Sriram Shankaran

A higher-order generalized ghost fluid method for the poor for the three-dimensional two-phase flow computation of underwater implosions

The ghost fluid method for the poor (GFMP) is an elegant, computationally efficient, and nearly conservative method for the solution of two-phase flow problems. It was developed in one dimension for the stiffened gas equation of state (EOS) and one-step time-discretization algorithms. It naturally extends to three dimensions but its extension to higher-order, multi-step time-discretization schemes is not straightforward. Furthermore, the original GFMP and many other ghost fluid methods fail to handle the large density and pressure jumps that are encountered in underwater implosions. Therefore, the GFMP is generalized in this work to an arbitrary EOS and multi-fluid problems with multiple EOSs. It is also extended to three dimensions and developed for higher-order, multi-step time-discretization algorithms. Furthermore, this method is equipped with an exact two-phase Riemann solver for computing the fluxes across the material interface without crossing it. This aspect of the computation is a departure from the standard approach for computing fluxes in ghost fluid methods. It addresses the stiff nature of the two-phase air/water problem and enables a better handling of the large discontinuity of the density at the air/water interface. As the original GFMP, the proposed method is contact preserving, computationally efficient, and nearly conservative. Its superior performance in the presence of large density and pressure jumps is demonstrated for shock-tube problems. Its practicality and accuracy are also highlighted with the three-dimensional simulation of the implosion of an air-filled and submerged glass sphere.

Continuous Adjoint Method for Unstructured Grids

Adjoint-based shape optimization methods have proven to be computationally efficient for aerodynamic problems. The majority of the studies on adjoint methods have used structured grids to discretize the computational domain. Because of the potential advantages of unstructured grids for complex configurations, in this study we have developed and validated a continuous adjoint formulation for unstructured grids. The hurdles posed in the computation of the gradient for unstructured grids are resolved by using a reduced gradient formulation. The methods to impose thickness constraints on unstructured grids are also discussed. The results for two- and three-dimensional simulations of airfoils and wings in inviscid transonic flow are used to validate the design procedure. Finally, the design procedure is applied to redesign the shape of a transonic business jet configuration; we were able to reduce the inviscid drag of the aircraft from 235 to 216 counts resulting in a shock-free wing. Although the Euler equations are the focus of the study in this paper of the adjoint-based approach, the solution of the adjoint system and gradient formulation can be conceptually extended to viscous flows. The approach presented in this study has been successfully used by the first and third authors for viscous flows using structured grids. However, particular aspects of the design process, such as the robustness of the mesh deformation process for unstructured grids, need more attention for viscous flows and are therefore the subject of ongoing research.

Multi-point Aero-Structural Optimization of Wings Including Planform Variations

This paper focuses on wing optimization via control theory using a multi-point design method. Based on the design methodology previously developed for wing section and planform optimization at a specific flight condition, it searches for a single wing shape that performs well over a range of flight conditions. Our previous experience with multipoint design without a detailed FE structural model, showed improvements in performance measures such as drag divergence Mach number and the lift-to-drag ratio over a range of Mach numbers. In the current work, the flow solution is modified to allow for shape deformation under load. We achieve this by coupling SYN107 to FEAP (Robert Taylor, University of California at Berkeley). The resulting aero-elastic simulation is then used to determine the optimal airfoil section and wing planform definition. In the multi-point design the actual shape will now be dierent at the dierent design points. With the coupled aero-structural analysis we hope to determine the best jig shape for the multipoint design.

Aerodynamic Shape Optimization of Complete Aircraft Configurations using Unstructured Grids

