9TH. INTERNATIONAL SYMPOSIUM ON FLOW VISUALIZATION, 2000

WAKE FLOW MEASUREMENTS IN TOWING TANKS WITH PIV

J. T u k k e r \ JJ . Blok1, G. Kuiper1, R.HJVÏ. HuIJsmans'

Keywords: PIV, propeller wake flow, lee slde wake, vortex shedding, towing tank

ABSTRACT

Partiele Image Velocimetry (PIV) is a promising measuring techniquefor the maritime fluid mechanics research. PP/ may visualize the spatial structure of'unsteadyflows and may deliver data setsfor validation of (maritime) Computational Fluid Dynamics (CFD).

The feasibility of PIV in towing tanks has been studied in three different flow applications in two towing tanks using a two-dimensional PIV system (2D-PIV). These flow applications are a propeller wake, a lee side wake and a cylinder wake.

The measuring set-ups and the results of the feasibility study are presented. Attention has been pakt to features of PIV in towing tanks, such as the dimensions of the measuring set-up, the seeding ofa large quantity of water, the visibüity of the particles in water, the towedset up, calibration and measuring accuracy.

The results of this study show that PIV is applicable in towing tanks and holds great promise for the maritime research on fluid mechanics.

1 INTRODUCTION

A good deal of experimental research for the maritime industry (shipyards, ship owners, ship builders, oil companies, etc.) takes place in towing tanks. In these tanks designs of ships, of propellers, of offshore constructions and of other floating structures are experimentally tested- In maritime research qualitative flow visualization techniques are important instruments to ga in more insight into the spatial structure of the flow. Apart from this, point-measuring systems, such as Pitot tubes and Laser Doppler Velocimetry (LDV), are being used for the acquisition of mean flow data. But nowadays, this is not enough. There is a growing demand for quantitative visualization of the spatial, unsteady flow structure. This interest is being stimulated by the growth of Computational Fluid Dynamics (CFD), which needs experimental data for calibration and validation. Furthermore, insight into the spatial, instantaneous fluid structure will support the theoretical and numerical modeling of the detailed flow structures, and may be helpful for the interpretation of the measured or computed mean flow fields.

For measuring unsteady spatial structures of a flow the Partiele Image Velocimetry technique (PIV) is a promising technique. Description of this technique can been found in [1], [5], [6], among others. PIV has been applied in various flow applications already. Some industrial applications are pipe flows [4], and wind tunnels [1], [2], [10]. The application of PIV in the maritime research is emerging, beginning in water tunnels. For towing tanks the measuring set-up is more complex than for channels, because of the requirement of towing the whole set up and the required large dimensions of the measuring plane. A first application in towing tanks is given in [3]. For the application of PIV in towing tanks some special requirements should be fulfüled. These requirements are related to the dimensions of the measuring set-up, the seeding of a large quantity of water, the visibüity of the particles in water, and the towed set up. To gain insight in the applicability of PIV in towing tanks, an experimental feasibility PIV study was executed at the Maritime Research Institute Netherlands (MARIN). In these study three different flows have been cons'idered:

Paper number 373 37J-I

J. Tukker, J.J. Blok, G. Kuiper, R.H.M. Huijsmans

a wake behind a rotating propeller in a ship wake a wake at the lee side of a ship model under a drift angle a wake behind a cylinder (vortex streel).

The PIV tests were executed in two towing tanks: the Shallow Water Basin and the High Speed Towing Tank of MARIN. In the Shallow Water Basin a stationary set-up (fixed on the tank bottom) was used for the propeller problem and maneuvering problem (lee side wake) and in the High Speed Towing Tank a towed set-up was used for the flow around the cylinder.

