Grid Arrangement Research Articles

Vortex induced vibrations of rectangular cylinders arranged on a grid

A grid arrangement of hundred rectangular cylinders fixed to the facade of a house generates strong and disturbing mono-harmonic noise. The cross-flow vibration of the rectangular cylinders is identified as the origin of the noise. The present article proposes a complete investigation of the Vortex Induced Vibration (VIV) combined with a grid effect. It is based on in situ measurements, numerical (finite elements and Computational Fluid Dynamics (CFD)) and extensive wind tunnel modelling. A comparison between unsteady pressure tap measurements and CFD results allow to understand the vortex shedding process and synchronization type depending on the wind incidence and spacing of the cylinders. On the basis of this multi-approaches parametric investigation, a deep understanding of the VIV-grid phenomenon enables to propose two mitigation techniques. These techniques are tested and their effectiveness is reported in terms of vibration amplitude and acoustic intensity.

Numerical investigation of complete evaporation process inside porous evaporator using staggered and non-staggered grid arrangements

The complete evaporation process inside an asymmetrically heated porous channel, under steady-state condition, has been numerically investigated in this article, based on the modified enthalpy formulation along with the assumption of Local Thermal Non-Equilibrium (LTNE). The governing equations have been discretised using finite volume method on both staggered and non-staggered grid arrangements and solved iteratively in a SIMPLE-like manner. All simulations have been carried out by applying the proposed smoothing algorithm for the effective diffusion coefficient in order to avoid the non-physical jump in the predicted temperature distributions. The performance of staggered and non-staggered grid layouts have been compared only on orthogonal coordinates for various parameters and the results show that the accuracy and effectiveness of the non-staggered and staggered grid layouts are identical. Different models for the partitioning of the wall heat flux have no influence on the total evaporated volume fraction. Effects of various parameters on the temperature and liquid saturation distributions have been carefully investigated, which clearly indicate that imposed heat flux, Reynolds number, Darcy number and thermal conductivity of the solid phase strongly influence the initiation and termination of phase change process, whereas the porosity has only a minor impact. Therefore, operating conditions and properties of porous media are required to be properly designed in order to achieve the desired objective. In addition, the results obtained using the modified h- and H-formulations have been compared and excellent agreement have been observed. It has been found that the modified h-formulation requires considerably less computation time as compared to that for the H-formulation and hence the method is strongly recommended for the future use. Nevertheless, it should now be extended in order to accommodate the multi-dimensional complex geometries that require the employment of curvilinear coordinates using non-staggered grid layout.

Chip-to-Chip Switched Beam 60 GHz Circular Patch Planar Antenna Array and Pattern Considerations

A 60 GHz switched beam chip-to-chip antenna array is introduced. The array consists of four center fed circular patch elements with side vias in a $2{\times} 2$ grid arrangement forming a planar array. The array is designed to fit on a typical multicore chip for reconfigurable interchip wireless communication. The array main beam is switched by changing the interelement phase shifts in the azimuth plane. The switching of the main beam is analyzed and verified through full-wave simulation. The design presented is an improvement over a previous design of a two-element antenna array. The Friis transmission equation with polarization components taken into account is used to model the interchip wireless link. To verify the model, a transmission coefficient measurement is made between a pair of the two-element arrays separated by a 10 mm distance. Both simulated and measured radiation patterns of the two-element array are presented for use in the Friis equation to calculate the transmission coefficients. Full-wave simulation of the array pair is also performed. The calculated results obtained from the Friis model agree well with both the measured and full-wave simulation results. The Friis model is used to calculate both signal and interference levels.

Energy Storage by Melting Commercial Change Phase Materials in Hexagonal-Shaped Heat Exchangers

A two-dimensional melting of a technical-grade phase-change material is modeled. The phase-change material is placed in the annular space formed by an outer regular hexagonal tube and an inner tube. A nonorthogonal boundary fitted coordinate method is implemented on a staggered grid arrangement. The mushy region of the impure phase-change material has been accommodated through the enthalpy-porosity scheme. A set of parametric studies is carried out. Selected results are presented as a function of time for the velocity and temperature fields, the cumulatively stored energy, the total melt fraction, and the average Nusselt number on the inner tube. The oblate-shaped inner tube results in the highest melting rate and stores the maximum energy among the studied units irrespective of the shape and vertical position of the inner tube. Among the three vertical positions of the inner circular tube, when the center of the inner tube is placed at one-third height from the base of the outer tube, it shows the greatest thermal efficiency, and the worst performance is obtained for the upper position of the inner tube at the two-thirds height of the outer tube. With the increase in the Rayleigh number (wall temperature), the amount of energy storage is enhanced.

