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NASA NTRS2015

Grid Convergence for Turbulent Flows(Invited)

A detailed grid convergence study has been conducted to establish accurate reference solutions corresponding to the one-equation linear eddy-viscosity Spalart-Allmaras turbulence model for two dimensional turbulent flows around the NACA 0012 airfoil and a flat plate. The study involved three widely used codes, CFL3D (NASA), FUN3D (NASA), and TAU (DLR), and families of uniformly refined structured grids that differ in the grid density patterns. Solutions computed by different codes on different grid families appear to converge to the same continuous limit, but exhibit different convergence characteristics. The grid resolution in the vicinity of geometric singularities, such as a sharp trailing edge, is found to be the major factor affecting accuracy and convergence of discrete solutions, more prominent than differences in discretization schemes and/or grid elements. The results reported for these relatively simple turbulent flows demonstrate that CFL3D, FUN3D, and TAU solutions are very accurate on the finest grids used in the study, but even those grids are not sufficient to conclusively establish an asymptotic convergence order.

Diskin, Boris↗

NASA NTRS1985

A comparison of Euler and Navier-Stokes solutions for supersonic flow over a conical delta wing

The flow around a thin elliptic cone at Mach number 2 and angle of attack 10 deg is simulated numerically, comparing the results obtained using a fine grid and the Navier-Stokes (NS) equations with those obtained using both coarse and fine grids and the Euler (E) equations. On the coarse grid, the E results are found to reproduce roughly the NS predictions of leading-edge separation and primary and secondary vortices on the leeward surface, but the E solution on the fine NS grid (showing no separation and a crossflow-shock-induced vorticity) reveals this agreement to be spurious. The fine-grid E prediction is shown to be a valid solution of the E equations, indicating their unsuitability as approximators of viscous flow. The imposition of a Kutta condition on the E computation is found to be ineffective in correcting this discrepancy.

Newsome, R. W.↗

NASA NTRS1998

Integrated Thermal Insulation System for Spacecraft

An integrated thermal protection system (TPS) for a spacecraft includes a grid that is bonded to skin of the spacecraft, e.g., to support the structural loads of the spacecraft. A plurality of thermally insulative, relatively large panels are positioned on the grid to cover the skin of the spacecraft to which the grid has been bonded. Each panel includes a rounded front edge and a front flange depending downwardly from the front edge. Also, each panel includes a rear edge formed with a rounded socket for receiving the rounded front edge of another panel therein, and a respective rear flange depends downwardly from each rear edge. Pins are formed on the front flanges, and pin receptacles are formed on the rear flanges, such that the pins of a panel mechanically interlock with the receptacles of the immediately forward panel. To reduce the transfer to the skin of heat which happens to leak through the panels to the grid, the grid includes stringers that are chair-shaped in cross-section.

Kolodziej, Paul↗

NASA NTRS2004

Simulation of Flow Through Breach in Leading Edge at Mach 24

A baseline solution for CFD Point 1 (Mach 24) in the STS-107 accident investigation was modified to include effects of holes through the leading edge into a vented cavity. The simulations were generated relatively quickly and early in the investigation by making simplifications to the leading edge cavity geometry. These simplifications in the breach simulations enabled: 1) A very quick grid generation procedure; 2) High fidelity corroboration of jet physics with internal surface impingements ensuing from a breach through the leading edge, fully coupled to the external shock layer flow at flight conditions. These simulations provided early evidence that the flow through a 2 inch diameter (or larger) breach enters the cavity with significant retention of external flow directionality. A normal jet directed into the cavity was not an appropriate model for these conditions at CFD Point 1 (Mach 24). The breach diameters were of the same order or larger than the local, external boundary-layer thickness. High impingement heating and pressures on the downstream lip of the breach were computed. It is likely that hole shape would evolve as a slot cut in the direction of the external streamlines. In the case of the 6 inch diameter breach the boundary layer is fully ingested.

