Some characteristics of macro-turbulence in flow past a normal wall

ARCH1EF

Lab.

V.

Scheepsbouwkuncle

Technische Hogeschool

INTERNATIONAL ASSOCIATION FOR HYDRAULIC RESEARCH

Delft

SOME CHARACTERISTICS OF MACRO-TURBULENCE IN

FLOW PAST A NORMAL WALL

Frederick A. Locher Research Associate

and Eduard Naudaechek Research Engineer

Institute of Hydraulic Research The University.of Iowa Iowa City, Iowa, U. S. A.

SYNOPSIS

Abrupt changes, in boundary form are the rule rather than the exception in much of Civil Engineering design. The normal wall of finite thickness place on a boundary is among the geometric configukations often encountered in hydraulic structures -e. g. in gated outlet works- An extensive investigation of the pressUre fluctuations

in

the vicinity of such a

wan

has been undertaken to obtain a better understanding of the mechanisms by which structural vibrations are induced. The results presented herein include the spectral distribution and RMS values of the pressure fluctuations near A stationary wall

as

affected by the relative wall thickness and cavitation. A dominant frequency is shown to be associated with an unstable flow reattachment

near the downstream edge of the wail and with the unsteadiness of the overall extent of the separation zone. Cavitation is found to increase both the periodicity and the amplitude of the pressure fluctuations.

RESUME

De brdsques changetehte dana is forme des patois sont la regle plutat que

exception dans nombre d'ouvrages de Genie Civil. Une poutre prismatique d' epaisseur finieplacee perpendiculairement a una paroi eat une des configurations geometriques sotVent reteentree dans lee OtVrages hydkauliquee, par ekeMple dens lee otvrages d'Ivacuationl vannes. Une recherche extensive set les fluctuattions. de la pression aux abords d'Une: telle poutte a ete entreprise pour obtenir the meilleure comprehension des mecaniemes kesponsables des vibrations dans, les structures. Les tesultats Presentee

id

i comprtent la distribution spectrale at l'ecart quadratique moyen des fluctuations de is pression au voisinage d'une poutre fixe, en Tonction.de l'epaisseur relative de is pottre et de l'intensite de is cavitation. Ii eat montre qu'Une.freqtence doMinante est associee

a

un reattachement unstable de l'ecoulement pres du bord aval de robstacle, et au caractere non permanent de la tone entiere de decoullement-On montre que le phenothene de cavitation accroit is petiodicite et

ausei

l'atplitude des fluctuations de is pression.

INSTITUTE OF

HYDRAULIC RESEARCH

UNIVERZIV OF

lOwVA

Reprint No. 234

-

-Introduction

In rebent years, considerable attention has been directed toward the role of macro-turbulence in the generation of hydro-elastic vibrations, as more engineers both in research and in practice have become increasingly aware of such phenomena as the singing of turbine blades, the buffetting of structures, and the vibration of high-head gates. The last Of these examples has inspired a series of investigations at the Iowa Institute of Hydraulic Research [(1), (2), and (3)], a few of the more important results of which are presented herein. These studies, sponsored by the U. S. Army Corps of Engineers have been aimed at a better under-standing of fundamental vibration-inducing mechanisms. The letters and symbols used in the text are defined as they appear, and are listed in the appendix for

reference. .

Several investigators have reported the vibration of high-head gates at partial gate openings, with a particularly severe oscillation occurring as the gate lip approaches the conduit ceiling (4). In general, the modelling of such a complex situation, involving the elastic and damping characteristics of the struc-ture as well as the pertinent flow parameters is no easy task. To obtain complete similitude of the structure and flow field is neither practical, nor particularly helpful in gaining insight into the problem (5). Therefore, a more basic approach has been followed. Rather than observing the response of a model with specific elastic and damping characteristics, the authors have chosen to first investigate the dynamics of the flow itself in order to determine if there are basic flow in-stabilities present which could serve as triggering mechanisms for flow-induced structural vibrations.

