ISTP-16, 2005, PRAGUE 16TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA

1

AbstractEnergy loss due to wall skin friction in a

turbomachinery impeller directly related to the efficiency. Generally this energy loss was modeled as a fluid flow in an enclosed rotating disk, and determined by means of drag friction moment in the rotating disk experimental. In the former times many studies have been carried out to analyze not only the friction drag moment but also in the effort to reduce the skin friction drag.

In this study, the new type of drag reduction phenomena on an enclosed rotating disk was clarified experimentally by means of the torque measurement device and the hot film anemometer. Test disk is made of the etching process of fine spiral grooves of a disk surface.

Experimental result showed that for the disks with 150 and 155 grooves the moment coefficient in the turbulent region in the Reynolds number range of

54 106Re104 for the small axial clearance 1mm, with 0.1 and 0.2 mm depth and for the large axial clearance 20 mm, with 0.1mm depth in the transition region in the Reynolds number range of 3.3 105 < Re < 4.0105 were lower than those on the smooth disk. The maximum drag reduction ratio was obtained about 15 % in the small clearance case.

The experimental results of the the flow visualization cleared that the fine spiral grooves control the secondary flow of the boundary layer on the disk and have the effect which delays the generation of the local turbulence in the transition range.

1. Introduction

Since the analytical result of the frictional resistance of a rotating disk has been reported by K�rm�n [1], many studies have been done experimentally or analytically on the characteristics of the three-dimensional boundary layer at the disk surface. Frictional resistance of an impeller of a turbo-machinery is calculated by applying that of a rotating disk flow. It can be tried to improve the performance of a turbo-machinery by applying a drag reduction to the flow. Drag reduction phenomena have been studied by some researchers on a rotating disk in drag reducing additives[2] or a disk with hydrophobic wall[3]. However, the drag reducing method reported in a past remains a problem that the degradation or the durability becomes the failure for the practical application

Rotating disks may be classified in two broad categories: First, "free disk ", a disk which rotates in a fluid mass of infinite extent and initially at rest, second, "enclosed disk", a disk which rotates within a chamber of finite dimensions. Experimental measurement of disk friction in a finite housing have shown that the case of an enclosed disk is quite different from the case of a disk in an infinite medium, although many of the theoretical correlations follow the trend of that for an infinite system[4].The problem of disk flows has occupied a central position in the field of fluid mechanics

Effect of Fine Spiral Grooves on Drag Reduction of an Enclosed Rotating Disk

Budiarso *, Keizo Watanabe** and Satoshi Ogata**

* Depart. of Mech. Eng., Faculty of Engineering University of IndonesiaDepok 16424, Indonesia

** Depart. of Mech. Eng., Graduate School of Engineering Tokyo Metropolitan University1-1 Minami Ohsawa, Hachiooji-shi, Tokyo 192-0397

Corresponding author: mftbd@eng.ui.ac.id , 62-21-7270032, 62-21-7270033

Keywords: Boundary Layer, Rotating Disk, Viscous Drag Reduction, Friction Moment, Micro Groove Surface

Budiarso, Keizo Watanabe, Satoshi Ogata

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in recent years. Disk flows have immediate technical applications (rotating machinery, lubrications, viscometry, heat and mass exchangers, biomechanics, oceanography), but quite apart from that they intrinsic interest. Relevant previous research concerned itself almost entirely with infinite-disk flows. The sole reason for this, one suspect, is that similarity transformation, available when the disks are infinite, reduces the number of spatial dimensions of the problem to one. Although it is questionable whether the reduced model approximates to the physical problem of flow between finite disks, the nonlinear ordinary differential equations that define the phenomenon have been the subject of intense analytical and numerical probing. In spite of this, the nature of the basic flow is not well understood and the researchers of infinite disk flows are responsible for one of the long standing controversies of fluid mechanics, which concerns the uniqueness of the basic motion.

The purpose of this study is to obtain the new type of the drag reduction for the frictional moment of an enclosed rotating disk by using the many fine spiral grooves on the disk surface.

