Calculated Velocity Distributions Research Articles

A numerical model for calculating velocity distribution in cross-section of an open channel

Flow velocity in open channels is a fundamental hydraulic parameter with wide-ranging applications, including the development of rating curves and the study of sediment transport. While some river engineering projects may only require the calculation of average flow velocity, others, such as the design of hydraulic structures and stable channels, as well as the assessment of boundary shear stress, necessitate a more comprehensive understanding of flow dynamics, including the two-dimensional velocity distribution within open channels. To address this, various mathematical models have been proposed for estimating the two-dimensional distribution of flow velocity across transverse and depth directions. However, these models often come with complexities that hinder their practical application. In this research, we introduce a simplified numerical model that combines simplified Navier–Stokes equations with an eddy viscosity formula. This innovative approach aims to estimate velocity distribution in both rectangular and trapezoidal channels. The accuracy of our developed model hinges on the momentum transfer coefficient used in the eddy viscosity formula. Through the execution of the numerical model and the utilization of observational data, we determined the optimal value of the momentum transfer coefficient to be 0.241. To validate the effectiveness of our numerical model, we compared its predictions with laboratory data encompassing diverse hydraulic conditions. The results demonstrated a high level of accuracy, with the calculated velocity distribution and flow discharge differing by no more than 7.6% and 6.8%, respectively.

Permanent magnet bottom-stirred swirling flow in coaxial shallow cylindrical containers

Here, an original rotating permanent magnet (RPM) system placed coaxially with the liquid metal container is studied as an effective means of generating flow in shallow cylinders for potential application in aluminum metallurgy (e.g., for ladle stirring and metal dosing). The studied RPM system generates volume force with strong axial variation and force maximum near the radial midpoint. The numerical and experimental data show that, in the shallow cylinder case, the azimuthal velocity follows the force radial distribution. The resulting velocity maximum occurs near the radial midpoint, unlike in the traditional rotating magnetic field (RMF) stirrer systems, where the velocity maximum occurs near the outer radius. An analytical description is developed to explain the velocity radial distribution. The numerically calculated velocity distribution shows a peculiar result that the bottom-stirred liquid metal container results in peak angular momentum at the top of the container. The solution to asymptotic boundary layer equations shows that this is due to the force axial variation.

Study of Radial Wall Jets from Ceiling Diffusers at Variable Air Volume

The knowledge of the air velocity distribution in the supply jets is essential when designing ventilation and air conditioning systems. In this study, we tested and analyzed the velocity distributions in the radial wall jets—these jets are commonly used in ventilated rooms. Tests included jets from two ceiling diffusers of different constructions, at three airflow rates. The mean air speed distributions were measured with a 16-channel hot-sphere anemometer both in the self-similarity zone and in the terminal zone. A specially developed method of converting the mean speed to mean velocity was used. The measurement results show that the spread coefficients of the jets from both diffusers were the same, but the positions of the virtual origin were different. Due to the friction of the jet with the ceiling and the transfer of momentum to the recirculating flows, the momentum flux in the self-similarity zone decreased by up to 50%. An improved method for calculating velocity distributions in radial wall jets was developed and validated. This method takes into account the decrease of momentum, non-zero position of the jet origin, and faster velocity decrease in the terminal zone. A reliable method of predicting air velocity distribution in radial wall jets (RWJs) from ceiling diffusers may allow to properly select the diffuser size, its location, and the range of flow rate changes. The design process for variable air volume systems can be facilitated.

