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A verification of unsteady Navier-Stokes solutions around oscillating airfoils

A finite difference solution code for the two dimensional Navier-Stokes equations was combined with a moving-grid system. The thin layer Navier-Stokes equations with a turbulence model are solved in a time-accurate manner in order to study the unsteady aerodynamics around airfoils undergoing small amplitude pitching or heaving motions in the transonic regime. The accuracy of the solutions obtained by the use of the present moving-grid technqiue is investigated. The effects of the minimum grid size and the integrating time-step size on the solutions are also checked. Some of the solutions obtained by the present method are compared with experimental results. It is demonstrated that the unsteady aerodynamics around oscillating airfoils can be predicted fairly well by the present code for cases in which the dynamic angle of attack or displacement is small.

Nakamichi, J.

The linear Boltzmann equation in slab geometry - Development and verification of a reliable and efficient solution

The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.

Stamnes, K.

On the Lagrangian description of unsteady boundary layer separation. Part 2: The spinning sphere

A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.

Vandommelen, Leon L.

On the Lagrangian description of unsteady boundary-layer separation. II - The spinning sphere

A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.

Van Dommelen, Leon L.

Verification of a Viscous Computational Aeroacoustics Code Using External Verification Analysis

The External Verification Analysis approach to code verification is extended to solve the three-dimensional Navier-Stokes equations with constant properties, and is used to verify a high-order computational aeroacoustics (CAA) code. After a brief review of the relevant literature, the details of the EVA approach are presented and compared to the similar Method of Manufactured Solutions (MMS). Pseudocode representations of EVA's algorithms are included, along with the recurrence relations needed to construct the EVA solution. The code verification results show that EVA was able to convincingly verify a high-order, viscous CAA code without the addition of MMS-style source terms, or any other modifications to the code.

Computational

Verification of a Viscous Computational Aeroacoustics Code using External Verification Analysis

The External Verification Analysis approach to code verification is extended to solve the three-dimensional Navier-Stokes equations with constant properties, and is used to verify a high-order computational aeroacoustics (CAA) code. After a brief review of the relevant literature, the details of the EVA approach are presented and compared to the similar Method of Manufactured Solutions (MMS). Pseudocode representations of EVA's algorithms are included, along with the recurrence relations needed to construct the EVA solution. The code verification results show that EVA was able to convincingly verify a high-order, viscous CAA code without the addition of MMS-style source terms, or any other modifications to the code.

Computational

Supporting Crew Autonomy in Deep Space Exploration: Preliminary Onboard Capability Requirements and Proposed Research Questions. Technical Report of the Autonomous Crew Operations Technical Interchange Meeting

Communication delays are a critical challenge posed by long duration deep space exploration. Space missions historically have relied on an ever-present Mission Control Center (MCC) to direct operations in near real-time. As unanticipated anomalies that defeat fault detection and resolution systems do arise, the lack of real-time communication will significantly weaken what the MCC support represents: a reliable safety net for the flight crew through its deep and diverse areas of expertise and investigative resources. As a consequence, future space vehicles and habitats need to be equipped with capabilities to support the flight crew to operate with little or no ground support. Considerations must be given to vehicle and mission designs that will fortify the traditionally ground-centered safety net and forge new support systems, when communication delays exist. In August 2018, NASA’s Human Research Program, through its Human Factors and Behavioral Performance Element, convened a Technical Interchange Meeting (TIM) on Autonomous Crew Operations at NASA Ames Research Center. The goal of the meeting was to gather input from NASA centers, industry, academia, and branches of the Department of Defense (DoD) to address how intelligent technologies can be applied to augment onboard capabilities to support crew anomaly response. The TIM featured 24 presentations by 29 speakers and hosted a total of 59 attendees, including 43 from 5 NASA centers (Ames, Johnson, Langley, Marshall, and Jet Propulsion Lab) and 4 from the DoD (3 from Army Research Lab and 1 from Naval Postgraduate School), with remaining attendees from academia (e.g., UC Davis, CMU) and industry (e.g., IBM, Siemens). Discussions were centered around three themes: standards and guidelines, lessons learned in analog environments, and technologies. To help provide a framework for discussion, a concept matrix describing anomaly response processes was created prior to the TIM (Figure 1, page 6). The matrix captures the steps involved (monitoring and detection, diagnosis, solution development and evaluation, solution implementation and verification, resolution documentation) as well as the resources and capabilities required to support these steps (data, knowledge, analysis, synthesis, resource management). A wallpaper size printout of the matrix was utilized at the TIM to solicit attendee inputs along the three themes; the activity garnered 108 submissions of ideas. Overall, what emerged from TIM discussions was a picture of mismatch between crew anomaly response needs and support that can be provided by existing intelligent technologies. The needs are broad, spanning multiple steps and processes/resources, with many of which lacking support from existing technologies, such as knowledge management throughout the steps of problem solving (especially in resolution documentation) and manpower management. The solutions provided by existing intelligent technologies are specific to the steps/processes that they are designed to support and constrained to solving only problems similar to those that have occurred before. What is lacking from technologies is typically made up by humans, specifically their complex critical thinking, creative problem solving, and domain expertise. In the end, the TIM highlighted the pressing need to support responses to onboard anomalies during autonomous crew operations, particularly those that have eluded the system tests, inspection, and other assurance processes. Such anomalies can potentially threaten crew and vehicle safety, as well as significantly impact overall operations with additional workload. These fairly rare events are difficult to anticipate and prepare for, given the state-of-the-art in intelligent technologies. This is true even for anomalies that stem from “unknown knowns”—cases in which there is sufficient external information to characterize the problem but the overall pattern fails to be recognized by the problem solver, or in which the internal knowledge needed to solve a problem is held tacitly and potentially accessible by the problem solver but not articulated. It follows that the ability to tackle anomalies lies not only with the availability of relevant information and knowledge but also their accessibility in times of need. To that end, we propose research questions along the following three broad themes: • How intelligent technologies can help make relevant knowledge and information available? • How intelligent technologies can help make relevant knowledge and information accessible? • How intelligent technologies can help support the crew operating as a team in anomaly response processes?