2 EXPERIMENTS

2.1 Experimental set-up

The PrV-system consisted of a sensitive, double-frame, PIV camera (1280 x 1024 pixels, 12 bits quantisation), and a double-pulsed YAg-laser for the illumination. The maximum light intensity was 50 mJ/flash. For this feasibility study a special support structure for the camera and the laser was designed (see Fig. 1). A typical distance of the camera to the measuring region center was 1.5 m. In the experiments reported in this paper the light sheet thickness was 9 ± 1 mm, measured in the center of the observation region. To suppress undesired reflections of the laser sheet at the ship huil, the stern at the lee side and the propeller were painted black. Furthermore, the lights in the tank and on the carriage were switched off, to suppress the background light in the PIV recordings

The flow was seeded with highly reflective particles Ti02. The range of the partiele dimensions range was 20 -180 (im. The seeding mixture was injected into the flow with the help of local injection rakes. For the use in towing tanks this material has some advantages: non-toxic, non-reactive with water, high reflective, easily to mix and cheap. It can be injected in bulk quantities and after some time it sinks to the bottom. The downward velocity of these particles in stagnant water is smaller than 1 mm/s. The form of the particles is not round and this is a disadvantage for PIV. In the data analysis these partiele characteristics should be taken into account.

PIV measurements on the propeller wake and on the lee side wake flow were carried out in the Shallow Water Basin of MARIN. This basin is a towing tank with a length of 216 m, a width 15.75 m and a water depth of 1.0 m. Because of this shallow water condition, it was possible to place the Prv set-up (camera, laser) on the tank bottom. In this stationary set-up the ship model was towed past the PIV set-up, and the laser sheet was oriented perpendicular to the tow direction (see Fig. la). When the ship crossed the measuring section at a certain position x/L (say x/L = 0.15), a trigger signal started the PIV-measurements. The measuring time between the recordings was 0.22 s. The co-ordinate system defined in Fig. 2 was tank fixed. lts origin lay at starboard side of the measuring region. The ship model represented an oil tanker, at a scale factor of 96.4. The diameter of the five-blade propeller was 0.10 m.

For the measurements on the cylinder wake, the PIV system (camera/laser) was placed on the towing carriage of the High Speed Basin (see Fig. lb). In this towed set-up the laser sheet was oriented in the tow direction. PIV tests were performed at different velocities between: 0.2 m/s and 1.2 m/s. The seeding mixture was injected about 3 m upstream with two injection rakes. The co-ordinate system is defined in Fig. 2b.

The PIV-recordings have been analyzed with a cross-correlation technique (described in manual [8]). For the measurements in the propeller wake and in the model wake at the lee side, interrogation regions of 64x64 pixels with 50% overlap have been used. These analyses yield raw vector maps of 39x31 vectors. For the cylinder wake a smaller interrogation region has been applied: 32x32 pixels (with 50% overlap), because of the higher partiele density. The raw data have been validated or rejected by a so-called moving-average-validation algorithm. The rejected vectors have been replaced by vectors estimated from surrounding values (see [8]). The last step was the calibration of the velocity vectors and the measuring grid to correct the perspective deformation (see below).

9* International Symposium on Flow Visualization, Heriot-Watt Universtty, Edirjjurgh, 2000 37,3.-2 Editors C M Carlomagno and I Grant,

WAKE FLOW MEASUREMENTS IN TOWING TANKS WITH PIV

2.2 Perspective deformation

In this feasibility study the camera set-up differs from the Standard 2D-setup (with the camera looking at the light sheet under a right angle. In our case the camera was looking under an angle of 30° or 45° at the light sheet (see Fig. 1). This unusual 2D set-up was unavoidable in view of the need to measure in a transverse, vertical cross-section around the stern in the stationary set-up, because the camera could not be placed in the path of the towed model. In the cylinder wake tests this restriction was not present. Yet, the same set-up (camera/laser) has been used here, for technical reasons. For testing of the feasibility of PIV this set-up is useful, but the consequence is a deformation of the image. This implies a position-depended calibration factor and a measuring uncertainty called perspective error (see below). This position-dependency of the calibration factor can be expressed in a linear relation for the calibration factor 5,:

^=50 > i(l + A ^ ) fori = x ,y (1)

In which x, y are the directions in the PlV-recordings (horizontal and vertical respectively). This relation is an adapted version of the back projection algorithm for stereo PIV (see Raffel [1], p. 178). Imperfections in the camera opties have been neglected here. Values for the parameters Sa,i and Aj are determined from an image analysis of the camera images of a spatial grid (with cells of lxl cm) placed into the measuring region. The relative measuring uncertainty is about 1%.

