Velocity Distribution Research Articles

Effects of the chirp rate on single-shot coherent Rayleigh-Brillouin scattering

Single-shot coherent Rayleigh-Brillouin scattering (CRBS) is modeled using direct simulation Monte Carlo (DSMC). In CRBS, an optical lattice generated by the interference of two pump lasers traps the neutral particles via the dipole force. The gradient of refractive index due to the trapped particles of the gaseous media leads to coherent scattering of a probe beam, resulting in the CRBS signal. Additionally, using a chirped laser beam, CRBS signals can be obtained in a single laser shot, shortening the measurement time of the gas flow (on the order of 100 ns). The DSMC results of single-shot CRBS assuming Maxwellian velocity distribution functions (VDFs) show good agreement with experimental data, including argon, carbon dioxide, and xenon, for different gas pressures. One of the key observations obtained from the present simulations is that the CRBS signals become asymmetric when using a fast chirp rate due to finite time for collisionless trapping and collisional thermalization. Published by the American Physical Society 2024

An implicit solution for Asay foil trajectories generated by separable, sustained-production ejecta source models

We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a “compatibility score” metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory.

Observation of radial velocity along the Yangtze River based on sentinel-1A

ABSTRACT Estuaries and coasts runoff plays a crucial role in the dynamics of the ocean system. However, the current emphasis on synthetic aperture radar (SAR) retrieved current velocities has been on studying strong boundary currents and large-scale ocean circulation, resulting in relatively limited observational research on estuarine current velocities. This study aims to observe the current velocities in the Yangtze River estuary area using Sentinel-1A SAR data. The findings indicate a high agreement between the current velocities retrieved by Sentinel-1A and those observed at hydrographic stations, showcasing the characteristics of current velocity distribution associated with seafloor topography. This highlights the significant potential of SAR in observing estuarine current velocities, contributing to the analysis of benthic topography and the statistics of river runoff.

Comparisons between full molecular dynamics simulation and Zhang's multiscale scheme for nanochannel flows.

In a very small surface separation, the fluid flow is actually multiscale consisting of both the molecular scale non-continuum adsorbed layer flow and the intermediate macroscopic continuum fluid flow. Classical simulation of this flow often takes over large computational source and is not affordable owing to using molecular dynamics simulation (MDS) to model the adsorbed layer flow, if the flow field size is on the engineering size scale such as of 0.01-10mm or even bigger like occurring in micro or macro hydrodynamic bearings. The present paper uses full MDS to validate Zhang's multiscale flow model, which yields the closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate continuum fluid flow. Here, full MDS was carried out for the pressure-driven flow of methane in the nano slit pore made of silicon respectively with the channel heights 5.79nm, 11.57nm, and 17.36nm. According to the number density distribution, the flow areas were respectively discriminated as the adsorbed layer zone and the intermediate fluid zone. The values of the characteristic parameters for Zhang's multiscale scheme were extracted from full MDS and input to Zhang's multiscale flow equations respectively for calculating the flow velocity profile and the volume flow rates of the adsorbed layers and the intermediate fluid. It was found that for these three channel heights, the flow velocity profiles calculated from Zhang's model approximate those calculated from full MDS, while the total flow rates through the channel calculated from Zhang's model are close to those calculated from full MDS. The accuracy of Zhang's multiscale flow model is improved with the increase of the channel height. The recent modification of the optimized potential for liquid simulation (MOPLS) model was used to calculate the interaction force between two methane molecules. In order to calculate the interaction force between the wall atoms and the methane molecules accurately, our previous non-equilibrium multiscale MDS was used. The interaction forces between the methane molecule and the wall atom were obtained from the coupled potential function by the L-B mixing rule when the fluid molecules arrived at near wall. The methane molecule diameter was obtained from the radial distribution function by using equilibrium MDS under the same initial conditions. The local viscosities across the adsorbed layer were obtained from the local velocity profile by using the Poiseuille flow method. The motion equation of the methane molecule was solved by the leapfrog method. The temperature of the simulation system was checked by Bhadauria's method, i.e., the system temperature was rectified by the velocities in the y- and z-directions. The flow velocity distributions across the channel height and the volume flow rates through the channel were also calculated from Zhang's closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate fluid flow. The results respectively obtained from full MDS and Zhang's multiscale flow equations were then compared.