autonomous crew operations

Transonic flow over wing/fuselage configurations

Wing Body Code (WIBCO) program simulates flow-field configurations for reduction of design cost and improvement of aircraft performance. Inputs to WIBCO consist of ambient flow conditions and geometric configuration data; grid control and relaxation parameters are internally set. Outputs include input data echo, grid system verification, relaxation-solution convergence history, and computed velocities, pressures, forces, moments, reference lengths, and areas. Program is written in FORTRAN IV for batch execution.

Boppe, C. W.

Verifying performance requirements

Today, it is impossible to verify performance requirements on Ada software, except in a very approximate sense. There are several reasons for this difficulty, of which the main reason is the lack of use of information on the mapping of the program onto the target machine. An approach to a partial solution to the verification of performance requirements on Ada software is proposed, called the rule based verification approach. This approach is suitable when the target machine is well defined and when additional effort and expense are justified in order to guarantee that the performance requirements will be met by the final system.

Cross, Joseph

Inspection and Verification of Domain Models with PlanWorks and Aver

When developing a domain model, it seems natural to bring the traditional informal tools of inspection and verification, debuggers and automated test suites, to bear upon the problems that will inevitably arise. Debuggers that allow inspection of registers and memory and stepwise execution have been a staple of software development of all sorts from the very beginning. Automated testing has repeatedly proven its considerable worth, to the extent that an entire design philosophy (Test Driven Development) has been developed around the writing of tests. Unfortunately, while not entirely without their uses, the limitations of these tools and the nature of the complexity of models and the underlying planning systems make the diagnosis of certain classes of problems and the verification of their solutions difficult or impossible. Debuggers provide a good local view of executing code, allowing a fine-grained look at algorithms and data. This view is, however, usually only at the level of the current scope in the implementation language, and the data-inspection capabilities of most debuggers usually consist of on-line print statements. More modem graphical debuggers offer a sort of tree view of data structures, but even this is too low-level and is often inappropriate for the kinds of structures created by planning systems. For instance, god or constraint networks are at best awkward when visualized as trees. Any any non-structural link between data structures, as through a lookup table, isn't captured at all. Further, while debuggers have powerful breakpointing facilities that are suitable for finding specific algorithmic errors, they have little use in the diagnosis of modeling errors.

Bedrax-Weiss, Tania

A Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors

A capability to couple NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This paper summarizes the efforts in applying the installed coupling software to demonstrate/investigate fluid-structure interaction (FSI) between pressure wave and flexible inhibitor inside reusable solid rocket motor (RSRM). First a unified governing equation for both fluid and structure is presented, then an Eulerian-Lagrangian framework is described to satisfy the interfacial continuity requirements. The features of fluid solver, Loci/CHEM and structural solver, CoBi, are discussed before the coupling methodology of the solvers is described. The simulation uses production level CFD LES turbulence model with a grid resolution of 80 million cells. The flexible inhibitor is modeled with full 3D shell elements. Verifications against analytical solutions of structural model under steady uniform pressure condition and under dynamic condition of modal analysis show excellent agreements in terms of displacement distribution and eigen modal frequencies. The preliminary coupled result shows that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor.

