Numerical study of hydrofoil boundary layers

Ocean Engng, Vol. 22. No. 1, pp. 87-95. 1995 Copyright 0 1994 Ekvier Science Lfd Printed in Great Britain. All rights reserved 0029%8018/95 $7.cm + .oa

Pergamon

TECHNICAL NUMERICAL

STUDY

NOTE

OF HYDROFOIL LAYERS

R. Baubeau*

BOUNDARY

and R. Latorret

*Bassin d’Essais des Carenes, Paris, France; tSchoo1 of Naval Architecture and Marine Engineering, 911 Engineering Building, University of New Orleans, New Orleans LO 70148, U.S.A. Abstract-This paper presents the results of numerical boundary layer calculations for the RAE 101 foil section. The positioned boundary layer laminar-turbulent transition, surface pressure distribution are shown to be in good agreement with experimental wind tunnel measurements at chord Reynolds number of 1.6 x 106. The measured and calculated displacement boundary layer thickness and momentum thickness are shown to be in good agreement for the suction side of the RAE 101 foil.

NOMENCLATURE b c z H32 &

t V X

Y Y’ a a, 6 61 w v

span of foil

chord length of foil pressure coefficient shape factor H = i32/81 second shape factor HJ203/e Reynolds number F foil thickness velocity location along chord offset of foil offset of foil with boundary layer angle-of-attack effective angle-of-attack boundary layer thickness at lJ = 0.999 V boundary layer displacement thickness boundary layer momentum thickness kinematic viscosity

Subscripts

r

upper surface lower surface

1.

INTRODUCTION

In earlier studies, Baubeau and Latorre (1986, 1987, 1990) compared the measured and calculated locations of the laminar-turbulent boundary layer transition loction on NACA 16-012 and NACA 4412 hydrofoil sections. They showed the need for using the correct surface pressure distribution in the boundary layer calculations (Baubeau, 87

R. Baubeau and R. Latorre

88

1987, 1990). This correction involves performing the calculations at an effective angleof-attack (Y, to reflect the growth of the boundary layer 6 as well as the blockage from the upper and lower test section walls separation distance h to foil chord h/c ratio. While it was possible to compare the calculation results with those obtained from the NASA program [ Eppler (1980)], there was no direct boundary layer measurements on the NACA 16-012 and NACA 4412 foil sections. This paper addresses this verification by comparing the calculated and measured pressure distribution and boundary layer thickness 6, displacement 6* and momentum thicknesses 0 for the RAE 101 foil (Fig. 1). Brebner and Bagley (1952) performed extensive measurements on a RAE 101 foil with 0.762 m chord tested in the 3.5 m high X 2.6 m wide wind tunnel (No. 2 wind tunnel Aircraft Establishment). The foil was made of wood with an accuracy of 20.003 c. Surface pressure taps (0.8 mm diameter) were drilled 0.05 m either side of the foil centerline. By staggering the taps, 26 chordwise measuring points were arranged on the pressure and suction side of the foil. The boundary layer on the foil section midway between the rows of pressure holes was traversed perpendicular to the chord-line by a pitot tube mounted on a movable gantry. The reported error in the velocity and surface pressure was within ~0.5%. The traversing mechanism was electrically driven and the distance from the pitot tube to the foil surface was within 1 mm. The pitot tube has a flattened square cut nose measuring 5 x 10 mm, so the center of the pitot tube did not approach nearer than 0.0003 c of the foil surface. The tests were made at 30.48 m/set corresponding to a chord Reynolds numb.er of 1.6 x 106. The position of the boundary layer transition was visualized using the liquid film evaporation technique. The coordinates of the RAE 101 foil are summarized in the Appendix. 2.

