scholarly journals Flow around a rotating, semi-infinite cylinder in an axial stream

2016 ◽  
Vol 472 (2190) ◽  
pp. 20150850 ◽  
Author(s):  
S. Derebail Muralidhar ◽  
B. Pier ◽  
J. F. Scott ◽  
R. Govindarajan
Keyword(s):  
Boundary Layer ◽  
Rotating Cylinder ◽  
Infinite Cylinder ◽  
Wall Jet ◽  
Large Rotation ◽  
Reynolds Number Flow ◽  
Rotation Rates ◽  
Classical Boundary ◽  
Number Flow ◽  
High Reynolds

This paper concerns steady, high-Reynolds-number flow around a semi-infinite, rotating cylinder placed in an axial stream and uses boundary-layer type of equations which apply even when the boundary-layer thickness is comparable to the cylinder radius, as indeed it is at large enough downstream distances. At large rotation rates, it is found that a wall jet appears over a certain range of downstream locations. This jet strengthens with increasing rotation, but first strengthens then weakens as downstream distance increases, eventually disappearing, so the flow recovers a profile qualitatively similar to a classical boundary layer. The asymptotic solution at large streamwise distances is obtained as an expansion in inverse powers of the logarithm of the distance. It is found that the asymptotic radial and axial velocity components are the same as for a non-rotating cylinder, to all orders in this expansion.

scholarly journals Triple-deck analysis of transonic high Reynolds number flow through slender channels

2014 ◽  
Vol 372 (2020) ◽  
pp. 20130346 ◽  
Author(s):  
A. Kluwick ◽  
M. Kornfeld
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Channel Height ◽  
Micro Electro Mechanical Systems ◽  
Reynolds Number Flow ◽  
Flow Phenomena ◽  
Classical Boundary ◽  
Number Flow ◽  
High Reynolds

In this work, laminar transonic weakly three-dimensional flows at high Reynolds numbers in slender channels, as found in microsupersonic nozzles and turbomachines of micro-electro-mechanical systems, are considered. The channel height is taken so small that the viscous wall layers forming at the channel walls start to interact strongly rather than weakly with the inviscid core flow and, therefore, the classical boundary layer approach fails. The resulting viscous–inviscid interaction problem is formulated using matched asymptotic expansions and found to be governed by a triple-deck structure. As a consequence, the properties of the predominantly inviscid core region and the viscous wall layers have to be calculated simultaneously in the interaction region. Weakly three-dimensional effects caused by surface roughness, upstream propagating flow perturbations, boundary layer separation as well as bifurcating solutions are discussed. Representative results for subsonic as well as supersonic conditions are presented, and the importance of these flow phenomena in technical applications as, for example, a means to reduce shock losses through the use of deformed geometry is addressed.

The interacting boundary-layer flow due to a vortex approaching a cylinder

1997 ◽  
Vol 346 ◽  
pp. 319-343 ◽  
Author(s):  
Z. XIAO ◽  
O. R. BURGGRAF ◽  
A. T. CONLISK
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Two Dimensions ◽  
Unsteady Boundary Layer ◽  
Reynolds Number Flow ◽  
Boundary Layer Equations ◽  
Number Flow ◽  
Layer Flow ◽  
High Reynolds

In this paper the solution to the three-dimensional and unsteady interacting boundary-layer equations for a vortex approaching a cylinder is calculated. The flow is three-dimensional and unsteady. The purpose of this paper is to enhance the understanding of the structure in three-dimensional unsteady boundary-layer separation commonly observed in a high-Reynolds-number flow. The short length scales associated with the boundary-layer eruption process are resolved through an efficient and effective moving adaptive grid procedure. The results of this work suggest that like its two-dimensional counterpart, the three-dimensional unsteady interacting boundary layer also terminates in a singularity at a finite time. Furthermore, the numerical calculations confirm the theoretical analysis of the singular structure in two dimensions for the interacting boundary layer due to Smith (1988).