Analysis of Flow Field Characteristics in the Three-Phase Jet Fire Monitor Head

To enhance the jet performance of the three-phase jet fire monitor (TPJFM), an analysis was conducted on the internal flow field (IFF) characteristics of the monitor head. Using the volume of fluid method, the impact of key structural parameters, such as the powder-pipe bending angle and the supporting blade length, on the turbulent kinetic energy (TKE) of the IFF, the velocity distribution uniformity at the nozzle outlet, and the pressure drop (PD) between the inlet and outlet of the internal flow field, was analyzed. The study revealed that increasing the bending angle of the powder pipe will lead to a significant improvement in the uniformity of velocity distribution in the IFF. Extending the supporting blade length helps reduce the average TKE at the nozzle outlet but has a minimal impact on the velocity distribution uniformity and the PD between the inlet and outlet. Reasonable design of the distance between the supporting blades and the bending section of the powder pipe can improve the IFF characteristics, reducing local pressure losses and peak TKE. The research results can effectively improve the IFF characteristics, enhance jet performance, and provide theoretical basis and technical support for the design and optimization of the TPJFM.

Validating full-spectrum fitting with a synthetic integral-field spectroscopic observation of the milky way

Abstract Ongoing deep IFS observations of disk galaxies provide opportunities for comparison with the Milky Way (MW) to understand galaxy evolution. However, such comparisons are marred by many challenges such as selection effects, differences in observations and methodology, and proper validation of full-spectrum fitting methods. In this study, we present a novel code GalCraft to address these challenges by generating mock IFS data cubes of the MW using simple stellar population models and a mock MW stellar catalog derived from E-Galaxia. We use the widely adopted full-spectrum fitting code pPXF to investigate the ability to recover kinematics and stellar populations for an edge-on mock MW IFS observation. We confirm that differences in kinematics, mean age, [M/H], and [α/Fe] between thin and thick disks can be distinguished. However, the age distribution is overestimated in the ranges between 2 − 4 and 12 − 14 Gyr compared to the expected values. This is likely due to the age spacing and degeneracy of SSP templates. We find systematic offsets in the recovered kinematics due to insufficient spectral resolution and the variation of line-of-sight velocity distribution with age and [M/H]. With future higher resolution and multi-[α/Fe] SSP templates, GalCraft will be useful to validate key signatures such as [α/Fe]-[M/H] distribution at different R and |z| and potentially infer radial migration and kinematic heating efficiency to study detailed chemodynamical evolution of MW-like galaxies.

Exploration of moiré tomography in spatial distribution measurement of wind velocity

In this paper, moiré tomography is applied to measure the spatial velocity distribution of thermal wind field. To verify the feasibility of our method, three sets of experiments are carried out, each lasting for 5 min. And then, its spatial distribution is obtained based on the theoretical relation between the refractive index extracted from moiré fringes and the wind velocity. Finally, some validation is performed for the reliability and accuracy of the method. The radial distribution of wind velocity matches well with those estimated results based on a reported theoretical model. Besides, the general trend of wind velocity values at different times of moiré tomography measurement is almost consistent with those recorded by the anemometer, and the relative error between them maintains within 3 %. In further, some reasonable analysis of the factors contributing to error is provided. In a word, this paper demonstrates that moiré tomography has the potential application to offer a feasible means for the spatial measurement of wind velocity.

Analysis of Brownian motion and thermophoresis effects with chemical reaction on Williamson nanofluid flow over permeable stretching sheet

This study warrants a broad analysis on the simultaneous effects of Brownian and thermophoresis on the chemically reacting Williamson nanofluid flow via a permeable expanding sheet. The analysis includes the properties of slip velocity and thermal radiation, providing a more representative picture of the physical phenomena. The differential equations governed by demonstrating the fluid flow phenomena are renewed to a set of nonlinear differential equations utilizing similarity rules. These transformed equations are subsequently handled numerically adopting the fourth-order Runge-Kutta method. The results reveal the significant control of Brownian motion together with thermophoresis and additionally, the inclusion of velocity slip and thermal radiation remarkably affect the velocity, temperature, and concentration distributions. Parametric studies show the validation of the present system to variations in the Williamson fluid parameter, slip parameter, radiative heat parameter, Brownian motion parameter, and thermophoresis parameter.

