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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Validity condition for the local sheath impedance boundary condition and a nonlocal generalization

ICRF sheaths can cause unwanted interactions of high-power RF waves with material surfaces in magnetic fusion devices. In previous work, a local RF sheath impedance boundary condition (BC) was derived for use in ICRF codes together with a microscale (i.e., Debye or sheath width scale) model for obtaining the sheath impedance used in that BC. This local RF sheath BC matches the normal component of current and electrostatic potential across the sheath-plasma interface. Collapsing the matching conditions at the sheath-plasma interface to a BC depends on the assumption of scale separation, which can be violated when conditions along the local radius of curvature of the surface vary sufficiently rapidly. The validity condition is explored in this contribution, with special attention to the case where the magnetic field approaches being tangent to the surface. When the local sheath BC no longer applies, a non-local sheath BC is developed under the assumption of a more relaxed scale separation assumption. It is shown that the non-local sheath BC reduces to the previous local sheath BC under appropriate conditions. Furthermore, a surface-integrated sheath admittance parameter describes the 2D physics in the new BC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1987

How good is the impedance boundary condition?

The impedance boundary condition (IBC) is often used in scattering problems involving material-coated conducting bodies. It is shown that for some commonly encountered coating configurations, the value of the impedance varies significantly as functions of the incident angle and polarization. Hence, the use of IBC in a rigorously formulated problem may affect the accuracy of the final solution.

Lee, Shung-Wu↗
NASA NTRS1996

Large Eddy Simulation in a Channel with Exit Boundary Conditions

The influence of the exit boundary conditions (vanishing first derivative of the velocity components and constant pressure) on the large eddy simulation of the fully developed turbulent channel flow has been investigated for equidistant and stretched grids at the channel exit. Results show that the chosen exit boundary conditions introduce some small disturbance which is mostly damped by the grid stretching. The difference between the fully developed turbulent channel flow obtained with LES with periodicity condition and the inlet and exit and the LES with fully developed flow at the inlet and the exit boundary condition is less than 10% for equidistant grids and less than 5% for the case grid stretching. The chosen boundary condition is of interest because it may be used in complex flows with backflow at exit.

Cziesla, T.↗
NASA NTRSDate not supplied

On the Implementation and Further Validation of a Time Domain Boundary Element Method Broadband Impedance Boundary Condition

A time domain boundary integral equation with Burton-Miller reformulation is presented for acoustic scattering by surfaces with liners in a uniform mean flow. The Ingard-Myers impedance boundary condition is implemented using a broadband multipole impedance model and converted into time domain differential equations to augment the boundary integral equation. The coupled integral-differential equations are solved numerically by a March-On-in-Time (MOT) scheme. While the Ingard-Myers condition is known to support Kelvin-Helmholtz instability due to its use of a vortex sheet interface between the flow and the liner surface, it is found that by neglecting a second derivative term in the current time domain impedance boundary condition formulation, the instability an be effectively suppressed in computation. The proposed formulation and implementation are validated using a NASA Langley Research Center Grazing Flow Impedance Tube (GFIT) experimental dataset with satisfactory results. Moreover, a minimization procedure for finding the poles and coefficients of the broadband multiple impedance model is formulated in this paper by which, unlike the commonly used vector-fitting method, passivity of the model is ensured. Numerical tests show the proposed minimization approach is effective for modeling liners that are commonly used in aeroacoustic applications.

Time Domain Impedance Boundary Condition↗
NASA NTRS1997

Improved Boundary Conditions for Cell-centered Difference Schemes

Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.

