Lateral motion of a slender body between two parallel walls

1969 ◽  
Vol 39 (1) ◽  
pp. 97-115 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Cross Flow ◽  
Approximate Solutions ◽  
The Body ◽  
Slender Body ◽  
Stream Velocity ◽  
Plane Normal ◽  
The Cross ◽  
Flow Plane

The method of matched asymptotic expansions is used to determine the lateral flow of an ideal fluid past a slender body, when the flow is constrained by a pair of closely spaced walls parallel to the long axis of the body. In the absence of walls, the flow field would be nearly two-dimensional in the cross-flow plane normal to the body axis, but the walls introduce an effective blockage in the cross-flow plane, which causes the flow field to become three-dimensional. Part of the flow is diverted around the body ends, and part flows past the body in the inner cross-flow plane with a reduced ‘inner stream velocity’. An integro-differential equation of identical form to Prandtl's lifting-line equation is derived for the determination of this unknown inner stream velocity in the cross-flow plane. Approximate solutions are applied to determine the added mass and moment of inertia for accelerated body motions and the lift force and moment acting on a wing of low aspect ratio. It is found that the walls generally increase these forces and moments, but that the effect is significant only when the clearance between the body and the walls is very small.

Some Remarks on the Behaviour of Surface Source Distributions near the Edge of a Body

1973 ◽  
Vol 24 (1) ◽  
pp. 25-33
Author(s):  
J W Craggs ◽  
K W Mangler ◽  
M Zamir
Keyword(s):  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Symmetric Case ◽  
The Body ◽  
Dimensional Problem ◽  
Surface Source ◽  
Asymmetric Case ◽  
Main Flow Direction ◽  
Flow Plane

SummaryWhen the incompressible potential flow past a three-dimensional body is represented by source distributions on the body surface, these source distributions have singularities near an edge or corner, for example á trailing edge of a wing or the (unfaired) intersection of a body and a wing. The nature of these singularities is discussed. When assuming slow variations of the geometry in the main flow direction we can consider a two-dimensional problem in the cross-flow plane. Here the tangential velocities and source distributions are proportional to certain powers of the distance from the corner. For example at a convex right-angled corner these powers are − ⅓ in the asymmetric case (the bisector is a potential line) and ⅓ in the symmetric case (the bisector is a streamline) for both sources and tangential velocities. At a concave right-angled corner the corresponding values for the source distributions are ⅓ (asymmetric case) and − ⅓ (symmetric case) whereas they are 1 and 3 respectively for the tangential velocities.

Three-dimensional laminar boundary layers in crosswise pressure gradients

1974 ◽  
Vol 66 (4) ◽  
pp. 641-655 ◽  
Author(s):  
J. H. Horlock ◽  
A. K. Lewkowicz ◽  
J. Wordsworth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Laminar Boundary Layers ◽  
The Cross

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.

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.

Streamwise evolution of longitudinal vortices in a turbulent boundary layer

2009 ◽  
Vol 623 ◽  
pp. 27-58 ◽  
Author(s):  
OLA LÖGDBERG ◽  
JENS H. M. FRANSSON ◽  
P. HENRIK ALFREDSSON
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Vortex Core ◽  
Cross Flow ◽  
General Point ◽  
Natural Setting ◽  
Viscous Effects ◽  
Array Configuration ◽  
The Cross ◽  
Flow Plane

In this experimental study both smoke visualization and three-component hot-wire measurements have been performed in order to characterize the streamwise evolution of longitudinal counter-rotating vortices in a turbulent boundary layer. The vortices were generated by means of vortex generators (VGs) in different configurations. Both single pairs and arrays in a natural setting as well as in yaw have been considered. Moreover three different vortex blade heights h, with the spacing d and the distance to the neighbouring vortex pair D for the array configuration, were studied keeping the same d/h and D/h ratios. It is shown that the vortex core paths scale with h in the streamwise direction and with D and h in the spanwise and wall-normal directions, respectively. A new peculiar ‘hooklike’ vortex core motion, seen in the cross-flow plane, has been identified in the far region, starting around 200h and 50h for the pair and the array configuration, respectively. This behaviour is explained in the paper. Furthermore the experimental data indicate that the vortex paths asymptote to a prescribed location in the cross-flow plane, which first was stated as a hypothesis and later verified. This observation goes against previously reported numerical results based on inviscid theory. An account for the important viscous effects is taken in a pseudo-viscous vortex model which is able to capture the streamwise core evolution throughout the measurement region down to 450h. Finally, the effect of yawing is reported, and it is shown that spanwise-averaged quantities such as the shape factor and the circulation are hardly perceptible. However, the evolution of the vortex cores are different both between the pair and the array configuration and in the natural setting versus the case with yaw. From a general point of view the present paper reports on fundamental results concerning the vortex evolution in a fully developed turbulent boundary layer.

