On the Axisymmetric Vortex Flow Over a Flat Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 614-619 ◽  
Author(s):  
E. W. Schwiderski
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Numerical Study ◽  
Lower Boundary ◽  
Tangential Velocity ◽  
Slow Motion ◽  
Boundary Layer Separation ◽  
Local Boundary ◽  
Self Similar

The numerical study of the interaction of a potential vortex with a stationary surface recently published by Kidd and Farris [1] is extended through a transformation of the boundary-value problem to Volterra integral equations. The new calculations verified the results by Kidd and Farris and improved the bounds of the critical Reynolds number Nc, beyond which no self-similar vortex flows exist, to 5.5 < Nc < 5.6 The breakdown of the self-similar motions develops through an instability in the lower boundary layer, which is indicated by two inflection points in the tangential velocity profile. At the critical Reynolds number the lower inflection point reaches the surface and indicates the beginning of boundary-layer separation in the wake-type flow. If the Stokes linearization is applied, one arrives at a new Stokes paradox. However, this “paradox” can be resolved by correcting the free-stream pressure distortion of the Stokes approximation. The new slow-motion approximation is nonlinear and yields an integral which is also free of the Whitehead paradox. The properties of the new exact solution confirm the novel flow features previously detected in almost self-similar motions, which were constructed by adjustable local boundary-layer approximations.

Prospects of Studies in Region of Low-Sized Aircraft (Review)

2014 ◽  
Vol 9 (2) ◽  
pp. 95-115
Author(s):  
Ilya Zverkov ◽  
Alexey Kryukov ◽  
Genrich Grek
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Separation ◽  
Aerodynamic Characteristics ◽  
Point Of View ◽  
Wavy Surface ◽  
Local Boundary ◽  
Effective Operation ◽  
Forward Edge ◽  
The Given

In the given review the problem of improvement of aerodynamic characteristics of the low-sized aircraft is considered with point of view of the fundamental phenomena of the mechanics of liquid, gas and plasma. It is a problem of the local boundary layer separation (separated bubbles) and flow separation from a wing forward edge at which all global structure of a flow varies. The review of the works establishing this interrelation and methods of the influence, eliminating harmful consequences of the separations is submitted. The method of separation elimination with help of a wavy surface, as the most perspective and easily sold on practice is in more details allocated in this review. The second part of the review is devoted to the analysis of a flow of elements of designs of various low-sized aircraft with indication of probably problem places where the flow is realized at Reynolds number less than 106 and where can arise the local separations. Application of a wavy surface in such places can improve aerodynamic characteristics of the flying device promoting its more effective operation

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

scholarly journals On the scaling of shear-driven entrainment: a DNS study

2013 ◽  
Vol 732 ◽  
pp. 150-165 ◽  
Author(s):  
Harm J. J. Jonker ◽  
Maarten van Reeuwijk ◽  
Peter P. Sullivan ◽  
Edward G. Patton
Keyword(s):  
Reynolds Number ◽  
Lower Boundary ◽  
Square Root ◽  
Simulation Design ◽  
Self Similarity ◽  
Original Experiment ◽  
Turbulent Layer ◽  
Entrainment Velocity ◽  
Constant Shear Stress ◽  
Self Similar

AbstractThe deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol. 37, 1969, pp. 643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as$R{i}^{- 1/ 2} $. In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

scholarly journals Aerodynamics of airfoil moving along a circular trajectory

2021 ◽  
Vol 2119 (1) ◽  
pp. 012154
Author(s):  
D M Bozheeva ◽  
D A Dekterev ◽  
Ar A Dekterev ◽  
A A Dekterev ◽  
D V Platonov
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Computational Study ◽  
Stationary Flow ◽  
Boundary Layer Separation ◽  
Velocity Fields ◽  
Incoming Flow ◽  
Calculation Methods ◽  
Circular Trajectory ◽  
Qualitative Comparison

Abstract An experimental and computational study of the NACA0016 airfoil has been carried out for two cases: a stationary airfoil in an incoming flow on an aerodynamic stand and an airfoil moving along a circular trajectory in a stationary flow in a hydrodynamic stand. The Reynolds number for both cases was 60000. A qualitative comparison of the velocity fields for the cases with smooth airflow and boundary layer separation was carried out. It is shown that the used calculation methods describe the task under study with sufficient quality.

Numerical Study of Wall Influence on Boundary-Layer Transition for Two-Dimensional NACA 16-012 and 4412 Hydrofoil Sections

1990 ◽  
Vol 34 (01) ◽  
pp. 38-47
Author(s):  
R. Latorre ◽  
R. Baubeau
Keyword(s):  
Boundary Layer ◽  
Test Section ◽  
Numerical Study ◽  
Suction Side ◽  
Boundary Layer Separation ◽  
Boundary Layer Transition ◽  
Layer Transition ◽  
Turbulent Separation ◽  
Side Pressure ◽  
Effective Angle

One of the difficulties in hydrofoil model tests is the relatively low Reynolds number of the test piece and the presence of the test section walls. This paper presents the results of systematic calculations of the potential flow field of NA 4412 and NACA 16-012 hydrofoil in a test section with wall-to-chord ratios h/c -1.0. The corresponding boundary-layer calculations using the CERT calculation scheme are presented to show the influence of the nearby walls on shifting the location of the boundary-layer laminar-turbulent separation as well as turbulent separation. By introducing an effective angle of attack, it is possible to obtain close agreement in the calculated and measured suction side pressure distortion as well as the locations of the boundary-layer separation and transition.

Turbine blade boundary layer separation suppression via synthetic jet: An experimental and numerical study

2012 ◽  
Vol 21 (5) ◽  
pp. 404-412 ◽  
Author(s):  
C. Bernardini ◽  
M. Carnevale ◽  
M. Manna ◽  
F. Martelli ◽  
D. Simoni ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Turbine Blade ◽  
Numerical Study ◽  
Boundary Layer Separation ◽  
Synthetic Jet ◽  
Layer Separation

On the interaction between shock waves and boundary layers

1951 ◽  
Vol 47 (3) ◽  
pp. 545-553 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Reynolds Number ◽  
Shock Waves ◽  
Boundary Layers ◽  
Weak Shock ◽  
Boundary Layer Separation ◽  
Weak Shock Wave ◽  
Layer Separation ◽  
Boundary Layer Equations

AbstractThe effect on the boundary-layer equations of a weak shock wave of strength ∈ has been investigated, and it is shown that ifRis the Reynolds number of the boundary layer, separation occurs when ∈ =o(R−i). The boundary-layer assumptions are then investigated and shown to be consistent. It is inferred that separation will occur if a shock wave meets a boundary and the above condition is satisfied.

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