Boundary Conditions For Calculation Research Articles

Transition term method for the analysis of the reflected and the transmitted acoustic signals from water-saturated porous plates

Ultrasound reflection (R) and transmission (T) from an immersed porous plate of QF-20 (a registered trademark of Filtros, Ferro Corporation) are investigated. Assuming open pores boundary conditions for the theoretical computations, values of the physical constants given by Johnson et al. [D. L. Johnson, D. L. Hemmick, and H. Kojima J. Appl. Phys. 76(1), 115-125 (1994)] are used at first. Comparisons of R and T with experimental results show a discrepancy. It is then assumed that visco-elastic losses exist inside the solid part. When a small imaginary constant part is considered for the bulk moduli, a better fit is obtained between theoretical and experimental values of /R/ and /T/. However, the numerous and very close peaks prevent easy measures of the resonance amplitudes and widths. The transition terms built up from the linear combinations R-T and R+T allow these peaks to be separated. Comparisons between theory and experiments are made. This work validates, in the frequency range where the agreement is good, a method for the location of the symmetrical and antisymmetrical modes of the plate. A discrimination is also possible between modes resulting from the fluid phase motions and from the solid phase motions.

Manufactured Solution for Computational Fluid Dynamics Boundary Condition Verification

Order-of-accuracy verification is necessary to ensure that software correctly solves a given set of equations. One method for verifying the order of accuracy of a code is the method of manufactured solutions. This study documents the development of a manufactured solution that allows verification of not only the Euler, Navier-Stokes, and Reynolds-averaged Navier-Stokes equation sets, but also some of their associated boundary conditions: slip, no-slip (adiabatic and isothermal), and outflow (subsonic, supersonic, and mixed). To demonstrate the usefulness of this manufactured solution, it has been used for order-of-accuracy verification in a compressible computational fluid dynamics code. All of the results shown are on skewed, nonuniform, three-dimensional meshes. The manufactured solution and sequence of meshes are designed to allow asymptotic results to be obtained with reasonable computational cost. In addition to the order of accuracy of the full code for various equation sets and boundary conditions, the order of accuracy of code portions used to calculate solution gradients has been measured as well.

Modeling boundary conditions for computation of piezoelectric fields in quantum dots with image charge analogy

We present a simple approach for calculating the piezoelectric fields exerted by a stressor quantum dot buried in a semi-infinite piezoelectric matrix with a weak electromechanical coupling factor. It aims to take into account the electrical boundary conditions by introducing an image quantum dot mirrored the original dot with respect to the matrix surface. The technique is applied to a spherical InAs dot embedded in the GaAs semi-infinite matrix and the computation results exhibit an excellent agreement with more rigorous calculations reported by Pan [E. Pan, J. Appl. Phys. 91, 3785 (2002)]. We demonstrate that the approach can also be used in computing the piezoelectric fields for a square pyramid embedded in a semi-infinite matrix. It is furthermore anticipated that application of the method can remarkably simplify calculations of piezoelectric fields generated by arrays of the quantum dots of various shapes grown in a matrix material. These fields are known to be of considerable importance in quantum dot devices.

Computational investigation of turbulent jet impinging onto rotating disk

PurposeThe main purpose of the paper is the validation of a broad range of RANS turbulence models, for the prediction of flow and heat transfer, for a broad range of boundary conditions and geometrical configurations, for this class of problems.Design/methodology/approachTwo‐ and three‐dimensional computations are performed using a general‐purpose CFD code based on a finite volume method and a pressure‐correction formulation. Special attention is paid to achieve a high numerical accuracy by applying second order discretization schemes and stringent convergence criteria, as well as performing sensitivity studies with respect to the grid resolution, computational domain size and boundary conditions. Results are assessed by comparing the predictions with the measurements available in the literature.FindingsA rather unsatisfactory performance of the Reynolds stress model is observed, in general, although the contrary has been expected in this rotating flow, exhibiting a predominantly non‐isotropic turbulence structure. The best overall agreement with the experiments is obtained by the k‐ω model, where the SST model is also observed to provide a quite good performance, which is close to that of the k‐ω model, for most of the investigated cases.Originality/valueTo date, computational investigation of turbulent jet impinging on to “rotating” disk has not received much attention. To the best of the authors' knowledge, a thorough numerical analysis of the generic problem comparable with present study has not yet been attempted.

Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer

We present a generalised treatment of the wall boundary conditions for RANS computation of turbulent flows and heat transfer. The method blends the integration up to the wall (ItW) with the generalised wall functions (GWF) that include non-equilibrium effects. Wall boundary condition can thus be defined irrespective of whether the wall-nearest grid point lies within the viscous sublayer, in the buffer zone, or in the fully turbulent region. The computations with fine and coarse meshes of a steady and pulsating flow in a plane channel, in flow behind a backward-facing step and in a round impinging jet using the proposed compound wall treatment (CWT) are all in satisfactory agreement with the available experiments and DNS data. The method is recommended for computations of industrial flows in complex domains where it is difficult to generate a computational grid that will satisfy a priori either the ItW or WF prerequisites.

Numerical simulation of a radial diffuser turbulent airflow

In the present work are presented results from numerical simulations performed with the ANSYS-CFX ® code. We have studied a radial diffuser flow case, which is the main academic problem used to study the flow behavior on flat plate valves. The radial flow inside the diffuser has important behavior such as the turbulence decay downstream and recirculation regions inside the valve flow channel due to boundary layer detachment. These flow structures are present in compressor reed valve configurations, influencing to a greater extent the compressor efficiency. The main target of the present paper was finding the simulation set-up (computational domain, boundary conditions and turbulence model) that better fits with experimental data published by Tabatabai and Pollard. The local flow turbulence and velocity profiles were investigated using four different turbulence models, two different boundary conditions set-up, two different computational domains and three different flow conditions ( Re in – Reynolds number at the diffuser inlet). We used the Reynolds stress (BSL); the k– ε; the RNG k– ε; and the shear stress transport (SST) k– ω turbulence models. The performed analysis and comparison of the computational results with experimental data show that the choice of the turbulence model, as well as the choice of the other computational conditions, plays an important role in the results physical quality and accuracy.

Modelling of Effect of Inflow Turbulence on Large Eddy Simulation of Bluff Body Flows

A random flow generation (RFG) algorithm for a previously established large eddy simulation (LES) code is successfully incorporated into a finite element fluid flow solver to generate the required inflow/initial turbulence boundary conditions for the LES computations of viscous incompressible turbulent flow over a nominally twodimensional circular cylinder at Reynolds number of 140,000. The effect of generated turbulent inflow boundary conditions on the near wake flow and the shear layer and on the prediction of integral flow parameters is studied based on long time average results. No-slip velocity boundary function is used but wall effects are taken into consideration with a near wall modelling methodology based on van Driest Damping approach. The numerical results obtained from simulations are compared with each other and with the experimental data for different turbulent inflow boundary conditions to assess the functionality of the RFG algorithm for the present LES code and hence its influence on the vortex shedding mechanism and the resulting flow field predictions.

Approximate near-wall treatments based on zonal and hybrid RANS–LES methods for LES at high Reynolds numbers

Two strategies, combining a LES scheme with different near-wall RANS approximations, are investigated by reference to simulations for plane channel flow and two separated flows at moderate and high Reynolds numbers, respectively. One strategy is a hybrid modelling scheme, wherein the subgrid-scale model in the outer LES domain is interfaced with a RANS model in a predefined near-wall layer. The other is a zonal method in which a thin-shear-flow RANS solution in the near-wall layer, embedded within the LES domain which covers the entire flow, is used to provide boundary conditions for the LES computation, the two thus being loosely coupled. Both methods allow the thickness of the near-wall RANS layer to be chosen freely. In the hybrid LES–RANS scheme, the near-wall layer is interfaced to the outer LES region, subject to compatibility conditions for velocity and turbulent viscosity imposed across the interface. These conditions are extracted dynamically as the simulation progresses. In the zonal approach, a mixing-layer model provides the eddy-viscosity field in the near-wall layer, while in the hybrid approach, a two-equations ( k– ϵ) model is used.