Gnoffo, Peter A.↗

NASA NTRSDate not supplied

Scale resolving simulations of the NASA Juncture Flow Model using the LAVA solver

Two distinct simulation methodologies: Delayed Detached Eddy Simulation (DDES) and stress based Wall-modelled Large Eddy Simulation (WMLES) are evaluated using structured overset curvilinear grids for the NASA juncture flow model. While both methodologies are shown to mitigate the primary shortcomings of steady state Reynolds Averaged Navier Stokes(RANS) simulations, several unresolved aspects are identified. Strong sensitivity to RANS-typegrid refinement is observed in the DDES with a substantial deterioration of the solution quality with increasing spatial resolution associated with deficiencies in the shielding function. Mean profiles for attached boundary layers on the fuselage show spurious inflections suggesting modelled stress depletion on finer grids. Lower numerical dissipation in terms of spatial discretization and time step size is seen to improve the solution quality, and the advantage of using RC and QCR2000 corrections in the underlying RANS closure is demonstrated for DDES on RANS-type meshes. Equilibrium Wall-Modelled LES used grids that resolved the tripping dots over the fuselage nose and the wing leading edge, consistent with the experiment setup. These simulations resulted in a cost-competitive approach compared to DDES on RANS-type grids. Although the agreement between WMLES predictions of first and second order single point statistics with experimental measurements is promising, a fundamental shortcoming is noted in terms of an overshoot in streamwise momentum in corner regions of the wing-fuselage juncture. This excess momentum subsequently delays the onset of separation,thereby resulting in an underprediction in length of the separation bubble. Some quantitative sensitivity to numerical discretization is observed; lowering of numerical dissipation shows better agreement with the experiment.

T^3↗

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.↗

DOE OSTI2024

Modular Staged Pressurized Oxy-Combustion (SPOC) Power Plant for Coal and Biomass – Integration of Combustor Boiler and DCC

Utilities and grid operators worldwide are under significant pressure to incorporate intermittent renewable sources while strategizing on how to maintain the necessary stability and reliability of the grid. The development of a power plant which will be capable of flexible operation to meet the needs of the grid as more intermittent sources like wind and solar energy are incorporated is key to maintain the reliability of the grid. Through the use of innovative and cutting-edge technologies that improve efficiency and reduce carbon emissions, and being small compared to today's conventional utility-scale power plants, the modular Staged, Pressurized Oxy-Combustion (SPOC) process envisioned by and under development at Washington University in St. Louis (WUSTL) has the potential to achieve these goals. Specifically, the process offers: 1) a modular plant design that allows for better operational flexibility; 2) the utilization of fuel-staging and pressurized oxy-combustion, resulting in smaller plant size, improved plant efficiency, and reduced costs for pollutant and CO2 removal compared to traditional power plants with post-combustion capture technology; and 3) the use of small modular boilers and pollutant removal units that can be constructed off-site leading to reduced capital costs for the plant. WUSTL is advancing the development of the critical components for the SPOC power plant, including the integrated combustor-boiler system and the direct contact cooler. To demonstrate the boiler convective section and to obtain critical data for commercial-scale pressurized boiler design, a simulated convective heat transfer boiler test section was designed and integrated with the combustor (radiant section). A direct contact cooler (DCC) was integrated with the combustor-boiler to demonstrate the dynamic operation of the integrated system and the performance of the DCC, including the efficiency for simultaneous removal of NOx and SOx. This talk will present an update on the evaluation of the critical components for system integration, including heat transfer data from the simulated boiler, scrubbing efficiency for the DCC under different operating conditions, and CFD modeling and validation for burner and boiler development.

