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NASA NTRS2022

VULCAN-CFD User Manual: Ver. 7.2.0

VULCAN-CFD offers a comprehensive set of capabilities to enable the simulation of continuum flowfields from subsonic to hypersonic conditions. The governing equations that are employed include allowances for both chemical and thermal nonequilibrium processes, coupled with a wide variety of turbulence models for both Reynolds-averaged and large eddy simulations. The software package can simulate two-dimensional, axisymmetric, or three-dimensional problems on structured multiblock meshes or fully unstructured meshes. A parabolic (i.e., space-marching) treatment can also be used for any subset of a structured mesh that can accommodate this solution strategy. The flow solver provides a significant level of geometric flexibility for structured grid simulations by allowing for arbitrary face-to-face C(0) continuous and non-C(0) continuous block interface connectivities. The unstructured grid paradigm allows for mixed element unstructured meshes that contain any combination of tetrahedral, prismatic, pyramidal, and hexahedral cell elements. The flow solver is also fully parallelized using MPI (Message Passing Interface) libraries in a data-parallel fashion, allowing for efficient simulations on modern High Performance Computing (HPC) systems. This document provides information related to the installation and execution of the VULCAN-CFD software package. A detailed description of the physical and numerical models available in the software are provided in the VULCAN-CFD Theory Manual.

VULCAN-CFD User Manual↗
NASA NTRS1976

A rapid solver for hyperbolic systems of equations

A numerical method is proposed for solving the time-dependent compressible Navier-Stokes equations in two dimensions. The equations are time-split into a hyperbolic part and a parabolic part. This paper describes an explicit numerical method for solving the hyperbolic (inviscid) part. The hyperbolic operator is explicit, conservative, uses characteristic relations to predict convection and pressure fields, and is stable under a specified condition.

Maccormack, R. W.↗
NASA NTRS1992

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Meade, Andrew J., Jr.↗
NASA NTRSDate not supplied

Modeling Boundary-Layer Transition in Subsonic Flow over a Swept Wing

Predicting the onset of boundary-layer transition is often more accurate using physics-based models that directly compute disturbance growth rather than phenomenological models often implemented into industrial CFD codes. The aim of this ongoing study is to calibrate linear, physics-based computations of transition in subsonic flows over swept wings against a large set of experimental data. Advancing the calibration of linear models of transition contributes to the CFD-Vision-2030 goal of automated boundary-layer transition prediction. This progress report uses the dual N-factor method to model transition over the swept NACA 64-2-015A wing. The flow conditions match selected test conditions from an extensive experimental dataset acquired from the NASA Ames 12-ft Pressure Tunnel. The OVERFLOW 2.4b flow solver is used to obtain laminar basic states based on an infinite-span assumption. Stability analyses are performed on 365 distinct configurations with linear stability theory (LST) and parabolized stability equations (PSE) from the Langley Stability and Transition Analysis Codes (LASTRAC), modeling the growth of Tollmien-Schlichting (TS) and stationary crossflow (SCF) disturbances. From a total of 67 data points for unswept, i.e., TS-dominant configurations, the critical N-factor based on PSE is found to be N_TS = 9. The SCF critical N-factor is found to be near 8 for the highly swept, SCF-dominant configurations. Dual N-factor curves for both LST and PSE computations demonstrate a high level of interaction between TS and SCF. It may be worthwhile to investigate an alternate metric to visualize maximal SCF amplification upstream of the transition location to account for the growth of SCF modes near the leading edge, which is not considered in the conventional applications of the dual N-factor criterion.