P-wave velocities of the upper mantle of the Tethysalpine geosynclines

The aim of the work is to calculate the velocity distribution of the longitudinal seismic waves (VP) in the upper mantle at depths from the discontinuity M to 400 km. The object is the territory of Tethys — the belt of alpine geosynclines crossing all of Eurasia from Gibraltar to the Indonesian archipelago.The model of the first approximation is constructed according to previous studies and our results on island arcs. It was possible to choose the velocity distribution in the upper mantle of Tethys, according to which the travel time close to the observed one was calculated. The degree of coordination is quite sufficient for the recognition of the used distribution of velocity as real. The data on approximately 18,000 earthquakes, the waves from which reached 27 seismic stations, are used. The location of the epicenters of earthquakes and stations ensured the passage of seismic rays precisely along the upper mantle of different Tethys regions. On the island of Sumatra a comparison was made of the constructed travel times with those obtained earlier in the study of the upper mantle of island arcs and coastal ridges of the Pacific Ring. Harmonization of the travel times is considered satisfactory. The VP distribution obtained in this way is compared with the calculated from the ideas of the advective-polymorphic hypothesis. The velocity model of the upper mantle of the Precambrian platform outside the zones of modern activation is complemented by the influence of the anomalous temperatures of both signs in the subsoil of the geosyncline. The result is somewhat different from the calculated earlier for the upper mantle island arc. There are two main reasons for this difference: probability of a somewhat higher radiogenic heat generation in the rocks of the upper mantle of the arc and somewhat smaller typical crustal thickness under the arc. The discrepancies between the models are small, averaging about 0.03 km/s. They do not exceed associated only with the errors of calculations. A noticeable excess of the magnitude of the discrepancies is detected only at a depth of 400 km, where the uncertainty of the calculation results is maximum.The discrepancy between the experimental and calculated velocity distributions in the upper mantle of Tethys is 0.05 km/s. They can be considered coincident.

Optimization strategy for the velocity distribution based on tool influence function non-linearity in atmospheric pressure plasma processing

Atmospheric pressure plasma processing (APPP) is proved to be potential in the fabrication of optical elements with high efficiency and near-zero damage. However, high convergence rate in the figuring process is hard to achieve because of the tool influence function (TIF) non-linearity. Directly solved dwell time map by conventional deconvolution methods does not consider the non-linear thermal effect, which leads to significant figuring error. In this paper, the optimization strategy for TIF non-linearity based on the velocity distribution in APPP is presented. The exponential model of TIF with non-linearity is established by trench experiments. A series of simulations are also conducted to analyze the thermal effect of non-linearity on the figuring process, indicating the TIF constantly changes with velocity distribution. Two evaluation parameters, relative balance factor and velocity concentration factor, are proposed to investigate the figuring capacity of calculated velocity distribution. With two evaluation parameters, the optimization strategy of velocity distribution based on TIF selection is proposed to suppress the non-linearity. Verification experiments are carried out to validate the two optimized TIFs. The results show that high convergence is achieved to be 72.41% and 82.81% for root-mean-square value respectively, which proves the feasibility of the proposed optimization strategy.

Emergent vegetation flow with varying vertical porosity

The vertical distribution of an emergent vegetation in wetlands and marshes is generally non-uniform due to the variations of the stem thickness and the leaf density. This study focuses on the effect of the varying vertical porosity on the hydrodynamic characteristics of the emergent vegetation flow. The new governing equation for the emergent vegetation flow with varying vertical porosity is established by applying the poroelastic media flow theory. According to the movement mechanism of the water flow in the porous media and the experimental data, the best fitted expression of the permeability is established for the emergent vegetation flow. The velocity distribution is obtained with the finite analytic method. Then, a flume experiment is performed using truncated cones to simulate the actual vegetation with varying vertical porosity. The calculated velocity distribution is compared with the measured data, which shows that the theoretical results are in good agreement with the experimental data. Finally, the influence of the vertical porosity distribution on the vegetation flow characteristics is analyzed graphically. The study can provide a useful reference and technical support for further study of the flow with a complex shape vegetation.

