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NASA NTRS2007

Enhanced Elliptic Grid Generation

An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.

Kaul, Upender K.↗

NASA NTRS1994

An Approach for Dynamic Grids

An approach is presented for the generation of two-dimensional, structured, dynamic grids. The grid motion may be due to the motion of the boundaries of the computational domain or to the adaptation of the grid to the transient, physical solution. A time-dependent grid is computed through the time integration of the grid speeds which are computed from a system of grid speed equations. The grid speed equations are derived from the time-differentiation of the grid equations so as to ensure that the dynamic grid maintains the desired qualities of the static grid. The grid equations are the Euler-Lagrange equations derived from a variational statement for the grid. The dynamic grid method is demonstrated for a model problem involving boundary motion, an inviscid flow in a converging-diverging nozzle during startup, and a viscous flow over a flat plate with an impinging shock wave. It is shown that the approach is more accurate for transient flows than an approach in which the grid speeds are computed using a finite difference with respect to time of the grid. However, the approach requires significantly more computational effort.

Slater, John W.↗

NASA NTRS1995

The National Grid Project: A system overview

The National Grid Project (NGP) is a comprehensive numerical grid generation software system that is being developed at the National Science Foundation (NSF) Engineering Research Center (ERC) for Computational Field Simulation (CFS) at Mississippi State University (MSU). NGP is supported by a coalition of U.S. industries and federal laboratories. The objective of the NGP is to significantly decrease the amount of time it takes to generate a numerical grid for complex geometries and to increase the quality of these grids to enable computational field simulations for applications in industry. A geometric configuration can be discretized into grids (or meshes) that have two fundamental forms: structured and unstructured. Structured grids are formed by intersecting curvilinear coordinate lines and are composed of quadrilateral (2D) and hexahedral (3D) logically rectangular cells. The connectivity of a structured grid provides for trivial identification of neighboring points by incrementing coordinate indices. Unstructured grids are composed of cells of any shape (commonly triangles, quadrilaterals, tetrahedra and hexahedra), but do not have trivial identification of neighbors by incrementing an index. For unstructured grids, a set of points and an associated connectivity table is generated to define unstructured cell shapes and neighboring points. Hybrid grids are a combination of structured grids and unstructured grids. Chimera (overset) grids are intersecting or overlapping structured grids. The NGP system currently provides a user interface that integrates both 2D and 3D structured and unstructured grid generation, a solid modeling topology data management system, an internal Computer Aided Design (CAD) system based on Non-Uniform Rational B-Splines (NURBS), a journaling language, and a grid/solution visualization system.

Gaither, Adam↗

NASA NTRS1999

Parallel Grid Manipulations in Earth Science Calculations

The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center is moving its data assimilation system to massively parallel computing platforms. This parallel implementation of GEOS DAS will be used in the DAO's normal activities, which include reanalysis of data, and operational support for flight missions. Key components of GEOS DAS, including the gridpoint-based general circulation model and a data analysis system, are currently being parallelized. The parallelization of GEOS DAS is also one of the HPCC Grand Challenge Projects. The GEOS-DAS software employs several distinct grids. Some examples are: an observation grid- an unstructured grid of points at which observed or measured physical quantities from instruments or satellites are associated- a highly-structured latitude-longitude grid of points spanning the earth at given latitude-longitude coordinates at which prognostic quantities are determined, and a computational lat-lon grid in which the pole has been moved to a different location to avoid computational instabilities. Each of these grids has a different structure and number of constituent points. In spite of that, there are numerous interactions between the grids, e.g., values on one grid must be interpolated to another, or, in other cases, grids need to be redistributed on the underlying parallel platform. The DAO has designed a parallel integrated library for grid manipulations (PILGRIM) to support the needed grid interactions with maximum efficiency. It offers a flexible interface to generate new grids, define transformations between grids and apply them. Basic communication is currently MPI, however the interfaces defined here could conceivably be implemented with other message-passing libraries, e.g., Cray SHMEM, or with shared-memory constructs. The library is written in Fortran 90. First performance results indicate that even difficult problems, such as above-mentioned pole rotation- a sparse interpolation with little data locality between the physical lat-lon grid and a pole rotated computational grid- can be solved efficiently and at the GFlop/s rates needed to solve tomorrow's high resolution earth science models. In the subsequent presentation we will discuss the design and implementation of PILGRIM as well as a number of the problems it is required to solve. Some conclusions will be drawn about the potential performance of the overall earth science models on the supercomputer platforms foreseen for these problems.

