Search NASA⌕ Search

SEARCH · Search NASA

Results for “Implicit methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35

Incompressible Navier-Stokes Computations with Heat Transfer

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

Kiris, Cetin↗

Progress In Incompressible Pump Flow Calculations

Steady and unsteady flows for propulsion systems are efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard kappa - epsilon model equations. The resulting computer code is applied to the flow analysis inside an advanced rocket pump impeller in steadily rotating reference frames. Numerical results are compared with experimental measurements. The effects of exit and shroud cavities with the leak-age flow are investigated. Time-accurate incompressible Navier-Stokes formulation with the overlapped grid scheme capability was evaluated by using MIT flapping foil experiment. The grid dependency, turbulence model effects, and the effect of order of differencing were investigated. Numerical results were compared against experimental data. The resulting procedure were applied to unsteady flapping foil calculations. Two upstream NACA 0025 foils perform high frequency synchronized motion and generate unsteady flow conditions to the downstream larger stationary foil. Comparison between unsteady experimental data and numerical results from two different moving boundary procedures will be presented.

Kiris, Cetin↗

Incompressible Navier-Stokes Computations for the Development of a Ventricular Assist Device

An incompressible flow analysis code, INS3D, has been applied to the development of a mechanical heart assist device. The solution method is based on the artificial compressibility approach and uses an implicit-upwind differencing scheme together with a Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal and the Coriolis force terms are included as source terms. The resulting computational procedure is validated for liquid rocket engine analysis and applied subsequently to analyze a Ventricular Assist Device (VAD). A new design configuration is developed which includes an inducer upstream of the impeller main blades, and substantial improvement is observed in the performance of the VAD.

Kiris, Cetin↗

An Initial Exploration of Improved Numerics within the Guidelines of the Negative Spalart-Allmaras Turbulence Model

A simple modification to the negative Spalart-Allmaras turbulence model is suggested so that when the turbulence working variable, ~v, is negative, diagonal dominance is increased, as is the tendency for the time-advancement scheme to push e toward positive values. Owing to the fact that the modification is only active when ~v is less than zero, the physical model is left unchanged. Using the proposed modification with a strong implicit solver based on Newton's method, convergence rates can be somewhat improved, with typical reductions in iterations and computer time on the order of 15-50%. The benefits are realized primarily when second- or higher-order accuracy is used for discretizing the convective terms in the turbulence model because of large overshoots that can occur with these schemes at the edges of boundary layers and wakes. For flowfields with few regions of negative ~v, or on very fine meshes where ~v is always greater than zero, little or no benefits should be expected.

Anderson, William K.↗

Improving the efficiency of aerodynamic shape optimization

The computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid-point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newton's method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients. The modified design procedure is demonstrated by optimizing the shape of an internal-external nozzle configuration. Practically identical optimization results are obtained that are independent of the method used to represent the surface. A substantial factor of 8 decrease in computational time for the optimization process is achieved by implementing both of the design procedure improvements.

Burgreen, Greg W.↗

Mechanical System Reliability and Cost Integration Using a Sequential Linear Approximation Method

The development of new products is dependent on product designs that incorporate high levels of reliability along with a design that meets predetermined levels of system cost. Additional constraints on the product include explicit and implicit performance requirements. Existing reliability and cost prediction methods result in no direct linkage between variables affecting these two dominant product attributes. A methodology to integrate reliability and cost estimates using a sequential linear approximation method is proposed. The sequential linear approximation method utilizes probability of failure sensitivities determined from probabilistic reliability methods as well a manufacturing cost sensitivities. The application of the sequential linear approximation method to a mechanical system is demonstrated.

Kowal, Michael T.↗

Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

Liu, C.↗

Shape optimization of single- and two-element airfoils on multiblock grids

A multiblock, discrete sensitivity analysis method is used to couple a direct optimization method and a flow analysis method. The domain is divided into smaller subdomains for which the sensitivities are obtained separately. Then, an effective sensitivity equation is solved to complete the coupling of all the sensitivity information. The flow analysis is based on the thin-layer Navier-Stokes equations solved by an implicit, upwind-biased, finite-volume method. The method of feasible directions is used for the present gradient-based optimization approach. First, a transonic airfoil is optimized to investigate the behavior of the method in highly nonlinear flows as well as the effect of different blocking strategies on the procedure. A supercritical airfoil is produced from an initially symmetric airfoil with multiblocking affecting the path but not the final shape. Secondly, a two-element airfoil is shape optimized in subsonic flow to demonstrate the present method's capability of shaping aerodynamically interfering elements simultaneously. For a very low and a very high Reynolds number cases, the shape of the main airfoil and the flap are optimized to yield improved lift-to-drag ratios.

Lacasse, James M.↗

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

Kang, Kab S.↗

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Homicz, G. F.↗

CFD applications in pump flows

The objective of the proposed paper is to develop a computational procedure that solves incompressible Navier-Stokes equations for pump flows. The solution method is based on the pseudo-compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. As a benchmark problem, the flow through the Rocketdyne inducer is numerically simulated. A coarse grid solution is obtained with a single zone by using an algebraic turbulence model. In multi-zone fine grid computation, a one-equation Baldwin-Barth turbulence model is utilized. Numerical results are compared with experimental measurements and a good agreement is found between the two. The resulting computer code is then applied to the flow analysis inside a two-stage fuel pump impeller operating at 80 percent, 100 percent, and 120 percent of design flow.