An integrated method for seismic velocity modeling based on collocated cokriging

The modeling results of seismic velocity (VP and VS) largely influence the accuracy of seismic inversion and depth migration. In the process of velocity modeling, seismic attributes and sedimentary facies are very important as covariates, especially sedimentary facies, which affect geological conditions in the whole area. Because of the sparse distribution of well loggings in the early stage of petroleum exploration, integrating multiple variables to control the modeling process becomes essentially critical. The conventional cokriging method and the two-step modeling approach, which do not use sedimentary facies as quantitative data, are not able to introduce enough information to enhance the quality of a velocity model. The proposed collocated cokriging with sedimentary facies (CCK with sedimentary) method directly uses the digital model of sedimentary facies as a covariate to calculate the velocity results. CCK with sedimentary integrates three kinds of data, logging, seismic attributes, and sedimentary facies, where the logging data is the primary variable, and seismic attributes and sedimentary facies are the two covariates. Field examples indicated that the velocity models of the P-wave for CCK with sedimentary is better than that for collocated cokriging (CCK), and the interval velocity has been proven to be a better seismic attribute of the kriging method. The same is true for the VS results. The velocity models obtained by CCK with sedimentary contain less abnormal values with high continuity and stability. Therefore, CCK with sedimentary has been proven to be an effective method to calculate velocity distributions from seismic data, and its applicability for other elastic properties needs further research.

Hydrodynamic characteristics of submerged vegetation flow with non-constant vertical porosity.

In order to investigate the influence of the vertical variation of porosity on open-channel flow with submerged vegetation, vertical non-homogeneous stumps and stems in submerged vegetation flow are simulated with truncated cones in a laboratory flume. First, porosity is defined as a function of water depth. A new governing equation for vegetation flow is established on the basis of the poroelastic media flow theory, and its analytical solution is obtained with the finite analytic method. Then, the fitting expression of permeability is established with experimental data, which shows the variation in permeability with vertical porosity and vegetation density. Finally, the calculated velocity distribution is compared with the measured velocity distribution. The theoretical results are in good agreement with the experimental data, which indicates that the theoretical formula accurately and practically predicts vertical velocity distribution in complex open-channel flow with submerged vegetation.

Radial distribution of fragment velocity of asymmetrically initiated warhead

Cylinder casing filled with explosive under asymmetric initiation is an easy way to increase the warhead efficiency. The radial distribution of fragment velocity is an important design parameter for the asymmetrically initiated warhead. Available formulas either can only apply to calculating fragment velocity of certain radial direction, or their applications need experiments to determine unknown parameters. Establishment of a new math model to calculate velocity distribution was presented in this paper. Firstly, in the central section of warhead cylinder (treated as 2D problem), a stationary point was proposed existing between the asymmetric initiation point and the warhead center. From this stationary point the warhead can be radially cut into many segments of explosive and fragments. Then the ratios of charge mass to casing mass of those segments were computed, corrected and used to obtain fragments velocities by Gurney formula. Most importantly, the position of the stationary point was theoretically determined by the one-dimensional detonation pushing piston theory (Zhang et al., 2001) [14]. The math model established in the present work was finally validated with the numerical modeling and the experiment results. The results indicate that the model can accurately compute the radial distribution of fragment velocity of asymmetrically initiated warhead and is completely theoretically enclosed, needing no experiments to determine unknown parameters. In addition, the fragment velocity distribution gotten from experiments was found to be different with the theoretical velocity distribution near the initiation side because of influence of the initiator volume.

Numerical Simulation of Three-Dimensional Dendritic Growth of Alloy: Part I—Model Development and Test

