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NASA NTRS2011

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗

NASA NTRS2010

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗

NASA NTRS2013

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.↗

NASA NTRSDate not supplied

Beyond Guesswork: Code Verification for Acoustic Duct Mode Prediction

The code used in the work (Swirl) is a frequency-domain linearized Euler equation solver that is designed to predict the effect of acoustic liners on acoustic modes propagating in realistic sheared and swirling mean flows, guiding the design of more efficient liner configurations. The purpose of this study is to validate Swirl using the Method Of Manufactured Solutions (MMS). This study also investigated the effect of the integration and spatial differencing methods on the convergence for a given Manufactured Solution. In addition, the effect of boundary condition implementation was tested. Through rigorous validation of the Swirl code using the MMS, this research underscores the significance of integration and spatial differencing methods on convergence, evaluates boundary condition implementations, and systematically assesses the impact of various filters.

Code Verification↗

NASA NTRS2006

Verification of Software: The Textbook and Real Problems

The process of verification, or determining the order of accuracy of computational codes, can be problematic when working with large, legacy computational methods that have been used extensively in industry or government. Verification does not ensure that the computer program is producing a physically correct solution, it ensures merely that the observed order of accuracy of solutions are the same as the theoretical order of accuracy. The Method of Manufactured Solutions (MMS) is one of several ways for determining the order of accuracy. MMS is used to verify a series of computer codes progressing in sophistication from "textbook" to "real life" applications. The degree of numerical precision in the computations considerably influenced the range of mesh density to achieve the theoretical order of accuracy even for 1-D problems. The choice of manufactured solutions and mesh form shifted the observed order in specific areas but not in general. Solution residual (iterative) convergence was not always achieved for 2-D Euler manufactured solutions. L(sub 2,norm) convergence differed variable to variable therefore an observed order of accuracy could not be determined conclusively in all cases, the cause of which is currently under investigation.

Carlson, Jan-Renee↗

NASA NTRS2013

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↗

NASA NTRS2017

Stabilized Finite Elements in FUN3D

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Anderson, W. Kyle↗

NASA NTRSDate not supplied

Economical Third-Order Methods for Accurate Surface Heating Predictions on Simplex Element Meshes

A node-centered edge-based finite volume discretization of the compressible Navier-Stokes equations is presented with the heat flux reformulated as a first order system. A dissipation vector is derived for the reformulated system, such that the heat flux can be upgraded to O(h^3) on simplex element meshes in the same fashion as the inviscid fluxes. The method of manufactured solutions is used to demonstrate this uniform order property in heat flux. This new system is shown to efficiently produce accurate surface heating predictions on hypersonic hemisphere flow using an anisotropic simplex element mesh, achieving O(h^3) accuracy at relatively low computational cost compared to similar methods.

Computational Fluid Dynamics↗

NASA NTRS2008

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.↗

NASA NTRS2014

Turbulence Modeling Verification and Validation

Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important steps in the process. Verification insures that the CFD code is solving the equations as intended (no errors in the implementation). This is typically done either through the method of manufactured solutions (MMS) or through careful step-by-step comparisons with other verified codes. After the verification step is concluded, validation is performed to document the ability of the turbulence model to represent different types of flow physics. Validation can involve a large number of test case comparisons with experiments, theory, or DNS. Organized workshops have proved to be valuable resources for the turbulence modeling community in its pursuit of turbulence modeling verification and validation. Workshop contributors using different CFD codes run the same cases, often according to strict guidelines, and compare results. Through these comparisons, it is often possible to (1) identify codes that have likely implementation errors, and (2) gain insight into the capabilities and shortcomings of different turbulence models to predict the flow physics associated with particular types of flows. These are valuable lessons because they help bring consistency to CFD codes by encouraging the correction of faulty programming and facilitating the adoption of better models. They also sometimes point to specific areas needed for improvement in the models. In this paper, several recent workshops are summarized primarily from the point of view of turbulence modeling verification and validation. Furthermore, the NASA Langley Turbulence Modeling Resource website is described. The purpose of this site is to provide a central location where RANS turbulence models are documented, and test cases, grids, and data are provided. The goal of this paper is to provide an abbreviated survey of turbulence modeling verification and validation efforts, summarize some of the outcomes, and give some ideas for future endeavors in this area.