VanderWijngaart, Rob F.↗
DOE OSTI2021

Chiral propulsion: The method of effective boundary conditions

We propose to apply an “effective boundary condition” method to the problem of chiral propulsion. For the case of a rotating helix moving through a fluid at a low Reynolds number, the method amounts to replacing the original helix (in the limit of small pitch) by a cylinder, but with a special kind of partial slip boundary conditions replacing the non-slip boundary conditions on the original helix. These boundary conditions are constructed to reproduce far-field velocities of the original problem and are defined by a few parameters (slipping lengths) that can be extracted from a problem in planar rather than cylindrical geometry. We derive the chiral propulsion coefficients for spirals, helicoids, helically modulated cylinders and some of their generalizations using the introduced method. In the case of spirals, we compare our results with the ones derived by Lighthill and find a very good agreement. Here, the proposed method is general and can be applied to any helical shape in the limit of a small pitch. Furthermore, we have established that for a broad class of helical surfaces the dependence of the chiral propulsion on the helical angle θ is universal, x ~ cos θ sin 2θ with the maximal propulsion achieved at the universal angle θ m = tan –1 (1/√2) ≈ 35.26°.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Stochastic boundary condition effects on supersonic leading edge blowing

The present manuscript studies the robustness of leading edge blowing for active control of the upstream bow shock and overall aerothermal characteristics of a supersonic airfoil subject to variability in the injection conditions. The injection boundary conditions were considered stochastic and their randomness was propagated to the flow topology and aerothermal quantities of interest by means of non-intrusive Polynomial Chaos Expansions. The evaluations needed to build these expansions were carried out via steady two-dimensional Reynolds-Averaged Navier Stokes simulations. Two different injection port sizes were considered, with the smallest promoting a Coanda effect that gives rise to non-symmetric flow topologies. The uncertain boundary conditions lead to significant variations in the flow topology, particularly at the injection exit and the bow shock position, with variations of up to 75% of the nominal value. Here this study identifies the key operating conditions to ensure the optimal application of leading-edge injection for active control of supersonic airfoils.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations

A nonreflecting boundary condition is presented for the numerical solution of the time-dependent compressible Navier-Stokes equations when these equations are used to obtain a steady state. This boundary condition is shown to be effective in reducing reflections at a subsonic outflow boundary. Numerical calculations using a model problem were made to compare this boundary condition with other outflow boundary conditions. The nonreflecting boundary condition contains a parameter whose optimal value is estimated using the analysis of a simplified set of equations.

Rudy, D. H.↗
NASA NTRS1990

Time-dependent boundary conditions for hyperbolic systems. II

A general boundary condition formalism is developed for all types of boundary conditions to which hyperbolic systems are subject; the formalism makes possible a 'cookbook' approach to boundary conditions, by means of which novel boundary 'recipes' may be derived and previously devised ones may be consulted as required. Numerous useful conditions are derived for such CFD problems as subsonic and supersonic inflows and outflows, nonreflecting boundaries, force-free boundaries, constant pressure boundaries, and constant mass flux. Attention is given to the computation and integration of time derivatives.

Thompson, Kevin W.↗
NASA NTRS1986

An outflow acoustic boundary condition for internal duct flows

A boundary condition for the linear acoustic equation has been developed that allows the acoustic pressure waves to propagate out of the computational domain boundary, just as they would propagate in an infinitely long duct. The problem is divided into two domains: numerical and analytical. The boundary condition provides a matching of the two domains. Examples show this method works well in an acoustic panel program for a model problem (simple source in a rectangular duct with several propagating modes present). The boundary condition is described so that it can be used with various duct various duct geometries and numerical methods.

Mosher, M.↗
NASA NTRS1991

Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions

Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.

Kane, James H.↗
NASA NTRS1991

Wideband finite difference time domain implementation of surface impedance boundary conditions for good conductors

Surface impedance boundary conditions are used to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be used to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A one dimensional implementation is presented for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique. In order to illustrate the FDTD surface impedance boundary condition, a planar air-lossy dielectric interface is considered.