Magalhaes, Duarte↗

NASA NTRS1985

Computations of unsteady transonic flows

During the last eight years, the subject of computational unsteady transonic aerodynamics has undergone a period of rapid growth. A brief survey of some of the fundamental advances during this period is provided, and some of the research done at NASA Ames Research Center is described in detail. The small-distance potential equation is considered, taking into account features of the unsteady transonic flow, the governing equation, the pressure coefficient, the wake condition, the airfoil tangency condition, the downstream boundary condition, the alternating direction implicit (ADI) algorithm, a grid system, boundary conditions, an airfoil with oscillating trailing edge flap, three types of shock-wave motion, and an example of a simple aeroelastic problem. A description is given of an implicit algorithm for the unsteady full potential equation in conservation form.

Goorjian, P. M.↗

NASA NTRS1985

Calculations of two and three-dimensional transonic cascade flow fields using the Navier-Stokes equations

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and non-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive 'O'-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (about 80-150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.

Weinberg, B. C.↗

NASA NTRS1989

Upwind Navier-Stokes solutions for leading-edge vortex flows

An incompressible Navier-Stokes solver using an upwind finite-difference algorithm is employed to investigate low-speed, three-dimensional, laminar, leading-edge vortex flows over three round-edged low-aspect-ratio wings. The effects of grid density, Reynolds number, and wing planform on the flowfield structures and integral values are studied. Computed results show good qualitative and quantitative agreement with the available experimental data.

Hsu, C.-H.↗

NASA NTRS1990

Simulation of leading-edge vortex flows

An implicit upwind-relaxation finite-difference algorithm solving the incompressible Navier-Stokes equations is employed to simulate low-speed, three-dimensional, laminar, leading-edge vortex flows over three round-edged low-aspect-ratio wings. The effects of grid density, angle of attack, Reynolds number, and wing planform on the flowfield structures and integral values are studied. Computed results are presented and compared with experimental data.

Hsu, C.-H.↗

NASA NTRS1989

A comparative study of Navier-Stokes codes for high-speed flows

A comparative study was made with four different codes for solving the compressible Navier-Stokes equations using three different test problems. The first of these cases was hypersonic flow through the P8 inlet, which represents inlet configurations typical of a hypersonic airbreathing vehicle. The free-stream Mach number in this case was 7.4. This 2-D inlet was designed to provide an internal compression ratio of 8. Initial calculations were made using two state-of-the-art finite-volume upwind codes, CFL3D and USA-PG2, as well as NASCRIN, a code which uses the unsplit finite-difference technique of MacCormack. All of these codes used the same algebraic eddy-viscosity turbulence model. In the experiment, the cowl lip was slightly blunted; however, for the computations, a sharp cowl leading edge was used to simplify the construction of the grid. The second test problem was the supersonic (Mach 3.0) flow in a three-dimensional corner formed by the intersection of two wedges with equal wedge angles of 9.48 degrees. The flow in such a corner is representative of the flow in the corners of a scramjet inlet. Calculations were made for both laminar and turbulent flow and compared with experimental data. The three-dimensional versions of the three codes used for the inlet study (CFL3D, USA-PG3, and SCRAMIN, respectively) were used for this case. For the laminar corner flow, a fourth code, LAURA, which also uses recently-developed upwind technology, was also utilized. The final test case is the two-dimensional hypersonic flow over a compression ramp. The flow is laminar with a free-stream Mach number of 14.1. In the experiment, the ramp angle was varied to change the strength of the ramp shock and the extent of the viscous-inviscid interaction. Calculations were made for the 24-degree ramp configuration which produces a large separated-flow region that extends upstream of the corner.

Rudy, David H.↗

NASA NTRS1992

Singularity classification as a design tool for multiblock grids

A major stumbling block in interactive design of 3-D multiblock grids is the difficulty of visualizing the design as a whole. One way to make this visualization task easier is to focus, at least in early design stages, on an aspect of the grid which is inherently easy to present graphically, and to conceptualize mentally, namely the nature and location of singularities in the grid. The topological behavior of a multiblock grid design is determined by what happens at its edges and vertices. Only a few of these are in any way exceptional. The exceptional behaviors lie along a singularity graph, which is a 1-D construct embedded in 3-D space. The varieties of singular behavior are limited enough to make useful symbology on a graphics device possible. Furthermore, some forms of block design manipulation that appear appropriate to the early conceptual-modeling phase can be accomplished on this level of abstraction. An overview of a proposed singularity classification scheme and selected examples of corresponding manipulation techniques is presented.