boundary-layer transition↗
NASA NTRSDate not supplied

Modeling Boundary-Layer Transition in Subsonic Flow over a Swept Wing

Predicting the onset of boundary-layer transition is often more accurate using physics-based models that directly compute disturbance growth rather than phenomenological models often implemented into industrial CFD codes. The aim of this ongoing study is to calibrate linear, physics-based computations of transition in subsonic flows over swept wings against a large set of experimental data. Advancing the calibration of linear models of transition contributes to the CFD-Vision-2030 goal of automated boundary-layer transition prediction. This progress report uses the dual N-factor method to model transition over the swept NACA 64-2-015A wing. The flow conditions match selected test conditions from an extensive experimental dataset acquired from the NASA Ames 12-ft Pressure Tunnel. The OVERFLOW 2.4b flow solver is used to obtain laminar basic states based on an infinite-span assumption. Stability analyses are performed on 365 distinct configurations with linear stability theory (LST) and parabolized stability equations (PSE) from the Langley Stability and Transition Analysis Codes (LASTRAC), modeling the growth of Tollmien-Schlichting (TS) and stationary crossflow (SCF) disturbances. From a total of 67 data points for unswept, i.e., TS-dominant configurations, the critical N-factor based on PSE is found to be N_TS = 9. The SCF critical N-factor is found to be near 8 for the highly swept, SCF-dominant configurations. Dual N-factor curves for both LST and PSE computations demonstrate a high level of interaction between TS and SCF. It may be worthwhile to investigate an alternate metric to visualize maximal SCF amplification upstream of the transition location to account for the growth of SCF modes near the leading edge, which is not considered in the conventional applications of the dual N-factor criterion.

computational modeling↗
NASA NTRS1982

Numerical solution of Space Shuttle Orbiter flow field

The supersonic, viscous laminar flow around the Space Shuttle Orbiter forebody has been computed with a parabolized Navier-Stokes code using a generalized coordinate transformation. The initial solution for the nose part of the Orbiter geometry was obtained with a three-dimensional time-dependent Navier-Stokes solver. It was necessary to employ a wind axis oriented coordinate system to obtain the initial solution with the time-dependent code. The generalized PNS technique used in this study allows the solution to be marched from the given initial data surface to any desired surface downstream. A grid point clustering scheme was employed to accurately describe the body shape by clustering points at the wing tip and at the wing body juncture. The computed heat transfer coefficients, pressure coefficients, and shock shapes are compared with the available experimental data for 0 degrees and 30 degrees angle of attack.

Venkatapathy, E.↗
NASA NTRS1991

Numerical investigations in three-dimensional internal flows

In previous efforts, a two-dimensional full Navier-Stokes (FNS) code (SCRAM2D) was used in a design process that involved parametric modifications of the inlet geometry to arrive at what appeared to be an optimum inlet flowfield that produced a uniform flow at the exit in a very short distance. In these previous studies, the technologies for determining the contours with a 'man-in-the-loop' approach for both the ramp and cowl of the inlet were demonstrated, and nearly shock-free exiting flowfields were shown to be obtainable. The resulting two-dimensional compression contours were then used with swept sidewalls to form a three-dimensional inlet. Then the three-dimensional Navier-Stokes code (SCRAM3D) was used to investigate the inlet's three-dimensional flow. One of the major difficulties encountered in the previous studies was that associated with the relatively long time required to obtain a solution using even the 2D FNS code in the design process. Since one of the goals of high-speed inlet design is to produce inputs to the overall aircraft design in a timely manner, it was proposed for this year's research to examine 2D and 3D viscous flow solver techniques alternative to the NFS codes used to date. Areas of the inlet particularly identified for code speed up are those associated with the forebody and external flow ramp systems of the inlet. In these areas, parabolized, or space-marched, Navier-Stokes codes were proposed to be investigated for their applicability in the design process developed previously. This report describes the results of an investigation into the use of two other codes for analyzing the forebody and inlet ramp systems of high-speed inlets.

Rose, William C.↗
NASA NTRS2011

Assessing Uncertainties in Boundary Layer Transition Predictions for HIFiRE-1 at Non-zero Angles of Attack

