Numerical Boundary Conditions Research Articles

Numerical determination of the heat transfer coefficient for volumetric air receivers with wire meshes

Volumetric receivers made of metallic plain-weave wire meshes are a promising technology that could lead to many different designs and configurations. This work deals with the numerical determination of the convective heat transfer coefficient between an air flow and stagger stacked plain-weave wire mesh screens that constitute the volumetric receivers. For that purpose, six geometries are studied with different geometrical characteristics, but with the constraint of finding pairs with similar porosities. The commercial code STAR-CCM+ was used for the detailed geometries for solving the microscopic equations. The numerical methodology, boundary conditions and main assumptions are presented. Based on a parametrical study over the velocity and wall temperature for each analyzed mesh, a correlation of the local volumetric convective heat transfer was found and depends on the Reynolds and Prandtl numbers. The different correlations were compared among them and with literature data showing similar trends and order of magnitudes. One of the correlations obtained was validated by using it in a homogeneous equivalent model assuming a local thermal non-equilibrium between the solid and fluid phases. The results were compared to the temperature profiles computed by a detailed simulation and show a very good agreement.

An Outflow Boundary Condition Model for Noninvasive Prediction of Fractional Flow Reserve in Diseased Coronary Arteries.

This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the "functional significance" of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and

A Steady-state Spectral Model for Electron Acceleration and Cooling in Blazar Jets: Application to 3C 279

Abstract We introduce a new theoretical model to describe the emitting region in a blazar jet. We adopt a one-zone leptonic picture and construct the particle transport equation for a plasma blob experiencing low-energy, monoenergetic particle injection, energy-dependent particle escape, shock acceleration, adiabatic expansion, stochastic acceleration, synchrotron radiation, and external Compton radiation from the dust torus and broad-line region (BLR). We demonstrate that a one-zone leptonic model is able to explain the IR though -ray spectrum for 3C 279 in 2008–2009. We determine that the BLR seed photons cannot be adequately described by a single average distribution, but rather we find that a stratified BLR provides an improvement in the estimation of the distance of the emitting region from the black hole. We calculate that the jet is not always in equipartition between the particles and magnetic field and find that stochastic acceleration provides more energy to the particles than does shock acceleration, where the latter is also overshadowed by adiabatic losses. We further introduce a novel technique to implement numerical boundary conditions and determine the global normalization for the electron distribution, based on analysis of stiff ordinary differential equations. Our astrophysical results are compared with those obtained by previous authors.

A High-Order Finite Difference WENO Scheme for Ideal Magnetohydrodynamics on Curvilinear Meshes

A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially non-oscillatory (WENO) scheme. It computes a high-order numerical flux by a Taylor expansion in space, with the lowest-order term solved from a Riemann solver and the higher-order terms constructed from physical fluxes by limited central differences. The scheme coupled with several Riemann solvers, including a Lax-Friedrichs solver and HLL-type solvers, is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems. In particular, a HLLD solver on Cartesian meshes is extended to curvilinear meshes with proper modifications. A numerical boundary condition for the perfect electrical conductor (PEC) boundary is derived for general geometry and verified through a bow shock flow. Numerical results also confirm the advantages of using low dissipative Riemann solvers in the current framework.

Wind Environment Assessments of a High Density Urban District Using CFD Tool

The urban expansion of Dalian city over the past 60 years from approximately 50 km2 to 500 km2 has been characterized by a high-density downtown morphological pattern, while the urban wind speed per year has trended downward. To evaluate natural ventilation performance in the high-density downtown area of Dalian, an in situ wind environmental survey was performed, and the results were used as a reference to configure CFD numerical simulation boundary conditions. The results indicate that urban edifices, such as enclosed city blocks, strip apartments in rows and, especially, high-rise buildings with large podium bulk, were unfavourable to natural ventilation and could reduce the mean wind speed by up to 78% relative to the approaching speed. The natural ventilation performance of different building morphologies were further evaluated via CFD simulations, which indicated such strategies as using ventilation paths, hybrid buildings with different heights, and increasing building height while decreasing their land coverage could improve the urban ventilation performance. Increasing the building height and reducing land coverage was one of the most efficient strategies and increased wind velocities up to 2.4 times the real case. Green land significantly cooled and humidified its surroundings, particularly the downwind spaces.

