Drag Coefficient Research Articles

ВИЗНАЧЕННЯ АЕРОДИНАМІЧНИХ ХАРАКТЕРИСТИК ЛІТАЛЬНОГО АПАРАТА З НАДЗВУКОВИМ ШВИДКОСТЯМИ ПОЛЬОТУ

The aircraft aerodynamic characteristics at supersonic flight modes can be determined with a high level of accuracy through testing the aircraft in wind tunnels or through time-consuming three-dimensional and analytical computational methods. However, in certain cases when the aircraft aerodynamic characteristics are already known within a given Mach number range for supersonic flight, it is possible to develop a relatively simple mathematical model for the aircraft aerodynamic characteristics at supersonic speeds using the aerodynamic properties of the supersonic wing leading edge for flight speeds Mf ≥ 1.2M. The object of the study is the aircraft aerodynamic characteristics at supersonic flight speeds. The subject of the study is the impact of the aircraft geometric features on the mathematical model, which is used to determine its aerodynamic characteristics in the supersonic flight speed range. The study hypothesizes that to determine the aerodynamic characteristics of an aircraft at Mf ≥ 1.2, it is sufficient to identify the values of the aircraft aerodynamic parameters at a flight speed of Mf =1.2 and then use aerodynamic analytical dependencies for the supersonic wing leading edge to determine these parameters at Mf ≥ 1.2. A mathematical model of the aircraft aerodynamic characteristics in the supersonic flight speed range was developed. Coefficients of drag polar and zero-lift drag for the reference mode Mf = 1.2 have been identified by the developed mathematical model. Then, the Mach number range for the aerodynamic characteristics of the NASA 1044 configuration has been extended to supersonic speeds of Mf = 1.8…4.0. The resultsof the aerodynamic calculations, obtained in the form of dependencies of the drag polar and zero-lift drag coefficients on Mach number, and the aircraft polar plot, have been compared with known NASA data for the 1044 configuration aircraft. The average modeling error of the aircraft aerodynamic characteristics in the supersonic speed range is less than 3%.

Hydrodynamic optimization and performance verification of fairings for round-ended cofferdams using dam-break wave experiments and numerical simulations

Round-ended cofferdams are crucial for large-scale marine projects but are vulnerable to the complex marine environment, including waves, tides, and storms. Enhancing the hydrodynamic performance of these cofferdams is essential for improving safety and efficiency in marine construction. This study introduces a novel fairing design aimed at reducing water flow resistance during the quasi-stable stage of a tsunami. The flow field is analyzed using computational fluid dynamics (CFD) simulations, and an adaptive surrogate model is employed to optimize the parameterized fairing shape. The results demonstrate that the optimized shape significantly suppresses vortex shedding, leading to a 16.59 % reduction in the drag coefficient and a 44.3 % reduction in the lift coefficient under flow conditions. Experimental and numerical simulations of dam-break waves are conducted for two designs, R1 and R0. By comparing their flow field and force characteristics, it is found that R1 effectively separates waves during the impulse stage, reduces wave climb height, and decreases impact loads. In the quasi-stable stage, R1 mitigates the blockage effect, reducing the liquid level difference between the front and back, and thus lowering flow forces. Experimental data further reveals that when the downstream is a dry riverbed, R1′s load reduction is particularly notable, with maximum reductions of 45.62 % in the impulse stage and 28.75 % in the quasi-stable stage. When the riverbed is wet, the maximum load reduction rates are 18.04 % and 8.72 %, respectively. Therefore, R1 not only reduces the resistance of round-end cofferdams under water currents but also under extreme wave forces, providing valuable insights for advancing ocean engineering design.

