Three-Dimensional Planing at High Froude Number

1971 ◽  
Vol 15 (03) ◽  
pp. 221-230 ◽  
Author(s):  
D. P. Wang ◽  
P. Rispin
Keyword(s):  
Aspect Ratio ◽  
Pressure Distribution ◽  
Froude Number ◽  
Order Term ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Steady Motion ◽  
Iteration Process ◽  
Leading Edge ◽  
Aspect Ratios

The steady motion of a planing surface of moderate aspect ratio at small angles of attack is considered. Linearized theory is used with a square-root type of pressure singularity representing the flow near the leading edge. An asymptotic solution for the pressure distribution on the planing surface at large Froude number (or small β, the inverse of the Froude number) is sought. The lowest-order term of the pressure distribution, obtained by setting β equal to zero, is found to be the same as the pressure distribution on the lower side of the corresponding thin wing. Higher-order terms in β are obtained by an iteration process. Explicit solutions are obtained to order β2 for rectangular planforms. Numerical results are calculated for rectangular flat plate planing surfaces of aspect ratios from 0.5 to 2.0. It is found that for large aspect ratios the lift coefficient is reduced by the gravity effect and for small aspect ratios it is increased, the dividing aspect ratio being about 1.5. The results compare reasonably well with experimental data.

Low-Aspect-Ratio Flat Ship Theory for Moderate Froude Numbers

1991 ◽  
Vol 35 (04) ◽  
pp. 325-330
Author(s):  
S. L. Cole
Keyword(s):  
Aspect Ratio ◽  
Froude Number ◽  
Potential Flow ◽  
Order Term ◽  
Leading Edge ◽  
Wave Resistance ◽  
Intermediate Region ◽  
Leading Order ◽  
Cross Sectional ◽  
Low Aspect Ratio

Low-aspect-ratio flat ship theory models ships whose dimensions satisfy draft << beam <<length. This paper systematically derives the inner and outer linearized problems for moderate Froude number potential flow past such a ship and their solutions. These solutions are matched through an intermediate region. It is found that the leading-order term for the wave resistance for moderate speed low-aspectratio flat ship theory is the same as found in slender ship theory for ships with equivalent cross-sectional areas. Flat ship theory, however, predicts singularities in the flow along the outside of the ship's leading edge which are not present in slender ship theory. A simple example demonstrating these spurious singularities is worked out.

scholarly journals Optimizing Effect of Wavy Leading Edge (WLE) in Rectangular Wing and Taper Wing

2021 ◽  
Vol 1 (2) ◽  
pp. 56-68
Author(s):  
Iis Rohmawati ◽  
Hiroshi Arai ◽  
Hidemi Mutsuda ◽  
Takuji Nakashima ◽  
Rizal Mahmud
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Wing Shape ◽  
Aspect Ratios ◽  
Impressive Result ◽  
Rectangular Form ◽  
Numerical Research ◽  
Wing Aspect Ratio

Experimental and numerical research have been performed to investigate the Wavy Leading Edge (WLE) effect on the rectangular wing. The WLE is inspired by humpback whale flipper morphology which is blunt and rounded in certain form pattern. This flipper shape plays an important role for its behaviour specially capturing their prey. This advantage could be applied to other systems such as fin stabilizers or wind turbines. Steady cases in various aspect ratios were conducted to find out the optimum effect of WLE with baseline NACA 0018 profile at Reynolds number 1.4 x 105. The chord length of the wing (c) was 125 mm. The WLE shape defined as wavelength (W) 8% of c and amplitude (d) is 5% of c. The aspect ratio (AR) variations were 1.6; 3.9; 5.1; 7.9 and 9.6.  A simple rectangular form of the wing was selected to analysis the WLE effect on the various ARs. The taper wing shape is applied to find out the WLE effect at the AR 7.9. three types of taper ratio (TR) are 0.1; 0.3 and 0.5. The results show that the WLE on the taper wing has better advantage to control the stall in steady case. Another impressive result was the WLE wing with AR 7.9 and TR 0.3 has the best lift coefficient and pressure distribution.Keywords: stall, wavy leading edge, steady case, rectangle wing, taper wing, aspect ratio. 

Two-dimensional planing at high Froude number

1958 ◽  
Vol 4 (5) ◽  
pp. 466-478 ◽  
Author(s):  
E. Cumberbatch
Keyword(s):  
Integral Equation ◽  
Pressure Distribution ◽  
Flat Plate ◽  
Froude Number ◽  
Water Surface ◽  
Flow Characteristics ◽  
Iteration Process ◽  
Leading Edge ◽  
Two Dimensional ◽  
High Froude Number

This paper examines the flow characteristics of a body of small slope planing at high Froude number over a water surface. An equation is obtained relating the slope of the planing surface to an integral containing the pressure distribution on the planing surface. The equation is expanded for large Froude number and a solution is obtained by an iteration process. At each stage of the iteration process the integral equation of ordinary thin aerofoil theory is solved. The pressure distribution on the planing surface is derived as a series in inverse powers of the Froude number F, as far as the F−4 term. Computations are performed for the planing of a flat plate, a parabolic surface, and a suitable linear combination of these shapes which results in a flow without a splash at the leading edge.

