The influence of initial flow direction on the turbulent base pressure in supersonic axisymmetric flow
Turbulent base pressure on conical afterbodies in supersonic axisymmetric flow, including initial direction effect
Hall, C. R., Jr.↗
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Influence of initial flow direction on the turbulent base pressure in supersonic axisymmetric flow
Turbulent base pressure on conical afterbodies in supersonic axisymmetric flow, including initial direction effect
Hall, C. R., Jr.↗
Hydrostatic calculations of axisymmetric flow and its stability for the AGCE model
Baroclinic waves in the atmospherics general circulation experiment (AGCE) apparatus by the use of numerical hydrostatic primitive equation models were determined. The calculation is accomplished by using an axisymmetric primitive equation model to compute, for a given set of experimental parameters, a steady state axisymmetric flow and then testing this axisymmetric flow for stability using a linear primitive equation model. Some axisymmetric flows are presented together with preliminary stability calculations.
Miller, T. L.↗
An investigation of transonic turbulent boundary layer separation generated on an axisymmetric flow model
Experimental data are presented describing the transonic turbulent separated flow generated by an axisymmetric flow model. The model consisted of a circular-arc bump affixed to a straight circular cylinder aligned with the flow direction. Measurements of the mean velocity, turbulence intensity, and Reynolds shear stress profiles were made in the separated flow. These data revealed the dramatic changes in the shear stress levels as the flow passed from the interaction through to reattachment. Information on the behavior of the turbulence reaction to the imposed pressure gradients, as presented in this investigation, will be required for the development of the turbulence models used in predicting nonequilibrium turbulent flow fields.
Bachalo, W. D.↗
Transonic, turbulent boundary-layer separation generated on an axisymmetric flow model
Experimental data describing the transonic, turbulent, separated flow generated by an axisymmetric flow model are presented. The model consisted of a circular-arc bump affixed to a straight, circular cylinder aligned with the flow direction. Measurements of the mean velocity, turbulence intensity, and Reynolds shear-stress profiles were made in the separated flow. These data revealed dramatic changes in the shear-stress levels as the flow passed through the interaction to reattachment. Behavior of the turbulence reaction to the imposed pressure gradients was examined in terms of the mixing length and the excursions of the turbulence from equilibrium.
Bachalo, W. D.↗
Hysteresis and the transition between axisymmetric flow and wave flow in the baroclinic annulus
A numerical model is employed to establish the transitions between axisymmetric flow and wave flow in the rotating, differentially heated annulus experiments of Fein for both rigid lid and free surface cases. It is shown that, for most of the transitions, the method of computing a steady axisymmetric flow and then testing its linear stability to wave disturbance results in good agreement with the experiments. Implications for the investigation of the dynamics of the earth's atmosphere are considered.
Miller, Timothy L.↗
Time-dependent solution for axisymmetric flow over a blunt body with ideal gas, CF4, or equilibrium air chemistry
A time-asymptotic method has been used to obtain steady-flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, and spherically blunted cones. Comparisons with experimental data and results of other computational methods have demonstrated that accurate solutions can be obtained using this approach. The method should prove useful as an analysis tool for comparing with experimental data and for making engineering calculations for blunt reentry vehicles.
Hamilton, H. H., II↗
General solution of the laminar compressible boundary layer in the stagnation region of blunt bodies in axisymmetric flow
General solution of compressible laminar boundary layer in stagnation region of blunt bodies in axisymmetric flow
SOLUTION↗
On the nonlinear characteristics of the axisymmetric flow regime: Cylindrical and spherical systems
The physical relationship between steady axisymmetric flows that might be observed in the atmosphere and in laboratory vessels is investigated theoretically. This is accomplished by comparing both the nonlinear structure and the thermal forcing mechanisms in two truncated spectral models of flow in the atmosphere and the rotating laboratory cylinder, respectively. Under statically stable conditions, the response of the internally forced spherical model (which is developed here from a set of new orthonormal basis functions) exhibits steady behavior different from that in the externally forced cylindrical model. Two regions of multiple steady solutions occur in the cylindrical model, under stable conditions, that are not found in the spherical one. The possible physical relevance of these multiple solutions is investigated by determining their location in parameter space with respect to the classical Hadley-Rossby transition curve. The results suggest that the wave flow regime, in an annulus, might develop catastrophically when an upper symmetric flow ceases to exist.
Higgins, R. W.↗
Distorted turbulence in axisymmetric flow
A solution to the rapid-distortion theory for small-scale turbulence in flow round an axisymmetric obstacle is derived. General formulae for velocity covariances and Eulerian time scales are obtained and are evaluated for the particular case of flow round a sphere. The large-scale limit for this flow is also discussed.
