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At least 883 records · Page 49

Progress in incompressible Navier-Stokes computations for propulsion flows and its dual-use applications

Development of an incompressible Navier-Stokes solution procedure was performed for the analysis of a liquid rocket engine pump components and for the mechanical heart assist devices. The solution procedure for the propulsion systems is applicable to incompressible Navier-Stokes flows in a steadily rotating frame of reference for any general complex configurations. The computer codes were tested on different complex configurations such as liquid rocket engine inducer and impellers. As a spin-off technology from the turbopump component simulations, the flow analysis for an axial heart pump was conducted. The baseline Left Ventricular Assist Device (LVAD) design was improved by adding an inducer geometry by adapting from the liquid rocket engine pump. The time-accurate mode of the incompressible Navier-Stokes code was validated with flapping foil experiment by using different domain decomposition methods. In the flapping foil experiment, two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions for a downstream larger stationary foil. Fairly good agreement was obtained between unsteady experimental data and numerical results from two different moving boundary procedures. Incompressible Navier-Stokes code (INS3D) has been extended for heat transfer applications. The temperature equation was written for both forced and natural convection phenomena. Flow in a square duct case was used for the validation of the code in both natural and forced convection.

Kiris, Cetin↗

Compressibility effects on flow friction in a fully developed pipe flow

A method was evolved to account for the effects of compressibility in flows through long circular pipes of uniform diameter. Velocity and density variations across the flow cross section were approximated by profile shapes recommended for a flow past flat plates. The wall of the pipe was assumed to have attained an adiabatic condition. An integral method was used to obtain solutions for the governing equations of flow. The method was then used to analyze the detailed pressure measurements made in a long pipe for flow of air at different flow rate settings. Flow friction values derived from these pressure measurements were compared with the standard incompressible pipe flow data available in existing literature.

Murthy, Sreedhara V.↗

Velocity and extraneous boundary conditions of viscous flow problems

A novel method for treating certain troublesome boundary conditions in the numerical solution of time-dependent incompressible viscous flow problems is presented. This new method is developed on the basis of an integral representation for the velocity vector which contains the entire kinematics of the problem, including the boundary conditions of concern. It is shown that for the exterior flow problem the free-stream condition is satisfied at infinity exactly and the need to treat a far-field condition is removed by the use of the integral representation. The distribution of a nonvelocity variable on the solid boundary - i.e., the 'extraneous' boundary condition needed for both the exterior and the interior flows - is shown to be governed by the kinematics of the problem.

Wu, J. C.↗

Direct simulations of turbulent flow using finite-difference schemes

A high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow. The methods used include a kinetic energy conserving central difference scheme and an upwind difference scheme. The methods are evaluated in test cases for the evolution of small-amplitude disturbances and fully developed turbulent channel flow. It is suggested that the finite-difference approach can be applied to complex geometries more easilty than highly accurate spectral methods. It is concluded that the upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries.

Rai, Man Mohan↗

Validation of Calibrated k–ε Model Parameters for Jet-in-Crossflow

Previous efforts determined a set of calibrated, optimal model parameter values for Reynolds-averaged Navier–Stokes (RANS) simulations of a compressible jet in crossflow (JIC) using a $k–ε$ turbulence model. These parameters were derived by comparing simulation results to particle image velocimetry (PIV) data of a complementary JIC experiment under a limited set of flow conditions. Here, a $k–ε$ model using both nominal and calibrated parameters is validated against PIV data acquired from a much wider variety of JIC cases, including a realistic flight vehicle. The results from the simulations using the calibrated model parameters showed considerable improvements over those using the nominal values, even for cases that were not used in the calibration procedure that defined the optimal parameters. This improvement is demonstrated using a number of quality metrics that test the spatial alignment of the jet core, the magnitudes of multiple flow variables, and the location and strengths of vortices in the counter-rotating vortex cores on the PIV planes. These results suggest that the calibrated parameters have applicability well outside the specific flow case used in defining them and that with the right model parameters, RANS solutions for the JIC can be improved significantly over those obtained from the nominal model.

42 ENGINEERING↗

Study of viscous flow about airfoils by the integro-differential method

An integro-differential method was used for numerically solving unsteady incompressible viscous flow problems. A computer program was prepared to solve the problem of an impulsively started 9% thick symmetric Joukowski airfoil at an angle of attack of 15 deg and a Reynolds number of 1000. Some of the results obtained for this problem were discussed and compared with related work completed previously. Two numerical procedures were used, an Alternating Direction Implicit (ADI) method and a Successive Line Relaxation (SLR) method. Generally, the ADI solution agrees well with the SLR solution and with previous results are stations away from the trailing edge. At the trailing edge station, the ADI solution differs substantially from previous results, while the vorticity profiles obtained from the SLR method there are in good qualitative agreement with previous results.

Wu, J. C.↗

Calculation of two-dimensional shear-driven cavity flows at high Reynolds numbers

The time-dependent Navier-Stokes equations are numerically integrated for two-dimensional incompressible viscous flow in a shear-driven square cavity. Using a time-splitting method and finite differences on a staggered mesh, the momentum and pressure equations are directly solved by a tensor product method where one finite difference direction is diagonalized by eigenvalue decomposition. The effects of increasing Reynolds number are studied and the developing boundary layer is captured by using a finely clustered mesh. At Re = 30,000 the flow is in a continuously developing unsteady regime. Power spectrum plots indicate that the unsteady flow oscillates with one fundamental frequency and exhibits some characteristics of transition between laminar and turbulent states.