Experimental Configuration and Measurements

The geometrical configuration investigated, shown in Fig. 1, is a.high-ly idealized representation of a high-head gate just protruding into the flow.. It is, in effect, a fixed, rigid normal wall in two-dimensional conduit flow. The experimental results repotted were obtained at Reynolds numbers R = VoBp/u in the range 1.1 - 1.4 x 10°. Here, B is the height of the conduit, V, is the velocity in the uniform flow upstream from the wall, o is the fluid density, and 1.1 is the dynamic viscosity of the fluid. Instantaneous pressures in the vicinity of the normal wall were measured by pressure transducers located at the points shown in Fig. 1. By means of suitable electronic circuitry (a phrase which in-eludes a multitude of headaches!) the EMS values of the pressure fluctuations as well as the Corresponding spectral distribution functions were obtained. The term "spectral distribution function", rather than "power spectrum" or "energy density" will be used in this paper. Although the latter two terms have definite physical significance in communication engineering and in the interpretation of turbulent velocity fluctuations, the dimensions of the spectral distribution func-tion unfortunately preclude a corresponding interpretafunc-tion in the case of pressure fluctuations. Hence, the spectral distribution function may be considered a sta-tistical decomposition of the variable in question with respect to frequency, in-dicating the relative intensity of the frequency components. A. peak in the

299

Locher, F. A., "A Preliminary Investigation of the Pressure Fluctuations in the Vicinity of a Normal Wall," M.S. thesis, University of Iowa, 1965. Tatinclaux, J. C., "Pressure Fluctuations in the Vicinity of Normal Walls of Variable Thickness," M.S. thesis, University of Iowa, 1966.

Chu, Yen-hsi, Pressure Fluctuations in a Cavitating Flow Past a Wall," M.S. thesis, University of Iowa, 1967.

Campbell, F. B., "Vibration Problems in Hydraulic Structures," Transactions, ASCE, Vol. 127, Part I, 1962.

Naudascher, E., Discussion of Proc. Paper 4564, Proceedings, ASCE, Vol, 92, 4-i:5711.32':1C; No. fEM4August.19.66.

300

spectral distribution function implies a definite trend toward periodicity in the

presdure fluctuations, and thus may be interpreted as a "dominant

frequency" in

the hydrodynamic loading of the structure.

3.

Non CaVitating Flat?:

;Discussion and Results

It is well known that the shape of the gate lip is important in

control-ling the magnitude of the downpull and the vibration characteristics of the high,

head gates (6).

Consequently, significant variations in the spectral distribution

function were expected with changes in wall geometry.

One of the most important

geometric effects is the reattachment of the flow to the norMal wall.

As

depict-ed in Fig. 2, three different flow conditions were observdepict-ed to occur: Firat, for

'ratios of wall thickness to wall height, d/b, less than two, the flow remains

separated from the normal wall; second, for 2.5 < aib < 4.5, a region of Unstable

reattabhtebt exists; and third, for values of

d/b

greater than 4.5 the

reattach-ment becomes! stable.

For

d/b

equal to one, i.e. for flows remaining separated from the

normal wall, the spectral distribution function decreases continuously with in,

creasing frequency (Fig. 3a).

Figure 3a, it shotld be noted, presents the

normal-ized spectral distribution functions.

A typical example of the experimental

re-sults is shown in Fig. 3b. As a reference, a curve of the form

(V0/b)0

=

= 1/[A+C(fb/V0)2]

which is a fair representation of spectral measurements in

isotropic turbulence, has been arbitrarily fitted to the data (7).

In this

rela-tionship, 0 is the ordinate of the spectral distribution function,

A

and

C

are arbitrary constants, and f

is the frequency.

One may conclude from the

agreement between the shape of the two curves that no dominant large scale

ef-fects are present'.

Further, if the eddies generated in the free shear layer for

this case have any dominant frequency at all, the corresponding pressure

fluctua-tions are not transmitted to Point B on the normal wall..

The most interesting aspect of this investigation regarding

macro-turbulent effects concerns values of

d/b

between 2.5 and 4.5.

As

d/b

becomes

larger than about 2.5, the free shear layer begins to reattach itself to the

down-stream edge of the normal wall.

However, unless the value Of

d/b

is greater

than about 4.5, this reattachment is highly unstable, and as a result, a strong

oscillating pressure field is set up in the immediate vicinity of the normal wall.

