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DOE OSTI2022

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2012

Prediction of Broadband Shock-Associated Noise Including Propagation Effects Originating NASA

An acoustic analogy is developed based on the Euler equations for broadband shock-associated noise (BBSAN) that directly incorporates the vector Green s function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) to describe the mean flow. The vector Green s function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation rate. An adjoint vector Green s function solver is implemented to determine the vector Green s function based on a locally parallel mean flow at different streamwise locations. The newly developed acoustic analogy can be simplified to one that uses the Green s function associated with the Helmholtz equation, which is consistent with a previous formulation by the authors. A large number of predictions are generated using three different nozzles over a wide range of fully-expanded jet Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise experimental facilities. In addition, two models for the so-called fine-scale mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include propagation effects.

Miller, Steven↗

NASA NTRS1992

Single expansion ramp nozzle simulations

The single-expansion-ramp-nozzle (SERN) experiment underway at NASA Ames Research Center simulates the National Aerospace Plane propulsive jet-plume flow. Recently, limited experimental data has become available from an experiment with a generic nozzle/afterbody model in a hypersonic wind tunnel. The present paper presents full three-dimensional solutions obtained with the implicit Navier-Stokes solver, FL3D, for the baseline model and a version of the model with side extensions. Analysis of the computed flow clearly shows the complex 3-D nature of the flow, critical flow features, and the effect of side extensions on the plume flow development. Flow schematics appropriate for the conditions tested are presented for the baseline model and the model with side extensions. The computed results show excellent agreement with experimental shadowgraph and with surface pressure measurements. The computed and experimental surface oil-flows show the same features but may be improved by appropriate turbulence modeling.

Ruffin, Stephen M.↗

NASA NTRS1988

Calculation of the recirculating compressible flow downstream a sudden axisymmetric expansion

Significant progress has been made during the last five years to adapt conventional Navier-Stokes solver for handling nonconservative equations. A primary type of application is to use transport equation turbulence models, but the extension is also possible for describing the transport of nonpassive scalars, such as in reactive media. Among others, combustion and gas dissociation phenomena are topics needing a considerable research effort. An implicit two step scheme based on the well-known MacCormack scheme has been modified to treat compressible turbulent flows on complex geometries. Implicit treatment of nonconservative equations (in the present case a two-equation turbulence model) opens the way to the coupled solution of thermochemical transport equations.

Vandromme, D.↗

NASA NTRS1988

Aerodynamic applications of an efficient incompressible Navier-Stokes solver

A robust and accurate upwind scheme based on flux-difference splitting for three-dimensional, incompressible flows in general coordinates is described. Viscous effects are included through a thin-layer approximation to the Navier-Stokes equations. Turbulent flows are simulated with extensions to the Baldwin-Lomax (1978) turbulence model. The effects of accuracy and gridding on the computed flow field results are assessed. The results obtained from the code for vortical flows over a delta wing, a double delta wing, and a tangent-ogive forebody compare well with experimental data.

Hartwich, Peter M.↗

DOE OSTI2024

A High-Performance Discrete-Element Framework for Simulating Flow and Jamming of Moisture Bearing Biomass Feedstocks

We developed and verified a high-performance open-source discrete element method (DEM) solver with simultaneously-supported feedstock-specific interaction models, including bonded-sphere, liquid bridge, cohesion, and non-linear contact models. Our solver uses parallel data structures on hybrid central and graphics processing unit (CPU/GPU) architectures, with favorable strong scaling performance observed for large problem sizes comprised of (100 M particles), and 4X single-node GPU speedup. The particles for corn stover feedstock were conceptualized and calibrated based on experimental measurements and results. Sensitivity analyses demonstrate that the mass flow rate from a wedge hopper is governed primarily by moisture content, friction coefficient, and cohesion energy density. The model is used to reproduce experimentally observed hopper jamming results, highlighting that the experimental no-flow trends can only be achieved by using non-spherical particles, liquid bridge and cohesion models, highlighting the importance of using concurrent feedstock specialized models for the effective representation of biomass material handling problems.

