\\'orking Parly i\Ieeting which will be held at I3i\IT Fluid i\Iechanics Limited. Ted- dington. ...... The same approach is now being extended to curvilinear co-ordinates in order to make ..... ASME Turbo Expo - Land, Sea & Air, Brussels. ...... adaptiye walls, The flow is driven by an injector system (air) and can be cooled down.
TURBULENCE CONTROL BY PASSIVE MEANS
FLUID MECHANICS AND ITS APPLICATIONS Volume 4 Series Editor:
R. MOREAU MADYLAM
Ecole Nationale Superieure d' Hydraulique de Grenoble Boite Postale 95 38402 Saint Martin d'Heres Cedex, France
Aims and Scope of the Series
The purpose of this series is to focus on subjects in which fluid mechanics plays a fundamental role. As well as the more traditional applications of aeronautics, hydraulics, heat and mass transfer etc., books will be published dealing with topics which are currently in a state of rapid development, such as turbulence, suspensions and multiphase fluids, super and hypersonic flows and numerical modelling techniques. It is a widely held view that it is the interdisciplinary subjects that will receive intense scientific attention, bringing them to the forefront of technological advancement. Fluids have the ability to transport matter and its properties as well as transmit force, therefore fluid mechanics is a subject that is particulary open to cross fertilisation with other sciences and disciplines of engineering. The subject of fluid mechanics will be highly relevant in domains such as chemical, metallurgical, biological and ecological engineering. This series is particularly open to such new multidisciplinary domains. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of a field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity.
For a list of related mechanics titles, seefinal pages.
Turbulence Control by Passive Means Proceedings of the 4th European Drag Reduction Meeting
edited by
E. COUSTOLS ONERAICERT, Toulouse Cedex, France
KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON
ISBN-13: e-ISBN-13: DOl: 10.1007/ Library of Congress Cataloging in Publication Data European Drag ReductIon Meeting (4th 1989 Lausanne. Switzerland) Turbulence con t ro l by pass Iv e means proceedings of the Fo ur t h European Dra g Reduction MeetI ng ! edI ted by E. Coustol s. p. cm. "T he ~ ourt h European Drag Reduction Meeting was held. July 24. 1989 i n Lausa nn e . Sw i tzerla nd . " I n c luc es o l bl 1 ograp hi ca l ref e r ences an d
index.
ISBN 0-7923 -1 020-9 F1 L l a dynam l cs--Congresses. 2. Tur bulent bound ar y l ayer -Co ngress es. I . Coustols. E. I I. T itle. TA357.5 .T87E93 1989 620.1 '064--jc2 G 90-48907 I .
ISBN-13: 978-94-010-7471-1
e-ISBN-13: 978-94-009-2159-7
001: 10.1007/978-94-009-2159-7
Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell , MA 02061, U.S .A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
Printed on acid-free paper
All Rights Reserved © 1990 by Kluwer Academic Publishers
Softcover reprint of the hardcover 1st edition 1990 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Contents
Preface
vii
Final programme
ix
External Manipulators (LEEUs) Balallce of turbulent kinetic energy downstream a single flat plate Inaniplllator : comparisons betll'een detailed experiments and modelling. C. Tf 1/ a ud. I run ny.
IP. Bonnet C' I Dclville
.\Ianipulation and modelling of turbulent pipe flow: some parametric studies of single and tandem ring devices. A. Pollard. H. Thoma n 11 C A .Jl. SUl'ili Large eddy simulation of manipulated boundary layer and channel flows. 11.
1,'hin C' R. Friedrich
The importance of LEBF de\'ice shape [or turbulent drag reduction.A. Butril"ud
23 -\1
f,7
Internal Manipulators (Riblets)
Boundary layer flO\\' visualisation patterns on a riblet surface. JJ C. C/n Ik Simultaneous flow \'isualisation and LDA studies over longit uclillallllicro-grom'ecl surfaces. C.I.l. Pulles. K.K. Prasad () F. T..U. "YiuUL'stailt Effects of longitudinal pressure gradients on turbulent drag reduction with riLkts.
7') LJ7
1,'.S. Choi
IOl)
IT. Schmitt
12.\
Synthesis of experimental riblet studies in transonic conditions. E. COI/sto/.' C Effect of ri blet s on either fully dewloped boundary layers or illt ernal flo\\"" ill laminar regime. I Liandrat. E. COllslo/s. L. Djenidi. F. Ansc/})ut. )( de SO/III-
\'iclol'. F. Fioc [;' L. Fu/achier
1-\1
Internal and External 1\1anipulators Turhulent houndar\' layer OHT a ribleted surfClce with tandelll l11i111ipulators 1),ing surfac(' drag balances. I'.D ..Ygllycn. I Dickinson. }'. .]U/II. L Cha/Irollr. "I.
Small!. A. Pogc C F. PaquEt
List of referees
15')
In
Preface In the last decades, a lot of effort has been directed towards manipulation of turbulent boundary layers by passive devices such as external manipulators (thin flat plates or aerofoil section devices embedded in the outer layer) and/or internal manipulators (small streamwise grooves acting directly on the inner region) for the purpose of reducing viscous drag. The former are commonly referred to as LEI3U s or BLADEs and the laHer riblets or grooves. Though the details of the mechanisms are not firmly understood, world-wide experimenta.! data are available and consistent enough in order to assert the potential of such devices for turbulent drag reduction. It should be noted that following on from recent and successful flight tests, the concept of using grooved surfaces is rather close to finding industrial applications. During the last few years, in Europe, there has been considerable interest in lookillg at the behaviour of such passi,'e turbulence manipulators. A lot of intense research, concerning both experimental and theoretical studies. has been carried out in some European research centres. For the last fi\'e years. informal gatherings. called ,.\ \'orking Pi\l'ty i\Ieetings" , have been set up, once a year; the aim of these meetings is not only to bring together European researchers acti,'e in the field of turbulent drag reduction by passi"e means and to hear about recent de\'c!opments but also to o u t1 ine sui tit ble directions for future research or collaborative programmes. Thus, follO\\'ing on from previous meetings at EPF Lausanne (September 1st:3rd, 1986), ONEllA/CEllT Toulouse (September lOth, 1987) and ONEnA/Chalillon (September 20th-:30th, 1988), the fourth European Drag Reduction WorLing Party :'Ieeting \\'itS held at EPF Lausanne on July 2 Hh, 1989 under the auspices of the £11COFTAC Pilot Centre by invitation of Professor 1.1. 11yhming and Doctor T.V. Truong. T\\'ellty six participants from fi \'e European count ries (Fra nce, CermallY, S \\' i tzerl a nd, The N etherla nels and U ni ted Kingdom), together \\'il h collaborating colleagues from Canada, presented 18 contributions of \\'ork which eilher had heen recently completed or was in progress. The purpose of this Proceedings Book is to pro\'ide papers '\'hich reflect the contents of the talks given at that conference. It should lw lloled that "A report on the 4 th European Drag neduction \\'orking Party T\lccting" \\"as published in the EHCOFTAC Bulletin IV. December 19S'} c
011 a personal note, I would like to say how grateful I am to all the rc1'erees for reviewing some of the dozen or so papers offered after the meeting. Thanks to their assist ance. this Proceedings Book should be published in time for the :5th \\'orking Parly i\Ieeting which will be held at I3i\IT Fluid i\Iechanics Limited. Teddington. Uniled Kingdom. I would also like to thank Doctor Nigel Hollillg\\'orth, frolll KIll wer academic ))ll blishers, for all his va 1uable commen b dming the preparation of this Proceedings Book.