As may be seen from the spectral distribution functions for

d/b

values of 3 and

3.5, the pressure fluctuations at Point B exhibit a well-defined "dominant

fre-quency" at

fb/Vo

equal to approximately 0.016-

The corresponding increase in

periodicity is also evident from a comparison of the oscillograms of the pressure

fluctuations for

d/b = 1 and 3 (Fig. 4a and 4b).

Thus as d/b

increases, the

peaks in the spectral distribution functions attain a maximum around d/b = 3

and then diminish.

The geometry more closely resembles a conduit contraction than a normal

wall for values of

d/b > 4.5.

Under these conditions the flow remains

permanent-ly reattached to the wall: (Fig. 2c), and the peak in the spectral distribution

function disappears entirely, as is evident from the results obtained for d/b = 7

(Fig. 3a).

The shape of the curve resembles that for

d/b = 1, although the

corresponding ordinates are of different magnitude.

One cannot expect that the

limiting case

d/b

will again coincide with the results for

d/b = 1,

since

the modified. geometry of, the separation zone will have some influence, on the

pres-sure fluctuations.

(6)

Naudascher, E., "On the Role of Eddies in Flow.,-Induced Vibrations,

Proc.

Tenth Congress I.A.HR., London, 1963.

(f)

Roshko, A., "On the Development of Turbulent Wakes from Vortex Streets,"

301

A comparison of the RM;- values of the pressure fluctuations is also

quite revealing.

With reference to Figs. 5a and 5b for the region of

noncavitat-ing flow, notice that the relative RMS value for d/b = 3 is almost twice the

val-ues for d/b = 1.

A change in the wall geometry from

d/b = 1

to

d/b = 3

not

only increases the periodicity of the pressure fluctuations, but increases their

intensity as well.

The structure would therefore experience a dominant frequency

in the hydrodynamic loading together With a twofold increase in its intensity,

and if the natural frequency of the structure is in the neighborhood of the

domi-nant frequency of the loading, hydro-elastic vibrations will certainly occur.

As far as macro-turbulent effects at the other points of measurement

indicated in Fig. I are concerned, the results at Point E are the most

signifi-cant.

This point, it should be noted, coincides With the Mean position of the

end of the separation zote for d/b < 1. As might have been anticipated, the

in-herent unsteadiness of the location of this instantaneous stagnation point has a

preferred frequency of o§cillation, as is clearly indicated in the spectral

dis-tribution functions for Point E (Fig. 6). The effects of these oscillations are

transmitted upstream to Point D and may be recognized as peaks in the respective

spectral distribution functions shown in Fig. 7.

_{It is interesting to note that}

the dominant frequencies at Point D are slightly less than those at Point E for

similar flow conditions.

CaVitating_Flow:_ Discussion_and.Results

Cavitation, is another aspect of the flow past a normal wall which is of

interest to engineers.

According to other investigators (8),.cavitation seems to

stabilize the eddies generated in a free shear layer.

The results of some

cavi-tation studies for the flow past a normal wall reinforces this conclusion.

Plots

of the variation of the relative RMS values of the pressure fluctuations for

d/b

equal to 1 and 3 show a definite increase in the RMS values with decreasing

val-ues of the cavitation number K = p0 - pv/(pV02/2), (Figs. 5a and 5b).

Herein,

p,

is the pressure in the uniform flow upstream from the normal wall, and pv is

the vapor pressure of the fluid.

The maximum value is attained at

K = 2.21,

followed by a decrease in RM values, a rise to a secondary peak at

K

1.82

and a final, sharp drop.

Observations made during the experiments indicate that

cavitation has two distinct effects on the flow.

The.first of these is to

stabi-lize the eddies generated within the free shear layer, enhance the periodicity of

the pressure fluctuations and contribute to the intensity of the pressure

fluctua-tion.

Part of the increase in RMS pressure is a result of the high-frequency

cavitation noise transmitted to the pressure transducer.

This noise gives rise

to the "fuzzy" appearance of the oscillograms shown in Fig. 4c and d compared to

the non-cavitatitg conditions shown in Fig. 4a and b.

The second effect of

cavi-tation, indicated by the minor peak at

K = 1.82,

is a manifestation of the

in-stability of the cavitation pocket developing in the separation zone downstream

from the normal wall, and is Most likely coupled with the instabilities of the

free shear layer itself.

