scholarly journals The skin friction of flat plates to Oseen's approximation

1933 ◽  
Vol 140 (842) ◽  
pp. 543-561 ◽  
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Recent Observation ◽  
Reynolds Numbers ◽  
Simultaneous Equations ◽  
Viscous Effects ◽  
Flat Plates ◽  
Thin Boundary Layer ◽  
The Subject ◽  
Opposite Extreme

Recent observation that flow past tangential flat plates may remain steady up to Reynolds’ numbers so great as 5 x 10 5 has renewed interest in the problem of calculating the motion. For large motions, such as are characterized by Prandtl’s thin boundary layer of viscous effects, there has long existed the well-known theory of Blasius which recent experiments by Hansen tend to confirm. Approaching the problem from the opposite extreme, Bairstow and Misses Cave and Lang have obtained a solution according to Oseen’s approximation to the equations of viscous flow. Their result is given in the form of an integral equation for the distribution of doublets along the plate which will exactly satisfy Oseen’s suggestion and the boundary conditions for an infinite fluid. But the solution of the equation has depended so far upon constructing a group of simultaneous equations with numerical coefficients determined by graphical means. The process is cumbersome and only two evaluations have been attempted, viz., at Reynolds’ numbers 4 and 4 x 10 4 . Exact treatment of Bairstow and Misses Cave and Lang’s integral equation presents difficulties, but it is possible to find an analytical solution of the equation whose errors throughout the experimental range are probably less than those involved in graphical manipulation. This enquiry is the subject of Section I of the present paper. Section II gives the streamlines and other details of the flow.

Low-Reynolds-Number Turbulent Boundary Layers

1981 ◽  
Vol 103 (4) ◽  
pp. 624-630 ◽  
Author(s):  
B. R. White
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Reynolds Numbers ◽  
Viscous Sublayer ◽  
Factor H ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Boundary Layer Height ◽  
Wind Tunnel Data ◽  
Logarithmic Velocity Profile

This paper presents experimental wind-tunnel data that show the universal logarithmic velocity profile for zero-pressure-gradient turbulent boundary layer flows is valid for values of momentum-deficit Reynolds numbers Rθ as low as 600. However, for values of Rθ between 425 and 600, the von Ka´rma´n and additive constants vary and are shown to be functions of Rθ and shape factor H. Furthermore, the viscous sublayer in the range 425<Rθ<600 can no longer maintain its characteristically small size. It is forced to grow, due to viscous effects, into a super sublayer (6-9 percent of the boundary layer height) that greatly exceeds conventional predictions of sublayer heights.

Pressure Gradient and Leading Edge Effects on the Corner Boundary Layer

1979 ◽  
Vol 30 (3) ◽  
pp. 471-484 ◽  
Author(s):  
M. Zamir ◽  
A.D. Young
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Direction ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Flat Plates ◽  
Low Reynolds Numbers ◽  
Small Incidence ◽  
Made In

SummaryResults are presented of velocity and pressure measurements made in the initially laminar boundary layer in a streamwise corner formed by two flat plates at 90° to each other set at various incidences. The leading edges of the plates were sharp in contrast to earlier tests with an aerofoil type leading edge. It was found impossible to obtain a steady enough flow for useful measurements to be made at zero incidence and pressure gradient, a small incidence associated with a favourable pressure gradient was necessary. This is believed to be because of the development of separation bubbles at the sharp leading edge at very small incidences due to small variations of flow direction to be expected in a wind tunnel. The profiled nose used in earlier tests afforded flow conditions much closer to the ideal theoretical model involving zero pressure gradient, but it is argued that any nose however shaped may introduce disturbances in the form of characteristic secondary flows that may well determine the downstream response of the boundary layer. In any case the corner flow is highly unstable at all but very low Reynolds numbers, and in the absence of a region of favourable pressure gradient a Reynolds number in terms of distance downstream of the leading edge greater than about 105is unlikely to be attained in practice with the flow remaining smooth and laminar.

Scale and Roughness Effects in Ship Performance from the Designer’s Viewpoint

1995 ◽  
Vol 32 (02) ◽  
pp. 126-131
Author(s):  
Victor Mishkevich
Keyword(s):  
Boundary Layer ◽  
Scale Effect ◽  
Large Scale ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Full Scale ◽  
Viscous Effects ◽  
Lifting Force ◽  
Lift Forces ◽  
The Difference

Evaluation of the scale effect in the absence of flow separation is usually based on two independent calculation procedures for the drag and lifting forces. Prediction of the full-scale drag forces is based on modeling of the viscous part of the resistance in accordance with the difference in Reynolds numbers. As a rule, a lifting force coefficient for full-scale bodies is treated as a lift coefficient for a model having the same Froude number. The proposed method is based on the idea that an initiation of the lifting force is associated with the viscous effects in the boundary layer. According to this approach, an estimation of the scale effect is based on a calculation of potential, boundary layer and wake flows with viscous/nonviscous interaction for given Froude and Reynolds numbers. The roughness of a surface is taken into account due to the use of special velocity profile parameters. These parameters depend on type and height roughness (casting, milling grooves, polishing, paint, fouling, acid deposit, etc.). As a result, the effects of viscosity (Reynolds number) and surface roughness are determined as the difference between the drag and lift forces calculated for the model and full-scale conditions. The magnitude of the scale effect may reach 50% to 70% for the drag and 10% to 20% for the lift forces. The unusually large scale effect for the lift may play a significant role in engineering applications. Results of the systematic calculations and experimental evaluations are reported for a broad range of ship types and propellers.