Jones, Alan K.↗

NASA NTRS2003

Failure of Anisotropic Unstructured Mesh Adaption Based on Multidimensional Residual Minimization

An automated anisotropic unstructured mesh adaptation strategy is proposed, implemented, and assessed for the discretization of viscous flows. The adaption criteria is based upon the minimization of the residual fluctuations of a multidimensional upwind viscous flow solver. For scalar advection, this adaption strategy has been shown to use fewer grid points than gradient based adaption, naturally aligning mesh edges with discontinuities and characteristic lines. The adaption utilizes a compact stencil and is local in scope, with four fundamental operations: point insertion, point deletion, edge swapping, and nodal displacement. Evaluation of the solution-adaptive strategy is performed for a two-dimensional blunt body laminar wind tunnel case at Mach 10. The results demonstrate that the strategy suffers from a lack of robustness, particularly with regard to alignment of the bow shock in the vicinity of the stagnation streamline. In general, constraining the adaption to such a degree as to maintain robustness results in negligible improvement to the solution. Because the present method fails to consistently or significantly improve the flow solution, it is rejected in favor of simple uniform mesh refinement.

Wood, William A.↗

NASA NTRSDate not supplied

Evaluation of a Laser-Dot Grid-Projection System for Lunar Lander Crater-Shape and Ejecta-Sheet Measurements

Development, testing, and evaluation of an active-illumination laser-dot grid-projection system was performed to evaluate its potential inclusion on an upcoming uncrewed lunar lander mission to the south pole region of the moon. Active illumination may be required for this mission due to the shallow angle of the sun at the landing location, which may cast shadows in the landing region, hindering the stereo camera imaging system’s ability to determine the pre-and post-landing lunar surface/crater shape. Testing includes characterization of the diffractive optical elements used for the grid projection, single-camera tests to determine the imaged laser dot intensity as a function of camera exposure and imaging angle relative to the laser grid projection, laser dot brightness/saturation impact on depth map calculations, angle of imaged laser grid impact on depth map calculations for steep crater edges, impact of density gradients on the depth map calculations, and the feasibility of making measurements of the ejecta sheet.

Joshua M. Weisberger↗

NASA NTRS2001

A Study of Grid Resolution, Transition and Turbulence Model Using the Transonic Simple Straked Delta Wing

Three-dimensional transonic flow over a delta wing is investigated using several turbulence models. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition aft of the leading edge or are fully turbulent are performed. These computations show that grid resolution, transition location and turbulence model significantly affect the 3D flowfield.

Bartels, Robert E.↗

DOE OSTI2025

Graph-Based Attention Mechanisms for Solving the AC Optimal Power Flow Problem in Electrical Power Networks

With the increasing complexity and data availability in modern power systems, learning-based approaches to AC Optimal Power Flow (AC OPF) have garnered significant attention. In particular, the structure of smart grids lends itself naturally to graph-based representations, where Graph Neural Networks (GNNs) can capture spatial and relational dependencies. This paper investigates attention-based GNN architectures tailored to heterogeneous graph representations of electric grids. We evaluate two major paradigms: relational attention, which distinguishes between edge types during message passing, and meta-path attention, which captures high-level semantics through multi-hop, typed paths. Using a large corpus of public AC OPF scenarios, we benchmark representative models of each type of attention. Our results demonstrate the benefits of heterogeneous attention-based models in accurately capturing grid dynamics; heterogeneous attention models achieve superior performance in both standard and perturbed settings. The findings highlight the importance of semantic-aware architectures for improving prediction robustness and interpretability in power system applications.

Trigui, Ali [Qubit Engineering Inc.]↗