scholarly journals Cavity flow past a slender pointed hydrofoil

1961 ◽  
Vol 11 (2) ◽  
pp. 187-208 ◽  
Author(s):  
E. Cumberbatch ◽  
T. Y. Wu
Keyword(s):  
Angle Of Attack ◽  
Cross Flow ◽  
The Body ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Slender Body Theory ◽  
Flow Past ◽  
Two Dimensional Flow ◽  
Cavity Boundary ◽  
The Cross

A slender-body theory for the flow past a slender, pointed hydrofoil held at a small angle of attack to the flow, with a cavity on the upper surface, has been worked out. The approximate solution valid near the body is seen to be the sum of two components. The first consists of a distribution of two-dimensional sources located along the centroid line of the cavity to represent the variation of the cross-sectional area of the cavity. The second component represents the cross-flow perpendicular to the centroid line. It is found that over the cavity boundary which envelops a constant pressure region, the magnitude of the cross-flow velocity is not constant, but varies to a moderate extent. With this variation neglected only in the neighbourhood of the hydrofoil, the cross-flow is solved by adopting the Riabouchinsky model for the two-dimensional flow. The lift is then calculated by intergrating the pressure along the chord; the dependence of the lift on cavitation number and angle of attack is shown for a specific case of the triangular plan form.

Paper 7. Unsteady Flow around a Slender Fish-Like Body

1972 ◽  
Vol 14 (7) ◽  
pp. 43-52 ◽  
Author(s):  
Th. Y. Wu ◽  
J. N. Newman
Keyword(s):  
Unsteady Flow ◽  
Theoretical Calculations ◽  
Cross Flow ◽  
Vortex Sheet ◽  
The Body ◽  
Dynamic Force ◽  
Cross Sectional ◽  
Vortex Sheets ◽  
Flat Fish ◽  
The Cross

This paper attempts to extend some recent theoretical calculations on the unsteady flow generated by body movements of a slender ‘flat’ fish by further including the effect of finite body thickness in the consideration for various configurations of side and caudal fins as major appendages. Based on the slender-body approximation, the cross-flow is determined for different longitudinal body sections which are characterized by a variety of cross-sectional shapes and flow conditions (such as having smooth or fin-edged body contours, with or without vortex sheets alongside the body section). The effect of body thickness is found to arise primarily from its interaction with the vortex sheet already existing in the cross-flow. New results for the transverse hydro-dynamic force acting on the body are obtained, and their physical significances are discussed.

Two-Dimensional Apparent Masses for Cross-Flow Sections of Wing-Store Configurations

1982 ◽  
Vol 49 (3) ◽  
pp. 471-475
Author(s):  
M.-K. Huang
Keyword(s):  
Approximate Method ◽  
Cross Flow ◽  
Slender Body ◽  
Two Dimensional ◽  
Aerodynamic Stability ◽  
Slender Body Theory ◽  
Rolling Moment ◽  
Stability Derivatives ◽  
The Cross ◽  
Body Theory

On the basis of the assumption that the external stores are small compared with the wing, an approximate method has been developed for estimation of two-dimensional apparent masses for the cross-flow sections of wing-store combinations. The results obtained may be applicable to the analysis of the effects of the stores on the aerodynamic stability derivatives in slender-body theory. The theory has also been applied to estimate the rolling moment due to sideslip for high-wing configurations. The presented results are in agreement with those of other investigations.

scholarly journals Extensions of d'Alembert's paradox for elongated bodies

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150106
Author(s):  
Philippe R. Spalart
Keyword(s):  
Cross Section ◽  
Unit Length ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Added Mass ◽  
The Body ◽  
Pitching Moment ◽  
Constant Cross Section ◽  
Slender Body Theory ◽  
The Cross

The steady incompressible irrotational flow past a three-dimensional body of any shape generates no forces. The historic paradox refers only to drag, but lift is also zero, which has been known but not emphasized. The new material concerns a body with a long constant cross section, such as a train. The final results for forces and moments are very simple. With zero angle of attack, we show that the force vectors on the front and rear parts of the body are each (asymptotically) equal to zero, if the pressure is referred to the freestream pressure. The lift and drag coefficients, based on frontal area, vanish proportionally to d / l and ( d / l ) 2 , respectively, where d / l is the diameter-to-length ratio. This applies to any shape of the cross section, and of the ends. With an angle of attack, the nose and tail forces are non-zero but depend only on the angle of attack and the cross section's added mass per unit length. The pitching moment is proportional to the total added mass and the sine of twice the angle of attack. The present results clarify slender-body theory results. The practical consequence is that, for a long body with constant cross section, the shape of the nose or the tail is irrelevant to its own ‘partial’ drag and lift, and to the pitching moment.

