Fluids, Volume 8, Issue 6 (June 2023) – 24 articles

Fog interferes with traffic flow and causes major accidents. In foggy conditions, traffic accident death rates are higher than in other weather conditions. Research on fog dissipation technology is needed to reduce the incidence of accidents caused by fog. There are various artificial methods to remove fog. In this study, two methods of natural dissipation by gravity sedimentation and a solid carbon dioxide seeding fog dissipation mechanism were compared and analyzed in cold fog conditions. Solid carbon dioxide was selected as the fog dissipation particle. In this experiment, solid carbon dioxide seeding with three different values of weight (500 g, 1000 g, and 1500 g) was considered. This is because fog particles can be supercooled and fog can be removed. A light detection and ranging (LiDAR) sensor were used to quantitatively check the effect of improving visibility when solid carbon dioxide was seeded in the fog. The LiDAR sensor detects the surrounding environment through distance measurements by emitting lasers and processing the laser responses. A camera was used to visually observe the phenomenon occurring inside the calorimetric chamber. As a result, the fog dissipation mechanism using solid carbon dioxide seeding under cold fog conditions was proven to be effective in improving the visible distance compared with natural dissipation. Full article

Spectral proper orthogonal decomposition (SPOD) has seen renewed interest in recent years due to its unique ability to decouple organised motion at different timescales from large datasets with limited available information. This paper investigated the unsteady components of the flow field within a simplified turbine centre frame (TCF) model by applying SPOD to experimental, time-resolved flow speed data captured by particle image velocimetry (PIV). It was observed that conventional methods failed to capture the two significant active bands in the power spectrum predicted by preliminary hot wire anemometry measurements. Therefore, a modification to the SPOD procedure, which employs subsampling of the time sequence recorded in the experiment to artificially lower the PIV data acquisition frequency, was developed and successfully deployed to analyse the TCF flow field. The two dynamically active bands were identified in the power spectra, resulting in a closer match to the preceding analyses. Within these bands, SPOD’s ability to capture spatial coherence was leveraged to detect several plausible coherent, fluctuating structures in two perpendicular planes. A partial three-dimensional reconstruction of the flow phenomena suggested that both bands were associated with a distinct mode of organised motion, each contributing a significant percentage of the system’s total fluctuating energy. Full article

The reliable non-contact dispensing of droplets in the pico- to microliter range is a challenging task. The dispensed drop volume depends on various factors such as the rheological properties of the liquids, the actuation parameters, the geometry of the dispenser, and the ambient conditions. Conventionally, the rheological properties are characterized via a rheometer, but this adds a large liquid overhead. Fluids with different Ohnesorge number values produce different spatiotemporal motion patterns during dispensing. Once the Ohnesorge number is known, the ratio of viscosity and surface tension of the liquid can be known. However, there exists no mathematical formulation to extract the Ohnesorge number values from these motion patterns. Convolutional neural networks (CNNs) are great tools for extracting information from spatial and spatiotemporal data. The current study compares seven different CNN architectures to classify five liquids with different Ohnesorge numbers. Next, this work compares the results of various data cleaning conditions, sampling strategies, and the amount of data used for training. The best-performing model was based on the ECOmini-18 architecture. It reached a test accuracy of 94.2% after training on two acquisition batches (a total of 12,000 data points). Full article

Transonic planar flows around a circular cylinder are investigated numerically for laminar and turbulent flow conditions with Reynolds numbers of $50\le R{e}_D\le 300$ and $8890\le R{e}_D\le$ 80,000 and free stream Mach numbers in the range of $0.2\le M{a}_{\infty }\le 2$. A commercially available CFD tool is used and validated for this purpose. The results show that the flow phenomena occurring can be grouped into eight regimes. Compared to the incompressible flow regimes, several new phenomena can be found. In contrast, at higher $M{a}_{\infty }$ of $0.6\le M{a}_{\infty }\le 0.8$ vortices in the wake of the cylinder are suppressed for $R{e}_D=50$. In some cases, $M{a}_{\infty }=0.8$ and $R{e}_D\ge 300$, $\lambda$-shocks are formed in the near cylinder wake. For supersonic $M{a}_{\infty }$, two different phenomena are observed. Beside the well-known oblique and detached shocks, for $50\le R{e}_D\le 300$ a wake with instabilities is formed downstream of the cylinder. Furthermore, the temporal mean drag coefficient ${\overline{C}}_{\mathrm{D}}$, the Strouhal number $Str$, as well as the critical Mach number $M{a}_{\mathrm{crit}}$ are calculated from the simulation results and are interpreted. Full article

