Calculation Of Velocity Field Research Articles

A 3D numerical/experimental study on a stagnation flow of a polyisobutylene solution

A combined 3D numerical/experimental method for the evaluation of viscoelastic constitutive equations is described. The method is applied to a three-dimensional (3D) stagnation flow, which exhibits strong elongational deformations. A polyisobutylene solution is investigated. Laser Doppler anemometry and flow induced birefringence are used to measure pointwise velocities and linewise (in the depth of the flow cell) integrated stresses, respectively. The numerical simulations are decoupled: the 3D velocity field is derived from finite element calculations with the viscous Carreau model, whereafter the viscoelastic stresses are calculated with a four mode Giesekus and Phan-Thien–Tanner (PTT) model. The validity of this approach is checked by comparing the calculated and measured velocities. The optical FIB signal is calculated from the integrated stresses, using the small retardance approximation. The approach is first evaluated for two slit flows with different depth/height ratios (8:1 and 2:1). Calculated velocities and stresses show a good agreement with measurements. In the stagnation flow device, the calculated velocity field diverges from measured velocities at the higher Weissenberg-numbers, at all Weissenberg numbers both viscoelastic models predict much too low stresses near the stagnation line. A modification of the PTT model is proposed to improve the stress predictions in the elongational flow domain.

Computational modelling of heat⧹mass transfer near the LIQUID–SOLID interface during rapid solidification of binary metal alloys under laser treatment

This paper presents the results of an investigation into the problem of planar solid–liquid interface stability during rapid solidification of binary metal alloys under laser treatment. A new quantitative model is proposed. This model describes the self-organized development of stable spatially-periodic vortices in the melt near the solid–liquid interface due to concentration- (or thermal) capillary effects fn2 fn2 The basic idea of the feasibility of thermal-capillary convection at the liquid–solid interface belongs to Dr G. L. Tsarev (Physical-Technical Institute, Minsk, Belarus). together with effects due to the influence of normal concentration or temperature gradients directed from the interface towards the melt. These vortices give rise to a cellular structure at the solid–liquid interface of rapidly frozen melts. A computer code was developed to solve the set of second-order linear differential equations which describe heat and mass transfer at the liquid–solid interface. This model allows calculation of the liquid phase velocity field, the second component concentration field in the melt, as well as the temperature field in the liquid and solid phases near the solid–liquid interface at a given solidification rate.

Experimental and numerical characterization of viscous flow and mixing in an impinging jet contactor

AbstractThe laminar flow in an impinging jet contactor is examined as a first step toward the development of new technology for fast mixing of viscous fluids. The flow, velocity, and stretching fields in an impinging jet contactor are quantified for low Reynolds number flow using three‐dimensional numerical simulations and particle image velocimetry measurements. Computational and experimental velocity fields are in close agreement, as quantified by the velocity probability density functions. Two steady‐state flow regimes are found to exist: for jet Reynolds numbers (Rej) < 10, the jets do not impinge and the velocity field scales linearly with Reynolds number; for Rej > 10, the jets begin to impinge and recirculation regions form above and below the impingement point. The magnitude of the rate‐of‐strain tensor is calculated as a function of Rej. While areas of essentially zero stretching occupy most of the flow domain, very high rates of stretching occur at specific locations in the flow. The maximum and average rates of stretching in the contactor increase roughly linearly as a function of Reynolds number. Mixing simulations show that no mixing occurs for the steady flow in a symmetric‐jet contactor. However, mixing is improved substantially by a slight modification of the impinging jet geometry that disrupts geometric symmetry.

Groundwater pollution due to discharge of industrial effluents in Venkatapuram area, Visakhapatnam, Andhra Pradesh, India

Hindustan Polymers Limited was established in the Venkatapuram area in the northwestern part of Visakhapatnam urban agglomeration. Untreated industrial effluent from the plant is discharged with total dissolved solids concentrations reaching up to 6500 mg/l. The groundwater pollution was identified as early as 1981 and a hydrogeologic and water-quality database is available from 1981. The groundwater quality in the plant environs is found to be in the range of 3500–4500 mg/l. Major chemical constituents of industrial-waste waters consist of Na, Cl, and SO4. Some characteristic parameters of the aquifer were estimated. The available hydrogeologic and hydrologic data was analyzed to conceptualize the groundwater regime. A mathematical groundwater flow model was constructed to compute the hydraulic head at the center of finite-difference grid. The computed head distribution and effective porosity of the formations were used to calculate the groundwater flow velocity. The computed velocity field was ultimately used to prognose the pollutant migration in groundwater accounting for the advection and dispersion processes in the mass transport model and for determining the time-dependent pathlines of pollutant. Areal migration of pollutants from the source was predicted up to year 2002.

