Session: 2.1 - Recent development in CFD and Verification and Validation methods

Paper Number: 158616

158616 - Verifying & Validating the Integro-Differential Scheme Capability to Solve the 1D Unsteady Gas Dynamic Equations 

Abstract: 

No doubt, today there still exists a wide range of unsolved unsteady fluid dynamic problems that are of enormous interest to both designers and engineers. An example of an unsteady flow field of significant interest is the wake behind a bluff body, for example, the flow field behind a circular cylinder at all Mach numbers. In this case, systems of eddies and vortices are formed behind the cylinder. It is of interest to note that the systems of eddies and vortices, once created, remain closely behind the cylinder, and move in the same direction of the flow but at relatively lower speeds, while perpetually shedding and recreating themselves. The systems of eddies and vortices generated by bluff bodies are difficult to predict, and moreover, the flow field is difficult to comprehend. Further, their behaviors are complicated by vortex shedding. The unsteady wake phenomena is especially notorious in their creation of body oscillations that are self-induced by the fluctuating fluid dynamic forces created by the wake. Now, imagine the enormous tasks faced by designers who are task with creating a vehicle, for example, the helicopter, that is required to operate efficiently in this unpredictable environment. At this stage it becomes clear that solving the unsteady Navier-Stokes (NS) equations under the appropriate set of boundary and initial conditions may go a long way in providing the designers with the scientific insights required to support their endeavors. A possible solution to this problem, is to arm engineers with a tool that solves the unsteady Navier-Stokes equation under a wide range of Mach and Reynold numbers.

Recently, an unsteady integro-differential scheme (IDS) was formulated for use with the unsteady Navier-Stokes equations to simulate complex fluid fields under conditions that include a wide range of Reynolds and Mach numbers. A list of complex CFD problems were solved and their flow field analyzed (see Refs/Moody Award). CFD problems that were successfully solved include: jet flows, flow separation for varying Re, shock-vortex interactions, shock boundary-layer interactions, Isolator shock-train simulation and control and two-phase shock-bubble interactions. The IDS results showed that, when provided with the appropriate initial and boundary conditions, the IDS technique simulated the physics within the prescribed flow fields. Further, in all cases, the results compare very well with the available experimental data, (see AIAA Flow-viz Showcase Ref.). However, the dissipative and dispersive qualities of the newly developed IDS method have not been fully explored. In addition to establishing the order of the errors generated by the scheme and the stability criteria of the scheme, it is also the intention of this paper to apply the IDS technique to the 1D+ unsteady gas dynamics model to analyze its ‘dissipative and dispersive’ characteristics. Plans are to evaluate the IDS dissipative and dispersive characteristics analytically and numerically. The IDS simulation capabilities will be verified and validated through the use of both, the inviscid and the viscous gas dynamic models. Further, the 1D+ flow fields with the initial and boundary conditions of interest to the shock-tube aerodynamics community will be of primary focus. Plans are also underway to study the error characteristics of the IDS simulation results in comparison to those generated by the 5th Order WENO scheme. Further, in the completed paper, the 1D Unsteady IDS scheme will be used to simulate the internal structure of the normal shock wave front. The viscous effects within the normal shock will be analyzed.

Presenting Author: Frederick Ferguson North Carolina A&T State University

Presenting Author Biography: Dr. Frederick Ferguson
Professor, ME Department, NCAT

Dr. Frederick Ferguson is a Professor in the Mechanical Engineering Department at North Carolina A&T State University (NCAT). In the past, he served as the Program Manager for Fluid Dynamics Program at the Army Research Office (ARO) (from Dec., 2009 through Dec., 2013). At NCAT, he served as the director for the Center for Aerospace Research from 1997 until 2009. Dr. Ferguson received his PhD. in Aerospace Engineering from the University of Maryland in 1993 and a MS. in Applied Mathematics from Kharkov State University in the former Soviet Union in 1986. He speaks the Russian language fluently. Dr. Ferguson is considered an expert in the areas of Computational Fluid Dynamics, Hypersonic Waveriders and Scramjet Propulsion Systems.
Currently, Dr. Ferguson and his students have created a CFD numerical code that is capable of generating solutions to the full set of Navier-Stokes Equations for a wide class of boundary conditions. The CFD code is capable of generating solutions under realistic aircraft operating conditions, while delivering results that contains all the required flow physics. Additionally, Dr. Ferguson is an expert in the design of hypersonic vehicle configurations using inverse numerical techniques, and has contributed to the expansion of the waverider design concept to include the design of a tip-to-tail vehicle. He currently conducts research in high speed aerodynamics, and is working on the development of efficient algorithms for simulating complex viscous flows in three dimensions; including turbulent flow fields in which finite-rate chemistry effects are dominant. In the past, Dr. Ferguson has managed research projects in the following areas: UAVs, Reusable launch vehicle (RLV), International Space Station (ISS), optimized aerospace vehicle design, software safety and image analysis and processing. At NCAT, Dr. Ferguson research projects have served to satisfied the graduation requirements of over 35 MS and PhD students, and has authored and/or co-authored over 120 scientific articles. Dr. Ferguson also worked as an experimentalist for over ten years. At AEDAR Corporation, he was actively involved with scientists from JPL in the implementation and mapping of artificial intelligent algorithms (Fuzzy logic, expert systems, and Neural Networks) to field processing gate arrays (FPGAs) in the construction of affordable reconfigurable hardware. Some of his past research activities include multi-target tracking and the design of thermal systems for reentry vehicle. Earlier in his career, he worked at PALL Corporation in Long Island, NY, where he was involved in the design and manufacturing of aerosol filters for the semi-conductor industry.