is free to deform within the blade passage so that the streamlines on the blade surfaces are not known a priori; thus it is difficult and not so useful to prescribe the blade surface pressure or velocity distribution and determine the resulting blade profile. It therefore seems logical to prescribe the swirl schedule within the bladed region for designing a turbomachinery blade profile in three-dimensional flow. Furthermore, specifying r bar-V(sub theta) has the following advantages: (1) it is related to the circulation around the blade (i.e., it is an aerodynamic quantity); (2) the work done or extracted is approximately proportional to the overall change in r bar-V(sub theta) across a given blade row (Euler turbine equation); and (3) the rate of change of r bar-V(sub theta) along the mean streamline at the blade is related to the pressure jump across the blade and therefore the blade loading. Since the publications of those two papers, the technique has been applied to the design of a low speed as well as a high speed radial inflow turbine (for turbocharger applications) both of which showed definite improvements in performance over that of wheels of conventional designs, the design study of a high pressure ratio radial inflow turbine with and without splitter blades.
Tests were performed on an airfoil in a low-turbulence subsonic wind tunnel at fixed incidence for different speeds of the wind, the airfoil being in translatory motion normal or parallel to the wind. The resulting aerodynamic forces and moment on the airfoil were measured along with local pressure and skin friction. When the incidence is small and the boundary layer attached, no unsteady effects were observed. However, for a large incidence (16 deg), in the case of boundary layer separation, strong unsteady effects are revealed when the boundary layer is reattached in periodic flow. Reattachment can be explained assuming that for the same value of free stream velocity, the gradient of the modulus of the periodic component of the relative airspeed at the upper surface of the airfoil in a direction normal to this surface is greater than the gradient of the relative air speed at the upper surface when the airfoil is not oscillating.
A method was devised and calculations were performed to determine the effects of reflected molecules on the aerodynamic force and moment coefficients for a body in free molecule flow. A procedure was developed for determining the velocity and temperature distributions of molecules reflected from a surface of arbitrary momentum and energy accommodation. A system of equations, based on momentum and energy balances for the surface, incident, and reflected molecules, was solved by a numerical optimization technique. The minimization of a 'cost' function, developed from the set of equations, resulted in the determination of the defining properties of the flow reflected from the arbitrary surface. The properties used to define both the incident and reflected flows were: average temperature of the molecules in the flow, angle of the flow with respect to a vector normal to the surface, and the molecular speed ratio. The properties of the reflected flow were used to calculate the contribution of multiply reflected molecules to the force and moments on a test body in the flow. The test configuration consisted of two flat plates joined along one edge at a right angle to each other. When force and moment coefficients of this 90 deg concave wedge were compared to results that did not include multiple reflections, it was found that multiple reflections could nearly double lift and drag coefficients, with nearly a 50 percent increase in pitching moment for cases with specular or nearly specular accommodation. The cases of diffuse or nearly diffuse accommodation often had minor reductions in axial and normal forces when multiple reflections were included. There were several cases of intermediate accommodation where the addition of multiple reflection effects more than tripled the lift coefficient over the convex technique.
A FORTRAN-IV computer program, MERIDL, has been developed that obtains a subsonic or shock-free transonic flow solution on the hub-shroud mid-channel flow surface of a turbomachine. The blade row may be fixed or rotating and may be twisted and leaned. Flow may be axial or mixed, up to 45 deg from axial. Upstream and downstream flow variables can vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the flow surface and approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference stream-function solution. Transonic solutions are obtained by a velocity-gradient method, using information from a finite-difference stream-function solution at a reduced mass flow.
Tests were conducted in a low speed wind tunnel to determine the aerodynamic performance of several flared fan nozzles. Each of the flared nozzles was a downstream-facing inlet to a model fan that was used to simulate a variable pitch fan during reverse thrust operation. The total pressure recovery of each of the flared nozzles as well as that of an unflared nozzle and a serrated flare nozzle was obtained for comparison. The aerodynamic performance of a selected flared nozzle was considered in further detail. The nozzle surface pressures for a flared nozzle were also determined. Results indicated that the differences in aerodynamic performance among the nozzles were most apparent at the wind-tunnel-off condition. A nonzero free stream velocity significantly reduced the perforamnce of all the nozzles, and crosswind flow (free stream flow perpendicular to the model axis) further reduced the performance of the nozzles. The unflared nozzle and the serrated flare nozzle had reduced aerodynamic performance compared to a solid surface flared nozzle.
A multi-level model, based on the primitive equations, is developed for simulating the temperature and velocity fields produced in the world ocean by differential heating and surface wind stress. The model ocean has constant depth, free slip at the lower boundary, and neglects momentum advection; so that there is no energy exchange between the barotropic and baroclinic components of the motion, although the former influences the latter through temperature advection. The ocean model was designed to be coupled to the UCLA atmospheric general circulation model, for the study of the dynamics of climate and climate changes. But here, the model is tested by prescribing the observed seasonally varying surface wind stress and the incident solar radiation, the surface air temperature and humidity, cloudiness and the surface wind speed, which, together with the predicted ocean surface temperature, determine the surface flux of radiant energy, sensible heat and latent heat.
Axisymmetric transonic flow is of interest not only because of its practical application to missile and launch vehicle aerodynamics but also because of its relation, in terms of area rule, to fully three dimensional flow. RAXBOD computer program analyzes steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses finite-difference relaxation method to solve numerically exact formulation of disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important.
A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.
Estimates of the minimum free-stream wind speed that is required for initiating the motion of surficial material on Mars have ranged from 30 to about 200 meters per second. Thus the best value for this quantity is not well established. Graphical comparison of much of the pertinent data taken in the laboratory and in the field on Earth provides a minimum value for the Bagnold coefficient of 0.08 and this in turn provides a minimum value for the threshold friction velocity of 1.3 meters per second for initiating motion of particulate matter on Mars at low elevations where the pressure is 7 millibars. The most appropriate value of the ratio of friction velocity to free-stream velocity for putative unstable condition appears to be 0.026. Thus the minimum free-stream wind speed for initiating motion is obtained as 50 meters per second. If the surface material on Mars, however, is less cohesive than that on earth, the minimum value may be smaller.