Toulouse, August 1990
E. Coustols vii
Final Programme
4th European Turbulent Drag Reduction \\lorking Meeting 1989 S,viss Federal Institute of Technology Lausanne EPFL - July 24th, 1989
Session 1 - External l\1anipulators in Internal and External Flows (Chairman: E. Coustols) High speed LEBU device drag measurements. J.P. Bonnet &; J. Delville Complementary drag reduction measurements. L.C. Squire &; A.:'.I. Savill I-Combination of riblets and manipulators at low Re ; 2-Some observations of tllC static pressure distributions in pipe flow perturbed by a LEEU ring. Y.D. I\guyen &; J. Dickinson Turbulent pipe flow manipulation and modelling. A. Pollard, A.'\1. Sa,'ill &; H. Thomann
Session :2 - Internal l\1anipulators : Riblets. (Chairman: A.::\I. Savill) Effects of pressure gradients on riblets. K.S. Choi Pressure grilc1icnts on riblcts in subsonic and transonic flm\"s. E. Coustols Further supc'I".sonic riblet results. L. Gauclet (presented by A.:\f. Sa\'ill) ::\[ultiple light-plane flow visualisation of the structure \\"ithin riblcts. D. Clark Rihlcts ill Cl difl"llser. Ph. Puh'in Hiblets in a channel flow. ::\1.\1. Lm\'son Flml" \'isllalisdtion ancl turbulence measurements moer micro-grooves. 1\:. Prasad c\.: IT. Schwarz Hiblds on a cylinder. D . .'\eumalln
Session j - Other Drag Reduction Approaches and l\lodelling. (Chairman: 1.L. Hyhming) Complltations of turbulent How in L-shaped riblets. R.E. Launder &; Li Shaopillg Computations for L-shaped riblets in laminar boundary layers. E. Coustols :further riblet computations in a laminar boundary layer. :r. Anselmet ,\.: L. Djenicli CurYs, the techniques proposed can be divided into active and passive ones [2], [15]. One of the passive methods consists in immerging thin ribbons, having either rectangular or aerofoil section, within the external part of a turbulent boundary layer. This method, so called external turbulence manipulation, is studied in this article. Experimental investigations have shown that the mechamisms leading to drag reduction are complex. Among several effects, one can notice that the externalmanipulator induces large skin friction reductions and spectacular modifications on turbulent profiles (excess of turbulence level in the device wake. important decreases belm\' the mean axis of this wake, ... ). Furthermore, the manipulated boundary layer is highly out of equilibrium O\'er a large dmvnstream extent. Besides these experiments, numerical studies have been undertaken. The goal was then to check usual turbulent closures, using several transport equations, for specific geometrical configurations. l"lost of the numerical codes, used up to now. '\Tre based on boundary layer assumption and thereby started downstream of the device with the initial data given from experiments. These numerical studies have been reviewed by Coustols &: Savill [4]. Let us point out that, using appropriate initialisations. authors were able to represent the mean and fiuctuating velocity profiles at further stations downstream of the manipulator with a satisfactory agreement with experiments. However, if one aims, for instance, at optimizing the device geometry, it is necessary to start the computation upstream of the device and to follow the whole of the fiow development. This second approach has been used in works previously undertaken at the Aerodynamic department of ONERA/CERT [3]. [13]. On a given experimental configuration, check of several closure models have been done: two, three and fiw transport equations, using cOlwentional turbulence models. The conclusions ,'>as, though the k - E model was able to reproduce qualitati"ely the behaviour of such manipulated flow, better results have been obtained using three or five transport equations. The mean and turbulence velocity profiles as well as the skin friction coefficient have been calculated in better agreement with the experimental data [3] [13]. Let us point out that three or five equations models give rather comparable results, except that the latter allows to get a better representation of the C f evolution. A remaining question can be pointed out: Is these conclusions on the CERT configuration stay valid for different device geometries? The purpose of this study is then to check the predictive capabilities of the C.E.R.T. numerical code on an other configuration given from the C.E.A.T. Poitiers, for which detailed experiments were available in the downstream vicinity of an external manipulator having rectangular section [9], [10]. We decided to restrict the present numerical approach by using only the three transport equations code. This option gives a good compromise between computer time saving, previous prediction
3
quality and detailed description of the turbulent field. A brief description of the numerical procedure is first given ; the experimental apparatus and techniques are described, then a comparison between experiments and modelling on the mean and fluctuating profiles at further locations downstream of the manipulator is discussed. The experiments provide the energetic balance of the kinetic energy equation. Then, for further information, we compare the numerical terms of the k transport equation with their experimental estimations.
Numerical approach.
2 2.1
Basic equations.
The equations of the mean flow are the The usual two-dimensional assumptions tion and y the axis normal to the wall. ones in the :r direction are neglected. It
aU a:r
Reynolds averaged Navier-Stokes equations. are used; x represents the streamwise direcThe unsteady terms as well as the diffusion follows:
aV ay
-+-=0.
a ([J[j) aol'
+ a(UV) ay
= _~ aP
a(0'V) ax
+ a(11V) ay
=
pool'
(1)
+.!!.[~ (aU)] + .!!.- (-U'2) + .!!.- (-177l) ay p ay ax ay (2)
_~ of +.!!.- [~(a1l)] +.!!.- (-u'v') +.!!.- (_v'2) p ay ay p ay a:r ay
(3)
For the turbulent motion, a two-layer model is adopted: 1. Although the flow is out of equilibrium even close to the ,Yall, a mixing length scheme is applied, for simplicity, in the near wall regions (up to y+ = 60), including the lower and upper sides of the device. This scheme is based upon an eddy \'iscosity assumption: -,-,
III
- u·u- = I
P
]
The eddy viscosity coefficient as follows:
{LI
(aU; aUj ) aXj + -ax;
2 -kfJ
3
IJ
(4)
is expressed, using a mixing length formulation.
(5) where I is the mixing length and F the Van Driest type corrector function for the viscous sublayer. The use of this scheme, close to the manipulator, can be
4
made if we assume that the boundary layers, developping on both sides of the device, are turbulent. Let us notice that this assumption is not clearly evidenced by the available experiments. 2. A three transport equations model is used everywhere else (y+ equations are : • t he
>
GO). These
kinetic energy equation in a general form : €
~
It
au: au:
p
aXj aXj
--(6)
C" and D" are respectively the convect.ion and molecular diffusion terms; they do not require any modelisation. The turbulent diffusion term T" is modeled as follows [8] : (7) Let 11S notice that this model is based upon a high turbllient Reynolds number assumption (RI = pk 2 / w:). Close to the limit y+ = GO or in the deyice wake the RI values could be moderate; therefore, we use a wall damping function
III :
11'
[
= exp (1
-3.4
+ Rt/50)2
]
with
The pressure-velocity correlation
-0.1 -0.2
98 * 297 grid
-0.3 -0.4 -0.5 -0.6 -0.7
-o.B
o
Experiment
+
Calculation Pipe Flow
o
Calculation Single Manipulator
-0.9 20
40
X/D
Figure 3: Cp vs. X/D for pipe flow with single manipulator with leading edge at X/D=27.3, r/R=O.8, Re=180,OOO.
+ +
"+
"+
" " o
o
Experimental data (Laufer) (Fully developed)
o
Calculation 68
+
Calculation 98 • 267
20
40
* 147
60
BO
y+ (=y • Utau /
100
nul
Figure 4: Comparison of calculated turbulence kinetic energy profiles at X/D=30 to Laufer's fully developed pipe flow data.
38
I~
~
as proper transport velocity. For more details, see Richter et al. (1987). The velocity component normal to solid walls is set to zero. Resolution restrictions require approximate boundary conditions tangential to walls as Piomelli et
48
al. (1989) propose for flows of engineering interest. By means of Schumann's (1975) condition the instantaneous wall shear-stress is in phase with the instantaneous velocity in the logarithmic layer. This assumption is supported by experimental investigations (Piomelli et al. 1989). The same concept is applied at surfaces of manipulators. The authors are aware that the validity of the logarithmic law is questionable there. However, the inviscid damping of vertical velocity fluctuations as the primary effect of manipulators is considered correct. In the case of the boundary layer flow we specify Dirichlet conditions at the top of the computational domain for the tangential velocity components and the SGS turbulence energy. The normal velocity is obtained from the continuity equation. 'Ve use periodic boundary conditions in both flow types in the spanwise direction. Results Three different LESs were performed for boundary layer as well as for channel flows. l.) Two different LESs serve to produce inflow boundary condi tions for both flows. a) Boundary layer flow: LES of a zero-pres sure-gradient boundary layer flow (ZPGBL) with inflow / outflow boundary conditions. Some sort of structural periodicity (Richter et al. 1987) is assumed in this case to generate inflow conditions. b) Channel flow: LES of a fully developed channel flow (FDCF) with periodic boundary conditions in the main flow direction. 2.) LESs of the manipulated boundary layer (MBL) and manipulated channel flow (MCF) with inflow boundary conditions from l.) 3.) LESs of the standard boundary layer (SBL) and standard channel flow (SCF) with the same inflow conditions as in 2.). "Standard" refers to unmanipulated flows.
Boundary layer flow Two computational domains of different length haye been chosen. In terms of boundary layer thickness 5 at the inflow plane the long domain measures 24 x 4 x 2 (x,y,z-directions) and the short one 8x4x2. A 192x32x32 and 64x32x32 equidistant grid have been used. The results are independent of the length of the computational domain except in the outflow-region. Based on Ur,l and 5 the Reynolds number is 3240, which corresponds to a value of 8700 based on free-stream velocity U oo and momentum thickness 02' All quantities are non-dimensionalized with Ur,l and 5. An infinitely thin manipulator is fixed at a distance 25 downstream of the inflow plane. Since the gap h m between the manipulator and the wall should decrease with increasing Reynolds number in order to get the maximum skin-friction reduction (Sa\'ill et al. 1988), we have set h m = 0.31255. The length 1m of the device is l.55. This is in accordance with Savill et al. (1988), who obtain the largest integrated skin-friction reduction when the length of a manipulator is greater than the boundary layer thickness.
