Variation Of Drag Coefficient Research Articles

Theoretical Calculation and Experimental Verification of Wind-Driven Rain Aerodynamic Forces on the Bridge Main Beam

Regarding the issue of changes in the aerodynamic force of the bridge main beam under the action of wind-driven rain, this article explores the changes in air density caused by rainfall, the calculation theory of raindrop impact force and its simplified mass-weighted equivalent method (MWEM), and the calculation method of water accumulation thickness on the surface of the main beam. The calculation shows that the changes in air density caused by rainfall can be ignored, and the error of the MWEM increases with the increase in rainfall intensity; however, even at a rainfall intensity of 709 mm/h, the deviations in the MWEM value of the horizontal and vertical raindrop impact force is only about +5% and −4%, respectively. Then, based on the above analysis, a calculation model for the aerodynamic three-component forces of the main beam caused by rainfall under the action of wind-driven rain is provided. Finally, taking two typical main beam sections as an example, static three-component force tests are carried out on the main beam model under different rainfall intensities. The experimental results show that the drag coefficient variations obtained through the MWEM are in good agreement with experimental data, which proves the correctness of the theoretical model of the raindrop impact force. But for the lift and torque coefficient, the differences between theoretical and experimental values are much more significant than the drag coefficient, and it increases with the increase in rain intensity. It can be seen that the surface ponding model and influence of rainfall intensity need to be further explored. In summary, the theoretical calculation method for the additional aerodynamic force of wind-driven rain on the main beam proposed in this article is convenient and practical, and it can provide a certain reference for the rapid safety assessment of bridges under extreme meteorological conditions.

Parasitic Drag and Requirements for Aircraft External Surface Finish

Statistical data are presented on the number and frontal areas for principal types of manufacturing and constructive imperfections characterizing the condition of aircraft external surface and the level of parasitic drag. Basic laws of varying drag coefficients for various types of surface excrescences as functions of Mach and Reynolds numbers are analyzed. The methodology is considered for evaluating requirements for aircraft surface finish based on the specified level of parasitic drag.

Effect of relative opening on the moving thin plate under the action of ocean wave in the surging direction: A numerical simulation approach

This paper aims to develop the simulated numerical methodology for sloping beach with nonlinear free-surface waves of sloshing water in a 2D rectangular tank. The current computational tool would be the first step in accurately modeling wave energy converters. The 2D tank model was developed by ANSYS FLUENT software, and Navier–Stokes equations are discretized on a regular structured grid based on the finite volume method (FVM). The model is validated for nonlinear sloshing cases. In addition, tank flexibility is analyzed for its impact on liquid sloshing. The test was conducted in five different wave steepness conditions. There were five conditions of wave steepness used in the test. This study looked at fluid–structure interaction around moving plates. The output power of the plate wave energy converter for different plate heights and streamline motion around the plate are important studies in the flow field. Variations of drag coefficient with the wave steepness are the important study in this paper. It shows that the drag coefficient increases with the increase in wave steepness and plate length. In particular, the new structure can give a new, highly accurate formula for determining the wave power of the ocean structures. Its application is seen in wave energy converter (WEC), where the interaction of solid objects, such as wind turbines with water waves, extracts renewable wave energy from the ocean. A highly efficient CFD approach method is introduced to capture the interaction of solid object with a two-phase flow. The effect of wave steepness using second-order stokes wave theory on a moving thin plate in intermediate water is a new discussion. This research is a highly relevant source of information in the development of many practical systems and has direct employment in the design of WEC in order to extract ocean energy.