Huser, A.↗

A Note on the Wave Action Density of a Viscous Instability Mode on a Laminar Free-shear Flow

Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave traveling on top of a laminar free-shear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually non-negligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.

Balsa, Thomas F.↗

On Possible Similarity Solutions for Three-Dimensional Incompressible Laminar Boundary-Layer Flows Over Developable Surfaces and with Proportional Mainstream Velocity Components

Analysis is presented on the possible similarity solutions of the three-dimensional, laminar, incompressible, boundary-layer equations referred to orthogonal, curvilinear coordinate systems. Requirements of the existence of similarity solutions are obtained for the following: flow over developable surface and flow over non-developable surfaces with proportional mainstream velocity components.

Hansen, Arthur G.↗

Temporal Large-Eddy Simulation

In 1999, Stolz and Adams unveiled a subgrid-scale model for LES based upon approximately inverting (defiltering) the spatial grid-filter operator and termed .the approximate deconvolution model (ADM). Subsequently, the utility and accuracy of the ADM were demonstrated in a posteriori analyses of flows as diverse as incompressible plane-channel flow and supersonic compression-ramp flow. In a prelude to the current paper, a parameterized temporal ADM (TADM) was developed and demonstrated in both a priori and a posteriori analyses for forced, viscous Burger's flow. The development of a time-filtered variant of the ADM was motivated-primarily by the desire for a unifying theoretical and computational context to encompass direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaged Navier-Stokes simulation (RANS). The resultant methodology was termed temporal LES (TLES). To permit exploration of the parameter space, however, previous analyses of the TADM were restricted to Burger's flow, and it has remained to demonstrate the TADM and TLES methodology for three-dimensional flow. For several reasons, plane-channel flow presents an ideal test case for the TADM. Among these reasons, channel flow is anisotropic, yet it lends itself to highly efficient and accurate spectral numerical methods. Moreover, channel-flow has been investigated extensively by DNS, and a highly accurate data base of Moser et.al. exists. In the present paper, we develop a fully anisotropic TADM model and demonstrate its utility in simulating incompressible plane-channel flow at nominal values of Re(sub tau) = 180 and Re(sub tau) = 590 by the TLES method. The TADM model is shown to perform nearly as well as the ADM at equivalent resolution, thereby establishing TLES as a viable alternative to LES. Moreover, as the current model is suboptimal is some respects, there is considerable room to improve TLES.

Pruett, C. D.↗

Stability of viscous flow past a circular cylinder

A spectral method which employs trigonometric functions and Chebyshev polynomials is used to compute the steady, incompressible laminar flow past a circular cylinder. Linear stability methods are used to formulate a pair of decoupled generalized eigenvalue problems for the growth of symmetric and asymmetric (about the dividing streamline) perturbations. It is shown that, while the symmetric disturbances are stable, the asymmetric perturbations become unstable at a Reynolds number about 40 with a Strouhal number about 0.12. The critical conditions are found to depend on the size of the computational domain in a manner similar to that observed in the laboratory.

Zebib, A.↗

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Bratanow, T.↗

Calculation of flow about two-dimensional bodies by means of the velocity-vorticity formulation on a staggered grid

A method for calculating the incompressible viscous flow about two-dimensional bodies, utilizing the velocity-vorticity form of the Navier-Stokes equations using a staggered-grid formulation is presented. The solution is obtained by employing an alternative-direction implicit method for the solution of the block tridiagonal matrix resulting from the finite-difference representation of the governing equations. The boundary vorticity and the conservation of mass are calculated implicitly as a part of the solution. The mass conservation is calculated to machine zero for the duration of the computation. Calculations for the flow about a circular cylinder, a 2-pct thick flat plate at 90-deg incidence, an elliptic cylinder at 45-deg incidence, and a NACA 0012, with and without a deflected flap, at - 90-deg incidence are performed and compared with the results of other numerical investigations.

Stremel, Paul M.↗

Calculation of compressible boundary layer flow about airfoils by a finite element/finite difference method

Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.

Strong, Stuart L.↗

Flow of Gas Through Turbine Lattices

This report is concerned with fluid mechanics of two-dimensional cascades, particularly turbine cascades. Methods of solving the incompressible ideal flow in cascades are presented. The causes and the order of magnitude of the two-dimensional losses at subsonic velocities are discussed. Methods are presented for estimating the flow and losses at high subsonic velocities. Transonic and supersonic flows in lattices are then analyzed. Some three-dimensional features of the flow in turbines are noted.

BOUNDARY LAYER - AIRFOILS - CASCADES↗

Turbulent flow field predictions in sharply curved turn around ducts

In this investigation, two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative indication of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa-epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa-esilon model predictions are included.

Santi, L. M.↗

Turbulent flow field predictions in sharply curved turn-around ducts

Two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative induction of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa - epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa - epsilon model predictions are included.

Santi, L. M.↗

Distortion of the vortex core during blade-vortex interaction

The effect of vortex distortion on the flow arising from the interaction of a convecting vortex and an airfoil is analyzed for two-dimensional, incompressible, inviscid flow. Significant distortion of the vortex structure, owing to interaction with the airfoil, can occur, especially during close interactions. The vorticity field is represented by multiple vortices. Vortex instability and diffusion, resulting from discretization in space and time, are discussed. An integral boundary element method is used to represent the airfoil surface. The body panels are re-distributed on the surface as the vortices are convected past to calculate the effect of the vorticity field more accurately. The method is applied to several cases to examine effects of vortex strength, distribution, initial separation position, and airfoil angle of attack. Calculations of vortex trajectory and distortion, and airfoil surface-pressure distribution, lift, drag, and circulation as functions of time are presented.

Lee, G. J.↗