The effects of laser patterning 10CeTZP-Al2O3 nanocomposite disc surfaces: Osseous differentiation and cellular arrangement in vitro

Customized square grid arrangements of different groove depths (1.0, 1.5 and 3.0 µm) and separations (10 and 30 µm) were successfully laser patterned, using a nanosecond pulsed fibre laser, on the surface of 10 mol% ceria-stabilized zirconia and alumina (10CeTZP-Al2O3) nanocomposite discs (diameter: 10 mm; thickness: 1.5 mm). The patterned surfaces and the in vitro biological response of osteoblasts (SAOS-2) towards them were thoroughly analysed. In terms of composition, the laser treatment was found to cause superficial monoclinic-tetragonal zirconia phase transformation and alumina evaporation. In vitro, the most effective grid configuration for osseous differentiation was found to be 1.5 µm groove depth and 10 µm groove separation, and confocal microscopy revealed that the cells show a tendency to be sorted as groove depth increases. It is thought that custom-made patterns could be produced to guide cell attachment in vivo, which could favour implant integration and reduce healing time.

Multiple grid arrangement improves ligand docking with unknown binding sites: Application to the inverse docking problem

The identification of comprehensive drug–target interactions is important in drug discovery. Although numerous computational methods have been developed over the years, a gold standard technique has not been established. Computational ligand docking and structure-based drug design allow researchers to predict the binding affinity between a compound and a target protein, and thus, they are often used to virtually screen compound libraries. In addition, docking techniques have also been applied to the virtual screening of target proteins (inverse docking) to predict target proteins of a drug candidate. Nevertheless, a more accurate docking method is currently required. In this study, we proposed a method in which a predicted ligand-binding site is covered by multiple grids, termed multiple grid arrangement. Notably, multiple grid arrangement facilitates the conformational search for a grid-based ligand docking software and can be applied to the state-of-the-art commercial docking software Glide (Schrödinger, LLC). We validated the proposed method by re-docking with the Astex diverse benchmark dataset and blind binding site situations, which improved the correct prediction rate of the top scoring docking pose from 27.1% to 34.1%; however, only a slight improvement in target prediction accuracy was observed with inverse docking scenarios. These findings highlight the limitations and challenges of current scoring functions and the need for more accurate docking methods. The proposed multiple grid arrangement method was implemented in Glide by modifying a cross-docking script for Glide, xglide.py. The script of our method is freely available online at http://www.bi.cs.titech.ac.jp/mga_glide/.

Influence of jet discharge velocity profile on CFD simulation of pump-around jet mixing tank

The present paper shows the effect of jet discharge velocity profile (or jet nozzle configuration) on CFD simulation of an open 45° inclined side entry pump-around jet mixing tank. The CFD model was carefully developed by using appropriate grid arrangement, boundary conditions, and numerical methods. The two different jet discharge velocity profiles, including top hat and fully developed profiles, were simulated by using the inlet mass flow rate of about 0.22 kg·s-1. The overall mixing times and normalized concentration profiles predicted by two different jet discharge velocity profiles were compared with the previous reliable experimental data. The results revealed that the different jet discharge velocity profiles resulted in different jet flow and mixing patterns inside the vessels.

Influence of grid distribution on CFD model of compressible flow inside the primary nozzle and mixing chamber used in refrigeration application

In this study, the influence of grid distribution on CFD model of the primary nozzle and mixing chamber used in refrigeration application was primarily investigated. The only one geometry of primary nozzle and mixing chamber was modeled. The two different grid distributions, fine near-wall grid and regular grid with the identical total grid number, were simulated to investigate the flow phenomena inside the considered system. The appropriate boundary conditions and numerical methods were carefully employed. The simulated entrainment ratios obtained by two different grid arrangements were validated by comparing with the reliable experimental data. The results revealed that the Mach number distributions of these models were different. Further, the outlet total pressure predicted by fine near-wall grid was about 1.3% higher than that obtained by regular grid.