We continue our study of the transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a ${128}^3$ periodic grid. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time. The six runs that previously went to near equilibrium are here extended into equilibrium. As before, we neglect dissipation as we are primarily concerned with behavior at the largest scale where this behavior has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. These six runs have various combinations of imposed rotation and mean magnetic field and represent the five cases of ideal, homogeneous, incompressible, and MHD turbulence: Case I (Run 1), with no rotation or mean field; Case II (Runs 2a and 2b), where only rotation is imposed; Case III (Run 3), which has only a mean magnetic field; Case IV (Run 4), where rotation vector and mean magnetic field direction are aligned; and Case V (Run 5), which has non-aligned rotation vector and mean field directions. Statistical mechanics predicts that dynamic Fourier coefficients are zero-mean random variables, but largest-scale coherent magnetic structures emerge and manifest themselves as Fourier coefficients with very large, quasi-steady, mean values compared to their standard deviations, i.e., there is ‘broken ergodicity.’ These magnetic coherent structures appeared in all cases during transition to near equilibrium. Here, we report that, as the runs were continued, these coherent structures remained quasi-steady and energetic only in Cases I and II, while Case IV maintained its coherent structure but at comparatively low energy. The coherent structures that appeared in transition in Cases III and V were seen to collapse as their associated runs extended into equilibrium. The creation of largest-scale, coherent magnetic structure appears to be a dynamo process inherent in ideal MHD turbulence, particularly in Cases I and II, i.e., those cases most pertinent to planets and stars. Furthermore, the statistical theory of ideal MHD turbulence has proven to apply at the largest scale, even when dissipation and forcing are included. This, along with the discovery and explanation of dynamically broken ergodicity, is essentially a solution to the ‘dynamo problem’. Full article

Multi-droplet impingement is a fundamental aspect inherent to all kinds of technical spray processes which typically aim at enhancing the convective exchange of reagents or heat at the impinged surface. In this paper, the impingement of multiple droplets onto a structured surface is investigated by a comprehensive CFD model, which resolves the dynamics of the individual droplets and the film on a micro-scale level based on the Volume of Fluid (VOF) method. The considered surface topology includes cavities and is typical for protective masks used in the spray etching of Printed Circuit Boards (PCBs). The agitation of the liquid film in terms of the convective mass transfer rates across virtual horizontal evaluation planes is studied and the influence of film height and droplet impaction velocity is elaborated. Passive tracer tracking is employed to investigate the release and re-entrainment of fluid at the surface cavities. Two modes of mass exchange between the cavities and the main flow upon droplet impingement are identified, which are central inflow accompanied by lateral outflow (1) and lateral inflow with outflow at the opposing side (2). A statistical analysis of the allocation of tracer particles shows that high impaction velocities and low film heights correlate with an enhanced decay of tracer particles within the cavities. The susceptibility to re-entrainment is also reduced by high impaction velocities, whereas increased film heights are found to promote re-entrainment. Full article

Grid refinement is used to reduce computing costs while maintaining the precision of fluid simulation. In the lattice Boltzmann method (LBM), grid refinement often uses interpolated values. Here, we developed a method in which interpolation in space and time is not required. For this purpose, we used the moment matching condition and rescaled the nonequilibrium part of the populations, thereby developing a recalibration procedure that allows for the transfer of information between different LBM stencils in the simulation domain. Then, we built a nonuniform lattice that uses stencils with different shapes on the transition. The resulting procedure was verified by performing benchmarks with the 2D Poisselle flow and the advected vortex. It is suggested that grids with adaptive geometry can be built with the proposed method. Full article