Key issues in developing numerical models for artificial weather modification

The scientific foundation of artificial weather modification is meso- and small-scale dynamics and cloud–precipitation microphysics. Artificial weather modification requires the realistic coupling of weather patterns, dynamical processes, and microphysical processes. Now that numerical models with weather dynamical characteristics have been widely applied to artificial weather modification, several key points that should not be neglected when developing numerical models for artificial weather modification are proposed in this paper, including the dynamical equations, model resolution, cloud–precipitation microphysical processes, numerical computation method, and initial and boundary conditions. Based on several examples, approaches are offered to deal with the problems that exist in these areas.

Offshore monopile in the southern North Sea: Part I, calibrated input sea state

Safe, reliable access is an essential precondition for the successful maintenance of offshore wind farms. Access from vessels to wind turbines depends on the severity of the sea state in the vicinity of the turbine support structure. This paper presents a validation of a numerical boundary condition developed to reproduce the seasonal sea state at Teesside Offshore Wind Farm, off the coast of the UK. The boundary condition, called customSpectrum, was derived from wave energy spectra obtained by analysis of existing field measurements of wave free-surface displacement at the wind farm site and implemented in OpenFoam, the open-source computational fluid dynamics library. OpenFoam was then used to simulate typical spring, summer, autumn and winter sea states as uni-directional waves. Predicted surface elevations and significant wave heights were found to be in agreement with in situ buoy data, thus validating the OpenFoam model. Satisfactory agreement was achieved between analytical and numerically predicted spectral density functions for the horizontal and vertical water particle velocity components. It was found that the wave activity at Teesside is uni-modal in spring and autumn, and bi-modal in summer and winter. Extending the procedure to multi-directional waves in crossing seas is recommended.

References and benchmarks for pore-scale flow simulated using micro-CT images of porous media and digital rocks

We generate a novel reference dataset to quantify the impact of numerical solvers, boundary conditions, and simulation platforms. We consider a variety of microstructures ranging from idealized pipes to digital rocks. Pore throats of the digital rocks considered are large enough to be well resolved with state-of-the-art micro-computerized tomography technology. Permeability is computed using multiple numerical engines, 12 in total, including, Lattice-Boltzmann, computational fluid dynamics, voxel based, fast semi-analytical, and known empirical models. Thus, we provide a measure of uncertainty associated with flow computations of digital media. Moreover, the reference and standards dataset generated is the first of its kind and can be used to test and improve new fluid flow algorithms. We find that there is an overall good agreement between solvers for idealized cross-section shape pipes. As expected, the disagreement increases with increase in complexity of the pore space. Numerical solutions for pipes with sinusoidal variation of cross section show larger variability compared to pipes of constant cross-section shapes. We notice relatively larger variability in computed permeability of digital rocks with coefficient of variation (of up to 25%) in computed values between various solvers. Still, these differences are small given other subsurface uncertainties. The observed differences between solvers can be attributed to several causes including, differences in boundary conditions, numerical convergence criteria, and parameterization of fundamental physics equations. Solvers that perform additional meshing of irregular pore shapes require an additional step in practical workflows which involves skill and can introduce further uncertainty. Computation times for digital rocks vary from minutes to several days depending on the algorithm and available computational resources. We find that more stringent convergence criteria can improve solver accuracy but at the expense of longer computation time.

Statistical Approach for Computational Fluid Dynamics State-of-the-Art Assessment: N-Version Verification and Validation

A statistical approach for computational fluid dynamics (CFD) state-of-the-art (SoA) assessment is presented for specified benchmark test cases and validation variables, based on the combination of solution and N-version verification and validation (V&V). Solution V&V estimates the systematic numerical and modeling errors/uncertainties. N-version verification estimates the random simulation uncertainty. N-version validation estimates the random absolute error uncertainty, which is combined with the experimental and systematic numerical uncertainties into the SoA uncertainties and then used to determine whether or not the individual codes/simulations and the mean code are N-version validated at the USoAi and USoA intervals, respectively. The scatter is due to differences in models and numerical methods, grid types, domains, boundary conditions, and other setup parameters. Differences between codes/simulations and implementations are due to myriad possibilities for modeling and numerical methods and their implementation as CFD codes and simulation applications. Industrial CFD codes are complex software with many user options such that even in solving the same application, different results may be obtained by different users, not necessarily due to user error but rather the variability arising from the selection of various models, numerical methods, and setup options. Examples are shown for ship hydrodynamics applications using results from the Seventh CFD Ship Hydrodynamics and Second Ship Maneuvering Prediction Workshops. The role and relationship of individual code solution V&V versus N-version V&V and SoA assessment are discussed.