CONJUGATE HEAT TRANSFER OF A FINNED OVAL TUBE PART B: HEAT TRANSFER BEHAVIORS

Conjugate heat transfer in a high-performance finned oval lube heat exchanger element has been calculated for a thermally and hydrodynamically developing three-dimensional laminar flow. The influence of Reynolds number in the range 100–500 and of a Jin parameter Fi, the product of the dimensionless fin thickness and its thermal conductivity, on the heat transfer behavior have been studied. In part I, the computed velocity field was presented. Here we present the heal transfer behavior, including heat flux on the tube, fin temperatures, fin Nusselt numbers and heat flux distributions, fin efficiencies, Colburn j factor, and apparent friction factor fapp For the investigated configuration, the ratio of heat transfer on the tube to that on the fin remains under 10%. The fin temperature and fin efficiency depend weakly on Fi.

On the Utility and Disutility of JEBAR*

The usefulness of the concept of JEBAR, the joint effect of baroclinicity and relief, in large-scale ocean dynamics is critically analyzed. The authors address two questions. Does the JEBAR term properly characterize the joint impact of stratification and bottom topography on the ocean circulation? Do estimates of the JEBAR term from observational data allow reliable diagnostic calculations? The authors give a negative answer to the first question. The JEBAR term need not give a true measure of the effect of bottom relief in a stratified ocean. A simple two-layer model provides examples. As to the second question, it is demonstrated that the large-scale pattern of the transport streamfunction is captured by the smoothed solution, especially with the Mellor et al. formulation of the JEBAR term. However, the calculated velocity field is very noisy and the relative errors are large.

The field of crustal velocity in Asia calculated from Quaternary rates of slip on faults

Rates of Quaternary faulting, when treated as measures of strain rates within regions several times larger than the depths of brittle faulting, yield a velocity field for Asia that matches the average relative velocity between the Indian and Eurasian plates over the past 2 Myr (NUVEL-1A), and the velocity of Shanghai with respect to Eurasia, measured with Very Long Baseline Interferometry (VLBI). By using rates of slip on discrete surfaces (faults) to define average strain rates, we explicitly assume that the large-scale deformation can be treated as that of a continuum. Depending on the jcales over which strain rates are averaged, 87 to 93 per cent of the assumed strain ites are fit within assigned 1-sigma uncertainties, and 97 to 99 per cent are fit within 2-sigma. The internal consistency of these data and the agreement with independent rates (NUVEL-1A and VLBI) test the validity of treating large-scale deformation of continents as that of a continuum. In the calculated velocity field, a large fraction, ∼ 85 per cent, of India's convergence with Eurasia is absorbed by crustal, or lithospheric, thickening. Among consistently misfit assumed strain rates are those dominated by high rates of strike-slip faulting. Strain associated with 20-30 mm a-1 of slip on the Altyn Tagh, Karakax, and Karakorum faults is inconsistent with the distributions of strain in surrounding regions. We conclude that these rates, all of which are based on correlations of ages of offset landforms with changes in global climate, and not on radiometric dating, have been systematically overestimated. Lateral transport out of India's northward path is relatively minor; South China is calculated to move east-southeast at less than 10 mm a-1.

Numerical modeling of the process of emplying a tank with a cryogenic liquid

Results of calculation of temperature and velocity fields in a cylindrical vessel with a cryogenic liquid (liquid hydrogen) upon its emptying are discussed. A problem is formulated for a viscous incompressible fluid at thermal boundary conditions of the first kind. Streamlines and isotherms for a variable fluid column are presented. Solutions are obtained for Rayleigh Ra = 10 7 … 10 10 and Reynolds Re = 10 3 … 10 4 numbers.

Combined analysis of spatial and velocity displacement artifacts in phase contrast measurements of complex flows.