CALCULATION

OF PRESSURE

DISTRIBUTION

AND

BOUNDARY

LAYER

The boundary layer calculations were made using the CERT boundary layer program developed at the Centre d’Etudes et de Recherches de 1’Ecole Nationale Superieure de I’Aeronautique et de 1’Espace a Toulouse (CERT). The details of the program are summarized in Arnal (1980, 1081) and Baubeau (1986). In contrast to the earlier calculations [Baubeau (1987, 1990)], the present calculations were made without adopting the measured pressure distribution C,(x/c). The present set of calculations were made with the offsets from Table Al (Appendix), which were corrected by adding the displacement boundary layer thickness S, calculated in earlier iterations to the physical foil offsets and recalculating the foil boundary layer: Y’WC)

= Y(XlC> + (hr

RAE

101

+ w(X/c)

FOIL

SECTION

Fig. 1. Profile of RAE 101 Foil (Riegels, 1961) tic = 0.10 (Offsets in Table Al)

(1)

Technical

(Y, = (a,

+

Note

89

Aa).

(2)

In the case of the relatively thin (t/c = 0.10) and symmetrical RAE 101 hydrofoil, the calculations quietly converged by the third iteration; the calculated boundary layer values were unchanged. Therefore the validation includes: 1. Comparison of the measured and calculated pressure distributions C,(xlc). 2. Comparison of the measured and calculated boundary layer thickness Zil and momentum thickness &, 8. This validation 3.

is summarized

COMPARISON

The measured

in the next section.

OF CALCULATED AND MEASURED DISTRIBUTIONS

and calculated

pressure

coefficient

C, is defined

PRESSURE

by

p - PO c, = 1/2pv2

(3)

and is plotted in Figs 2-4 as a function of the chord length x/c for (Y = 0, 4.09 and 8.17”. The comparison in Fig. 2 shows excellent agreement between the calculated and measured pressure distribution for (Y = 0”. The numerical results are within &2% of the expected values. This excellent agreement is also shown in Fig. 3 for (Y = 4.09 and in Fig. 4 for a = 8.17”. The CERT predicted the transition. This is further confirmed by the good agreement in the calculated and measured boundary layer thickness and transition location.

PRESSURE COEFF: Cp COMPARISON RAE 101 Suction Side ODeg Rn = 1.6 x106 ~ KEY . Exp.

-04 CP

-

Cal

-02

0.L

0

Fig. 2. Comparison

0.2 of RAE

0.4 101 pressure

06 coefficient.

__

08

x/c

.^ 1u

a = 0”. R, = 1.6

x

106.

R.

90

Baubeau and R. Latorre

PRESSURE COEFFCOMPARISION RAE101 4.09Deg Rn= 16~10~

Fig. 3. Comparison

of RAE

101 pressure

coefficient.

1

u = 4.09”. R, = 1.6 X loh.

-0.8 CP -06 l

0.4

Fig. 4. Comparison

4.

COMPARISON

0

of RAE

02

04

101 pressure

06 coefficient.

EXP

08 x/c 10 a = 8.18”. R, = 1.6

OF CALCULATIONS AND MEASURED LAYER AND TRANSITION

x

lob.

BOUNDARY

Numerical calculations were made for the suction side transition location, as well as the displacement boundary layer thickness 6,/c and shape factor HI2 = S,/&. Figure 5 shows the location of the laminar-turbulent boundary layer transition measured using the liquid film evaporation technique. In the case of the transition location at (Y = o”,

Technical

91

Note

TRANSITION x/, RAE 101 Rn:1.6x106 ’

Fig. 5. Comparison

of RAE

EXP

0

02

0.L

0.6

x,+

1.O

0

02

0.L

0.6

x/~

1.0

101 location

of boundary

layer transition

location

XIC

the experimental results show the transition location at R, = 1.6 X lo6 is at x/c = 0.6 and at R, = 3.2 x lo6 it moves forward to x/c = 0.5. This follows the results of earlier calculations for the NACA 4412 and 16-012 foils [Baubeau and Latorre (1986, 1990)]. The comparison in Fig. 5 shows good agreement between the calculated location of transition and the measured values. This reflects the use of the correct foil surface pressure distribution in the numerical calculations. The displacement thickness 8,/c and the shape factor Hi2 = IS,/& obtained by the integration of the RAE 101 foil suction side surface velocity measurements are summarized in Table 1 for R, = 1.6 X 106. The corresponding calculated RAE 101 foil suction side calculated boundary layer values are also summarized in Table 1 and shown in Figs 6-8. Examining Table 1 and Figs 6-8, it becomes evident that there is excellent agreement in the displacement thickness 6i/c and shape factor Hi2 = 6i& when the comparisons are made in regions after the end of the boundary layer transition. In the case of the measured values at x/c = 0.3 and 0.4 at OL= o”, poor agreement is shown. This discrepancy is due to the presence of the laminar separation which occurs near the foil’s leading edge. The presence of laminar separation near the foil’s leading edge at small angles-of-attack and low Reynolds number has been cited in earlier comparisons (Caat, 1974; Huang, 1976) as a scaling problem which has been difficult to account for in extrapolating model measurements to full scale. This reviews an area for further numerical and experimental research. 5.

