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Nonequilibrium inviscid flow about arbitrarily shaped body with detached shock waves, using method with time derivative and bypassing boundary conditions
Inviscid gas flow over nose region of supersonic yawed axisymmetric blunt body treated by integral relations in body oriented coordinate system
Two-body satellite of axisymmetric rigid bodies interconnected by lossy universal joint, calculating transient oscillation damping of forced precession under external torque
The effect of shoulder radiusing and circumferentially grooving the afterbodies of bluff bodies to reduce the base drag at low speeds is discussed. Shoulder radii as large as 2.75 body diameters are examined. Reynolds number based on body diameter varied from 20,000 to 200,000. Results indicate that increasing the shoulder radius to 2.75 body diameters can reduce the drag levels to those of a streamline body having 67 percent greater fineness ratio. For zero shoulder radius, circumferential grooves were found to be effective in reducing body drag for zero shoulder radius in both laminar and tripped flow. Circumferential grooves on the afterbody with a shoulder radius of one-half the body diameter were only effective in reducing drag for laminar flow.
The effect of shoulder radiusing and grooving (longitudinally and circumferentially) the afterbodies of bluff bodies to reduce the base drag at low speeds is investigated experimentally. Shoulder radii as large as 2.75 body diameters are examined. Reynolds number (ReD) based on body diameter varied from 20,000 to 200,000. Results indicate that increasing the shoulder radius to 2.00 body diameters can reduce the drag levels to those of a streamline body having 67 percent greater fineness ratio. For the relatively sharp shoulder case, body drag reductions as large as 50 and 33 percent are obtained using circumferential or longitudinal grooves, respectively.
The effect of shoulder radiusing and grooving (longitudinally or circumferentially) the afterbodies of bluff bodies of reduce the base drag at low speeds is discussed. Shoulder radii as large as 2.75 body diameters are examined. Reynolds number based on body diameter varied from 20,000 to 200,000. Results indicate that increasing the shoulder radius to 2.75 body diameters can reduce the drag levels to those of a streamline body having 67 percent greater fineness ratio. For the relatively sharp shoulder case, body drag reductions as large as 50% are obtained using circumferential or longitudinal grooves.
A numerical method was developed for calculating axisymmetric transonic (M greater than 1) flow about a blunt body; the bow shock wave location was investigated. A Rankine-Hugoniot jump was applied at the shock while relaxation on the isentropic equation of motion was used between shock and body. The shock wave is adjusted by a Newton type iteration scheme. Results are given for a sphere in the Mach number range 1.62 down to 1.02.
The aerodynamic characteristics of potential flow past an axisymmetric slender body and a thin airfoil are calculated using a uniform perturbation analysis method. The method is based on the superposition of potentials of point singularities distributed inside the body. The strength distribution satisfies a linear integral equation by enforcing the flow tangency condition on the surface of the body. The complete uniform asymptotic expansion of its solution is obtained with respect to the slenderness ratio by modifying and adapting an existing technique. Results calculated by the perturbation analysis method are compared with the existing surface singularity panel method and some available analytical solutions for a number of cases under identical conditions. From these comparisons, it is found that the perturbation analysis method can provide quite accurate results for bodies with small slenderness ratio. The present method is much simpler and requires less memory and computation time than existing surface singularity panel methods of comparable accuracy.
Thin radiating shock layer about axisymmetric blunt bodies, investigating energy-momentum transport coupling
Multicomponent nonequilibrium air flow past axisymmetric blunt body, calculating flow distribution at various attack angles with time dependent technique
The development of a design/analysis flow solver at NASA Lewis Research Center is discussed. The solver is axisymmetric and can be run inviscidly with assumed or calculated blockages, or with the viscous terms computed. The blade forces for each blade row are computed from blade-to-blade solutions, correlated data or force model, or from a full three dimensional solution. Codes currently under development can be separated into three distinct elements: the turbomachinery interactive grid generator energy distribution restart code (TIGGERC), the interactive blade element geometry generator (IBEGG), and the viscous/inviscid multi-blade-row average passage flow solver (VIADAC). Several experimental test cases were run to validate the VIADAC code. The tests, representative of typical axial turbomachinery duct axisymmetric wind tunnel body problems, were conducted on an SR7 Spinner axisymmetric body, a NASA Rotor 67 Fan test bed, and a transonic boatail body. The results show the computations to be in good agreement with test data.
The viscous, radiating hypersonic flow past an axisymmetric blunt body is analyzed based on the Navier-Stokes equations, plus a radiative equation of transfer derived from the Milne-Eddington differential approximation. The fluid is assumed to be a perfect gas with constant specific heats, a constant Prandtl number of order unity, a viscosity coefficient varying as a power of the temperature, and an absorption coefficient varying as the first power of the density and as a power of the temperature. The gray gas assumption is invoked, thereby making the absorption coefficient independent of the spectral frequency. Limiting forms of the solutions are studied as the freestream Mach number freestream Reynolds number and the temperature ratio across the shock wave, go to infinity, and as the Bouguer number and the density ratio across the shock wave go to zero. The method of matched asymptotic expansions is used in the analysis, and it is shown that there is a far-field precursor, composed of two regions, in which the fluid mechanics can be neglected for all practical purposes but included for completeness.
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.
A finite-difference relaxation method is presented for numerical solution of the full potential equation and exact boundary conditions for general axisymmetric bodies is inviscid, steady transonic flow. Body-normal coordinates are used in the nose region and sheared cylindrical coordinates are used on the afterbody to accommodate corners such as boattails and flares. An improved difference scheme is used which does not require that the flow be nearly alined with a coordinate direction in supersonic regions, and which treats either subsonic or supersonic free streams. Numerical results are illustrated for some simple classical shapes such as spheres and ellipsoids, and for more practical shapes like tangent-ogives with boattails. Special attention is given to bodies which have been studied for area-rule applications. Agreement with available experimental results is good in cases where viscous effects and wind-tunnel wall interference are not important.
Inviscid hypersonic flow of uniform equilibrium gas past axisymmetric blunt body
Boundary layer flow in thin shock layer about axisymmetric blunt bodies studied by Blasius type series expansion technique
A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.