Sawyer, W.↗

NASA NTRS2004

Spaceflight Operations Services Grid (SOSG)

In an effort to adapt existing space flight operations services to new emerging Grid technologies we are developing a Grid-based prototype space flight operations Grid. This prototype is based on the operational services being provided to the International Space Station's Payload operations located at the Marshall Space Flight Center, Alabama. The prototype services will be Grid or Web enabled and provided to four user communities through portal technology. Users will have the opportunity to assess the value and feasibility of Grid technologies to their specific areas or disciplines. In this presentation descriptions of the prototype development, User-based services, Grid-based services and status of the project will be presented. Expected benefits, findings and observations (if any) to date will also be discussed. The focus of the presentation will be on the project in general, status to date and future plans. The End-use services to be included in the prototype are voice, video, telemetry, commanding, collaboration tools and visualization among others. Security is addressed throughout the project and is being designed into the Grid technologies and standards development. The project is divided into three phases. Phase One establishes the baseline User-based services required for space flight operations listed above. Phase Two involves applying Gridlweb technologies to the User-based services and development of portals for access by users. Phase Three will allow NASA and end users to evaluate the services and determine the future of the technology as applied to space flight operational services. Although, Phase One, which includes the development of the quasi-operational User-based services of the prototype, development will be completed by March 2004, the application of Grid technologies to these services will have just begun. We will provide status of the Grid technologies to the individual User-based services. This effort will result in an extensible environment that incorporates existing and new spaceflight services into a standards-based framework providing current and future NASA programs with cost savings and new and evolvable methods to conduct science. This project will demonstrate how the use of new programming paradigms such as web and grid services can provide three significant benefits to the cost-effective delivery of spaceflight services. They will enable applications to operate more efficiently by being able to utilize pooled resources. They will also permit the reuse of common services to rapidly construct new and more powerful applications. Finally they will permit easy and secure access to services via a combination of grid and portal technology by a distributed user community consisting of NASA operations centers, scientists, the educational community and even the general population as outreach. The approach will be to deploy existing mission support applications such as the Telescience Resource Kit (TReK) and new applications under development, such as the Grid Video Distribution System (GViDS), together with existing grid applications and services such as high-performance computing and visualization services provided by NASA s Information Power Grid (IPG) in the MSFC s Payload Operations Integration Center (POIC) HOSC Annex. Once the initial applications have been moved to the grid, a process will begin to apply the new programming paradigms to integrate them where possible. For example, with GViDS, instead of viewing the Distribution service as an application that must run on a single node, the new approach is to build it such that it can be dispatched across a pool of resources in response to dynamic loads. To make this a reality, reusable services will be critical, such as a brokering service to locate appropriate resource within the pool. This brokering service can then be used by other applications such as the TReK. To expand further, if the GViDS application is constructed using a services-based mel, then other applications such as the Video Auditorium can then use GViDS as a service to easily incorporate these video streams into a collaborative conference. Finally, as these applications are re-factored into this new services-based paradigm, the construction of portals to integrate them will be a simple process. As a result, portals can be tailored to meet the requirements of specific user communities.