Semi-analytical load models describing the progressive immersion of a fixed vertical cylinder in a breaking wave

This paper is part of the DIMPACT (Design of floating wind turbines and impacts of energetic steep and breaking waves) project concerning slamming loads on floating offshore wind turbines. Two semi-analytical models accounting for the progressive immersion of a vertical cylinder in a breaking wave are presented. These models are based on the rate of change of the fluid momentum and the continuity of the added mass during immersion. The first model is based on the Generalized von Kármán Model where the real shape of the body and its added mass are accounted for. To account for the nonlinearity of the flow kinematics, the second-order terms of the momentum equation are considered in the inertia load. The total load is obtained by adding the drag force using a variable drag coefficient. To better predict the slamming load, a second model based on Wagner’s theory is presented. The Modified Logvinovich Model provides the pressure distribution at the first instants of impact. It is assumed that the flow does not separate from the structure. The load models are applied in a strip-theory approach under the Froude–Krylov assumption. For comparison, a Navier–Stokes solver is used to generate four phase-focused breaking waves. The resulting free surface shape and the ambient kinematics of the two-dimensional waves are used in the semi-analytical models. The present models are compared with existing slamming load formulations and a three-dimensional numerical simulation with an actual cylinder, where the load on four sections of the cylinder are considered. The force in the deeply immersed sections is in good agreement in all models considered. In the partially submerged section, the proposed load formulations and the three-dimensional simulation predict a similar load. Other standard engineering formulas predict a much lower force in this section. In the area impacted by the crest, the Froude–Krylov-based approaches predict a much higher force than that given by the Navier–Stokes result, likely due to the free surface being disturbed by the cylinder.

Supersonic flow unsteadiness induced by control surface deflections

Control surface deployment in a supersonic flow has many applications, including flow control, mixing, and body-force regulation. The extent of control surface deflections introduces varying flow unsteadiness. The resulting fluid dynamics influence the downstream flow characteristics and fluid–structure interactions significantly. In order to understand the gas dynamics, an axisymmetric cylindrical body with a sharp-tip cone at zero angles of attack (α=0°) is examined in a free stream Mach number of M∞=2.0 and Reynolds number of ReD=2.16×106 (D = 50 mm). Four static control surface deflection angles (θ=π/36,π/6,π/3, and π/2 rad) are considered around the base body. The cases are computationally investigated through a commercial flow solver adopting a two-dimensional detached eddy simulation strategy. Recirculation bubble length, drag coefficient's variation, wall-static pressure statistics, acoustic loading on the model and the surroundings, x − t trajectory and x − f spectral analysis, pressure fluctuation's correlation coefficient on the model, and modal analysis are obtained to understand the flow unsteadiness. At θ=[π/36], the wall-static pressure fluctuations behind the control surface are minimal and periodic, with a mere acoustic load of about 50 dB. At θ=[π/2], a violent periodic fluctuation erupted everywhere around the control surface, leading to a higher acoustic load of about 150 dB (three times higher than the previous). For θ=[π/6] and [π/3], high-frequency fluctuations with small- and large-scale structures continuously shed along the reattaching shear layer, thereby causing a broadened spectra in the control surface wake.

Thermal Analysis of Radiative Darcy–Forchheimer Nanofluid Flow Across an Inclined Stretching Surface

Nanofluids have unique features that make them potentially valuable in a variety of medicinal, technical, and industrial sectors. The widespread applications of nanotechnology in modern science have prompted researchers to study nanofluid models from different perspectives. The objective of the current research is to study the flow of non-Newtonian nanofluid over an inclined stretching surface immersed in porous media by employing the Darcy-Forchheimer model. Both titanium oxide (TiO2) and aluminum oxide (Al2O3) are nanoparticles which can be found in blood (based fluid). The consequences of viscous dissipation, thermal radiations, and heat generation are also incorporated. Boundary layer approximations are employed to model the governing system of partial differential equations (PDEs). The governing PDEs with their associated boundary conditions are further altered to a dimensionless form by employing appropriate transformations. The results of the transformed model are collected using local non-similarity approach up to the second level of truncation in association with the built-in finite difference code in MATLAB (bvp4c). Additionally, the impacts of emerging factors on the fluid flow and thermal transport features of the considered flow problem are displayed and analyzed in graphical forms after achieving good agreement between accomplished computational results and published ones. Numerical variations in drag coefficient and Nusselt number are elaborated through the tables. It has been perceived that the enhancement in Casson fluid parameter diminishes the velocity profile. Moreover, it is noted that the porosity parameter and Lorentz's forces reinforce the resulting frictional factor at the inclined stretching surface.