MR phase contrast (PC) velocity imaging is a promising tool for quantifying blood flow velocity in vivo. PC velocity imaging is, however, susceptible to artifacts that result from the displacement of spins during the finite duration pulse sequences. Such displacement artifacts can lead to errors in velocity measurements, especially in the presence of oblique and accelerating flows, which are common throughout the cardiovascular system. By tracking particles (representing spins) through a computed velocity field, and assuming that spatial and velocity encodings occur at discrete times during the pulse sequence, we simulate the separate and combined effects of oblique and acceleration artifacts on PC velocity images. We demonstrate, both by simulation and MR measurement, the errors associated with such artifacts in PC velocity measurements in a representative flow geometry. Using example particle trajectories, we provide a fluid dynamic basis for characteristic phase-velocity image distortions that can arise when imaging complex, physiologically relevant flows.

PC-based blank design system for deep-drawing irregularly shaped prismatic shells with arbitrarily shape flange

A method for determining optimum blank shapes for the production of irregularly shaped prismatic shells with an arbitrarily shaped flange and stepped bottoms is proposed. All of the procedures for calculation are incorporated into a CAD system that can output the optimum blank shape in a few seconds using a personal computer. The calculation method is based on the slip-line field theory, a kinematically admissible velocity field for the flange region is determined from the theory and the calculated velocity field is used to conduct a backward calculation of the metal flow, from the designed flange shape to the initial blank shape. In the calculation it is assumed that the material is isotropic and that the thickness of the blank does not change during the deep-drawing process. A deep-drawing experiment is conducted for a square shell with six different flange shapes, using aluminum alloy sheet A5182-0 1.0mm thick and cold-rolled steel sheet SPCE 0.5mm thick. Experimental flange shapes are in good agreement with the designed (predetermined) ones. The influence of material characteristics on the blank design is found to be relatively small.

Shape Design Sensitivity and Optimization Using P-Version Design Modeling and Finite Element Analysis*

ABSTRACT A methodology that supports shape design modeling, structural shape design sensitivity analysis (DSA), and optimization of elastic solids, using p-version finite element analysis (FEA), is developed. The p-version FEA approach is attractive for shape design optimization, due to its high accuracy of analysis results, even with coarse mesh; ease of creation of design and finite element models; consistency between design and finite element models; insensitivity to finite element mesh distortion and aspect ratio; and tolerance for large shape changes during design optimization iterations. A continuum-based DSA method that is applicable to both planar and spatial structures is developed with an established p-version FEA code, STRESS CHECK. A shape design parameterization method that uses the geometric entities of STRESS CHECK is proposed and implemented. In STRESS CHECK, the shape design model is identical to the finite element model, so finite element modeling errors are eliminated. Design optimization is carried out by integrating the shape design parameterization, design velocity field computation; first-order shape design sensitivity computation, STRESS CHECK; and an optimization code, DOT. Examples are run successfully in full-batch mode to demonstrate the feasibility of the proposed integrated optimization method

Real-time parallel computation of disparity and optical flow using phase difference

A phase-difference-based algorithm for disparity and optical flow estimation is implemented on a TI-C40-based parallel DSP system. The module performs real-time computation of disparity maps on images of size 128 × 128 pixels and computation of optical flows on images of size 64 × 64 pixels. This paper describes the algorithm and its parallel implementation. Processing times required for the computation of disparity maps and velocity fields and measures of the algorithm's performance are reported in detail.

Tidal currents in the Indonesian Seas and their effect on transport and mixing

We have investigated the characteristics of tides and tidal currents in the Indonesian Seas, with particular emphasis on the predominant constituents, the barotropic M2 and K1 components. The calculated harmonic constants of the M2 and K1 tides agree well with those obtained from extensive tide gauge observations: the mean root‐mean‐square errors between models and observations for M2 and K1 over the entire Indonesian Seas are 11.2 and 8.65 cm, respectively, smaller than previous studies. The features of the tidal current field are qualitatively similar to those reported by Wyrtki [1961]. Relatively strong tidal currents are found in the Java Sea and in the vicinities of the narrow straits, such as the Lombok and Malacca Straits. Tracking of numerous labeled particles in the calculated velocity field clearly shows that the tidal currents play essential roles in the transport and mixing processes in the Indonesian Seas. For example, in the eastern Indonesian Seas a significant clockwise residual circulation appears around Buru Island, due primarily to the tidal rectification over variable bottom topography, with a minor impact from the nonlinear effects around narrow straits. The tide‐induced residual transport from the Seram Sea to the eastern Banda Sea attains about 3.8 Sv (1 Sv = 106 m3 s−1), comparable to that of the Indo‐Pacific throughflow along the eastern route. In the western Indonesian Seas (the Java Sea and the Makassar Strait) the residual transport is much smaller than the throughflow transport along the western route. Our result suggests, however, that the properties of water flowing through this route could be modified by strong tidal mixing around the shelf of the southern Makassar Strait and the Lombok Strait.

