Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution

The derivation of the mean velocity profile for a given vorticity distribution over the pipe cross-section is presented in this paper1. The velocity profile and the vorticity distribution are axisymmetric, which means that the radius is the only variable. The importance of the vortex field for the flow analysis is discussed in the paper. The polynomial function with four free parameters is chosen for the vorticity distribution. Free parameters of this function are determined using boundary conditions. There are also two free exponents in the polynomial. These exponents are determined based on the comparison of this analytical formula with experimental data. Experimental data are taken from the Princeton superpipe data which consist of 26 velocity profiles for a wide range of Reynolds numbers (Re). This analytical formula for the mean velocity profile is more precise than the previous one and it is possible to use it for the wide range of Reynolds number <31,577; 35,259,000>. This formula is easy to use, to integrate, or to derivate. The empirical formulas for the profile parameters as a function of Re are also included in this paper. All information for the mean velocity profile prediction in the mentioned Re range are in the paper. It means that it is necessary to know the average velocity v(av), the pipe radius R, and Re to be able to predict the turbulent mean velocity profile in a pipe.

Numerical Analysis of the Effects of Periodic Gust Flow on the Wake Structure of Ventilated Supercavities

A computational model is established to investigate the effects of a periodic gust flow on the wake structure of ventilated supercavities. The effectiveness of the computational model is validated by comparing with available experimental data. Benefited from this numerical model, the vertical velocity characteristics in the entire flow field can be easily monitored and analyzed under the action of a gust generator; further, the unsteady evolution of the flow parameters of the closed region of the supercavity can be captured in any location. To avoid the adverse effects of mounting struts in the experiments and to obtain more realistic results, the wake structure of a ventilated supercavity without mounting struts is investigated. Unsteady changes in the wake morphology and vorticity distribution pattern of the ventilated supercavity are determined. The results demonstrate that the periodic swing of the gust generator can generate a gust flow and, therefore, generate a periodic variation of the ventilated cavitation number σ. At the peak σ, a re-entrant jet closure appears in the wake of the ventilated supercavity. At the valley σ, a twin-vortex closure appears in the wake of the ventilated supercavity. For the forward facing model, the twin vortex appears as a pair of centrally rolled-up vortices, due to the closure of vortex is affected by the structure. For the backward facing model, however, the twin vortex appears alternately as a pair of centrally rolled-up vortices and a pair of centrally rolled-down vortices, against the periodic gust flow.

Using reflection seismic method to estimate the fluid dynamics parameters related to wakes

&lt;p&gt;In this study, when using reflection seismic data to study the wakes of the Batan Islands, a method for estimating the fluid dynamics parameters such as the relative vorticity (relative Rossby number) and the relative potential vorticity is proposed. Although the relative Rossby number estimation method proposed in this study cannot guarantee absolute accuracy in the calculation value, this method is more accurate in describing the positive and negative vorticity distribution for the wakes, and the resolution of the positive and negative vorticity distribution described by this method is higher than the result of the reanalysis data. For the wakes developed in the Batan Islands, the reflection events in the wake development area have the larger inclination than the reflection events in the western Pacific water distribution area. It is also found that the negative vorticity wakes are mainly distributed on the west side of the island/ridge, and the positive vorticity wakes are mainly distributed on the east side of the island/ridge. This is consistent with the understanding of previous wakes simulations. The strong vorticity values in the study area are mainly distributed at depths above 300m, and the maximum impact depth of wakes can reach 600m. At the downstream position of the wake on the survey line 7, it can be seen that the bottom boundary layer has separated, and there is the negative vorticity wakes on the west side intruding into the positive vorticity wakes on the east side , which is presumed to be caused by the disturbance of the small anticyclone existing near the Batan Islands. For the survey line 7, the negative potential vorticity is mainly distributed on the west side of the island/ridge, and the influence range can reach the sea depth of 600m. In the negative potential vorticity region, there is strong energy dissipation and vertical shear. In this study, we don&amp;#8217;t find the existence of submesoscale coherent vortices on the survey line 7, but find the reflection structure similar to filaments on the seismic section. Combined with the analysis of the balanced Richardson number angle of survey line 7, we speculate that the wake in the negative potential vorticity distribution area has the characteristics of symmetrical instability, and the symmetrical instability may destroy the process of filaments forming submesoscale coherent vortices.&lt;/p&gt;