Boundary layer stability was analyzed for the HIFiRE-1 flight vehicle geometry for ground tests conducted at the CUBRC LENS I hypersonic shock test facility and the Langley Research Center (LaRC) 20- inch Mach 6 Tunnel. Boundary layer stability results were compared to transition onset location obtained from discrete heat transfer measurements from thin film gauges during the CUBRC test and spatially continuous heat transfer measurements from thermal phosphor paint data during the LaRC test. The focus of this analysis was on conditions at non-zero angles of attack as stability analysis has already been performed at zero degrees angle of attack. Also, the transition onset data obtained during flight testing was at nonzero angles of attack, so this analysis could be expanded in the future to include the results of the flight test data. Stability analysis was performed using the 2D parabolized stability software suite STABL (Stability and Transition Analysis for Hypersonic Boundary Layers) developed at the University of Minnesota and the mean flow solutions were computed using the DPLR finite volume Navier-Stokes computational fluid dynamics (CFD) solver. A center line slice of the 3D mean flow solution was used for the stability analysis to incorporate the angle of attack effects while still taking advantage of the 2D STABL software suite. The N-factors at transition onset and the value of Re(sub theta)/M(sub e), commonly used to predict boundary layer transition onset, were compared for all conditions analyzed. Ground test data was analyzed at Mach 7.2 and Mach 6.0 and angles of attack of 1deg, 3deg and 5deg. At these conditions, the flow was found to be second mode dominant for the HIFiRE-1 slender cone geometry. On the leeward side of the vehicle, a strong trend of transition onset location with angle of attack was observed as the boundary layer on the leeward side of the vehicle developed inflection points at streamwise positions on the vehicle that correlated to angle of attack. Inflection points are a strong instability mechanism that lead to rapid breakdown and transition to turbulence. The transition onset location on the windward side of the vehicle displayed no trend with angle of attack or freestream Reynolds number and transition was observed farther down the vehicle than observed on the leeward side of the vehicle. In analysis of both windward and leeward sides of the vehicle, use of the N factor methodology to develop trends to predict boundary layer transition onset showed improvements over the Re(sub theta)/M(sub e) empirical correlation methodology. Stronger correlations and less scatter in the data were observed when using the N factor method for these cases.

Marek, Lindsay C.↗
NASA NTRS1993

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Day, Brad A.↗
NASA NTRS1991

Parabolized Navier-Stokes methods for hypersonic flows

A representative sampling of the techniques used in the integration of the Parabolized Navier-Stokes (PNS) equations is presented. Special atention is given to recent algorithms developed specifically for application to high speed flows, characterized by the presence of strong embedded shock waves and real gas effects. It is shown that PNS solvers are being used in the analysis of sonic boom signatures. Methods for modeling physical effects are discussed, including an overview of commonly used turbulence models and a more detailed discussion of techniques for including equilibrium and finite rate real gas effects.

Lawrence, Scott L.↗
NASA NTRS1986

An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable

The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.

Demkowicz, L.↗
NASA NTRS2006

RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.

Mizuno, Yosuke↗
NASA NTRS2013

Summary of the 2008 NASA Fundamental Aeronautics Program Sonic Boom Prediction Workshop

The Supersonics Project of the NASA Fundamental Aeronautics Program organized an internal sonic boom workshop to evaluate near- and mid-field sonic boom prediction capability at the Fundamental Aeronautics Annual Meeting in Atlanta, Georgia on October 8, 2008. Workshop participants computed sonic boom signatures for three non-lifting bodies and two lifting configurations. A cone-cylinder, parabolic, and quartic bodies of revolution comprised the non-lifting cases. The lifting configurations were a simple 69-degree delta wing body and a complete low-boom transport configuration designed during the High Speed Research Project in the 1990s with wing, body, tail, nacelle, and boundary layer diverter components. The AIRPLANE, Cart3D, FUN3D, and USM3D ow solvers were employed with the ANET signature propagation tool, output-based adaptation, and a priori adaptation based on freestream Mach number and angle of attack. Results were presented orally at the workshop. This article documents the workshop, results, and provides context on previously available and recently developed methods.