Yang, H. Q.

Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors

Flexible inhibitors are generally used in solid rocket motors (SRMs) as a means to control the burning of propellant. Vortices generated by the flow of propellant around the flexible inhibitors have been identified as a driving source of instabilities that can lead to thrust oscillations in launch vehicles. Potential coupling between the SRM thrust oscillations and structural vibration modes is an important risk factor in launch vehicle design. As a means to predict and better understand these phenomena, a multidisciplinary simulation capability that couples the NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This capability is crucial to the development of NASA's new space launch system (SLS). This paper summarizes the efforts in applying the coupled software to demonstrate and investigate fluid-structure interaction (FSI) phenomena between pressure waves and flexible inhibitors inside reusable solid rocket motors (RSRMs). The features of the fluid and structural solvers are described in detail, and the coupling methodology and interfacial continuity requirements are then presented in a general Eulerian-Lagrangian framework. The simulations presented herein utilize production level CFD with hybrid RANS/LES turbulence modeling and grid resolution in excess of 80 million cells. The fluid domain in the SRM is discretized using a general mixed polyhedral unstructured mesh, while full 3D shell elements are utilized in the structural domain for the flexible inhibitors. Verifications against analytical solutions for a structural model under a steady uniform pressure condition and under dynamic modal analysis show excellent agreement in terms of displacement distribution and eigenmode frequencies. The preliminary coupled results indicate that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor. This insight could have profound implications for SRM and flexible inhibitor designs for current and future launch vehicles including SLS.

Yang, H. Q.

Application of FUN3D and CFL3D to the Third Workshop on CFD Uncertainty Analysis

Two Reynolds-averaged Navier-Stokes computer codes - one unstructured and one structured - are applied to two workshop cases (for the 3rd Workshop on CFD Uncertainty Analysis, held at Instituto Superior Tecnico, Lisbon, in October 2008) for the purpose of uncertainty analysis. The Spalart-Allmaras turbulence model is employed. The first case uses the method of manufactured solution and is intended as a verification case. In other words, the CFD solution is expected to approach the exact solution as the grid is refined. The second case is a validation case (comparison against experiment), for which modeling errors inherent in the turbulence model and errors/uncertainty in the experiment may prevent close agreement. The results from the two computer codes are also compared. This exercise verifies that the codes are consistent both with the exact manufactured solution and with each other. In terms of order property, both codes behave as expected for the manufactured solution. For the backward facing step, CFD uncertainty on the finest grid is computed and is generally very low for both codes (whose results are nearly identical). Agreement with experiment is good at some locations for particular variables, but there are also many areas where the CFD and experimental uncertainties do not overlap.

Rumsey, C. L.

Numerical Modeling of Ablation Heat Transfer

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Ewing, Mark E.

Full Multigrid Flow Solver

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Mineck, Raymond E.

Verification and Validation Studies for the LAVA CFD Solver

The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) solver is presented. A modern strategy for verification and validation is described incorporating verification tests, validation benchmarks, continuous integration and version control methods for automated testing in a collaborative development environment. The purpose of the approach is to integrate the verification and validation process into the development of the solver and improve productivity. This paper uses the Method of Manufactured Solutions (MMS) for the verification of 2D Euler equations, 3D Navier-Stokes equations as well as turbulence models. A method for systematic refinement of unstructured grids is also presented. Verification using inviscid vortex propagation and flow over a flat plate is highlighted. Simulation results using laminar and turbulent flow past a NACA 0012 airfoil and ONERA M6 wing are validated against experimental and numerical data.

Validation

A coupled solution method for predicting the thermostructural response of decomposing, expanding polymeric composites

A new solution method has recently been developed to analyze the thermal and structural response of polymeric composites during chemical decomposition (Sullivan and Salamon, 1992a). This method couples the equations of energy, mass transport and momentum and solves these equations simultaneously at each time step. In this paper, the couples solution method is applied to analyze the response of a glass phenolic composite during its chemical decomposition. The numerical solution to this particular problem was originally performed by Henderson, et al. (1985) and the actual response was measured by Henderson and Hagen (1985) and Ramamurthy (1988). In addition to further verification of the coupled solution method, the present solution offers additional insight into certain physical events which occur during chemical decomposition.

Sullivan, Roy M.