An approximate solution for two-dimensional transonic flow past thin airfoils

1965 ◽  
Vol 61 (2) ◽  
pp. 573-593 ◽  
Author(s):  
T. Evans
Keyword(s):  
Approximate Solution ◽  
Linear Equation ◽  
Transonic Flow ◽  
The Body ◽  
Perturbation Equation ◽  
Two Dimensional ◽  
Maximum Thickness ◽  
Pressure Distributions ◽  
Flow Past ◽  
Two Dimensional Flow

AbstractThe transonic, two-dimensional flow past a thin airfoil is treated by approximating the transonic small perturbation equation by a linear equation valid in the neighbourhood of the airfoil. The solution is derived by representing the body by a line of suitable sources. Pressure distributions are given for airfoils with maximum thickness both forward and aft, and agreement with experiment improves as the position of maximum thickness moves aft.

scholarly journals Petiole-Lamina Transition Zone: A Functionally Crucial but Often Overlooked Leaf Trait

Plants ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 774
Author(s):  
Max Langer ◽  
Thomas Speck ◽  
Olga Speck
Keyword(s):  
Transition Zone ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Body Plan ◽  
The Body ◽  
Vascular Bundles ◽  
Cross Sectional ◽  
Thin Sections ◽  
Transition Zones ◽  
The Cross

Although both the petiole and lamina of foliage leaves have been thoroughly studied, the transition zone between them has often been overlooked. We aimed to identify objectively measurable morphological and anatomical criteria for a generally valid definition of the petiole–lamina transition zone by comparing foliage leaves with various body plans (monocotyledons vs. dicotyledons) and spatial arrangements of petiole and lamina (two-dimensional vs. three-dimensional configurations). Cross-sectional geometry and tissue arrangement of petioles and transition zones were investigated via serial thin-sections and µCT. The changes in the cross-sectional geometries from the petiole to the transition zone and the course of the vascular bundles in the transition zone apparently depend on the spatial arrangement, while the arrangement of the vascular bundles in the petioles depends on the body plan. We found an exponential acropetal increase in the cross-sectional area and axial and polar second moments of area to be the defining characteristic of all transition zones studied, regardless of body plan or spatial arrangement. In conclusion, a variety of terms is used in the literature for describing the region between petiole and lamina. We prefer the term “petiole–lamina transition zone” to underline its three-dimensional nature and the integration of multiple gradients of geometry, shape, and size.

The flow past a rapidly rotating circular cylinder

1957 ◽  
Vol 242 (1228) ◽  
pp. 108-115 ◽  
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Present Theory ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Rotating Circular Cylinder ◽  
Flow Past ◽  
Separating Flow ◽  
Two Dimensional Flow ◽  
Uniform Stream

This paper considers the two-dimensional flow past a circular cylinder immersed in a uniform stream, when the cylinder rotates about its axis so fast that separation in suppressed. The solution of the flow in the boundary layer on the cylinder is obtained in the form of a power series in the ratio of the stream velocity to the cylinder's peripheral velocity, and expressions are deduced for the value of the circulation and the torque on the cylinder. The terms calculated explicitly are sufficient to give reliable numerical values over the whole range of rotational speeds for which the postulate of non-separating flow is justifiable. The previously accepted theory, due to Prandtl, predicted that the circulation should not exceed a certain limit, while the present theory indicates that the circulation increases indefinitely with increase of rotaional speed. Strong arguments against the older theory are put forward, but the experimental evidence available is inconclusive.

Steady small-disturbance transonic dense gas flow past two-dimensional compression/expansion ramps

2018 ◽  
Vol 848 ◽  
pp. 756-787 ◽  
Author(s):  
A. Kluwick ◽  
E. A. Cox
Keyword(s):  
Gas Dynamics ◽  
Gas Flow ◽  
External Forcing ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Dense Gas ◽  
Dimensional Flow ◽  
Flow Past ◽  
Two Dimensional Flow ◽  
Dimensional Parameters

The behaviour of steady transonic dense gas flow is essentially governed by two non-dimensional parameters characterising the magnitude and sign of the fundamental derivative of gas dynamics ($\unicode[STIX]{x1D6E4}$) and its derivative with respect to the density at constant entropy ($\unicode[STIX]{x1D6EC}$) in the small-disturbance limit. The resulting response to external forcing is surprisingly rich and studied in detail for the canonical problem of two-dimensional flow past compression/expansion ramps.

scholarly journals A study of two-dimensional flow past an oscillating cylinder

1999 ◽  
Vol 385 ◽  
pp. 255-286 ◽  
Author(s):  
H. M. BLACKBURN ◽  
R. D. HENDERSON
Keyword(s):  
Experimental Studies ◽  
Cross Flow ◽  
Relaxation Oscillator ◽  
Two Dimensional ◽  
Flow State ◽  
Long Time ◽  
Two Dimensional Flow ◽  
Vorticity Production ◽  
Oscillation Frequencies ◽  
Motion Amplitude

In this paper we describe a detailed study of the wake structures and flow dynamics associated with simulated two-dimensional flows past a circular cylinder that is either stationary or in simple harmonic cross-flow oscillation. Results are examined for Re=500 and a fixed motion amplitude of ymax/D=0.25. The study concentrates on a domain of oscillation frequencies near the natural shedding frequency of the fixed cylinder. In addition to the change in phase of vortex shedding with respect to cylinder motion observed in previous experimental studies, we note a central band of frequencies for which the wake exhibits long-time-scale relaxation oscillator behaviour. Time-periodic states with asymmetric wake structures and non-zero mean lift were also observed for oscillation frequencies near the lower edge of the relaxation oscillator band. In this regime we compute a number of bifurcations between different wake configurations and show that the flow state is not a unique function of the oscillation frequency. Results are interpreted using an analysis of vorticity generation and transport in the base region of the cylinder. We suggest that the dynamics of the change in phase of shedding arise from a competition between two different mechanisms of vorticity production.

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