Adjoint based shape optimization methods have proven to be computationally efficient for aerodynamic problems. The majority of the studies on adjoint methods have used structured grids to discretize the computational domain. Due to the potential advantages of unstructured grids for complex configurations, in this study we have developed and validated a continuous adjoint formulation for unstructured grids. Initial results from this study was presented at the summer AIAA conference at Orlando in June, 2003. We have since tested the computational methodology on a few other aircraft configurations and also initiated a CAD based geometry handling process to support single and multidisciplinary analysis and design. 1. Introduction With the availability of high performance computing platforms and robust numerical methods to simulate fluid flows, it is possible to shift attention to automated design procedures which combine CFD with optimization techniques to determine optimum aerodynamic designs. The feasibility of this is by now well established, 1–6 and it is actually possible to calculate optimum three dimensional transonic wing shapes in a few hours, accounting for viscous effects with the flow modeled by the Reynolds averaged Navier Stokes (RANS) equations. By enforcing constraints on the thickness and span-load distribution one can make sure that there is no penalty in structure weight or fuel volume. Larger scale shape changes such as planform variations can also be accommodated. 7 It then becomes necessary to include a structural weight model to enable a proper compromise between minimum drag and low structure weight to be determined. Aerodynamic shape optimization has been successfully performed for a variety of complex configurations using multi-block structured meshes. 8, 9 Meshes of this type can be relatively easily deformed to accommodate shape variations required in the redesign. However, it is both extremely time-consuming and expensive in human costs to generate such meshes. Consequently we believe it is essential to develop shape optimization methods which use unstructured meshes for the flow simulation. Typically, in gradient-based optimization techniques , a control function to be optimized (the wing shape, for example) is parameterized with a set of

Aerodynamic-Structural Design Studies of Low-Sweep Transonic Wings

The current generation of wing designs for civilian air transport typically have a swept wing. However, these wings were designed without the aid of modern high-fidelity simulation and multidisciplinary optimization tools. With rapid advances in numerical simulation of high-Reynolds-number flows and efficient shape-optimization techniques, it is now possible to revisit the designs of modern commercial wide-body aircraft to quantitatively and qualitatively determine the sweep of transonic wings. Results from the aerodynamic shape optimization of a low-sweep wing of a modern transonic civil transport aircraft shows that it is possible to delay the drag rise of this wing to beyond Mach Number of 0.8 if the sections are redesigned. It is conceivable that future aircraft designs will be governed by the need to deliver improved performance with reduced fuel consumption. In this study, we systematically study the feasibility of designing wings with low sweep without aerodynamic or structural performance penalties. The study presented here explores the possibility of extending some commonly accepted limits related to the general layout of an efficient transonic wing. Specifically, the Mach―sweep―thickness relationships are revisited at a cursory level. Pure aerodynamic optimization of wings with varying sweeps (5 to 35 degrees) shows that the design space is relatively flat. These optimized configurations are then studied using an aerostructural optimization package along with planform variations. The aerostructural optimization reveals that the design space is again relatively flat, confirming the assumption that wings with low sweep can be effectively used as an alternative to current sweptback configurations. The results obtained from the optimization studies show that it may be possible to significantly reduce wing sweep without incurring either aerodynamic or structural penalties, especially for M ≤ 0.8 aircraft designs.

Collision Avoidance Strategies for a Three-Player Game

Collision avoidance strategies for a game with three players, two pursuers and one evader, are constructed by determining the semipermeable curves that form the barrier. The vehicles are assumed to have the same capabilities, speed, and turn-rates. The game is assumed to be played on a two-dimensional plane. We consider avoidance strategies for a particular form of the game defined in the following way: the pursuers are assumed to act noncooperatively, the evader upon realizing that one (or both) of the pursuers can cause capture, takes an evasive action. We find states from which the pursuer can cause capture following this evasive action by the evader. The envelope of states that can lead to capture is denoted by the barrier set. Capture is assumed to have occurred when one (or both) pursuers have reached within a circle of radius, l, from the evader. The usable part and its boundary are first determined along with the strategy along the boundary. Semipermeable curves are evolved from the boundary. If two curves intersect (they have a common point), the curves are not extended beyond the intersection point. As in the game of two cars, universal curves and the characteristics that terminate and emanate from the universal curve are used to fill voids on the barrier surface. For the particular game (and associated strategies) considered in this paper, numerical simulations suggest that the enlarged set of initial states that lead to capture is closed. As the game considered here is a subset of the more complete game, when two pursuers try to cause capture of a single evader, the avoidance strategies are most likely to belong to the set of strategies for the complete game.

