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Particle image velocimetry measurements of wave-current interaction in a laboratory flume
Optics and Lasers in Engineering 16 (1992) 239-264
Particle Image Velocimetry Measurements of W a v e Current Interaction in a Laboratory Flume A. Liu,* X. Shen,** G. H. Smith & I. Grant The Fluid Loading Instrumentation Centre, Heriot-Watt University, Riccarton, Edinburgh, UK EH14 4AS (Received 1 February 1991; revised version received 1 April 1991; accepted 31 August 1991)
ABSTRACT The hydrodynamics of wave-current interaction is of interest to those concerned with marine and offshore structures. In particular the fluid loading characteristic may be radically altered in a sea state consisting of a mean current flow mixed with freely propagating gravity waves. The present paper describes water flume experiments, using Particle Image Velocimetry (PIV), executed to examine hydrodynamics of wave-current interaction. A variety of wave and current conditions were investigated to determine the major influences on the combined
flOW. This paper describes the experimental procedures used to obtain simultaneous measurements of the resulting wave velocity vectors over an extended region of the wave. It also describes how the directional ambiguity inherent in the basic PIV method was resolved by 'pulse tagging' technique. Velocity vectors under waves at various phase points for different current and wave conditions are presented and compared in some cases with measurements derived using Laser Doppler Anemometry ( LDA). The resulting velocity vectors are used to estimate how the mutual interaction, between wave and current, effect the calculation of structural loads using Morrison's equation. * To whom correspondence should be addressed at: Schlumberger Industries, Flow Measurement, P.O. Box 3, Talbot Road, Stretford, Manchester, UK M32 0XX. **Present address: Department of Engineering Mechanics, Tsinghua University, Beijing, People's Republic of China. 239 Optics and Lasers in Engineering 0143-8166/92/$05-00 t~) 1992 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
240
A. Liu, X. Shen, G. H. Smith, 1. Grant
1 INTRODUCTION Wave-current interaction is a significant element defining the marine and offshore environment.~ The presence of a uniform or shear current superimposed on gravity water waves will modify the characteristics of the wave-induced particle motions near the water surface. 2'3 When gravity waves propagate in the same direction as the current, both the wave length and the maximum fluid velocity increase. When waves travel against a current, there is an increase in wave steepness with a corresponding greater probability of wave breaking? In either case the fluid loading on marine and offshore structures will increase over that calculated assuming a wave only sea state. The normal practice in estimating wave-loading is to use the Morrison equation. s'6 This calculates the loading on a structure as the sum of a drag force proportional to velocity squared and the inertial force, proportional to acceleration of the fluid as dF
dy
parD 2 8 V
CM
4
Ot + CD
V IVI
(1)
where CM and Co are the inertia and the drag coefficients respectively. Hence, a clear knowledge and accurate assessment of how the presence of a current will modify the wave only fluid velocity is required. Any improvement in the description of the water particle motions will lead to a more accurate estimate of the induced fluid loading on marine and offshore structures. The evolution of improved design relies on this process. Many studies of wave-current interaction have been made. The complexity of the motion and concomitant experimental difficulties, however, have meant that a great reliance is placed on analytical or numerical modeling, v-m Most experimental investigations reported have provided particle motion measurements as a time series at a particular point in the flow. Laser Doppler A n e m o m e t e r s (LDAs) 2'3"~1 or hot-film gauges and conductivity probes, ~2 have been most commonly used. The measurement over large regions by such methods is time consuming, and more importantly, the instantaneous relationship between flows in disparate regions would be lost. In practice, the wave-current loading is frequently obtained from Morrison's equation using a velocity/acceleration field derived from linear wave theory and the superimposition principle. This is because of the lack of experimental data describing wave-current interaction.
P I V measurements o f wave-current interaction
241
The present paper describes how Particle Image Velocimetry (PIV) was used to provide simultaneous velocity data at many stations over an extended region. The work was concentrated on the wave-current interaction in the case of current travelling with waves and at the region near the still water level. A variety of wave and current conditions were investigated to determine the major influences on the combined flow. The difficulty of resolving directional ambiguity in the particle, inherent in the investigation of wave-current interaction, was solved using a 'pulse tagging' method. The validity of the common practice of estimating fluid loading from Morrison's equation assuming a velocity field calculated from a linear addition of wave-only and current-only velocity fields is discussed. 2 BASIC T E C H N I Q U E
2.1 Particle image velocimetry PIV is an optical velocimetry technique which enables two, in-plane, velocity components to be instantaneously measured over an extended area of flow. The area of flow under investigation is illuminated with a thin 'sheet' of laser light. The flow following seed particles are photographed. The light source is pulsed during an exposure to provide stroboscopic illumination producing multiple images of each seed particle. A knowledge of the time between light pulses and the optical magnification of the imaging system enables an estimate of the local 'in-sheet' component of the flow velocity vector to be obtained, x3
2.2 Resolution of directional ambiguity using pulse 'tagging' The directional ambiguity experienced in the basic PIV image interpretation was overcome in the present study by inserting extra 'tagging pulses' into the principal laser pulse train. 14 The tagging pulses were of different duration from the principal illuminating pulses. The image size of a seed particle was proportional to the pulse duration and the flow velocity. 15 Hence, each principal image was partnered by a small tag image. The relative times of occurrence of the principal and tagging pulses were known and therefore the placing of the corresponding image gave an unambiguous measure of direction. Since the flow trajectory produced when a surface gravity wave interacted with a current was trochoidal, the identification of local flow direction was of great importance. For example, around the wave zero crossing point region, even for the particles located very close to each
