Karman 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.

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.

Structural Modeling and Optimization of the Joined Wing of a High-Altitude Long-Endurance (HALE) Aircraft

Recent research trends have indicated an interest in High-Altitude, Long-Endurance (HALE) aircraft as a low-cost alternative to certain space missions. These missions require a lightweight vehicle operating at low speeds, high lift and minimum drag. These conditions necessitate high-aspect ratio wings. Due to its large span and light weight, the wing structure is very flexible. The wings undergo significant deflections as a result of the fluid loads acting on them, and require the consideration of aeroelastic effects. To reduce the structural deformation and increase the total lift, a sensorcraft model with a joined-wing configuration is employed. The results of the simulation of the complex, three-dimensional flow past the joined wing of a HALE aircraft are used as an input for the structural analysis. In the existing studies to date, only simplified structural models have been examined. In the present work, a semi-monocoque structural model is developed. All stringers, skin panels, ribs and spars are represented by appropriate elements in a finite-element model. Linear and nonlinear static analyses under the aerodynamic load are performed. The stress distribution in the wing is explored. Starting with a structural model with uniform mass distribution, a design optimization is performed. The optimized model has a maximum stress 42% lower and a maximum deflection 26% lower than obtained for the initial model. Linear and nonlinear buckling analyses are performed as well. The nonlinear analysis yields a critical buckling load 18% lower than that predicted by linear analysis. This paper will discuss the details of the structural modeling as well as the results obtained before and after optimizing the model.

ANALYSIS OF SEPARATED FLOW IN A LOW -PRESSURE TURBINE LINEAR CASCADE, USING MULTI -BLOCK STRUCTURED GRID

As the gas turbine engine operates from take - off to high -altitude cruise the flow Reynolds number (Re) in Low -pressure turbines vary over a wide range. At lower Re, the prevailing flow separation zones and transition regions result in degradation of performance. Therefore, it is important to accurately predict flow separation to improve the turbine efficiency. A 12 - block periodic structured grid of multiple topologies generated by the grid generation software, GRIDPRO, is used to solve the flow through a linear turbine cascade. An unsteady Navier -Stokes analys is is being used to analyze the flow through turbine cascade. A MPI based higher -order, parallel version of the FDL3DI code, developed by the Air Force Research Laboratory at Wright Patterson Air Force Base, used as the flow solver is extended for the pre sent turbomachinery application. The objective of the present study is to show the ability of higher -order accurate compact difference scheme to predict the flow separation that occurs inside a low -pressure turbine cascade. In the present paper, the resu lts for Re = 25,000 are presented for the LPT blade geometry. Nomenclature a1, a2, a3 direction cosines cax axial chord length Cp pressure coefficient, ref ref ref s U P P 2 ref ax ref ref c u ∝ �