Stream Velocity Field Research Articles

Dimensionality reduction for regularization of sparse data-driven RANS simulations

Data assimilation can reduce the model-form errors of RANS simulations. A spatially distributed corrective parameter field can be introduced into the closure model, whose optimal values can be efficiently found by an adjoint method and gradient-based optimization. When assimilating experimental data, which in most cases are sparsely distributed or based on a low-resolution grid, the inverse problem is highly underdetermined and thus ambiguous. Therefore, to reduce the ambiguity, regularization is required. Established regularization approaches such as total variation and Sobolev gradient methods can produce smooth and physically meaningful velocity fields in many cases. However, if the measurements are located close to walls, spiky and unphysical wall shear stress profiles can occur. A new regularization strategy based on a piecewise linear approximation of the corrective field is proposed. This method is shown to lead to a very accurate free stream velocity field and smooth wall shear stress profiles. The resulting skin friction drag error for the case of flow over periodic hills was around 1.38% which is seven times lower than the error obtained with the Sobolev gradient and two orders of magnitude lower than that obtained with the other two methods.

Periodic magnetohydrodynamic mixed convection flow along a cone embedded in a porous medium with variable surface temperature

The entrained flow and heat transfer in Newtonian fluid along the thermally and electrically conducting cone embedded in porous medium by encountering the variable surface temperature is carried out. The proposed process is time dependent that is the source of oscillation in all considered variables. The primary phenomenon is given a mathematical form in partial differential equations which are non-linear and coupled. By means of dimensionless formulation, the resulting set of constitutive equations is reduced to non-dimensional form. A suitable formulation that produces the smoothness in algorithm is utilized for the transformation of dimensionless form of equations to smooth ones. The pertinent material properties of interest such as velocity, temperature and magnetic profiles along with their derivatives are portrayed in graphical way under the impact of pertinent parameters. The main finding about the current communication is that for elevating the variable surface temperature parameter ζ, the main stream velocity and temperature field get declined and opposite attitude is noted in magnetic profile. Furthermore, maximum value for velocity and temperature are secured at ζ=0.1 and ζ=8.0 respectively but reverse scenario is seen in magnetic profile.

Numerical Simulation on the Acoustic Streaming Driven Mixing in Ultrasonic Plasticizing of Thermoplastic Polymers.

The acoustic melt stream velocity field, total force, and trajectory of fluorescent particles in the plasticizing chamber were analyzed using finite element simulation to investigate the acoustic streaming and mixing characteristics in ultrasonic plasticization micro-injection molding (UPMIM). The fluorescence intensity of ultrasonic plasticized samples containing thermoplastic polymer powders and fluorescent particles was used to determine the correlation between UPMIM process parameters and melt mixing characteristics. The results confirm that the acoustic streaming driven mixing occurs in ultrasonic plasticization and could provide similar shear stirring performance as the screw in traditional extrusion/injection molding. It was found that ultrasonic vibrations can cause several melt vortices to develop in the plasticizing chamber, with the melt rotating around the center of the vortex. With increasing ultrasonic amplitude, the melt stream velocity was shown to increase while retaining the trace, which could be altered by modulating other parameters. The fluorescent particles are subjected to a two-order-of-magnitude stronger Stokes drag force than the acoustic radiation force. The average fluorescence intensity was found to be adversely related to the distance from the sonotrodes’ end surface, and fluorescence particles were more equally distributed at higher parameter levels.

Magnetohydrodynamic electro-osmotic flow of Maxwell fluids with patterned charged surface in narrow confinements

We study the magnetohydrodynamic electro-osmotic flow of Maxwell fluids through two microparallel plates with patterned charged surfaces. The combined influences of two imposed time periodic electric fields (one along the lateral direction and the other along the axial direction) and an external vertical magnetic field are taken into account. The flow is driven by Lorentz force and electric field force and is 2D due to charge modulated surfaces. Upon the assumptions of the Debye–Hückel linearization, the analytical solutions of the stream function and velocity field are derived. The variations in velocity with the dimensionless relaxation time De, the Hartmann number Ha, and the oscillating Reynolds number Re are depicted graphically. Furthermore, the parameters that influence the generation of vortexes in the flow field are also discussed.

