Inverse Methods in the Linearized Theory of Fully Cavitating Hydrofoils

1964 ◽  
Vol 86 (4) ◽  
pp. 641-654 ◽  
Author(s):  
B. R. Parkin ◽  
R. S. Grote
Keyword(s):  
Inverse Problem ◽  
Pressure Distribution ◽  
Cavitation Number ◽  
Inverse Methods ◽  
Two Dimensional ◽  
Physical Constraints ◽  
Two Dimensional Flow ◽  
Linearized Theory ◽  
Profile Design ◽  
Major Emphasis

Theoretical and numerical procedures are given for the design of fully cavitating hydrofoils in a steady two-dimensional flow. The only boundary in the flow is that provided by the hydrofoil and its cavity. The cavity is always assumed to spring from the nose and trailing edge of the profile. The methods used are those of linearized inverse airfoil theory, in which one prescribes the pressure distribution on the wetted surface of the profile and then calculates its shape. The theory at zero cavitation number is considered anew in order to highlight the physical constraints involved in this inverse problem. However, major emphasis is given to basic procedures for profile design at nonzero or zero cavitation numbers. Optimum hydrofoil design is discussed from an engineering viewpoint.

The aerodynamic theory of sails. I. Two-dimensional sails

1961 ◽  
Vol 261 (1306) ◽  
pp. 402-422 ◽  
Keyword(s):  
Lift Coefficient ◽  
Linear Equations ◽  
Three Dimensional ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Two Dimensional Flow ◽  
Linearized Theory ◽  
High Degree ◽  
Additional Equation

This paper deals with the preliminaries essential for any theoretical investigation of three-dimensional sails—namely, with the two-dimensional flow of inviscid incompressible fluid past an infinitely-long flexible inelastic membrane. If the distance between the luff and the leach of the two-dimensional sail is c , and if the length of the material of the sail between luff and leach is ( c + l ), then the problem is to determine the flow when the angle of incidence α between the chord of the sail and the wind, and the ratio l / c are both prescribed; especially, we need to know the shape of, the loading on, and the tension in, the sail. The aerodynamic theory follows the lines of the conventional linearized theory of rigid aerofoils; but in the case of a sail, there is an additional equation to be satisfied which ex­presses the static equilibrium of each element of the sail. The resulting fundamental integral equation—the sail equation—is consequently quite different from those of aerofoil theory, and it is not susceptible to established methods of solution. The most striking result is the theoretical possibility of more than one shape of sail for given values of α and l / c ; but there appears to be no difficulty in choosing the shape which occurs in reality. The simplest result for these realistic shapes is that the lift coefficient of a sail exceeds that of a rigid flat plate (for which l / c = 0) by an amount approximately equal to 0.636 ( l / c ) ½ . It seems very doubtful whether analytical solutions of the sail equation will be found, but a method is developed in this paper which comes to the next best thing; namely, an explicit expression, as a matrix quotient, which gives numerical values to a high degree of accuracy at so many chord-wise points. The method should have wide application to other types of linear equations.

Pressure Distributions and Forces on Rectangular and D-shaped Cylinders

1972 ◽  
Vol 23 (1) ◽  
pp. 1-6 ◽  
Author(s):  
B R Bostock ◽  
W A Mair
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Drag Coefficient ◽  
Pressure Distribution ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Two Dimensional Flow ◽  
Rectangular Cylinders ◽  
Shaped Section

SummaryMeasurements in two-dimensional flow on rectangular cylinders confirm earlier work of Nakaguchi et al in showing a maximum drag coefficient when the height h of the section (normal to the stream) is about 1.5 times the width d. Reattachment on the sides of the cylinder occurs only for h/d < 0.35.For cylinders of D-shaped section (Fig 1) the pressure distribution on the curved surface and the drag are considerably affected by the state of the boundary layer at separation, as for a circular cylinder. The lift is positive when the separation is turbulent and negative when it is laminar. It is found that simple empirical expressions for base pressure or drag, based on known values for the constituent half-bodies, are in general not satisfactory.