Raising the working speed of hydraulic pumps to maximize the efficient matching range of electric motors is one of the possible ways to achieve energy efficiency in electric machinery. By means of a simulation method verified with subsequent experiments in terms of filling efficiency, this paper first analyzed the suction capacity of crescent-type internal gear pumps with different geometric parameters at high speed, and the gear pair that is more suitable for high-speed operation was obtained. Subsequently, as the more significant contributions, two pairing solutions of a non-positive displacement pump and an internal gear pump were proposed to pressurize the inlet of the gear pump to keep it from cavitating. In the compact design solution, the inclined-holes type and axial-flow blade pumps share the same speed as the hydraulic pump, while the decentralized layout solution allows for flexible adjustment of the centrifugal impeller-type pump speed to maximize the filling capability. The final simulation results show that, with the help of inclined-holes type and centrifugal impeller type pumps, the filling efficiency of the internal gear pump at 6000 rpm can be improved by 3.59% and 5.84%, respectively, while the axial-flow blades pump fails to eliminate cavitation regardless of speed. Moreover, when the hydraulic pump works at 6000 rpm, the centrifugal impeller speed needs to be set above 2500 rpm to make sense. Full article

In computations of unsteady flow problems by the arbitrary Lagrangian–Eulerian (ALE) method, the introduction of the grid velocity in the transport terms of the governing equations is not a sufficient condition for conservativeness if topology changes in the dynamic mesh are present and the number of mesh cells changes. We discuss an extension to second-order time differencing schemes (Implicit Euler and Crank–Nicolson) in the finite volume framework, to achieve second-order time-accuracy of the solution. Numerical experiments are given to illustrate the effectiveness of the presented method. Full article

This study investigated the diffusion impact on the chemical perturbation of NO_x and O₃ caused by the streamer and leader parts of a blue jet in the low stratosphere (18–30 km), using the coupling of a detailed stratospheric chemistry model and a typical diffusion model. The study found that diffusion significantly impacted the evolution of chemical perturbations at both short-term and long-term time scales after the blue jet discharge, with changes in NO_x and O₃ concentrations observed at different altitudes (18–28 km). At 18 km, the concentrations of NO_x and N₂O that account for diffusion start to decrease after 1 s, whereas those without diffusion remain at their peak concentrations. Meanwhile, O₃ is slowly destroyed with less NO_x, rather than dropping to an unrealistic low value immediately after the discharge without diffusion. The perturbation caused by the blue jet discharge disappears within a few tens of seconds at 18 km when molecular diffusion is considered. At 30 km, the chemical perturbation from four point sources was observed through changes in NO₂ concentrations. However, the total concentration of NO₂ perturbed by the streamer part discharge at the given surface was negligible when considering diffusion. Overall, this study provided a useful model tool for a more accurate assessment of the chemical effects of individual blue jets. Full article

The causes of many bridge failures have been reported to be local scour around abutments. This study examines roughening elements as devices with which to intercept the downflow responsible for the formation of the principal vortex, which is what triggers local scour around abutments. Two vertical wall abutments with different widths were examined under four different hydraulic conditions in a clear-water regime. Elements with different thicknesses (t) and protrusions (P) with the same dimensions, (P = t = 0.05 L, 0.1 L, 0.2 L, and 0.3 L, where L is the length of the abutment) and with varying depths of installation (Z) were considered. Elements were installed in two positions: between the sediment surface and water elevation and buried within the sediment. To determine the optimum depth of installation, one element was first installed on the sediment surface, and the number of elements was increased in each subsequent test. The results show that installing elements between water surface elevation and the sediment’s initial level did not show any defined trend on scour depth reduction. However, the optimum installation depth of the elements is 0.6–0.8 L below the initial bed level. Moreover, the roughening elements with thickness and protrusion of P = t = 0.2 L resulted in the most effective protection of the foundation. The best arrangement, (P = t = 0.2 L and Z = >0.6–0.8 L) reduced the maximum scour depth by up to 30.4% and 32.8% for the abutment with smaller and larger widths, respectively. Full article