Compression Processes and Performance Analysis of a High-Pressure Reciprocating Gas Compressor

Compression processes and compressor performance in a two-stage 41.34 MPa (6000 lb/in2) reciprocating gas compressor were investigated by transient multi-dimensional and transient global thermodynamic models. The transient multi-dimensional model was adopted to predict the two-dimensional compression processes in the second-stage cylinder of the high-pressure reciprocating gas compressor. Calculated results showed no significant temperature gradients anywhere in the compressor cylinder except near the wall, throughout one complete compressor cycle. On the other hand, the calculated velocity fields and streamline contours showed a convergent flow pattern during the process of compression with discharge and a large recirculation vortex during the process of expansion with suction. A parametric study based on the transient global thermodynamic model was conducted to investigate the effect of various parameters, that is clearance volume, wall temperature of cylinder head and stroke length, on the compressor performance. Among these parameters, it was found that the clearance volume had the strongest effect on the compressor performance. A reduced clearance volume increased volumetric efficiency. Also, it was found that decreasing the stroke length would not degrade the compressor performance, but it could reduce the compressor size and thereby the manufacturing cost significantly.

Analysis and Refinement of a Method for Numerically Modeling Deep- Penetration Welding Processes Using Geometric Constraints

A detailed analysis and refinement of a method of numerically modeling deep-penetration welding processes using geometric constraints based on boundary information obtained experimentally is presented. The general features of the numerical method have been described previously. This paper considers issues concerning accurate numerical calculation of temperature and velocity fields in regions of the melt pool where the flow of fluid is characterized by quasi-stationary Stokes flow. It is this region of the melt pool that is closest to the heat-affected zone and that represents a significant fraction of the fusion zone.

Calculation of a Mass-Consistent Two-Dimensional Wind Field with Divergence Control

Abstract The aim of this paper is the calculation of mass-consistent wind velocity field in a two-dimensional domain Ω on the basis of sparse measurements collected by wind-measuring stations. Measured data are used to estimate an initial field. The result is obtained by a weighted interpolation method. An iterative scan procedure is used in which the radius of influence of each station over the surrounding grid points is decreased at each step of iteration. To adjust the initial field into a mass-consistent velocity wind field, a new technique is presented that is meant to extract only the purely divergent component of the wind velocity field. This component is then either suitably manipulated, reduced and reintroduced in the total wind field, or completely neglected. The main idea of the method is to obtain a mass-consistent wind by controlling the magnitude of the purely divergent component without completely destroying all the information connected with its spatial pattern. On the basis of a test case...

Numerical simulation of airflow in the human nasal cavity.

An anatomically correct finite element mesh of the right human nasal cavity was constructed from CAT scans of a healthy adult nose. The steady-state Navier-Stokes and continuity equations were solved numerically to determine the laminar airflow patterns in the nasal cavity at quiet breathing flow rates. In the main nasal passages, the highest inspiratory air speed occurred along the nasal floor (below the inferior turbinate), and a second lower peak occurred in the middle of the airway (between the inferior and middle turbinates and the septum). Nearly 30 percent of the inspired volumetric flow passed below the inferior turbinate and about 10 percent passed through the olfactory airway. Secondary flows were induced by curvature and rapid changes in cross-sectional area of the airways, but the secondary velocities were small in comparison with the axial velocity through most of the main nasal passages. The flow patterns changed very little as total half-nasal flow rate varied between resting breathing rates of 125 m/s and 200 ml/s. During expiration, the peaks in velocity were smaller than inspiration, and the flow was more uniform in the turbinate region. Inspiratory streamline patterns in the model were determined by introducing neutrally buoyant point particles at various locations on the external naris plane, and tracking their path based on the computed flow field. Only the stream from the ventral tip of the naris reached the olfactory airway. The numerically computed velocity field was compared with the experimentally measured velocity field in a large scale (20x) physical model, which was built by scaling up from the same CAT scans. The numerical results showed good agreement with the experimental measurements at different locations in the airways, and confirmed that at resting breathing flow rates, airflow through the nasal cavity is laminar.