Aerodynamic and acoustic evaluation of a cylinder covered by stretched grooved fabric near critical Reynolds numbers

This study investigates aerodynamic drag and acoustic noise generated from a circular cylinder by wrapping longitudinally grooved fabrics. The fabrics are stretched to different levels to explore their potential for flow and acoustic control near critical Reynolds numbers. To analyze the fabrics' surface characteristics, 3D scanning and several microscopic techniques were employed. The parallel-mounted load cells and an array of microphones were used to measure the drag and noise at Reynolds numbers, based on cylinder diameter, ranging from \num{3.3e4} to \num{1.1e5} in an anechoic wind tunnel. Additionally, hotwire anemometry was used to examine the wake structures in the vicinity of the cylinder. The surface scanning results revealed that stretching the fabric transversely to twice its original size reduced the groove depth by approximately $54\%$ and increased the width by around $25\%$, resulting in an overall reduction of the arithmetic surface roughness $S_a$ by $18.6\%$. Based on the wind tunnel data, it was observed that a grooved fabric with higher stretch, and thus lower surface roughness exhibited a minimum drag coefficient at a higher Reynolds number, along with reduced acoustic tonal noise levels.

Drag coefficients and water surface profiles in channels with arrays of linear rigid emergent vegetation

Although vegetation in watercourses has an important ecological function, from a hydraulic point of view, it increases flow resistance, determinates higher water levels and generates a greater risk of flooding. In engineering practice, to determine water levels, the drag coefficient must be known, whose experimental values, in literature, are provided for uniform or quasi-uniform flow. In this paper, the expression of a drag coefficient, previously proposed by the authors for the case of emergent rigid vegetation arranged in a linear manner, was used to simulate experimental water surface profiles, employing the effective width for the first time. The formula was validated by simulating 26 experimental profiles observed at the University of Calabria, over 1100 points in total, plus 8 published in literature. In some of these applications, the vegetation density was much higher than that for which the drag coefficient expression was derived. For this reason, it is possible to consider a new, wider field of validity for it. The proposed equation is independent of the Reynolds stem number, so that it can be used in natural streams and rivers, provided that viscosity effects can be considered negligible. Finally, some comments are offered on the application of a new formula proposed in literature regarding the computation of the profile when downstream depth is taken as a boundary condition.

A universal drag model for liquid-solid fluidization: Experiment, data-driven modeling, CFD modeling and simulation

Various industrial applications are performed in liquid-solid fluidized beds where drag force plays a significant role in affecting the expansion characteristics of granular-bed, and then determines the mass/heat transfer performance. This study employs dimensionless learning data-driven modeling method, which is derived from the principle of dimensional invariance, to automatically discover the relationship between the drag coefficient and hydraulic dimensionless numbers from the liquid-solid fluidization data. It is found that the Fr number (=ul2/gds) also plays important role in improving the prediction accuracy of drag model except for Re number (=dsulρl/μl). The proposed data-driven modeling method has desired robustness, and the yielded drag model can be applicable to other liquid-solid systems, such as water-polystyrene spheres and water-coal particles, although it is derived from the fluidization of spherical glass beads in rising tap-water. The proposed drag model can also provide good CFD simulation results that agree very well with the experiment data with the relative error less than 5 %.

Performance analysis of natural draft power plant cooling tower: Mathematical modeling of cross-flow type, application in capital cities of Iranian provinces

Cooling towers are heat exchangers that reduce the hot water temperature produced by process equipment through heat and mass transfer between water and air stream. This study investigates the performance of cross-flow cooling towers under various geometrical, physical, and environmental conditions. For this purpose, thermodynamic modeling of the cross-flow cooling tower was conducted, and the governing equations were numerically solved using the finite difference method. Unlike previous studies, the effects of water droplet deformation into an elliptical shape during its fall along the cooling tower were also considered. This deformation, which influences the drag coefficient, Reynolds number of the water droplets, droplet surface area, and its cross-section area, along with the incorporation of buoyancy force in the droplet momentum equation, led to an improvement in the results. Consequently, the maximum computational error in this case was reduced to 1.97 %, compared to the scenario where droplet deformation and buoyancy force were neglected. The change in geometrical parameters of the tower in Tehran and Rasht was investigated, revealing that increasing the outlet radius of the tower from 20 m to 22.5 m decreased the outlet water temperature by 1.21 °C and 0.67 °C and increased the thermal efficiency of the tower by 4.94 % and 2.88 % respectively, while increasing the tower height from 100 m to 120 m, only decreased the outlet water temperature by 0.47 °C and 0.26 °C, and increased the thermal efficiency of the tower by 1.89 % and 1.09 % respectively. Additionally, the cooling tower performance was assessed in the centers of different provinces .of Iran. Results showed that with an initial droplet radius of 1 mm and an inlet water temperature of 50 °C, the maximum and minimum temperature reductions occurred in Shahrekord by 20.16 °C and Bandarabbas by 12.37 °C, respectively.