Exploring the influence of flexural rigidity variability of aquatic plants on stem deflection geometry and flow characteristics

The existing assumption of a constant flexural rigidity (EI) for the entire height of aquatic plants in the analysis of flow past flexible vegetation may not translate in to real scenario as EI of a flexible plant stem varies along the height due to variation in tissue structure and cross section. This variation is therefore needed to be effectively quantified for better analysis of flow-vegetation interaction. In this regard, the own-weight cantilever method was used to represent the variability of EI along the stem height of three plants: water lily, water chestnut, and lotus. Analytical models are proposed to predict stem deflection geometry and vertical velocity distribution across channel depth incorporating EI as a function of stem height. Analytical and experimental data, obtained from open-channel flume tests, significantly support the developed models and confirm the assumption of variable flexural rigidity. Further investigations show that the flexural rigidity, transcends being a mere constant numeric value; it profoundly influences various aspects of the fluid-vegetation interaction such as: the extent of deflection geometry, velocity reduction, Reynold stress variation, and penetration length. Therefore, this study is crucial for better understanding of the physics of sediment transport, pollutant mixing, and wetland management and restoration.

Numerical investigation of synergistic effects of magnetic fields and bluff bodies on heat transfer enhancement and pressure drop reduction in microchannels

Efficient thermal management is essential for designing compact and high-performance heat sinks and heat exchangers. This study addresses the challenge of optimizing heat transfer while minimizing pressure losses in systems exposed to concentrated heat flux by proposing a novel approach that employs both active and passive vortex generators. Specifically, a uniform magnetic field generated by permanent magnets and a bluff body are utilized within a microchannel containing a 2 vol% ferrofluid. Numerical simulations were performed across Reynolds numbers ranging from 100 to 500 and magnetic field intensities up to 0.5 T to evaluate the system's performance. The results demonstrate that the combination of magnetic fields and a bluff body induces vortex generation, alters velocity distribution, and enhances flow mixing, resulting in a 30 % increase in heat transfer efficiency and an 11 % reduction in pressure drop under optimal conditions. Although the introduction of barriers led to a 3 % rise in pressure drop, the uniform magnetic field effectively mitigated friction by reducing flow separation and limiting surface contact. These findings highlight the potential of this method for improving the design of advanced thermal management systems.

4D flow MRI velocity uncertainty quantification.

An automatic method is presented for estimating 4D flow MRI velocity measurement uncertainty in each voxel. The velocity distance (VD) metric, a statistical distance between the measured velocity and local error distribution, is introduced as a novel measure of 4D flow MRI velocity measurement quality. The method uses mass conservation to assess the local velocity error variance and the standardized difference of means (SDM) velocity to estimate the velocity error correlations. VD is evaluated as the Mahalanobis distance between the local velocity measurement and the local error distribution. The uncertainty model is validated synthetically and tested in vitro under different flow resolutions and noise levels. The VD's application is demonstrated on two in vivo thoracic vasculature 4D flow datasets. Synthetic results show the proposed uncertainty quantification method is sensitive to aliased regions across various velocity-to-noise ratios and assesses velocity error correlations in four- and six-point acquisitions with correlation errors at or under 3.2%. In vitro results demonstrate the method's sensitivity to spatial resolution, venc settings, partial volume effects, and phase wrapping error sources. Applying VD to assess in vivo 4D flow MRI in the aorta demonstrates the expected increase in measured velocity quality with contrast administration and systolic flow. The proposed 4D flow MRI uncertainty quantification method assesses velocity measurement error owing to sources including noise, intravoxel phase dispersion, and velocity aliasing. This method enables rigorous comparison of 4D flow MRI datasets obtained in longitudinal studies, across patient populations, and with different MRI systems.

Scrutiny of pseudoplastic nanofluid flow under the influence of magnetic hydrodynamics with chemical reaction across the cylinder with slip boundary condition