49
I
o
50
The ZPGBL was computed with 36,000 time steps. Inflow data of 12,000 time steps for the MBL and SBL were stored on magnetic tape. Consequently the simulations of the MBL and SBL covered 12,000 time steps out of which 6,000 are needed for statistics. Besides time averaging spatial averaging is used in the homogeneous y-direction. Figures 1a,b give a qualitative impression of how a single flat plate manipulator affects a boundary layer flow. The contour surfaces are plotted for high \'alues of the instantaneous (-u" w" )-correlation. The Reynolds stress mainly results from these structures. In the SBL the (-u" w")-structures are uniformly distributed over the whole computational domain (fig.1a). Figure 1b shows the suppressing effect of the manipulator. Unlike the portion of the flow field upstream of the manipulator, there is no similarity in the MBL and SBL downstream of the plate. The manipulator destroys larger structures and breaks them up into smaller ones.
8
I I I 10
1~
12
1B
16
22
20
X
2~
Fig.2 Mean longitudinal velocity component.
The effect of the manipulator on the mean longitudinal velocity component is demonstrated in fig.2. The plate produces a wake, which develops downstream and is nearly indistinguishable in the last profile. In this context, it has to be mentioned that the grid-resolution is to low to get detailed information concerning the wake and the developing boundary layers on the manipulator surfaces. However. the dewlopment of the wake is more obvious from plotting the momentum deficit 6=MBL-SBL downstream of the manipulator, compare fig.3. It is shown that the maximum deficit shifts towards the wall. This phenomenon coincides with the" downwashing" of the wake.
SC"LEI - - - 8 -4.000E+OO
z I
)
e '=' 8
10
12
I
I I
I I
J = § tc;
I
~
)
J
El
16
18
,
.::l
=
§ 20
, ~ 22
Fig.3 \fomcntum deficit 6=MBL-SBL downstream of the manipulator.
X
24
51
The rms-values of the longitudinal velocity fluctuations clearly reflect the suppressing-effect of the manipulator, compare fig.4. The solid line refers to the manipCllated and the dashed line to the standard boundary layer, respectively. \Vhile a slight influence is found immediate downstream of the manipulator at x=48 (~=0.58), the turbulence intensity is considerably reduced at x=98 (~=5.58). It is of interest that the velocity fluctuations are reduced mainly between z=hm and the wall. The measurements of Coustols et al. (19S6,19S9) confirm these results. Further downstream the urms-values recover gradually and reach almost the level of the SBL at x=198 (~=15.58). SCALE' - - - • 6.000[1'00
z
2
10
12
14
16
1B
20
22
X
24
Fig.4 rrns-Hlues of longitudinal velocity fluctuations.
- lIIBL, - - SBL. Figures 5a,b demonstrate the effect of suppressing and destruction of large-scale structures in a ~\'IBL by comparing the fluctuating wlocity-vectors in a (x,z)-plane with those in a SBL. Fig.5a gives an impression of the turbulence dynamics in a SBL at two different instants. The flow field is characterized by ejection and sweep type events. A typical turbulence structure, marked with arrows, travels more than 28 downstream in the course of 100 time steps. \;Vhat happens to this structure when a manipulator obstructs the flow? Fig.5b shows the flow field in a :vIBL at the same moments. At time step 6S00 the vectors which form the same structure just described are aligned with the plate. Still more importanL the structure is clearly weakened 'while trawlling downstream (lower plot of fig.5b). Furthermore, the plots for nt=6S00 show how the sweep and ejection type ewnts at the end of the computational domain are influenced by the manipulator. The instantaneous flow fields of the MBL and SBL are compared in plate 1 by means of cartographic representations of velocity fluctuations and the SGS kinetic energy. The upper panel of each figure corresponds to the SBL and the 100\'er panel to the \IBL. The blue, green and red regions are characterized by strong negative. nearly zero and strong positive \'alues, respectively. In the 100\'er panels the flow field upstream of the manipulator is still the same as in the SBL. As the manipulator breaks up the oncoming structures, the flow field downstream is changed. \Yhile the longitudinal velocity fluctuations are scarcely affected (compare plate la), the changes are more obvious in the other wlocity components. The figures of the spanwise (plate Ib) and the vertical velocity fluctuations (plate lc) illustrate the wake of the manipulator, which divides the flow field into an upper and lower
52
.... . . . . . . . . .......... .. .......... .. . . . . .. . . . . . .. .. .. .. .. .. .. .. .. . .... . ...... .... , .. .. .. .. .. .. .. .. .. ...... . .........
Q
.. . ...
~~~~~~~~ll~;ll~~~~~j~~
tttfHU1HU~llU}lll
o
2
3
2
3
2
3
5
6
7
t
x
t
x
b
Fig ..5a.b Fluctuating velocity-vectors in a (x.z)-plane. (a) SBL. (b) '\lBL.
53
1
o
o
6
B
10
12
14
~.
/
16
18
20
'~ 22
X
24
Fig.12 rms-values of longitudinal velocity fluctuations.
- MCF, - - SCF.
Figures 13a,b compare the fluctuating (u, w)-velocity \'ectors in a l--.ICF and a SCF in their time-development. The plots of fig.13a demonstrate how two largescale structures in the upper and lower part of the SCF (marked with arrows) trawl downstream in the course of 2xlOO time steps. Fig.13b presents the vector fields of the :tIfCF at the same moments. Remember, that the inflow conditions for both flows are the same. Therefore at time step 5800 the same large-scale structure is found in front of the upper manipulator. 100 time steps later the structure has
58
.
~::"'-""' ,,:?~ I.:·:~:":-::::·;;;::'::~~! .".,- .. " , .... "':: .. ~::;..;:
:.:::::1
i~?~:' .':::~~£~::;i
i::~::: ::~::::::::::: ;::::-::: i
~U:::":~O Present study
• Smooth surface
025
0
Figure 3
)( Riblet surface Previous data (ChOI, 1989) \\\ Smooth surface /1/ Riblet surface I
0
25
50
75
Mean velocity profiles in linear form. Figure sequence and symbols as for Figure 2.
114
0.15,-----....,----r------,
0.15 ~-;':::::::i!::=;~~ dp/dx < 0
~t?:;;s;;:;:?===7==;:~==~
dp/dx > 0
Pre-sent study • Smooth surface)( Rjbl~t surface-
0.05
Previous dato(Choi.1989):
\\\Smooth surface II/Riblet surface
OL-______l -_ _ _ _ _ _
o
Figure 4
25
~
50
______
~
75
y'
Profiles of the u-component turbulence intensity. Figure sequence and symbols as for Figure 2.
(Mellor, 1966). The comparison with the previous results in the ze:o pressure gradient condition by Choi (1989) is very good as shown ~n Figure 2, although the extent of logarithmic region is slightly shorter in the present case owing to its smaller Reynolds number of Re ~ 2.7 x 10 3 compared with Re
~
4.6 x 10 3 in Choi (1989).
The corresponding linear profiles of the mean velocity are given in Figure 3, together with the data by Choi (1989) in the zero pressure gradient condition. The general shape of the present profiles as well as the differences in profiles between the smooth and rib let cases are in good agreement with those by Choi (1989). The difference in the "fullness" of the linear profiles is again due to the effect of the Reynolds number, as mentioned above, through the change in the skin friction coefficient. The turbulence intensity profiles for the u-component velocity are given in Figure 4. In this figure, a reduction of between 5 to 13% in turbulence intensity is observed over the riblet surface at the maximum point of intensity of y+~14. It is also observed that the reduction is slightly greater in the favourable pressure gradient case compared with the adverse pressure condition case. At zero pressure gradient, the present result of 8% reduction compares reasonably well with the
liS
previous results by Choi (1989), who obtained 10% reduction The mean velocity and turbulence intensity profiles in pressure gradient case were obtained using a cross-type hot has limited some measurements close to the wall surface. the turbulence statistics were obtained, however, using a sensor. Figures 5 and 6 show the velocity
very
close
skewness
to
at y +=18. the adverse wire, which The rest of single-wire
kurtosis of the u-component + wall surface (y 0
I
20~-~
o
J
j
10 y'
15
20
Kurtosis of the u-component velocity and the wall-skin friction in the favourable, zero and adverse pressure gradient cases.
sensors to measure the wall-skin friction fluctuation because of the heat conduction to the substrate. Positioning of hot-film sensors in the valleys of riblets may also have some effects on the turbulence statistics over the riblet surface. These should not, however, seriously affect the changes in these values due to pressure gradients. The effects of riblets on the turbulence statistics in the adverse pressure gradient case, the difference between riblet and smooth data in Figures 5 and 6, become smaller with y+ faster than the other two pressure gradient cases. This suggests that the effects of riblets on the higher order statistics of turbulence in the adverse pressure gradient case does not extend further away from the wall surface compared with the zero or favourable pressure gradient cases. Figures 7, 8 and 9 show the probability densities of the u-component velocity near the wall surface of the boundary layer as well as that of wall-skin
friction
(y+~O).
