On the Lagrangian description of unsteady boundary-layer separation. Part 1. General theory

Dommelen, L. L. van; Cowley, Stephen J.

doi:10.1017/s0022112090001410

Cited by 75 publications

(50 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Peridier et al [28,29] examined the interaction of a vortex with a boundary layer. Some additional research has also focused on some geometrically simpler configurations such as a circular cylinder set into motion impulsively [47,40]. Improved understanding of the temporal and spatial scales associated with the dynamic stall process have been obtained from these studies.…”

Section: Literature Surveymentioning

confidence: 99%

Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil

Choudhuri

Knight

1996

J. Fluid Mech.

View full text Add to dashboard Cite

Public reporting burden for this collection of information is estimated to average 1 hour per respoinse. including the time for reviewing instructions. searching existing data sources. gathering and maintaining the data needed, and comoleting anrd ryaevwing the collection of information. Send comments re< arding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden. SUPPLEMENTARY NOTESThe view, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy,--or decision, -unless so designated by other documentation. 12a. DISTRIBUTION /AVAILABILITY STATEMENT 12b. DISTRIBUTION CODEApproved for public release; distribution unlimited. ABSTRACT (M-xiMum200words)The effects of compressibility, pitch rate and Reynolds number on the initial stages of 2-D unsteady separation of laminar subsonic flow over a pitching NACA-0012 airfoil have been studied numerically. Computations have been performed using two separate algorithms (structured grid algorithm of Beam and Warming, and unstructured grid algorithm employing fluxdifference splitting method of Roe) for the compressible laminar NavierStokes equations. The simulations show the appearance of a primary recirculating region near the leading edge, followed by a secondary and tertiary recirculating regions. The primary and secondary recirculating regions interact with each other to give rise to the unsteady separation of the boundary layer. Increasing the Mach number from 0.2 to 0,5 causes a delay in the formation of the primary recirculating region. Increasing the pitch rate also delays the formation. Increasing the Reynolds number hastens the appearance of the primary recirculating region and leads to the appearance of a shock on the top surface alon g with the formation of multiple recirculating regions near the leading edge. A linear stability anal ,sis has shown that the appearance of the primary recirculating region is related

show abstract

Section: Literature Surveymentioning

confidence: 99%

Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil

Choudhuri

Knight

1996

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…The advantages of using Lagrangian coordinates in the study of unsteady boundary layers are discussed in a number of works, for example Refs. 5,7,[18][19][20][21] Previous works by others, including Cebeci, 22 were unable to proceed as close to the singularity in time as van Dommelen and Shen because their numerical methods, which were based on an Eulerian coordinate system, were less able to resolve the solution in its vicinity. Cowley 15 found an accurate small time asymptotic solution and did some analytical work based on the consideration of poles and zeroes in the complex plane to support the van Dommelen and Shen 5 prediction that a singularity occurs at time tϭ3.…”

Section: Introductionmentioning

confidence: 99%

On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder

1997

View full text Add to dashboard Cite

The unsteady flow of a homogeneous viscous fluid past a straight circular cylinder (radius l*) confined between two infinite parallel plates (a distance d* apart) relative to a rapidly rotating frame is considered. The cylinder is impulsively started from rest to a uniform velocity. The unsteady form of the boundary-layer equations for a rotating fluid is used to examine the flow Rossby number Ro∼O(E1/2), where E≪1 is the Ekman number. A range of values of the non-dimensional parameter N=lE1/2/Ro (where l=l*/d*) is considered. For 0⩽N<1, the flow pattern resembles that of the non-rotating case (N=0). Initially, the wall shear around the cylinder is positive everywhere. After a time, flow reversal begins at the rear stagnation point and then the position of zero wall shear moves upstream, towards the front stagnation point. The boundary-layer thickness in the region of reversed flow grows with time until a singularity/eruption at a point in the flow occurs. The boundary-layer equations are written in terms of Lagrangian coordinates in order to numerically investigate the finite-time singularity for 0⩽N<1. The flow close to the rear stagnation point is also examined in detail for a range of values of N and results are compared with the large-time asymptotic forms for the growth of the displacement thickness. The analysis suggests the displacement thickness in this region grows exponentially with time, for certain ranges of N. For 0<N<1, the displacement thickness grows exponentially with time in a manner similar to the non-rotating case. For N>1, the wall shear remains positive for all time. However, for 1⩽N<2, the displacement thickness of the boundary layer close to the rear stagnation point again grows exponentially with time. For 2<N<3 the flow close to the rear stagnation point also grows exponentially with time, although the form of solution differs from that for 0⩽N<2. For N>3, the solution tends to a truly steady limit, consistent with previous studies on the steady problem.

show abstract

“…In three dimensions, however, the work is much more limited. It includes the Lagrangian description of unsteady boundary-layer separation in three dimensions by Van Dommelen & Cowley [35] and numerical calculation in an Eulerian framework performed by Wu & Shen [36] and Affes et al [13] in the context of the interaction of a tip-vortex with a cylinder simulating a helicopter airframe. They all found that a singularity emerges and displays essentially the same nature as in two dimensions.…”

Section: (A) Classical Non-interactive Boundary Layersmentioning

confidence: 99%

Unsteady separation in vortex-induced boundary layers

Cassel

Conlisk

2014

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

This paper provides a brief review of the analytical and numerical developments related to unsteady boundary-layer separation, in particular as it relates to vortex-induced flows, leading up to our present understanding of this important feature in high-Reynolds-number, surface-bounded flows in the presence of an adverse pressure gradient. In large part, vortex-induced separation has been the catalyst for pulling together the theory, numerics and applications of unsteady separation. Particular attention is given to the role that Prof. Frank T. Smith, FRS, has played in these developments over the course of the past 35 years. The following points will be emphasized: (i) unsteady separation plays a pivotal role in a wide variety of high-Reynolds-number flows, (ii) asymptotic methods have been instrumental in elucidating the physics of both steady and unsteady separation, (iii) Frank T. Smith has served as a catalyst in the application of asymptotic methods to high-Reynolds-number flows, and (iv) there is still much work to do in articulating a complete theoretical understanding of unsteady boundary-layer separation.

show abstract

On the Lagrangian description of unsteady boundary-layer separation. Part 1. General theory

Cited by 75 publications

References 37 publications

Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil

Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil

On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder

Unsteady separation in vortex-induced boundary layers

Contact Info

Product

Resources

About