2. Experimental apparatus and experiment method2.1 Experimental apparatus

Fig.1 shows the experimental apparatus. Two D-C motors ⑭ served as the drive unit, and two shaft speeds were controlled by means of a control unit ⑭ attached to the D-C motors. The first motor was directly coupled to shaft 1 ⑭, towhich an interchangeable disk ⑭ could be attached, and the other motor was directly coupled to shaft 2 ⑭, to which a support disk ⑭was attached. The tested disk ⑭ was 180 mm in diameter and 3 mm thick. A bronze support disk ⑭ covered one side and the edge of the tested disk. The axial and radial gaps between the tested and the support disks were both 3 mm. Support disk was rotated at the same speed and direction as the tested disk by controlling the D-C motors. Thus, the torque acting on one side of the rotating disk could be measured directly

using strain gages cemented to the top of the shaft. The clearance s between the disk (rotor) and the side wall (stator) ⑭ was varied between 1, and 20 mm with the use of two pair spacer ⑭and housings ⑭.

2.2 Rotating Disk

The rotating disk was made from aluminium and its diameter 2a and thickness b are 180 mm and 3 mm, respectively. As a result, the experiments were carried out under the condition of a clearance ratio (s/a) = 0.011, and 0.22. It is well known that fluid in the boundary-layer on a rotating disk surface flow with keeping a flow angle[5]. By considering this flow pattern, was made a disk with new passive drag reduction wall by grooving of one side of the rotating disk wall by an etching process Fig.2. The shape of this fine spiral groove was assumed to be one along the following logarithm spiral curved based on a previous experiment result, with the curve:

tan θπexprr

1801 (1)

where is a flow angle, r1 is a constant, and r and are the curve coordinates. The flow angle is the ratio of the wall shearing stress in the tangential and radial direction. The angle of grooves () was obtained from experimental results[6], which determine the flow angle as a function of the Reynolds number,

= 115 – 6.55 ln ReL (2)

ReL (local Reynolds number) = r2/ (3)

where is a angular velocity (rad/s) and is a kinematic viscosity (m2/s). The flow angle in every radial location can be obtained by using Eq. (2), and for obtaining a groove trajectory the flow angle value can be substituted to Eq. (1). For developing Eq. (3), the value of disk

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EFFECT OF FINE SPIRAL GROOVES ON DRAG REDUCTION OF AN ENCLOSED ROTATING DISK

revolution (N) is 1500 rpm and tap water at temperature 20 oC is used as a working fluid.

In the experiment, six (6) disks were used with different depths h and numbers of grooves n, i.e., 0.1 and 0.2 mm, and 150, 155 and 160, respectively. Cross-sectional view of a spiral grooves is shown in Fig.3 The value of the pitch (p) is a function of a flow angle () and a chord between two grooves (l = 2πr/n), where the value of the width of the rib (p-w) is 0.1 mm. From experimental measurement for r = 90 mm and n = 150 to 160 the width of the groove (w) in an outer circumference of a disk is about 0.63 to 0.64 mm. A smooth aluminium disk is known to have a non-slip condition is also tested for comparison with the grooved disk.

The tested fluids were tap water, and aqueous of glycerin with 20wt% and 30wt% concentrations, which were both Newtonian fluids.

2.2 Flow visualization

The experimental apparatus which was used is the half side of the right hand side of the apparatus which was used for measuring moment coefficient (Fig.1), which was shifted to the right. Number (n) and depth (h) of the grooves disk which was used in the experimental are 150 and 0.1 mm, respectively. The axial clearance ratio (s/a) = 0.011 and 0.22. The surface disks was painting by non reflecting black color paint and after painting the surface of the disks was smoothing by a sand paper. The disks was rotated anti-clockwise and has speed at Re = 1.2 x 105 and 2.5 x 105 for s/a = 0.011 and 0.22 respectively.