Drag Force on Submerged Flexible Vegetation in an Open‐Channel Flow

AbstractThe movement of submerged flexible vegetation leads to an increase in resistance to the stream flow. In this study, a formula that can directly calculate the drag force on a highly flexible submerged vegetation, called Ceratophyllum, by using the vegetation swaying characteristics and the flow field information in a steady‐uniform open‐channel flow is derived. The drag force on submerged flexible vegetation is characterized by the time‐averaged flow velocity, turbulence intensity, and the additional force arising from the vegetation swaying. Based on the results of the numerical models in the previous studies (Wang et al., 2022a, 2022b, https://doi.org/10.1017/jfm.2022.598, https://doi.org/10.1017/jfm.2022.899), the drag coefficient is determined. It is revealed that the drag coefficient is influenced by a combination of factors, including the flow conditions, and the distribution and movement characteristics of vegetation. The drag coefficient decreases with an increase in velocity and is approximately linearly related to the cubic power of the bulk flow velocity. In the case of an inter‐plant spacing of 0.5 times the initial plant height, the drag coefficient ranges from 10.72 to 2.11, as the Reynolds number varies from 20,000 to 50,000. Besides, the vegetation distribution density and the relative submergence influence the drag coefficient. In this context, the drag coefficient decreases linearly with an increase in the inter‐plant spacing. For the Reynolds number equaling 50,000, the drag coefficient ranges from 2.11 to 2.02, when the inter‐plant spacing varies from 0.5 to 2 times the plant height, and from 2.47 to 1.79, when the flow depth varies from 1.5 to 3 times the plant height.

Influence of Rarefaction Degree and Aft-Body Geometry on Supersonic Flows

During atmospheric entry, super-/hypersonic vehicles cross distinct atmospheric layers characterized by large density variations and thus experience different flow regimes ranging from free molecular, transition, slip, to continuous regimes. Due to the distinct modeling strategy between these regimes and complex physical phenomena appearing near the vehicles (boundary-layer/shock interaction, base-flow recirculation, etc.), assessing their aerodynamic properties may be difficult. The present work focuses on supersonic flows around sharp-base geometries in both continuous and slip-flow regimes and aims at highlighting the influence of both rarefaction degree and base geometry on the vehicles’ aerodynamic features. For this purpose, three axisymmetric cone-cylinder geometries with right-angled, rounded, or flared rear parts are considered. Flow visualization, pressure, and drag measurements are carried out at Mach number Ma=4 and Knudsen numbers ranging from Kn=4×10−4 to 1×10−2 in the supersonic rarefied MARHy wind tunnel. The experimental data are compared with numerical results of simulations performed with a continuous-flow Navier–Stokes (NS) solver and two rarefied flows codes: a discrete-ordinate Bhatnagar–Gross–Krook (K) solver and a direct simulation Monte Carlo (SPARTA) solver. While the NS solver overestimates frictional drag as Kn rises, the rarefied K and SPARTA results show satisfactory agreement with experimental data. The latter numerical results highlight the main effects of rarefaction: as Kn increases, shocks become more diffuse, skin friction strengthens (leading to a significant increase in drag coefficients), and the extent of the base-recirculation decreases. Regarding the aft-body geometry, its influence on the base recirculation vanishes with increasing Kn.