Bradford, Robert N.↗

DOE OSTI2024

Validation of Interconnection and Interoperability of Grid-Forming Inverters Sourced by Hydrogen Technologies in View of 100% Renewable Microgrids

Grid-forming assets are required in microgrids to act as voltage-frequency masters. These grid-forming assets can operate in two modes of operation: grid-following mode and grid-forming mode. In grid-following mode of operation, these assets will follow real power and reactive power setpoints and in grid-forming mode of operation these assets will follow voltage and frequency setpoints. Traditionally, diesel generators or natural gas-based generators are widely used to act as a voltage-frequency master. However, many utilities are aiming to replace generators with grid forming-inverters supplied by solar photovoltaics (PV), batteries or fuel cells. Since grid-forming assets need a long-term reliable energy source, fuel cells are a reasonable and viable choice to supply the grid-forming inverters, but some of the challenges facing the wide deployment of grid-forming fuel cell inverters need to be addressed. Specifically, in our proposed work, we aim to focus on the interconnection and interoperability requirements of grid-forming fuel cell inverters. Currently, state-of-the-art fuel cell inverters follow the general interconnection requirements of distributed energy resources (DERs) and general interoperability requirements of DERs, but these requirements were built with PV and battery systems in mind. Fuel cells have different operational requirements, and therefore these requirements need to be appropriately modified for the grid operators to use. These additional steps add to the investment and operational cost to the grid operators. Through the ARIES platform, this proposed project aims to bridge this gap and use power hardware-in-the-loop (PHIL) and controller hardware-in-the-loop (CHIL) experiments to inform the creation of open-source interconnection and interoperability information that can aid in faster and cheaper installation and operation of grid-forming fuel cell inverters.

controller hardware-in-the-loop↗

DOE OSTI2026

Potential of Data Center Controls in Grid Services

The rapid proliferation of large data centers brings both challenges and opportunities for grid reliability. The data center resources and their potential flexibility have the potential to contribute resources to grid operations. Through capabilities like energy shifting and resource coordination, data centers can help reduce their net demand on the transmission network, as well as provide additional grid services to support reliable operation on the grid. While transient and long-term grid planning and operations are the scenarios that draw most attention, the quasi-steady state timeseries (QSTS) operation of data centers and grid bring interesting scenarios that can help evaluate the data center controls to aid grid services. This work is focused on modeling data centers for QSTS applications – incorporating the AI data center load profiles and building on the PNNL digital twin model for the thermal management loads to enable simulation studies to reveal the impact of data center controls on grid performance. This includes the integration of a QSTS battery and natural gas generator model to incorporate local resource impacts to the system. The simulation study is performed with a modified IEEE 24-Bus transmission system. Scenarios are focused on evaluating the data center load impacts on the transmission system and leveraging both data center and local generation controls to mitigate those impacts and provide additional grid services. The data center controls revealed the ability to contribute to two main kinds of grid services: preventing congestion on a weak grid by coordinating the data center resources with the collocated BESS and onsite generation; and the ability to help the grid operations during stressed times of operation like during a contingency. Leveraging these and other capabilities has the potential to help data centers become grid responsive assets, aiding in both their integration into the power system and grid reliability.

power grid simulation↗

NASA NTRS1992

Interactive solution-adaptive grid generation

TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.

Choo, Yung K.↗

NASA NTRS1999

Development of Three-Dimensional DRAGON Grid Technology

For a typical three dimensional flow in a practical engineering device, the time spent in grid generation can take 70 percent of the total analysis effort, resulting in a serious bottleneck in the design/analysis cycle. The present research attempts to develop a procedure that can considerably reduce the grid generation effort. The DRAGON grid, as a hybrid grid, is created by means of a Direct Replacement of Arbitrary Grid Overlapping by Nonstructured grid. The DRAGON grid scheme is an adaptation to the Chimera thinking. The Chimera grid is a composite structured grid, composing a set of overlapped structured grids, which are independently generated and body-fitted. The grid is of high quality and amenable for efficient solution schemes. However, the interpolation used in the overlapped region between grids introduces error, especially when a sharp-gradient region is encountered. The DRAGON grid scheme is capable of completely eliminating the interpolation and preserving the conservation property. It maximizes the advantages of the Chimera scheme and adapts the strengths of the unstructured and while at the same time keeping its weaknesses minimal. In the present paper, we describe the progress towards extending the DRAGON grid technology into three dimensions. Essential and programming aspects of the extension, and new challenges for the three-dimensional cases, are addressed.

