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At least 343 records · Page 19

SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications

This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.

Kirk, Benjamin S.↗

Asymptotic theory of two-dimensional trailing-edge flows

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.

Melnik, R. E.↗

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.↗

Aerodynamic design of gas and aerosol samplers for aircraft

The aerodynamic design of airborne probes for the capture of air and aerosols is discussed. Emphasis is placed on the key parameters that affect proper sampling, such as inlet-lip design, internal duct components for low pressure drop, and exhaust geometry. Inlet designs that avoid sonic flow conditions on the lip and flow separation in the duct are shown. Cross-stream velocities of aerosols are expressed in terms of droplet density and diameter. Flow curvature, which can cause aerosols to cross streamlines and impact on probe walls, can be minimized by means of a proper inlet shape and proper probe orientation, and by avoiding bends upstream of the test section. A NASA panel code called PMARC was used successfully to compute streamlines around aircraft and probes, as well as to compute to local velocity and pressure distributions in inlets. A NACA 1-series inlet with modified lip radius was used for the airborne capture of stratospheric chlorine monoxide at high altitude and high flight speed. The device has a two-stage inlet that decelerates the inflow with little disturbance to the flow through the test section. Diffuser design, exhaust hood design, valve loss, and corner vane geometry are discussed.

Soderman, Paul T.↗

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.↗

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

Abstract Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Yang, Hyung Jun↗

Numerical Modeling of Three-Dimensional Confined Flows

A three dimensional confined flow model is presented. The flow field is computed by calculating velocity and enthalpy along a set of streamlines. The finite difference equations are obtained by applying conservation principles to streamtubes constructed around the chosen streamlines. With appropriate substitutions for the body force terms, the approach computes three dimensional magnetohydrodynamic channel flows. A listing of a computer code, based on this approach is presented in FORTRAN IV language. The code computes three dimensional compressible viscous flow through a rectangular duct, with the duct cross section specified along the axis.

Greywall, M. S.↗

A quasi-three-dimensional blade surface boundary layer analysis for rotating blade rows

A quasi-three-dimensional approximation has been developed for a blade boundary layer which involves the calculation of the effect of nonzero pressure gradients, turbulent flow, and blade twist, but includes only a simple coupling between streamlines. The resulting set of equations is solved using Keller's box scheme. The solution scheme is checked against available incompressible flow solutions and then applied to a NASA low aspect ratio transonic compressor stage for which extensive experimental and computational data are available. It is found that the three-dimensional boundary layer separates significantly sooner and has a much larger influence on rotor performance than would be expected from a two-dimensional analysis.

Thompkins, W. T., Jr.↗

Investigation of viscous/inviscid interaction in transonic flow over airfoils with suction

The viscous/inviscid interaction over transonic airfoils with and without suction is studied. The streamline angle at the edge of the boundary layer is used to couple the viscous and inviscid flows. The potential flow equations are solved for the inviscid flow field. In the shock region, the Euler equations are solved using the method of integral relations. For this, the potential flow solution is used as the initial and boundary conditions. An integral method is used to solve the laminar boundary-layer equations. Since both methods are integral methods, a continuous interaction is allowed between the outer inviscid flow region and the inner viscous flow region. To avoid the Goldstein singularity near the separation point the laminar boundary-layer equations are derived in an inverse form to obtain solution for the flows with small separations. The displacement thickness distribution is specified instead of the usual pressure distribution to solve the boundry-layer equations. The Euler equations are solved for the inviscid flow using the finite volume technique and the coupling is achieved by a surface transpiration model. A method is developed to apply a minimum amount of suction that is required to have an attached flow on the airfoil. The turbulent boundary layer equations are derived using the bi-logarithmic wall law for mass transfer. The results are found to be in good agreement with available experimental data and with the results of other computational methods.

Vemuru, C. S.↗

Analysis and testing of two-dimensional vented Coanda ejectors with asymmetric variable area mixing sections

The analysis of asymmetric, curved (Coanda) ejector flow has been completed using a finite difference technique and a quasi-orthogonal streamline coordinate system. The boundary layer type jet mixing analysis accounts for the effect of streamline curvature in pressure gradients normal to the streamlines and on eddy viscosities. The analysis assured perfect gases, free of pressure discontinuities and flow separation and treated three compound flows of supersonic and subsonic streams. Flow parameters and ejector performance were measured in a vented Coanda flow geometry for the verification of the computer analysis. A primary converging nozzle with a discharge geometry of 0.003175 m x 0.2032 m was supplied with 0.283 cu m/sec of air at about 241.3 KPa absolute stagnation pressure and 82 C stagnation temperature. One mixing section geometry was used with a 0.127 m constant radius Coanda surface. Eight tests were run at spacing between the Coanda surface and primary nozzle 0.01915 m and 0.318 m and at three angles of Coanda turning: 22.5 deg, 45.0 deg, and 75.0 deg. The wall static pressures, the loci of maximum stagnation pressures, and the stagnation pressure profiles agree well between analytical and experimental results.

Maroti, L. A.↗

Topology of two-dimensional and three-dimensional separated flows

It is shown that topology rules can define a small number of singular points on an aerodynamic surface and in the flow which can be combined in various ways to create the structures and characterize the physical mechanisms of three-dimensional separated flows. This topological development is based on the hypothesis that vector fields of skin-friction lines and external streamlines remain continuous. Among examples treated are the lee-side separated flows about slender bodies at angle of attack with symmetric or asymmetric wake structures; about a protuberance normal to a wall; and over a rearward-facing axisymmetric step.