Collision frequencies across collision regimes in two-component systems

Agglomeration is the most important growth process in particle systems but modelling efforts typically assume mono-disperse primary particle distributions for the closure of the collision frequency that determines the growth rates. Real systems such as sooting flames, however, involve poly-disperse primary particle distributions. Also, systems with multiple components, where primary particles are of distinct but different sizes, cannot be treated as mono-disperse. Here, we introduce bi-disperse primary particle distributions and use Langevin dynamics simulations to develop closures for the collision kernels that are applicable over a wide range of agglomerate characteristics. The simulations cover fractal dimensions from 1.4 to 2.2, primary particle diameters from 5 nm to 50 nm, primary particle size ratios from 2 to 10 and agglomerates of up to a size of 200 primary particles with varying particle compositions. The Langevin dynamics simulations cover all collision regimes from ballistic to diffusive and allow to deduce expressions for the respective collision diameters, the hydrodynamic radii and the projected area as functions of particle characteristics. It is shown that existing expressions for the transition regime that were developed for the modelling of the collision kernel of spherical particles continue to hold for collision kernels of agglomerates in two-component systems under the condition that the collision diameters and drag coefficients are modelled accurately. An example ‘a posteriori’ simulation for a particle size ratio of 6 uses the population balance equation and demonstrates that bi-variate kernels are needed for the accurate prediction of the growth rates. Errors in predicted number density at the end of the simulations are less than 12 % while mono-variate kernels developed for mono-disperse primary particle systems overpredict the growth rate by 46%.

Similarities in the meandering of yawed rotor wakes

This study investigated the meandering of yawed wind turbine rotor wakes, focusing on the similarities across different yaw angle scenarios. Spectrum analysis of velocity fluctuations reveals that the meandering of the yawed rotor wake is symmetrical about the wake center, despite its skewness. The non-zero lateral force of the yawed rotor enhances meandering in the lateral direction compared to the vertical direction. However, the lateral profiles of meandering strength exhibit similarities across different yaw angle scenarios, indicating a consistent wake meandering mode. The wake meandering frequency increases with the yaw angle. A relationship involving wake meandering frequency, drag coefficient, and yaw angle is formulated for wind turbine rotor wakes under different yaw angles. This relationship is also applicable to thin plate wakes within a certain range of inclination angles/yaw angles. The present study reveals the similarity in wake meandering characteristics across different yaw angle scenarios, which is instrumental in improving our understanding of wake meandering and in developing analytical wake models for wind turbines.

Active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning

This paper presents a novel framework for the active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning (DRL). The research, conducted in a wide range of Mach numbers and flutter velocities, involves an elastically mounted airfoil with two degrees of freedom of pitching and plunging oscillations, subjected to transonic flow conditions at varying Mach numbers. Synthetic jets with zero-mass flux are strategically placed on the airfoil's upper and lower surfaces. This fluid–structure interaction (FSI) problem is treated as the learning environment and is addressed by using the arbitrary Lagrangian–Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with a structural solver on dynamic meshes. DRL strategies with proximal policy optimization agents are introduced and trained, based on the velocities probed around the airfoil and the dynamic responses of the structure. The results demonstrate that the pitching and plunging motions of the airfoil in the limited cycle oscillation (LCO) can be effectively alleviated across an extended range of Mach numbers and critical flutter velocities beyond the initial training conditions for control onset. Furthermore, the aerodynamic performance of the airfoil is also enhanced, with an increase in lift coefficient and a reduction in drag coefficient. Even in previously unseen environments with higher flutter velocities, the present strategy is achievable satisfactory control results, including an extended flutter boundary and a reduction in the transonic dip phenomenon. This work underscores the potential of DRL in addressing complex flow control challenges and highlights its potential to expedite the application of DRL in transonic flutter control for aeronautical applications.

