Calculation Of Velocity Field Research Articles

Comparison of c‐space and p‐space particle tracing schemes on high‐performance computers: accuracy and performance

AbstractThe present paper presents a comparison of four different particle tracing schemes which were integrated into a parallel multiblock flow simulation program within the frame of a co‐visualization approach. One p‐space and three different c‐space particle tracing schemes are described in detail. With respect to application on high‐performance computers, parallelization and vectorization of the particle tracing schemes are discussed. The accuracy and the performance of the particle tracing schemes are analyzed extensively on the basis of several test cases. The accuracy with respect to an analytically prescribed and a numerically calculated velocity field is investigated, the latter in order to take the contribution of the flow solver's error to the overall error of the particle traces into account. Performance measurements on both scalar and vector computers are discussed. With respect to practical CFD applications and the required performance especially on vector computers, a newly developed, improved c‐space scheme is shown to be comparable to or better than the investigated p‐space scheme. According to accuracy the new c‐space scheme is considerably more advantageous than traditional c‐space methods. Finally, an application to a direct numerical simulation of a turbulent channel flow is presented. Copyright © 2002 John Wiley & Sons, Ltd.

선미 후류에서 작동하는 혼타의 압력분포에 관한 연구

Hull-propeller-rudder interactions are studied by the iterative computational procedures. Hull effects on the propeller are reflected through the effective velocities computed by the vortex ring method which used the measured nominal wake as input data. A potential based panel method has been developed to solve the propeller-rudder interactions using the obtained effective velocities. Steady flow characteristics around the rudder surface can be obtained by computing the induced velocities on the rudder by the propeller and vice versa are computed by the iterative manner until the converged solutions are obtained. Flow characteristics around the propeller and the rudder are measured by Laser Doppler Velocimetry(L.D.V.) in large cavitation tunnel at Samsung Heavy industries. The gap flow model is adopted to solve the characteristics of the horn rudder. Numerical results are compared with the experimental values and the computed velocity fields and pressure distributions with rudder angle on the horn rudder surface show good agreement with measured ones in large cavitation tunnel.

Numerical Prediction of Dispersion Characteristics in an Urban Area Based on Grid Refinement and Various Turbulence Models

A detailed simulation of the Goettinger Strasse pollutant dispersion problem is performed using the CFD code CFX-TASCflow for different wind directions. Two turbulence models, the k − e and the RSM are adopted on three grid refinement levels. Besides the typical reference grid imple- mented by the TRAPOS group, two different grid resolutions are introduced. The first refinement is in the whole street canyon region on the x−y level, while the second one is local in all three directions. Validation of all involved computational schemes is performed based on relative available experimental data. The computed velocity fields and concentration contours imply that the typical reference grid is a suitable choice for the velocity fields, while local grid refinement in all three directions in a small region containing the receptor is required to upgrade the pollutant concentration results with modest additional computational effort. Finally the RSM model resulted in smaller concentration levels. The k − e model compared to the RSM seems a more appropriate choice to solve this particular problem.

Fluid Mechanics on Triangular Sediment Oxygen Demand Chamber

Benthal respiration rates are often measured in situ by a sediment oxygen demand (SOD) chamber in which a continuous flow is generated above the sediment. The steady three-dimensional turbulent flow field inside a triangular SOD chamber (previously used in field investigations) is computed using the renormalization group (RNG) k–e model on an unstructured tetrahedral mesh. The numerical predictions reveal a highly complicated flow characterized by (1) a jet flow near the level of the inlet, with strong downflow near the outlet end; (2) significant reverse bottom currents; and (3) strong secondary circulations in the triangular cross section. Good mixing is achieved, with mean near-bottom velocities about 10 times greater than that determined from the inflow discharge and cross-sectional area. The computed velocity field is well supported by laboratory velocity measurements using laser-Doppler anemometry (LDA). The implications on SOD chamber design are also discussed with reference to computed flow fields...

