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NASA NTRS1992

Overview of the relevant CFD work at Thiokol Corporation

An in-house developed proprietary advanced computational fluid dynamics code called SHARP (Trademark) is a primary tool for many flow simulations and design analyses. The SHARP code is a time dependent, two dimensional (2-D) axisymmetric numerical solution technique for the compressible Navier-Stokes equations. The solution technique in SHARP uses a vectorizable implicit, second order accurate in time and space, finite volume scheme based on an upwind flux-difference splitting of a Roe-type approximated Riemann solver, Van Leer's flux vector splitting, and a fourth order artificial dissipation scheme with a preconditioning to accelerate the flow solution. Turbulence is simulated by an algebraic model, and ultimately the kappa-epsilon model. Some other capabilities of the code are 2-D two-phase Lagrangian particle tracking and cell blockages. Extensive development and testing has been conducted on the 3-D version of the code with flow, combustion, and turbulence interactions. The emphasis here is on the specific applications of SHARP in Solid Rocket Motor design. Information is given in viewgraph form.

Chwalowski, Pawel↗

NASA NTRS1993

Sensitivity calculations for a 2D, inviscid, supersonic forebody problem

The use of a sensitivity equation method to computer derivatives for optimization based design algorithms are discussed. The problem of designing an optimal forebody simulator is used to motivate the algorithm and to illustrate the basic ideas. Finally, how an existing computational fluid dynamics (CFD) code can be modified to compute sensitivities and a numerical example is presented.

Borggaard, Jeff↗

NASA NTRS1999

Performance and Applications of ENSAERO-MPI on Scalable Components

The latest improvements and results generated by ENSAERO-MPI are presented in this paper. ENSAERO-MPI is a parallelized, high-fidelity, multi-block code with fluids, structures and controls capabilities developed at NASA Ames Research Center under the support of HPCC. It is capable of multidisciplinary simulations by simultaneously integrating the Navier-Stokes equations, the finite element structural equations as well as control dynamics equations using aeroelastically adaptive, patched grids. Improvements have been made to the code's robustness, moving grid capabilities and performance.

Farhangnia, Mehrdad↗

NASA NTRS1998

Flow Applications of the Least Squares Finite Element Method

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Jiang, Bo-Nan↗

NASA NTRSDate not supplied

Heated Supersonic Axisymmetric Jet Cases for the NASA Turbulence Modeling Resource

Three new supersonic jet cases were built for the NASA Turbulence Modeling Resource (TMR). These cases were taken from the 6th AIAA Propulsion Aerodynamics Workshop (PAW) nozzle test problem, which utilized data taken at NASA GRC consisting of non-intrusive measurements of jet plume velocities and temperatures, including both mean values and turbulence statistics. The three jet cases all used a Mach 1.63 axisymmetric nozzle: a heated jet for each at on-design conditions, a temperature-matched on-design condition at Mach 1.63, and an off-design heated condition for the Mach 1.63 nozzle. Computational fluid dynamics (CFD) solutions are obtained using three established Reynolds-averaged Navier-Stokes (RANS) codes: Wind-US, FUN3D, and VULCAN-CFD, all using the Menter Shear Stress Transport k- turbulence model with vorticity source term (SST-V). The NASA TMR requires at least two CFD codes yielding essentially identical results to certify that the approaches are verified, meaning that they solve the posed CFD equations as intended. The three codes generally provided very close agreement with each other for jet plume quantities, with the only exception being static temperature. This discrepancy was determined to be the result of whether or not turbulent kinetic energy was considered in the definition of total energy. Validation of the SST-V turbulence model for this case (its level of agreement/disagreement with experimental data) is also addressed.

turbulance↗

NASA NTRS1984

Dynamics of two-phase face seals

An analytic study is presented of the effects of phase change on load support for parallel and tapered face seals. Consideration is given to an adiabatic model for low Reynolds number flow. Numerical integration is carried out of the descriptive fluid equations, giving the opening force due to fluid film pressure. The loci of steady-state solutions are then plotted for water to provide curves of load support as a function of film thickness. For axial excursions of the seal rings, a quasi-steady transient analysis is made. It is found that the load support generated by fluid pressure can be multivalued for a given film thickness. Another finding is that axial disturbances of the seal rings may lead to sudden drops in load support generated by fluid pressure with three possible results. The first is that sufficient damping may permit the seal to return to the previous equilibrium operating position. The second is that the seal may collapse to an equilibrium position of smaller film thickness where face contact is more likely and a significantly higher operating temperature is assured. The third is that a limit cycle of self-sustained oscillation in the axial direction may occur if damping is sufficiently low.