�� ��

1 41 31 09

1 1

3

65

7

4

2

181 21 31 4

1 6

1 5

1 7

D ra in

000 000

A i r ven t

F ine g rooves

①Torque measurement device ① Bearing units① Test rotating disk ① Oil seal① Support disk ① Slipring① Spacer ① Coupling① Side plate 1 ① DC motor① Side plate2 ① Sliding unit① Housing ① Strain meter① Shaft 1 ① Control unit① Shaft 2

Fig. 2 Experimental apparatus for torque measurement

Fig. 1 Experimental apparatus for torque measurement

Fig.2 Photograph of the fine grooves

Fig.3 Cross-sectional view of spiral grooves (rectangular)

p

w

h

Budiarso, Keizo Watanabe, Satoshi Ogata

4

Flow visualization was performed using tracer. The tracer technique was applied by mixing aluminum powder in a tap water in the approximate concentration of 0.2 mg/liter. A slit light from a projector lamp unit was used to generate a flat beam (0.5 mm x 90 mm). Photographs of streaks of aluminum powder within 0.5 mm of the disk surface were captured by using a digital camera and the camera shutter-speed was 1/60s. The apparatus were covering by black curtain for obtaining a dark condition in order to find a good result of photographs. The photographs obtain was taken in the first quadrant of the disk in order to avoid an error in width of the light beam.

3. Results and discussionTo determine the effect of the number of

grooves on the friction moment of the rotating disk, an experimental work was carried out by using disks with the groove numbers of 150, 155, and 160, for depths of 0.1 and 0.2 mm, for s = 1 mm (s/a = 0.011, small axial clearance) and s = 20 mm (s/a= 0.22, large axial clearance). According Daily and Nece[7],and Yamada and Ito[8] that the axial clearance (s) is small axial clearance when the boundary layer is merged, there is no geostrophic core, and from their experimental result the value of spacing ratio is (s/a) < 0.016. Experimental results for the moment coefficient of the disk with many grooves compared to the smooth disk in the aqueous solution of glycerin (Newtonian fluid) in the laminar, transitional and turbulent regions for s/a = 0.011 and is shown in Fig.5. Line number I shows the semi theoretical formulae in the laminar region for one surface of a smooth disk given by Daily and Nece and Yamada and Ito for a small ratio axial gap (s/a 0.016, merged boundary layer), and line numbers II and III show the formulas in turbulent region for one surface of a smooth disk given by Yamada and Ito for a small ratio axial gap (s/a 0.008, merged boundary layer) and for large one (s/a 0.016, separate boundary layer), respectively.

Fig.5 indicates that in the laminar region, either for smooth or grooved disks, the slope is in good agreement with the formulae, but there

is a discrepancy in value which it might be precipitated by the (s/a) value, where the (s/a) value in this experiment is smaller than that used in the formulae. No drag reduction occurs in this region. The transitions of the laminar to turbulent flow almost cannot be seen, but seem to originate from the fact that the value of (s/a) = 0.011 is already close to the large gap value where the separate boundary layer and secondary flow will present. The secondary flow, also described as a fluid core between the stator and rotor, imposes both a different degreeof external turbulence and a radial pressure on the disk boundary layer. The latter subjects the radial flow to an adverse pressure gradient, while the former is expected to have an effect upon the transition since the boundary layer is fed from the face of the rotating core to compensate for the radial outflow[7]. This secondary flow has a progressive vortex movement effect on the center of rotation. The vortices occur in the flow at the critical Reynolds number, despite they still laminar flow. These vortices are thought to be very weak at the time of generation, which explains their value to cause an abrupt increase of the frictional moment[8]. While in the turbulent region the slope and value of the moment coefficient for a smooth disk are in good agreement with formulae number II, this means that the influence of (s/a) is not significant for the friction moment Cm when Re is as large as in turbulent region. To determine the effect of the number of grooves on the friction moment of the rotating disk for the case of the large axial clearance, an experimental work was carried out by using disks with the groove numbers of 150, 155, and 160, for depths of 0.1 and 0.2 mm. Daily et al. and Yamada et al state that the axial clearance(s) is large when the boundary layer is separate, a geostrophic core is developed, and from their experimental result the value of axial clearance ratio is (s/a) ≥ 0.016. Experimental results for the moment coefficient of the disk with many grooves compared to the smooth disk in the aqueous solution of glycerin (Newtonian fluid) in the laminar, transitional and turbulent regions are shown in Fig.6 for (s/a) = 0.22.