bioenergy↗

NASA NTRS2012

Computational Optimization of a Natural Laminar Flow Experimental Wing Glove

Computational optimization of a natural laminar flow experimental wing glove that is mounted on a business jet is presented and discussed. The process of designing a laminar flow wing glove starts with creating a two-dimensional optimized airfoil and then lofting it into a three-dimensional wing glove section. The airfoil design process does not consider the three dimensional flow effects such as cross flow due wing sweep as well as engine and body interference. Therefore, once an initial glove geometry is created from the airfoil, the three dimensional wing glove has to be optimized to ensure that the desired extent of laminar flow is maintained over the entire glove. TRANAIR, a non-linear full potential solver with a coupled boundary layer code was used as the main tool in the design and optimization process of the three-dimensional glove shape. The optimization process uses the Class-Shape-Transformation method to perturb the geometry with geometric constraints that allow for a 2-in clearance from the main wing. The three-dimensional glove shape was optimized with the objective of having a spanwise uniform pressure distribution that matches the optimized two-dimensional pressure distribution as closely as possible. Results show that with the appropriate inputs, the optimizer is able to match the two dimensional pressure distributions practically across the entire span of the wing glove. This allows for the experiment to have a much higher probability of having a large extent of natural laminar flow in flight.

Hartshom, Fletcher↗

NASA NTRSDate not supplied

Multi-point Jig Twist Optimization of Mach 0.745 Transonic Truss-Braced Wing Aircraft and High-Fidelity CFD Validation

This paper presents a multi-point jig twist optimization study of the Mach 0.745 Transonic Truss-Braced Wing (TTBW) aircraft using an in-house developed aero-structural analysis solver VSPAERO coupled to BEAM3D. A vortex-lattice model of the TTBW model is developed, and a transonic small disturbance /integral boundary layer correction method is implemented in the VSPAERO model to account for transonic and viscous flow effects. A correction method for the wing-strut interference aerodynamics is developed and applied to the VSPAERO solver. Also, a structural dynamic finite-element model of the TTBW aircraft is developed. This finite-element model includes the geometric nonlinear effect due to the tension in the struts which causes a deflection-dependent nonlinear stiffness. The VSPAERO model is coupled to the corresponding finite-element model to provide a rapid aero-structural analysis. The VSPAERO model has been validated against wind tunnel test data and FUN3D CFD simulation data. Three different flight conditions corresponding to Mach 0.745 at 40,000 ft are selected for the TTBW aircraft jig twist optimization to reduce the drag coefficients at the design and off-design cruise lift coefficients. The preliminary optimization results show that the TTBW aircraft with the optimized jig twist achieves a drag reduction of about 9 counts, 7 counts, and8 counts corresponding to the lift coefficients 0.68, 0.73, and 0.78, respectively. A high-fidelity CFD solver FUN3D is used to validate the jig twist optimization.

Multi-point↗

NASA NTRS1993

A new Lagrangian method for three-dimensional steady supersonic flows

In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.

Loh, Ching-Yuen↗

NASA NTRS1999

Isolated Nozzle Analysis Using OVERFLOW

LaRC conducted a code validation study for the OVERFLOW code to ascertain its accuracy for boattail drag prediction. The OVERFLOW results compared favorably with the LaRC 16-ft. Transonic Wind Tunnel (TWT) data, and prior CFD solutions from PAB3D and CFL3D. The ultimate goal is to investigate the installation drag of the nacelle boattails with powered nozzles at transonic mach numbers. The OVERFLOW solver was chosen because of its ability to accept volume overlapping structured grid for very complex airframe configurations. Structured grid components for representing the transonic nozzle boattail can be added to the BCAG grid for a TCA airframe with 2D bifurcated inlet and flow through nacelle without alteration. The focus of this research was to determine the suitability of the OVERFLOW solver for accomplishing this ultimate goal. This presentation will first introduce the transonic nozzle boattail wind-tunnel model geometry, followed by an examination of aerodynamic features based on the current OVERFLOW solutions and the solutions obtained previously using PAB3D, comparisons of Cp on the flap surface between the OVERFLOW solutions, wind tunnel data, and solutions from other CFD codes, an assessment of boattail drag count prediction, and a work plan for FY99.

Wong, Tin-Chee↗

NASA NTRS1999

Multi-Dimensional Quantum Tunneling and Transport Using the Density-Gradient Model

We show that quantum effects are likely to significantly degrade the performance of MOSFETs (metal oxide semiconductor field effect transistor) as these devices are scaled below 100 nm channel length and 2 nm oxide thickness over the next decade. A general and computationally efficient electronic device model including quantum effects would allow us to monitor and mitigate these effects. Full quantum models are too expensive in multi-dimensions. Using a general but efficient PDE solver called PROPHET, we implemented the density-gradient (DG) quantum correction to the industry-dominant classical drift-diffusion (DD) model. The DG model efficiently includes quantum carrier profile smoothing and tunneling in multi-dimensions and for any electronic device structure. We show that the DG model reduces DD model error from as much as 50% down to a few percent in comparison to thin oxide MOS capacitance measurements. We also show the first DG simulations of gate oxide tunneling and transverse current flow in ultra-scaled MOSFETs. The advantages of rapid model implementation using the PDE solver approach will be demonstrated, as well as the applicability of the DG model to any electronic device structure.