Beeler, R. M.↗

NASA NTRS1979

A computational fluid dynamic technique valid at the centerline for non-axisymmetric problems in cylindrical coordinates

A technique is described for the numerical solution of non-axisymmetric flow problems posed in cylindrical coordinates when the z-axis is included in the flowfield. The highlight of the technique is the manner in which the singularities at the centerline are handled. Specifically, the governing flowfield equations at r = 0 are put in a special form by applying L'Hospital's Rule. The required radial derivatives are evaluated using a one-sided, second-order accurate, first-difference. This leads to a smooth, convergent calculation of the flowfield at the centerline. This appears to be the first generally applicable numerical method for avoiding coordinate system singularities in the context of a finite-difference scheme, and could have application to many nonaxisymmetric flows. The technique is illustrated by specific results for the time-dependent flowfield inside an internal combustion engine.

Griffin, M. D.↗

DOE OSTI2021

nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. Here, in this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.

42 ENGINEERING↗

NASA NTRS1991

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially nonoscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗

NASA NTRS1997

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗

NASA NTRS1997

Adventures with Implicit Methods

In this lecture we trace the historical developments of alternating direction implicit methods. In particular, we emphasize contributions originating in the Computational Fluid Dynamics Branch at Ames Research Center in the 1970's and early 1980's. Joe Steger played a seminal role in demonstrating the practicality of using an efficient, vectorized, implicit code for solving the compressible Navier-Stokes equations. Numerous discussions with Joe had a significant impact on our own research and it is a pleasure to dedicate this lecture to honor his memory.

Warming, Robert F.↗

NASA NTRS2012

Three-Dimensional Magnetohydrodynamic Modeling of the Solar Wind Including Pickup Protons and Turbulence Transport

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfer from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons.We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 deg - .90 deg and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.

Usmanov, Arcadi V.↗

NASA NTRS2016

Coupled CFD-PBE Predictions of Renal Stone Size Distributions in the Nephron in Microgravity

In this paper, a deterministic model is developed to assess the risk of critical renal stone formation for astronauts during space travel. A Population Balance Equation (PBE) model is used to compute the size distribution of a population of nucleating, growing and agglomerating renal calculi as they are transported through different sections of the nephron. The PBE model is coupled to a Computational Fluid Dynamics (CFD) model that solves for steady state flow of urine and transport of renal calculi along with the concentrations of ionic species, calcium and oxalate, in the nephron using an Eulerian two-phase mathematical framework. Parametric simulation are performed to study stone size enhancement and steady state volume fraction distributions in the four main sections of the nephron under weightlessness conditions. Contribution of agglomeration to the stone size distribution and effect of wall friction on the stone volume fraction distributions are carefully examined. Case studies using measured astronaut urinary calcium and oxalate concentrations in microgravity as input indicate that under nominal conditions the largest stone sizes developed in Space will be still considerably below the critical range for problematic stone development. However, results also indicate that the highest stone volume fraction occurs next to the tubule and duct walls. This suggests that there is an increased potential for wall adhesion with the possibility of evolution towards critical stone sizes.

Microgravity↗

NASA NTRS2016

Coupled CFD-PBE Predictions of Renal Stone Size Distributions in the Nephron in Microgravity