Tobak, M.↗

Prediction of swirling reacting flow in ramjet combustors

Numerical computations have been undertaken for a basic two-dimensional axisymmetric flowfield which is similar to that found in conventional gas turbine and ramjet combustors. A swirling flow enters a larger chamber via a sudden or gradual expansion. The calculation method involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation turbulence energy-turbulence dissipation rate turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. The results include recirculation zone characterization and predicted mean streamline patterns. Predictions with and without chemical reaction are obtained. An associated isothermal experimental flow study is providing a useful data base. Successful outcomes of the work can be incorporated into the more combustion- and hardware-oriented activities of industrial concerns.

Lilley, D. G.↗

Effect of pressure gradients on Gortler instability

Gortler instability for boundary-layer flows over generally curved walls is considered. The full linearized disturbance equations are obtained in an orthogonal curvilinear coordinate system. A perturbation procedure to account for second-order effects is used to determine the effects of the displacement thickness and the variation of the streamline curvature on the neutral stability of the Blasius flow. The pressure gradient in the mean flow is accounted for by solving the nonsimilar boundary-layer equations. Growth rates are obtained for the actual mean flow and the Falkner-Skan flows. The results demonstrate the strong influence of the pressure gradient and the nonsimilarity of the basic flow on the stability characteristics.

Ragab, S. A.↗

Recent Advances in Visualizing 3D Flow with LIC

Line Integral Convolution (LIC), introduced by Cabral and Leedom in 1993, is an elegant and versatile technique for representing directional information via patterns of correlation in a texture. Although most commonly used to depict 2D flow, or flow over a surface in 3D, LIC methods can equivalently be used to portray 3D flow through a volume. However, the popularity of LIC as a device for illustrating 3D flow has historically been limited both by the computational expense of generating and rendering such a 3D texture and by the difficulties inherent in clearly and effectively conveying the directional information embodied in the volumetric output textures that are produced. In an earlier paper, we briefly discussed some of the factors that may underlie the perceptual difficulties that we can encounter with dense 3D displays and outlined several strategies for more effectively visualizing 3D flow with volume LIC. In this article, we review in more detail techniques for selectively emphasizing critical regions of interest in a flow and for facilitating the accurate perception of the 3D depth and orientation of overlapping streamlines, and we demonstrate new methods for efficiently incorporating an indication of orientation into a flow representation and for conveying additional information about related scalar quantities such as temperature or vorticity over a flow via subtle, continuous line width and color variations.

Interrante, Victoria↗

A Numerical and Experimental Investigation of Flow Separation Control over a Wall-Mounted Hump Model

Numerical simulations and wind tunnel experiments were performed to investigate flow separation and its control over a wall-mounted hump model. Three-dimensional, unsteady fluid dynamic simulations were used to capture the relevant flow physics of unsteady flow separation and its control via active and passive flow control methods. Surface pressure measurements and surface oilflow visualization were obtained in the experiments. Current measurements documented a considerably thinner incoming boundary layer, but similar pressure distribution, compared to the reference data reported in the CFD (Computational Fluid Dynamics) Validation (CFDVAL 2004) Experiments. Consistent with the data available in the literature, numerical simulations predicted a longer separation bubble, which manifested itself as a shift in the pressure distributions. Streamwise vortices generated by passive vortex generators increased the suction pressure and provided substantial pressure recovery. Numerical simulations of vortex generators qualitatively predicted the effects of control, and revealed patterns of attached/separated flow regions. On the other hand, active flow control using steady discrete jets reduced, but was not able to eliminate, flow separation for the tested configuration. Although the major disagreement between the numerical and experimental results was in the pressure recovery region due to the inaccurate prediction of separation bubbles, the relative pressure recoveries from the baselines were comparable. Surface oilflow visualization and simulated surface streamlines were qualitatively in good agreement revealing the key flow features.

Koklu, Mehti↗

Goertler instability

Goertler instability for boundary-layer flows over generally curved walls is considered. The full-linearized disturbance equations are obtained in an orthogonal curvilinear coordinate system. A perturbation procedure to account for second-order effects is used to determine the effects of the displacement thickness and the variation of the streamline curvature on the neutral stability of the Blasius flow. The streamwise pressure gradient in the mean flow is accounted for by solving the nonsimilar boundary-layer equations. Growth rates are obtained for the actual mean flow and compared with those for the Blasius flow and the Falkner-Skan flows. The results demonstrate the strong influence of the streamwise pressure gradient and the nonsimilarity of the basic flow on the stability characteristics.

Ragab, S. A.↗

Preliminary Axial Flow Turbine Design and Off-Design Performance Analysis Methods for Rotary Wing Aircraft Engines: Validation - Part 1

For the preliminary design and the off-design performance analysis of axial flow turbines, a pair of intermediate level-of-fidelity computer codes, TD2-2 (design; reference 1) and AXOD (off-design; reference 2), are being evaluated for use in turbine design and performance prediction of the modern high performance aircraft engines. TD2-2 employs a streamline curvature method for design, while AXOD approaches the flow analysis with an equal radius-height domain decomposition strategy. Both methods resolve only the flows in the annulus region while modeling the impact introduced by the blade rows. The mathematical formulations and derivations involved in both methods are documented in references 3, 4 for TD2-2) and in reference 5 (for AXOD). The focus of this paper is to discuss the fundamental issues of applicability and compatibility of the two codes as a pair of companion pieces, to perform preliminary design and off-design analysis for modern aircraft engine turbines. Two validation cases for the design and the off-design prediction using TD2-2 and AXOD conducted on two existing high efficiency turbines, developed and tested in the NASA/GE Energy Efficient Engine (GE-E3) Program, the High Pressure Turbine (HPT; two stages, air cooled) and the Low Pressure Turbine (LPT; five stages, un-cooled), are provided in support of the analysis and discussion presented in this paper.

Chen, Shu-cheng, S.↗