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Three-dimensional turbulent horseshoe vortex flow past strut/endwall configurations having both unswept and 45-degree swept leading edges is studied by numerical solution of the compressible Reynolds-averaged Navier-Stokes equations. The Cartesian form of the equations is transformed to a general nonorthogonal coordinate system which is fitted to the geometry of interest and then solved using a consistently-split linearized block implicit (LBI) algorithm. The turbulence model and computational mesh provides for resolution of the viscous sublayer and employs an isotropic eddy viscosity based on solution of the turbulence kinetic energy equation and a specified length scale. Although no flow measurements are available for the region near the leading edge, predictions of the horseshoe vortex formation near the leading edge are in qualitative agreement with flow visualization studies of similar flows. Predictions of the relatively weak secondary flow in the corner region well downstream of the unswept leading edge do not agree with available measurements, and this is believed to be the result of numerical truncation error and/or inadequacy of the turbulence model. (Author)

The ICWAKE computer code solves the Navier-Stokes equations for axisymmetric, incompressible, swirling, turbulent flow with large axial gradients. This document is a guide to the use of the code. Included are descriptions of the input parameters and the code structure, some general comments about using the code and a sample calculation.

This report is a recent paper presented by the authors, slightly modified to include comparison with more recently measured data. The steady flow about a surface ship model with a transom stern moving at high speed is analyzed. Viscous effects are included through the use of a numerical solution of the Reynolds-averaged Navier-Stokes equations subject to nonlinear free-surface boundary conditions. The k-epsilon turbulence model is employed. The structured grid maintains its hull boundary-layer resolution into the wake. This assures the capturing of the strong viscous/free-surface interaction of the boundary-layer wake with the stern wave field, This interaction is demonstrated by comparison with results of inviscid computations. Comparisons with measured data are also presented. The results represent a step forward in a long history of progress on the challenging problem of the computation of flows about transom sterns.

Separation ahead of a flat-face blunt fin in a supersonic turbulent boundary layer was studied numerically. The following observations and conclusions were made: (1) the length of separation increases to about 5.2 D, compared with about 2.0 to 2.5 D for the typical hemi-cylindrical results, and this numerical result confirms experimental observation; (2) even though there is a kink in pressure in the present case, there is no secondary separation under the main horseshoe vortices and there are three vortices, leading to the conclusion that the number of vortices is not always an even number; and (3) for the case investigated the separation point is connected to the inner (first) horseshoe vortex, rather than the outer (second) one. The four layers of fluid entrain in the three vortices, respectively.

A multi-scale method is developed that couples a macro-scale, high-order resolution particle-mesh method for computation of particle-laden compressible flow in blast waves and high-speed combustors, with a meso-scale, full-resolution, high-fidelity first principles model for direct numerical simulations of shocked flows. At the macro scale the particles are modeled using reduced point cloud methods that rely on semi-empirical forcing models. The semi-empirical models are closed through metamodels that assimilate meso-scale physics through simulations in a multi-dimensional parameter space. The performance of several meta-models are compared and assessed. Meso, macro and multi-scale computations of shock interaction with a cloud of particles are performed for a range of parameters to test the method.

A control-volume based finite difference computation of a turbulent transonic flow over an axisymmetric curved hill is presented. The numerical method is based on the SIMPLE algorithm, and hence the conservation of mass equation is replaced by a pressure correction equation for compressible flows. The turbulence is described by a k-epsilon turbulence model supplemented by a near-wall turbulence model. In the method, the dissipation rate in the region very close to the wall is obtained from an algebraic equation and that for the rest of the flow domain is obtained by solving a partial differential equation for the dissipation rate. The other flow equations are integrated up to the wall. It is shown that the present turbulence model yields the correct location of the compression shock. The other computational results are also in good agreement with experimental data.

A procedure which solves the governing boundary layer equations within Keller's box method was developed for calculating unsteady laminar flows with flow reversal. This method is extended to turbulent boundary layers with flow reversal. Test cases are used to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. Turbulent flow calculations are performed. The governing equations for both models are solved. As in laminar flows, the unsteady turbulent boundary layers are free from singularities, but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. Predictions of both turbulence models are the same for all practical purposes.