The
general
trends
of
the probability
117
Deviation
Figure 9
Figure 7 00
------------.---~-
dp/dx = 0 • Smooth 5urfac~
y'
I)
0
16
•
RlbI~t 5Urfac~
Probability densities of the u-component velocity and the wall-skin friction in the favourable (Figure 7) , zero (Figure 8) and adverse (Figure 9) pressure gradient cases. A circle symbol denotes smooth surface, a cross denotes riblet surface. Dashed line represents Gaussian probability density.
6
.is
E o
a:
oJ
r'
u,_~,,..
smooth
h=O.023mm
I>
1,2 >--- + h=O.033mm I>
h=O.OSlmm
+
I>
1>1>
+
1,1 I>
1,0
0
+ -'1]
+
•
I 0,9
0,63
0
0,67
+
;I-
0
~
• •• 0,71
[D
1/--
•
•
•
) 1= 0,75
Figure 7: Synthesis of drag measurements does not behaxe as smoothly as, for instance, on the cylinder. Nevertheless, one can end up with an average value, integrated all along the rib let model between 15% and 100% chord length. This value is not identical on both sides of the aerofoil : indeed, for a free-stream I\Iach number of 0.72, on the pressure (resp. suction) side, ht=0.7 (resp. 0.6) for a given groove height h=lflm. As these average values are rather close, a mean value of 0.6.5 per pm would characterize the riblet model, root of passive turbulent manipulation on both sides of the aerofoil. That mean value h~=0.65 is slightly modified by the variations of the free-stream Mach number. 2.2.3
Performances of grooved surfaces
For the reference configuration, the total drag coefficient of the aerofoil - Cd - covered with smooth ,·im·l sheet. has been determined as a function of the free-stream Mach number at a str~amwise abscissa located half-chord behind the trailing edge : Cd increases smoothly with 1\1 00 , Data concerning three grooved surfaces are plotted on figure 7 ; for each model, 7 surveys have been, at least, performed in order to scrutillize the whole free-stream Mach nurnber range. For h=2:3pm, drag reductions (:::::: -:3.:3%) are recorded; moreover, the level of reduction seems to be independant of 1'11'::0' On the other hand, for higher rib sizes drag increases have been obtained:::::: +1 % (resp. :::::: +10%) for h=33pm (resp. 51flm). 'vVithin the experimental ullcertainty, results given by the smaller rib let (17 pm) are almost identical to those provided with the model h=23/1m. For the model h=23pm, wake surveys have been carried out for an intermeelia le configuration: grooved surfaces on the pressure side between 15% anel 100% chord length and smooth film everywhere else. A decrease in the total drag coefficient was recorded:::::: -l.;,)%. That reduction is approximately half the one obtained with ribs on both sides of the aerofoil, which means that, besides the fact that the intensities of pressure gradients are different, the grooves behan> in a similar manner. In fact, this test was performed at the beginning of the campaign undertaken
133
[1
25
I
20
/:::,. Cd - (%) Cd
friction
15
--
over L
I
c
-
CAST 7 Cylinder Cylinder
~
10
------
V / V/
5 0
-
-5 -10
~
V
o
10
Jr V / / -B-
L-------'"
20
30
-
_h: -
40
SO
Figure 8: Synthesis of drag data (with and without pressure gradient) in the T2-wind tunneL As the level of recorded skin-friction reductions was relatively low, it was decided to cover not only the pressure side but also the suction one in order to increase the percentage of manipulated wetted area, and with that the drag variations_ From these preliminary results, it was tried to estimate the variations of the friction drag coefficient over the manipulated aerofoil surface, the percentage of which. towards the total wetted area, is close to 85%. Let us recall that boundary layer computations showed up that the contribution of the friction part in the total drag balance represented between 58% and 48% depending upon the ,-alue of the free-st ream :-1ach number. The variations of the friction drag coefficient. over L, are plot t eel on figure S versus h1;;, mean value of both integrated h-:: parameters e,-aluated along the manipulated surface on pressure and suction sides. Data are compared to those obtained on the cylinder; because of the scatter in this laUer experiment the upper and 10\\'er curves of the data domain are represented. R('sults obtained by lTlanipulating the turbulent boundary layer which develops on the CAST 7 aerofoil are plotted in the shape of rectangular boxes: the horizontal box side expresses the variation of h~ with 1\L;;v, when the vertical one denotes the slight dependency of drag varia tions \\'i tll 1\ I 0::' and the experimental scatter. The skin-friction drag variat ions brought about b.y the two smallest riblet models (2:3 and 33{Lm) are in agreement \\"ith those recorded on the cylinder without any pressure gradient. Howewr, the lewl of cl rag increase obtained from the deeper rib (51pm) is higher. This difference could be explained probably by a bad quality of the model surface finition or a cross-section non uniforlllity, since the other two models do not seem to show up a noticeable effect of pressure gradients on riblet performances. Thus, when grooved surfaces cover about 8-5% of the aerofoil wetted area, friction drag reclLlctiollS have been recorded [or ht :::; 20. 1\Iaximum total drag decrease of about 3.5% was obtained for the smaller rib hei~, which corresponds to maximum skin-friction reduction of almost 7.5 - 8% at h1;; close to 12 - 16. This result is obtained by assuming thai grooves do not modify the pressure drag but act only on the frictioll drag. For free-stream rvIach numbers less than the di\-ergence iV1ach
134
number, the average pressure gradient parameter estimated along the manipulated area, {J - Clauser parameter - for instance, is weak on the suction side since the local l\Jach number is almost constant over 35 - 40% chord length; on the pressure side, this parameter is stronger but still moderate. The performances of grooved surfaces under pressure gradient conditions have been investigated by some researchers in incompressible flows by Choi et ai, [8], Coustols, [9], Truong et ai, [23], in transonic flows by Squire et ai, [22] and also in flight by ?I1cLean et ai, [19]. The data collected from all these experiments seem to be consistent, though the drag variations were estimated through different measurement techniques. In summary, significant riblet data are available, for flows subject to adverse and/ or favourable pressure gradients, to suggest their drag reduction efficiencies as the pressure gradient is moderate, which is the case for most of the wing surface, where grooved surfaces might be applied. 2.2.4
Miscellaneous
For these experiments, the grooved surfaces were applied onto the trailing edge of the CAST 7 aerofoil. Then, depending upon the considered vinyl sheet, smooth ftlm or rib let one, the thickness of the aerofoil base val'ies from 0.2111111 (reference case) up to 0.282mm (h=0.0.51mm). Compared to the aerofoil covered with smooth film, changing the rib size from 2:3llm to 51pm would raise the base drag of about 25%. For the reference configuration, at 1\100=0.7, an estimate pointed out that the base drag accounts for a little bit more than 1 %. As in all these experiments, one is looking for small variations of the total drag coefficient, it would be better to keep constant the thickness of the trailing edge, so that, when manipulating the turbulent boundary layer, the only recorded changes ,\'attld be devoted to skin-friction reductions or increases. Of course, this remark is useful for small models in wind tunnel. but "'oldd be useless for aircraft applications.
3
Experhnents in the Sl-wind tunnel of Modane
Following the successful tests, as regards the efficiency of ribbed surfaces, either on an axisymmetric body for zero-pressure gradient flows or on an aerofoil, in transonic regime, further experiments were carried out at the ONERA/Modane Sl-wind tunnel in collaboration with Aerospatiale, [10], [l i l]. The area of the test section, the length of which is Um, is close to 40 m 2 .
3.1
Experimental apparatus
The model is a 1/11 th scale Airbus A:320 model, mounted on a straight sting, which is maintained through a tripod set-up. The considered model configuration has no fill and no horizontal tail. The fuselage length, I, is 3.416m and the mean aerodynamic chord length is 0.:381m. The experiments have been performed at ambient stagnation temperature (c:::: 300 K) at a stagnation pressure equal to the local atmospheric pressure (0.9 bar). The unit Reynolds number range is : .5 ..5 - 1l.8 10 6 . The free-stream ~\lach number varied from 0.:3 up io 0.82 ; this latter value corresponds to the configuration "fuselage
135
alone", for which the maximum Reynolds number based on the fuselage length is a pproximaiely equal to 40 10 6 . The angle of attack of the model could vary between _2° and +3°. Boundary layers were tripped on the fuselage and on the wings, using carborundum bands. Their locations had been defined by Aerospatiale during other sets of experiments performed with this specific Airbus model. Only one symmetric V-groove riblet, manufactured by the 31\11 Company in an adhesive backed film, with an aspect ratio of one, has been tested on the fuselage and wings. The knowledge of the flow field around the fuselage, obtained from the wingbody configuration, allowed us to perform boundary layer calculations, based upon the resolution of integral equations ; thus, for instance, at ]\1==0.7 and 0=3.7°, one could get the evolution of h~ along the upper and lower symmetric lines, the lateral mid-lines and so forth. It appeared that this quantity was not varying too much with either the streamwise abscissa or the peripheral co-ordinate; so, a mean \"alue - though it might change with the angle of attack and the free-stream 11ach number - would be representative of the rib let scale. Thus, in the case of ~roove depth of 0.02:3mm, for the rib let material set on the fuselage, an optimized h;;, value close to 8 - 0 was found at ~-Ioo =0. 7. 1Ieasuremenis have been performed for fuselage and \\"ing-body type arrangements. Several configurations have been considered: - Fuselage alone without riblets ; - Fuselage coyered with riblets ; - Wing-body configuration without riblets ; - Wing-body configuration with riblets set only on the fuselage; - Vving- body configuration covered with riblets. Along 1he wings, the grooves were approximately aligned with the external free-stream flow direction. No grooved surface was set in areas subject either to high geometric curvature (nose or tail cone) or to important streamline curvature (more than 1:5° from the ribs direction), i.e. wing-fuselage intersection, upper surface of the wing near the trailing edge, ... The corresponding percentage of wetted areas co\"ered with longitudinal grooves is approximately: - Fuselage alone: 7:3% ; - Wing- body configuration ,,·ith riblets set only upon the fuselage: 47o/c : - Wings and fairings: .57% ; - Wing-body configuration (fuselage, wings and fairings covered with riblets) : 66%.