Parameterization of the Urban Water Budget with the Submesoscale Soil Model

Abstract This paper presents the hydrological component of the Submesoscale Soil Model, urbanized version (SM2-U). This model is an extension of the rural Interactions between Soil, Biosphere, and Atmosphere (ISBA) soil model to urban surfaces. It considers in detail both rural and urban surfaces. Its purpose is to compute the sensible heat and humidity fluxes at the canopy–atmosphere interface for the computational domain lower boundary condition of atmospheric mesoscale models in order to simulate the urban boundary layer in any weather conditions. Because it computes separately the surface temperature of each land use cover mode while the original model computes a unique temperature for the soil and vegetation system, the new version is first validated for rural grounds by comparison with experimental data from the Hydrological Atmospheric Pilot Experiment-Modélisation du Bilan Hydrique (HAPEX-MOBILHY) and the European Field Experiment in a Desertification Threatened Area (EFEDA). The SM2-U water budget is then evaluated on the experimental data obtained at a suburban site in the Nantes urban area (Rezé, France), both on an annual scale and for two stormy events. SM2-U evaluates correctly the water flow measured in the drainage network (DN) at the annual scale and for the summer storm. As for the winter storm, when the soil is saturated, the simulation shows that water infiltration from the soil to the DN must be taken care of to evaluate correctly the DN flow. Yet, the addition of this soil water infiltration to the DN does not make any difference in the simulated surface fluxes that are the model outputs for simulating the urban boundary layer. Urban hydrological parameters are shown to largely influence the available water on artificial surfaces for evaporation and to influence less the evapotranspiration from natural surfaces. The influence of the water budget and surface structure on the suburban site local climatology is demonstrated.

OPTIMAL CONVERGENCE OF NON-OVERLAPPING SCHWARZ METHODS FOR THE HELMHOLTZ EQUATION

The non-overlapping Schwarz method with absorbing boundary conditions instead of the Dirichlet boundary conditions is an efficient variant of the overlapping Schwarz method for the Helmholtz equation. These absorbing boundary conditions defined on the interface between the subdomains are the key ingredients to obtain a fast convergence of the iterative Schwarz algorithm. In a one-way subdomains splitting, non-local optimal absorbing boundary conditions can be obtained and leads to the convergence of the Schwarz algorithm in a number of iterations equal to the number of subdomains minus one. This paper investigates different local approximations of these optimal absorbing boundary conditions for finite element computations in acoustics. Different approaches are presented both in the continuous and in the discrete analysis, including high-order optimized continuous absorbing boundary conditions, and discrete absorbing boundary conditions based on algebraic approximation. A wide range of new numerical experiments performed on unbounded acoustics problems demonstrate the comparative performance and the robustness of the proposed methods on general unstructured mesh partitioning.

Design and Testing of a Transonic Linear Cascade Tunnel With Optimized Slotted Walls

In linear cascade wind tunnel tests, a high level of pitchwise periodicity is desirable to reproduce the azimuthal periodicity in the stage of an axial compressor or turbine. Transonic tests in a cascade wind tunnel with open jet boundaries have been shown to suffer from spurious waves, reflected at the jet boundary, that compromise the flow periodicity in pitch. This problem can be tackled by placing at this boundary a slotted tailboard with a specific wall void ratio s and pitch angle α. The optimal value of the s-α pair depends on the test section geometry and on the tunnel running conditions. An inviscid two-dimensional numerical method has been developed to predict transonic linear cascade flows, with and without a tailboard, and quantify the nonperiodicity in the discharge. This method includes a new computational boundary condition to model the effects of the tailboard slots on the cascade interior flow. This method has been applied to a six-blade turbine nozzle cascade, transonically tested at the University of Leicester. The numerical results identified a specific slotted tailboard geometry, able to minimize the spurious reflected waves and regain some pitchwise flow periodicity. The wind tunnel open jet test section was redesigned accordingly. Pressure measurements at the cascade outlet and synchronous spark schlieren visualization of the test section, with and without the optimized slotted tailboard, have confirmed the gain in pitchwise periodicity predicted by the numerical model.