Stacked plate heat exchangers are widely used in thermal energy storage systems and a comprehensive and accurate analysis is necessary for their application and optimization. The fluid flow distribution between the plates is important to ensure even and full usage of the thermal energy storage potential. However, due to the complex topography of the plate surface, it would be computationally expensive to simulate the flow distribution in the multiple channels using a full three-dimensional model, so this work applies a reduced-dimensional model to significantly reduce the computational cost of the simulation and provides a comprehensive analysis of the effect of the internal structure on the internal flow distribution. The work extends a previously presented model to consider transient flow and a multichannel height distribution strategy to allow for simulating multiple channels between stacks of plates. Based on fully-developed flow assumptions, the three-dimensional model is reduced to a planar model, thus obtaining simulation results with satisfactory accuracy at a significantly lower computational cost. The model is verified by a three-dimensional simulation of a sliced two-channel model representing the considered system. The reduced-dimensional model gives similar results to the three-dimensional model for different geometrical and physical parameters. Lastly, the extended reduced-dimensional model is used to simulate the flow of a full two-channel model and the influence of the plate topography on the internal flow distribution is investigated through a comprehensive parametric analysis. The analysis shows that the complex topography of the plate surface eliminates the variation in inlet velocity and significantly changes the internal fluid flow, eventually resulting in a consistent velocity distribution. Full article

Viscous linear surface waves are studied at arbitrary wavelength, layer thickness, viscosity, and surface tension. We find that in shallow enough fluids no surface waves can propagate. This layer thickness is determined for some fluids, water, glycerin, and mercury. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for a given horizontal wave number. In contrast, there are two types of non-propagating modes. One kind of them exists at all wavelength and material parameters, and there are infinitely many such modes for a given wave number, distinguished by their decay rates. The other kind of non-propagating mode that is less attenuated may appear in zero, one, or two specimens. We notice the presence of two length scales as material parameters, one related to viscosity and the other to surface tension. We consider possible modes for a given material on the parameter plane layer thickness versus wave number and discuss bifurcations among different mode types. Motion of surface particles and time evolution of surface elevation is also studied at various parameters in glycerin, and a great variety of behaviour is found, including counterclockwise surface particle motion and negative group velocity in wave propagation. Full article

Cavitation, as a unique technology for influencing liquid substances, has attracted much attention in the oil refining industry. The unique capabilities of cavitation impact can initiate the destruction of molecular compounds in the liquid. At the same time with a large number of successful experimental studies on the treatment of liquid hydrocarbon raw materials, cavitation has not been introduced in the oil refining industry. Often the impossibility of implementation is based on the lack of a unified methodology for assessing the intensity and threshold of cavitation creation. The lack of a unified methodology does not allow for predicting the intensity and threshold of cavitation generation in different fluids and cavitation-generating devices. In this review, the effect of cavitation on various rheological properties and fractional composition of liquid hydrocarbons is investigated in detail. The possibility of using the cavitation number as a single parameter for evaluating the intensity and threshold of cavitation generation is analyzed, and the limitations of its application are evaluated. The prospects of introducing the technology into the industry are discussed and a new vision of calculating the analog of cavitation numbers based on the analysis of the mutual influence of feedstock parameters and geometry of cavitators on each other is presented. Full article

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of $1\times {10}^{-4}$ and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results. Full article

In this study, a numerical simulation of fluid flow through railway ballast in the time domain is presented, providing a model for unsteady-state flow. It is demonstrated that the position of the free surface with respect to time can also be used to solve the steady flow case. The effect of ballast fouling is included in the model to capture the realistic behavior of railway ballast, which is critical to understanding the impact of flooding. A thorough comparison with a range of previous studies, including theoretical and experimental approaches, is made, and very close agreement is obtained. The significant impact of ballast fouling on fluid flow and its potential consequences for railway infrastructure are highlighted by the simulation. Valuable insights into the behavior of water flow through porous media and its relevance to railway ballast management are offered by this study. Full article