CALCULATION OF «VULNERABILITY» ZONE IN CASE OF TERRORIST ATTACK WITH CHEMICAL AGENTS

Purpose. The work involves the development of a numerical model for calculating the «vulnerability» zone of a possible terrorist attack objective with the use of a chemical agent in a built-up environment. The «vulnerability» zone is a territory near the attack objective, where the emission of a chemical agent during the attack will lead to undesirable consequences. The emission of a chemical agent outside the «vulnerability» zone will not create a dangerous concentration near the attack objective. Methodology. To solve this problem, we use the equation for the velocity potential, on the basis of which we determine the wind stream velocity field, and the equation adjoint to the equation of mass transfer in the atmospheric air of the chemical agent emitted in the event of a terrorist attack. During simulation, we take into account the uneven wind stream velocity field, atmospheric diffusion and the rate of emission of a chemically hazardous substance. For the numerical integration of the velocity potential equation, we use the method of A. A. Samarsky. For numerical solution of the adjoint equation, we introduce new variables and use an implicit difference splitting scheme. The peculiarity of the developed numerical model is the possibility of operative estimation of the «vulnerability» zone near a possible attack objective. Findings . The developed numerical model and computer program can be used for scientifically grounded assessment of the «vulnerability» zone near significant facilities in the event of possible attacks with the use of chemical (biological) agents. The constructed numerical model can be implemented on computers of small and medium power, which allows it to be widely used to solve the problems of this class when developing the emergency response plan. The results of the computational experiment are presented, which allow us to evaluate the possibilities of the proposed numerical model. Originality . An effective numerical model is proposed for calculating the «vulnerability» zone near the facility, which may be the target of a terrorist attack with the use of a chemical agent. The model is based on the numerical integration of the velocity potential equation and the equation adjoint to the equation of mass transfer of a chemically dangerous substance in the atmosphere. Practical value. The developed model can be used to organize protective actions near the target facility of a possible chemical attack by terrorists.

Mesolevel Analysis of Hydrodynamics of Flow Over Hydrophobic Surfaces

In this study, hydrodynamics of flow over a super-hydrophobic surface was investigated using Lattice Boltzmann method. Lattice Boltzmann method is a meso-level approach, to capture the mico-level details in the flow regime. From the numerical analysis it was found that, an effective mixing was induced in the flow domain with the introduction of hydrophobic surfaces in the channel. The cross stream velocity fields induced potentially proves its capability to create induced mixing in the channel. The result was found to be in fine agreement with the results in the literature. The exceptional capability of reducing the pumping power makes this modification more acceptable.

Combined influence of velocity slip, temperature and concentration jump conditions on MHD peristaltic transport of a Carreau fluid in a non-uniform channel

The effect of velocity slip, temperature and concentration jump conditions on the MHD peristaltic flow of a Carreau fluid in a non-uniform channel with heat and mass transfer is investigated. Using a perturbation technique, for small Weissenberg number, solutions are obtained for the non-linear differential equations with appropriate boundary conditions. The expressions for the stream function, velocity, temperature and concentration fields; and the heat transfer coefficient are obtained. The effects of the physical parameters on the velocity and temperature fields are presented through graphs, and are discussed. Also, the trapping phenomenon is analyzed. It is observed that the size of the trapping bolus increase with an increase in the velocity slip parameter β1.

Design of an Extra-Tall Mast Above Blade-Tip Heights for Wind Resource Assessments Across Complex Terrain Regions

Wind energy predictions for many rural, complex terrain regions are based solely on large-scale meteorological models that may poorly characterize the local resource. Changes in government policies, energy economics, and wind technologies suggest that the best wind resources across such a complex terrain region in southeast Ohio may be economically viable. The wind energy and assessment visualization (WEAV) assessment approach is a meso-scale strategy to locate the best resource in a marginal wind region. The measurement component is described here. Wind characteristics measurements on a communications tower at six heights up to 240 m, are being acquired. This data will be input into a complex-terrain wind simulator with terrain information to model the wind resource across approximately 2000 square miles (5200 km2). Advantages of the WEAV assessment strategy include explicit measurement of wind shear and velocities, long-term characterization of the free stream velocity field, and evaluation of a much larger assessment region. Included is a description of, the motivation for and advantages of this approach, details of the design, installation, and challenges of an extra-tall tower wind measurements, and a discussion of the economics of both Class 2 wind (∼250 W/m2) and the WEAV assessment approach compared with conventional wind assessments.