Zheng, Yao↗

NASA NTRS2004

Space-based Science Operations Grid Prototype

Grid technology is the up and coming technology that is enabling widely disparate services to be offered to users that is very economical, easy to use and not available on a wide basis. Under the Grid concept disparate organizations generally defined as "virtual organizations" can share services i.e. sharing discipline specific computer applications, required to accomplish the specific scientific and engineering organizational goals and objectives. Grids are emerging as the new technology of the future. Grid technology has been enabled by the evolution of increasingly high speed networking. Without the evolution of high speed networking Grid technology would not have emerged. NASA/Marshall Space Flight Center's (MSFC) Flight Projects Directorate, Ground Systems Department is developing a Space-based Science Operations Grid prototype to provide to scientists and engineers the tools necessary to operate space-based science payloads/experiments and for scientists to conduct public and educational outreach. In addition Grid technology can provide new services not currently available to users. These services include mission voice and video, application sharing, telemetry management and display, payload and experiment commanding, data mining, high order data processing, discipline specific application sharing and data storage, all from a single grid portal. The Prototype will provide most of these services in a first step demonstration of integrated Grid and space-based science operations technologies. It will initially be based on the International Space Station science operational services located at the Payload Operations Integration Center at MSFC, but can be applied to many NASA projects including free flying satellites and future projects. The Prototype will use the Internet2 Abilene Research and Education Network that is currently a 10 Gb backbone network to reach the University of Alabama at Huntsville and several other, as yet unidentified, Space Station based science experimenters. There is an international aspect to the Grid involving the America's Pathway (AMPath) network, the Chilean REUNA Research and Education Network and the University of Chile in Santiago that will further demonstrate how extensive these services can be used. From the user's perspective, the Prototype will provide a single interface and logon to these varied services without the complexity of knowing the where's and how's of each service. There is a separate and deliberate emphasis on security. Security will be addressed by specifically outlining the different approaches and tools used. Grid technology, unlike the Internet, is being designed with security in mind. In addition we will show the locations, configurations and network paths associated with each service and virtual organization. We will discuss the separate virtual organizations that we define for the varied user communities. These will include certain, as yet undetermined, space-based science functions and/or processes and will include specific virtual organizations required for public and educational outreach and science and engineering collaboration. We will also discuss the Grid Prototype performance and the potential for further Grid applications both space-based and ground based projects and processes. In this paper and presentation we will detail each service and how they are integrated using Grid

Bradford, Robert N.↗

NASA NTRS2018

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.

Park, Michael A.↗

NASA NTRS1984

Ion beamlet steering for two-grid electrostatic thrusters

An experimental study of ion beamlet steering in which the direction of beamlets emitted from a two grid aperture system is controlled by relative translation of the grids, is described. The results can be used to design electrostatic accelerating devices for which the direction and focus of emerging beamlets are important. Deflection and divergence angle data are presented for two grid systems as a function of the relative lateral displacement of the holes in these grids. At large displacements, accelerator grid impingements become excessive and this determines the maximum allowable displacement and as a result the useful range of beamlet deflection. Beamlet deflection is shown to vary linearly with grid offset angle over this range. The divergence of the beamlets is found to be unaffected by deflection over the useful range of beamlet deflection. The grids of a typical dished grid ion thruster are examined to determine the effects of thermally induced grid distortion and prescribed offsets of grid hole centerlines on the characteristics of the emerging beamlets. The results are used to determine the region on the grid surface where ion beamlet deflections exceed the useful range. Over this region high accelerator grid impingement currents and rapid grid erosion are predicted.

