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Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cylinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.
Nonequilibrium inviscid flow about arbitrarily shaped body with detached shock waves, using method with time derivative and bypassing boundary conditions
A new method for predicting turbulent flow reattachment location has been developed. The method predicts the reattachment location using the surface static pressure distribution and requires only a single empirical parameter. The method is based on the well-known Stratford’s flow separation criterion, which results from an approximate solution to the equations of motion within the boundary layer. Because of the large pressure rise, the original Stratford separation criterion is not valid for reattaching flows. In order to apply the Stratford criterion for reattaching flows, the reference location was moved to the pressure drop conditions instead of pressure rise conditions. In addition, the pressure distribution was scaled using a technique that was originally introduced for supersonic base flows. A new empirical parameter was also obtained for the modified Stratford criterion. The method has been tested for 30 different separated flow configurations from the literature. The variety of test cases include subsonic flows, transonic flows, 2D flows, and axisymmetric flows, with experimental as well as high resolution numerical simulation results. The flow reattachment predictions with the new method agree very well with the reported data. The error is less than 5% and typically about 2%. The new method is an extremely simple and a quick way of finding the reattachment location. Given the complexities of the existing experimental techniques for finding the reattachment location, the method easily and quickly provides the flow reattachment location, which could be used to estimate the physical extent of separation bubbles, as a performance index for flow control methods, or to assess the predictive capability of turbulence models.
Numerical methods used in several implementations of the Generalized Acoustic Analogy for the prediction of turbulent jet noise are discussed. The equation governing sound propagation in the analogy formulation is presented along with analytical simplifications to reduce the computational burden of obtaining solutions. Numerical methods for the resulting boundary-value problem for two classes of jet flows, axisymmetric and non-axisymmetric mean flows, are discussed in detail. Example results from problems of the two classed of jets are presented.
The paper reviews some recent work on the stability of supersonic flow past axisymmetric bodies. Results indicate that tranverse curvature effect can both be stabilizing or destabilizing depending upon the particular instability modes involved. Small nose bluntness is found to have a stabilizing influence on the flow past a cone. The relevance of these results to supersonic boundary-layer transition is brought out and comparison with the experimental data is made where possible.
Turbulent nonreactive and reactive flows with and without swirl are analyzed, with particular attention given to the flow fields of a gas-fueled nonpremixed swirl-stabilized combustor and a premixed opposed-jet combustor. Local mean flow properties, including velocity, temperature, and major species concentrations, are calculated by solving numerically the governing partial differential equations with associated submodels for turbulence and combustion. The results of the study indicate that the constant-density k-epsilon turbulence model provides a satisfactory representation of the aerodynamics in most practical combustor flows. The exception is the case of jet-stabilized combustor flow, due to the fact that the k-epsilon model cannot replicate the highly dissipative phenomenon found in such flows.
A finite-difference procedure for computing the turbulent, swirling, compressible flow in axisymmetric ducts is described. Arbitrary distributions of heat and mass transfer at the boundaries can be treated, and the effects of struts, inlet guide vanes, and flow straightening vanes can be calculated. The calculation procedure is programmed in FORTRAN 4 and has operated successfully on the UNIVAC 1108, IBM 360, and CDC 6600 computers. The analysis which forms the basis of the procedure, a detailed description of the computer program, and the input/output formats are presented. The results of sample calculations performed with the computer program are compared with experimental data.
A boundary-layer-type solver is developed for the numerical solution of axisymmetric separated flows. A new fully implicit coupling scheme for the viscous and inviscid regions is demonstrated. This fully implicit coupling technique is similar to the work of Carter, Veldman, and an extension of an earlier work of Halim and Hafez. A comparison is made for the convergence rate using this new fully implicit coupling technique and the semiimplicit coupling of Halim and Hafez. Numerical results using the fully implicit coupling are obtained for laminar incompressible separated flows, including a boattail and a series of trough geometries. Also, the near-wake flow problem is considered using the present formulation. A clear conclusion of this investigation is that the present scheme using the fully implicit coupling method converges at a faster rate than the semiimplicit coupling and the partially parabolized Navier-Stokes (PPNS) procedures.