3.2
Drag measurements and repeatability
The total forces, especially drag and moments, were measured through an internal six-component balance; the total drag coefficient, Cd, was obtained by taking into account the model reference surface (1.012m2). As the expected differences in the drag forces would be very small. the measurements consistancy was a t first checked by making a fel\" continuous sweeps in incidence for any cOllfigu~'ation and at different free-stream ?llach numbers. As shown on figure 9, an excellent repeatability on Cd measurements has been achieved, the scatter being: - for the fuselage-configuration, ~Cd < 0 ..5 10- 4 in 09% cases and < 0.:3 10- 4 in 0 1% cases ; - for the wiug-body configuration, ~Cd < 1.0 10- 4 in all cases and < 0.5 10- 4 in c
136
CL test
47-0.800 53 --- 0.800 63 ·-·0.800
2 1 (
0
-2
Mao 104 0.699 113 --- 0.700
73 ·······0.800
)
6C"x10' 2
Mo>
test
0,5
114·-·0.699 0,3 0,2 b)
-1
a)
0,1
-2
6C Dx10' ~
-2
0
2
Figure 0: Repeatability of drag measurements a) Fuselage configllration b) (cing-body configu ration 93% cases. As tbis repeatability is of excellent quality, it was witb confidence that the efficiency of grooved surfaces has been checked under very good conditions. Furthermore, let us point out that for both configurations, a rather good repeatability on a.ngle of attack measurements was recorded since < 0.010 in 00% cases. A dozen of pressure taps was inserted within the fuselage (sting cavity) allowing to check the homogeneity of these pressure measurements as well as their constancy during all tIle drag measurements.
c.a
3.3
Performances of grooved surfaces
For the fuselage configuration, the variations of the total drag coefficient are plotted. on figure 10, \'ersus the model angle of attack for three values of the free-stream ]Vlach number: O..j, 0.7 and O.S. Thus, a very positive effect in terms of drag reduction has been e\'idcnced, whatever the value of the angle of attack is, especially for large \'alues of :-1.::0' Indeed, at 1'1'1==0.7 and O.S, the total drag coefficient decrease is almost constant when the angle of attack, a, varies. For C\ corresponding to the Cl cruise value (Cl=0.5), nett drag reductions of 1.9%, :2.:3% and :2.'1% were recorded respectively for 1\100=0.5, 0.7 and O.S. The angle of attack corresponding to CI = 0.5 varies, of course, with the free-stream Mach number. \Vhen considering the wing-body configuration with riblets set only on the fuselage, nett drag reductions were also obtained at 1\L)()=0.5 and 0.7, for different Cl values lying lJctween 0.1 and 0.6. Furthermore, adding riblets on the wings and fairings allowed to get 10\\'er Cd values, than the ones corresponding to the preceding configuration. The nett reduction in Cd was 1.6% at 1\'1,:0=0.7 and at cruise level,
137
( 6 Cd
I
Cd )U:CI cruise
1.9 %
I
( 6 Cd Cd )0( CI cruise
2.3 %
'" = 0,7
'" = 0,8
2
2
-1
-1
-1
-2
-2
-2
o
o
t.Cd=Cd ribleC Cd smooth
figure 10: Synthesis of drag data (Fuselage configuration)
(~ Cd) Cd
= 1.2 %
Clcrulse
( ~CCdd)
= 1.6 %
Clcrulse
Cl '" = 0,5
0,5
'" = 0,7
0,5
0,4
0,4
0,3
0,3
0,2
0,2
0,1
0,1
t.Cd=Cd ribleC Cd smooth
Figure 11: Synthesis of drag data (Wing-body configllration)
138
with negligible changes in llCd over the Cl range: 0.1 - 0.6 (figure 11). Thus, at these explored free-stream Mach numbers, the benefit of covering wings with riblets was observed, though the percentage of grooved surface compared to the wing wet ted area was rather small (~ 57%). Moreover, though the grooves were aligned with the external free-stream velocity, the effect of behaviour of riblets in three-dimensional flows might be different from the influence of misalignment in hYodimensional flo,,-s. Indeed, the main difference comes from the feature that the yelocity vector varies very quickly in the wall vicinity; so, non negligible angle deflections exist over distances within the turbulent boundary layer as large as groo,-e depths. Let us mention that the performances of riblets are under investigation at CERT in three-dimensional flows: riblets are covering parts of the pressure and suction sides of an aerofoil, set at an angle of sweep close to that of an Airbus-type wing. \Vhate,-er configuration is concerned, it is rather difficult to guess a correct estima te of the skin friction reduction mainly because the sting caused pressure field modification and, consequently, drag interferences. Anyway, at i\L;,,=0.7 and at cruise level, though the model has no fin and no horizontal tail, if one assumes that friction represents about 50% of the total drag, the average nett skin-friction drag reduction, estimated m-er ille 66% manipulated wetted area, is close to 4.8.5%. This benefit is not certainly the highest one, because: - the percentage of wetted areas covered with ribbed surfaces was rather smalL especially on the wings due to boundary layer tripping; - on the fuselage, close to wing-body junction, the grooves had not been re-aligned because of streamline curvature. Compared to the fuselage configuration, tested at first. several strips of riblet film had only been taken off ; - the grom-es size had not been optimized on the wings; the same depth and geometry as the ones used on the fuselage were considered, mainly because of material availa bili ty. In spite of these observations, substantial drag gains have been recorded on the wing-body configuration. Furthermore, these results roughly agree with the friction drag gains measured under laboratory conditions, for instance with data obtained at CERT on either the cylinder or the CAST 7 aerofoil in the T2-wind tunnel.
4
Conclusions
All the experiments carried out under transonic conditions have alloweu to verify the efficiency of internal manipulators, riblets or grooved surfaces, for the purpose of reducing turbulent skin-friction drag. Thus, from different research groups, significant I'iblet data are now available to firmly establish the potential of such devices for drag reduction performances. It appears that maximum drag reduction is found \\' hen groow geometries, such as the height or the spanwise spacing is t}-pically of the order of 10 - 1;3 v JUT. Furthermore, experiments performed on a complete A320 model, in the Sl-wind tunneL showed up that important total drag coefficient reductions could be achieved, at cruise conditions. Since the fuselage Reynolds number reaches around 40 10 6 , it is expected that these results could be rather easily applied to practica.l flight test conditions where the Reynolds number is only increased by a factor :3. Although the mechanisms involved in such a drag reducing process have not,
139
yet, been understood, a couple of flight tests have already been performed with fuselage, wings, fin, horizontal tail and nacelles equipped with riblets. Some information concerning the flight tests, carried out by Airbus Industrie and its partners, as a consequence of the promising Sl-wind tunnel results, on the Airbus A320 N°1, could be found in [21]. Conscquently to these useful results obtained in transonic conditions, the next step would consist to look at the behaviour of grooved surfaces in supersonic regime. Indeed, for a Concorde-type aircraft, the friction drag represents about 30 - 35% of the total drag, which implies that improvement of aerodynamic performances of such supersonic planes could be achieved by friction drag reduction. To our knowledge, the only supersonic drag measurements of a riblet film were performed by Gaudet at a Mach number of 1.25, [18]. \Valsh et aI, [27], reported that the supersonic data falls within the transonic data band. Let us mention that experiments will be carried out at Ol'\ERA, under zero-pressure gradient conditions, for higher values of Mach numbers up to 2..5. Acknowledgements Financial support was provided by Airbus Industrie and the "Service Technique des Programmcs Aeronautiques". Special thanks are due to F. l\'larentic from 3?11-USA and A. Dcladwnal from 31\I-France, for providing us \yith all of the riblet material.
