Flow Interaction Near the Tail of a Body of Revolution—Part 1: Flow Exterior to Boundary Layer and Wake

1976 ◽  
Vol 98 (3) ◽  
pp. 531-537 ◽  
Author(s):  
A. Nakayama ◽  
V. C. Patel ◽  
L. Landweber
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Potential Flow ◽  
Present Method ◽  
Iterative Procedure ◽  
The Body ◽  
Body Of Revolution ◽  
Near Wake ◽  
Momentum Integral ◽  
Good Agreement

An iterative procedure for the calculation of the thick attached turbulent boundary layer near the tail of a body of revolution is presented. The procedure consists of the potential-flow calculation by a method of integral equation of the first kind and the calculation of the development of the boundary layer and the wake using an integral method with the condition that the velocity remains continuous across the edge of the boundary layer and the wake. The additional terms that appear in the momentum integral equation for the thick boundary layer and the near wake are taken into account and the pressure difference between the body surface and the edge of the boundary layer and the wake can be determined. The results obtained by the present method are in good agreement with the experimental data. Part 1 of this paper deals with the potential flow, while Part 2 [1] describes the boundary layer and wake calculations, and the overall iterative procedure and results.

Flow Interaction Near the Tail of a Body of Revolution—Part 2: Iterative Solution for Flow Within and Exterior to Boundary Layer and Wake

1976 ◽  
Vol 98 (3) ◽  
pp. 538-546 ◽  
Author(s):  
A. Nakayama ◽  
V. C. Patel ◽  
L. Landweber
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Potential Flow ◽  
Reasonable Agreement ◽  
Complete Solution ◽  
Iterative Solution ◽  
The Body ◽  
External Potential ◽  
Iterative Technique ◽  
Body Of Revolution

This part deals with the calculation of the flow within the attached boundary layer and the wake of a body of revolution and its interaction with the external potential flow which was treated in Part 1. The iterative technique described in Part 1 is used to obtain a complete solution to the flow in the neighborhood of the tail of the body. The results of the calculations are compared with two sets of experimental data and reasonable agreement is demonstrated.

Survey on the Indirect Methods of Potential Flow Used for the Optimization of Airships Profile

2014 ◽  
Vol 554 ◽  
pp. 717-723
Author(s):  
Reza Abbasabadi Hassanzadeh ◽  
Shahab Shariatmadari ◽  
Ali Chegeni ◽  
Seyed Alireza Ghazanfari ◽  
Mahdi Nakisa
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flow Field ◽  
Drag Coefficient ◽  
Body Surface ◽  
Potential Flow ◽  
The Body ◽  
Indirect Methods ◽  
Singularity Method ◽  
Singularity Distribution

The present study aims to investigate the optimized profile of the body through minimizing the Drag coefficient in certain Reynolds regime. For this purpose, effective aerodynamic computations are required to find the Drag coefficient. Then, the computations should be coupled thorough an optimization process to obtain the optimized profile. The aerodynamic computations include calculating the surrounding potential flow field of an object, calculating the laminar and turbulent boundary layer close to the object, and calculating the Drag coefficient of the object’s body surface. To optimize the profile, indirect methods are used to calculate the potential flow since the object profile is initially amorphous. In addition to the indirect methods, the present study has also used axial singularity method which is more precise and efficient compared to other methods. In this method, the body profile is not optimized directly. Instead, a sink-and-source singularity distribution is used on the axis to model the body profile and calculate the relevant viscose flow field.

Potential and Viscous Parts of the Thrust Deduction and Wake Fraction for an Ellipsoid of Revolution

1960 ◽  
Vol 4 (03) ◽  
pp. 1-16
Author(s):  
Stavros Tsakonas ◽  
Winnifred R. Jacobs
Keyword(s):  
Boundary Layer ◽  
Potential Flow ◽  
Functional Dependence ◽  
Longitudinal Axis ◽  
Layer Growth ◽  
The Body ◽  
Displacement Thickness ◽  
Layer Effect ◽  
Ellipsoid Of Revolution ◽  
Equivalent Sources