Reduction of energy expenditures required for various technological processes is a pressing issue in today’s economy. One of the ways to solve this issue in regard to liquefied natural gas (LNG) storage is the recovery of its vapours from LNG tanks using an ejector system. In that respect, studies on the outflow of the real gas through the nozzle, the main element of the ejector, and identifying differences from the ideal gas outflow, are of high relevance. Particularly, this concerns the determination of the discharge coefficient µ as the ratio of the actual flowrate to the ideal one, taking into account the energy losses at gas outflow through the nozzle. The discharge coefficient values determined to date for various nozzle geometries are, as a rule, evaluated empirically and contradictory in some cases. The authors suggest determining the discharge coefficient by means of an experiment. This paper includes µ values determined using this method for the critical outflow of air to atmosphere through constrictor nozzles with different outlet diameters (0.003 m; 0.004 m; 0.005 m) in the pressure range at the nozzle inlet of 0.5–0.9 MPa. The obtained results may be used for the design of an ejector system for the recovery of the boil-off gas from LNG tanks, as well as in other fields of industry, for the design of technical and experimental devices with nozzles for various applications. Full article

The acoustic cavitation of fluids, as well as related physical and chemical phenomena, causes a variety of effects that are highly important in technological processes and medicine. Therefore, it is important to be able to control the conditions that allow cavitation to begin and progress. However, the accurate prediction of acoustic cavitation is dependent on a complex relationship between external influence parameters and fluid characteristics. The multiparameter problem restricts the development of successful theoretical models. As a result, it is critical to identify the most important parameters influencing the onset of the cavitation process. In this paper, the ultrasonic frequency, hydrostatic pressure, temperature, degassing, density, viscosity, volume, and surface tension of a fluid were investigated using machine learning to determine their significance in predicting acoustic cavitation strength. Three machine learning models based on support vector regression (SVR), ridge regression (RR), and random forest (RF) algorithms with different input parameters were trained. The results showed that the SVM algorithm performed better than the other two algorithms. The parameters affecting the active cavitation nuclei, namely hydrostatic pressure, ultrasound frequency, and outgassing degree, were found to be the most important input parameters influencing the prediction of the cavitation threshold. Other parameters have a minor impact when compared to the first three, and their role can be compensated for by alternative variables. The further development of the obtained results provides a new way to optimize and improve existing theoretical models. Full article

Studying transport processes in the brain’s extracellular space is a complicated problem when considering the brain’s tissue. Tests of corresponding physical and mathematical problems, as well as the need for materials with cheap but realistic properties to allow for testing of drug delivery systems, lead to the development of artificial phantom media, one kind of which is explored in this work. We report results from quantifying the spread of a standard contrast agent used in clinical computed tomography, Iopromide, in samples of collagen-based hydrogels. Its pure variant as well as samples supplied with lipid and surfactant additives were explored. By comparing to solutions of the diffusion equation which reproduce these data, the respective diffusion coefficients were determined. It was shown that they are relevant to the range typical for living tissue, grow with elevation in the lipid content and diminish with growth in surfactant concentration. Full article

The impingement of a short-duration water jet on a pool of molten Rose’s metal is studied experimentally herein. Short-duration water jet impacting on the free surface of a molten metal pool with a temperature of 300 °C are generated with a pneumatic water delivery system, with two-camera high-speed video registration. A total of 14 experimental series, each containing 5 repeated tests, are performed for a water volume of 0.2–1 mL and a jet impact velocity of 4.1–9.0 m/s. The cavity development in the melt layer is studied, with the main stages described herein. Despite the significantly higher density of melt in comparison with water, the cavity can reach the melt pool bottom; furthermore, its further collapse results in the formation of a central jet rising to the height of a few centimeters. The maximum height of the central jet is shown to depend linearly on the total momentum of the water jet, and a semi-logarithmic correlation is found for the maximum diameter of the cavity. Repeatability analysis is performed within each experimental series, and the relative standard deviation for the melt splash height is shown to be from 8.8% to 26.8%. The effects of the pool depth, the vessel shape, and the water temperature are weaker in the range of the experimental parameters used here. Full article

