Symmetric, Rotational, Supercavitating Flow About a Slender Wedge

1964 ◽  
Vol 86 (3) ◽  
pp. 569-575 ◽  
Author(s):  
R. L. Street
Keyword(s):  
Drag Coefficient ◽  
Cavity Length ◽  
Rotational Flow ◽  
Drag Coefficients ◽  
Irrotational Flow ◽  
Supercavitating Flow ◽  
Slender Bodies ◽  
Linearized Theory

Two approximations to the linearized theory for supercavitating flow about slender bodies are applied to the case of a symmetric, rotational flow about a slender wedge. Both approximations produce relationships for the cavity length and drag coefficients; one approximation also gives certain nonunique solutions not encountered in the corresponding irrotational flow. The presence of rotation is shown to create significant changes in the length of the trailing cavity, but small changes in the drag coefficient.

A linearized theory for rotational supercavitating flow

1963 ◽  
Vol 17 (4) ◽  
pp. 513-545 ◽  
Author(s):  
Robert L. Street
Keyword(s):  
Shear Flow ◽  
Flow Past ◽  
Supercavitating Flow ◽  
Harmonic Perturbation ◽  
Two Dimensional Flow ◽  
Slender Bodies ◽  
Linearized Theory ◽  
Particular Solution ◽  
Effects Of Rotation ◽  
Rotational Problem

In this paper methods are given for establishing qualitative and quantitative measures of the effects of rotation in supercavitating flows past slender bodies. A linearized theory is developed for steady, two-dimensional flow under the assumption that the flow has a constant rotation throughout. The stream function of the rotational flow satisfies Poisson's equation. By using a particular solution of this equation, the rotational problem is reduced to a problem involving Laplace's equation and harmonic perturbation velocities. The resulting boundary-value problem is solved by use of conformal mapping and singularities from thinairfoil theory. The theory is then applied to asymmetric shear flow past wedges and hydrofoils and to symmetric shear flow past wedges. The presence of rotation is shown to create significant changes in the forces acting on the slender bodies and in the shape and size of the trailing cavities.

scholarly journals The Effect of a Longitudinal Gravitational Field on the Supercavitating Flow Over a Wedge

1961 ◽  
Vol 28 (2) ◽  
pp. 188-192 ◽  
Author(s):  
A. J. Acosta
Keyword(s):  
Gravitational Field ◽  
Drag Coefficient ◽  
Froude Number ◽  
Cavitation Number ◽  
Streamline Flow ◽  
Flow Past ◽  
Supercavitating Flow ◽  
Linearized Theory

The free-streamline flow past a symmetrical wedge in the presence of a longitudinal gravitational field is determined with a linearized theory. The proportions of the cavity depend upon the cavitation number and Froude number. The drag coefficient is likewise affected by gravity, though to a smaller extent.

INVESTIGATIONS ON THE DRAG REDUCTION OF HIGH-SPEED NATURAL SUPERCAVITATION BODIES

2009 ◽  
Vol 23 (03) ◽  
pp. 405-408 ◽  
Author(s):  
WENJUN YI ◽  
JUNJIE TAN ◽  
TIANHONG XIONG
Keyword(s):  
Aspect Ratio ◽  
Drag Reduction ◽  
Drag Coefficient ◽  
High Speed ◽  
Cavitation Number ◽  
Drag Coefficients ◽  
Supercavitating Flow ◽  
Disk Cavitator ◽  
Reduction Characteristics ◽  
Flow Experiments

In order to investigate the drag reduction characteristics of a high-speed body with supercavitation shape, four types of typical disk cavitator models with different parameters were designed and tested. By measuring the velocity decrease histories during supercavitating flow experiments, the average drag coefficients were determined, which allows analysis and comparison of the influence of cavitator diameter, projectile aspect ratio, and cavitation number on the drag reduction. Based on the experimental results, numerical simulation of the drag reduction of supercavitation body was also carried out using a commercial software FLUENT6.2, and the results obtained agree well with the experimental data. Moreover, it is shown that the drag coefficients of the four bodies are in inverse ratio to the head area of cavitator when operating under natural supercavitating flow condition, and the smaller drag coefficient can be obtained by increasing the slender ratio of the bodies. Therefore, higher aspect ratio reduces drag coefficient, with the reduction of more than 95% under certain condition of cavitation number and supercaviation shape.