Expressions are developed for wake fraction and thrust deduction due to the potential flow and to the boundary-layer effects for a fully-submerged prolate ellipsoid of revolution. The functional dependence of wake fraction and thrust deduction on axial-propeller clearance, body slenderness, after body geometry, and Reynolds number (scale effect) are exhibited for both potential and viscous-flow cases. Closed-form expressions are derived for the potential-flow case by representing the body by a line source-sink distribution and the propeller action by a sink disk. The boundary-layer effect is determined by Lighthill's method of equivalent sources distributed on the surface having strength proportional to the displacement thickness and its derivative. The wake is replaced by a cylinder of diameter equal to twice the displacement thickness at the stern. Although in practice the propeller is usually fully submerged in the wake of the hull, in this case the substitute cylinder has been shown by computation to be no wider than the hub diameter and thus the propeller is operating in a potential field. This consideration is fundamental to the construction of a possible mathematical model having the surface sources mentioned and an equivalent sink on the longitudinal axis whose position is determined on the basis of the velocity distribution in the wake. Computational work is carried out for a modification of the airship Akron. Four different methods, with various degrees of accuracy, are used for the evaluation of the boundary-layer growth in order to ascertain the degree of sensitivity of the thrust deduction and wake fraction to the boundary-layer development.

A Note on the Resistance of Bodies of Revolution and Ship Forms

1974 ◽  
Vol 18 (03) ◽  
pp. 153-168
Author(s):  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Reasonable Agreement ◽  
The Body ◽  
Experimental Results ◽  
Body Of Revolution ◽  
Bodies Of Revolution ◽  
Boundary Layer Development ◽  
Layer Development

A simple so-called 'equivalent' body of revolution is proposed for reflex ship forms in an attempt to simplify calculation of the boundary layer over a ship's hull when there is no wavemaking. How­ever, exhaustive testing of one body of revolution did not produce a favorable comparison with re­sults for the corresponding reflex model. Gadd's recently proposed theory was used to calculate the boundary-layer development over the body of revolution. Reasonable agreement was obtained between the calculated and experimental results.

A New Solution of the Turbulent Near-Wake Recompression Problem

1972 ◽  
Vol 23 (2) ◽  
pp. 121-130
Author(s):  
S J Shamroth ◽  
H McDonald
Keyword(s):  
Integral Equation ◽  
Transverse Momentum ◽  
Uniqueness Condition ◽  
Two Dimensional ◽  
Interaction Theory ◽  
Initial Value ◽  
Near Wake ◽  
Singular Behaviour ◽  
Momentum Integral ◽  
Suitable Approximation

SummaryA method is presented for predicting the behaviour of a two-dimensional supersonic turbulent near-wake during the recompression process. In contrast to most previous extensions of Crocco-Lees strong interaction theory, the proposed analysis includes a transverse momentum integral equation. In addition, a modified strip method for conservation of streamwise momentum replaces the usual integral equations. Although a straightforward treatment of the equations results in the appearance of a singularity analogous to the well-known Crocco-Lees critical point, it is shown that solutions can be obtained which do not exhibit a singular behaviour, either by posing the problem as a boundary-value problem rather than an initial-value problem or by making a suitable approximation which suppresses the quasi-elliptic behaviour of the equations. Both procedures lead to an unambiguously defined uniqueness condition for the near-wake recompression solution.

Transition Behavior of a Blasius-Type Boundary Layer Subjected to Uniform Blowing or Suction

1978 ◽  
Vol 45 (2) ◽  
pp. 450-453
Author(s):  
M. Sokolov ◽  
G. Karpati
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Boundary Layer Thickness ◽  
Leading Edge ◽  
Transient Behavior ◽  
The Other ◽  
Intermediate States ◽  
Type Boundary ◽  
Time Required ◽  
Momentum Integral

The momentum integral equation is used to study the transient behavior of a Blasius-type boundary layer which is suddenly subjected to uniform blowing or suction. The time required for the boundary layer to adjust itself from one steady state (Blasius) to the other (constant blowing or suction) was found to be proportional to the distance from the leading edge. Boundary-layer thickness of intermediate states and skin friction coefficients are also reported.

On Integral Methods for Predicting Shear Layer Behavior

1969 ◽  
Vol 36 (4) ◽  
pp. 673-681 ◽  
Author(s):  
S. J. Shamroth
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Integral Equations ◽  
Boundary Layers ◽  
Specific Problem ◽  
Shear Layers ◽  
Near Wake ◽  
Integral Methods ◽  
Layer Behavior ◽  
Momentum Integral

The origin and consequences of a nonphysical constraint which may arise when boundary-layer momentum integral equations are used to predict the behavior of shear layers are examined. It is pointed out that should the constraint occur within the domain of integration of the momentum integral equations, the effect may either be catastrophic or significantly constrain the solution. Several methods of solution having the usual advantages associated with boundary-layer momentum integral equations, but free from this constraint, are proposed for the specific problem of the plane turbulent near wake. One method developed to avoid this constraint in the case of a plane turbulent near wake appears to be perfectly general, and therefore, it may be possible to apply this method to both boundary layers and wakes.