Buoyancy Term Evolution in the Multi Relaxation Time Model of Lattice Boltzmann Method with Variable Thermal Conductivity Using a Modified Set of Boundary Conditions

During the last few years, a number of numerical boundary condition schemes have been used to study various aspects of the no-slip wall condition using the lattice Boltzmann method. In this paper, a modified boundary condition method is employed to simulate the no-slip wall condition in the presence of the body force term near the wall. These conditions are based on the idea of the bounce-back of the non-equilibrium distribution. The error associated with the modified model is smaller than those of other boundary condition models available in the literature. Additionally, various schemes to simulate body forces have been studied. Based on the numerical results, the model demonstrating minimum error has been reported. Finally, it has been shown that the present model is capable of simulating the effect of high nonlinearity in the heat transfer equation in the presence of a variable thermal conductivity. This has been accomplished by employing a multi relaxation time scheme to model a Rayleigh-Benard natural convection current in a 2-D domain with high Rayleigh numbers. Previous studies reported that the onset of oscillation occurs at Ra≈30,000 and Pr=6.0. By the modified boundary condition method which is used in this study, the oscillation is removed until at least Ra≈ 45,000 and Pr=6.0. The results show that applying scheme 3 for the current boundary condition yields the least amount of error compared to the semi-empirical correlation. The Rayleigh-Benard convection problem has been revisited in the presence of a variable thermal conductivity and the simulation results remain stable for flows with a large variation of thermal conductivity ( = 0.7) and Rayleigh numbers up to 1,000,000 and Pr=0.7.

Simulation of viscous flows by highly accurate aeroacoustic schemes on regular grids

Highly accurate finite-difference schemes that are widely used in computational aeroacoustics and referred to as dispersion-relation-preserving (DRP) schemes are adapted for the simulation of viscous flows. The main result consists in the construction and verification of numerical boundary conditions on a solid body, artificial boundaries, and on their interface. Calculations are performed for several test problems, including dissipation of the Lamb–Oseen vortex and decay of the Taylor–Green vortex in two-and three-dimensional cases and in infinite and semi-infinite (open-outlet) plane channels.

Comparative study between Conditional Moment Closure (CMC) and Conditional Source-term Estimation (CSE) applied to piloted jet flames

Conditional Moment Closure (CMC) and Conditional Source-term Estimation (CSE) are investigated in a direct side-by-side comparison of the Sandia flames. The objective of the present study is to determine the strengths and weaknesses of each modelling approach given the same initial conditions and computational set-up. The predictions from both CMC and CSE are compared to detailed experimental data. In case of Sandia flame D, the CMC and CSE turbulent flow and mixing fields are similar near the nozzle exit, in agreement with the experimental data, with some differences farther downstream. The CMC and CSE conditional mass fractions for the major species are in good agreement with the experimental data downstream of the nozzle for lean mixtures. For fuel rich mixtures, an underprediction of the conditional mass fractions of methane and corresponding overestimation of the conditional mass fraction of water are observed at some axial locations. The CMC and CSE conditional mass fractions of the minor species and conditional temperature reproduce the general characteristics of the experimental profiles. However, major differences are observed for Sandia flame E. The discrepancies are attributed to the use of RANS and the boundary conditions set in CMC and some approximations made in the chemistry tables in CSE. Favre-averaged profiles are comparable in CMC and CSE. The computational time for each model is investigated and CSE appears to be faster. Further discussion on some of the strengths and weaknesses of each combustion model is also presented. Overall, both CMC and CSE are shown to produce results of comparable quality given the same numerical schemes, mesh, and boundary conditions.