Effect of wettability and surface roughness on flow and heat transfer characteristics in nanochannels

The flow and heat transfer processes of liquid argon within nanochannels with random roughness are investigated using the molecular dynamics method. This study explores the effects of surface roughness and wettability on flow and heat transfer performance. The results indicate that both surface roughness and wettability significantly influence temperature jumps, velocity slip, flow resistance, and temperature distribution. Specifically, hydrophilic surfaces can reduce temperature jumps and velocity slip due to their enhanced ability to adsorb liquid atoms, which effectively improves heat transfer while simultaneously increasing flow resistance. The fractal dimension D characterizes the surface roughness, which decreases as D increases. Additionally, both the Nusselt number and drag coefficient decrease with increasing D. In this study, we investigate cases where D ranges from 2.5 to 2.9, with D = 2.5 representing the highest roughness, and the smooth channel corresponding to the lowest roughness. For hydrophilic nanochannels at D = 2.5, the Nusselt number and drag coefficient increased by factor of 2.2 times and 5.2 times compared to smooth channels, respectively. For hydrophobic nanochannels at D = 2.5, the Nusselt number and drag coefficient increased by a factor of 4.5 times and 29.1 times compared to smooth surface channels, respectively. Considering both flow and heat transfer performances, the best comprehensive performance is achieved with D = 2.8 for channels with hydrophilic surfaces and D = 2.6 for channels with hydrophobic surfaces. This work systematically investigates the coupled effects of random roughness and wettability on the flow and heat transfer characteristics in nanochannels, providing new theoretical insights for optimizing nanochannel design.

Research on the impact of hydrodynamic parameter design deviation on the motion performance of fully actuated AUV

Abstract This study, based on the Simulink simulation platform, investigates the influence of hydrodynamic parameters on the navigation speed of fully actuated Autonomous Underwater Vehicles (AUVs) and conducts a sensitivity analysis of AUV motion performance to different design deviations in hydrodynamic parameters. The results show that the velocity of underwater motion in each direction exponentially decreases as the corresponding viscous drag coefficient increases while being less influenced by viscous drag coefficients in other directions. Additionally, the sensitivity of the viscous drag coefficient to the underwater motion of AUVs is much greater than that of the inertial drag coefficient.

Contribution of rolling resistance to the drag coefficient of spheres freely rolling on a rough inclined surface

The drag coefficient (CD) of a sphere freely rolling without slipping on a rough plane is presented in this study. Increasing panel roughness has been found to increase CD, although lubrication theory predicts that the larger gap imposed by the rougher panel should yield a smaller drag. We propose that this increase in drag is due to the effects of rolling resistance, which increases with panel roughness. The total drag on a sphere is decomposed into fluid drag and drag due to rolling resistance, where the fluid drag is predicted using a combined analytical–numerical approach. It is shown that rolling resistance can be modeled as a resistive torque opposing the sphere motion, generated by the offset contact normal force from the sphere center plane. This coefficient of rolling resistance (μr) can be predicted using the root mean square roughness (Rq) of the panel. Additionally, μr is observed to increase with sphere down-slope velocity and an empirical relationship between μr, Rq, and non-dimensional velocity (U∗) is given. A comparison of the drag predicted by the proposed model with measured data indicates good agreement for all the four panels considered. Consistent with previous literature, a non-linear relationship between μr, Rq, and U∗ is proposed. Although increasing panel roughness leads to a smaller fluid drag due to the larger gap imposed by rougher panels, the drag due to rolling resistance increases more rapidly. This leads to an increase in total drag with increase in the panel roughness. Additionally, increasing panel roughness is observed to have a significant effect on the sphere wake, leading to irregular wake shedding and increase in the Strouhal number.

Momentum exchange method for quantum Boltzmann methods

The past years have seen a surge in quantum algorithms for computational fluid dynamics (CFD). These algorithms have in common that whilst promising a speed-up in the performance of the algorithm, no specific method of measurement has been suggested. This means that while the algorithms presented in the literature may be promising methods for creating the quantum state that represents the final flow field, an efficient measurement strategy is not available. This paper marks the first quantum method proposed to efficiently calculate quantities of interest (QoIs) from a state vector representing the flow field. In particular, we propose a method to calculate the force acting on an object immersed in the fluid using a quantum version of the momentum exchange method (MEM) that is commonly used in lattice Boltzmann methods to determine the drag and lift coefficients. In order to achieve this we furthermore give a scheme that implements bounce back boundary conditions on a quantum computer, as those are the boundary conditions the momentum exchange method is designed for.