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EFFECT OF FINE SPIRAL GROOVES ON DRAG REDUCTION OF AN ENCLOSED ROTATING DISK

Fig.6 show that the moment coefficient (Cm) from experimental result using the smooth disk for both on the laminar and turbulent flows regime of clearance ratio (s/a) = 0.22 was agreed well with Yamada and Ito. This indicates that separate boundary layer case were present in that conditions. Whereas for friction moment coefficient of the grooves disk has different behavior which is depends on the axial clearance ratio (s/a), number, flow angle, and the depth of the grooves. Line number I and II show the semi theoretical formulae in the laminar and turbulent region for one surface of a smooth disk given by Yamada and Ito for a large ratio axial gap (s/a ≥ 0.016, separate boundary layer), respectively.

Drag reduction occurred for the disks with number of grooves (n) 150 and 155 with 0.1 mm depth and 150 with 0.2 mm depth for 20 mm clearance in the Reynolds number range of 3.4 x105 < Re < 3.8 x105 . The drag reduction was achieved for n = 150 with h = 0.2 and s/a = 0.22 is about 11 %.

Fig.7 show the flow visualization results from the tracer technique for smooth and groove disk, the disks was rotated anti-clockwise and has speed at Re = 1.2 x 105 for s/a = 0.011. In this case for s/a 0.011 the turbulent flow region according to Yamada and Ito began at Re = 1.0 x 105. Thus, it represents the turbulent flow ranges. The tangential direction of the streaks for the smooth and fine spiral grooves disk in

6x10-3

(s/a)=0.22 smoothh=0.1mmh=0.2 mm

n= 150

n=155

2x10-3

2x10-3

105

n =1 6 0

2x10-3

Re

C m

7x105

Cm =0 .05 ( s / a )1/14 Re -1/5

Cm =1 .74(s / a )1/14 Re-1/2

Fig.6 Moment Coefficient versus Re for s/a = 0.22

n =

n =

10 -2

3x10 -3

Fig.5 Moment Coefficient versus Re for s/a = 0.011

10 -2

3 x 10-3

(s/a)=0.011 smoothh=0.1 mmh=0.2 mmCm

n = 150

105

10-2

7x 105

n = 160

4

II Cm = 0.031 (s/a)-1/5Re -1/4

III Cm = 0.05 (s/a)1/14Re -1/5I Cm = π (s/a)-1Re -1

Re

2 x 10

3x 10

-3

n = 155

Budiarso, Keizo Watanabe, Satoshi Ogata

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that figures are represent flow vortices in the turbulent region. The streaks are not clear due to the flow was turbulent. In the smooth disk the streaks were appears slightly strong than those in the grooves disk especially from the middle to the edge of the disk, where the turbulent flow was predicted occur. Meanwhile in the grooves disk the streaks were appear weak and smooth. If the contrast between dark and light strips is strong, the vortices near the rotating disk can be considered to be powerful because the reflected light intensity of the aluminum powder indicates the strength of the flow. Consequently, the vortices in the grooves disk were weaker than those in the smooth disk. Hence, the groove reduces the amplitude of the circular vortex on the rotating disk. There is also seen an obvious difference in the two flows. The turbulent flow in the fine spiral grooves flows in order align with the grooves angle. It is inferred that the spanwise spread of vortices was constrained within the rib groove. Therefore, can reduce the momentum exchange properties caused by streamwise vortices, with a consequent reduce the surface shear stress and decreasing the turbulence intensity during the burst and between the bursts[9].

Figs.8 (a) and (b) show the flow visualization results, the disks was rotated at 2.5 x 105 for axial large clearance ratio s/a = 0.22. In this case for s/a 0.22 Daily and Nece (1960) reported the transition to turbulent flow began at Re = 3.0 x 105. Thus, it represents the transition flow range.