Buoyantly induced flows possess diversified utilizations in numerous engineering processes for instance, reactor cooling through passive strategy, LED lights, pipes manufacturing, ship funnel and many more. Galvanized sheets sticked to form a hollow cylinder is used for fast cooling in naval ship and chimney of steam power plant. In view of such mesmerizing significance of flow and thermal attributes of fluid over vertical cylinder, current effort is articulated. For this purpose, Williamson fluid model is accounted and nanoparticles are also induced to envision advanced thermal features in the flow over vertically oriented cylinder. Physical effectiveness of magnetic field implications and chemical reactive species are entertained to notice change in hydrothermal and mass fields. Slip boundary constraint along with stagnant flow at the surface of cylinder is considered to inspect behavior in free stream region. The fundamental governing equations of problem are attained in the sense of PDEs by utilizing the concept of boundary layer approximation and converted into coupled nonlinear ODEs by substituting specific similar variables. Numerically the resulting ODEs are resolved by making the use of bvp4c built in MATLAB routine, the outcomes are attained and arranged in graphical and tabular manner. The influence of pertinent flow parameters such as (0.1 ≤ We ≤ 1.0), (1.0 ≤ M ≤ 3.0), (1.0 ≤ Pr ≤ 11), thermophoresis parameter (0.5 ≤ Tp ≤ 4.5), (1.0 ≤ Bp ≤ 5.0), (0.05 ≤ Nr ≤ 0.7), and (0.5 ≤ Kc ≤ 5.0) are examined on the momentum, thermal and concentration distributions. It is manifested that the velocity distribution depreciates by uplifting magnetic field strength. Increment in magnitude of wall drag and convective heat transfer is perceived by enhancing Prandtl number. It is inferred that friction coefficient in absolute sense and heat flux coefficient tends to exceed against elevation in (We). From comprehensive analysis, declination in velocity and thermal field is depicted versus Reynold number whereas, contrary aspects are visualized in concentration. Enhancement in the value of surface drag and thermal flux is revealed versus (Re).

Particle motion characteristics on the rotational flow pneumatic conveying of horizontal-vertical pipeline

In this study, a rotational flow device (rotational blade) is developed and installed in the upstream of the particle inlet with the aim of improving the efficiency and capacity of pneumatic conveying. Firstly, this study analyzed the energy-saving effect of rotational flow based on the pressure drop and power consumption. The results shown that the optimal velocity can be reduced by a maximum of 18.7 % and the power consumption coefficient can be reduced by a maximum of 9.8 %. Furthermore, the distributions of particle concentration, velocity and pulsation velocity are analyzed by using electrical capacitance tomography (ECT) and particle image velocimetry (PIV) system. It is found that the particle velocity and velocity pulsation intensity for rotational flow are higher, and they have the ability to enhance particle suspension. Then, the power spectrum of the particle pulsation velocity shown that the rotational flow exhibited higher peak value at lower frequencies, indicating the particles are not easily deposited at pipe bottom. Finally, the auto-correlation of particle pulsation velocity indicated that the particle motion is more stable and has a longer period at low particle concentrations. The skewness factor and probability density function of particle pulsation velocity indicated that the use of rotational blades makes the particle pulsation velocity to deviate from the Gaussian distribution.

Study on the hydraulic conveyance characteristics of suspended coarse particles within pipelines

The Flow Regime Transition Device transforms the gelled crude oil mass into gelled crude oil particles for hydraulic conveying. The gelled crude oil particles may reaggregate into gelled crude oil mass at the later stage of hydraulic conveying. Therefore, understanding the patterns of hydraulic suspension conveying gelled crude oil particles is vital for safely gathering and efficiently conveying crude oil. This paper employs the CFD-DEM coupling technique to conduct a numerical study on the hydraulic conveying characteristics of gelled crude oil particles. The accuracy of the model and the solution method is verified by comparing them with the experimental data of particle concentration distribution, and single particle rise behavior, and particle transport flow of gelled crude oil. The size range of gelled crude oil particles spans from 0.0001 m to 0.003 m. We operate the transportation within a velocity range of 0.5 to 4 m/s and a concentration range of 0.022 to 0.0537. Simulation results indicate two flow regimes in the hydraulic conveying of gelled crude oil particles: an upper-moving bed flow and a heterogeneous suspension flow. With increased conveying velocity, the upper moving bed flow gradually transitions to a heterogeneous suspension flow. Beneath the upper moving bed flow, some scattered particles exist, likely resulting from the action of turbulent diffusion. Changes in conveying concentration and particle size have a minor impact on the velocity distribution of particles and fluid but a more significant effect on the particle distribution across the pipe cross-section. Also, when conveying particles of different sizes, most smaller particles travel along the pipe wall.