Use of an Infrared Camera for Accurate Determination of the Temperature of Polymer Filaments

An infrared (IR) camera was used to measure the temperature of polymer filaments held in a stream of hot air. Filament diameters of 0.1−4 mm were tested. The air stream velocity and temperature fields were independently measured with a Pitot tube and a thermocouple. Under certain conditions, the air temperatures determined by the thermocouple closely approximate the temperatures of the polymer filaments. These air-temperature measurements were compared to the temperature readings given by the IR camera. This procedure allowed the development of calibration curves for the infrared camera. The calibration curves were found to depend on (a) the diameter of the filament and (b) the image size of the filament upon the pixel array in the IR camera. These calibration curves can be used with the IR camera to allow online measurement of fiber temperature during melt spinning, melt blowing, and other fiber production processes.

Standing regular wave groups with oblique incidence: Phase averaging and bottom boundary layer in constant depth

This article analyzes the phase‐averaged hydrodynamics induced by regular wave groups and the related long waves under reflective conditions outside of the wave‐breaking zone. The solutions of the inviscid region and wave‐group bottom boundary layer (WGBL) are analytically investigated for a regular wave group at a constant depth, impinging obliquely on an alongshore uniform reflective wall. The problem is formulated and solved by using the classical multiple‐scale approach. Phase averaging is defined on the basis of the cascade of spatial and temporal scales of the problem leading to a weak unsteady (hydrodynamic) regime (WUR), a steady regime (SR), weak nonhomogeneous regime (WNHR), and homogeneous regime (HR) of instantaneous quantities. The analysis of the inviscid region hydrodynamics shows that depending on the time scale used for the averaging, modulation scales of O(100 m) and O(1 km) may appear in the time‐averaged pressure and the free stream velocity fields. These modulations are related to the nonlinear interference of the incoming and reflected wave‐group motions. Supermodulation scales of O(10 km) are also possible. Such scales result from the superposition of the bound long waves and the oscillatory free long wave mode released during the reflection of the wave train. The SR of the total pressure field and the WUR of the radiation stresses are also analyzed. The WGBL solution shows that multiple‐scale modulation of the inviscid region hydrodynamics can be fully transmitted to the Eulerian drift in the viscous region. We also found that under reflective conditions and nearly normal wave incidence, the WUR of the Eulerian drift may present standing modulated patterns with scales of O(100 m), O(1 km), and O(10 km). In the SR, there can be scales of O(100 m) and O(1 km). The mechanisms which determine the vertical structure and direction of the WUR and SR of the Eulerian drift beneath wave groups are also investigated as a function of the main parameters of the WGBL model. Physical implications of and qualifications to the theory presented on nearshore sediment transport are discussed.

Polyamide-6 polymerization and its melt flow in the VK tube reactor with optimized baffle structure

The flow mechanism of Polyamide-6 (PA6) melt over conical perforated baffles in the VK tube is elucidated by computerized analysis based on a rational assumption of Stokes' flow. The governing equations for a two-dimensional flow are solved by the finite difference method to generate the stream function profile, velocity field and residence time distribution. Optimization of the geometries of the baffle structure brings about a uniform residence time distribution, so as to ensure a homogeneous extent of reaction for the final product. The complete mathematical model for PA6 polymerization while flowing through the VK tube was established according to PA6 hydrolytic polymerization kinetics. The optimized baffle structure was shown to be compatible with the desired polymerization variables. Der Fließmechanismus einer Polyamid-6-Schmelze über konische perforierte Stauelemente in einem VK-Rohr wurde mittels Computeranalyse unter der Annahme Stokesschen Fließens berechnet. Das Gleichungssystem für zweidimensionales Fließen wurde mit der Finite-Differenz-Methode gelöst, um das Strömungsprofil, das Geschwindigkeitsfeld und die Verweilzeitverteilung zu generieren. Die Optimierung der Stauelementgeometrie führt zu einer gleichförmigen Verweilzeitverteilung, womit ein homogener Reaktionsumfang für das Endprodukt erreicht wird. Das vollständige mathematische Modell für die PA6-Polymerisation im VK-Rohr wurde auf der Grundlage der Kinetik der hydrolytischen PA6-Polymerisation aufgestellt. Die optimierte Stauelementstruktur erwies sich als kompatibel mit den erwünschten Polymerisationsvariablen.