Using a CFD approach for the study of street-level winds in a built-up area

The street-level winds in a built-up area are simulated numerically using a conventional method that is commonly applied in the industry. The method is described in terms of computational domain, grid density, turbulence model and boundary conditions. Testing of the domain size and the grid density is also conducted to minimize the numerical errors and the computed values are compared with the wind tunnel data available from a previous study. The computed values agree favourably with the measured values in the case of H / h = 1 where all the buildings have the same height. In other cases ( H / h = 2 and 4) where the central building is taller than its surrounding blocks, the agreement between the computation and experiment becomes relatively unsatisfactory. The accuracy requirement of using CFD in the environmental wind studies is discussed and this study suggests that applying the relatively simple CFD approach is adequate to investigate the street-level winds during the phase of preliminary design while more attention is required when the building layout becomes complicated.

Radiation and Wall Boundary Conditions for Computational Aeroacoustics: A Review

A review of unsteady computational boundary conditions for computational aeroacoustics (CAA) problems is presented. This review is meant to serve as a general overview of previous work on solid wall, radiation and outflow boundary conditions that have been proposed and used in CAA calculations. Both the physical nature of the boundary condition problem as well as the numerical considerations affecting their implementation are discussed.

Analytical Euler Solution for Two Dimensional Compressible Ramp Flow with Experimental Comparison

A newly developed procedure for obtaining analytical asymptotic solutions of the two-dimensional steadystate Euler equations is applied to compressible flow past a ramp to further demonstrate its general utility. The procedure has been shown to be applicable into the low transonic range (shock free). The equations are written in natural streamline coordinates with mass flux and flow angle as dependent variables. Higher-order effects, for example, compressibility, appear as nonhomogeneous forcing terms. This new solution procedure does not require aG reen’s function for the forcing terms and has general applicability to many other disciplines, for example, heat transfer, besides fluid dynamics. Application of the new approach to flow problems having geometric corners, for example, ramp, reveals the typical singularity compounding at higher order. The analytical nature of the solution guides implementation of a nonconformal mapping and a new type of coordinate straining strategy to control the phenomenon and ensure uniform validity. Understanding of the nature of the inviscid flow near a geometric corner can be used to devise improved computational fluid dynamics surface boundary conditions at such singular points, for example, airfoil trailing edge. The analytical validity of the ramp solution is corroborated for this purpose by

Numerical boundary layers of conservation laws with relaxation extension

This paper is concerned with the asymptotic equivalence between scalar conservation law and its relaxing scheme in the presence of boundaries. The main goals are to understand the evolution and structures of numerical boundary layers. We first construct formally the approximate solution up to any order of accuracy by using the matched asymptotic analysis and multiple scale expansions. Next, we prove that the weak numerical boundary layers (those with suitably small strength) are always nonlinearly stable, thus the effects of numerical boundary layers are localized. Finally, we show that the strong numerical boundary layers are nonlinearly stable also which depend crucially on the structures of the numerical boundary layers. The proofs are based weighted energy estimates. Such analysis also gives us some hints to choose boundary conditions in practical computations.

3-D force-balanced magnetospheric configurations

Abstract. The knowledge of plasma pressure is essential for many physics applications in the magnetosphere, such as computing magnetospheric currents and deriving mag-netosphere-ionosphere coupling. A thorough knowledge of the 3-D pressure distribution has, however, eluded the community, as most in situ pressure observations are either in the ionosphere or the equatorial region of the magnetosphere. With the assumption of pressure isotropy there have been attempts to obtain the pressure at different locations,by either (a) mapping observed data (e.g. in the ionosphere) along the field lines of an empirical magnetospheric field model, or (b) computing a pressure profile in the equatorial plane (in 2-D) or along the Sun-Earth axis (in 1-D) that is in force balance with the magnetic stresses of an empirical model. However, the pressure distributions obtained through these methods are not in force balance with the empirical magnetic field at all locations. In order to find a global 3-D plasma pressure distribution in force balance with the magnetospheric magnetic field, we have developed the MAG-3-D code that solves the 3-D force balance equation computationally. Our calculation is performed in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials as . The pressure distribution, , is prescribed in the equatorial plane and is based on satellite measurements. In addition, computational boundary conditions for ψ surfaces are imposed using empirical field models. Our results provide 3-D distributions of magnetic field, plasma pressure, as well as parallel and transverse currents for both quiet-time and disturbed magnetospheric conditions. Key words. Magnetospheric physics (magnetospheric configuration and dynamics; magnetotail; plasma sheet)

