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At least 235 records · Page 13

A Navier-Stokes solver for high speed equilibrium flows and application to blunt bodies

This paper presents a finite element method for the solution of Navier-Stokes equations with the assumption of thermodynamic and chemical equilibrium. The method employs an upwind finite element technique with an implicit time-marching scheme for the solution, and uses an adaptively generated unstructured triangular mesh with several layers of quadrilateral elements near solid walls. The complexity associated with the assumption that the flow is in equilibrium is treated consistently, and the inviscid flux Jacobian matrices are derived. Several problems involving inviscid and viscous hypersonic flow past blunt are solved. Results are compared with other numerical results and experimental data, and generally good agreement is observed.

Prabhu, Ramadas K.↗

Flow-establishment times for blunt bodies in an expansion tube

Flow establishment results are presented as obtained from shock standoff distance, pressure, and heat transfer measurements in the Langley expansion tube. The models tested were flat-faced cylinders with varying radius and a sphere with a constant radius, and they were positioned at the acceleration section exit and tested in the open jet at zero angle of attack. The experimental results were obtained as spinoff from various studies using helium, air, and CO2 test gases at freestream velocities in the range 5-7 km/sec. Time histories of shock detachment distance illustrate that the shock formation about the smaller-radii flat-faced cylinders and the sphere is symmetrical, whereas a complex, asymmetric formation is observed for the larger-radii cylinders. Flow is shown to establish more readily about the sphere than a flat-faced cylinder of the same diameter. A quasi-steady flow exists about relatively large blunt models during two-thirds of the approximate 250-microsec expansion tube test period.

Miller, C. G.↗

Computations of non-reacting and reacting viscous blunt body flows, volume 1

The computer programs developed for computation of viscous shock layer flow distribution surrounding the nose of a shuttle orbiter during reentry are presented. The problem formulation and the numerical procedures used to solve the basic set of equations are described. The results of flow distribution properties at several trajectory points, ranging from the high altitude rarefied region to the low altitude boundary layer region are analyzed.

Li, C. P.↗

Hypersonic ionizing air viscous shock-layer flows over nonanalytic blunt bodies

The equations which govern the viscous shock-layer flow are presented and the method by which the equations are solved is discussed. The predictions of the present finite-difference method are compared with other numerical predictions as well as with experimental data. The principal emphasis is placed on predictions of the viscous flowfield for the windward plane of symmetry of the space shuttle orbiter and other axisymmetric bodies which approximate the shuttle orbiter geometry. Experimental data on two slender sphere-cones at hypersonic conditions are also considered. The present predictions agreed well with experimental data and with the past predictions. Substantial differences were found between present predictions and more approximate methods.

Miner, E. W.↗

A study of the sonic-boom characteristics of a blunt body at a Mach number of 4.14

An experimental and theoretical study has shown that the applicability of far-field sonic-boom theory previously demonstrated for more slender shapes may now be extended to bodies with ratios of diameter to length as great as 2 and to Mach numbers at least as high as 4.14. This finding is of special significance in view of the limitations to the use of existing methods for the extrapolation of close-in experimental data.

Carlson, H. W.↗

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Gnoffo, P. A.↗

Solution of axisymmetric and two-dimensional inviscid flow over blunt bodies by the method of lines

Comparisons with experimental data and the results of other computational methods demonstrated that very accurate solutions can be obtained by using relatively few lines with the method of lines approach. This method is semidiscrete and has relatively low core storage requirements as compared with fully discrete methods since very little data were stored across the shock layer. This feature is very attractive for three dimensional problems because it enables computer storage requirements to be reduced by approximately an order of magnitude. In the present study it was found that nine lines was a practical upper limit for two dimensional and axisymmetric problems. This condition limits application of the method to smooth body geometries where relatively few lines would be adequate to describe changes in the flow variables around the body. Extension of the method to three dimensions was conceptually straightforward; however, three dimensional applications would also be limited to smooth body geometries although not necessarily to total of nine lines.

Hamilton, H. H., II↗

Complete supersonic flowfields over blunt bodies in a generalized orthogonal coordinate system

A general orthogonal coordinate system is used to describe various axisymmetric and two-dimensional shapes. Close approximations to planetary probe configurations are possible. The full Navier-Stokes equations are discretized in this coordinate system in a manner based on Allen and Cheng's numerical procedure. The blow shock is treated as a discontinuity which floats between grid points. Completely coupled flows over the forebody, base, and near wake were calculated over a cylinder, sphere, and an approximation to the Viking Aeroshell. Some problem areas in determining the base flow for increasing Reynolds number are discussed. In particular, it is found that the mean free path of the fluid near the wall immediately below the corner of the Viking Aeroshell, which experiences a severe expansion, can become greater than the local mesh size required to resolve the boundary layer in the forebody.

Gnoffo, P. A.↗