Control of the von Kármán vortex street with focusing and vectoring of jet using synthetic jet array

In the present study, a novel flow control technique based on jet focusing and vectoring from a synthetic jet array (SJA) for controlling the wake of a bluff body is proposed and demonstrated. A numerical investigation into the flow past a square cylinder modified by the SJA has been carried out at a free stream Reynolds Number of 100. The SJA consists of four independently controlled synthetic jet actuators operating at a peak velocity of eight times the free stream and fifteen times the natural vortex shedding frequency of the square cylinder. The SJA is operated in two different regimes; a focusing regime involving phase delay (Δφ) with non-linear variation between the actuators and a vectoring regime with a linear phase delay without changing the geometric or operating parameters of the SJA. It has been found that jet focusing is able to reduce the coefficient of drag by as much as 43% for Δφ=90°. Focusing is also observed to reduce the fluctuations in the wake velocity with the maximum reduction in fluctuations also corresponding to Δφ=90°. Jet vectoring is able to deflect the von Kármán vortex street in a singular direction along with shifting of the front stagnation point with maximum deflection for Δφ=60°. Furthermore, vectoring leads to an asymmetry in the wake velocity field with the shifting of the velocity deficit region in the direction of the vectoring along with an asymmetry in the wake velocity fluctuations. This novel approach toward synthetic jet induced active flow control allows for greater manipulation of the flow field characteristics of bluff bodies than present methods with applications in areas of underwater and micro air vehicle maneuvering, automobile, and building aerodynamics among others.

Computational fluid dynamics analysis of aerodynamic characteristics in long-endurance unmanned aerial vehicles

Long-endurance unmanned aerial vehicles (UAVs) play an increasingly important role in various aspects of societal life. In response to the national emphasis on air force development, a study on the aerodynamic characteristics of long-endurance UAVs was conducted. This paper utilizes SolidWorks software to construct a geometric model based on the MQ-9 UAV, and a CFD method to establish a simulation model for UAV cruising flight. The aerodynamic coefficients, required thrust, and total mass during UAV cruise were calculated, and the variation of aerodynamic coefficients as airflow passes through the UAV was described. A comparative analysis was performed on the effects of different angles of attack, flight speeds, and flight altitudes on aerodynamic efficiency. The study results indicate that at an altitude of 10 km, with a 0° angle of attack, the UAV achieves a lift coefficient of 0.8888, a drag coefficient of 0.0679, and a lift-to-drag ratio of 13.0988. The required thrust is approximately 2236 N, and the total flight mass is approximately 3090 Kg. The angle of attack has the greatest impact on aerodynamic efficiency, followed by flight altitude, while flight speed has the least impact on aerodynamic performance. The lift-to-drag ratio initially increases sharply and then decreases rapidly with increasing angle of attack. It is recommended to control the angle of attack within the range of 0°–6°. The lift-to-drag ratio increases slowly with increasing flight speed, suggesting that the flight speed should be maintained near the maximum cruise speed. The lift-to-drag ratio generally decreases with increasing flight altitude, and it is recommended to maintain the flight altitude within the range of 9 km–11 km.

The variation of particle concentration with height of wind-blown coral sand

Wind-blown coral sand movement is common in the marine coral sand island environment but received much less research attention compared to desert and coastal sands. We used the particle image velocimetry technique with wind tunnel experiments to determine the decay trends of the particle number density, nominal particle area density, and actual particle area density with height for wind-blown coral sands from the South China Sea. Then, a new morphology factor FM that consists of volume V, density ρs, drag coefficient CD, and projected area A of coral sands, was defined to evaluate the influences of particle characteristics on wind-blown sand movement and the results were compared with those of quartz sands from an inland desert. We found that the average FM of coral sands is more comparable to that of coarse quartz sands than smaller size groups. Coral sands tend to move nearer the surface during aeolian processes compared to smaller quartz ones due to their larger FM. The decay rate of particle number density of coral sands with height is similar to that of coarse (0.8–1 mm) quartz sands, but significantly larger than that of smaller quartz ones. The decay rate of the actual particle area density of coral sands with height is larger than that of their nominal particle area density, so that significant deviations may exist if a fixed particle size and spherical shape are assumed to study wind-blown particle movement. The present work contributes to understand the effect of particle characteristics on the wind-blown sand movement from a physical mechanism perspective for both desert quartz sands and marine coral sands.