A suitable k-epsilon model for CFD simulation of pump-around jet mixing tank with moderate jet reynolds number

This paper presents the appropriate turbulence model for predicting the overall mixing time inside an open 45° inclined side entry pump-around jet mixing tank with moderate jet Reynolds number of about 17,515. The model was carefully developed by using appropriate hexahedral grid arrangement and proper numerical methods. The two different k-epsilon turbulence models, including realizable k-epsilon model and low Reynolds number k-epsilon model, were simulated. The overall mixing times predicted by these turbulence models were compared with the previous data reported by Patwardhan (Chem. Eng. Sci. 57 (2002) 1307-1318). The results revealed that the low Reynolds number k-epsilon model was a suitable model for predicting the overall mixing time of jet mixing tank with moderate jet Reynolds number.

A dual grid, dual level set based cut cell immersed boundary approach for simulation of multi-phase flow

A numerical methodology based on dual grid dual level set function is presented for simulating 2D multiphase flows through complex geometries on a non-body fitted Cartesian computational grid. A Cut Cell based immersed boundary method (IBM) is used to sharply resolve complex geometries. The cut cells near the immersed boundary are identified using a fictitious level set function. The governing equations are discretized using the finite volume method (FVM) on a m × n staggered grid. The dynamics of fluid-fluid interface is tracked by an other level set function defined on dual grid (2m × 2n). The use of dual grid arrangement for fictitious level set function results in an accurate calculation of diffusion and advection fluxes at the cut cell near the immersed boundary. A module by module validation of the developed numerical methodology is carried out with several test cases. Two single phase flow problems corresponds to Poiseuille flow and flow through a convergent-divergent section while the two multiphase problems selected are the standard Young’s Laplace law test – semicircular fluid rod on a horizontal surface – and the bubble rise phenomenon in an inclined channel. The obtained results show an excellent agreement with those derived analytically or taken from literature. Furthermore, the performance study carried out on the present model shows that the method is between first and second order accurate.

Accounting for biotic spatial variability in fields: Case of resistance screening against sunflower Verticillium wilt.

In breeding for disease resistance, the magnitude of the genetic response is difficult to appreciate because of environmental stresses that interact with the plant genotype. We discuss herein the fundamental problems in breeding for disease resistance with the aim being to better understand the interactions between plant, pathogen, and spatial patterns. The goal of this study is to fine tune breeding decisions by incorporating spatial patterns of such biotic factors into the definition of disease-occurrence probability. We use a preexisting statistics method based on geostatistics for a descriptive analysis of biotic factors for trial quality control. The plant-population structure used for spatial-pattern analysis consists of two F1-hybrid cultivars, defined as symptomatic and asymptomatic controls with respect to the studied pathogen. The controls are inserted at specific locations to establish a grid arrangement over the field that include the F1-hybrid cultivars under evaluation. We characterize the spatial structure of the pathogen population and of the general plant environment—with undetermined but present abiotic constraints—not by using direct notation such as flower time or rainfall but by using plant behavior (i.e., leaf symptom severity, indirect notation). The analysis indicates areas with higher or lower risk of disease and reveals a correlation between the symptomatic control and the effective level of disease for sunflowers. This result suggests that the pathogen and/or abiotic components are major factors in determining the probability that a plant develops the disease, which could lead to a misinterpretation of plant resistance.

Verification and validation of numerical solutions of two-dimensional reactive flow in rocket engine nozzles

Two-dimensional mathematical models for gaseous H2/O2 reactive flows are solved for two geometries: a conical and a parabolic one. Five different physical models are studied: two one-species and three multi-species models (frozen, equilibrium and non-equilibrium flows). In the mathematical model, temperature is used as unknown in the energy equation and velocity is obtained for all speed flows. For all analyses, a non-orthogonal finite volume code was implemented, taking into account first (UDS) and second (CDS) order interpolation schemes and co-located grid arrangement. Model predictions of the pressure distribution and Mach number in the nozzle with a conical geometry, calculated using a CDS scheme, were found to agree well with experimental results. For both geometries, numerical results for apparent orders of convergence agreed well with the asymptotic (expected) ones for one-species flows. Some other analyses were provided for mixture of gases flows; in this case, for frozen flow, the apparent order values tend to the asymptotic ones in all cases; for local equilibrium flow, the use of CDS degenerated the apparent order to unity; this fact can be associated to the use of UDS interpolation scheme in the source term of the energy equation. Numerical solutions, including their error estimates, are provided for UDS and CDS schemes. Their analysis shows that global variables of interest (such as thrust and specific impulse) are less affected by the chosen physical model than are local variables of interest (such as the temperature at the symmetry line).