Homa, J. M.↗

NASA NTRS1987

Composite grid and finite-volume LU implicit scheme for turbine flow analysis

A composite grid was generated in an attempt to improve grid quality for a typical turbine blade with large camber in terms of mesh control, smoothness, and orthogonality. This composite grid consists of the C grid (or O grid) in the immediate vicinity of the blade and the H grid in the upstream region and in the middle of the blade passage between the C grids. It provides a good boundary layer resolution around the leading edge region for viscous calculation, has orthogonality at the blade surface and slope continuity at the C-H (or O-H) interface, and has flexibility in controlling the mesh distribution in the upstream region without using excessive grid points. This composite grid eliminates the undesirable qualities of a single grid when generated for a typical turbine geometry. A finite-volume lower-upper (LU) implicit scheme can be used in solving for the turbine flows on the composite grid. This grid has a special grid node that is connected to more than four neighboring nodes in two dimensions and to more than six nodes in three dimensions. But the finite-volume approach poses no problem at the special point because each interior cell has only four neighboring cells in two dimensions and only six cells in three dimensions. The finite-volume LU implicit scheme was demonstrated to be robust and efficient for both external and internal flows in a broad flow regime.

Choo, Yung K.↗

NASA NTRS1987

Composite grid and finite-volume LU implicit scheme for turbine flow analysis

A composite grid was generated in an attempt to improve grid quality for a typical turbine blade with large camber in terms of mesh control, smoothness, and orthogonality. This composite grid consists of the C grid (or O grid) in the immediate vicinity of the blade and the H grid in the upstream region and in the middle of the blade passage between the C grids. It provides a good boundary layer resolution around the leading edge region for viscous calculation, has orthogonality at the blade surface and slope continuity at the C-H (or O-H) interface, and has flexibility in controlling the mesh distribution in the upstream region without using excessive grid points. This composite grid eliminates the undesirable qualities of a single grid when generated for a typical turbine geometry. A finite-volume lower-upper (LU) implicit schemes can be used in solving for the turbine flows on the composite grid. This grid has a special grid node that is connected to more than four neighboring nodes in two dimensions and to more than six nodes in three dimensions. But the finite-volume approach poses no problem at the special point because each interior cell has only four neighboring cells in two dimensions and only six cells in three dimensions. The finite-volume LU implicit scheme was demonstrated to be robust and efficient for both external and internal flows in a broad flow regime.

Choo, Yung K.↗

NASA NTRS1992

Grid generation research at OSU

In the last two years, effort was concentrated on: (1) surface modeling; (2) surface grid generation; and (3) 3-D flow space grid generation. The surface modeling shares the same objectives as the surface modeling in computer aided design (CAD), so software available in CAD can in principle be used for solid modeling. Unfortunately, however, the CAD software cannot be easily used in practice for grid generation purposes, because they are not designed to provide appropriate data base for grid generation. Therefore, we started developing a generalized surface modeling software from scratch, that provides the data base for the surface grid generation. Generating surface grid is an important step in generating a 3-D space for flow space. To generate a surface grid on a given surface representation, we developed a unique algorithm that works on any non-smooth surfaces. Once the surface grid is generated, a 3-D space can be generated. For this purpose, we also developed a new algorithm, which is a hybrid of the hyperbolic and the elliptic grid generation methods. With this hybrid method, orthogonality of the grid near the solid boundary can be easily achieved without introducing empirical fudge factors. Work to develop 2-D and 3-D grids for turbomachinery blade geometries was performed, and as an extension of this research we are planning to develop an adaptive grid procedure with an interactive grid environment.