The streaks were appear stronger than in Fig7, because the flow was appear in the transition to turbulent flow. In the case of smooth disk (Fig.8 a) the streaks appear clearly and strong than those in grooves disk, indicated that the vortices in the vortices in the smooth disk was stronger than those in grooves disk. Therefore, the groove reduces the amplitude of the circular vortex on the rotating disk. It is also seen that the flow angles of grooves disk are larger than those for the smooth disk. In other words, the flow direction near the disk is turned outwards by the grooves. According Ogata [10] the increased of angle on the rotating disk and decreased amplitude of circular vortex due to the grooves surface led to drag reduction for the rotating disk.

4. Conclusion.

Effect of many fine grooves in an enclosed rotating disk with certain depth and groove angle under several conditions of clearance ratio in the Reynolds number range of 105 < Re < 7x105 has been examined by measuring friction moment coefficient, and visualization for clarifying the drag phenomena. The conclusion of this study are summarized as follows:

(1) The frictional moment in small axial clearance ratio (s/a = 0.011) becoming small in the turbulent region compare with the smooth disk. The maximum drag reduction of approximately 15 % was obtained.

(b) Fine spiral grooves disk(a) Smooth disk

Fig.7 Flow pattern on rotating disk for s/a = 0.011

ω ω

Fig.8 Flow pattern on rotating disk for s/a = 0.22

(a) Smooth disk (b) Fine spiral grooves disk

ωω

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EFFECT OF FINE SPIRAL GROOVES ON DRAG REDUCTION OF AN ENCLOSED ROTATING DISK

(2) In large axial clearance ratio (s/a = 0.22), fine spiral grooves has an effect of delaying the transition of flow from laminar to turbulent. The maximum drag reduction of approximately 11 % was obtained.

(3) It is inferred that drag reduction has associated with a Reynolds number, curvature angle of grooves, geometry of the groove and clearance ratio.

References[1] K�rm�n, Th. Von. �ber Laminare un Turbulente

Reibung, Zamm 1, pp. 233-252, 1921.[2] Watanabe, K. Frictional Resistance of a Rotating

Disk in Polymer Solutions, Bulletin of JSME,Vol. 21, No.153, March, pp. 455-462, 1978.

[3] Watanabe, K. and Ogata, S. Drag Reduction for a Rotating Disk with Highly Water-Repellent Wall , Proc. of Int. Symp. on Pumping Machinery-III, FEDSM97-3380, 1997.

[4] Schultz F. – Grunow. Der Reibungswiderstand Rotierender Scheiben in Gehausen, Zeitschrift fr angewandte Mathematik und Mechanik, Vol.15, July, pp.191-204, 1935.

[5] Gregory, N.,Stuart, J.T.,and Walker, W.S. On The Stability of Three-Dimensional Boundary Layers with Application to the Flow due to a Rotating Disk, Phil. Trans. Royal Soc.of London, A248, pp.155-199, 1955.

[6] Kato, H., Watanabe, K. and Naya, K., Visualization of Fluid Flow Near a Rotating Disk in Dilute Polymer Solutions, Bulletin of the JSME, Vol. 21, No. 161, November, pp. 1618-1625, 1978.

[7] Daily, J.W. and Nece, R.E.Chamber Dimension Effects on Induced Flow and Frictional Resistance of Enclosed Rotating Disks, Trans.ASME Ser.D, 217-232, 1960.

[8] Yamada, Y. and Ito, M. On the Frictional Resistance of Enclosed Rotating Cones, Bull. of JSME,Vol.18, No. 123, September, pp. 1026-1034, 1975.

[9] Walsh, M.J. Turbulent Boundary Layer Drag Reduction Using Riblets , AIAA Paper 82-016, 1982.

[10] Ogata, S.and Watanabe, K., Limiting Max. Drag Reduction Asymtote for the Moment Coeff. of a Rot. Disk in Drag Reduction Surfactant Solution, J. Fluid Mech. Vol. 457, pp. 325-337, 2002.