References [1] Archambaud J.P., Blanchard A., Seraudie A. : 11th Congress on Instrumentation in Aerospace Simulation Facilities - Stanford, (1985) [2] Arnal D. : V.K.I. Lecture Series - AGARD Report W 709 (1984) [3] Arnal D., Jelliti 1\-1. : CERT Internal Technical Report (1985) [4] Bacher E.V., Smith C.R. : AIAA Journal, Vol. 24, W8, pp. 1:382-138.5, (1986) [.5] Blackwelder R.F. : AIAA Paper 89-1009 (1989) [6] Bushnell D.l\1., IVlcGinley C.B. : Ann. Rev. Fluid 1\1ech., Vol. 21, pp. 1-20, (1989) [7] Choi K.S. : J. Fluid Mech., Vol. 208, pp. 417-458, (1989) [8] Choi K.S., Pearcey H.H., Savill A.M. : Int. Conf. on Turbulent Drag Reduction by Passive Means, London (1987) [9] Coustols E. : AIAA Paper 89-0963 (1989) [10] Coustols E. : 4th Int. Conf. on Drag Reduction, Davos (1989) [11] Coustols E., Gleyzes C., Schmitt V., Berrue P. : 24ieme Colloque AAAF Poit-iersFrance (1987) [12] Coustols E., Cousteix J. : 16th ICAS Congress, Jerusalem (1988) [n] Coustob E., Seraudie A., 1\Iignosi A, Breil J.F. : CERT Internal Technical Report (1988) [11] Coustols E., Savill. A.1\1. : Applied Scientific Research, Vol. 46, pp. 183-196, ( 1989) [1.5] Coustols E., Cousteix J. : 2nd IUTAM Symp., Zurich (1989) [16] Coustols E., Cousteix J. : 7th Symp. on Turb. Shear Flows, Stanford (1989) [17] Djenicli L., Liandrat J., Anselmet F., Fulachier 1. : 2nd European Turb. Conf. (1988)
140
[18] Gaudet L. : Applied Scientific Research, Vol. 46, pp. 245-25'1, (1989) [19] }\1cLean J.D., George-Falvy D.N., Sullivan P.P. : Int. Conf. on Turbulent Drag Reduction by Passive Means, London (1987) [20] Prudhomme S., Coustols E., Mignosi A., Dor J.B., Plazanet M. : CERT Internal Technical Report (1989) [21] Robert J.P. : to be published in that Proceedings Volume (1990) [22] Squire L.e., Savill A.~1.: Int. ConL on Turbulent Drag Reduction by Passi\"e !\leans, London (1987) [2:3] Truong T.Y., Pulvin P. : Applied Scientific Research, Yolo 46, pp. 217-227, (1989) [24] Walsh 1\1.3. : AIAA Paper 82-0169 (1982) [25] \\"alsh :\1.3., Lindeman A.IV!. : AIAA Paper 84-0:347, (1984) [26] Walsh :\1.3., Sellers III \V.L., McGinley C.B. : AlA A Paper 88-2.,)54, (1988) [27] 'Walsh 11.J., Anders J1'. J.B. : Applied Scientific Research, Yol. c16, pp. 2.5,')-262. ( 1989)
Effect of Riblets on either Fully Developed Boundary Layers or Internal Flows in Larninar Reghne J. LIANDRAT 1 , E. COUSTOLS 2 , L. DJEI'\IDIl, F. ANSELMET 1 , X. de SAINT-VICTOR2 , F. FIOC 2 & L. FULACHIER 1 1
2
Illstitut de Mecanique Statistique de la Turbulence, Unite Mixte [inivasite. CNRS I\'" 38033, Marseille, France; ONERA-CERT, Aerothernwdynamics Department. Toulouse. France.
SUMMARY - The present paper summarizes the status of the numerical research carried out both at OKERA/CERT and IMST, as regards the efficiency of internal manipulators, more commollly named by many researchers, riblets, in external as well as internal flows, under laminar conditions. First results obtained at CERT during preliminary studies will briefly be recalled. From a numerical point of view, many difficulties arose; most of them stemmed from the singularity at the riblet edge. First of all, results issued from different grid refinements will be presented. Then, emphasis will be put on analogies and differences between manipulated fully developed internal and external flows in the presence of either \'- or L-shaped riblets ; the latter corresponds in fact to half of a U-shaped groove. These theoretical studies showed up that the wetted area increase did not induce extra skin friction in laminar boundary layers over V- or L-shaped grooves.
1
Introduction
It is clear from various experiments, performed up to now in turbulent boundary layers, that l'iblets of suitable dimensions can reduce wall friction by about 6 - S% (see. for instance, Bushnell [:3], Coustols [.5] or Walsh et al [19]). In the case of internal turbulent flows there are much fe\ver experimental results but it seems from Liu et al (sec [:20]), Lowson et al [Ue] and Rohr et al [16], that similar reduction could exist. This reduced skin-friction seems indeed to be related to an increased stability of near-wall structures (i.e. Bacher and Smith [1], Choi [4]). But, what is the physic~l mechanism responsible for this stabilisation? By considering the most usual situation of Y-groO\'es with s=h, (s denotes the spacing between two adjacent grooves and h the rib depth), the wetted a.rea increase can be greater than 100%. If one considers that this specific increase tends to enhance skin friction, as pointed out experimentally by Pulles et al [1.5] and numerically by Launder et al [13], it is difficult to accept that turbulence Oll its own can compensate for and even overshoot this negative effect. Thus, it is reasonable to think that a purely viscons mechanism is involved and either entirely or partly counteracts this areil increase. This is the reason why an experimenlal study on laminar boundary layers o\,er triangular l'iblets has bee;! performed in the I.lVI.S.T water tunnel [11]. Results have shown that, over grooves 141
142
with s=2.3h, [10], [7], (32% wetted area increase) and riblets with s=l.2h (94 % wetted area increase, unpublished results so far), the overall skin friction is practically the same as that oyer the smooth wall: there is, thus, no straight relationship between skin friction a11(1 wetted area. In order to specify whether skin friction is slightly increased or eventually reducecL a numerical study has been undertaken at Il\lST, in the same conditions as in experiments, based on a code initially developed at CERT [6]. First results, obtained at IMST, [8], showed a small drag reduction of about 3%. although the grid mesh had to be refined in particular in the crest vicinity [9]. These calculations were ca.rried out over V-shaped riblets and the rectangular grid was not orthogonal to walls: this is, mainly, one of the reasons why computations over L-shaped grooyes have been pursued at CERT and performed using different grid refinements. \' evertheless, these first Il\JST results were in agreement with Kahn's ones, [12] : indeed, Kahn computed the boundary layer development over a V-groove riblet, s=2h, and reported a 17c reduction in laminar regime. As far as laminar internal flows are concerned, there seems to be only a single experiment
Reidy et 01 [17]
[16]
!::, Liu et 01
1.05
.2
•
Coustols
[18]
1.00
(.)