Exploring the significance of nanoparticle shapes and the impact of thermal radiation on MHD viscoelastic nanofluid flow in porous channels

ABSTRACT This study investigates analytically the influence of nanoparticle shapes on an unsteady mixed convective viscoelastic MHD nanofluid flow in a horizontal channel with oscillating walls in a saturated porous medium. The effect of radiation is also considered in the energy equation. The considered NPs are Cu, Ag, Al2O3, TiO2, and Fe3O4, with base fluids H2O and C2H6O2. The considered different shapes of NPs are cylinder, platelet, blade, and brick. The study examines three flow situations based on physical boundary conditions. The perturbation method is employed to solve the flow governing equations for three different flow situations based on physical boundary conditions: Case (i) flow in a horizontal channel with both lower and upper walls stationary; Case (ii) the upper wall of the channel is in oscillation while the lower one is constant; Case (iii) both walls of the channel are in oscillatory motion. The velocity and temperature distributions, as well as the skin friction coefficient and heat transfer rate, are analyzed through graphs and tables to assess the impact of various governing parameters. From the results, it is found that brick-shaped NPs exhibit more strength to the velocity and temperature distributions, followed by cylinder, platelet, and blade for both water-based and EG-based NF.

Cooling positronium to ultralow velocities with a chirped laser pulse train.

When laser radiation is skilfully applied, atoms and molecules can be cooled1-3, allowing the precise measurements and control of quantum systems. This is essential for the fundamental studies of physics as well as practical applications such as precision spectroscopy4-7, ultracold gases with quantum statistical properties8-10 and quantum computing. In laser cooling, atoms are slowed to otherwise unattainable velocities through repeated cycles of laser photon absorption and spontaneous emission in random directions. Simple systems can serve as rigorous testing grounds for fundamental physics-one such case is the purely leptonic positronium11,12, an exotic atom comprising an electron and its antiparticle, the positron. Laser cooling of positronium, however, has hitherto remained unrealized. Here we demonstrate the one-dimensional laser cooling of positronium. An innovative laser system emitting a train of broadband pulses with successively increasing central frequencies was used to overcome major challenges posed by the short positronium lifetime and the effects of Doppler broadening and recoil. One-dimensional chirp cooling was used to cool a portion of the dilute positronium gas to a velocity distribution of approximately 1 K in 100 ns. A major advancement in the field of low-temperature fundamental physics of antimatter, this study on a purely leptonic system complements work on antihydrogen13, a hadron-containing exotic atom. The successful application of laser cooling to positronium affords unique opportunities to rigorously test bound-state quantum electrodynamics and to potentially realize Bose-Einstein condensation14-18 in this matter-antimatter system.

Understanding the Energy-Saving mechanism of ceramic balls in tumbling mills

This study investigates why ceramic balls achieve superior grinding performance compared to steel balls at lower densities and lower energy consumption. Particle motion analysis shows that increasing the filling level significantly improves the velocity distribution of the grinding media. The energy input from the mill is mainly converted into the kinetic and potential energy of the media, with potential energy being dominant. As the filling level increases, the efficiency of kinetic energy conversion improves. Collisions between media and mineral particles dominate energy transfer, and lower media density enhances collision energy distribution uniformity. Reducing media density decreases grinding energy consumption while maintaining the same grinding effect.

CoOMBE: A suite of open-source programs for the integration of the optical Bloch equations and Maxwell-Bloch equations