Simulation Opportunities by a Three-dimensional Calculation of Injection Moulding based on the Finite Element Method

Abstract The simulation of injection moulding is essential to meet quality requirements and to increase the efficiency of the design process. In this paper a 3D-finite element model for the simulation of injection moulding is presented. The model's capability comprises the calculation of velocity, pressure and temperature fields as well as the prediction of the flow front position. The numerical approach is mainly based on the Galerkin formulation. Special emphasis is placed on the handling of polymer compressibility in order to enable a realistic simulation of the packing phase. The numerical efficiency has been largely enhanced through the employment of an automatic time step control. In order to demonstrate the code's capabilities and outline advantages and disadvantages over other simulation systems, the calculation results are compared to experimental data and to results obtained from other numerical models.

Extensive validation of computed laminar flow in a stirred tank with three Rushton turbines

AbstractHigh‐resolution CFD results, supplemented by extensive experimental validation, are presented for Newtonian laminar flow fields in a stirred tank equipped with three Rushton turbines. Flow fields are computed using the ORCA software suite for Reynolds numbers ranging from 20 to 200 with an unstructured tetrahedral mesh containing roughly 2 million tetrahedra. Each of the flow solutions takes less than 8 h to converge when running in parallel on eight desktop workstations. Excellent agreement is obtained between computed velocity fields and planar velocity vectors obtained using particle image velocimetry. Planar laser‐induced fluorescence was used to expose persistent poor‐mixing regions, in excellent agreement with numerical results. The computational results used illustrate strong flow compartmentalization and significant spatial heterogeneity with respect to local deformation rates within the vessel.

Vortex surface method: some numerical problems of the potential calculation

AbstractThe singularities method is used to analyze the flow around an isolated profile or through a plane cascade. In this paper, a numerical study has been developed in order to discuss the accuracy of solutions. The aims of this study are summarized as follows: (1) to expose the elements that influence the method—precision in the geometrical profile definition, trailing‐edge geometry, smoothing problems, number of discretization points, precision of calculation, etc.; (2) to provide an accurate solution for these different problems. For example, some profiles, obtained by the Joukowski transformation, present, in spite of an analytical definition, a crossing of the suction and pressure sides at the trailing edge. This crossing causes a serious error in the velocity field computation. A new procedure to solve this problem is presented. Copyright © 2001 John Wiley & Sons, Ltd.

Temperature-driven fluid flow in porous media using a mixed finite element method and a finite volume method

We present a numerical scheme for the computation of conservative fluid velocity, pressure and temperature fields in a porous medium. For the velocity and pressure we use the primal–dual mixed finite element method of Trujillo and Thomas while for the temperature we use a cell-centered finite volume method. The motivation for this choice of discretization is to compute accurate conservative quantities. Since the variant of the mixed finite element method we use is not commonly used, the numerical schemes are presented in detail. We sketch the computational details and present numerical experiments that justify the accuracy predicted by the theory.

Qualitative vision for the guidance of legged robots in unstructured environments

Visual procedures especially tailored to the constraints and requirements of a legged robot are presented. They work for an uncalibrated camera, with pan and zoom, freely moving towards a stationary target in an unstructured environment that may contain independently moving objects. The goal is to dynamically analyse the image sequence in order to extract information about the robot motion, the target position and the environment structure. The development is based on the deformations of an active contour fitted to the target. Experimental results confirm that the proposed approach constitutes a promising alternative to the prevailing trend based on the costly computation of displacement or velocity fields.

Optimum taphole length and flow induced stresses

The flow induced shear stress on the wall of a blast furnace hearth has been computed by solving the Navier–Stokes and Darcy flow equations in the hearth numerically. The Navier–Stokes equations were used to compute the flow field in the coke free zone, while the Darcy flow equation was used for the flow of liquid metal in the coke packed porous zone (known as the deadman). The computed velocity field was utilised to determine the shear stresses on the side wall of the hearth for various lengths of taphole and different types of deadman when the hearth is filled with liquid metal. It was found that the peak stress on the wall of the blast furnace reduces significantly as the length of the taphole increases. However, the peak stress again increases above a certain length of taphole, for a floating deadman, indicating an optimum taphole length to be used to minimise the fluid induced shear stress. For the case of a sitting deadman the increase of peak stress with taphole length, above the optimum length, is marginal, but it was possible to determine a clearly defined optimum taphole length. For the case of no deadman the peak stress was found to decrease continuously with increase in taphole length; hence, an optimum taphole length could not be determined. It was also found that the location of the maximum equivalent shear stress shifts in the increasing direction of θ almost linearly with an increase in taphole length.