Using pseudo-spectral method on curved grids for SH-wave modeling of irregular free-surface

This paper uses curved grids in the context of a pseudo-spectral method to model 2-D SH-wave propagation in a medium with an irregular free-surface. A technique originally developed for computational fluid dynamics (CFD) is first used to generate curved grids following the irregular free-surface. Then the SH-wave equations in curved coordinates are derived, together with numerical boundary conditions at a free-surface are presented. Finally, a Fourier-Chebyshev pseudo-spectral method is used to simulate SH-wave propagation in curved coordinates and solutions in Cartesian coordinates are obtained. This numerical scheme is tested against the analytical solution for Lamb's problem in a uniform elastic half space with a sloping surface. An excellent agreement is found, which confirms the accuracy of the method present here. In addition, the scheme is applied to the model of topography with discontinuous derivative, and the results are compared with those obtained from the modeling on conventional curved grids by algebraic transform. It shows that the new scheme is more accurate than that on algebraic grids.

Effects of inflow conditions on mountainous/urban wind environment simulation

Inflow conditions play a key role in the Computational Fluid Dynamics (CFD) simulation of wind environment. Taking the micro wind climate of Hong Kong Kowloon Bay costal town as a research object, two kinds of widely used inflow condition determination methods are adopted to test their performances. One is to fit the velocity profile into the empirical (logarithmic/exponential) law, hereafter referred to as the Fitted Empirical Profile (FEP) method. The other is to interpolate the outflow velocities and turbulence properties from a pre-simulation of the upstream region, hereafter referred to as the Interpolated Multiscale Profile (IMP) method. The GIS data of this mountainous/ urban area are digitalized and simplified into the CFD geometry model. Computational treatments for numerical algorithms, domain size, grid systems and boundary conditions are carefully configured according to the published CFD Best Practice Guidelines (BPGs). By validating with one year of real scale wind measurement data from two meteorological stations, it is found that these two inflow conditions lead to considerably different results. Having less consideration for the blockage effects of terrain/buildings, the FEP method tends to predict higher wind speed. As more thermal effects are removed by increasing wind speed thresholds, the results of IMP method demonstrate an incremental agreement with the measurement data. Finally, the validated simulation results are applied to the spatial representativeness assessment of two meteorological stations. Both the point-to-surface consistency indicator and point-centered semivariance are employed. The results show that the meteorological stations show a good representation within a range of 400 m.

Evaluation of Powerhouse Cavern for the SachKhas Hydroelectric Project in Himachal, India

Evaluation of an underground powerhouse cavern’s stability is a challenging task and needs to be carried out carefully by taking care of its location, orientation and dimensioning. This article deals with the stability evaluation of a large underground powerhouse cavern, which is located at the toe of the valley side slope where the depth varies between 59m (minimum) and 70m (maximum). The planned powerhouse cavern has a dimension consisting 130m length, 23m wide and 48 m high. The manuscript evaluates the extent of pre-construction phase engineering geological investigations of the project, discusses on the selection of input parameters and carries out assessment on the displacement conditions at the cavern and also assesses the extent of yielded zone at the toe slope. Finally, recommendations are suggested on the location and orientation of the powerhouse cavern, uncertainties involved in numerical analysis and boundary conditions for 2D and 3D models under gravitational field stress.HYDRO Nepal JournalJournal of Water Energy and EnvironmentIssue: 20Page: 23-30

Testing the μ(I) granular rheology against experimental silo data

Industrial storage of granular material using silos is common, however, improved understanding of silo flow is needed. Various continuum models attempt to describe the velocity of dense granular flow in silos. Kinematic, and recently, stochastic models, based upon the diffusion of some quantity, perform well when there is a single orifice, and when the yield criterion is satisfied. However, if system stresses are insufficient to satisfy the yield criterion, or if there is a second orifice, these models fail to capture the entire flow behaviour. Advances in granular rheology have allowed a pressure dependent friction law to be defined which can capture the behaviour of granular silo flow including un-yielded zones, flow-rate independence of fill height, the Beverloo flow-rate, and various other phenomena. We performed silo discharge experiments in a flat bottomed planar silo with a single and two adjacent orifices, for two grain types. The velocity was measured using Particle Image Velocimetry. Results were compared to a mathematical model based on the μ (I) rheology which was shown to qualitatively capture the observed phenomena including plug-like zones where the yield criterion is not satisfied. These preliminary results strongly encourage future investigations into the effect of friction parameters and numerical boundary conditions.