Rumsey, Christopher L.↗

NASA NTRS2015

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↗

NASA NTRS2015

Verification of a Viscous Computational Aeroacoustics Code using External Verification Analysis

Computational↗

NASA NTRS1984

Solidification interface shape for continuous casting in an offset mold - Two analytical methods

A solution method for finding the unknown solidification interface in manufacturing slab ingots as a continuous casting is presented, which involves a product solution in the potential plane and the use of conjugate harmonic functions. It is argued that the method may be more direct for some geometries than the Cauchy boundary value method. Moreover, the usefulness of the Cauchy boundary value method is demonstrated through the example of a nonsymmetric horizontal mold where the walls are offset to support the lower ingot boundary.

Siegel, R.↗

NASA NTRS1982

Inexpensive Antireflection Coating for Solar Cells

Continuous method for applying antireflection coating to solar cells increases efficiency of devices by preventing energy from being reflected away, but adds little to manufacturing cost. Method consists of spraying solution on cells or glass collector plates, drying sprayed layer, and curing it. Solution is formulated to spread evenly over surfaces.

Tracy, C. E.↗

NASA NTRS1972

Polymeric compositions and their method of manufacture

Filled polymer compositions are made by dissolving the polymer binder in a suitable sublimable solvent, mixing the filler material with the polymer and its solvent, freezing the resultant mixture, and subliming the frozen solvent from the mixture from which it is then removed. The remaining composition is suitable for conventional processing such as compression molding or extruding. A particular feature of the method of manufacture is pouring the mixed solution slowly in a continuous stream into a cryogenic bath wherein frozen particles of the mixture result. The frozen individual particles are then subjected to the sublimation.

Moser, B. G.↗

NASA NTRSDate not supplied

Verification of Viscous Goal-Based Anisotropic Mesh Adaptation

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics. A key ingredient for the broader acceptance of unstructured mesh adaptation is the verification of these implementations. Anisotropic metric construction methods are evaluated with analytically defined primal fields and the corresponding entropy variables as adjoint fields. This allows the comparison of different metric formulations and different implementations of the same formulation without the complications of a flow and adjoint solution method. The convergence of the output associated with the entropy variable adjoint is studied for mesh adaptation to these fields and a manufactured solution. Mesh adapted drag output is studied for two simple wings in compressible laminar flow to show fine-mesh convergence of multiple metric construction methods to less than a single drag count. The documentation of these verification exercises helps to prepare these goal-based methods for routine use in more complex simulations for production workflows.

mesh adaptation↗

NASA NTRS1986

Silicon carbide sintered products and a method for their manufacturing

SiC based sinters are produced by pressureless sintering from a SiC-AlN solid solution containing Al2 to 20, N 0.2 to 10, O 0.2 to 5, a Group IIIB element 0 to 15 percent, the remainder being Si and C. Thus, a 90:10 mixture of SiC and AlN powders were cold pressed at 2000 kg/sq cm and sintered for 5 hours at 2100 C in a nitrogen atmosphere. The resulting product had density of 3.11 g/cu cm and bending strength at ambient and 1400 C at 68.5 and 66.3 kg/sq mm.

Suzuki, K.↗

NASA NTRS2015

Puncture-Healing Thermoplastic Resin Carbon-Fiber-Reinforced Composites

A composite comprising a combination of a self-healing polymer matrix and a carbon fiber reinforcement is described. In one embodiment, the matrix is a polybutadiene graft copolymer matrix, such as polybutadiene graft copolymer comprising poly(butadiene)-graft-poly(methyl acrylate-co-acrylonitrile). A method of fabricating the composite is also described, comprising the steps of manufacturing a pre-impregnated unidirectional carbon fiber preform by wetting a plurality of carbon fibers with a solution, the solution comprising a self-healing polymer and a solvent, and curing the preform. A method of repairing a structure made from the composite of the invention is described. A novel prepreg material used to manufacture the composite of the invention is described.

Gordon, Keith L.↗