A calculation of gaseous slip velocity and microscale flow fields from a molecular-continuum matching analysis

Small-scale gaseous flows cannot be described as a continuum, especially at boundaries where molecular interactions of the fluid with a wall takes place. Work has been done to match molecular dynamics simulations near a wall to continuum flow away from a wall [S.T. O'Connel, P.A. Thompson, Phys. Rev. E 52, R5792.2.]. Microscale flow fields have also been calculated by solving the Navier–Stokes equations with a Maxwellian slip boundary condition [E.B. Arkilic et al., J. Microelectromech. Systems 6 (2) (1997) 167–178.]. This paper, in two dimensions, calculates microscale flow fields and slip velocities ab initio by matching, with a novel computer algorithm, analysis of molecular interaction with boundaries to continuum flow away from the boundaries for wall-velocity-step-jumped-time-varying Poiseuille flow. Slip velocities are also calculated in the steady-state case for Poiseuille flow. Drift velocities approximately one mean free path from the walls are found to be between 20–30% of the maximum flow field velocity along the length of the channel for transient analysis of helium gas and 5–36% of the maximum velocity for steady-state analysis of various gases. These ratios are consistent with past calculations of flow fields calculated with a prescribed Maxwellian slip boundary condition (E.B. Arkilic et al., 1997.).

SAAREMAA DEEP HARBOUR LAYOUT DESIGN AND COMPUTER SIMULATION OF THE WAVE CLIMATE AND SEDIMENT TRANSPORT

The layouts for the three proposed sites for the Saaremaa Island deep harbour were designed at Corson Consulting. The layouts were designed on the basis of geological, hydro- meteorological, and wave and current conditions. Emphasis was given to the impact of the future harbour on nature. The layouts were used as the basis for wave and velocity field calculations using program MIKE 21. Wave and velocity characteristics were determined for wind directions that are significant for the harbour sites. SandCalc 2.0 was applied for calculation of wave generated shear stresses on the bottom of the seabed around the harbour sites taking into account the local bed characteristics. The calculated shear stresses were used for the analysis of the sediment processes. The results indicate that Suuriku-Kuriku site is the most favourable site for the harbour. The proposed layout protects satisfactorily the harbour basin from most wind directions. The movement of the alluvial material into the harbour basin does not generate problems due to the characteristics of the seabed. Calculation shows that at Suuriku-Kuriku less dredging work is needed than at the other sites.

Coupled Groundwater Flow and Transport in Porous Media. A Conservative or Non-conservative Form?

A new formulation for the modeling of density coupled flow and transport in porous media is presented. This formulation is based on the development of the mass balance equation by using the conservative form. The system of equations obtained by coupling the flow and transport equations using a state equation is solved by a combination of the mixed hybrid finite element method (MHFEM) and the discontinuous finite element method (DFEM). The former is applied in order to solve the flow equation and the dispersive part of the transport equation, whilst the latter is used to solve the advective part of the transport equation. Although the advantages of the MHFEM are known (efficiency calculation of velocity field and continuity of fluxes from one element to an adjacent one), its application in a classical development form (volumetric fluxes as unknowns) leads to the non-conservative version of the mass balance equation. The associated matrix of the system of equations obtained by hybridization is positive definite but non-symmetrical. By using a new approach (mass fluxes as unknowns) the conservative form of the continuity equation is preserved and the associated matrix of the system of equations obtained by hybridization becomes symmetrical. When applied to Elder's problem involving a strong density contrast, this new approach, with a lower calculation cost, leads to similar or identical results to those found in the specialized literature. The comparison between the conservative and non-conservative formulations solved with the same MHFEM and DFEM combination emphasizes the rigor and the pertinence of this new approach. Furthermore, we show the existence of a limit refinement defining the stability of the numerical solution for Elder's problem.

