A Numerical Optimization Technique Applied to the Design of Two-Dimensional Cavitating Hydrofoil Sections

A numerical nonlinear optimization technique is applied to the systematic design of two-dimensional partially or supercavitating hydrofoil sections. The design objective is to minimize the hydrofoil drag for given lift and cavitation number. The hydrodynamic analysis of the cavitating hydrofoil is performed in nonlinear theory, via a low-order potential-based panel method. The effects of viscosity are taken into account via a uniform friction coefficient applied on the wetted foil surface. The total drag, lift, cavitation number, and other quantities involved in the imposed constraints, are expressed in terms of quadratic functions of the main parameters of the hydrofoil geometry, angle of attack, and the cavity length. The optimization is based on the method of multipliers by coupling the Lagrange multiplier terms and the penalty function terms. The robustness and convergence of the method are extensively investigated, and the results are compared with those from applying other design methods.

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A Potential-Based Panel Method for the Analysis of a Two-Dimensional Super-or Partially-Cavitating Hydrofoil

Journal of Ship Research ◽

10.5957/jsr.1992.36.2.168 ◽

1992 ◽

Vol 36 (02) ◽

pp. 168-181 ◽

Cited By ~ 1

Author(s):

C.-S. Lee ◽

Y.-G. Kim ◽

J.-T. Lee

Keyword(s):

Cavity Length ◽

Cavitation Number ◽

Panel Method ◽

Cavity Surface ◽

Two Dimensional ◽

Closure Condition ◽

Surface Pressure Distribution ◽

Cavity Closure ◽

Cavitating Hydrofoil ◽

Method Show

A potential-based panel method is presented for the analysis of a super-or partially-cavitating two-dimensional hydrofoil. The method employs normal dipoles and sources distributed on the foil and cavity surfaces. It is shown that the source plays an important role in positioning the cavity surface through an iterative process. The cavity closure condition is found very effective in generating the cavity shape. Upon convergence, the method predicts the cavitation number together with the lift, drag, and surface pressure distribution for a given cavity length. Systematic convergence tests of the present numerical method show fast and stable characteristics. Good correlations are obtained with existing theories and experimental results for both partially-and supercavitating flows.

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Hydrodynamic Trends for Preliminary Design of Fully Cavitating Hydrofoil Sections

Marine Technology and SNAME News ◽

10.5957/mt1.1977.14.1.70 ◽

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.

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Improvement of Hydrofoil Performance by Partial Ventilated Cavitation in Steady Flow and Periodic Gusts

Journal of Fluids Engineering ◽

10.1115/1.2842147 ◽

2008 ◽

Vol 130 (3) ◽

Cited By ~ 34

Author(s):

Jim Kopriva ◽

Roger E. A. Arndt ◽

Eduard L. Amromin

Keyword(s):

Cavity Length ◽

Excitation Frequency ◽

Nonlinear Effects ◽

Cavitation Number ◽

Wave Impact ◽

Linear Perturbations ◽

Lift And Drag ◽

Cavitating Hydrofoil ◽

Sea Wave

This paper describes a study of the response of a recently developed low-drag partially cavitating hydrofoil (denoted as OK-2003) to periodical perturbations of incoming flow. A two-flap assembly specially designed to simulate sea wave impact on the cavitating hydrofoil generates the perturbations. The design range of cavitation number was maintained by ventilation. Unsteady flow can be simulated over a range of ratios of gust flow wavelength to cavity length. The measurement of time-average lift and drag coefficients and their fluctuating values over a range of inflow characteristics allows a determination of hydrofoil performance over a range of conditions that could be expected for a prototype hydrofoil. Both regular interaction with practically linear perturbations and resonancelike singular interaction with substantial nonlinear effects were noted. The observations are accompanied by a numerical analysis that identifies resonance phenomena as a function of excitation frequency.

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Wall Effects in Cavitating Hydrofoil Flow

Journal of Ship Research ◽

10.5957/jsr.1957.1.4.31 ◽

1957 ◽

Vol 1 (04) ◽

pp. 31-50

Author(s):

Hirsh Cohen ◽

C. D. Sutherland ◽

Tu Yih-O

Keyword(s):

Flat Plate ◽

Linear Theory ◽

Cavity Length ◽

Two Dimensional ◽

Cavity Model ◽

Transition Flow ◽

Wall Effects ◽

Special Cases ◽

Two Dimensional Flow ◽

Cavitating Hydrofoil

A linearized version of the transition-flow cavity model is used to obtain the effects of solid channel walls on cavitating hydrofoils. The formulation is in terms of two dimensional flow but includes any shape hydrofoil within the scope of the linear theory and any location of the foil between the walls. The case of the flat plate foil is considered in numerical detail. Three special cases of position, the foil midway between walls, near to only one wall, and the foil in an infinite stream (walls infinitely far apart), are taken up. The effect of the walls on lift and cavity length are discussed for each case.

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Influence of Thermodynamic Effect on Blade Load in a Cavitating Inducer

International Journal of Rotating Machinery ◽

10.1155/2010/302360 ◽

2010 ◽

Vol 2010 ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

Kengo Kikuta ◽

Noriyuki Shimiya ◽

Tomoyuki Hashimoto ◽

Mitsuru Shimagaki ◽

Hideaki Nanri ◽

...