To improve the computational efficiency of the three-dimensional (3D) cellular-automaton–finite-volume-method (CA-FVM) model for describing the dendritic growth of alloy, the block-correction technique (BCT) and the parallel computation approach are introduced. Accordingly, a serial of investigations on the efficiency of the optimized codes in dealing with the designed cases for the melt flow and the heat transfer problems is carried out. Moreover, the accuracy of the present codes is evaluated by the comparisons between the solution to the melt flow and the heat transfer problems and the results from analytical equations and the commercial software. Additionally, the capability of the present CA model is evaluated by comparing the steady growth parameters of the equiaxed dendritic tip and the morphology and the secondary dendrite arm spacing (SDAS) of columnar dendrites with the LGK analytical model and the experimental results of the unidirectional solidification of high-carbon steels. The results show that with the introduction of the 3D BCT, the iteration process of the serial tri-diagonal matrix algorithm (TDMA) code changes from the fluctuation type to the smooth one, and thus, the computational cost is reduced significantly. Moreover, the parallel Jacobi code with one two-dimensional (2D) iteration in 3D BCT is proved to be the most efficient one among the codes compiled in the present work, and therefore, accordingly it is employed to simulate the 3D dendritic growth of alloys. The calculated velocity distribution and temperature variation agree well with the results from the analytical equations and the commercial software. The predicted steady tip velocities agree with the LGK analytical model as the undercooling is 6 K to 7 K. Moreover, the predicted columnar dendritic morphology and SDAS of high-carbon Fe-C alloys during the unidirectional solidification agree with the experimental results.

Fragment Velocity Distribution of Cylindrical Rings Under Eccentric Point Initiation

AbstractA design mode, in which a casing is filled with a charge initiated off‐centre (eccentric point initiation), is common in the field of explosion and structural protection. The fragment velocity distribution along the circumference of the casing is distinctly non‐uniform due to the difference in blast loading around the circumference of the casing. To quantify the fragment velocity distribution, two kinds of cylindrical rings with different structural parameters were adopted. Static explosive experiments with three eccentric coefficients (0, 0.5, 1.0) were conducted with pulsed X‐ray diagnostics. Using coefficients derived from experimental data and calculating the effects of both the eccentricity of initiation and angle around the circumference, an angle‐dependent ratio βθ of charge mass to casing mass has been derived as a mean to modify the fragment velocity formula of Gurney for this application. The derived formula was shown to correctly predict the fragment velocity distribution around the circumference of the cylindrical ring. The calculated velocity distributions show good agreement with the experimental results.

Effects of rarefaction, viscous dissipation and rotation mode on the first and second law analyses of rarefied gaseous slip flows confined between a rotating shaft and its concentric housing

A parametric analytical study is carried out to scrutinize the mechanism of fluid flow, heat transfer and entropy generation in a low-speed rarefied gaseous flow confined between a shaft and its concentric housing, i.e., the cylindrical Couette flow. In the first law analysis, closed form solutions for the radial temperature profiles are obtained by incorporating the calculated velocity distribution into the energy equation. The derivations for three thermal cases, which are founded on imposing different thermal conditions, namely, the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT) boundary conditions, are presented. In the second law analysis, the contributions of thermal diffusion and fluid friction irreversibility to the total entropy generation in the micro domain are illustrated, and the relevant expressions for the Bejan number and the entropy generation number as well as the average entropy generation rate are derived. Finally, the variations of major variables with influential parameters such as the Knudsen number, the Brinkman number and rotation mode are investigated to elucidate the associated effects of rarefaction phenomenon, viscous dissipation and geometric condition on the characteristics of the flow.

ICONE19-43536 Development of CFD Analysis Method Based on Droplet Tracking Model for BWR Fuel Assemblies