Machine Learning Based Developing Flow Control Technique Over Circular Cylinders

Abstract This paper demonstrates the feasibility of blowing and suction for flow control based on the computational fluid dynamics (CFD) simulations at a low Reynolds number flows. The effects of blowing and suction position, and the blowing and suction mass flowrate, and on the flow control are presented in this paper. The optimal conditions for suppressing the wake of the cylinder are investigated by examining the flow separation and the near wake region; analyzing the aerodynamic force (lift and drag) fluctuations using the fast Fourier transform (FFT) to separate the effects of small-scale turbulent structures in the wake region. A method for stochastic analysis using machine learning techniques is proposed. Three different novel machine learning methods were applied to CFD results to predict the variation in drag coefficient due to the vortex shedding. Although, the prediction power of all the methods utilized is in the acceptable accuracy range, the Gaussian process regression (GPR) method is more accurate with an R2(coefficient of determination) > 0.95. The results indicate that by optimizing the blowing and suction parameters like mass flowrate, slot location, and the slot configuration, up to 20% reduction can be achieved in the drag coefficient.

Direct numerical simulation of different finite cylinders rolling on a horizontal surface: The thickness effects on the aerodynamics

The flow around a cylinder rolling along a horizontal ground plane is investigated using direct numerical simulation for a Reynolds number based on the cylinder diameter, D, of ReD=3×104. Three cylinder thicknesses, T/D=0.040, 0.126, and 0.400, are considered. The time-averaged drag coefficients are found to be 0.87, 0.69, and 0.97 for the three cylinders, respectively. The non-monotonic variation in drag coefficient with thickness suggests a transition in the proportion of contributions of friction and pressure drag to the total drag which changes about 30% with thickness increase. Indeed, the ratio of friction drag to pressure drag varies from 0.333 to 0.085 and finally to 0.013 for the three cylinders. The pressure coefficient become more negative in the aft of the thicker cylinders, because the cylinder become more bluff body which suggests more pronounced pressure drag. Temporal fluctuations in the drag coefficient associated with vortex shedding events increase monotonically with thickness, though the root-mean-square of the drag coefficient follows the same trend as the mean drag coefficient. The lift coefficients are −0.057, 0.066, and 0.64 for the three respective cylinders. The negative value for the thinnest cylinder indicates down force. The transition from negative lift on the thin cylinder to positive lift on the thick cylinder is associated with elevated surface pressure just upstream of the ground contact point as thickness increases. As the flow is more detached from the cylinder sides, the friction lift is less significant with thickness increase. Furthermore, the pressure coefficient is negative spatially larger in the top of the thicker cylinders which the expansion offers a more significant upward pressure lift.

Computational modeling of coupled waves and vegetation stem dynamics in highly flexible submerged meadows

In this study, we have developed a two-way fully coupled hydrodynamic-vegetation model that includes a spatially and temporally variable drag coefficient of flexible submerged aquatic vegetation (SAV). The developed model consists of a nonhydrostatic wave model (NHWAVE) that solves the Navier-Stokes equations and a numerical model for vegetation stem dynamics that solves the instantaneous forces applied by flow on vegetation stems. The results of the developed model are validated against a number of laboratory-scale experiments on wave attenuation, stem orientation, and stem base forces, and then applied to an idealized configuration to further investigate the effects of vegetation induced drag coefficient on waves velocity field, wave attenuation, and vegetation dynamics along a numerical flume. The model was able to reproduce experimental results without parameter tuning. By adopting the N-pendula approach, the stem dynamics model solves the instantaneous orientation of segments along each stem and uses this information to compute a spatially and temporally varying vegetative drag coefficient within the meadow. When compared with laboratory experiments, incorporating this new mechanism for flexible vegetation in the wave model resulted in improvement over results with rigid vegetation. Through highly detailed representation of vegetation, the model can reliably predict wave attenuation over marshes and seagrass meadows, evaluate potential storm damages to these features, and calculate instantaneous orientation of plant stems or shoots which has implications for their photosynthesis.