Modification of the Carrier, Greengard, and Rokhlin FMM for Independent Source and Target Fields

The Greengard–Rokhlin fast multipole method (FMM) provides an efficient numerical algorithm to calculate the two-dimensional stream function and velocity field at a number of target points associated with a large system of vortices (sources). In this paper we discuss an extension to their adaptive scheme. The added feature allows the specification of target points that do not have to coincide with the location of the sources. This is useful when specifying separate source and target fields for calculating boundary conditions, trajectories of passive scalar quantities, data for stream-function plots, etc. A simple algorithm has been developed to optimize the method for cases where the number of sources differs significantly from the number of target points.

Measurement of Turbulent Flow Fields in a Stirred Vessel with Four Baffles by Laser-Doppler Velocimetry. (Analysis with Periodic Averaged Velocity Profiles)

The 3-D flow field relative to a rotating paddle blade is obtained by synchronizing LDV measurements with the output of a shaft-mounted encoder, thus making it possible to determine the impeller stream velocity field, including details of the discharge flow region behind the blades. Mean velocities, ensemble-averaged between a specific impeller blade pair(over 90°)show the extent determinde from both the passage and structure of the discharge flow region. Pumping capacities are consequence of fluid entrainment into the discharge flow region. Mean velocities taken in a rotating frame of reference reveal a significant periodic variation near to those taken in a fixed frame.

Measurement of Turbulent Flow Fields in a Agitated Vessel with Four Baffles by Laser-Doppler Velocimetry. Analysis with periodic averaged velocity profiles.

The 3-D flow field relative to a rotating paddle blade is acquired by synchronizing LDV measurements with the output of a shaft-mounted encoder. This makes it possible to capture the impeller stream velocity field, including the details of the discharge flow region behind the blades. Mean velocities ensemble-averaged between a specific impeller blade pair (over 90°) show the extent of periodicity and the passage and structure of the discharge flow region. Pumping capacities are determined at both sides of impeller and tip of impeller, and it is shown that the radial jet is a consequence of fluid entrainment into the discharge flow region. Mean velocities taken in a rotating frame of reference reveal a significant periodic variation near the impeller than those taken in a fixed frame.

On MHD flow past an infinite porous plate with variable suction

The two-dimensional flow of a viscous incompressible and electrically conducting fluid past an infinite porous plate in the presence of a transverse magnetic field has been considered. The plate moves with constant velocity in the direction of fluid flow. The suction velocity normal to the plate and the free stream velocity field vary exponentially with time. The expressions for the velocity field and the skin-friction have been obtained in non-dimensional form for two cases: (1) exponentially increasing small perturbation and (2) exponentially decreasing small perturbation. It has been concluded that there is a reverse type flow near the surface of the plate when it moves in the opposite direction to that of the flow. The skin-friction when the plate moves in the direction of flow is less than it is when the plate moves in the opposite direction.

Mean velocity field relative to a Rushton turbine blade

AbstractThe 3‐D flow field relative to a rotating Rushton turbine blade is acquired for fully turbulent tank conditions by synchronizing LDA measurements with the output of a shaft‐mounted encoder. This makes it possible to capture the impeller stream velocity field, including the details of the voritices behind the blades. Mean velocity data at three impeller speeds show the extent of periodicity and the axes and structure of the vortices. Pumping capacities are determined and it is shown that the radial jet is a consequence of fluid entrainment into the vortices. Deformation rates based on gradients of mean velocity are calculated. Close to the blade they can exceed impeller rotational frequency by as much as two orders of magnitude. To a first approximation, the normalized mean flow field is independent of impeller speed.