A qualitative comparison of the oscillograms for d/b = 3

indicates that cavitation has increased the periodicity of the flow (Figs-. 4b and

4d).

Noteworthy is the fact that the larger of the two peaks shown in Figs. 5a

and 5b occurs in the initial. stages of cavitation, which is associated with a

hissing sound rather than the sharp, slapping noises heard in the later stages of

cavitation.

High speed cinematography shows that cavitation does not seem to

con-tribute to a greater two-dimensionality of the eddies

in

the flow.

Since the

cores of the eddies cavitate more readily as a result of the low pressures within

them, they become easily visible in the motion pictures.

Near the leading edge

(8)

Vigander, S., "An Experimental Study of Wall-Pressure Fluetuations in a

Cavitating Shear Flaw," Stud. in Eng. Mech., Rep. 21, Univ. of Kansas, 1965.

-302

of the Wall, these eddies are alignedarallel to the wall; within a relatively

short distance downstream, however, their ekes become more nearly aligned with

the direction of the flow, as the eddies are stretched by the action of the mean

shear stresses.

Once the cavitation number becomes less than 1.82, transition to

supercavitating floW'tekes place.

There is a great deal of water vapor mixed with

the fluid, which prevents effective transmission of the pressUre fluctuations to

the transducer under these conditions,.

The RMS values drop Sharply and are quite

insignificant as the separation tone becomes a Vapor cavity,

Future Considerations

It should be emphasized that all of the results presented in this paper

were Obtained with the normal wall held stationary.

Once oscillation of the wall

begins, the flow pattern will be modified considerably, with the breakdown of the

free shear layer strongly affected by the oscillating edge [(8) and (9)1.

Al-though it is known that phasing of the vortices With the vibratory motion exists

under certain conditions, little is known concerning their effects on the-forces

induced upon the vibrating structure.

The logical next step in the research

pro-gram is

therefore, to force oscillations of the normal wall at specific

ampli-tudes and frequencies.

From measurements of the fluctuating- forces induced oh

the bottom surface of the wall, one might expect to gain insight into the

mecha-nisms of hydro-elastic interaction as well as some indication of structural

load-ing under oscillatload-ing conditions - a subject on which there is only rather sparse

information.

Conclusion

In summary, the macro-turbulent structure of the flow ih the vicinity

of a stationary normal wall has been shown to be strongly dependent on the wall

geometry.

Basic flow instabilities associated with the reattachment of the free

Shear layer along the normal wall definitely possess a dominant frequency of

os-cillation as indicated by spectral analysis of the wall tressuret,

Cavitation

reinforces the oscillatory character of the flow, leading to increased

periodici-ty and higher RMS values of the pressure fluctuations.

It is quite certain that

these phenomena play an important role in triggering flow-induced structural

vi-brations.

APPENDIX: NOMKETCLATURE

A,, C

arbitrary constants

height of the conduit

cavitation number, defined as

pc,

pv /(0V02/2)

Vo

velocity in the uniform flow upstream from the normal wall

projection of the normal wall into the tlow

thickness of the normal wail

,130

Tressure in the uniform flow upstreaff from the normal wall

21'2

vapor pressure of the fluid

RMS value of the pressure fluctuations

fluid density

dynamic viscosity of the fluid

ordinate of the spectral distribution function, i.e. the spectral density

fb/Vo

dimensionless frequency parameter

Reynolds number

VoBp/u

(V /b)

dimensionless spectral density

qrgpV02/2)

relative ENS value of the pressure fluctuations

(9)

Vigander, S., "A Study of Flow Through Abrupt Two-Dimensional Expansions,"

-303

1).75 b A. . . ',bra 5.87b A

BC

. .. '

l

y...i,e

.'< ....,...y...,n13?

E

\

--...J

I '

Z

_{PRESSURE TRANSDUCERS].} DOWNSTREAM EDGE UPSTREAM EDGE FLOW

./1NOTE B.6b

/////////

f

FIG. I 'DEFINITION SKETCH CROQUIS DE DEFINITION

/

/./

/ /

./

/.

/ / /

MEAN FREE STREAMLINE

NO REAT TACHMENT ( FOR d/b <2)

/

I"!