Drag force on a circular cylinder in stratified flow: A two-dimensional numerical study

Using two-dimensional numerical simulations, we investigate a circular cylinder in a stratified flow with a pycnocline of a smooth density profile. We are particularly concerned about the difference between stratified flows and their homogeneous, or unstratified, counterparts in drag coefficients. It is well known that the characteristics of a stratified flow depend on the Reynolds number Re and the internal Froude number Fr. First, we change the incoming flow velocity, with the Reynolds number and the internal Froude number varying simultaneously, in the ranges of 76≤Re≤579 and 0.14≤Fr≤1.046, respectively. We find that the flow experiences a sequence of flow patterns, namely “multiple centerline structures,” “isolated mixed regions,” and “vortex shedding,” as we increase this combination, agreeing well with the previous experiments in the low Re and Fr ranges. Meanwhile, the mean drag coefficient decreases, and it drops below the value for a homogeneous state as an empirical stability parameter, k, drops below unity, indicating the transition from a lee-wave dominant wake to an unsteady, vortex shedding wake. This unique variation of drag coefficient is more clearly shown in another situation, when we fix the Reynolds number at Re = 234 while varying the Froude number within 0.094≤Fr≤4.192. In such a situation, we observe a stable “double eddy” pattern at Fr = 1.87, around which a minimum of mean drag coefficient is reached. At this critical point, we understand that the stratification in the flow inhibits lee-side separation, while the internal waves have not yet played a significant role. Although we observe turbulence-like, strong mixing regions in the far downstream wake for some specific cases, it is argued that the current two-dimensional simulations might not be able to resolve the high Reynolds number or high Froude number cases.

Observational study on drag reduction of continental-shelf bottom boundary layer

Long-term and high-frequency observing of the oceanic bottom boundary layer was implemented using a seabed-mounted tripod equipped with multiple high-frequency instruments in a semidiurnal tide-dominated channel around the Zhoushan Islands, China. The estimated turbulent parameters, e.g., turbulent intensity, friction velocity, and bottom drag coefficient, varied with quarter-diurnal frequency. The amplitudes of turbulent intensity, bottom stress, and friction velocity were larger in spring tide than those in neap tide. As the Reynolds number increased from 103 to 105, the measured bottom drag coefficient initially increased, peaked at a Reynolds number of approximately 1.4 × 105, and then decreased. The observed drag reduction is similar to the variations of drag coefficient of cross-flow around a circular cylinder and the fluid friction of the pipe flow in the transitional state, which can provide a necessary and important proof for further theoretical and experimental investigations. Several plausible explanations are raised for this reduction: the stratification caused by the gradient of salinity or sediment suspension and the occurrence of recirculation vortices generated by seabed topography.

The Vertical Structure and Entrainment of Subglacial Melt Water Plumes

AbstractBasal melting of marine‐terminating glaciers, through its impact on the forces that control the flow of the glaciers, is one of the major factors determining sea level rise in a world of global warming. Detailed quantitative understanding of dynamic and thermodynamic processes in melt‐water plumes underneath the ice‐ocean interface is essential for calculating the subglacial melt rate. The aim of this study is therefore to develop a numerical model of high spatial and process resolution to consistently reproduce the transports of heat and salt from the ambient water across the plume into the glacial ice. Based on boundary layer relations for momentum and tracers, stationary analytical solutions for the vertical structure of subglacial non‐rotational plumes are derived, including entrainment at the plume base. These solutions are used to develop and test convergent numerical formulations for the momentum and tracer fluxes across the ice‐ocean interface. After implementation of these formulations into a water‐column model coupled to a second‐moment turbulence closure model, simulations of a transient rotational subglacial plume are performed. The simulated entrainment rate of ambient water entering the plume at its base is compared to existing entrainment parameterizations based on bulk properties of the plume. A sensitivity study with variations of interfacial slope, interfacial roughness and ambient water temperature reveals substantial performance differences between these bulk formulations. An existing entrainment parameterization based on the Froude number and the Ekman number proves to have the highest predictive skill. Recalibration to subglacial plumes using a variable drag coefficient further improves its performance.