Study of seasonal transport variations in the Indonesian seas

Seasonal transport variations between the Pacific and Indian Oceans via the Indonesian seas were studied by the Euler‐Lagrangian method. The velocity field was calculated with a fairly high resolution robust diagnostic model. The model well reproduces the features of seasonal variations in the Indonesian seas. The total volume transport of the Indonesian throughflow is 20±3 Sv (1 Sv = 106 m3 s−1), the maximum being from boreal spring to boreal summer and the minimum in boreal winter. The values are similar to those of previous general circulation models with a wide Indonesian passage despite resolution of the presence of the many small islands in the Indonesian seas. Although a large portion of the net transport is contained in the upper layer, deep transport below 1000‐m depth is about 5 Sv. This value corresponds to approximately 25% of the total transport, which means that disregard of the deep transport leads to underestimation of the volume transport of the throughflow. Tracking of numerous labeled particles in the calculated velocity field clarified the sources and pathways of the Indonesian throughflow. The major route is a western one through both the Makassar and Lombok Straits. Most of the North Pacific water supplied from the Mindanao Current passes along this route, entering the Indian Ocean within several months with almost no loss of its properties (intense vertical mixing around the Lombok sill reported by observations could not be reproduced in our model). In contrast, South Pacific water takes the eastern route into the eastern Indonesian seas and subsequently mixes with waters from the North Pacific and Indian Oceans in the Banda Sea, which means that it has a long travel time (at least a few years). Water taking the eastern route therefore loses its original properties before arriving in the Indian Ocean. The transport processes also are significantly affected by seasonal variations in equatorial circulation in the western Pacific. In the surface layer, North Pacific water is vigorously supplied to the western route only from boreal spring to summer in association with the linkage between the current flowing through the Makassar Strait and the Mindanao Current. In other seasons, because the Mindanao Current is strongly linked with the North Equatorial Countercurrent and the New Guinea Coastal Current primarily by northeasterly monsoonal winds, its upper water flows back to the Pacific Ocean. In the subsurface layer, a pronounced inflow of Mindanao Current water into the western route occurs from boreal winter to spring, when the subsurface link between that current and the Equatorial Undercurrent tends to weaken. In the deep, the quasi‐steady transport of Pacific water into the Indian Ocean via the eastern route is fed by the westward deep current in the equatorial Pacific.

Design Sensitivity Analysis and Optimization tool (DSO) for shape design applications

The Design Sensitivity Analysis and Optimization (DSO) tool, developed initially for sizing design application, has been extended to support shape design applications of structural components. The new capabilities including shape design parameterization, error analysis and mesh adaptation, design velocity field computation, shape design sensitivity analysis, and interactive design steps, are discussed. These capabilities are integrated on the top of the DSO framework that includes databases, user interface, foundation class and remote module. The DSO allows the design engineer to easily create geometric, design, and analysis models; define performance measures; perform design sensitivity analysis (DSA); and carry out a four-step interactive design process that includes visual display of design sensitivity, what-if study, trade-off analysis, and interactive design optimization. Additionally, a 3-D tracked vehicle clevis is presented in this paper to demonstrate the new capabilities.

Deposition of aerosols in asymmetric airway bifurcations

The statistical analysis of human bronchial morphometry data reveals distinct asymmetric features of the airway branching pattern, which may greatly affect the localized distribution of particles deposited within airway bifurcations. Our analysis of particle deposition patterns within an asymmetric bifurcation is based on a recently developed numerical method for the calculation of air velocity fields and aerosol particle trajectories in a three-dimensional bifurcation model ( Balásházy and Hofmann (1993) J. Aerosol Sci. 24, 745–772). In this numerical model, airflow is computed by solving the Navier-Stokes equations with a finite difference method, and trajectories of aerosol particles under the simultaneous action of inertial impaction, gravitational settling, Brownian motion, and interception are simulated by utilizing Monte Carlo techniques. In the present paper, the effects of asymmetry in airway diameter, branching angle, and flow division on both inspiratory and expiratory particle deposition patterns are explored for various particle sizes and flow rates. Model predictions are compared with the available experimental evidence, with other theoretical predictions, and with corresponding simulations for a symmetric bifurcation.