The evaluation of non-reflecting boundary conditions for duct acoustic computation

A simple method is used to quantify the performance of non-reflecting boundary conditions for duct acoustic applications. The method uses a two-dimensional wavesplitting technique to decompose the linearized Euler equations into its constitutive modes, allowing the magnitude of reflected waves from outflow boundaries to be accurately determined. Realistic conditions are simulated by conducting the boundary condition analysis using acoustic waves with characteristics often found in duct and turbomachinery problems. For this paper, the method is used to investigate the performance of three different buffer zone implementations and the Perfectly Matched Layer as non-reflecting boundary conditions. The effect of the damping properties of these boundary conditions and the incident acoustic wave characteristics on performance are considered. Results indicate that the buffer zone boundary condition using explicit damping of the solution vector after each timestep produces the best non-reflecting performance. A deterioration in performance was observed for incident waves at high angles relative to the boundary normal for all implementations.

Lax–Friedrichs sweeping scheme for static Hamilton–Jacobi equations

We propose a simple, fast sweeping method based on the Lax–Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton–Jacobi equations in any number of spatial dimensions. By using the Lax–Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss–Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss–Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min–max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton–Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

Validations of CFD against detailed velocity and pressure measurements in water turbine runner flow

AbstractThis work compares CFD results with experimental results of the flow in two different kinds of water turbine runners. The runners studied are the GAMM Francis runner and the Hölleforsen Kaplan runner. The GAMM Francis runner was used as a test case in the 1989 GAMM Workshop on 3D Computation of Incompressible Internal Flows where the geometry and detailed best efficiency measurements were made available. In addition to the best efficiency measurements, four off‐design operating condition measurements are used for the comparisons in this work. The Hölleforsen Kaplan runner was used at the 1999 Turbine 99 and 2001 Turbine 99—II workshops on draft tube flow, where detailed measurements made after the runner were used as inlet boundary conditions for the draft tube computations. The measurements are used here to validate computations of the flow in the runner.The computations are made in a single runner blade passage where the inlet boundary conditions are obtained from an extrapolation of detailed measurements (GAMM) or from separate guide vane computations (Hölleforsen). The steady flow in a rotating co‐ordinate system is computed. The effects of turbulence are modelled by a low‐Reynolds number k‐ω turbulence model, which removes some of the assumptions of the commonly used wall function approach and brings the computations one step further.The computational results are compared to the measurements with respect to detailed velocity and pressure distributions at several measurement sections and several operating conditions. The computational results are also compared to coarse grid wall function computations by the TASCflow CFD code, which uses a similar methodology as the CALC‐PMB CFD code used in the present work. The comparisons show where the computational method is sufficient and where it is not sufficient.The behaviour of the computational method is similar for both kinds of water turbines, which shows that experience of computations in water turbines will ultimately give quantitatively correct results. Copyright © 2003 John Wiley & Sons, Ltd.

Robust and high-order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer

A new approach is considered to construct effective boundary conditions for the solution of problems related to the scattering of electromagnetic waves by perfectly conducting cylinders coated by a thin dielectric shell. These boundary conditions aim to be both robust and of high order while remaining set in terms of surface differential operators involving at most second-order derivatives. Error estimates yield a theoretical basis for the use of these boundary conditions in practical computations. Some numerical experiments at frequencies beyond the range of validity of the usual impedance boundary conditions validate the efficiency of the approach.