Beggs, John H.↗
DOE OSTI2021

Considering computational speed vs. accuracy: Choosing appropriate mesoscale RVE boundary conditions

Modeling a material’s microstructure using continuum theories allows for inspection of the relationship between coarse scale and fine scale behaviors. Computational limits generally require selection of a sub-volume from a bulk sample in order to directly model the microstructure. Boundary conditions are applied to the sub-volume to mimic the excluded bulk material. Appropriate selection of boundary conditions helps effectively determine the appropriate spatial scale required of the sub-volume. Applicable boundary conditions include direct displacement, periodic, and uniform traction. While direct displacement and periodic boundary conditions are commonly used, uniform traction boundary conditions have seen limited use due to rigid body stability issues in simulations of compression or shear deformation. A new application of uniform traction boundary conditions was developed through linear constraint equations, similar to approaches employed by direct displacement and periodic boundary conditions, to quench rigid body motions with minimal interference of the relative deformation of the model. These boundary conditions were tested by compressing several synthetically generated periodic microstructures using the finite element method. Evaluating the effective stiffness along the compression axis, the direct displacement boundary condition produced the stiffest response, whereas the uniform traction boundary condition produced the most compliant. Periodic boundary conditions produced the same response for all volumes analyzed and both the direct displacement and uniform traction boundary conditions trended toward the periodic response as the domain volume increased. Computational performance was also evaluated for each boundary condition using implicit and explicit solvers. Direct displacement boundary conditions presented the lowest computational cost of all of the boundary conditions followed by periodic then uniform traction. The computational expense of periodic and uniform traction boundary conditions limited the viable spatial scale and mesh resolutions able to be simulated. Selection of appropriate boundary conditions for specific uses need to be a balance between allowable computational expense and accuracy of the method. Techniques for evaluating which boundary conditions to use are discussed.

42 ENGINEERING↗
NASA NTRS1997

Application of PML Absorbing Boundary Conditions to the Benchmark Problems of Computational Aeroacoustics

Accurate numerical non-reflecting boundary conditions are important in all the proposed benchmark problems of the Second Workshop. Recently, a new absorbing boundary condition has been developed using Perfectly Matched Layer (PML) equations for the Euler equations. In this approach, a region with a width of a few grid points is introduced adjacent to the non-reflecting boundaries. In the added region, Perfectly Matched Layer equations are constructed and applied so that the out-going waves are absorbed inside the layer with little reflection to the interior domain. It will be demonstrated in the present paper that the proposed absorbing boundary condition is quite general and versatile, applicable to radiation boundaries as well as inflow and outflow boundaries. It is also easy to implement. The emphasis of the paper will be on the application of the PML absorbing boundary condition to problems in Categories 1, 2, and 3. In Category 1, solutions of problems 1 and 2 are presented. Both problems are solved using a multi-domain polar grid system. Perfectly Matched Layer equations for a circular boundary are constructed and their effectiveness assessed. In Category 2, solutions of problem 2 are presented. Here, in addition to the radiation boundary conditions at the far field in the axisymmetric coordinate system, the inflow boundary condition at the duct inlet is also dealt with using the proposed Perfectly Match Layer equations. At the inlet, a PML domain is introduced in which the incident duct mode is simulated while the waves reflected from the open end of the duct are absorbed at the same time. In Category 3, solutions of all three problems are presented. Again, the PML absorbing boundary condition is used at the inflow boundary so that the incoming vorticity wave is simulated while the outgoing acoustic waves are absorbed with very little numerical reflection. All the problems are solved using central difference schemes for spatial discretizations and the optimized Low-Dissipation and Low-Dispersion Runge-Kutta scheme for the time integration. Issues of numerical accuracy and efficiency are also addressed.

Hu, Fang Q.↗
NASA NTRS1988

Far field boundary conditions for computation over long time

A new class of computational far field boundary conditions for hyperbolic partial differential equations is developed. These boundary conditions combine properties of absorbing boundary conditions for transient solutions and properties of far field boundary conditions for steady-state problems. The conditions can be used to limit the computational domain when both traveling waves and evanescent waves are present. Boundary conditions for scalar wave equations are derived and analyzed. Extensions to systems of equations are discussed and results from numerical experiments are presented.

Engquist, Bjorn↗