Impact of Leading Edge Roughness in Cavitation Simulations around a Twisted Foil

The simulation of fully turbulent, three-dimensional, cavitating flow over Delft twisted foil is conducted by an implicit large eddy simulation (LES) approach in both smooth and tripped conditions, the latter by including leading-edge roughness. The analysis investigates the importance of representing the roughness elements on the flow structures in the cavitation prediction. The results include detailed comparisons of cavitation pattern, vorticity distribution, and force predictions with the experimental measurements. It is noted that the presence of roughness generates very small cavitating vortical structures which interact with the main sheet cavity developing over the foil to later form a cloud cavity. Very similar to the experimental observation, these interactions create a streaky sheet cavity interface which cannot be captured in the smooth condition, influencing both the richness of structures in the detached cloudy cavitation as well as the extent and transport of vapour. It is further found to have a direct impact on the pressure distribution, especially in the mid-chord region where the shed cloud cavity collapses.

Aerodynamic Performance of an Octorotor SUAV with Different Rotor Spacing in Hover

To study the aerodynamic performance of hovering octorotor small unmanned aerial vehicles (SUAV) with different rotor spacing, the computational fluid dynamics (CFD) method is applied to analyze the flow field of an octorotor SUAV in detail. In addition, an experimental platform is built to measure the thrust and power of the rotors with rotor spacing ratios L/D of 1.0, 1.2, 1.4, 1.6, and 1.8, sequentially. According to the theory of momentum, rotor aerodynamic performance is obtained with qualitative analysis. Further analysis with numerical simulation is presented with the flow field of the octorotor SUAV, the vorticity distribution, velocity distribution, pressure distribution, and streamline. The results show that the aerodynamic performance varies with the rotor spacing. Specifically, the aerodynamic performance is poor at L/D = 1.0, which is accompanied with strong interaction of wake and tip vortexes and interaction with each other. However, the aerodynamic efficiency is much improved with a larger rotor spacing, especially achieving the highest at L/D = 1.8, which is considered to be the best rotor spacing ratio for this kind of octorotor SUAV.

Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution

In 1895, Korteweg and de Vries (Philos Mag 20:20, 1895) studied an equation describing the motion of waves using the assumptions of long wavelength and small amplitude. Two implicit assumptions which they also made were irrotational and inviscid fluids. Comparing experiment and observation seems to suggest that these two assumptions are well justified. This paper removes the assumption of irrotationality in the case of electrohydrodynamics with an assumption of globally constant vorticity in the fluid. A study of the effect of vorticity on wave profiles and amplitudes is made revealing some unusual features. The velocity potential is an important variable in irrotational flow; the vertical component of velocity takes place of this variable in our analysis. This allows the bypassing of the Burns condition and also demonstrates that waves exist even for negative values of the vorticity. The linear and weakly nonlinear models are derived.

On the Edge Singularity of the Actuator Disk Model

In this technical brief, the classic actuator disk theory is revisited with a view to shed some light on the singularity of the flow at the edge of the disk where the vortex tube starts and where vorticity is generated. The study is carried out using small perturbation assumption in two-dimensions and simplified boundary conditions in all cases. The problem of the two-dimensional thin cambered plate with constant vorticity distribution is solved and the leading edge singularity is analyzed as it is believed to be relevant to the axisymmetric flow at the actuator disk edge. Next, the velocity components induced by the cylindrical vortex tube of constant vorticity are obtained via the Biot–Savart law and the near edge behavior is investigated. It is shown that the velocity components behavior is consistent with that of the thin cambered plate with constant loading, thus reinforcing the notion that the axisymmetric slip-line behaves as r − R ∝ −xlnx near the disk edge.

Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution

In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and irrotational fluid. The resulting equation, the celebrated KdV equation, has been shown to be a very reasonable description of real water waves. However there are other phenomena which have an impact on the shape of the wave, that of vorticity and viscosity. This paper examines how a constant vorticity affects the shape of waves in electrohydrodynamics. For constant vorticity, the vertical component of the velocity obeys a Laplace equation and also has the usual lower boundary condition. In making the vertical component of the velocity take central stage, the Burns condition can be thus bypassed.

Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution

In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and irrotational fluid. The resulting equation, the celebrated KdV equation, has been shown to be a very reasonable description of real water waves. However there are other phenomena which have an impact on the shape of the wave, that of vorticity and viscosity. This paper examines how a constant vorticity affects the shape of waves in electrohydrodynamics. For constant vorticity, the vertical component of the velocity obeys a Laplace equation and also has the usual lower boundary condition. In making the vertical component of the velocity take central stage, the Burns condition can be thus bypassed.