It is well known that the minimum critical power ratio (MCPR) of the boiling water reactor (BWR) fuel assembly depends on the spacer grid type. Recently, improvement of the critical power is being studied by using a spacer grid with mixing devices attaching various types of flow deflectors. In order to predict the critical power of the improved BWR fuel assembly, we have developed an analysis method based on the consideration of detailed thermal-hydraulic mechanism of annular mist flow regime in the subchannels for an arbitrary spacer type. The proposed method is based on a computational fluid dynamics (CFD) model with a droplet tracking model for analyzing the vapor-phase turbulent flow in which droplets are transported in the subchannels of the BWR fuel assembly. We adopted the general-purpose CFD software Advance/FrontFlow/red (AFFr) as the base code, which is a commercial software package created as a part of Japanese national project. AFFr employs a three-dimensional (3D) unstructured grid system for application to complex geometries. First, AFFr was applied to single-phase flows of gas in the present paper. The calculated results were compared with experiments using a round cellular spacer in one subchannel to investigate the influence of the choice of turbulence model. The analyses using the large eddy simulation (LES) and re-normalisation group (RNG) k-ε models were carried out. The results of both the LES and RNG k-ε models show that calculations of velocity distribution and velocity fluctuation distribution in the spacer downstream reproduce the experimental results qualitatively. However, the velocity distribution analyzed by the LES model is better than that by the RNG k-ε model. The velocity fluctuation near the fuel rod, which is important for droplet deposition to the rod, is also simulated well by the LES model. Then, to examine the effect of the spacer shape on the analytical result, the gas flow analyses with the RNG k-ε model were performed for three kinds of spacers of actual fuel assemblies: a lattice type spacer, a round cell type spacer, and a grid spacer with mixing vanes, respectively. The results indicate that the swirling flow is generated by the mixing vane, and the turbulence energy increases near the surface of fuel rod. The Lagrangian method was applied to droplet behavior in turbulent gas flow around the round cell type spacer and that around a mixing vane spacer as trial analyses. It was confirmed that liquid droplet deposition is promoted in downstream from the mixing vane spacer because of swirling flow.

Physical and mathematical modeling of acousto-convective drying of rice

The present paper considers calculated and experimental data on acousto-convective drying of unhusked rice and analyzes the data on the drying of rise in three drying cells: in two installations of the Institute of Theoretical and Applied Mechanics (ITAM) of the Siberian Branch of the RAS — drying cells of small and medium cross-section — and in the large cross-section installation developed jointly by the Korea Polytechnic University and Doosan Co. LD. on the basis of the acousto-convective technology developed at the ITAM of the Siberian Branch of the RAS. In particular, calculated velocity distributions over the cell cross-section in the installation with a large cross-section are presented. The experiment has shown that the use of the twomode acoustic signal for drying rice does not influence drying results as compared to the one-mode regime. The drying rate of rice placed in the audio-frequency generator chamber differed from the drying rate in the drying cell. The calculation method has been verified by the amplitude-frequency characteristics of the Hartmann generator.

DETAILED ANALYSIS OF FILAMENTARY STRUCTURE IN THE WEIBEL INSTABILITY

We present results of a 2D3V kinetic Vlasov simulation of the Weibel instability. The kinetic Vlasov simulation allows us to investigate the velocity distribution of dilute plasmas, in which the effect of collisions between particles is negligible, and has the advantage that the accuracy of the calculated velocity distribution does not depend on the density of plasmas at each point in the physical space. We succeed in reproducing some features of the Weibel instability shown by other simulations, for example, the exponentially growing phase, the saturation of the magnetic field strength, the formation of filamentary structure, and the coalescence of the filaments. Especially, we concentrate on the behavior of the filaments after the saturation of the magnetic field strength and find that there is a kind of quasi-equilibrium states before the coalescence occurs. Furthermore, it is found that an analytical solution for stationary states of the 2D3V Vlasov-Maxwell system can reproduce some dominant features of the quasi-equilibrium, e.g, the configuration of the magnetic field and the velocity distribution at each point. The analytical expression could give a plausible model for the transition layer of a collisionless shock where a strong magnetic field generated by the Weibel instability provides an effective dissipation process instead of collisions between particles.

PIV Techniques for Velocity Fields of Internal Waves over a Slowly Varying Bottom Topography

This paper reviews transformation processes and nonlinear properties of internal waves over a uniform slope in a two-fluid system, attempting to reveal water particle kinematics by using particle image velocimetry (PIV). Attenuation and setup induced by wave breaking are predicted using an energy-dissipation model including the radiation stress. In the present paper, the radiation stress is associated with the time-averaged momentum flux owing to the interaction between incident and reflected internal waves. These predictions agree with experimental data obtained by an image processing technique with which the boundary plane between the upper and lower layers could be detected as a density interface. A set of halogen lamps and three high-definition digital video cameras are used to illustrate velocity vector fields during one wave period. Instantaneous velocity fields measured by the PIV system are compared with the calculated velocity distribution by the method of characteristics in combination with the first-order Stokes theory. The rundown behavior is then investigated, and its influence upon the undertow in the lower layer is explained with a simple turbulent-jet model. Furthermore, the theoretical approach for examining mass transport and undertow is discussed in relation to the measured mean velocity.