In general, the through-plane velocity component may influence the in-plane components measured by 2D-PIV, because the three-dimensional vector field is projected on a two-dimensional plane (the CCD-sensor). This projection may introducé the so-called perspective error (Raffel, [1], p. 47), or parallax error (Dantec [8], p. 4-63). In a 2D set up the contribution of the through-plane component cannot be separated from the in-plane components. This uncertainty may mostly be neglected in a two-dimensional flow having a weak through-plane component. However, the through-plane component may be strong in the three-dimensional wake flows around the ship model stern and behind a propeller. Furthermore, the perspective error has been increased by the non-perpendicular point of view (angle a) (see Fig. 1) and therefore the perspective error should be taken into account in this study. The dependency of the measured velocity components (vm en wm) on the flow components (U, V, and W) can be approximated as:

vm-V -Utan(a)

wm=W

These relations are valuable for the tank fixed set up. Only the horizontal component vm is corrupted by the impact of the large perpendicular component (U). In stereo 3D-PIV system the perspective contributions are used to determine the through-plane velocity component. In the case of the cylinder wake, the through-plane component is weak, because the wake flow is quite two-dimensional and the sheet is oriented in the tow direction. Therefore, in these tests the perspective error may be neglected.

3 RESULTS

3.1 Propeller wake

To study the propeller wake flow the vertical measuring region was placed perpendicular to the tow direction and the model was towed through the measuring plane. A number of tests were performed with different model velocities in the range from 0.20 m/s to 1.0 m/s and different rotating speeds

9* International Symposium on Flow Visualizatton, Heriot-Watt University. Eduiburgh, 2000 Editors G M Carlomagno and I Gram

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J. Tukker, J.J. Blok, G. Kuiper, R.H.M. Huijsmans

of the propeller: 100, 200, 300, 400 and 500 rpm. The experiments were carried out with two measuring regions. The dimensions of the first measuring region were 0.20 m wide and 0.145 m high (in center). In this camera set-up (P-I) the view angle ot was 30°. This measuring plane enclosed the whole propeller wake. For detailed measurements a smaller measuring plane was used (set-up P-II): 0.085 m in height and 0.12 m in width. The point of view a in this set-up was 45°. The seeding mixture was injected near the bow of the model. The region behind the propeller was well mixed, because the rotating propeller sucked the particles into the propeller region. The averaged concentration in an interrogation region of 64x64 was about 5 visible particles. This corresponds to a partiele concentration of about 8 tracer particles/cm3. This number of 5 particles is low; a larger number in an interrogation region (7) has been advised for single exposure images (Ref. [9]). Despite this low partiele density, PIV analyses were possible.

Fig. 3 shows some typical spatial velocity fields measured in the propeller wake with a model velocity of 0.52 m/s and a propeller speed of 500 rpm (8.3 Hz) with set-up P-I. The flash time difference was 0.5 ms. These maps have been measured near the propeller and at one propeller diameter behind the propeller. For presenting the global velocity structure the validated data has been filtered with a spatial filter (3x3). The dynamic velocity range of this test was -5.9 - +5.9 m/s and the measuring resolution was about 0.046 m/s. In the data the flow structure looks like realistic. The vorticity maps present the strong propeller hub vortex and some counter-rotating propeller tip vortices. The number of outliers (uro, vm > 2 m/s) in this vector map was low (less than 10%).

The non-uniform distribution of the through-plane component U was not measured already. A correction of the perspective error on the measured component vm cannot be made. Therefore, the PlV-data of this study cannot be used for a quantitative analysis, comparison with other data and validation of CFD-results. However, the objective of this feasibility study has been achieved. The results show that PIV measurements in a highly three-dimensional propeller wake are possible in a cross-section perpendicular to the tow direction, but for such a highly three-dimensional flow a stereo-PIV (three component) is necessary.

Table 1 Data of different camera set-ups

Setup Dimensions measuring plane Dimensions Interrogation region (64x64) View angle

a

Setup

Height [m]

Width [m]

Height [mm]

Width [mm]

View angle a

M-I 0.181 0.322 11 16 45° P-I 0.142 0.203 8.8 10 30° P-II 0.085 0.121 5.2 6.0 45° C-I 0.374 0.558 20 24 30°

3.2 Lee side wake

The flow around the ship stern largely determines the maneuvering behavior of a ship. Therefore the flow around the stern is an object of research for the Maneuvering Group of MARIN. As a part of the maneuvering research some PIV test were performed with a ship model under a drift angle. Main objectives with PIV were:

to visualize the spatial flow structure to generate data for calibration and validation of CFD-computations.

