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↗
Axisymmetric flows from fluid injection into a confined porous medium
In this work, we study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M , the viscosity ratio of displaced fluid relative to injected fluid, and Γ , which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R 2 /T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid ( Γ $\ll$ 1 and M < 1) where we identify a self-similar solution that indicates a parabolic interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity ( Γ $\ll$ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid ( Γ $\ll$ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow ( Γ $\gg$ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. “Axisymmetric gravity currents in a porous medium,” J. Fluid Mech. 543, 293–302 (2005)]. The various axisymmetric flows are summarized in a Γ - M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime. The implications of the regime diagram are discussed using practical engineering projects of geological CO 2 sequestration, enhanced oil recovery, and underground waste disposal.
42 ENGINEERING↗
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.↗
Interplay between fluctuation driven toroidal axisymmetric flows and resistive ballooning mode turbulence
An interplay between fluctuation driven toroidal axisymmetric flows (convective cell modes) and resistive ballooning mode turbulence after the pedestal collapse is numerically studied by a four-field reduced MHD model in the BOUT++ framework. The strong flow shear suppresses the radial transport of pressure filaments, and the pressure profile in the pedestal region is partially recovered. As a result, a secondary instability is quasilinearly excited, which yields a secondary collapse. Here, the subsequent damped oscillation is also analyzed by phase diagram analysis.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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.↗