Numerical Study on Aerodynamic Performance of Mars Parachute Models with Geometric Porosities

The supersonic flows around rigid parachute-like two-body configurations are numerically simulated at Mach number of 1.978 by solving three-dimensional compressible Navier-Stokes equations, where the two-body model consists of a capsule and a canopy, and a geometric structure (i.e., gap) is located on the canopy surface. The objective of this study is to investigate the effects of gaps with different porosities and positions on the aerodynamic performance of supersonic parachute. The complicated periodic aerodynamic interactions between the capsule wake and canopy shock occur around these two-body models. From the formation of canopy shock and drag coefficient variation, the cycled flow structures can be divided into three types:(1) narrow wake period, (2) open wake period, and (3) middle wake period. In addition, it was found that the geometric gaps have no obvious influences on the flow modes. However, compared with models with different gap positions, the two-body model with an upper gap (gap is close to the canopy vent, UG model) has a smaller drag coefficient fluctuation and better lateral stability. On the other side, the increase of porosity has a more significant impact on UG models.

Hydrodynamic characteristics of two side-by-side flexible cylinders with different diameters experiencing flow-induced vibration

Slender flexible cylindrical structures, such as marine risers and the tendons of tension leg platforms, have been widely used in offshore engineering. This paper mainly investigates the hydrodynamic characteristics of two flexible cylinders with unequal diameters in a side-by-side arrangement subjected to flow-induced vibration (FIV). A series of model tests are carried out in a towing tank. The aspect ratios and mass ratios of the two flexible cylinders are 350/181 and 1.90/1.47, respectively. A diameter ratio of 0.5 and a centre-to-centre spacing ratio of 6.0 are selected for the experimental tests. The experimental results of two cases, namely, those of an unequal-diameter cylinder system and an equal-diameter cylinder system, are compared and discussed. With the comparison of the hydrodynamic coefficients of large cylinder #1 and small cylinder #2 in the unequal-diameter cylinder system and small cylinder #3 in the equal-diameter cylinder system, the FIV features of two side-by-side unequal-diameter cylinders are systematically explored. The in-line (IL) and cross-flow (CF) vibration responses and hydrodynamic characteristics are specifically investigated. The wake effect caused by the vibration of the cylinders is more obvious and important for small cylinder #2 in the unequal-cylinder system. The lift coefficient CLy and fluctuating force coefficient CCF_rms of small cylinder #2 in the CF direction are obviously higher than those of the isolated cylinder in the larger reduced velocity range (Vrs = 7.52–17.54). The added mass coefficient Cax, varying drag coefficient CDx and fluctuating force coefficient CIL_rms in the IL direction decrease significantly when reduced velocity Vrs increases from 22.54 to 25.05. Compared with the two side-by-side cylinders in the equal-diameter cylinder system, the two cylinders in the unequal-diameter cylinder system exhibit a stronger interaction under the initial spacing ratio (S/d = 6.0).

The Role of Boundary Layer Theory in Soccer Ball Dynamics

The boundary layer theory plays a major role in the development of fluid mechanics applications especially in the sports ball dynamics. Whenever an object travels through the air, it experiences aerodynamic forces acting on it. Sport balls, uses these forces to deviate from its expected path of flight. Thus, creating an advantage which can be exploited by the playing members to improve their skills. The present study focuses on numerical simulation of aerodynamic flow over a soccer ball and estimated the drag coefficient. In order to a get more precise results, the effect of gravity is included to study the dynamics of flow. The variation of drag coefficient is plotted as a function of Reynolds number and wind speed. The computational result had a good agreement with existing empirical data.