Computational comparison of passive control for cavitation suppression on cambered hydrofoils in sheet, cloud, and supercavitation regimes

Cavitation is a transient, highly complex phenomenon found in numerous applications and can have a significant impact on the characteristics as well as the performance of the hydrofoils. This study compares the evolution of transient cavitating flow over a NACA4412(base) (NACA stands for National Advisory Committee for Aeronautics) cambered hydrofoil and over the same hydrofoil modified with a pimple and a finite (circular) trailing edge. The assessment covers sheet, cloud, and supercavitation regimes at an 8° angle of attack and the Reynolds number of 1×106, with cavitation numbers ranging from 0.9 to 0.2. The study aims to comprehensively understand the role of the rectangular pimple in controlling cavitation and its impact on hydrodynamic performance across these regimes. Numerical simulations were performed using a realizable model and the Zwart–Gerber–Belamri (ZGB) cavitation model to resolve turbulence and cavitation effects. The accuracy of the present numerical predictions has been verified both quantitatively and qualitatively with available experimental results. The present analysis includes the time evolution of cavities, temporal variation in total cavity volume, time-averaged total cavity volume, distributions of vapor volume fractions along the chord length, and their hydrodynamic performance parameters. Results demonstrate that rectangular pimples have significant impacts in the different cavitation regimes. In the sheet cavitation regime (σ=0.9), the NACA4412(pimpled) hydrofoil exhibits minimal cavity length and transient volume changes as compared to the NACA4412(base) hydrofoil. In the cloud cavitation regimes (σ=0.5), cavity initiation occurs differently, starting from the pimpled location for the NACA4412(pimpled) hydrofoil, unlike the initiation just downstream of the nose in the case of base hydrofoil. In the supercavitation regimes (σ=0.2), the cavity length remains comparable, but the NACA4412(pimpled) hydrofoil exhibits larger cavity volume evolution in both cloud and supercavitation regimes (σ=0.5 and σ=0.2) after initial fluctuations. Furthermore, hydrodynamic performance for the NACA4412(pimpled) hydrofoil shows 41%, 36%, and 17% lower lift coefficients, and 46%, 27%, and 9% lower drag coefficients in sheet, cloud, and supercavitation, respectively.

Interpreting the Projected Frontal Area in Front Crawl: Determining the Projected Frontal Area of Each Body Segment.

This study aimed to provide evidence for the interpretation of the projected frontal area (PFA) during front crawl. To achieve this goal, we developed a method for calculating the PFA of each body segment using digital human technology and compared the pressure drag under two calculation conditions: a combination of the PFA with and without accounting for the horizontal velocity of each body segment. Twelve competitive male swimmers performed a 15-meter front crawl at 1.20 m·s-1. The three-dimensional positions of the reflective markers attached to the swimmer's body were recorded using an underwater motion-capture system. Based on the body shape of each swimmer obtained from the photogenic body scanner, individual digital human body models were created with the color of the model's vertices divided into eight body segments. The time series of the volumetric swimming motion was reconstructed using inverse kinematics. The PFA of each body segment was then calculated by the automatic processing of a series of parallel frontal images. The pressure drag index, defined as the value excluding the drag coefficient while simultaneously considering the PFA and the horizontal velocity, was calculated under two conditions: the static condition (accounting for only the PFA of each body segment) and the dynamic condition (accounting for the PFA and horizontal velocity of each body segment). Notably, the pressure drag index was higher under the static condition than under the dynamic condition for the humerus, ulna, and hand segments (p < 0.001). The results obtained using our methodology indicate that the PFA of the upper limb segments overestimates their contribution to pressure drag during front crawl under the static condition.