/ / / /

/

UNSTABLE REATTACIIMENT(FOR 8.6 b, 2.3 <.0/0- < 4.5)

(d) STABLE REATTACHMENT(FOR B80.

0/0> 4.5)

FIG.. g EFFECTS OF WALL GEOMETRY ON FLOW REATTACHMENT

INFLUENCE DE LA GEOME:TMI2 DE LA POU-TRE Su)? LE kat:rack-papa DE L'ECOULEMENT

30 25 20 15 10 0 0.002 0.004

04- -

0.02 ,k/V.

FIG 3a SPECTRUM OF THE PRESSURE FLUCTUATIONS AT POINT B AS.1 FUNCTION OF d /0

SPECTRE DES FLUCTUATIONS DE LA PRESS1ON AU

POINT B EN, FONCTION OE'

/0

20 16 12 304 0 04 0.1 02 A. A

.

--,---b 177"72 1.0 0.061 3.0 0.121 3.3 0.115 REF 0.117 CURVE -1

\

I

'

A--

--F.

i

iii

I /".\\

1

\.

0 002 0 004 .001 0 02 004 0I

FIG. 30 TYPICAL EXPERIMENTAL DATA FOR, POINT .13

d/b (NOT NORMALIZED)

RESULTATS EXPER1MENTAUX TYPIOUES POUR LE POINT B d / b 5.5 (NON NORMALISES)

! 1 1 1 1 1 1 1 1 1 1 I I I I 1 1 ' 0.2

sec.-P1

4 c (1/13 I K

2.25

1.0 psi 1.0 psi 317.1 1.0 psi

E

0.2

sec.--4

1.0 sec. ----4 et

4 b

0/0° I

NO CAVITATION

.0/0

3 NO CAVITATION

0.2 sec.

1.0 sec. 4 e 4

0/8

I K

1.82

_0/0

3

1(11.82

FIG.

4

OSCILLOGRAMS OF THE PRESSURE FLUCTUATIONS

AT POINT

OSCILLOGRAMMES DES FLUCTUATIONS DE LA

PRESSION AU POINT

SO -NO CAVITATION

rl/b

3.0

306 4

FIG. 5c, VARIATION OF THE RELATIVE RIAS VALUES OF THE PRESSURE FLUCTUATIONS WITH CAVITATION NUMBER AT POINT B d/b I ECART GUADRATIGUE MOYEN REDUIT DES FLUCTUATIONS DE LA PRESS1ON EN FONC.TION DU NOMB-RE DE CAVITATION

.4I.1 POINT 8, d/b I

ECART QUADRAT1OUE MOYEN REDUIT DES FLUCTUATIONS DE LA PRESSION EN FONCTION DU NOMBRE DE CAVITATION

AU POINT II,

d/b 3

70.

2 O. 1 4 0.12 0.10 0.08 0.06 0.04 0.02

dib

1.0 040 4-NO CAVITA-TION. 0.00 0.06 0.04 0.02 0.00 0 2 3 4 5 7 8

FIG. 5b VARIATION OF THE RELATIVE RMS VALUES OF THEPRESSURE

FLUCTUATIONS WITH CAVITATION NUMBER AT POINT B, d/b.3 0.14 0.12 0.10

1.7

2..Le 2 aps

12 10 8 6 42, 4 2 0 0 002. 0 004

307

0 02 04 001 002

004

/

FIG. 8 SPECTRUM OF THE PRESSURE FLUCTUATIONS AT POINT E AS A FUNCTION OF d/b

SPECTRE DES FLUCTUATIONS DE LA PRESS1ON AU POINT E EN FONCT1ON DE el/0

0 002 0.004 0.01 0.02 004

0I

0.2

I bi,

FIG. 7 SPECTRUM OF THE PRESSURE FLUCTUATIONS AT POINT D

AS A FUNCTION OF d / b

SPECTRE DES FLUCTUATIONS DE LA PRESSION AU POINT 0 EN FONCT ION DE c I / b

04 o/o 17/pv.,72 0.0 0.151 1.0 0.125 ...

\

/

...

\

1

\

\

_\

% 1

\

\

\...

.... ... ...

4/b gkele

0.0 0.089 I. 0 0.095 --. i

/

/

,/

1 1 1 1 t

\

\

\

... 12 10 8 6 4 2