Effects of velocity ratio on dynamics of sand-water coaxial jets

Detailed laboratory experiments were performed to study the dynamics and mixing properties of vertically discharged sand-water coaxial jets in stagnant water. The effects of velocity ratio on the fluid dynamics of two-phase coaxial jets were studied. The axial and radial distributions of sand concentration and velocity were measured with an advanced optical fiber probe (PV6), and sand concentration and velocity measurements were formulated based on flow characteristics. The experimental results demonstrated that the axial velocity and concentration decay rate along the mixing zone, a length approximately six times greater than the nozzle diameter, were independent of the velocity ratio, Ru. Beyond the initial mixing zone, the axial decay rate of sand concentration increased with increasing velocity ratio and became similar to the concentration decay rate of slurry jets. The axial velocity decay of sand-water coaxial jets indicated an inverse relationship with velocity ratio: velocity decay rates decreased with increasing Ru. Experimental observations of sand-water coaxial jets showed that the spreading rate of coaxial jets decreased with increasing velocity ratio; for the coaxial jet with the highest Ru, the spreading rate reached the spreading rate of slurry jets. The integral quantities of jets such as mass and momentum fluxes were calculated using sand concentration and velocity profiles. Average drag coefficients were calculated using momentum balance and proposed equations for sand velocity and concentration. The variations of drag coefficient and interparticle collision parameter indicated that the particle grouping effect reduced the drag coefficient in sand-water coaxial jets with lower velocity ratios. The axial variations of the interparticle collision parameter indicated a strong correlation with velocity ratio. The strong correlation between velocity ratio and the mixing properties of sand-water coaxial jets suggests the velocity ratio is an effective design parameter to control and optimize particle mixing in stagnant water.

High subsonic flow of an organic vapor past a circular cylinder

A circular cylinder was tested in the cross-flow of an organic vapor (Novec™ 649) and of air over the subsonic (M < 0.4) and high subsonic (0.4 < M < 0.8) speed range in a continuously running pressurized closed-loop wind tunnel test facility. Time-averaged pressure measurements gave information on surface pressure distributions, and the corresponding drag and base pressure drag coefficients were obtained. Due to the charging of the wind tunnel, different values of the compressibility factor (0.876 < Z < 0.999) could be achieved for the organic vapor flow. This enabled in combination with the results for air an assessment of the impact of non-ideal gas dynamics on the form drag of a cylinder in the considered highly subsonic flow regime. The new experimental data were compared with available literature results. Changes in surface pressure distribution at higher subsonic velocities were identified and discussed. It was found that non-ideal gas effects did not strongly affect the overall drag. The variation of drag coefficient over the Mach number range was comparable with literature data for ideal-gas compressible flow, including shock-less and intermittent shock wave, and permanent shock wave flows regimes. At Mach 0.4, the flow of Novec™ 649 was in the shock-less regime and exhibited a pronounced dependency on the Reynolds number. An increase in drag was observed at Mach 0.6 which was attributed to the commencement of vortex shedding. Non-ideal thermodynamics only affected the flow locally and a reduction of the critical pressure coefficient in the high subsonic flow regime was observed in the surface pressure distribution. However, this mechanism did not alter significantly the overall drag behavior.Graphic abstractDrag coefficient CD against Re for several Mach numbers M and comparison with available literature results obtained for air (colored symbols indicate different Mach number clusters)

Estimation of sea ice parameters using an assimilated sea ice model with a variable drag formulation