Drag and Turbulent Boundary Layer of Flat Plates at Low Reynolds Numbers

1977 ◽  
Vol 21 (01) ◽  
pp. 30-39
Author(s):  
Paul S. Granville
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Reynolds Numbers ◽  
Flat Plates ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
New Formula ◽  
Similarity Law

A new formula is derived for flat plates which gives higher values of drag at low Reynolds numbers than does the Schoenherr formula. This is due to anomalous effects at low Reynolds numbers which are accounted for by adding viscosity to the outer law in the velocity similarity law analysis.

Boundary Layer Interactions With Compliant Coatings: An Overview

1986 ◽  
Vol 39 (4) ◽  
pp. 511-524 ◽  
Author(s):  
Mohamed Gad-el-Hak
Keyword(s):  
Boundary Layer ◽  
Reynolds Numbers ◽  
Turbulent Boundary Layers ◽  
Compliant Coating ◽  
The Past ◽  
High Reynolds Numbers ◽  
The Subject ◽  
High Reynolds ◽  
The Many ◽  
Work Done

During the past five years, several research programs have been conducted to reexamine the subject of boundary layer interactions with compliant coatings. One of the objectives of the research was to answer the question: Can compliant coatings delay transition and/or significantly reduce turbulence skin friction on bodies at high Reynolds numbers? Several significant developments have been achieved by the many investigators participating in these studies. The purpose of this article is to review the progress in our understanding of compliant coating interactions with laminar, transitional, and turbulent boundary layers. The paper will include some work done prior to the recent five year period and available in the open literature, but will emphasize more recent work, some of which is not as yet published.

The Effect of Pulsed Blowing on the Boundary Layer of a Highly Loaded Low Pressure Turbine Blade

2013 ◽  
Author(s):  
Marion Mack ◽  
Roland Brachmanski ◽  
Reinhard Niehuis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Trailing Edge ◽  
Low Pressure Turbine ◽  
Wide Range ◽  
Highly Loaded

The performance of the low pressure turbine (LPT) can vary appreciably, because this component operates under a wide range of Reynolds numbers. At higher Reynolds numbers, mid and aft loaded profiles have the advantage that transition of suction side boundary layer happens further downstream than at front loaded profiles, resulting in lower profile loss. At lower Reynolds numbers, aft loading of the blade can mean that if a suction side separation exists, it may remain open up to the trailing edge. This is especially the case when blade lift is increased via increased pitch to chord ratio. There is a trend in research towards exploring the effect of coupling boundary layer control with highly loaded turbine blades, in order to maximize performance over the full relevant Reynolds number range. In an earlier work, pulsed blowing with fluidic oscillators was shown to be effective in reducing the extent of the separated flow region and to significantly decrease the profile losses caused by separation over a wide range of Reynolds numbers. These experiments were carried out in the High-Speed Cascade Wind Tunnel of the German Federal Armed Forces University Munich, Germany, which allows to capture the effects of pulsed blowing at engine relevant conditions. The assumed control mechanism was the triggering of boundary layer transition by excitation of the Tollmien-Schlichting waves. The current work aims to gain further insight into the effects of pulsed blowing. It investigates the effect of a highly efficient configuration of pulsed blowing at a frequency of 9.5 kHz on the boundary layer at a Reynolds number of 70000 and exit Mach number of 0.6. The boundary layer profiles were measured at five positions between peak Mach number and the trailing edge with hot wire anemometry and pneumatic probes. Experiments were conducted with and without actuation under steady as well as periodically unsteady inflow conditions. The results show the development of the boundary layer and its interaction with incoming wakes. It is shown that pulsed blowing accelerates transition over the separation bubble and drastically reduces the boundary layer thickness.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

Effects of Reynolds Number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor Cascade

2000 ◽  
Author(s):  
Heinz-Adolf Schreiber ◽  
Wolfgang Steinert ◽  
Bernhard Küsters
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
High Reynolds Numbers ◽  
High Turbulence ◽  
High Reynolds

An experimental and analytical study has been performed on the effect of Reynolds number and free-stream turbulence on boundary layer transition location on the suction surface of a controlled diffusion airfoil (CDA). The experiments were conducted in a rectilinear cascade facility at Reynolds numbers between 0.7 and 3.0×106 and turbulence intensities from about 0.7 to 4%. An oil streak technique and liquid crystal coatings were used to visualize the boundary layer state. For small turbulence levels and all Reynolds numbers tested the accelerated front portion of the blade is laminar and transition occurs within a laminar separation bubble shortly after the maximum velocity near 35–40% of chord. For high turbulence levels (Tu > 3%) and high Reynolds numbers transition propagates upstream into the accelerated front portion of the CDA blade. For those conditions, the sensitivity to surface roughness increases considerably and at Tu = 4% bypass transition is observed near 7–10% of chord. Experimental results are compared to theoretical predictions using the transition model which is implemented in the MISES code of Youngren and Drela. Overall the results indicate that early bypass transition at high turbulence levels must alter the profile velocity distribution for compressor blades that are designed and optimized for high Reynolds numbers.

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