A Three-Dimensional Model for the Prediction of Shock Losses in Compressor Blade Rows

1983 ◽  
Author(s):  
Arthur J. Wennerstrom ◽  
Steven L. Puterbaugh
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Leading Edge ◽  
Compressor Blade ◽  
Turbine Engines ◽  
Test Case ◽  
Three Dimensional Model ◽  
Aspect Ratios ◽  
Flow Effects ◽  
Shock Loss

A design trend evident in newly evolving aircraft turbine engines is a reduction in the aspect ratio of blading employed in fans, compressors, and turbines. As aspect ratio is reduced, various three-dimensional flow effects become significant which at higher aspect ratios could safely be neglected. This paper presents a new model for predicting the shock loss through a transonic or supersonic compressor blade row operating at peak efficiency. It differs from the classical Miller-Lewis-Hartmann normal shock model by taking into account the spanwise obliquity of the shock surface due to leading-edge sweep, blade twist, and solidity variation. The model is evaluated in combination with two test cases. Each was a low-aspect-ratio transonic stage which had exceeded its efficiency goals. Use of the revised shock loss model contributed 2.11 points to the efficiency of the first test case and 1.08 points to the efficiency of the second.

A Three-Dimensional Model for the Prediction of Shock Losses in Compressor Blade Rows

1984 ◽  
Vol 106 (2) ◽  
pp. 295-299 ◽  
Author(s):  
A. J. Wennerstrom ◽  
S. L. Puterbaugh
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Leading Edge ◽  
Compressor Blade ◽  
Turbine Engines ◽  
Test Case ◽  
Three Dimensional Model ◽  
Aspect Ratios ◽  
Flow Effects ◽  
Shock Loss

A design trend evident in newly evolving aircraft turbine engines is a reduction in the aspect ratio of blading employed in fans, compressors, and turbines. As aspect ratio is reduced, various three-dimensional flow effects become significant which at higher aspect ratios could safely be neglected. This paper presents a new model for predicting the shock loss through a transonic or supersonic compressor blade row operating at peak efficiency. It differs from the classical Miller-Lewis-Hartmann normal shock model by taking into account the spanwise obliquity of the shock surface due to leading-edge sweep, blade twist, and solidity variation. The model is evaluated in combination with three test cases. Each was a low-aspect-ratio transonic stage which had exceeded its efficiency goals. Use of the revised shock loss model contributed 2.11 points to the efficiency of the first test case, 1.08 points to the efficiency of the second, and 1.38 points to the efficiency of the third.

scholarly journals Three-dimensional theory on supercavitating hydrofoils near a free surface

1975 ◽  
Vol 71 (2) ◽  
pp. 339-359 ◽  
Author(s):  
Okitsugu Furuya
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reference Level ◽  
Two Dimensional ◽  
Large Aspect Ratio ◽  
Dimensional Solution ◽  
Aspect Ratios ◽  
Lifting Line

Supercavitating hydrofoils of large aspect ratio operating near a free surface are investigated, assuming an inviscid and irrotational flow with the effects of gravity and surface tension neglected. The flow near the foil, treated as two-dimensional, is solved by a nonlinear free-streamline theory, then a three-dimensional ‘downwash’ correction is made using Prandtl's lifting-line theory. The strength of the lifting-line vortex is determined by information from the two-dimensional solution through a matching procedure, in which the inverse of aspect ratio is used as a small parameter for asymptotic expansions. The analysis incorporates a free-surface reference level to determine the submergence depth of the foil. The present method can be applied to any type of foil having an arbitrary planform or profile shape, including a rounded leading edge, a twist and even a small dihedral angle, within the assumption of large aspect ratio. Numerical computations made on rectangular flat-plate hydrofoils show excellent agreement of results with existing experimental data, even for large angles of attack and relatively low aspect ratios. The pressure distributions, shapes of the cavity and free surface are also calculated as a function of spanwise position.