Investigation of flow resistance in smooth open channels using artificial neural networks

An accurate prediction of the friction coefficient is very important in hydraulic engineering since it directly affects the design of water structures, the calculation of velocity distribution, and an accurate determination of energy losses. However, conventional approaches that are profoundly based on empirical methods lack in providing high accuracy for the prediction of the friction coefficient. Consequently, new and accurate techniques are still highly demanded. This study introduces an efficient approach to estimate the friction coefficient via an artificial neural network, which is a promising computational tool in civil engineering. The estimated value of the friction coefficient is used in Manning Equation to predict the open channel flows in order to carry out a comparison between the proposed neural networks based approach and the conventional ones. Results show that the proposed approach is in good agreement with the experimental results when compared to the conventional ones.

A108 オリフィス下流における流れ加速型腐食の評価 : 1. 流れ場の計測と数値解析(配管減肉(FAC),OS6 保全・設備診断技術(1),一般講演,地球温暖化防止と動力エネルギー技術)

In this study, in order to evaluate the effects of flow field on corrosion rate due to flow accelerated corrosion (FAC), an orifice flow was measured and calculated. The diameter of pipe is 50 mm and that of the orifice is 24.3 mm, and flow velocity in a water loop was set at 2.41 m/s. Flow field was measured by laser Doppler velocimetry (LDV) and particle image velocimetry (PIV), and compared with a calculation for the same flow conditions. Measurements of wall shear stress downstream of the orifice was also planed. The calculated velocity distributions of standard k- agreed qualitatively with PIV data and quantitatively with LDV data. Instantaneous flow field measured by PIV showed vortices around the jet from the orifice and some of them reached near the pipe wall.

A fast algorithm for inverse airfoil design using a transpiration model and an improved vortex panel method

A fast algorithm for inverse airfoil design using an efficient panel method for potential flow calculation is presented. The method employs linear vortex distributions on the panels and a consistent procedure for imposing the Kutta condition, thus eliminating the spurious aerodynamic loading that usually appears at a cusped trailing edge. The algorithm searches the airfoil ordinates attending to a given surface velocity distribution with fixed abscissas. It begins with a guessed starting shape and successively modifies it by an iterative process, such that the normal velocity vanishes and the calculated velocity distribution gradually approaches the required one. Each iteration is performed in two main steps: 1) the flow calculation step; 2) the geometrical marching step, where the calculated velocity distribution is compared with the required one and a transpiration model is applied to modify the current shape towards another one more close to the target shape. The geometrical marching is conducted by varying the panel slopes as a function of the normal velocity excess induced by the difference between the required and calculated velocities. A scheme is applied in order to close the body shape. Various test cases were carried out and are presented for the efficiency and robustness validation of the proposed inverse algorithm. Keywords : inverse method, panel method, airfoils, vortex distributions

Copper deposition and dissolution in seemingly parallel electric and magnetic fields: Lorentz force distributions and flow configurations

In two different cylindrical electrochemical cells, copper deposition and dissolution in the presence of a magnetic field mostly parallel to the electric field was investigated. Particle image velocimetry measurements show that even under such a field configuration where Lorentz forces are often a priori neglected may in fact dominate the flow. Further, depending on the electrode radius, a reversal of the secondary flow was found. This feature can be explained by the different Lorentz force configurations calculated from the magnetic field and the primary current distributions. The components of the magnetic field were determined by means of a traversed Hall probe and were calculated by a commercial finite element package. Experimentally and numerically determined field distributions match very well. A good agreement between the measured and calculated velocity distributions was also found, suggesting that in the present case the effect of the Lorentz force alone is sufficient to explain the magnetic field influence on the flow.