The same PIV set up and the same model (with a non-rotating propeller, without a rudder) were used as for the propeller wake tests (see above). The velocity fields were measured on the lee side near the model stern. The width of the measuring plane was 0.32 m and the height in the center was 0.180 m. The view angle of the camera was 45°.

Fig. 4 shows an example of a measured vector map with a corresponding PIV image. The tow velocity was 0.52 m/s. This corresponds with a ship velocity at full scale of 5.1 m/s (10 knots). The flash time difference was 1.5 ms. The center of the measuring region (z = 0) corresponds to the bottom of the ship. The dynamic velocity range of this test was -2.2 - +2.2 m/s and the measuring

9* International Symposium on Flow Visuaüzaüon, Hcriot-Watt University, Edinbargh, 2000 373-4 Editors G M Carlomagno and 1 GrarJ.

WAKE FLOW MEASUREMENTS IN TOWING TANKS WITH PIV

resolution was about 0.017 m/s. The averaged partiele concentration in an interrogation region of 64x64 was about 5 particles. This corresponds to a partiele concentration of about 4 tracer particles/cm3. This number of particles of 5 is low for accurate PlV-measurements (see ref. [9]). In the left corner of the PrV-images the ship model crosses the light sheet. Reflections of the laser light sheet on the ship huil are clearly visible. This part of the measuring region has been skipped in the vector map. Despite a low seeding concentration PIV measurements were possible in this wake flow. The measured flow field looks realistic. Behind the stern the flow is going up. This is a characteristic phenomenon of a ship wake.

The PIV vector maps have been compared with time-averaged CFD computations (Ref. [7]) and with measured, time-averaged velocity field, measured with 5-hole Pitot tubes, presented in Fig. 5. The conditions of the CFD-computations, the Pitot measurements and the PlV-tests are summarized in Table 2.

Table 2 test conditions of PIV, Pitot and CFD tests

Drift Angle

Model Scale

Ship velocity System of reference

Drift Angle

Model Scale Model

m/s Full scale

Knots

System of reference

PIV 10 96.4 0.52 10.0 Tank fixed Pitot 10 47 1.25 16.6 Ship fixed 1 CFD 20 47 0.75 10.0 Ship fixed |

The Pi tot-measurements and the CFD-data show an eddy near the stern at the lee side. The center of this eddy lies about at 3A of the draught T (z = -3/4 T). The PIV vector map hardly presents an eddy-like structure, but it shows, at z « 3AD a region of large transverse velocities in the opposite direction. (around the point (x,y) = (0.12, 0.04) in Fig. 5b). These vectors should indicate the presence of an eddy taking into account the contribution of the perspective error. The Pitot data show a large through-plane velocity component relative to the tank-fixed light sheet in the center of the eddy (see Fig. 5a). Note that the Pitot-data is presented in a model-based co-ordinate system. This large positive through-plane component results in a large negative projection error in transverse velocity (see above). This error overrules the flow structure of the eddy in the PIV map.

In conclusion, the PIV tests in a lee-side wake confirm the feasibility of PIV in towing tanks for the maritime research. However, a stereo-PIV system is required for accurate measurements of the three-dimensional flow, mainly because the dominant flow velocity is out of the laser sheet.

3.3 Cylinder wake

The PIV investigations on the cylinder wake constituted a pilot experiment for an extensive study on Vortex Induced Vibration on oil pipelines in offshore conditions. The contributions of the PIV may be the visualization of the instantaneous, spatial development of the unsteady vortical flow and the vortex shedding near the pipe, and the generation of a database for validation of CFD-computations.