A dual grid method for the compressible two-fluid model which combines robust flux splitting methodology with high-resolution capturing of incompressible dynamics

The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions). Dynamically simulating such flows requires resolution of acoustic and hydraulic waves existing at vastly different spatial and temporal scales. If simulated on the same numerical grid, the need for accuracy in hydraulic waves will necessitate an exaggerated resolution of acoustic waves. Likewise, time steps restricted by the speed of sound are small compared to the time scales active in hydraulic waves. This constitutes a waste of computational potential. The method proposed herein decouples the hydraulic and acoustic scales, greatly improving computational efficiency.The proposed dual grid method solves a four-equation compressible two-fluid model on a principal grid which robustly accounts for the pressure evolution and conserves mass and momentum. An incompressible two-equation model is at the same time solved on a finer grid, resolving the details of the hydraulic evolution. Information from both model formulations is coupled through the terms of the governing transport equations, providing consistency between the grids. Accurate and finely resolved schemes can then be employed for the incompressible two-fluid model without suffering from the time and stability restrictions otherwise enforced by acoustic waves. At the same time, the Hybrid Central-Upwind flux splitting scheme of Evje and Flåtten (2005a) allows for an explicit and numerically robust treatment of the acoustic waves without losing hydraulic accuracy.The dual grid method is tested against four dissimilar problems: A shock tube problem, the water faucet problem, a surge wave and pressure wave problem and a roll-wave case. In all problems, the proposed scheme provided significant increases in computational efficiency and accuracy as compared with a single grid arrangement.

Dynamic simulation of a coated microbubble in an unbounded flow: response to a step change in pressure

A numerical method is developed to study the dynamic behaviour of an encapsulated bubble when the viscous forces of the surrounding liquid are accounted for. The continuity and Navier–Stokes equations are solved for the liquid, whereas the coating is described as a viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed for the spatial discretization of the flow domain surrounding the bubble, with the standard staggered grid arrangement that uses biquadratic and bilinear Lagrangian basis functions for the velocity and pressure in the liquid, respectively, coupled with a superparametric scheme with $B$-cubic splines as basis functions pertaining to the location of the interface. The spine method and the elliptic mesh generation technique are used for updating the mesh points in the interior of the flow domain as the shape of the interface evolves with time, with the latter being distinctly superior in capturing severely distorted shapes. The stabilizing effect of the liquid viscosity is demonstrated, as it alters the amplitude of the disturbance for which a bubble deforms and/or collapses. For a step change in the far-field pressure the dynamic evolution of the microbubble is captured until a static equilibrium is achieved. Static shapes that are significantly compressed are captured in the post-buckling regime, leading to symmetric or asymmetric shapes, depending on the relative dilatation to bending stiffness ratio. As the external overpressure increases, shapes corresponding to all the solution families that were captured evolve to exhibit contact as the two poles approach each other. Shell viscosity prevents jet formation by relaxing compressive stresses and bending moments around the indentation generated at the poles due to shell buckling. This behaviour is conjectured to be the inception process leading to static shapes with contact regions.

An absorbing boundary condition for free surface water waves

In this paper, the use of an absorbing boundary condition (ABC) is investigated for the numerical simulation of free surface water waves. An enhanced type of an ABC based on the first- and second-order Higdon boundary conditions is presented. The numerical implementation of the ABC using a staggered grid arrangement is explained in detail. Numerical examples are provided to demonstrate the performance of the proposed boundary conditions.