B
0.95
t~t~
~~
Low-speed film dolo
4% bond 0.90 0
10
s+
20
30
Figure 10: Low speed drag data for riblets: M.J. Walsh & J.B. Anders; [2] p. 256
172
1.1
1.0
,g
~
t
+
0.8
0 0.7 0
+ + +1
I I
•
•+
06~R • .~ + + +
Riblets
0.9
u
I.,
I".! .-;1 b 0 AI
.A
( a)
I I
+
.s :x1deltai .t
50
150
100
A
1.1
.. Riblets.,
AI
1.0
,g
g
OA ,I
IA ~!~AI
0.9
+
0.8
If 1+ + + + +1
u
Riblets ALP.32 ALB.32 ALR.32
A 0
Ii
I
0
A6A
•+
I'.i~ ++ +
+
+
Riblets ALP.48 ALB.48 ALR.48
(b)
0.7 0
50
S'
100
lfIdeltai
150
~
1.1
1.0
i
.A
c3
t
0
•+
0.9
.. Riblets
I I
"1 I
AA AOI IA 00 1 1
I •• : I I. Gl + +1
A 0
•+
AAA
~~8 •• +
+
Riblets ALP.75 ALB.75 ALR.75
(c)
+
0.8 -I-_~=;;;:;;;;;;;;;L---r_ _.--_...--~
o
t: ~deltai
50
100
150
Figure 11: Cf/Cfo vs fBi measurements: A riblets: • LEBU alone: + LEBU plus riblets: 0 LEBU alone (Preston tube) (a) h/oi = 0.32 (b) h/oi = 0.48 (c) h/oi = 0.75
List of referees
F. Anselmel (IMST - Marseille - FRANCE) D. Arnal (ONERAj CERT - Toulouse - FRANCE) A. Bertelrud (FFA Aeronautical Reseal'ch Institute, Bromma, SWEDEN High Technology Corporation, Hampton, VA, USA) J.P. Bonnet (CEAT - Poitiers - FRANCE) D.t.L Bushnell (NASA Langley - Hampton, VA - USA) KoS. Choi (BMT - Middlesex - UK) D.G. Clark (Queen Mary College - London - me) J. Cousteix (ONERAjCERT - Toulouse - FRANCE) E. Coustols (ONERAj CERT - Toulouse - FRANCE) L. Djenidi (University of Cambridge - Cambridge - UK) R. Friedrich (Technische Univel'sitiit Miinchen - Miinchen - RFA) L. Fulachier (IMST - Marseille - FRANCE) 1. Gaudet (RAE - Bedford - UK) S. Gavrilakis (EPFL - Lausanne - SWITZERLAND) H. Klein (Tcchnische Universitiit Miinchen - Miincl~en - RFA) B.E. Launder (UMIST - Manchester - UK) J. Lemay (Laval University - Quebec - CANADA) J. Liandrat (IMST - Marseille - FRANCE) T. ~Iarkham (BAE Filton - Bristol - UK) H. Leijdens (Tcchnical University of Delft - Delft - THE NETHERLkVDS) V.D. Nguyen (Laval University, Laval, QUEBEC - National Research Council, Ottawa, ONTARIO - CANADA) K.K. Prasad (Technical University of Eindhoven - Eindhoven - THE NETHERLANDS) A.l'.I. Savill (University of Cambridge - Cambridge - UK) V. Schmitt (ONERAj Chatillon - Paris - FRANCE) L.C. Squire (University of Cambridge - Cambridge - UK) C. Tenaud (CEAT - Poitiel's - FRANCE) T.V. Truong (EPFL - Lausanne - STYITZERLAND) t.U. Walsh (NASA Langley - Hampton, E4 - USA)
173
Mechanics From 1990, books on the subject of mechanics will be published under two series. FLUID MECHANICS AND ITS APPLICATIONS
Series Editor: R. Moreau Aims and Scope of the Series The purpose of this series is to focus on subjects in which fluid mechanics plays a fundamental role. As well as the more traditional applications of aeronautics, hydraulics, heat and mass transfer etc., books will be published dealing with topics which are currently in a state of rapid development, such as turbulence, suspensions and multiphase fluids, super and hypersonic flows and numerical modelling techniques, It is a widely held view that it is the interdisciplinary subjects that will receive intense scientific attention, bringing them to the forefront of technological advancement. Fluids have the ability to transport matter and its properties as well as transmit force, therefore fluid mechanics is a subject that is particularly open to cross fertilisation with other sciences and disciplines of engineering, The subject of fluid mechanics will be highly relevant in domains such as chemical, metallurgical, biological and ecological engineering. This series is particularly open to such new multidisciplinary domains. M. Lesieur: TlIrblllence ill FllIids. 2nd rev. ed .. 1990
1. 2.
:vI. Lesieur and O. Metais (eds.): TlIrblllence alld Coherent S!rIlclllres. 1990
ISBN 0-7923-0645-7
3. 4.
R. :-'Ioreau: Magnetohydrodynamics. 1990 E. Coustols (ed.): TlIrbulence Control by Passive Means. 1990
ISBN 0-7923-0646-5 ISBN 0-7923-0937-5 ISBN 0-7923-1020-9
SOLID MECHANICS AND ITS APPLICATIONS Series Editor: G.M.L. Gladwell Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How mIlch? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies; vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity. plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. 1. 2.
R.T. Haftka, Z. GUrdel and M.P. Kamal: Elements of StrIlclllral Optimi:ation. 2nd rev.ed., 1990 ISBN 0-7923-0608-2 J.J. Kalker: Threedimel1siol1ai Elastic Bodies. 1990 ISBN 0-7923-0712-7
Kluwer Academic Publishers - Dordrecht / Boston / London
Mechanics 3. E.B. Magrab: Vibrations of Elastic Structural Members. 1979 ISBN 90-286-0207-0 4. R.T. Haftka and M.P. Kamat: Elements of Structural Optimization. 1985 Revised and enlarged edition see under Solid Mechanics and Its Applications. Volume 1
5. J.R. Vinson and R.L. Sierakowski: The Behavior of Structures Composed of Composite Materials. 1986 ISBN Hb 90-247-3125-9; Pb 90-247-3578-5 6. B.E. Gatewood: Virtual Principles in Aircraft Structures. Volume 1: Analysis. 1989 ISBN 90-247-3754-0 7. B.E. Gatewood: Virtual Principles in Aircraft Structures. Volume 2: Design, Plates, Finite Elements. 1989 ISBN 90-247-3755-9 Set (Gatewood 1 + 2) ISBN 90-247-3753-2 MECHANICS OF ELASTIC AND INELASTIC SOLIDS Editors: S. Nemat-Nasser and G.iE. Oravas 1. G.M.L. Gladwell: Contact Problems in the Classical Theory of Elasticity. 1980 ISBN Hb 90-286-0440-5; Pb 90-286-0760-9 2. G. Wempner: Mechanics of Solids with Applications to Thin Bodies. 1981 ISBN 90-286-0880-X 3. T. Mura: Micromechanics of Defects in Solids. 2nd revised edition, 1987 ISBN 90-247-3343-X 4. R.G. Payton: Elastic Wave Propagation in Transversely Isotropic Media. 1983 ISBN 90-247-2843-6 5. S. Nemat-Nasser, H. Abe and S. Hirakawa (eds.): Hydraulic Fracturing and Geothermal Energy. 1983 ISBN 90-247-2855-X 6. S. Nemat-Nasser, R.J. Asaro and G.A. Hegemier (eds.): Theoretical Foundation for Large-scale Computations of Nonlinear Material Behavior. 1984 ISBN 90-247-3092-9 ISBN 90-247-3660-9 7. N. Cristescu: Rock Rheology. 1988 8. G.I.N. Rozvany: Structural Design via Optimality Criteria. The Prager Approach to Structural Optimization. 1989 ISBN 90-247-3613-7 MECHANICS OF SURFACE STRUCTURES Editors: W.A. Nash and G.iE. Oravas 1. P. Seide: Small Elastic Deformations of Thin Shells. 1975 ISBN 90-286-0064-7 ISBN 90-286-0104-X 2. V. Pane: Theories of Elastic Plates. 1975 3. J.L. Nowinski: Theory ofThermoelasticity with Applications. 1978 ISBN 90-286-0457-X ISBN 90-286-0047-7 4. S. Lukasiewicz: Local Loads in Plates and Shells. 1979 5. C. Firt: Statics, Formfinding and Dynamics of Air-supported Membrane Structures. 1983 ISBN 90-247-2672-7 6. Y. Kai-yuan (ed.): Progress in Applied Mechanics. The Chien Wei-zang Anniversary Volume. 1987 ISBN 90-247-3249-2 ISBN 90-247-3367-7 7. R. Negruriu: Elastic Analysis of Slab Structures. 1987 8. J.R. Vinson: The Behavior of Thin Walled Structures. Beams, Plates, and Shells. 1988 ISBN Hb 90-247-3663-3; Pb 90-247-3664-1
Mechanics MECHANICS OF FLUIDS AND TRANSPORT PROCESSES Editors: R.I. Moreau and G.1E. Oravas I. I. Happel and H. Brenner: Low Reynolds Number Hydrodynamics. With Special
2. 3. 4. 5. 6. 7.
8. 9. 10.
