Urmila Ghia

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The flow over streamlined lifting airfoils has been a subject of considerable interest to fluid dynamicists, and to date, significant progress has been made towards the design of airfoils, wings, etc., by drawing together resources from experimental, numerical, analytical, and empirical studies. The detailed flow structure of airfoils and wings near maximum lift in low-to-high Reynolds-number (Re) flows still remains unresolved. The increasing interest in these flows stems from the desire for better control in civilian aircraft, and for high maneuvering capability in high-performance military aircraft. The improved performance can be realized from the potential of increasing maximum lift and simultaneously reducing drag under this condition. For some combination of flow parameters, the flow field around an airfoil experiences significant separation, which degrades its performance and leads to stall. The nature of the stall may be characterized by various phenomena such as separation, unsteadiness, transition, and turbulence. The present study is directed towards accurately simulating this flow field and providing further insight into this class of flows. Other important fluid-dynamics applications involving unsteady flows include blade rows in turbomachinery, marine propellers, helicopter rotor blades, and bluff bodies such as buildings, towers, underwater cables, etc., in cross flows. For this class of bluffy-body flows, understanding the vortex-shedding characteristics is very significant. The simulation technique presented here can also provide guidelines for analyzing some of these flow fields.

Boundary-Condition-Independent Reduced-Order Modeling of Heat Transfer in Complex Objects by POD-Galerkin Methodology: 1D Case Study

This technical note presents an introduction to boundary-condition-independent reduced-order modeling of complex electronic components using the proper orthogonal decomposition (POD)-Galerkin approach. The current work focuses on how the POD methodology can be used along with the finite volume method to generate reduced-order models that are independent of their boundary conditions. The proposed methodology is demonstrated for the transient 1D heat equation, and preliminary results are presented.

Higher-Order Accurate Solution for Flow Past a Circular Cylinder at Re = 13,400

Baseline results for flow past a circular cylinder are obtained at Re = 13,400 as a first step towards implementation of flow control for preventing or delaying flow separation. Implementation of flow separation control for low-pressure turbine cascade is the ultimate goal of this study. The complexity of the problem is reduced by initially studying flow separation control on a simplified geometry. The cylinder flow configuration serves to approximate the flow conditions of a low–pressure turbine (LPT) cascade. A fourth-order compact difference scheme with sixth-order filtering is employed to obtain an accurate prediction of unsteady separated flows governed by the Navier-Stokes (N-S) Equations. A multi-block structured grid is used for the present numerical study, and a MPI-based higher-order, Chimera version of the FDL3DI flow solver developed by the Air Force Research Laboratory at Wright Patterson Air Force base is used for the numerical computations. As a validation study, the cylinder flow for Re = 3,900 is simulated and the results obtained are compared with the numerical and experimental data available in the literature. The wake of the cylinder flow at Re = 13,400 displays presence of a wide range of vortical structures. The separating shear layers are subject to spanwise instability which leads to the formation of an unsteady and three-dimensional wake, with the characteristic features of typical turbulent flow.

Aerodynamic and Structural Analyses of Joined Wings of Hale Aircraft

High Altitude Long Endurance (HALE) aircraft high-aspect ratio wings undergo significant deflections that necessitate consideration of structural deformations for accurate prediction of the flow behavior. The objective of this research is to simulate the complex, three-dimensional flow past the joined wing of a HALE aircraft, and to predict its structural behavior based on three different structural models. A Reynolds-Averaged Navier-Stokes (RANS) based flow solver, COBALT, is used for determining the aerodynamic loads on the structure. The structural models considered include a 1-D approximation of the 3-D structure, a twin-fuselage equivalent box-wing model, and a reinforced shell model. Linear static and modal analyses are performed using ANSYS, a finite-element analysis software, to determine the deformation and mode shapes of the structure. The resulting structural deformations in turn affect the flow domain, which has to be re-meshed in a grid generator software and the flow analysis performed again on the deformed shape.

Velocity-Vorticity Simulation of Unsteady 3-D Viscous Flow within a Driven Cavity

A velocity-vorticity formulation of the unsteady three dimensional Navier-Stokes equations has been used to solve for the incompressible viscous flow within a driven cavity of spanwise aspect ratio 3:1 at a Reynolds number Re = 3200 on a non-uniform (65 × 65 × 49) grid covering one half of the span. An efficient Alternating-DirectionImplicit method which treats all cross derivative terms implicitly and which requires only six scalar tridiagonal sweeps has been developed for the vorticity transport equation. The divergence-curl formulation for the elliptic velocity problem is solved at each time step by a Multi-Grid Distributive Gauss-Seidel iterative scheme. The pressure is solved, only when desired, from the three-dimensional Pressure Poisson problem using a Multi-Grid Gauss-Seidel iterative scheme. Velocity, vorticity and pressure results are given for a characteristic time t = 50 after the upper surface of the cavity is impulsively started from rest.