Wave‐current interaction near the Gulf Stream during the Surface Wave Dynamics Experiment

This paper presents a case study on the wave‐current interaction near the local curvature of a Gulf Stream meander. The wave data were obtained from in situ measurements by a pitch‐roll discus buoy during the Surface Wave Dynamics Experiment (SWADE) conducted off Wallops Island, Virginia, from October 1990 to March 1991. Owing to the advection of the Gulf Stream by the semidiurnal tide, the discus buoy was alternately located outside and inside the Gulf Stream. The directional wave measurements from the buoy show the changes in wave direction, wave energy, and directional spreading when waves encountered the current in the Gulf Stream meanders. A wave refraction model, using the ray‐tracing method with an estimated Gulf Stream velocity field and meandering condition, was used to simulate wave refraction patterns and to estimate wave parameters at relative locations corresponding to buoy measurements. The numerical simulation shows that a focusing zone of wave rays was formed near the boundary and behind the crest of a simulated Gulf Stream meander. The focusing of wave rays causes changes in wave direction, increases in wave energy, and decreases in wave directional spreading, which are in good agreement with the results from the buoy measurements.

A two-dimensional heat and fluid-flow model of single-roll continuous-sheet casting process

Single-roll continuous-sheet casting process has been simulated using a mathematical model based on considerations of fluid flow, heat transfer, and solidification. The principal model equations include momentum and energy balances which are written for various zones comprising the process. The flow of liquid metal in the pool is taken to be a two-dimensional recirculatory flow. The concepts of vorticity and stream function are used to reduce the number of equations and number of unknowns, respectively. Model equations and boundary conditions are written in terms of dimensionless variables and are solved, using an implicit finite difference technique, to give stream functions and velocity fields in the metal pool, temperature fields in the metal pool, sheet, and caster drum, and the final sheet thickness for various operating parameters. The parameters examined are: (1) rotational speed of the caster drum, (2) liquid metal head in the tundish, (3) superheat of the melt, (4) caster drum material, and (5) cooling conditions prevailing at the inner surface of the caster drum. The final sheet thickness decreases with increasing rotational speed of the caster drum and melt superheat, but it increases with increasing standoff distance and metal head in the tundish.

Flow field around a cylindrical pile during steady penetration

An analytical solution is presented for the flow field around a cylindrical pile penetrating an inviscid and incompressible fluid. The problem is solved by using the theory of a complex variable and conformal mapping and by transforming the governing flow equation from cartesian to orthogonal curvilinear coordinates. The stream function, velocity field, and octahedral shear strain rates are fully determined and presented in graphical form. It is shown that the assumption of infinite extent of the pile results in the fluid velocity vanishing along the pile shaft. The flow field obtained is thought to represent a first approximation to in situ strains generated during the penetration of a cylindrical pile in very soft cohesive soils. Key words : flow field, cylindrical pile, soft cohesive soil, strain rates, velocity field.

Horizontal and Vertical Structure of the Gulf Stream Velocity Field at 68°W

Abstract A curent meter mooring, instrumented from the bottom into the thermocline, was deployed in the Gulf stream at 68°W for a year. Data from the uppermost instrument indicate the Gulf Stream moved back and forth across the mooring site, so that the horizontal as well as vertical structure of the Stream may be deduced. The two key points to the success of the analysis are: 1) the well-defined relationship between temperature and cross-stream distance in the thermocline, enabling the use of the former as a horizontal coordinate; and 2) a daily-changing definition of Gulf Stream flow direction based on the shear between the thermocline and 2000 m depth. Time-series of daily-rotated velocities may be used to calculate empirical orthogonal functions for the along- and cross-stream vertical structures, which are decoupled and are respectively baroclinic and barotropic. Using the inferred horizontal coordinate one can estimate masss, momentum and kinetic energy fluxes agree well with historical data. Bryden...