Applications to Particular Media. 1983 ISBN Hb 90-01-37115-9; Pb 90-247-2877-0 ISBN 90-247-2687-5 S. Zahorski: Mechanics of Viscoelastic Fluids. 1982 I.A. Sparenberg: Elements of Hydrodynamics Propulsion. 1984 ISBN 90-247-2871-1 B.K. Shivamoggi: Theoretical Fluid Dynamics. 1984 ISBN 90-247-2999-8 R. Timman. A.I. Hermans and G.c. Hsiao: Water Waves and Ship Hydrodynamics. An Introduction. 1985 ISBN 90-247-3218-2 M. Lesieur: Tllrbulence in Fluids. Stochastic and Numerical Modelling. 1987 ISBN 90-247-3470-3 L.A. Lliboutry: Very Slow Flows of Solids. Basics of Modeling in Geodynamics and Glaciology. 1987 ISBN 90-247-3482-7 B.K. Shivamoggi: Introduction to Nonlinear Fluid-Plasma Waves. 1988 ISBN 90-247-3662-5 V. Bojarevics. Ya. Freibergs, E.I. Shilova and E.V. Shcherbinin: Electrically Indllced Vortical Flows. 1989 ISBN 90-247-3712-5 I. Lielpeteris and R. Moreau (eds.): Liquid Metal Magnetohydrodynamics. 1989 ISBN 0-7923-0344-X
MECHANICS OF ELASTIC STABILITY Editors: H. Leipholz and G.1E. Oravas ISBN 90-286-0193-7 1. H. Leipholz: Theory of Elasticity. 1974 2. L. Librescu: Elastostatics and Kinetics of Aniosotropic and Heterogeneous Shell-type ISBN 90-286-0035-3 Stmctures. 1975 3. c.L. Dym: Stability Theory and Its Applications to Structural Mechanics. 1974 ISBN 90-286-0094-9 4. K. Huseyin: Nonlinear Theory of Elastic Stability. 1975 ISBN 90-286-0344-1 5. H. Leipholz: Direct Variational Methods and Eigenvalue Problems ill Engineering. 1977 ISBN 90-286-0106-6 6. K. Huseyin: Vibrations alld Stability of Militiple Parameter Systems. 1978 ISBN 90-286-0136-8 ISBN 90-286-0050-7 7. H. Leipholz: Stability of Elastic Systems. 1980 8. V.V. Bolotin: Random Vibrations of Elastic Systems. 1984 ISBN 90-247-2981-5 ISBN 90-247-3099-6 9. D. Bushnell: Computerized Buckling Analysis of Shells. 1985 10. L.M. Kachanov: Introduction to Continuum Damage Mechanics. 1986 ISBN 90-247-3319-7 11. H.H.E. Leipholz and M. Abdel-Rohman: Control of Structures. 1986 ISBN 90-247-3321-9 12. H.E. Lindberg and A.L. Florence: Dynamic Pulse Bucklillg. Theory and Experiment. 1987 ISBN 90-247-3566-1 13. A. Gajewski and M. Zyczkowski: Optimal Stl"llctllral Design IInder Stability Constraints. 1988 ISBN 90-247-3612-9
Mechanics MECHANICS: ANALYSIS Editors: V.J. Mizel and G.fE. Oravas 1. M.A. Krasnoselskii, P.P. Zabreiko, E.L Pustylnik and P.E. Sbolevskii: Integral ISBN 90-286-0294-1 Operators in Spaces of Sllmmable Functions. 1976 2. V.V. Ivanov: The Theory of Approximate Methods and Their Application to the ISBN 90-286-0036-1 Numerical Solution of Singular Integral Equations. 1976 3. A. Kufner, O. John and S. Pucfk: Function Spaces. 1977 ISBN 90-286-0015-9 4. S.G. Mikhlin: Approximation on a Rectangular Grid. With Application to Finite Element Methods and Other Problems. 1979 ISBN 90-286-0008-6 5. D.G.B. Edelen: Isol'ector Methods for Equations of Balance. With Programs for Computer Assistance in Operator Calculations and an Exposition of Practical Topics of the Exterior Calculus. 1980 ISBN 90-286-0420-0 6. R.S. Anderssen, F.R. de Hoog and M.A. Lukas (eds.): The Application and Numerical ISBN 90-286-0450-2 Soillfion of Integral Equations. 1980 7. R.Z. Has'minskil: Stochastic Stability of Differential Equations. 1980 ISBN 90-286-0100-7 8. A.I. Vol'pert and S.L Hudjaev: Analysis in Classes of Discontinuous Functions and ISBN 90-247-3109-7 Eqllations of Mathematical Physics. 1985 9. A. Georgescu: Hydrodynamic Stability Theory. 1985 ISBN 90-247-3120-8 10. W. Noll: Finite-dimensional Spaces. Algebra, Geometry and Analysis. Volume 1. 1987 ISBN Hb 90-247-3581-5; Pb 90-247-3582-3
MECHANICS: COMPUTATIONAL MECHANICS Editors: M. Stem and G.fE. Oravas I. T.A. Cruse: Boundary Element Analysis in Computational Fractllre Mechanics. 1988 ISBN 90-247-3614-5 MECHANICS: GENESIS AND METHOD Editor: G.fE. Oravas 1. P.-M.-M. Duhem: The Evolution of Mechanics. 1980
ISBN 90-286-0688-2
MECHANICS OF CONTINUA Editors: W.O. Williams and G.fE. Oravas 1. c.-C. Wang and C. Truesdell: Introduction to Rational Elasticity. 1973 ISBN 90-01-93710-1 2. P.l. Chen: Selected Topics ill Wave Propagation. 1976 ISBN 90-286-0515-0 3. P. Villaggio: Qualitative Methods in Elasticity. 1977 ISBN 90-286-0007-8
Mechanics MECHANICS OF FRACTURE Editors: G.c. Sih 1. G.C. Sih (ed.): Methods of Analysis and Solutions of Crack Problems. 1973 ISBN 90-01-79860-8 2. M.K. Kassir and G.C. Sih (eds.): Three-dimensional Crack Problems. A New Solution of Crack Solutions in Three-dimensional Elasticity. 1975 ISBN 90-286-0414-6 ISBN 90-286-0146-5 3. G.c. Sih (ed.): Plates and Shells with Cracks. 1977 4. G.c. Sih (ed.): Elastodynamic Crack Problems. 1977 ISBN 90-286-0156-2 5. G.c. Sih (ed.): Stress Analysis of Notch Problems. Stress Solutions to a Variety of Notch Geometries used in Engineering Design. 1978 ISBN 90-286-0166-X 6. G.c. Sih and E.P. Chen (eds.): Cracks in Composite Materials. A Compilation of Stress ISBN 90-247-2559-3 Solutions for Composite System with Cracks. 1981 7. G.c. Sih (ed.): Experimental Evaluation of Stress Concentration and Intensity Factors. Useful Methods and Solutions to Experimentalists in Fracture Mechanics. 1981 ISBN 90-247-2558-5 MECHANICS OF PLASTIC SOLIDS Editors: J. Schroeder and G.1E. Oravas 1. A. Sawczuk (ed.): Foundations of Plasticity. 1973 ISBN 90-01-77570-5 2. A. Sawczuk (ed.): Problems of Plasticity. 1974 ISBN 90-286-0233-X 3. W. Szczepitiski: Introduction to the Mechanics of Plastic Forming of Metals. 1979 ISBN 90-286-0126-0 4. D.A. Gokhfeld and O.F. Chemiavsky: Limit Analysis of Structures at Thermal Cycling. 1980 ISBN 90-286-0455-3 ISBN 90-247-2777-4 5. N. Cristescu and 1. Suliciu: Viscoplasticity. 1982
Kluwer Academic Publishers - Dordrecht / Boston / London
Mechanics From 1990, books on the subject of mechanics will be published under two series: FLUID MECHANICS AND ITS APPLICATIONS Series Editor: R.J. Moreau SOLID MECHANICS AND ITS APPLICATIONS Series Editor: G.M.L. Gladwell Prior to 1990, the books listed below were published in the respective series indicated below. MECHANICS: DYNAMICAL SYSTEMS Editors: L. Meirovitch and G ..tE. Oravas 1. E.H. Dowell: Aeroelasticity of Plates and Shells. 1975 ISBN 90-286-0404-9 2. D.G.B. Edelen: Lagrangian Mechanics of Nonconservative Nonholonomic Systems. 1977 ISBN 90-286-0077-9 3. J.L. Junkins: An Introduction to Optimal Estimation of Dynamical Systems. 1978 ISBN 90-286-0067-1 4. E.H. Dowell (ed.), H.C. Curtiss Jr., R.H. Scanlan and F. Sisto: A Modern Course in Aeroelasticity. Revised and enlarged edition see under Volume 11 5. L. Meirovitch: Computational Methods in Structural Dynamics. 1980 ISBN 90-286-0580-0 6. B. Skalmierski and A. Tylikowski: Stochastic Processes in Dynamics. Revised and enlarged translation. 1982 ISBN 90-247-2686-7 7. P.C. Miiller and W.O. Schiehlen: Linear Vibrations. A Theoretical Treatment of Multidegree-of-freedom Vibrating Systems. 1985 ISBN 90-247-2983-1 8. Gh. Buzdugan, E. Mihililescu and M. Rade§: Vibration Measurement. 1986 ISBN 90-247-3111-9 ISBN 90-247-3408-8 9. G.M.L. Gladwell: Inverse Problems in Vibration. 1987 10. G.!. Schueller and M. Shinozuka: Stochastic Methods in Structural Dynamics. 1987 ISBN 90-247-3611-0 11. E.H. Dowell (ed.), H.C. Curtiss Jr., R.H. Scanlan and F. Sisto: A Modern Course in Aeroelasticity. Second revised and enlarged edition (of Volume 4). 1989 ISBN Hb 0-7923-0062-9; Pb 0-7923-0185-4 12. W. Szempliriska-Stupnicka: The Behavior of Nonlinear Vibrating Systems. Volume I: Fundamental Concepts and Methods: Applications to Single-Degree-of-Freedom Systems. 1990 ISBN 0-7923-0368-7 13. W. Szempliriska-Stupnicka: The Behavior of Nonlinear Vibrating Systems. Volume II: Advanced Concepts and Applications to Multi-Degree-of-Freedom Systems. 1990 ISBN 0-7923-0369-5 Set ISBN (Vols. 12-13) 0-7923-0370-9 MECHANICS OF STRUCTURAL SYSTEMS Editors: J.S. Przemieniecki and G ..tE. Oravas 1. L. Fryba: Vibration of Solids and Structures under Moving Loads. 1970 ISBN 90-01-32420-2 ISBN 90-286-0086-8 2. K. Marguerre and K. Wolfel: Mechanics of Vibration. 1979