Because of the two-dimensional character of the flow around the cylinder the injection of the seeding was concentrated in a small region (the laser sheet) and was injected upstream. This resulted in good PlV-images with a high density of particles. The averaged concentration in an interrogation region of 32x32 was about 15 particles, measured in the center of the measuring region. This is enough for an accurate PIV measurement (Ref. [9]). The partiele concentration in this test was about 11 partic les/cm3. In this set up the vertical light sheet was placed in the tow direction and the wake flow is approximately two-dimensional. This implies that the through-plane velocity component is small; theoretically zero. Therefore the projection error may be neglected in these tests. In this set up the dimensions of the measuring region was: 0.38 m x 0.56 m (set up Cl , largest area). An interrogation region of 32x32 pixels corresponds to a region of 10x12 mm.

Various test were done with tow velocities between the 0.2 m/s and 1.2 m/s. The diameter of the cylinder was 0.048 m. The distance of two adjacent vortex pairs was about 5 cylinder diameters. In this paper only the data measured at tow velocity of 0.4 m/s are presented. This flow condition corresponds to a vortex frequency of 1.7 Hz. The dynamic velocity range of this test was

9* International Symposium on Flow Visualizalicn, Heriot-Watt University. Edinburgh, 2000 Editors G M CaTlomaf.no and I Grani

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J. Tukker, J.J. Blok, G. Kuiper, R.H.M. Huijsmans

-7.0 - +7.0 m/s and the measuring resolution was about 0.11 m/s. In the center of the PIV recordings the particles are clearly visible (see Fig. 6). However, at the top and at the bottom of the PlV-images hardly any particles were visible, because the light intensity was too low there to illuminate them.

The conclusion of this part of the feasibility study is that a large measuring region of 0,50x0,50 m. seems to be possible. However, this large measuring area requires a high laser power (say 200 mj/pulse) to illuminate the whole measuring area with sufficiënt light intensity.

4 DISCUSSION

For comparison with time-averaged CFD-data, the averaged flow field should be calculated from a sequence of PIV vector fields, measured in the same cross-section. Furthermore, a towed set-up is more efficiënt than a stationary set-up, because much more data can be acquired in one run of the towing carriage. Consequently, to apply PIV in towing tanks a towed set-up is preferred.

To study the spatial structure of unsteady flows, the dimensions of the largest dominating eddy will determine the dimensions of the measuring region. Besides, the size of the interrogation regions restricts the smallest structure to be visualized. However, flow structures smaller than the size of the interrogation regions imply a measuring uncertainty in the vector field, comparable to alliasing effects in digital time-dependent signals. The density of visible particles restricts the dimensions of the interrogation region. Therefore, to increase the spatial resolution, a larger partiele density is required. In case of a large measuring region of 0.60x0.40 m (cylinder case, see above) the partiele density should be about 25 particles/m3 to analyze with interrogation regions of 16x16 pixels, necessary to fulfil the criterion of minimum particles in one region (Ref. [9]). The experience of this study is that the control of the seeding contribution in towing tanks is possible, but requires a good deal more effort to realize an optimal measuring condition.

Another aspect related to the choice of the dimensions of the interrogation region is the velocity gradiënt within the interrogation region. The PrV-analysis assumes a uniform velocity field within an interrogation region. This aspect may be important in case of large measuring region in a highly turbulent flow. In this feasibility study, this aspect is not taken into account already.

5 CONCLUSIONS

The PIV measurements performed in three different wake flows (a propeller wake, a lee side wake near the ship stern and a cylinder wake) show the applicability of PIV in towing tanks. With PIV the unsteady, spatial flow dynamics can be visualized.

Yet for the three-dimensional wake flows a 2D-PIV-system is less suitable, because of the projection error. To measure correctly the three-dimensional flow field, a stereo PIV (three components) is necessary. To apply PIV in towing tanks a towed set-up is preferred above a-stationary set up.

It is possible to perform PIV-tests with a large measuring region of about 0.4 m x 0.6 m in water. However, for such large measuring regions in towing tanks a high power laser (say 200 mj/pulse) is necessary to illuminate the whole measuring region.

6 REFERENCES

[1] Raffel, M., WillerC. and Kompenhans, J.: Partiele Image Velocimetry, apractical guide. lst edilion, Springer, 1998.

[2] Kompenhans, J. et al: Partiele Image Velocimetry in aerodynamics: technology and applications in wind tunnels. Proc. VSJ-SPIE98, paper KL306, 1998

[3] Gui, L. Longo, J. and Stem, F.: Towing tank PIV measurement system and data and uncertainty assessment for DTMB Model 5512. Proc. The Third International Workshop on PIV'99, Santa Barbara, pp. 457-463, 1999.