The report presents an overview of jet noise computation utilizing the computational fluid dynamic solution of the turbulent jet flow field. The jet flow solution obtained with an appropriate turbulence model provides the turbulence characteristics needed for the computation of jet mixing noise. A brief account of turbulence models that are relevant for the jet noise computation is presented. The jet flow solutions that have been directly used to calculate jet noise are first reviewed. Then, the turbulent jet flow studies that compute the turbulence characteristics that may be used for noise calculations are summarized. In particular, flow solutions obtained with the k-e model, algebraic Reynolds stress model, and Reynolds stress transport equation model are reviewed. Since, the small scale jet mixing noise predictions can be improved by utilizing anisotropic turbulence characteristics, turbulence models that can provide the Reynolds stress components must now be considered for jet flow computations. In this regard, algebraic stress models and Reynolds stress transport models are good candidates. Reynolds stress transport models involve more modeling and computational effort and time compared to algebraic stress models. Hence, it is recommended that an algebraic Reynolds stress model (ASM) be implemented in flow solvers to compute the Reynolds stress components.

A computer program, VNAP2, for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow is presented. It solves the two dimensional, time dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing length model, a one equation model, or the Jones-Launder two equation model. The geometry may be a single or a dual flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference plane characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet powered afterbodies, airfoils, and free jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

An implicit time marching finite difference method is used to predict two dimensional turbulent flow at a Reynolds number of 440,000 and a Mach number of 0.574 over a shortened NACA 0012 airfoil with a trailing edge of 4.5% thickness and semicircular shape. The flow is found to be unsteady but periodic in the trailing edge region. Thus, lift and drag fluctuate at small amplitudes around mean values and at distinct frequencies.

Three-dimensional laminar and turbulent flow within 90-degree bends of strong curvature and both circular and square cross section are studied by numerical solution of the compressible Reynolds-averaged Navier-Stokes equations. The governing equations are expressed in a body-fitted orthogonal coordinate system and then solved using a consistently-split linearized block implicit (LBI) algorithm. The turbulence model and computational mesh provides for resolution of the viscous sublayer and employs an isotropic eddy viscosity based on solution of the turbulence kinetic energy equation and a specified length scale. Six different flow cases are considered , and the developing flow structure and its dependence on geometric and flow parameters is examined. The computed results are compared with available experimental measurements, and the sequence of comparisons helps to establish the accuracy with which these flows can be predicted by the present method using moderately coarse grids (approx = 10,000 points).

Recently a new procedure, which solves the governing boundary-layer equations with Keller's box method, has been developed for calculating unsteady laminar flows with flow reversal. In this report, we extend this method to turbulent boundary layers with flow reversal. Using the algebraic eddy viscosity formulation of Cebeci and Smith, we consider several test cases to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. We also perform turbulent flow calculations by using the turbulence model of Bradshaw, Ferriss, and Atwell; we solve the governing equations for both models by using the same numerical scheme and compare the predictions with each other. The study reveals that, as in laminar flows, the unsteady turbulent boundary layers are free from singularities, but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. The study also reveals that the predictions of both turbulence models are the same for all practical purposes. (Author)

A computer program, VNAP2, for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow is presented. It solves the two dimensional, time dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing length model, a one equation model, or the Jones-Launder two equation model. The geometry may be a single or a dual flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference plane characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet powered afterbodies, airfoils, and free jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

The three-dimensional, primitive equations of motion are solved numerically for the case of isotropic box turbulence and the distortion of homogeneous turbulence by irrotational plane strain at large Reynolds numbers. A Gaussian filter is applied to governing equations to define the large scale field. This gives rise to additional second order computed scale stresses (Leonard stresses). The residual stresses are simulated through an eddy viscosity. Uniform grids are used, with a fourth order differencing scheme in space and a second order Adams-Bashforth predictor for explicit time stepping. The results are compared to the experiments and statistical information extracted from the computer generated data.

A procedure which solves the governing boundary layer equations within Keller's box method was developed for calculating unsteady laminar flows with flow reversal. This method is extended to turbulent boundary layers with flow reversal. Test cases are used to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. Turbulent flow calculations are performed. The governing equations for both models are solved. As in laminar flows, the unsteady turbulent boundary layers are free from singularities, but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. Predictions of both turbulence models are the same for all practical purposes.

http://uf.catalog.fcla.edu/uf.jsp?st=UF001128593&ix=nu&I=0&V=D

A series of unsteady Reynolds-averaged Navier-Stokes computations are performed for the flow of a synthetic jet issuing into a turbulent boundary layer through a circular orifice. This is one of the validation test cases from a synthetic jet validation workshop held in March 2004. Several numerical parameters are investigated, and the effects of three different turbulence models are explored. Both long-time-averaged and time-dependent phase-averaged results are compared to experiment. On the whole, qualitative comparisons of the mean flow quantities are fairly good. There are many differences evident in the quantitative comparisons. The calculations do not exhibit a strong dependence on the type of turbulence model employed.