A multi-code-coupling interface for combustor/turbomachinery simulations

This paper describes the design, implementation and validation of a method to couple multiprocessor solvers whose solution domains share a common surface. Using Message Passing Interface (MPI) constructs, parallel communication pathways are established between various simulation codes. These pathways allow applications to exchange data, synchronize time integrations and reinitialize communication data structures when meshes change their relative positions. At an interface with another simulation code, applications request specific flow variables, typically for a ghost/halo layer of cells or nodes. Numerical estimates of these flow variables are provided by the simulation software on the other side of the interface through three-dimensional interpolation. With an aim at achieving conservative interfacing between applications, particular instances of the requested flow variables and interpolation stencils will be used for different problems. Communication tables are built for processes involved with the exchange of information and all exchanges occur strictly between specific processes, thereby minimizing communication bottlenecks. This paradigm has been used to build a code coupling interface for a three-dimensional combustor/turbine interaction simulation in which a new massively parallel computational fluid dynamic solution procedure for turbomachinery, called TFLO, has been coupled with an unstructured-grid, parallel procedure for combustors, called NCC. Numerical and physical issues regarding the exchange of information as well as the coupling of physics-disparate analyses will be discussed. Several development test cases have been used to ensure the soundness of the communication procedures. A multi-component simulation for a dump combustor/exit duct has been performed as a demonstration of the new interface.

An Assessment of Dual-Time Stepping, Time Spectral and Artificial Compressibility Based Numerical Algorithms for Unsteady Flow with Applications to Flapping Wings

The objective of this study is to compare and contrast three numerical algorithms that can be used to estimate the forces and pressure distribution on wings in flapping motion. All algorithms are used to solve the unsteady Navier-Stokes equations in two dimensions at low Reynolds Numbers. The four algorithms are a) an A-stable, implicit discretization b) the time-spectral algorithm that implicitly assumes that the flow-field in temporally periodic, c) incompressible formulations of a) and d) incompressible formulations of b) using the artificial com-pressibility method. The methods in a) and b) have been reported earlier in literature but their application to flapping wing flows at low Reynolds number is new. The algorithms introduced in c), and d) are new and previously not reported in literature. In this abstract, the four algorithms are used for roughly similar test cases to obtain preliminary estimates for their merits and demerits. The final version of the paper will use the same test case for all the algorithms to enable even-handed comparison of the different numerical methods. Background Insect flight control has been studied extensively from a physiological perspective, but its mechanics are not understood well. Even when the kinematic changes elicited by a given stimulus have been defined, their consequences for aerodynamic force production often remain obscure. Quasi-steady aerodynamics have been largely supplanted by unsteady theories and is widely accepted as the mechanism that leads to the forces produced by insects in flight. 3, 4 Lighthill 1 performed some of the earliest theoretical studies on the aerodynamics of insect flight shows the variation of lift and drag as observed by Weis-Fogh and Jensen. 2 A variety of experimental studies have enabled a better understanding of the nature of wing articulation by insects in hover and forward flight. While these studies enabled the authors to propose a variety of possible theories for insect flight, the lack of a complete understanding of the flight control mechanisms have prevented a more comprehensive understanding of insect flight control. It is not clear how many degrees of freedom an insect controls to enable it to perform its various maneuvers. Further, insects in controlled laboratory environments tend to produce lift and drag forces that are different from those observed in nature leading one to look for alternate analysis tools. It is also difficult to replicate subtle shifts in the center-gravity or even get a good estimate of the center of gravity …

Multi-agent avoidance control using an m-matrix property

In this paper a generalization of avoidance control for multi-agent dynamic systems is presented. Strategies for avoidance control for multiple agents are obtained using individual Liapunov-type functions. The overall system avoidance conditions are guaranteed using a vector Liapunov-type function via an M-matrix property.

Towards Multi-Component Analysis of Gas Turbines by CFD: Integration of RANS and LES Flow Solvers

The numerical prediction of the entire aero-thermal o w through an entire gas turbine is currently limited by its high computational costs. The approach presented here intends to use several specialized o w solvers based on the Reynolds-averaged Navier-Stokes equations (RANS) as well as Large Eddy Simulations (LES) running simultaneously and exchanging information at the interfaces. This study documents the development of the interface and proves its accuracy and efcienc y on simple testcases. Compressor computation currently underway