9* International Symposium on Flow Visuatization, Heriot-Watt Univcrsity, Edinburgh, 2000 373~6 Editors C M Cartomagno and I Gram

WAKE FLOW MEASUREMENTS IN TOWING TANKS WITH PIV

[4] Westerweel. J. et al.: Measurement of ftilly-developed turbulent pipe flow with digital Partiele Image Velocimetry. Experiments in Fluids, VoL 20, pp. 165-177, 1997

[5] Grant, I.: Partiele Image Velocimetry: a review. Proc. Proc Instn Mech Engrs, VoL 211 part C, pp. 55-76, 1997

[6] Adrian, R.J.: Particle-imaging techniques forexperimental fluid mechanics. Annu. Rev. FluidMech., No. 23, pp. 261-304, 1991.

[7] Koren. E.M.J., Roelofs. F. and Beemsterboer. C.J.J.: RANS pilot study: maneuvering. Repon ECN-C-98-067,1998.

[8] Dantec MT: FlowMap", Installation & User's guide, Fourth edition, Publication no. 904U3623. 1998.

[9] Kean. D. and Adrian, RJ.,: Theory ofcross-correlation analysisof PIV images. Applied Scientific Research, VoL 49, pp. 191-215, 1992.

[10] Stanislas, M., J. Kompenhans and J. Westerweel (ed.): Partiele Image Velocimetry, progress towards industrial Application, Kluwer Academie Publishers, 2000.

A.

Ship model

laser

W . ot

camera

B. cylinder

seeding

Vcar

laser

Fig. 1 PIV set ups, a. stationary set-up (top view); b. towed PIV set-up (top view).

9* International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000 373-7 Editors G M Carlomanno and I Grant.

J. Tukker, J.J. Blok, G. Kuiper, R.H.M. Huijsmans

A. propeller wake Lee side wake

port stem / ^ starboard \ stern

luff side

easunng region

B.

Fig. 2 Co-ordinatesystem: a. stationary set-up; b. towed set-up.

9* International Symposium on Flow Visualization, Heriot-Watt University. Edinburgh, 2000 Editors G M Carlomagno and l Gram,

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WAKE FLOW MEASUREMENTS IN TOWING TANKS WITH PIV

0.06

0.04

0.02

-0.02

-0.04

-0.08

' ^ r ; : : ; : : : : : :

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 6 0.18

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Fig. 3 Propeller wake at x = -0.01 m distance behind the propeller (C-I), U = 0.50 m/s, 500 rpm; a. PI V-image; b. vector field; c. vorticity field (blue = positive vocticity, red = negative vorticity).

9* International Symposium on Flow Visualization, Hcriot-Watt University, Edinburgh, 2000 Editors G M CaTlomafs.no and I Gram

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J. Tukker, J.J. Blok, G. Kuiper, R.H.M. Huijsmans

B

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Fig. 4 Lee side wake, measured near the stern (x/L = 1.8); a. PIV recording, b. validated vector map.

9* International Symposium on Flow Visualization, Heriot-Wait University, Edinburgh, 2000 373-10 Ediiors G M Cartomagno and I Crant.

WAKE FLOW MEASUREMENTS IN TOWING TANKS WITH PIV

STAT. B> - PJ. •m.B>A^.

B

VIEW-ANGLE

Reference vector (corresponds to ship speed) ^ >

Fig. 5 Lee side wake, Pitot measurements at x/L = 2: a. longitudinal velocity distribution (U), b. transverse velocity field (V, W).

9* International Symposium on Flow Visuatization, Heriot-Watt Untversity, Edinburgh, 2000 373-11 Editors G M Cartomagno and I GranL

J. Tukker, J.J. Blok, G. Kuiper, R.H.M. Huijsmans

Fig. 6 Cylinder wake, tow velocity U = 0.40 m/s (set up C-I), a. PlV-image, b. vector map; c. vorticity map.

9^ International Symposium on Flow Visualization, Heriot-Watt Üntverslty, Edinburgh, 2000 373-12 Editors G M Carlomagno and l Grant.