Simulation of a premixed turbulent flame with the discrete vortex method

The behaviour of a premixed turbulent flame is numerically studied in this paper. The numerical model is based on solving turbulent flow field by the discrete vortex method. The flame is considered to be of zero thickness boundary which separates burnt and unburnt regions with different constant density and propagates into the fresh mixture at a local curvature-dependent flame speed. The flame front is located by means of level-set algorithm. The flow turbulence is simulated through the unsteady vortex-shedding mechanism. The computed velocity fields, turbulence scalar statistics as well as flame brush thickness for the turbulent V-flame are well comparable to experimental results. The computed Reynolds stresses in the flame brush region based on unconditioned velocities are substantial, but the two conditioned Reynolds stresses are negligible. These results show that the intermittency effect is a major influence on turbulent statistics in premixed flame and should require careful consideration in numerical models. Copyright © 2000 John Wiley & Sons, Ltd.

Extending the strain path method analogy for modelling penetrometer installation

The Strain Path Method (SPM) is an approximate framework for simulating the disturbance caused by piles or penetrometers in soil. The key conceptual assumption of the SPM is that the deformation and strain fields caused during these penetration processes are strongly kinematically constrained (especially during undrained penetration of clays) and can be estimated independently from the actual constitutive properties of the surrounding soil. Previous applications of SPM have estimated strain fields for a variety of penetrometer geometries using velocity fields of ideal inviscid fluids. This paper refines the strain field for penetrometers with 60° conical tips using numerically computed velocity fields in viscous fluids with a variety of boundary conditions imposed on the penetrometer shaft. Following a parametric study, a set of flow conditions is selected which provides a best fit between computed soil deformations and physical displacement measurements made in three separate experiments. The approach is simple and rapid and, while highlighting some of the inaccuracies associated with the existing SPM solution, may also be used for comparative purposes to assist the development of other approaches to the deep penetration problem.

Fluid Mechanics of Triangular Sediment Oxygen Demand Chamber

Benthal respiration rates are often measured in situ by a sediment oxygen demand (SOD) chamber in which a continuous flow is generated above the sediment. The steady three-dimensional turbulent flow field inside a triangular SOD chamber (previously used in field investigations) is computed using the renormalization group (RNG) k–e model on an unstructured tetrahedral mesh. The numerical predictions reveal a highly complicated flow characterized by (1) a jet flow near the level of the inlet, with strong downflow near the outlet end; (2) significant reverse bottom currents; and (3) strong secondary circulations in the triangular cross section. Good mixing is achieved, with mean near-bottom velocities about 10 times greater than that determined from the inflow discharge and cross-sectional area. The computed velocity field is well supported by laboratory velocity measurements using laser-Doppler anemometry (LDA). The implications on SOD chamber design are also discussed with reference to computed flow fields...

A CAD-based design parameterization for shape optimization of elastic solids

In this paper a CAD-based design sensitivity analysis (DSA) and optimization method using Pro/ENGINEER for shape design of structural components is presented. The CAD-based design model is critically important for multidisciplinary shape design optimization. Only when each discipline can compute the design sensitivity coefficients of the CAD-based design model, can a true multidisciplinary what-if study, trade-off analysis, and design optimization be carried out. The proposed method will allow the design engineer to compute design sensitivity coefficients of structural performance measures such. as stress and displacement, evaluated using existing finite element analysis (FEA) tools, both h- and p-versions, with respect to design variables defined in the parameterized CAD model. The proposed method consists of (i) a CAD-based design parameterization technique that ties the structural DSA and optimization to a CAD tool; (ii) a design velocity field computation that defines material point movement due to design change in CAD geometry, satisfies linearity and regularity requirements, and supports both hand p-version FEA meshed using existing mesh generators; and (iii) a design optimization method that supports structural geometric and finite element model updates in Pro/ENGINEER during the optimization process.

Numerical Stability Conditions in the Calculation of Potential Velocity Fields

Numerical Stability Conditions in the Calculation of Potential Velocity Fields

Numerical stability conditions in the calculation of potential velocity fields

Numerical stability conditions in the calculation of potential velocity fields

Boundary element method for internal axisymmetric flow

We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three‐dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.