Park, Michael A.↗
NASA NTRS1994

Optimized design of a hypersonic nozzle

Conventional procedures for designing nozzles involve the design of an inviscid contour (using the method of characteristics) that is corrected with a displacement thickness calculated from boundary-layer theory. However, nozzles designed using this classical procedure have been shown to exhibit poor flow quality at Mach numbers characteristic of hypersonic applications. The nozzle to be designed will be a part of the NASA HYPULSE facility which is being used for hypervelocity flight research. Thus, the flow quality of the nozzle is a critical question that needs to be addressed. Design of nozzles for hypersonic applications requires a proper assessment of the effects of the thick boundary layer on the inviscid flowfield. Since the flow field is largely supersonic, the parabolized form of the Navier-Stokes (PNS) equations can be used. The requirement of a uniform flow at the exit plane of the nozzle can be used to define an objective function as part of an optimization procedure. The design procedure used in this study involves the coupling of a nonlinear (least-squares) optimization algorithm with an efficient, explicit PNS solver. The thick boundary layers growing on the walls of the nozzle limit the extent of the usable core region (region with uniform flow) for testing models (especially rectangular). In order to maximize the region of uniform flow, it was decided to have the exit plane of this nozzle to be (nearly) rectangular. Thus, an additional constraint on the nozzle shape resulted, namely the nozzle will have a shape transitioning from a circular one at the inlet to that of a rectangle at the exit. In order to provide for a smooth shape transition, the cross sectional contour of the nozzle is defined by a superellipse. The nozzle is taken to be a meter in length. The axial variations of the major and minor radii of the superellipse are governed by cubic splines. The design parameters are the coefficients of the splines associated with the local nozzle wall slopes. Extensive calculations have been made (with a three-dimensional Euler code) to understand the effects of various parameters such as location of the knot points of the spline function, different ways of characterizing the uniformity of the flow in the exit plane, as well as the effect of constraining the area of the nozzle to be invariant. Turbulent flow (measurements indicate that the flow at the nozzle inlet is turbulent) calculations are now being performed (with the inviscidly designed nozzle contours) to assess the flow quality.

Krishnamurthy, Ramesh↗
NASA NTRS1993

Flux-difference split parabolized Navier-Stokes algorithm for non-equilibrium chemically reacting flows

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rather than the steady Riemann problem, is solved. The algorithm allows either a second or an approximately third-order accurate upwind treatment of the convection terms by employing the unsteady approximate Riemann solver of Roe. The source terms of the species transport equations are treated in either an explicit or implicit manner, and the species diffusion terms are modeled with either a Fickian or a multicomponent model. A validation of the algorithm is performed by comparing computational results with the 2-D Mach 14, 15 degree compression-corner data of Holden. The three-dimensional capability of the algorithm is demonstrated by computing Mach 2.7 flow over a swept wedge scramjet fuel injector, and three-dimensional reacting flow capability is demonstrated by a computing a shock-jet interaction concept for mixing and combustion enhancement.

White, J. A.↗
NASA NTRS1994

Numerical simulation of receptivity and transition in a boundary layer on a flat plate with a suction hole

A Navier-Stokes solver has been modified to allow for unsteady boundary conditions to be imposed at the inflow boundary. Because the streamwise derivatives are discretized with three-point compact differences, there is no need for special treatment of the points adjacent to the inflow boundary, provided that all necessary derivatives are properly specified at the boundary points. The unsteady boundary conditions can be obtained from a previous computation, from a solution of the parabolized stability equations (PSE), or from an analytical exact or approximate solution of the Navier-Stokes equations, e.g. an asymptotic expansion solution to model a sound wave interacting with the boundary layer.

Fasel, Hermann F.↗
NASA NTRS1986

The calculation of supersonic viscous flows using the parabolized Navier-Stokes equations

Solution of the parabolic Navier-Stokes (PNS) equations for supersonic flows is discussed, and compatibility of the PNS method with the triple-deck theory of Stewartson (1974) is demonstrated. Characteristic and stability analyses show that use of an appropriate filter on the pressure term in the x-momentum equation can suppress the departure solutions, giving the usual desired weak interaction solution. An Alternating Direction Explicit procedure, with minimal computer storage requirements compared to the full Navier-Stokes solvers, is proposed to calculate strongly interacting flows using a global iteration procedure for the PNS equations. The PNS equations are used to solve the hypersonic viscous interaction problem, and good agreement is found with experimental results.

Davis, R. T.↗
NASA NTRS1990

A three-dimensional upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional flow of chemically reacting air around hypersonic vehicles. The code is a modification of the perfect gas, three-dimensional UPS code of Lawrence et al. (1986) which has been extended in the present study to permit the calculation of hypersonic, viscous flows in chemical nonequilibrium. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for real gas effects. The present code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. Results are presented for the hypersonic laminar flow over a cone at 0- and 10-deg angles of attack and for a generic hypersonic vehicle. Calculations are performed assuming either perfect gas, equilibrium air, or finite-rate chemistry.

Buelow, Philip E.↗