A method for numerical evaluation of the vibrations of a cylindrical shell structure induced by a low speed external turbulent flow is discussed. The direction of flow is along the axis of revolution of the shell, and the source of excitation is the pressure fluctuations in the turbulent boundary layer. For the investigation of vibration and noise problems it is usually more desirable to utilize the modal expansion approach. The axisymmetric shell structure can be modeled by the assemblage of conical-shell finite-elements. This modeling allows the eigenfunction psi sub mn (x,theta) to be represented in a rectangular product of a longitudinal modal function f sub mn (x) and a circular harmonic function cos m theta (or sin m theta).

Fully elliptic forms of the transport equations have been solved numerically for two flow configurations. The first is turbulent flow in a channel with transverse rectangular ribs, and the second is impingement cooling of a plane surface. Both flows are relevant to proposed designs for active cooling of hypersonic vehicles using supercritical hydrogen as the coolant. Flow downstream of an abrupt pipe expansion and of a backward-facing step were also solved with various near-wall turbulence models as benchmark problems. A simple form of periodicity boundary condition was used for the channel flow with transverse rectangular ribs. The effects of various parameters on heat transfer in channel flow with transverse ribs and in impingement cooling were investigated using the Yap modified Jones and Launder low Reynolds number k-epsilon turbulence model. For the channel flow, predictions were in adequate agreement with experiment for constant property flow, with the results for friction superior to those for heat transfer. For impingement cooling, the agreement with experiment was generally good, but the results suggest that improved modelling of the dissipation rate of turbulence kinetic energy is required in order to obtain improved heat transfer prediction, especially near the stagnation point. The k-epsilon turbulence model was used to predict the mean flow and heat transfer for constant and variable property flows. The effect of variable properties for channel flow was investigated using the same turbulence model, but comparison with experiment yielded no clear conclusions. Also, the wall function method was modified for use in the variable properties flow with a non-adiabatic surface, and an empirical model is suggested to correctly account for the behavior of the viscous sublayer with heating.

Both laminar and turbulent flows in strongly curved ducts, channels, and pipes are studied by numerical methods. The study concentrates on the curved square-duct geometry and flow conditions for which detailed measurements have been obtained recently by Taylor, Whitelaw, and Yianneskis. The solution methodology encompasses solution of the compressible ensemble-averaged Navier-Stokes equations at low Mach number using a split linearized block implicit (LBI) scheme, and rapid convergence on the order of 80 noniterative time steps is obtained. The treatment of turbulent flows includes resolution of the viscous sublayer region. A series of solutions for both laminar and turbulent flow and for both two- and three-dimensional geometries of the same curvature are presented. The accuracy of these solutions is explored by mesh refinement and by comparison with experiment. In summary, good qualitative and reasonable quantitative agreement between solution and experiment is obtained. Collectively, this sequence of results serves to clarify the physical structure of these flows and hence how grid selection procedures might be adjusted to improve the numerical accuracy and experimental agreement. For a three-dimensional flow of considerable complexity, the relatively good agreement with experiment obtained for the turbulent flow case despite a coarse grid must be regarded as encouraging. (Author)

Fully elliptic forms of the transport equations have been solved numerically for two flow configurations. The first is turbulent flow in a channel with transverse rectangular ribs, and the second is impingement cooling of a plane surface. Both flows are relevant to proposed designs for active cooling of hypersonic vehicles using supercritical hydrogen as the coolant. Flow downstream of an abrupt pipe expansion and of a backward-facing step were also solved with various near-wall turbulence models as benchmark problems. A simple form of periodicity boundary condition was used for the channel flow with transverse rectangular ribs. The effects of various parameters on heat transfer in channel flow with transverse ribs and in impingement cooling were investigated using the Yap modified Jones and Launder low Reynolds number k-epsilon turbulence model. For the channel flow, predictions were in adequate agreement with experiment for constant property flow, with the results for friction superior to those for heat transfer. For impingement cooling, the agreement with experiment was generally good, but the results suggest that improved modelling of the dissipation rate of turbulence kinetic energy is required in order to obtain improved heat transfer prediction, especially near the stagnation point. The k-epsilon turbulence model was used to predict the mean flow and heat transfer for constant and variable property flows. The effect of variable properties for channel flow was investigated using the same turbulence model, but comparison with experiment yielded no clear conclusions. Also, the wall function method was modified for use in the variable properties flow with a non-adiabatic surface, and an empirical model is suggested to correctly account for the behavior of the viscous sublayer with heating.