A Contribution to Study on the Lift of Ventilated Supercavitating Vehicle With Low Froude Number

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Yu Kaiping ◽  
Zhou Jingjun ◽  
Min Jingxin ◽  
Zhang Guang
Keyword(s):  
Numerical Simulations ◽  
Froude Number ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Gravitational Effect ◽  
Gas Leakage ◽  
Supercavitating Vehicle ◽  
Numerical Predictions ◽  
Low Froude Number

A ventilated cavity was investigated using three-dimensional numerical simulation and cavitation water tunnel experiments under the condition of low Froude number. A two-fluid multiphase flow model was adopted in numerical predictions. The drag between the different phases and gravitational effect, as well as the compressibility of gas, was considered in the numerical simulations. By comparing the ventilated coefficient computational results of three different turbulence models with the Epshtein formula, the shear-stress-transport turbulence model was finally employed. The phenomenon of double-vortex tube gas-leakage was observed in both numerical simulations and experiments. Based on the validity of the numerical method, the change law of the lift coefficient on the afterbody was given by numerical predictions and accorded well with experimental results. The cause for the appearance of an abrupt increase in lift was difficult to get from experiments for the hard measurement, whereas the numerical simulations provided some supplements to analyze the reasons. The distribution of lift coefficient on the afterbody had important significance to the design of underwater vehicles.

scholarly journals On the lift-optimal aspect ratio of a revolving wing at low Reynolds number

2018 ◽  
Vol 15 (143) ◽  
pp. 20170933 ◽  
Author(s):  
T. Jardin ◽  
T. Colonius
Keyword(s):  
Aspect Ratio ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Rossby Number ◽  
Subsequent Work ◽  
High Lift ◽  
Low Aspect Ratio ◽  
Axis Of Rotation ◽  
Edge Vortex ◽  
Convergent Solution

Lentink & Dickinson (2009 J. Exp. Biol. 212 , 2705–2719. ( doi:10.1242/jeb.022269 )) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.

Three-Dimensional Thermocapillary Convection in Open Cylindrical Annuli

2000 ◽  
Author(s):  
Bok-Cheol Sim ◽  
Abdelfattah Zebib
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Critical Frequency ◽  
Thermocapillary Convection ◽  
Three Dimensional ◽  
Time Dependent ◽  
Infinite Layer ◽  
Aspect Ratios ◽  
Temperature Oscillations ◽  
Good Agreement

Abstract Three-dimensional, time-dependent thermocapillary convection in open cylindrical containers is investigated numerically. Results for aspect ratios (Ar) of 1, 2.5, 8, and 16 and a Prandtl number of 6.84 are obtained to compare the results of numerical simulations with ongoing experiments. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re). Transition to oscillatory states occurs at critical values of Re which depend on Ar. With Ar = 1.0 and 2.5, we observe, respectively, 5 and 9 azimuthal wavetrains travelling clockwise at the free surface near the critical Re. With Ar = 8.0 and 16.0, there are substantially more, but pulsating waves near the critical Re. In the case of Ar = 16.0, which approaches the conditions in an infinite layer, our results are in good agreement with linear theory. While the critical Reynolds number decreases with increasing aspect ratio in the case of azimuthal rotating waves, it increases with increasing aspect ratio in the case of azimuthal pulsating waves. The critical frequency of temperature oscillations is found to decrease linearly with increasing Ar. We have also computed supercritical time-dependent states and find that while the frequency increases with increasing Re near the critical region, the frequency of supercritical convection decreases with Re.

Separating and Reattaching Flow Structure in a Suddenly Expanding Rectangular Duct

1995 ◽  
Vol 117 (1) ◽  
pp. 17-23 ◽  
Author(s):  
G. Papadopoulos ◽  
M. V. O¨tu¨gen
Keyword(s):  
Aspect Ratio ◽  
Flow Structure ◽  
Three Dimensional ◽  
Side Wall ◽  
Stream Velocity ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Wall Effects ◽  
Velocity Measurements ◽  
Aspect Ratios

The incompressible turbulent flow over a backward-facing step in a rectangular duct was investigated experimentally. The side wall effects on the core flow were determined by varying the aspect ratio (defined as the step span-to-height ratio) from 1 to 28. The Reynolds number, based on the step height and the oncoming free-stream velocity, was 26,500. Detailed velocity measurements were made, including the turbulent stresses, in a region which extended past the flow reattachment zone. Wall static pressure was also measured on both the step and flat walls. In addition, surface visualizations were obtained on all four walls surrounding the separated flow to supplement near-wall velocity measurements. The results show that the aspect ratio has an influence on both the velocity and wall pressure even for relatively large aspect ratios. For example, in the redevelopment region downstream of reattachment, the recovery pressure decreases with smaller aspect ratios. The three-dimensional side wall effects tend to slow down the relaxation downstream of reattachment for smaller aspect ratios as evidenced by the evolution of the velocity field. For the two smallest aspect ratios investigated, higher centerplane streamwise and transverse velocities were obtained which indicate a three-dimensional mean flow structure along the full span of the duct.

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