CONCLUDING

REMARKS

This paper has presented the calculated results of the RAE 101 foil pressure distribution, as well as the location of the laminar-turbulent boundary layer transition. The comparison of these results with the experimental measurements of Brebner and Bagley (1952) supports the following conclusions:

92

R. Baubeau

Table

1. Comparison

of measured

and calculated

and R. Latorre boundary

layer thickness

0

Angle-of-attack

x/c

side of RAE

101

X.18”

4.09”

Measured

Calculated

Measured

Calculated

Measured

Calculated

0.000111 0.00156 0.00255 0.00343 0.00451 0.00520 0.00661

0.00185 0.00257 0.00480 0.00669 0.00850 0.01105 0.01396

0.00190 0.00258 0.00464 0.00624 0.00774 0.00965 0.0137

1.42 1.46 1.62 1.66 1.73 1.98 1.93

1.414 1.487 1.523 1.555 1.595 1.679 1.928

6,lc

0.3 0.4 0.678 0.795 0.895 0.951 1.00

0.00045 0.00071 0.00103 0.00150 0.00189 0.00218 0.00266

0.00068 0.00098 0.0011 0.00145 0.00186 0.00223 0.00260

0.00078 0.00124 0.00266 0.00355 0.00456 0.00525 0.00731

%&

0.3 0.4 0.628 0.755 0.899 0.951 1.000

1.82 2.03 1.87 1.43 1.37 1.34 1.22

2.603 2.971 1.469 1.426 1.419 1.435 1.458

1.32 1.35 1.5x 1.50 1.54 1.57 1.59

6

RAE101

%

C CC3 r

Fig. 6. Comparison

for suction

of RAE

a=CDeg

1.438 1.445 1.455 1.463

1.478 1.510 1.581

Rn=16x106

KEY

101 suction

side boundary

layer displacement

H,, = 6,/S,. a = O",R, =

thickness

6,/c and shape

factor

1.6 x 10h.

The inclusion of the displacement thickness 6, in the RAE 101 foil calculations results in excellent agreement with surface pressure measurements. The RAE 101 laminar-turbulent boundary layer transition location calculation at R, = 1.6 x lo6 and 3.2 X lo6 shows excellent agreement with the measured transition location x/c. The RAE 101 suction side boundary layer calculations for the displacement thickness overall agreement. The only 6,/c and shape factor HI2 = i5,& show excellent discrepancy appears in the laminar region of the foil at a = 0” and R, = 1.6 X 10h. With this validation it is clear that the CERT boundary in Baubeau and Latorre (1986, 1987, 1990) can provide

layer calculation reported good estimates of the x/c

Technical

RAE101

ar4.09 Deg

93

Note

Rn=1.6x106

o~~~~~,?,::~.~~~~~:o~

r

1

Fig. 7. Comparison

0 0 00 0 0 90 ~1~1~"~~"',1,"1'J 025 0

of RAE

of RAE

05

x/c

05

025

10

0 0.0.000. 075

x/c

075

1.0

thickness

x,c

authors

layer transition, iSI&. are grateful

6,/c and shape

factor

6,/c and shape

factor

thickness

6,/c

10

101 suction side boundary layer displacement thickness H,, = Z&/6,, a = 8.18”, R, = 1.6 x 10h.

location of the boundary and momentum thickness Acknow[edgemenfs-The

0 0 do

075

101 suction side boundary layer displacement H,, = 6,iS,, Q = 4.09",R, = 1.6 x 10”.