Biegel, Bryan A.↗

NASA NTRS1986

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗

NASA NTRS1997

Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems

This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.

Lin, Wen H.↗

DOE OSTI2014

A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces

In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.

Lin, Guang↗

NASA NTRS1992

An approximate viscous shock layer technique for calculating nonequilibrium hypersonic flows about blunt-nosed bodies

An approximate axisymmetric method has been developed which can reliably calculate nonequilibrium fully viscous hypersonic flows over blunt-nosed bodies. By substituting Maslen's second-order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. This procedure is significantly faster than the parabolized Navier-Stokes and VSL solvers and would be useful in a preliminary design environment. Solutions have been generated for air flows over several analytic body shapes. Surface heat transfer and pressure predictions are comparable to VSL results. Computed heating rates are in good agreement with experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher-order procedures which require starting solutions.

Cheatwood, F. M.↗

NASA NTRS1990

Application of a patched-grid algorithm to the F/A-18 forebody-leading-edge extension configuration

A patched-grid algorithm for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver is presented. Results from both a spatial-flux and a time-flux conservation approach to patching across zonal boundaries are presented. A generalized coordinate transformation with a biquadratic geometric element is used at the zonal interface in order to treat highly stretched viscous grids and arbitrarily shaped zonal boundaries. Applications are made to the F/A-18 forebody-Ieading-edge extension configuration at subsonic, high-alpha conditions. Computed surface flow patterns compare well with ground-based and flight-test results; the large effect of Reynolds number on the forebody flowfield is shown.

Leading edge extension↗

DOE OSTI2021

Open source implementation of glued sphere discrete element method and nonspherical biomass fast pyrolysis simulation

Here, in this research, a glued-sphere Discrete Element Method (DEM) method was implemented in the open-source, Computational Fluid Dynamics (CFD) software MFiX. The implementation was verified using a cylinder-wall collision and then validated by simulating the packing and fluidization of non-spherical particles. The validated code was applied to simulate fast pyrolysis of non-spherical biomass particles in a bubbling fluidized bed. The glued sphere occupancy ratio was proposed to quantify the quality of shape resolution using glued sphere. Shape resolution showed significant influence on the packing height in the simulation of particle packing and an occupancy ratio of 80 % was recommended. Its influence is minor in fully fluidized bed but can be 8 times higher in fixed fluidized bed. Three tested heat transfer models predicted similar yields of elongated biomass fast pyrolysis. The solver developed in this research can be used to simulate other multiphase reacting flows involving non-spherical particles.

42 ENGINEERING↗

DOE OSTI2019

Experimental and Numerical Analysis of Additively Manufactured Coupons With Parallel Channels and Inline Wall Jets

Present paper developed a series of additively manufactured parallel cooling channels with streamwise wall jets inside, which could be suitable for double-wall and near-wall cooling configurations in gas turbine hot section components. The tested coupons consisted of parallel channels, each channel further divided into small chambers using several spanwise separation walls. Height of these walls was kept less than channel height, thus forming a slot with one of the end walls. Coolant entered from one side of channel and formed streamwise wall jet while crossing through the slot over to the downstream chamber. The test coupons were additively manufactured by selective laser sintering (SLS) technique using Inconel 718 alloy. Steady-state heat transfer experiments with constant wall temperature boundary condition were performed to analyze effect of pitch between subsequent slots and blockage ratio (ratio of separation wall height to channel height) on heat transfer. The channel Reynolds number ranged from 1800 to 5000. Numerical simulations were performed using ANSYS cfx solver with SST k–ω turbulence model to obtain detailed understanding of existing flow field. Experimental results showed heat transfer enhancement of up to 6.5 times that of a smooth channel for the highest blockage ratio of 0.75. Numerical results revealed complex flow field which consisted of wall jets along with impingement, separation, and recirculation zones in each chamber. For all configurations, gain in heat transfer was accompanied with high pressure drops. However, coupled with the high heat transfer, this design could lead to potential coolant savings.

Engineering↗