Euler and Navier-Stokes solutions for supersonic shear flow past a circular cylinder
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The objective of this experimental study was to investigate the influence of horseshoe vortex on the heat transfer on a flat plate near the base of a protruding cylinder. The partial shock reflection technique was used to produce the flow Mach number of 0.14 which simulated the mean inlet flow Mach number for the first stage vanes of the turbine after combustor. Fast response thin-film platinum heat gages were used to measure the heat transfer flux for radial distances of 0.75, 0.875, 1.0, 1.125 cylinder diameter. For a low Reynolds number of 20,000, r/D = 0.75, and angular location from the stagnation point = 60 deg, the maximum increase in the heat transfer rate with the cylinder was observed to be approximately 460 percent greater than without the cylinder. On the other hand, the increase in the heat flux for a high Reynolds number of 300,000 was approximately 70 percent greater. For the heat gages located along 30 deg and 60 deg angular locations from the stagnation point, the strong effect of the horseshoe vortex was observed in the junction region. The increase in the heat transfer rate depended on the type of boundary layer and on the boundary layer thickness ahead of the cylinder.
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Convective heat transfer to shrouded cylinders in transverse flow has been studied over the Reynolds number range 2000-20,000. The influence of shroud ventilation, relative shroud diameters, and orientation of the ventilation holes was studied. In some cases, average inner-cylinder Nusselt numbers were found to exceed the comparable bare-cylinder values by as much as 50 percent. Cylinder heat convection was influenced more by the degree of ventilation and shroud diameter than by hole orientation. An equivalent inner bare cylinder diameter, based on degree of shroud ventilation and shroud diameter, was developed which can be useful in shroud design studies.
A scattering model for defoliated vegetation is developed by treating a layer of defoliated vegetation as a collection of randomly oriented dielectric cylinders of finite length over an irregular ground surface. Both polarized and depolarized backscattering are computed and their behavior versus the volume fraction, the incidence angle, the frequency, the angular distribution and the cylinder size are illustrated. It is found that both the angular distribution and the cylinder size have significant effects on the backscattered signal. The present theory is compared with measurements from defoliated vegetations.
The windward fraction of the total mass or heat transport for flow past a cylindrical aerodynamic object was estimated using the available experimental data for the angular distribution of the Nusselt transfer coefficient, Nu(theta, Re). The Re dependence of the windward surface fraction was calculated for the values of Re between 2 and 400,000. The results obtained from polar integrations of data from eight sources indicate that, for Reynolds numbers up to about 2000, more than 70 percent of the total transfer occurs on the windward surface. For the Re values above 100,000, the windward percentage is less than 50 percent.
This paper presents the results of a computational study on the shock interference problems on a cylindrical body typical of an engine inlet cowl leading edge at a nominal Mach number of 16. The two-dimensional Navier-Stokes equations are solved assuming the flow to be in chemical and thermal equilibrium and using a finite element method. The algorithm employs a cell-centered fully implicit upwind scheme. Adaptively generated unstructured meshes of triangles and quadrilaterals are employed. Under certain conditions the finite element code resulted in oscillatory solutions for shock interference at Mach 16. Some of the causes of the unsteady behavior are identified, and to the extent possible, such situations are avoided in the present application. Two shock interference conditions involving a Type IV (supersonic jet) and a Type III (attaching shear layer) are solved. The results are compared with available experimental data and reasonable agreement is observed. A semi-empirical method is also used to estimate the maximum surface heat flux and static pressure.
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Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.
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A general method for studying the flow of a compressible fluid around a closed body was discussed in Part I of this report. Here, application is made to the specific case in which the linearized equation of state is used. For a given incompressible flow around a specific profile, a corresponding compressible flow is found. The flow at infinity remains unchanged. Detailed studies are made of the flow with circulation around a unit circle, and velocity distributions are found for a wide range of Mach number and angle of attack. Comparisons are made with other methods.
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Explore the source record for details and available documents.