The programs described in this article and distributed with it aim (1) at integrating the optical Bloch equations governing the time evolution of the density matrix representing the quantum state of an atomic system driven by laser or microwave fields, and (2) at integrating the 1D Maxwell-Bloch equations for one or two laser fields co-propagating in an atomic vapour. The rotating wave approximation is assumed. These programs can also be used for more general quantum dynamical systems governed by the Lindblad master equation. They are written in Fortran 90; however, their use does not require any knowledge of Fortran programming. Methods for solving the optical Bloch equations in the rate equations limit, for calculating the steady-state density matrix and for formulating the optical Bloch equations in the weak probe approximation are also described. Program summaryProgram Title: CoOMBECPC Library link to program files:https://doi.org/10.17632/5wsg9d52dk.1Developers' repository link:https://github.com/durham-qlm/CoOMBELicensing provisions: GPLv3Programming language: Fortran 90Nature of problem: The present programs can be used for the following operations: (1) Integrating the optical-Bloch equations within the rotating wave approximation for a multi-state atomic system. At the choice of the user, the calculation will return either the time-dependent density matrix at given times or the density matrix in the long time limit if the system evolves into a steady state in that limit. The calculation can be done with or without averaging over the thermal velocity distribution of the atoms. The number of atomic states which can be included in the calculation is limited only by the CPU time available and possibly by memory requirements. An arbitrarily large number of laser or microwave fields can be included in the calculation if these fields are all CW. This number is currently limited to one or two for fields that are not all CW. The calculation can be done in the weak probe approximation, or in the rate equations approximation, or without assuming either of these two approximations. Calculating refractive indexes, absorption coefficients and complex susceptibilities is also possible. (2) Integrating the 1D Maxwell-Bloch equations in the slowly varying envelope approximation for one or two fields co-propagating in a single-species atomic vapour. Although geared towards the case of atoms interacting with laser fields, this code can also be used for more general quantum systems with similar equations of motion (e.g., molecular systems, spin systems, etc.).Solution method: The Lindblad master equation is expressed as a system of homogeneous first order linear differential equations, which are transformed as required and solved to obtain the density matrix representing the state of the atomic system. A variety of methods are offered to this end. The same approach is also used in the calculation of the polarisation of the medium when integrating the Maxwell-Bloch equations. The latter are integrated over space using predictor-corrector methods. The library includes a general driving program making it possible to use these codes without additional program development. The distribution also includes examples of the use of a container for running these programs without a pre-installed Fortran compiler.

Parametric study of free turbulent slurry jet: influence of particle size and particle concentration on the flow dynamics and thermal behavior of high-speed slurry jet

A detailed computational investigation was conducted to explore the dynamics of high-speed free slurry jets, with a focus on how variations in abrasive size and concentration affect their behavior. The study yielded several significant observations: Firstly, it was observed that slurry jets containing larger particles exhibited notably higher average velocities, attributed to their inherent self-similar characteristics. Specifically, at the far field of the jet, slurry jets with larger particle sizes demonstrated a 15% increase in velocity compared to those with smaller particles. Additionally, an analysis of turbulent intensity revealed that beyond a certain axial distance (x/D = 10), turbulence levels progressively increased. However, intriguingly, for slurry jets with a high concentration (Co = 15%), there was a notable decrease (28%) in turbulent intensity compared to water jets, indicating a complex interplay between particle size and concentration. Secondly, the study found that as the concentration of particles in the slurry jet increased, there was a corresponding rise in the bulk temperature of the jet. This phenomenon was primarily attributed to the heightened thermal conductivity resulting from the increased density of particles in the water. Furthermore, an examination of the Nusselt number revealed interesting trends. While the Nusselt number exhibited a peak near the nozzle exit, indicative of enhanced heat transfer in this region, it showed a decremental trend along the axial direction of the jet, attributable to jet divergence. In summary, the computational analysis provided valuable insights into the behavior of high-speed slurry jets, highlighting the intricate relationships between abrasive size, concentration, velocity distribution, and thermal characteristics. These findings contribute to a deeper understanding of slurry jet dynamics and have significant implications for various industrial applications.

Semi-Empirical Model Based on the Influence of Turbulence Intensity on the Wake of Vertical Axis Turbines

In the context of energy shortages and the development of new energy sources, tidal current energy has emerged as a promising alternative. It is typically harnessed by deploying arrays of multiple water turbines offshore. Vertical axis water turbines (VAWTs), as key units in these arrays, have wake effects that influence array spacing and energy efficiency. However, existing studies on wake velocity distribution models for VAWTs are limited in number, accuracy, and consideration of influencing factors. A precise theoretical model (Lam’s formula) for wake lateral velocity can better predict wake decay, aiding in the optimization of tidal current energy array designs. Turbulence in the ocean, serving as a medium for energy exchange between high-energy and low-energy water flows, significantly impacts the wake recovery of water turbines. To simplify the problem, this study uses software ANSYS Fluent 2020 R2 for two-dimensional simulations of VAWT wake decay under different turbulence intensities, confirming the critical role of turbulence intensity in wake velocity decay. Based on the obtained data, a new mathematical approach was employed to incorporate turbulence intensity into Lam’s wake formula for VAWTs, improving its predictive accuracy with a minimum error of 1%, and refining some parameter calculations. The results show that this model effectively reflects the impact of turbulence on VAWT wake recovery and can be used to predict wake decay under various turbulence conditions, providing a theoretical basis for VAWT design, optimization, and array layout.