The Calculation of Three-Dimensional Turbulent Boundary Layers: Part I: Flow over the Rear of an Infinite Swept Wing

1967 ◽  
Vol 18 (1) ◽  
pp. 55-84 ◽  
Author(s):  
N. A. Cumpsty ◽  
M. R. Head
Keyword(s):  
Essential Feature ◽  
Three Dimensional ◽  
Cross Flow ◽  
Stream Velocity ◽  
Pressure Gradients ◽  
Swept Wing ◽  
Form Parameter ◽  
Method Of Calculation ◽  
Flow Profiles ◽  
Momentum Integral

SummaryA method of calculation has been developed in which all terms in the momentum integral equations in the streamwise and cross-flow directions are taken into account so that no restriction to small cross-flows is imposed. The essential feature of the method is the use of an entrainment equation which enables the development of the streamwise form parameter to be calculated along with the streamwise and cross-flow momentum thicknesses. Mager’s quadratic expression is used to relate streamwise and cross-flow profiles. The method has been applied to the idealised case of an infinite swept wing with free-stream velocity over the forward part of the chord and a linear adverse velocity gradient over the rear. The position of separation, the directions of the surface streamlines and the development of streamwise and cross-flow profiles have been calculated for a series of angles of sweep and for adverse pressure gradients of varying severity.

A Family of Hodograph Models for the Cross Flow Velocity Component of Three-Dimensional Turbulent Boundary Layers

1972 ◽  
Vol 94 (2) ◽  
pp. 321-329 ◽  
Author(s):  
J. R. Shanebrook ◽  
D. E. Hatch
Keyword(s):  
Flow Velocity ◽  
Boundary Layers ◽  
Velocity Component ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Flow Profiles ◽  
Rectangular Channels ◽  
Cross Flow Velocity ◽  
The Cross

A family of hodograph models for the cross flow velocity component of three-dimensional, turbulent boundary layers is presented. The principal advantage of this family is its flexibility which allows a wide variety of possible shapes for the hodograph. An integral method based on this family is developed and applied to data obtained in curved, rectangular channels. For the cases treated, the method gives acceptable results for cross flow profiles with and without flow reversal. Suggestions for refining the method are given.

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.

An Approach to Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Author(s):  
A. D. Carmichael
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Basic Assumption ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Factor H ◽  
Simple Method ◽  
The Cross

A relatively simple method for predicting some of the characteristics of three-dimensional turbulent boundary layers is presented. The basic assumption of the method is that the cross-flow is small. An empirical correlation of a basic shape factor of the cross-flow boundary layer against the streamwise shape factor H is provided. This correlation, together with data for the streamwise boundary layer, is used to predict the cross flow. The solution is very sensitive to the accuracy of the streamwise boundary-layer data which is predicted by conventional two-dimensional methods.

Three-Dimensional Calculation of Wall Boundary Layer Flows in Turbomachines

1987 ◽  
Author(s):  
W. L. Lindsay ◽  
H. B. Carrick ◽  
J. H. Horlock
Keyword(s):  
Boundary Layer ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Cross Flow ◽  
Flow Profile ◽  
Boundary Layer Flows ◽  
Wall Boundary Layer ◽  
Boundary Layer Development ◽  
Flow Through ◽  
The Cross

An integral method of calculating the three-dimensional turbulent boundary layer development through the blade rows of turbomachines is described. It is based on the solution of simultaneous equations for (i) & (ii) the growth of streamwise and cross-flow momentum thicknesses; (iii) entrainment; (iv) the wall shear stress; (v) the position of maximum cross-flow. The velocity profile of the streamwise boundary layer is assumed to be that described by Coles. The cross-flow profile is assumed to be the simple form suggested by Johnston, but modified by the effect of bounding blade surfaces, which restrict the cross-flow. The momentum equations include expressions for “force-defect” terms which are also based on secondary flow analysis. Calculations of the flow through a set of guide vanes of low deflection show good agreement with experimental results; however, attempts to calculate flows of higher deflection are found to be less successful.

Sign in / Sign up

Export Citation Format

Share Document