Hydrodynamic Trends for Preliminary Design of Fully Cavitating Hydrofoil Sections

1977 ◽  
Vol 14 (01) ◽  
pp. 70-85
Author(s):  
Blaine R. Parkin ◽  
Robert F. Davis ◽  
Joseph Fernandez
Keyword(s):  
Pressure Distribution ◽  
Lift Coefficient ◽  
Flow Theory ◽  
Cavity Flow ◽  
Cavitation Number ◽  
Viscous Drag ◽  
Preliminary Design ◽  
Two Dimensional ◽  
Cavity Thickness ◽  
Cavitating Hydrofoil

The object of this numerical study is to consider possible hydrodynamic trends for use in trade-off studies for the preliminary design of fully cavitating hydrofoil sections. Hydrodynamic data are obtained from inverse calculations which are based upon two-dimensional linearized cavity-flow theory. Supplementary data are also calculated from the direct problem of linearized cavity-flow theory in order to show off-design performance trends and to assess the effects of cavity-foil interference on the operating range of selected profiles. For the inverse calculations one specifies design values of the lift coefficient, cavitation number, and cavity thickness at the trailing edge, as well as the shape of the pressure distribution on the wetted surface of the hydrofoil section. In accordance with this specification, the ordinates of the profile wetted surface and upper-cavity contour are calculated, together with values of drag coefficient, moment coefficient, and attack angle at the design point. The paper summarizes the results of a parametric study of the effects of design cavitation number, lift coefficient, cavity thickness, and pressure distribution shape upon hydrofoil section performance and geometry. Three-dimensional wing effects, viscous drag, and the effects of structural design criteria are all outside the scope of the study. Results pertaining to steady two-dimensional cavity flows of an ideal incompressible fluid past a rigid hydrofoil section are presented.

The Role of Eigensolutions in Nonlinear Inverse Cavity-Flow Theory

1988 ◽  
Vol 110 (3) ◽  
pp. 315-324
Author(s):  
B. R. Parkin
Keyword(s):  
Inverse Problem ◽  
Free Surface ◽  
Direct Problem ◽  
Cavity Flow ◽  
Cavitation Number ◽  
The Novel ◽  
Cavity Shape ◽  
Linearized Theory ◽  
Exact Point

The method of Levi Civita is applied to an isolated fully cavitating body at zero cavitation number and adapted to the solution of the inverse problem in which one prescribes the pressure distribution on the wetted surface and then calculates the shape. The novel feature of this work is the finding that the exact theory admits the existence of a “point drag” function or eigensolution. While this fact is of no particular importance in the classical direct problem, we already know from the linearized theory that the eigensolution plays an important role. In the present discussion, the basic properties of the exact “point-drag” solution are explored under the simplest of conditions. In this way, complications which arise from non-zero cavitation numbers, free surface effects, or cascade interactions are avoided. The effects of this simple eigensolution on hydrodynamic forces and cavity shape are discussed. Finally, we give a tentative example of how this eigensolution might be used in the design process.

Numerical Data on Hydrofoil Response to Nonsteady Motions at Zero Cavitation Number

1962 ◽  
Vol 6 (04) ◽  
pp. 40-42
Author(s):  
Blaine R. Parkin
Keyword(s):  
Hydrodynamic Force ◽  
Numerical Data ◽  
Step Function ◽  
Cavitation Number ◽  
Two Dimensional ◽  
Response Functions ◽  
Force Response ◽  
Linearized Theory

This paper presents a tabulation of hydrodynamic force response functions for steady sinusoidal and step-function motions and gusts for o fully cavitated two-dimensional fiatplate hydrofoil at zero cavitation number. The cavity separation points are fixed at the nose and at the tail of the profile. Some results from the present linearized theory are compared with corresponding results of L. C. Woods.

A computational method for the flow through non-uniform gauzes: the general two-dimensional case

1969 ◽  
Vol 36 (2) ◽  
pp. 367-383 ◽  
Author(s):  
J. T. Turner
Keyword(s):  
Experimental Data ◽  
Computational Method ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Linearized Theory ◽  
Flow Through ◽  
Comparison With Experimental Data

A computational method is presented for the analysis of two-dimensional flow through a non-uniform gauze. The method, based upon the linearized theory due to Elder (1959), permits solutions for most practical cases to be obtained using relatively simple numerical techniques. Comparison with experimental data shows that the computed solutions are satisfactory provided the restrictions inherent in the linearized theory are observed.

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