Durbin, P. A.↗
Examination of a vortex-ring interaction phenomenon in an axisymmetric flow
Unsteady separated flow in an axisymmetric configuration is investigated, with the objective of analyzing vortex-ring formation and break-up and the ensuing interactions believed to be leading to breakdown of laminar flow. The model problem considered is an idealized representation of a combustor with a centerbody. Direct solution of the time-dependent incompressible Navier-Stokes equations is employed, with central-differencing for all spatial derivatives, to determine the response of this flow for Re = 2000, 5000 and 10,000. The last case revealed a rather novel unsteady vortex-ring interaction phenomenon. This case has been further investigated using third-order accurate upwind differencing for the convective terms. The flow is interrogated carefully by examining the corresponding instantaneous vorticity, stream-function and velocity fields, as well as by tracking mass-less marker particles in some of the critical regions. Such detailed examination is deemed essential, prior to assigning fundamental physical relevance to the observed vortex-interaction phenomenon.
Ghia, U.↗
A computational investigation of supersonic axisymmetric flow over boattails containing a centered propulsive jet
The influence of underexpanded jets on a supersonic afterbody flow field is investigated using computational techniques. The thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved using a time-dependent, implicit numerical algorithm. Solutions are obtained for supersonic flow over an axisymmetric conical afterbody containing a centered propulsive jet where the free-stream Mach number is 2.0 and the jet exit Mach number is 2.5. Exhaust-jet static pressures are considered in the range of 2 to 9 times the free-stream static pressure and with nozzle-exit half-angles from 15 deg to 43 deg. Comparisons are made with experimental results for base pressure, separation distance, afterbody pressure distribution, anf flow-field structure. Although good quantitative agreement with experimental separation distance and base pressure level is not observed, the parametric trends induced by exhaust-jet pressure level and nozzle-exit angle are well predicted, as are the flow-field details in the vicinity of the afterbody and in the exhaust plume.
Deiwert, G. S.↗
Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields
A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmetric flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thin-layer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results are in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.
Tweedt, Daniel L.↗
Computer program for calculating laminar, transitional, and turbulent boundary layers for a compressible axisymmetric flow
Finite-difference computer program calculates viscous compressible boundary layer flow over either planar or axisymmetric surfaces. Flow may be initially laminar and progress through transitional zone to fully turbulent flow, or it may remain laminar, depending on imposed boundary conditions, laws of viscosity, and numerical solution of momentum and energy equations.
Albers, J. A.↗
Transonic, Axisymmetric Flow Over Nozzle Afterbodies With Supersonic Jet Exhausts
Predictions require less computation than Navier-Stokes solutions. RAXJET computer program predicts transonic, axisymmetric flow over nozzle afterbodies with supersonic jet exhausts and includes effects of boundarylayer displacement, separation, jet entrainment, and inviscid jet plume blockage. RAXJET written in FORTRAN IV.
Wilmoth, R. G.↗
Nonexistence of axisymmetric separated flow.
Axisymmetric separated flow in Chapman model shown nonexistent by flow visualization technique
Ericsson, L. E.↗
Computation of steady axisymmetric flow using a one-dimensional time-dependent method
An iterative numerical method for computing steady, three dimensional, viscous, compressible flow fields, about aerodynamic bodies was studied. In order to develop the iterative method economically, the primary emphasis was directed towards supersonic, axisymmetric flow. However, the technique readily extends to three spatial dimensions. The viscous flow field about a cone-cylinder-flare body was calculated and compared to existing experimental data. Numerical predictions of the cone boundary layer and the flow field shock wave structure agreed with corresponding measurements. A separation was calculated at the cylinder-flare junction in six iterations; however, the size of the vortex did not correspond to the measured size. It was estimated that fifty iterations would be required to properly define the vortex. It was concluded that the iteration technique is of limited value for plane two dimensional and axisymmetrix flows, but of great value for three-dimensional flows.
Walitt, L.↗
Computer program for calculating laminar, transitional, and turbulent boundary layers for a compressible axisymmetric flow
A finite-difference program is described for calculating the viscous compressible boundary layer flow over either planar or axisymmetric surfaces. The flow may be initially laminar and progress through a transitional zone to fully turbulent flow, or it may remain laminar, depending on the imposed boundary conditions, laws of viscosity, and numerical solution of the momentum and energy equations. The flow may also be forced into a turbulent flow at a chosen spot by the data input. The input may contain the factors of arbitrary Reynolds number, free-stream Mach number, free-stream turbulence, wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and wall roughness. The solution may start from an initial Falkner-Skan similarity profile, an approximate equilibrium turbulent profile, or an initial arbitrary input profile.
Albers, J. A.↗