Boundary layer research

J.

Sixth International

Conference

of

Ship Tank Superintendents

September - 1951

Washingtön, DSC.

by

Donald Ross

Ordnance Research Laboratory

The Pennsylvania State College

Laborgtjum voor

Scheepshym

Athlf

Meke!weg 2,2628 CD

Ol?F

_Deft

O1.-y3i

BOUNDARY LAIER RE&RCH

Skin friction and boundary layer phenomena are intinate).y related: the local wall friction coefficient is determined by the velocity

distri-bution of the fluid closest to the surface and this velocity distridistri-bution

isthe subject of boundary layer studies. At the Ordnance Research

labo-ratory of The Permzylvania State College, we have been atüdying turbulent

boundary layers in connection with the flow in the

components

of the

L.8-inch water

tunnel

and also because of our interest in the drag and wake of bodies of revolution, Important in propulsion problems. As many of our

studies are related to the subject of Skin Friction and also to Scale ].ffect on Self.-Propulsion Factors(Subject

S),

we wi].]. report here brief)r on several aspects.

Friction in Entrance Region of a Pipe

The flow

in

the working section of a water tunnel corresponds to that

in

the first portion of a pipe For this reason, an

analysis was

made of the turbulent flow in the entrance region of a pipe An

applica-tion of the general three-dimensional boundary layer equaapplica-tions (Reference

1) to the special case of a smtl pressure gradient led immediately to a

set of comparatively simple differential equations (2). - To integrate these equations

analyticafl.y,

an expression was required for the wail

-2

ReynoldE number:

R

=

where:

e

=

f

}4

y.

and: _ui is the

velocity

outside the boundary layer, is the boundary layer thickness,

R is the conduit or body radius, and

y

is the distance perpendicular to the surface,

Two-dimensional expressions have been derived by Squire and Young (3) and

more recently by Granville (14) based on the Schoemberr mean line _{In order} to öbtain a three-dimensional curve, the original pipe friction and velo'-city distribution data of Nikuradae() were reana].yzed(6). As the

three-dinensional momentum thickness reduces to the two-dimensional value for boundary layers which are thin compared to the radius, it was hoped that the three-dimensiona]. friction coefficient curve would coincide with the

flat-plate Schoenherr-Granville curve. However, this was not the case.

The three-dnaional pipe formula lies aboutj 0.0003 - above the flat-' plate curve. This result warns -us against accepting flat-plate friction curves for use on curved bodies; as the results for fully-developed pipe flow diverge oppositely to that inferred from Land-weber' s analysis (7),

a more complicated phenomenon may be involved than that which he

consi-ders. These results also belie the usefulness of

the momentum thickness

Reynolds number as a un5.versaJ. parameter,

Skin Friction in an Adverse Pressure Gradient

The after portion of a ship or a body of revolution is a region in which the static pressure increases in the direction of flow. This adverse pressure gradient is related to the form drag of the body and also influences the skin friction. In fact, at the separation point, the skin friction is practically zero The variation of skin friction

in an adverse pressure gradient was originally studied indirectly by Nikuradse, Bun and others in connection. with..the flow in diffusers. Recently, measurements of wall shar stress were made at the Bureau of Standards (8) and in Germany (9) which show a progressive decrease in

the skin frIction. Analytic formulas for this effect which are in reasonable agreement with the experiments were developed independently

by Ludweig and Tiliman (9) and Ross and Robertson (10). The former analysis was improved upon and used by Granvilie in his recent analysis (4) of turbulent boundary layer5 for. bodies. of revolution. The _latter analysis has been used in connection with diffuser flow studies for the 'large water tunnel. Both analyses treat the boundary ilayer as a super-position of two effects: an inner, flow reÏaté primarily to the local wall friction and an outer flow governed by the cumulative effect of the

pressure gradient. It is probable that the pressuré gradient effect on ship drag is relively 5mkl1 but it should be conslderedin any detailed

Importance of Boundary Layer Research

To the designers

and builders of ships

this research on boundary

layers may seem

academic or irrelevant.

We wish to remark

at this tizne

that

the day may not be

too distant

when satisfactory drag -values

and

propeller-plane wakes

can be predicted

without resort

to model

tests.

This

is now being done

to some extent

in aeronautics.

Methods

have

recently been developed

(for example, ref. 3)

which enable

drag

calcu-lations

of airfoils to within a few percent

over a wide variety of

con-ditions.

Thesecaiculationa

include form drag

as well as skin friction

drag,

and in fact,- the two are really inseparable.

Progress alongthis

line has been made by Grariville (4)

for a body of revolution, though his

analysis is unfortunately limited to the case of a relatively thin

boundary

layer and is inapplicable

at the tail.

Although, the form of a ship is

complióated and calculations would be (if.cult, such boundary layer studies

should eventually lead to a better understanding of the phenomena and help

determine the relative sIgnificance of the factors

which influence scale

References

1.. "Equations of Motion for Three-Dimensional Boundary Láyer Flow," Ordnance

Research Láboratory Report, Serial No. NOrd 7958-154, September 30, 1949.

"Three-Dimensional Equations for the Growth of a Turbulent Boundary Layer in a Cylindrical Tube," by Donald Rosa, Ordnaxtce Research Laboratory Iziternal Memorandum, File #14.2430, August 29, 1950.

"The Calculation of the Profile Drag of Airfoils," by H. B. Squire and A.. D. Young, Aeronautical Research Committee R & M 1838, 1937.

"A Metd for the Calculatibn of the Turbulent Boundary Layer in a Pressure Gradient," by P. S. Granville, DTMB Report 752, May 1951.

"Gesetzmassigkeiten der turbulenten Str6mung in. glatten Rohren," by J. Nikuradse., Forschungsheft V. D. I. 356, 1932.

"A New Formula for the Turbulent Wall Friction Coefficient," by Donald Ross,

Ordnance

Research Laboratory Internal Memorandum, File #14.2430, July 16, 1951.

"Effect of Transverse Curvature on frictional Resistance, U by L. Landweber, DTMB Report 689, March 1949.

"Investigation of Separation of the Turbulent Boundary Layer," by G. B.. Schubauer and P. 5.. K].ebanoff, NACA Technical Note 2133, August 1950.

"Investigitions of Surface ShearngStresses.in ¶ltrbulentBoundary Layers," by H. Ludwieg and W. Tillmahn, translated in NACA Technical Memo 1285, May 1950.

10. "A Superposition Analysis of the Turbulent Boundary Layer in an Adverse Pressure Gradient," by Donald Ross and J. M. Robertson1 Journal Appliod Mechanics, Vol. 18, 95, Mardt 1951.