scholarly journals Discrete-vortex analysis of high Reynolds number flow past a rotating cylinder

AIP Advances ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 055104
Author(s):  
Wei Chen ◽  
Chang-Kyu Rheem ◽  
Yuanzhou Zheng ◽  
Atilla Incecik ◽  
Yongshui Lin ◽  
...  
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Rotating Cylinder ◽  
Discrete Vortex ◽  
Reynolds Number Flow ◽  
Flow Past ◽  
Number Flow ◽  
High Reynolds

Stability of high-Reynolds-number flow in a collapsible channel

2013 ◽  
Vol 714 ◽  
pp. 536-561 ◽  
Author(s):  
D. Pihler-Puzović ◽  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Small Amplitude ◽  
High Reynolds Number ◽  
Long Wavelength ◽  
Reynolds Number Flow ◽  
Boundary Layer Equations ◽  
Number Flow ◽  
High Reynolds ◽  
Viscous Boundary

AbstractWe study high-Reynolds-number flow in a two-dimensional collapsible channel in the asymptotic limit of wall deformations confined to the viscous boundary layer. The system is modelled using interactive boundary-layer equations for a Newtonian incompressible fluid coupled to the freely moving elastic wall under constant tension and external pressure. The deformation of the membrane is assumed to have small amplitude and long wavelength, whereas the flow comprises the inviscid core and the viscous boundary layers on both walls coupled to each other and to the membrane deformation. Firstly, by linking the interactive boundary-layer model to the small-amplitude, long-wavelength inviscid analysis, we conclude that the model is valid only when the pressure perturbations are fixed downstream from the wall indentation, contrary to the common assumption of classical boundary-layer theory. Next we explore possible steady states of the system, showing that a unique steady solution exists when the pressure is fixed precisely at the downstream end of the membrane, but there are multiple states possible if the pressure is specified further downstream. We examine the stability of these states by solving the generalized eigenvalue problem for perturbations to the nonlinear steady solutions and also by performing time integration of the full boundary-layer equations. Surprisingly, we find that no self-excited oscillations develop in the collapsible channel systems with finite-amplitude deformations. Instead, for each point in the parameter space, with the exception of points subject to numerical instabilities associated with the boundary-layer equations, exactly one of the steady states is predicted to be stable. We discuss these findings in relation to the results reported previously in the literature.

High Reynolds number flow past a flat 'plate with strong blowing

1972 ◽  
Vol 51 (2) ◽  
pp. 337-356 ◽  
Author(s):  
J. B. Klemp ◽  
A. Acrivos
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Flow Past ◽  
Number Flow ◽  
Flow Domain ◽  
High Reynolds ◽  
Matching Techniques

For the uniform flow past a semi-infinite flat plate subject to a blowing velocity profile equal to C(Uv/x),½ the conventional boundary-layer approximations break down as C approaches 0middot;6192. Here, we consider the structure of the flow for large Reynolds numbers R when C exceeds this critical value. It is shown that, for C > 0·6192, a region containing injected fluid O(R-1/3)) in thickness forms directly above the plate. To a first approximation the flow in this region is inviscid and the pressure a function of x only. This blowing region is separated from the free stream by a free shear boundary layer of thickness O(R-½). Thus the flow domain consists of three distinct regions which interact to yield a similarity solution valid for large values of Rx. This solution is then extended to higher order by expanding the stream function in each region in powers of (Rx)-1/3 and evaluating the first four terms in the resulting series using standard matching techniques. Finally, more general blowing profiles which also lead to boundary-layer ‘blow off’ are considered and an expression, valid far downstream of boundary-layer detachment, is derived for the position of the streamline separating the injected fluid from that of the free stream. For the case of uniform blowing the blowing region takes on the shape of a wedge, indicating that no solution can exist for the corresponding external flow if the plate is truly semi-infinite.

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