In this work, sea ice concentrations in the regions of Baffin Bay, Hudson Bay, the Labrador Sea and the Gulf of St. Lawrence were estimated using a standalone regional configuration of Los Alamos Sea ice Model, CICE. A sensitivity analysis of the mixed layer depth criteria that affects the predicted sea ice formation/ablation has been carried out to tune the model. Sea ice concentration from AMSR2 OSISAF, sea ice edge from SSMIS/ASCAT OSISAF, and sea surface temperature from OISST AVHRR-only products were then assimilated into the tuned model using a combined optimal interpolation method. Extending previous studies, which used a constant drag formulation in their assimilation schemes, we use a variable drag formulation to represent the friction associated with effective sea ice surface roughness at the ice–atmosphere and ice–ocean interfaces. The variable drag coefficient is estimated from properties of the sea ice cover such as the ice concentration, the vertical extent and area of the ridges, the freeboard, the floe draft, the size of floes and melt ponds. The new features of the assimilated model include tracers to estimate ridged ice, level ice, melt ponds, freeboard, sail height and keel depth. The estimates of ice concentration from the assimilated models are then compared with the ice concentration product from the Canadian Ice Service. The results show that the updates provided to the tracers through the assimilation of sea ice products are reasonable and the model estimates of ice concentration from the assimilated models are better than the non-assimilated model estimates. Finally, the estimates of updated sea ice parameters such as ridged ice area, volume and ice thickness are compared with the estimates from non-assimilated models and the literature to verify the results.

A study on the FIV hydrodynamic force coefficients of two staggered flexible cylinders via an inverse method

The flow-induced vibration (FIV) of two cylindrical structures may cause serious fatigue damage, which is a major concern in engineering fields. Few studies have focused on the FIV hydrodynamic characteristics of two staggered flexible cylinders. In this paper, the hydrodynamic coefficients of two staggered flexible cylinders are calculated using the structural responses acquired from the model tests. The cross-flow (CF) spacing ratios are set as 2, 3, 4 and 6, and the in-line (IL) spacing ratios are set as 4, 6, 8; thus, a total of twelve cases are considered. The fluctuating forces in the CF and IL directions are reconstructed using a finite element model. The forgetting factor least squares method is employed to decompose the CF/IL fluctuating force into lift/varying drag and CF/IL added mass force. In the CF direction, the hydrodynamic coefficients of the two staggered cylinders are significantly different from those of the single cylinder in the mode switch regions. The CF vibrations of the two staggered cylinders enter the higher-order mode earlier, resulting in an increase in the CF added mass coefficients. The downstream cylinder has larger lift coefficients due to the vortex shedding effect of the upstream cylinders. In the IL direction, the upstream cylinder has lower IL added mass coefficients due to the higher-order harmonics in the IL direction. The varying drag coefficients of the two staggered cylinders significantly differ from those of the single cylinder owing to the subharmonic frequency components. A hybrid aspect of wake-induced flutter and vortex-induced vibration is observed in the vibration of the downstream cylinder.

Analysis and Modeling of Particle Velocities in Premixed Abrasive Water Jets

The premixed abrasive jet possesses a strong strike ability and is widely used in oil and gas exploitation, machining, rust removal, and other fields. The superstrong, forceful impact of the premixed abrasive jet is mainly provided by high-speed abrasive groups. Hence, the abrasive velocity is the basis of this research, by applying the distribution law of abrasive impact force. In this paper, the particle velocity of the premixed abrasive jet is analyzed theoretically, and the corresponding particle velocity model is established. The real-time contrast interpolation method is employed to solve the problem of the variable drag coefficient. Factors such as the nozzle structure, average abrasive diameter, abrasive density, and jet flow are utilized to determine the abrasive velocity of the nozzle outlet. The numerical solution for the abrasive velocity is obtained by dividing the high-pressure pipe and nozzle into several sections, along the axis. Finally, the calculated particle velocity is compared with the particle image velocity measurement (PIV), to verify the correctness of the established model. These results demonstrate that the model calculation is in effective agreement with the experimental results. The deviation between the theoretical value and the experimental mean is 0.18 m/s. The standard deviation of the experimental results is 3.81-4.22 m/s, while the average error is less than 4%.