Effects of Uniform Heat Flux and Velocity-Slip Conditions at Interface on Heat Transfer Phenomena of Smooth Spheres in Newtonian Fluids

The effects of the uniform heat flux and a linear velocity-slip on the heat transfer phenomena of spheres in Newtonian fluids are numerically investigated using semi-implicit marker and cell (SMAC) method implemented on a staggered grid arrangement in spherical coordinates. The solver is thoroughly benchmarked through domain independence, grid independence, and comparison with literature. Further extensive results are obtained in the range of conditions as: Reynolds number, Re = 0.1–200; Prandtl number, Pr = 1–100; and dimensionless slip number, λ = 0.01–100. The results are presented and discussed such that the isotherm contours and the local and average Nusselt numbers of isoflux spheres with velocity-slip at the interface are compared with their isothermal spheres counterparts under identical conditions. Briefly, the results indicate that the average Nusselt numbers of isoflux spheres are large compared to those of isothermal spheres under identical conditions. Finally, an empirical correlation is developed for the average Nusselt numbers of the spheres in Newtonian fluids with velocity-slip and the uniform heat flux conditions along the fluid–solid sphere interface.

Numerical investigation of nanofluid turbulent flow in a wavy channel with different wavelengths, amplitudes & phase lag

Two dimensional incompressible turbulent nanofluid flow in a sinusoidal wavy channel is numerically investigated. Finite volume method and Rhie and Chow interpolation in a collocated grid arrangement are used for solving governing equations. The effects of the volume fraction of nanoparticles, Reynolds number, phase lag, frequency and amplitude of the wavy walls on the heat transfer rate are studied. The present work showed good agreement with existing experimental and numerical results. Increasing the frequency and amplitude of the wave and nanoparticles volume fraction has great effect on heat transfer rate.

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.

Computational Fluid Dynamics Study on Forced Convective Heat Transfer Phenomena of Spheres in Power-law Liquids with Velocity Slip at the Interface

ABSTRACTNumerical results on combined effects of the slip velocity, power-law fluid behavior index, Reynolds number, and Prandtl number on the forced convective heat transfer characteristics of single spheres in power-law liquids with velocity slip at the fluid-solid interface are reported on the basis of computational fluid dynamics approach. The governing conservation equations of the momentum and energy along with the appropriate boundary conditions are nondimensionalized using appropriate scaling parameters. These dimensionless equations are solved by a segregated approach using a finite difference method based simplified marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates. The detailed domain and grid independence studies along with appropriate validations are carried out to establish reliability and accuracy of the solver. Further extensive new results obtained in the range of conditions as: Reynolds number, 0.1–200; dimensionless slip number, 0.01–100; power-law index, 0.5–1.6; and Prandtl number, 1–100. The effects of these dimensionless parameters on the isotherm contours and local and average Nusselt numbers are thoroughly delineated. Finally, on the basis of present numerical results, an empirical correlation for the average Nusselt numbers of single spheres in power-law liquids with velocity slip at the interface is proposed.

Effect of velocity slip on settling of assemblages of spherical particles in power-law liquids at low to moderate Reynolds numbers

Combined effects of the velocity slip, volume fraction of spherical particles and power-law behavior index on the flow and drag phenomena of assemblages of spherical particles in power-law liquids with velocity slip at the interface are numerically investigated. The effects of varying degrees of the velocity slip at interfaces of the fluid–solid particles are incorporated in the solver by making use of a linear slip velocity model. Further, the assemblages of particles are mathematically simplified as clusters of mono-size spherical particles equidistant from each other and the effect of neighboring particles on the target particle nullified at midpoint between the centers of two neighboring spherical particles. Within the combination of these two models, the dimensionless governing conservation equations of mass and momentum for power-law fluids are solved using a simplified marker and cell method in spherical coordinates on a staggered grid arrangement. The convective and non-Newtonian terms of the momentum equation are discretized using quadratic upstream interpolation for convective kinematics scheme and a second-order central differencing scheme, respectively. The presented numerical solver is extensively tested for its reliability via routes of the grid independence and validation with the existing literature counterparts. Furthermore, extensive new results were obtained in the range of dimensionless parameters such as the holdup of spheres, \(\Phi = 0.1{-}0.5\); dimensionless slip number, \(\lambda = 0.01{-}100\); Reynolds number, \(Re = 0.1{-}200\); and power-law behavior index, \(n = 0.6{-}1.6\). Briefly, some results indicate that the drag coefficients of assemblages of spheres decrease with the decreasing slip number and/or decreasing power-law index and/or with the decreasing holdup of the spheres.