Kiris, Cetin↗

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.↗

A comparison of two methods for solving 3-D unsteady compressible viscous flows

Numerical solutions of 3D unsteady compressible flows for several steady and unsteady cases are obtained using two procedures - a noniterative Alternating Direction Implicit (ADI) scheme and a Generalized Minimal RESidual (GMRES) method. Results obtained are compared with each other and also with experimental data. It is found that the GMRES procedure can provide significant speedups compared to the noniterative ADI procedure.

Hixon, Ray↗

Fractional Step and Pseudocompressibility Methods for the Solution of Incompressible Navier-Stokes Equations

The fractional step and the pseudocompressibility methods for the solution of the incompressible Navier-Stokes equations are outlined. The fractional step method is based on finite-volume formulation and uses the pressure and the volume fluxes across the faces of each cell as dependent variables. The momentum equations are solved implicitly and the Poisson equation for the pressure is solved by using the multigrid method. The pseudocompressibility approach uses an implicit-higher-order-upwind differencing scheme for the convective terms together with the Gauss-Seidel line relaxation method. The dependent variables in the pseudocompressibility approach are the pressure and the cartesian velocity components in unstaggered mesh orientation. The 90-degree square duct flow, the wing-tip vortex wake flow and unsteady turbulent flows over an oscillating NACA 0015 airfoil are computed using both the fractional step and the pseudocompressibility methods. The results obtained from two different schemes are compared against experimental measurements.

Kiris, Cetin↗

Viscous analysis of three-dimensional rotor flows using a multigrid method

A three-dimensional code for rotating blade-row flow analysis was developed. The space discretization uses a cell-centered scheme with eigenvalues scaling for the artificial dissipation. The computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, non-periodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.

Arnone, A.↗

Time-marching methods for three-dimensional steady and unsteady viscous imcompressible flows

An implicit algorithm for the solution of three-dimensional, steady and unsteady, viscous, incompressible flows is presented. The algorithm is based on an upwind-relaxation finite-difference method. Steady-state solutions are carried out using a time-marching solution technique in combination with a local time-stepping strategy. To obtain time-accurate solutions, a subiterative procedure is employed at each physical time step using a global time step to ensure the divergence-free condition. Steady-state flows in several straight ducts and in a square duct with a 90-degree bend are computed and compared with analytical and experimental results. The classical problem of starting flow in a circular pipe is chosen to verify the time accuracy of the present scheme. Finally, the three-dimensional bubble-type vortex breakdown of a slender cylindrical vortex in an unbounded flow is investigated.

Hsu, C.-H.↗

Liquid Phase Modeling in Porous Media: Adsorption of Methanol and Ethanol in H-MFI in Condensed Water

Zeolites are used in the chemical and separation industries for their exceptional selectivity, adsorption capacity, regenerability, and stability in gas and liquid phase processing. Here, we developed an explicit solvation method for predicting solvent/condensed phase effects on adsorption free energies in microporous media such as zeolites based on the hybrid quantum mechanical/molecular mechanical free energy perturbation (QM/MM-FEP) technique. Our explicit solvation method for zeolite systems, called eSZS, aims to capture site-specific interactions during the adsorption process at the Brønsted acid sites of H-MFI zeolite while still considering the diverse configuration space of the solvent molecules. This strategy is ideal for chemical reactions or adsorbates that interact with the microporous medium in few distinct adsorbate/transition state configurations, i.e., the harmonic or similar approximations are acceptable for the adsorbate/transition state while such approximations break down for the solvent molecules that require extensive configuration space sampling. In this way, our approach effectively overcomes the limitations of implicit solvation models and classical force field methods for describing solvation effects on chemical reactions within porous materials such as zeolites. Specifically, in this study, we investigated various aspects of our hybrid QM/MM approach, including QM cluster size dependencies in a periodic electrostatically embedded cluster model (PEECM), rules for link atoms at the QM/MM boundary, and functional and basis set considerations for converged and reasonably accurate gas and aqueous phase methanol and ethanol adsorption free energy predictions in H-MFI. For gas phase adsorption of methanol and ethanol in H-MFI at a Brønsted acid site in T12 position, we compute adsorption free energies at 298 K of −0.61 and −0.75 eV, respectively, using a PEECM containing 50 Si and 1 Al atom with ωB97x-D/def2-TZVP level of theory. For solvent effect calculations, we sample the aqueous phase using grand canonical Monte Carlo (GCMC) simulations to (1) obtain a mean field of electrostatic interactions in the reaction system and (2) perform a rigorous free energy perturbation calculation. Similar to the experimentally and computationally observed endergonic solvation effects observed for hydrocarbon adsorption on metal surfaces, we also observe that a condensed aqueous environment destabilizes methanol and ethanol at these acid sites in H-MFI at 298 K. Specifically, the computed solvation free energies of adsorption (ΔΔG solv ) for methanol and ethanol are +0.44 and +0.54 eV, respectively. From this study, it is evident that adsorbates (methanol and ethanol) are competing with water for adsorption space inside the H-MFI zeolite, leading to an endergonic solvation effect. Here, we expect that the endergonic, aqueous solvent effect during adsorption in microporous zeolites is highly tunable by changing the pore size and hydrophobicity of the microporous material as this will affect the water density inside the pore structure.

Adsorption↗

High order finite difference and multigrid methods for spatially evolving instability in a planar channel

The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.

Liu, C.↗