Physics of forced unsteady flow for a NACA 0015 airfoil undergoing constant-rate pitch-up motion

The unsteady Navier-Stokes (NS) analysis of Osswald, Ghia and Ghia in velocity-vorticity variables is modified to study the dynamic stall phenomenon for a NACA 0015 airfoil undergoing constant Ω0 pitch-up maneuvers at Reynolds number Re = 10 000 and 45000. The use of third-order accurate biased upwind differencing for the nonlinear convective terms in the vorticity transport equation removes the spurious oscillations observed in the earlier studies by the authors for these values of Re. The fully implicit and vectorized ADI-BGE method of the authors is used to solve the unsteady NS equations. Instantaneous inertial surface vorticity, which is an invariant of the choice of reference frame selected, is employed to determine the location of separation of the boundary-layer flow on the suction surface; also a separation bubble embedded within the boundary layer is observed for both cases somewhere between the leading edge and the quarter-chord point. Primary, secondary, tertiary and quarternary vortices have been observed before the dynamic-stall vortex evolves and gathers its maximum strength.

Simulation of Self-Induced Unsteady Motion in the Near Wake of a Joukowski Airfoil

Recent impetus for research in unsteady separated flows stems from a wide range of applications from low- to high- Reynolds number, Re. The physics of high-Re flows, in general, is quite complex and often involves multiple nonuniqueness and chaos, beyond simple unsteady separation. For the low-Re case, e.g. in the manuevering of fighter aircraft at high angle-of-attack in near- and post-stall regime, the vortex interaction dominates the flow field. The passage of vortices over the suction surface and their subsequent shedding leads to self-excited persistently unsteady flows. This flow field is extremely complicated due to the global effect of unsteady separated flow, coupled with the presence of hydrodynamic instabilities which may trigger transition and eventually lead to chaos. Besides supermaneuverability, interest also lies in this low-Re case because of the need for design of efficient airfoil sections for Re in the range of 105–106, for improving the performance of mini-RPV’s (remotely piloted vehicles) operating at low altitudes, jet engine compressor and turbine blades, helicopter rotor blades, etc.

Direct method for solution of three-dimensional unsteady incompressible Navier-Stokes equations

A three-dimensional, unsteady analysis for the velocity-vorticity formulation of the Navier-Stokes (NS) equations is described. This formulation highlights the natural separation of the spin dynamics of a fluid particle from its translational kinematics. This separation is exploited to produce a single pass direct inversion of the full unsteady NS operator without the need to iterate either the future wall vorticity or the nonlinear vorticity convection terms. The method has uniform second-order accuracy in time and space. As an example, it is applied to the problem of the three-dimensional flow within a shear-driven cubical box. Results are obtained for Re = 100, 400, and 1000 using a preliminary (25, 25, 25) mesh.

Boundary-Condition-Independent Reduced-Order Modeling of Complex Electronic Packages by POD-Galerkin Methodology

The objective of the current work is to introduce the concept of boundary-condition-independent (BCI) reduced-order modeling (ROM) for complex electronic packages by employing the proper orthogonal decomposition (POD)-Galerkin methodology. Detailed models of complex electronic packages that consume large computational resources are used within system-level models in computational fluid dynamics (CFD)-based heat transfer analysis. If a package-level model that reduces computational resources (reduced-order model) and provides accurate results in many different flow situations (boundary-condition-independent model) can be deployed, it will accelerate the design and analysis of the end products that make use of these packages. This paper focuses on how the proper orthogonal decomposition-Galerkin methodology can be used with the finite volume method (FVM) to generate reduced-order models that are boundary-condition-independent. This method is successfully used in the present study to generate boundary-condition-independent reduced-order models for 1-D and 2-D objects for isothermal and isoflux boundary conditions. Successful implementation of the method is also shown on 2-D objects made of multiple materials and multiple heat generating sources for isoflux boundary conditions.

A Comparative Study of Chemical Mechanisms in the Simulation of One -Dimensional Detonation

In this study we validate reaction mechanisms in the prediction of detonation quantities. This is done to understand modeling of detonatio n and to validate the software Fluent 6.1 for use in Pulse Detonation Engine simulations. One -dimensional detonation is simulated with a hydrogen -air mixture for two mixture compositions using flow -adaptive grids. The mechanisms’ capability to predict the detonation velocity and von Neumann spike in pressure is studied. The resulting detonation structure is also compared with the ZND structure. A lean (equivalence ratio of 0.44), and stoichiometric hydrogen -air mixture is used in this study. Four differe nt mechanisms, based on the nature of detail of the chemical model, are studied. It is seen that a very fine grid with a detailed chemistry model was able to capture the ZND structure, but resulted in the failure of self -sustaining the detonation. It is found that the numerical resolution required to resolve the reaction zone was dependent on the richness of the mixture. It is also observed that a mechanism, which did not allow modeling of the intermediates, also resulted in failure of predicting a self -sustaining detonation wave. All the other mechanisms predicted the detonation velocity within less than 2 % error when compared to the theoretical CJ value.