We present the theoretical description of plane Couette flow based on the previously proposed equations of vortex fluid, which take into account both the longitudinal flow and the vortex tubes rotation. It is shown that the considered equations have several stationary solutions describing different types of laminar flow. We also discuss the simple model of turbulent flow consisting of vortex tubes, which are moving chaotically and simultaneously rotating with different phases. Using the Boussinesq approximation, we obtain an analytical expression for the stationary profile of mean velocity in turbulent Couette flow, which is in good agreement with experimental data and results of direct numerical simulations. Our model demonstrates that near-wall turbulence can be described by a coordinates-independent coefficient of eddy viscosity. In contrast to the viscosity of the fluid itself, this parameter characterizes the turbulent flow and depends on Reynolds number and roughness of the channel walls. Potentially, the proposed model can be considered as a theoretical basis for the experimental measurement of the eddy viscosity coefficient. Full article

We investigate the effect of horizontal quasi-periodic oscillation on the stability of two superimposed immiscible fluid layers confined in a horizontal Hele-Shaw cell. To approximate real oscillations, a quasi-periodic oscillation with two incommensurate frequencies is considered. Thus, the linear stability analysis leads to a quasi-periodic oscillator, with damping, which describes the evolution of the amplitude of the interface. Two types of quasi-periodic instabilities occur: the low-wavenumber Kelvin-Helmholtz instability and the large-wavenumber resonances. We mainly show that, for equal amplitudes of the superimposed accelerations, and for a low irrational frequency ratio, there is competition between several resonance modes allowing a very large selection of the wavenumber from lower to higher values. This is a way to control the sizes of the waves. Furthermore, increasing the frequency ratio has a stabilizing effect for both types of instability whose thresholds are found to correspond to quasi-periodic solutions using the frequency spectrum. For a ratio of the two superimposed displacement amplitudes equal to unity and less than unity, the number of resonances and competition between their modes also become significant for the intermediate values of the ratio of frequencies. The effects of other physical and geometrical parameters, such as the damping coefficient, density ratio, and heights of the two fluid layers, are also examined. Full article

This article focuses on the prediction of the small bubble holdups (assuming the existence of two major bubble classes) in two bubble columns (0.289 m in ID and 0.102 m in ID), operated with organic liquids under various conditions (including high temperature and pressure). A new correction factor has been established in the existing model for the prediction of the gas holdups in the homogeneous regime. The correction parameter is a single function of the Eötvös number (gravitational forces to surface tension forces), which characterizes the bubble shape. In addition, the behavior of small bubble holdups in 1-butanol (selected as a frequently researched alcohol) aerated with nitrogen, in a smaller BC (0.102 m in ID), at various operating pressures, is presented and discussed. The ratio of small bubble holdup to overall gas holdup, as a function of superficial gas velocity and operating pressure, has been investigated. All small bubble holdups in this work have been measured by means of the dynamic gas disengagement technique. Full article

In this work, we experimentally investigated the cavitation effects on the hydrodynamic behavior of a circular cylinder at different cavitating flows. We analyzed the cavitation dynamics behind the circular cylinder using a high-speed camera and also measured the associated hydrodynamic forces on the circular cylinder using a load cell. We studied the cavitation dynamics around the cylinder at various types of the cavitating regimes such as cloud cavitation, partial cavitation and cavitation inception. In addition, we analyzed the cavitation dynamics at three different Reynolds numbers: 1 × 10${}^5$, 1.25 × 10${}^5$ and 1.5 × 10${}^5$. The results showed that the hydrodynamics force on the circular cylinder can be increased with the formation of the cavitation behind the cylinder compared with the cylinder at cavitation inception regime. The three-dimensional flow caused complex cavitation behavior behind the cylinder and a strong interaction between vortex structures and cavity shedding mechanism. In addition, the results revealed that the effects of the Reynolds number on the cavitation dynamics and amplitude of the shedding frequency is significant. However the effects of the cavitation number on the enhancement of the amplitude of the shedding frequency in the cavitating flow with a constant velocity is slightly higher than the effects of Reynolds number on the enhancement of the amplitude of the shedding frequency at a constant cavitation number. Full article