Axisymmetric flows with regions of closed streamlines confined by rotational inertia or electromagnetic pinch, for containment for gas core reactors
Measurements have been made of the mean flow properties and turbulent fluctuations in adiabatic turbulent boundary layer flows subjected to distributed adverse pressure gradients. In the freestream region upstream of the adverse pressure gradient the Mach number was 3.86, the unit Reynolds number 5.3 million per foot. The boundary layer developed on the wall of an axisymmetric nozzle and straight test section. In order to avoid the effects of streamwise surface curvature the adverse pressure gradients at the test section wall were induced by contoured centerbodies mounted on the wind tunnel centerline. The flow under study simulated that which might be found in an axially symmetric engine inlet of a supersonic aircraft.
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.
A program called RAXBOD is presented for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. The method solves the exact equation for the disturbance velocity potential function and applies the exact surface boundary condition. Instructions on program usage and listings of the program and sample cases are given.
The flow paths in gas turbine passages encompass a wide range of flow properties such as Reynolds number and Mach number as well as many other variable flow conditions such as swirl, free-stream turbulence, and laminar/turbulent transition. An existing computer program, the Axisymmetric Diffuser Duct (ADD) code, which calculates compressible, turbulent, swirling flow through axisymmetric ducts has been modified to include the effects of free-stream turbulence and laminar/turbulent transition. The program has been evaluated on a matrix of test cases to determine its accuracy, robustness, and limits of applicability. This improved version of the ADD code calculates solutions which compare well with available data and can now be applied to a wider range of problems than previously possible. In addition a concept called local enhancement was developed and tested on a simple two-dimensional geometry in order to demonstrate a method to reduce computer time. In this concept the pressure distribution is calculated on a coarse grid using the ADD code and the viscous layer is locally enhanced using a boundary layer analysis. By applying this concept, an order of magnitude reduction in computer time was possible without any loss in accuracy.
The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux-difference splitting finite-volume scheme. The developed three-dimensional solver has been verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, isolated quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown have been captured. The problem has also been calculated using the Euler solver of the same code and the results are compared with those of the Navier-Stokes solver. The effect of the initial swirl has been tentatively studied.
Finite difference in time and the meridional plane, in conjunction with a spectral technique in the azimuthal direction, are used to approximate the Navier-Stokes equations in a model that can simulate a variety of thermally driven rotating flows in cylindrical and spherical geometries. Axisymmetric flow, linearized waves relative to a fixed or changing axisymmetric flow, nonlinear waves without wave-wave interaction, and fully nonlinear 3D flow, can in this way be calculated. A reexamination is conducted of the steady baroclinic wave case previously treated by Williams (1971) and Quon (1976).
Supersonic jet noise generation by radial annular jet flow impinging on first shock cell region of axisymmetric converging main jet flow
Assuming the Newtonian thin layer approximation to describe the structure of the shock layer between the cometary 'ionopause' and the inner shock, a 3D axisymmetric photochemical flow model of this layer is constructed. While sources of ions in this layer are the flow across the inner shock and photoionization of neutrals within it, the sinks are the flow into the flanks and dissociative recombination, the latter being the dominant one. For Halley's comet at the time of the Giotto encounter, the calculated thickness of the layer is very small, typically about 100 km for expected values of the dissociative-recombination coefficient. This is not inconsistent with the observations. The lateral flow speed near the point of encounter (inbound) is about 0.9 km/s, while the sonic line is at an angle of about 50 deg to the sun-comet line. Testing the validity of this model will have to await a cometary rendezvous mission such as the proposed CRAF/Cassini mission.
The Karamcheti (1966) suggestion concerning the use of higher order singularity techniques has been developed for the calculation of incompressible flow past an axisymmetric body at angle of attack. Attention is given to the results of a convergence study using this axial singularity method, where solution accuracy has been investigated for ellipsoids of slenderness ratio in the 1-10 range for both axial and inclined flow. Effects of singularity type, element number and size distribution, and singularity line inset distance, are noted, and a paneling scheme is developed which yields accurate results for the class of axisymmetric bodies having continuous body slopes with discontinuous curvature jumps.