0

Fig. 8. Comparison

0.5

025

/0

as well as the displacement

to Mrs M. Latapie

for typing

this manuscript.

REFERENCES Arnal, D., Habiballah, M. and Del Court, V. 1980. Synthese sur les Methodes de Calcul de la Transition Developees au DERAT. CERT Rapport Technique OA No. 11/5018 AYD, Toulouse, France. Amal, D. 1981. Calcul par une Methode Intergrale des Couches Limites Laminaires et Turbulentes. Office National d’Etudes et de Recherches Aerospatiales, Chatillon, France. Baubeau, R. and Latorre, R. 1986. Numerical study of the boundary-layer transition for two-dimensional NACA 16-012 and 4412 hydrofoil sections. J. Ship Res. 30, 43-50. Baubeau, R. and Latorre, R. 1987. Technique for predicting the influence of walls on the boundary layer on two-dimensional foils. ASME International Symposium on Cavifation Research Facilities and Techniques, FED Vol. 57, pp. 169-173. Baubeau, R. and Latorre, R. 1990. Numerical study of the wall influence on the boundary layer transition for two-dimension1 NACA 16-012 and 4412 hydrofoil sections. J. Ship Res. 34, 38-47. Brebner, G.G. and Bagley, J.A. 1952. Pressure and boundary-layer measurements on a two-dimensional wing at low speed. RAE Report and Memoranda No. 2886.

94

R. Baubeau

and R. Latorre

Casey, M.V. 1974. The inception of attached cavitation from laminary separation bubbles on hydrofoils. Proceedings of the Institute of Mechanical Engineers conference on Cavitation, Edinburgh, p. 160. Huang, T.T. and Peterson, F.B. 1976. Influence of viscous effects on model full scale cavitation scaling. J. Ship Res. 20, 215-233. Riegels, F.W. 1961. Aerofoil Sections (p. 159). Butterworths, London. APPENDIX Table Al summarizes

the RAE

101 coordinates

(Riegels,

1961) (tic = 0.10)

95

Technical Note

Table Al. Coordinates of RAE 101 symmetrical foil section (Riegals 1961). Body and tail

Nose section XIL 0.0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.0075 0.008 0.009 0.02 0.023 0.0235 0.024 0.026 0.028 0.02 0.025 0.03 0.035 0.04 0.05 0.06 0.07 0.075 0.08 0.09 0.1 0.12 0.14 0.15 0.16 0.18 0.2 0.22 0.24 0.25 0.26 0.28 0.3 0.32 0.34

lWY

XIL

lWY

0.0 0.3905 0.5518 0.6753 0.7792 0.8705 1.9529 1.0285 1.0642 1.0987 1.1644 1.2265 1.3416 1.3687 1.4469 1.5445 1.6357 1.7215 1.9174 2.0924 2.2513 2.3974 2.6593 2.8898 3.0959 3.1913 3.2822 3.4519 3.6073 3.8820 4.1162 4.2202 4.3163 4.4867 4.6304 4.7496 4.8455 4.8851 4.9190 4.9700 4.9969 4.9956 4.9724

0.35 0.36 0.38 0.4 0.42 0.44 0.45 0.46 0.48 0.5 0.52 0.54 0.55 0.56 0.58 0.60 0.62 0.64 0.65 0.66 0.68 0.70 0.72 0.74 0.75 0.76 0.78 0.8 0.82 0.84 0.85 0.86 0.88 0.90 0.92 0.925 0.94 0.95 0.96 0.975 0.88 0.9875 1.0

4.9536 4.9307 4.8728 4.8005 4.7153 4.6183 4.5657 4.5106 4.3932 4.2670 4.1329 3.9915 3.9183 3.8436 3.6899 3.5310 3.3676 3.2003 3.1154 3.0297 2.8563 2.6807 2.5034 2.3251 2.2357 2.1463 1.9674 1.7886 1.6097 1.4309 1.3414 1.2520 1.0731 0.8943 0.7154 0.6707 0.5366 0.4471 0.3577 0.2236 0.1711 0.1069 0