Two-Dimensional, Steady, Cavity Flow About Slender Bodies in Channels of Finite Breadth

1957 ◽  
Vol 24 (2) ◽  
pp. 170-176
Author(s):  
Hirsh Cohen ◽  
Robert Gilbert
Keyword(s):  
Cavity Length ◽  
Solid Wall ◽  
Cavity Flow ◽  
Cavitation Number ◽  
Integral Equation Formulation ◽  
Slender Bodies ◽  
Linearized Theory ◽  
Finite Breadth ◽  
Arbitrary Body ◽  
Cavity Width

Abstract The steady, cavitating flow past slender symmetrical bodies placed in a solid-wall channel is studied by means of the linearized theory of Tulin. The free-boundary condition is linearized and boundary conditions are applied on the line of symmetry of the flow in analogy with thin-air-foil theory. A singular integral equation formulation of the boundary-value problem is obtained and can be solved to yield expressions for cavity length, maximum cavity width, and drag coefficient as functions of the cavitation number and the channel breadth. These expressions are given for an arbitrary body and evaluated for the case of a wedge.

scholarly journals Coral Reef Drag Coefficients – Water Depth Dependence

2017 ◽  
Vol 47 (5) ◽  
pp. 1061-1075 ◽  
Author(s):  
S. J. Lentz ◽  
K. A. Davis ◽  
J. H. Churchill ◽  
T. M. DeCarlo
Keyword(s):  
Coral Reef ◽  
Coral Reefs ◽  
Drag Coefficient ◽  
Water Depth ◽  
Open Channel ◽  
Momentum Balance ◽  
Laboratory Studies ◽  
Drag Coefficients ◽  
Significant Term ◽  
The Cross

AbstractA major challenge in modeling the circulation over coral reefs is uncertainty in the drag coefficient because existing estimates span two orders of magnitude. Current and pressure measurements from five coral reefs are used to estimate drag coefficients based on depth-average flow, assuming a balance between the cross-reef pressure gradient and the bottom stress. At two sites wind stress is a significant term in the cross-reef momentum balance and is included in estimating the drag coefficient. For the five coral reef sites and a previous laboratory study, estimated drag coefficients increase as the water depth decreases consistent with open channel flow theory. For example, for a typical coral reef hydrodynamic roughness of 5 cm, observational estimates, and the theory indicate that the drag coefficient decreases from 0.4 in 20 cm of water to 0.005 in 10 m of water. Synthesis of results from the new field observations with estimates from previous field and laboratory studies indicate that coral reef drag coefficients range from 0.2 to 0.005 and hydrodynamic roughnesses generally range from 2 to 8 cm. While coral reef drag coefficients depend on factors such as physical roughness and surface waves, a substantial fraction of the scatter in estimates of coral reef drag coefficients is due to variations in water depth.

Force and Moment Measurements of Supercavitating Hydrofoils of Finite Span With Comparison to Theory

1975 ◽  
Vol 97 (4) ◽  
pp. 453-462
Author(s):  
P. Leehey ◽  
T. S. Stellinger
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Expansions ◽  
Cavity Length ◽  
Large Aspect Ratio ◽  
Drag Coefficients ◽  
Finite Span ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Lift And Drag ◽  
Good Agreement

Measurements were made of lift, drag, and moment coefficients, and cavity length for aspect ratio 3 and 5 supercavitating hydrofoils of elliptical planform. These measurements are compared with theoretical predictions obtained from matching asymptotic expansions for large aspect ratio. Good agreement was obtained for lift and drag coefficients for angles of attack from 10 deg to 15 deg and for a wide range of cavity lengths. Theoretical moment coefficients were too large indicating the need for lifting surface corrections.

Migration of Particles to a Hole Wall in a Drilling Well

1969 ◽  
Vol 9 (02) ◽  
pp. 147-154
Author(s):  
Richard E. Walker
Keyword(s):  
Turbulent Flow ◽  
Drag Coefficient ◽  
Past History ◽  
Drill Pipe ◽  
Round Hole ◽  
Drag Coefficients ◽  
Hole Cleaning ◽  
Hole Wall ◽  
Primary Object ◽  
Newtonian Liquids

Abstract The rate at which a particle will migrate from the rotating drill pipe to the hole wall was calculated as functions of the mud properties, pipe rotational speed, and hole size. The information can be used to estimate the relative carrying capacity of one mud compared to another Then the changes that need to be made when a hole. is not cleaning can be determined. An adaptive control process for field use is suggested Two major simplifying assumptions are that axial flow does not influence the liquid viscosity and that the viscous resistance to particle movement in the radial direction is proportional to the particle's velocity. The calculations assume a power model liquid, spherical cuttings, and concentric pipe in a round hole. A concept of "theoretical zones" where the calculations are valid interspersed with areas where the particles are uniformly redistributed, is used to relate the simplified theory to actual hole conditions. Introduction This theoretical study was conducted to improve the understanding of hole cleaning and how various drilling conditions and muds influence the ability to lift cuttings to the surface. The primary object of the study was to see how fast a particle might move from the drill pipe to the hole wall and how factors of drilling and liquid properties influence the rate of radial movement. The rate of movement may be important as the centrifugal force set up by the rotating drill pipe tends to force the particle toward the hole wall, an area of low vertical mud velocity and, therefore, poor lifting. PRIOR WORK Removal of cutting from a drilling well by circulating a structured liquid such as bentonite-water is a physically complex operation. Explicit prediction of the path of a cutting requires the ability to calculate the velocity of the particle relative to the liquid and the velocity field of the liquid. Various phases have been investigated. Williams and Bruce showed experimentally the path of particles in a laboratory wellbore and developed slip correlations for turbulent flow. Many investigations have been made for drag coefficients of particles settling in stationary Newtonian liquids under conditions of laminar and turbulent flow. The only work with inclined discs is with very low Reynolds numbers, an area of little interest in hole cleaning. Some investigations with drag coefficients in non-Newtonian liquids and the only work with structured liquids indicates the drag coefficient is different in stationary liquid from the drag coefficient in moving liquid. Various methods of predicting slip velocities are available, as well as correlations of hole cleaning based on experimental well tests. Bentonite drilling muds are generally a shear thinning liquid in which stress-rate relation at a fixed time depends on past history. Most rheological work is done under steady-state conditions to show the influence of chemical additives and temperature changes. There has been little work on dynamic response such as has been done with viscoelastic liquids to select time dependent constitutive equations or experiments with shear in two directions. Most pressure drop calculations for field use are based on annular flow without rotating drill pipe, and radial migration of particles and angular liquid velocities are neglected. Savins and Wallick calculated annular pressure drops, including rotating drill pipe, for a liquid described by a three constant Oldroyd model. The calculations were based on a viscosity relation for one-dimensional flow but used the vector sum of the longitudinal and angular components of stress to calculate the viscosity. This procedure was shown correct for a viscoelastic liquid. SPEJ P. 147ˆ