Crystal Growth↗

NASA NTRS2018

Convergence Analysis of Turbulent Flow Solutions

Data from the "Turbulence Modeling Resource" website for turbulent flow over an NACA-0012 airfoil is analyzed to determine the convergence behavior of three second-order CFD (Computational Fluid Dynamics) codes: CFL3D (Computational Fluids Lab 3 Dimensional flow solver), FUN3D (Fully Unstructured Navier-stokes flow solver), and TAU (German Aerospace Center (DLR) 2 dimensional code for unstructured hybrid grids solving the Reynolds-Averaged Navier-Stokes equations or the Euler equations). The convergence of both integrated properties and pointwise data are examined. Several different methods for estimating errors and computing convergence rates are compared. A high-order extension to the Richardson extrapolation is developed that improves the accuracy of the mesh limit values and provides a quantitative estimate of the threshold of the asymptotic regime. The coefficient of total drag exhibits second-order convergence for all three codes, and convergence is monotone over a sequence of 7 grids. Other force coefficients are not so well behaved. The convergence rates of the viscous component of drag on the three nest grids ranges from 3:0 for CFL3D to 1:0 for FUN3D. The three codes are converging to similar but not identical solutions. The largest differences between the codes are in the coefficient of lift for which the difference between CFL3D and FUN3D is greater than 10 (sup minus 4). The best agreement occurs in the viscous component of drag, which is the only force component for which all three codes are converging towards each other at a rate of second-order. The agreement between the two unstructured grid codes is good with all properties except lift converging towards common values at a rate of second-order. No one code was universally better than the other. The TAU code has the lowest error in total drag, FUN3D has the lowest error in lift, and CFL3D has the lowest error in the viscous component of drag.

Atkins, Harold L.↗

DOE OSTI2023

Verification methods for drift–diffusion reaction models for plasma simulations

Abstract Compared to other computational physics areas such as codes for general computational fluid dynamics, the documentation of verification methods for plasma fluid codes remains under developed. Current analytical solutions for plasma are often highly limited in terms of testing highly coupled physics, due to the harsh assumptions needed to derive even simple plasma equations. This work highlights these limitations, suggesting the method of manufactured solutions (MMSs) as a potential option for future verification efforts. To demonstrate the flexibility of MMS in verifying these highly coupled systems, the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework was utilized. Thanks to the MOOSE framework’s robustness and modularity, as well as to its physics module capabilities and ecosystem applications (i.e. Zapdos and the chemical reaction network) developed for plasma physics modeling and simulation, this report lays the groundwork for a structured method of conducting plasma fluid code verification.

DeChant, Corey (ORCID:0000000293779732)↗

NASA NTRS1970

The dynamics of oceanic fronts. Part 1: The Gulf Stream

The establishment and maintenance of the mean hydrographic properties of large scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density. The full time dependent diffusion and Navier-Stokes equations for a constant Coriolis parameter are used in this study. Scaling analysis reveals three independent length scales of the problem, namely a radius of deformation or inertial length scale, Lo, a buoyance length scale, ho, and a diffusive length scale, hv. Two basic dimensionless parameters are then formed from these length scales, the thermal (or more precisely, the densimetric) Rossby number, Ro = Lo/ho and the Ekman number, E = hv/ho. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on E alone for problems of oceanic interest. Under this scaling, the solutions are similar for all Ro. It is also shown that 1/Ro is a measure of the frontal slope. The governing equations are solved numerically and the scaling analysis is confirmed. The solution indicates that an equilibrium state is established. The front can then be rendered stationary by a barotropic current from a larger scale along-front pressure gradient. In that quasisteady state, and for small values of E, the main thermocline and the inclined isopycnics forming the front have evolved, together with the along-front jet. Conservation of potential vorticity is also obtained in the light water pool. The surface jet exhibits anticyclonic shear in the light water pool and cyclonic shear across the front.

Kao, T. W.↗

NASA NTRS1982

A basic code for the prediction of transient three-dimensional turbulent flowfields

A primitive pressure-velocity finite difference code has been developed to predict transient three-dimensional turbulent flow. The code is a simplified yet effective prediction procedure for use by persons with little experience in computational fluid dynamics, and into which user-oriented complexities can easily be added. The method is based on the transient two-dimensional Los Alamos SOLA prediction technique for laminar flows. Turbulence is simulated by means of a two-equation turbulence model; species diffusion and buoyancy are also included. Two applications of the code are presented to local destratification near the release structure of a reservoir and to the deflection of a jet entering normally into a uniform cross-flow. Predicted results exhibit good agreement with experimental data, showing that a useful characterization of fully three-dimensional flows is now available.

Busnaina, A. A.↗