A hybrid integral equation finite volume scheme for transonic potential flow about complex configurations

1994 ◽  
Vol 98 (972) ◽  
pp. 35-48
Author(s):  
A. K. Bhattacharya ◽  
N. L. Arora
Keyword(s):  
Integral Equation ◽  
Finite Volume ◽  
Potential Flow ◽  
Complex Geometry ◽  
The Body ◽  
Dirichlet Boundary Conditions ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Hybrid Integral ◽  
Integral Equation Approach

AbstractA hybrid integral equation finite volume scheme has been developed for the calculation of transonic potential flow about complex configurations. A new technique has been used for evaluating the potential values in the field cells intersecting the body surface panels. These potential values then serve as Dirichlet boundary conditions for computing the potentials in the field by a finite volume Successive Line Over Relaxation (SLOR) scheme. In this approach there is no need to evaluate the potentials anywhere in the field by direct application of Green's third identity, thus significantly reducing computer processing time and storage requirement, while improving accuracy of surface pressure prediction and shock capture, as results indicate. The capability of tackling additional complex geometry with ease, the primary advantage of the integral equation approach, is demonstrated by using the same field grid for wing-alone and wing-body combination cases, while maintaining the solution accuracy.

Laminar-To-Turbulent Transition on a Body of Revolution With an Extended Favorable Pressure Gradient Forebody

1984 ◽  
Vol 106 (2) ◽  
pp. 202-210 ◽  
Author(s):  
R. J. Hansen ◽  
J. G. Hoyt
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
The Body ◽  
Boundary Layer Transition ◽  
Single Element ◽  
Body Of Revolution ◽  
Laminar To Turbulent Transition ◽  
Turbulent Transition ◽  
Roughness Elements ◽  
Favorable Pressure Gradient

An experimental study of the laminar-to-turbulent transition and resulting hydrodynamic forces on a body of revolution with a long, favorable pressure gradient forebody (i.e., where pressure is dropping and the flow accelerating) is reported. Over a substantial range of body velocity and angle of attack the favorable pressure gradient is shown to postpone transition to the point of laminar separation, and this extended laminar region results in a much lower hydrodynamic drag than is characteristic of an all-turbulent body. The intermittency of the boundary layer and the propagation characteristics of turbulent spots in the extended favorable pressure gradient region are quantified by hot film probes mounted flush with the body surface. The sensitivity of the boundary layer transition to three-dimensional surface roughness elements located in tandem (along a streamline) is also quantified. A number of such elements in tandem causes transition at a lower Reynolds number than would a single element of the same size, this effect becoming more pronounced with increasing number of roughness elements and decreasing space between them.

Attached cavitation and the boundary layer: experimental investigation and numerical treatment

1985 ◽  
Vol 154 ◽  
pp. 63-90 ◽  
Author(s):  
J. P. Franc ◽  
J. M. Michel
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
The Body ◽  
Numerical Treatment ◽  
Laminar Separation ◽  
Complete Calculation ◽  
Detachment Criterion ◽  
Continuous Curvature ◽  
The One ◽  
Good Agreement

Attached cavitation on a wall with continuous curvature is investigated on the basis of experiments carried out on various bodies (circular and elliptic cylinders, NACA 16 012 foil). Visualization of the boundary layer by dye injection at the leading edge shows that a strong interaction exists between attached cavitation and the boundary layer. In particular, it is shown that the cavity does not detach from the body at the minimum pressure point, but behind a laminar separation, even in largely developed cavitating flow. A detachment criterion which takes into account this link between attached cavitation and boundary layer is proposed. It consists of connecting a cavitating potential-flow calculation and a boundary-layer calculation. Among all the theoretically possible detachment points, the actual detachment point is chosen to be the one for which the complete calculation predicts a laminar separation just upstream. This criterion, applied to the NACA foil, leads to a prediction which is in good agreement with experimental results.

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