蒸気タービンのブレード劣化効果に関する数値解析

Thermal power plants using steam turbines are required to be high efficient. However, various parts including nozzle guide vanes and rotor blades degrade through long time operations. To keep the high efficiency of the power plant, appropriate maintenances have to be done as necessary. It is important to understand aerodynamic characteristics in deteriorated steam turbines in order to realize the appropriate maintenance. In the present study, the aerodynamics of the deteriorated steam turbine is examined numerically. The nozzle and the rotor blade profiles of the 1st stage were obtained from a real steam turbine during the maintenance. The numerical boundary conditions were similar to the operation condition of the real thermal power plant. The numerical results show that the turbine power with the deteriorated blades is larger than that with the new blades because the mass flow of the main steam is larger. However, the turbine efficiency with the new blades is larger than that with the used blades.

The numerical boundary conditions of the wrapping pattern of thin insulation

The wrapping pattern of thin insulation is an important issue in cryogenic installations because it can significantly affect heat transport. The major objective of this study is to develop the numerical boundary conditions (BC) needed to model the wrapping pattern of thin insulation. An example of the practical application of the proposed BC includes the heat transfer of Rutherford NbTi cables immersed in superfluid helium (He II) across thin layers of electrical insulation. The proposed BC and a mathematical model of heat transfer in He II are implemented in the open source CFD toolbox OpenFOAM. The implemented mathematical model and the BC are compared with experiments. The study confirms that the thermal resistance of electrical insulation can be lowered by implementing the proper wrapping pattern. The proposed BC can be useful in the study of new patterns for wrapping schemes. Further possible improvements of the tool are indicated in the paper.

Can time-averaged flow boundary conditions be used to meet the clinical timeline for Fontan surgical planning?

Cardiovascular simulations have great potential as a clinical tool for planning and evaluating patient-specific treatment strategies for those suffering from congenital heart diseases, specifically Fontan patients. However, several bottlenecks have delayed wider deployment of the simulations for clinical use; the main obstacle is simulation cost. Currently, time-averaged clinical flow measurements are utilized as numerical boundary conditions (BCs) in order to reduce the computational power and time needed to offer surgical planning within a clinical time frame. Nevertheless, pulsatile blood flow is observed in vivo, and its significant impact on numerical simulations has been demonstrated. Therefore, it is imperative to carry out a comprehensive study analyzing the sensitivity of using time-averaged BCs. In this study, sensitivity is evaluated based on the discrepancies between hemodynamic metrics calculated using time-averaged and pulsatile BCs; smaller discrepancies indicate less sensitivity.The current study incorporates a comparison between 3D patient-specific CFD simulations using both the time-averaged and pulsatile BCs for 101 Fontan patients. The sensitivity analysis involves two clinically important hemodynamic metrics: hepatic flow distribution (HFD) and indexed power loss (iPL). Paired demographic group comparisons revealed that HFD sensitivity is significantly different between single and bilateral superior vena cava cohorts but no other demographic discrepancies were observed for HFD or iPL. Multivariate regression analyses show that the best predictors for sensitivity involve flow pulsatilities, time-averaged flow rates, and geometric characteristics of the Fontan connection. These predictors provide patient-specific guidelines to determine the effectiveness of analyzing patient-specific surgical options with time-averaged BCs within a clinical time frame.

Optimised prefactored compact schemes for linear wave propagation phenomena

A family of space- and time-optimised prefactored compact schemes are developed that minimise the computational cost for given levels of numerical error in wave propagation phenomena, with special reference to aerodynamic sound. This work extends the approach of Pirozzoli [1] to the MacCormack type prefactored compact high-order schemes developed by Hixon [2], in which their shorter Padé stencil from the prefactorisation leads to a simpler enforcement of numerical boundary conditions. An explicit low-storage multi-step Runge–Kutta integration advances the states in time. Theoretical predictions for spatial and temporal error bounds are derived for the cost-optimised schemes and compared against benchmark schemes of current use in computational aeroacoustic applications in terms of computational cost for a given relative numerical error value. One- and two-dimensional test cases are presented to examine the effectiveness of the cost-optimised schemes for practical flow computations. An effectiveness up to about 50% higher than the standard schemes is verified for the linear one-dimensional advection solver, which is a popular baseline solver kernel for computational physics problems. A substantial error reduction for a given cost is also obtained in the more complex case of a two-dimensional acoustic pulse propagation, provided the optimised schemes are made to operate close to their nominal design points.