Keyword(s):

Pressure Distribution ◽

Liquid Nitrogen ◽

Cavity Length ◽

Cold Water ◽

Pressure Rise ◽

Cavitation Number ◽

Design Parameters ◽

Trailing Edge ◽

Thermodynamic Effect ◽

Blade Tip

Distribution of the blade load is one of the design parameters for a cavitating inducer. For experimental investigation of the thermodynamic effect on the blade load, we conducted experiments in both cold water and liquid nitrogen. The thermodynamic effect on cavitation notably appears in this cryogenic fluid although it can be disregarded in cold water. In these experiments, the pressure rise along the blade tip was measured. In water, the pressure increased almost linearly from the leading edge to the trailing edge at higher cavitation number. After that, with a decrease of cavitation number, pressure rise occurred only near the trailing edge. On the other hand, in liquid nitrogen, the pressure distribution was similar to that in water at a higher cavitation number, even if the cavitation number as a cavitation parameter decreased. Because the cavitation growth is suppressed by the thermodynamic effect, the distribution of the blade load does not change even at lower cavitation number. By contrast, the pressure distribution in liquid nitrogen has the same tendency as that in water if the cavity length at the blade tip is taken as a cavitation indication. From these results, it was found that the shift of the blade load to the trailing edge depended on the increase of cavity length, and that the distribution of blade load was indicated only by the cavity length independent of the thermodynamic effect.

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A non-linear theory for a full cavitating hydrofoil in a transverse gravity field

Journal of Fluid Mechanics ◽

10.1017/s0022112067000849 ◽

1967 ◽

Vol 29 (2) ◽

pp. 317-336 ◽

Cited By ~ 9

Author(s):

Bruce E. Larock ◽

Robert L. Street

Keyword(s):

Gravity Field ◽

Linear Theory ◽

Mixed Boundary ◽

Linear Method ◽

Two Dimensional ◽

Mixed Boundary Value Problem ◽

Cavity Model ◽

Cavity Size ◽

Non Linear ◽

Cavitating Hydrofoil

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.

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Efficient Structural Design Using a Numerical Optimization Technique

IABSE Congress, New York, New York 2019: The Evolving Metropolis ◽

10.2749/newyork.2019.0499 ◽

2019 ◽

Author(s):

Qian Wang ◽

Lucas Schmotzer ◽

Yongwook Kim

Keyword(s):

Structural Design ◽

Numerical Optimization ◽

Optimization Technique ◽

Optimization Method ◽

Optimization Techniques ◽

Convergence Criteria ◽

Efficient Design ◽

Concrete Building ◽

Gradient Based ◽

Structural Responses

<p>Structural designs of complex buildings and infrastructures have long been based on engineering experience and a trial-and-error approach. The structural performance is checked each time when a design is determined. An alternative strategy based on numerical optimization techniques can provide engineers an effective and efficient design approach. To achieve an optimal design, a finite element (FE) program is employed to calculate structural responses including forces and deformations. A gradient-based or gradient-free optimization method can be integrated with the FE program to guide the design iterations, until certain convergence criteria are met. Due to the iterative nature of the numerical optimization, a user programming is required to repeatedly access and modify input data and to collect output data of the FE program. In this study, an approximation method was developed so that the structural responses could be expressed as approximate functions, and that the accuracy of the functions could be adaptively improved. In the method, the FE program was not required to be directly looped in the optimization iterations. As a practical illustrative example, a 3D reinforced concrete building structure was optimized. The proposed method worked very well and optimal designs were found to reduce the torsional responses of the building.</p>

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Steady Performance of a Flexible Hydrofoil Near a Free Surface

Journal of Ship Research ◽

10.5957/jsr.1990.34.4.302 ◽

1990 ◽

Vol 34 (04) ◽

pp. 302-310

Author(s):

Salwa M. Rashad ◽

Theodore Green

Keyword(s):

Mathematical Model ◽

Free Surface ◽

Cavity Length ◽

Leading Edge ◽

Cavity Flow ◽

Cavitation Number ◽

Deformation Characteristics ◽

Flow Depth ◽

Lift And Drag ◽

The Galerkin Method

A linearized cavity-flow theory is used to develop a mathematical model to study the steady characteristics of a flexible hydrofoil near a free surface. The Galerkin method is employed to account for the mutual interaction between the fluid and structure forces. Cheng and Rott's method [1]2 is used to derive general expressions for the deformation characteristics in steady flow of an arbitrarily shaped hydrofoil, with a clamped trailing edge and free leading edge. From the analysis it is possible to determine the lift and drag coefficients, cavity length, and the foil steady deformation for any given specific foil shape, cavitation number, angle of attack, flow depth/chord ratio and rigidity. Sample numerical results are given, and the effects of flexibility and the proximity of the free surface are discussed. Chordwise flexibility tends to increase drag and decrease lift coefficients. This effect is more serious near the free surface. A slight increase of the thickness near the leading edge diminishes the flexibility effects.

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