scholarly journals The estimation of applicability concerning the methods for calculation of asimple wing with wingtips inductive resistance during the flight near the earth surface

2020 ◽  
pp. 58-69
Author(s):  
Andrey N. Luchkov ◽  
Evgeny V. Zhuravlev ◽  
Egor Y. Cheban
Keyword(s):  
Drag Coefficient ◽  
Earth Surface ◽  
Drag Coefficients ◽  
End Plate ◽  
Induced Drag ◽  
The Earth ◽  
Wing Profile

One of the problems in the hovercrafts design is to dtermine the aerodynamic charactreistics of the wing near the earth surface. In this article, 4 methods for calculating the induced drag coefficient Cxi of a simple airfoil with an end plate at different relative heights were considered. Four methods of induced drag coefficient determination were considered for different relative flight’s heights. Calculations were performed according to the Phillips, Wieselsberge, Panchenkov-Surzhik, Mantle methods for the TsAGI-876 wing profile. The calculated values of induced drag coefficients were compared with the experimental wind tunnel’s data at the Central Aerohydrodynamic Institute.

scholarly journals Analysis of why sea turtles swim slowly: a metabolic and mechanical approach

2021 ◽  
Vol 224 (4) ◽  
pp. jeb236216
Author(s):  
Chihiro Kinoshita ◽  
Takuya Fukuoka ◽  
Tomoko Narazaki ◽  
Yasuaki Niizuma ◽  
Katsufumi Sato
Keyword(s):  
Drag Coefficient ◽  
Marine Mammals ◽  
Sea Turtles ◽  
Resting Metabolic Rate ◽  
Energy Costs ◽  
Metabolic Rates ◽  
Natural Conditions ◽  
Drag Coefficients ◽  
Green Turtles ◽  
Mechanical Approach

ABSTRACTAnimals with high resting metabolic rates and low drag coefficients typically have fast optimal swim speeds in order to minimise energy costs per unit travel distance. The cruising swim speeds of sea turtles (0.5–0.6 m s−1) are slower than those of seabirds and marine mammals (1–2 m s−1). This study measured the resting metabolic rates and drag coefficients of sea turtles to answer two questions: (1) do turtles swim at the optimal swim speed?; and (2) what factors control the optimal swim speed of turtles? The resting metabolic rates of 13 loggerhead and 12 green turtles were measured; then, the cruising swim speeds of 15 loggerhead and 9 green turtles were measured and their drag coefficients were estimated under natural conditions. The measured cruising swim speeds (0.27–0.50 m s−1) agreed with predicted optimal swim speeds (0.19–0.32 m s−1). The resting metabolic rates of turtles were approximately one-twentieth those of penguins, and the products of the drag coefficient and frontal area of turtles were 8.6 times higher than those of penguins. Therefore, our results suggest that both low resting metabolic rate and high drag coefficient of turtles determine their slow cruising speed.

Supercavitating Flow About a Slender Wedge in a Transverse Gravity Field

1963 ◽  
Vol 7 (03) ◽  
pp. 14-23
Author(s):  
R. L. Street
Keyword(s):  
Gravity Field ◽  
First Order ◽  
Flow Past ◽  
Supercavitating Flow ◽  
Linearized Theory

In this paper a linearized theory is developed for supercavitating flow past a slender strut or wedge in a transverse gravity field. The theory is expected to be valid when the effects of the gravity field are of first-order smallness consistent with the linearization approximations. The additional lift and moment forces acting on the strut as a result of the gravity field are calculated. The transverse gravity field is found to produce additional forces which should be considered in hydrodynamic design.

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