Nakamura, S.↗

NASA NTRS2002

On Accuracy of Adaptive Grid Methods for Captured Shocks

The accuracy of two grid adaptation strategies, grid redistribution and local grid refinement, is examined by solving the 2-D Euler equations for the supersonic steady flow around a cylinder. Second- and fourth-order linear finite difference shock-capturing schemes, based on the Lax-Friedrichs flux splitting, are used to discretize the governing equations. The grid refinement study shows that for the second-order scheme, neither grid adaptation strategy improves the numerical solution accuracy compared to that calculated on a uniform grid with the same number of grid points. For the fourth-order scheme, the dominant first-order error component is reduced by the grid adaptation, while the design-order error component drastically increases because of the grid nonuniformity. As a result, both grid adaptation techniques improve the numerical solution accuracy only on the coarsest mesh or on very fine grids that are seldom found in practical applications because of the computational cost involved. Similar error behavior has been obtained for the pressure integral across the shock. A simple analysis shows that both grid adaptation strategies are not without penalties in the numerical solution accuracy. Based on these results, a new grid adaptation criterion for captured shocks is proposed.

Yamaleev, Nail K.↗

NASA NTRS2009

Description of the F-16XL Geometry and Computational Grids Used in CAWAPI

The objective of the Cranked-Arrow Wing Aerodynamics Project International (CAWAPI) was to allow a comprehensive validation of Computational Fluid Dynamics methods against the CAWAP flight database. A major part of this work involved the generation of high-quality computational grids. Prior to the grid generation an IGES file containing the air-tight geometry of the F-16XL aircraft was generated by a cooperation of the CAWAPI partners. Based on this geometry description both structured and unstructured grids have been generated. The baseline structured (multi-block) grid (and a family of derived grids) has been generated by the National Aerospace Laboratory NLR. Although the algorithms used by NLR had become available just before CAWAPI and thus only a limited experience with their application to such a complex configuration had been gained, a grid of good quality was generated well within four weeks. This time compared favourably with that required to produce the unstructured grids in CAWAPI. The baseline all-tetrahedral and hybrid unstructured grids has been generated at NASA Langley Research Center and the USAFA, respectively. To provide more geometrical resolution, trimmed unstructured grids have been generated at EADS-MAS, the UTSimCenter, Boeing Phantom Works and KTH/FOI. All grids generated within the framework of CAWAPI will be discussed in the article. Both results obtained on the structured grids and the unstructured grids showed a significant improvement in agreement with flight test data in comparison with those obtained on the structured multi-block grid used during CAWAP.

Boelens, O. J.↗

NASA NTRSDate not supplied

Grid Refinement Techniques for the 𝜸-Re𝜽𝒕 Transition Model in FUN3D

There has been an increased focus on the overall accuracy and grid convergence of Reynolds-averaged Navier-Stokes (RANS)-based transition models from the recent AIAA and NATO-AVT workshops. Even though satisfactory grid convergence could be achieved for simple two-dimensional flow configurations, it required mesh counts that are substantially larger than those used in typical applications. In this paper, we focus our efforts on understanding how the grid resolution and topology influences the accuracy and convergence of results by studying the Schubauer and Skramstad flat-plate configuration and the NLF-0416 airfoil at an angle of attack equal to five degrees using FUN3D, a second-order finite-volume code. By focusing on these cases, we can analyze both natural and separation-induced transition scenarios. Multiple grid refinement strategies are investigated. First, we determine the relative effectiveness of zonal streamwise refinement in the transition region within structured grids as an alternative to the costly option of globally uniform refinement of a baseline grid. We also complement this zonal technique by globally varying the wall-normal resolution keeping the streamwise resolution fixed. The zonal streamwise refinement can accurately model natural transition in a flat-plate boundary layer and separation-induced transition, but struggles to accurately model natural transition in airfoil flows. A series of unstructured prismatic grids that have similar node counts and viscous wall spacings as the structured hexahedral grids are also tested, and they do not achieve grid convergence until an extremely fine resolution. Last, we employ adjoint-based unstructured grid adaptation in FUN3D to natural and separation-induced transition on the NLF-0416 airfoil. The adjoint-based refinement process converges to the same solution as the baseline family of structured grids, but leads to smaller errors on coarser grids.

Grid Adaptation↗