242
A. Liu, X. Shen, G. H. Smith, 1. Grant
other, the direction of the horizontal velocity component could differ by 180 °. The use of the pulse tagging methods meant that unambiguous measurements of flow velocity could be obtained over the whole field under investigation. 2.3 The wave-current experiment Velocity measurements from the combined wave-current flows were compared with results obtained by adding wave-only and current-only velocity fields. The velocity field arising from the linear addition was calculated in two ways. Firstly, the PIV measurements of waves alone, Vwp, and currents alone, Vcv, were added together as Vwcp. = V~,v + Vcv
(2)
where subscript a indicates the linear addition and p denotes a measurement using PIV. Secondly, a semi-empirical wave-only model, Vwm, and an empirical current-only model, Vcm, provided velocity information for the addition as, Vwcma= Vwm + Vcm
(3)
where m defines model values. In this comparison, firstly, the differences between the PIV measurements of combined flow and the results found from linear addition of the two isolated flows were highlighted. Any measured difference could then be used to determine the validity of the linear addition model when applied to Morrison's equation. Secondly, measurements of the flow fields arising from a variety of wave and current combinations were compared. From these, the relative contribution of wave and current parameters could be investigated. These 'base-line' measurements were used to draw general conclusions regarding wave-current interaction. Additionally, a number of velocity measurements obtained using PIV were compared with those obtained using a Laser Doppler Anemometer. This gave additional confirmation of the validity of PIV as a measurement technique. The detailed experiments and data analysis are discussed below.
3 EXPERIMENTAL PROCEDURES 3.1 The wave flume The experiments on w a v e / s h e a r - c u r r e n t interaction were carried out in a wave flume which was 7 m long, 0.3 m wide and 1 m deep. The water
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stood at a depth of 0-66 m, as shown in Fig. 1. A dry-back, flap-type wave maker was used to produce small amplitude gravity water waves. A short beach was employed to minimise wave reflection, which is detailed in Section 3.4. Shear currents, with different mean flow speeds were generated using a centrifugal p u m p with associated pipework. 3.2 PIV instrumentation The optical arrangement is shown in Fig. 2. An 18 W, cw, argon-ion laser was used as a light source. A mechanical chopper was used to produce a train of principal and 'tagging' light pulses. The pencil beam was shaped into a light sheet by passing it through a solid glass rod before illuminating the fluid. The thickness of the light sheet was approximately 2 mm. The area viewed by camera was near the water surface with a size of approximately 300 m m (wide) × 200 m m (depth) as shown in Fig. 2. The fluid was seeded with neutrally buoyant particles of specific gravity approximately 0-98-1.02. The particles were of an inert material used in industrial coating processes with an average diameter, by volume, of 60 # m . The density of the seeding particles ensured they did not drop out during testing. The likely error caused by using the particle velocity to infer the fluid velocity was estimated from the motion of a seeding particle relative to the fluid. The result showed that
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this error was under 35/~m/s. C o m p a r e d with the amplitude of flow velocity measured ( > m m / s ) , the uncertainty was not significant. 14'~6 The PIV photographs or images were recorded using a Nikon 35 m m camera and Ilford HP5 film. A contact printing technique was employed to improve the quality of the recorded images.17 The images recorded on the photographic negative were analysed using the arrangement shown in Fig. 3. The photographic negative was mounted on a X - Y transversing carriage which was driven, independently in either direction, by two stepper motors under computer control. Each step of the m o t o r moved the negative 5 × 10-6m. Repeated traversing over the whole area of the negative was found to introduce negligible additive error in positioning. A small area of the negative was imaged onto a JVC video camera using a fiat field microscope lens. The output from the video camera was digitised and held in a Seescan RD257 framestore. The video image
245
P I V measurements o f wave-current interaction
CARR lAG E
I Tv l MO N I TOR
IT"AVE~SIN?I I Fig. 3. PIV image processing system. area was divided into a matrix of 256 x 256 divisions or pixels. The light intensity at each pixel was represented by one of 256 grey levels. The matrix was transferred to the computer for further processing and could be viewed on a monitor as a digital picture. The spatial resolution was defined by the overall magnification of the imaging system. Typically, 15-30 pixels per m m (in the object plane) was obtained. 3.3 L D A system Measurements of the flow were also made using a single c o m p o n e n t L D A which could be traversed in the vertical direction. The system incorporated a 15 mw h e l i u m - n e o n laser in a forward scatter mode, with frequency shifting, to measure the horizontal velocity c o m p o n e n t at 15 points along one vertical section. Figure 4 shows the optical arrangement and traversing system used in the L D A measurements. Figure 5 is a plan view which demonstrates the simultaneous use of the PIV and L D A at a particular section of the water flume. The L D A measurements were made only at phase 0 ° and 180 °, i.e. at the crest and trough. 3.4 Wave motion and reflection Sinusoidal gravity waves were generated using a signal generator to drive the wave paddle. Considering the limitation of the flume length, a series of experiments were performed to study and minimise the wave reflection problem. This was done, photographically, by using a high laser pulse repetition rate with a long camera exposure time. W h e n the camera exposure was equal to the wave period, the entire trajectory (orbit) of a seeding particle could be observed. The wave motion state could then be judged from an analysis of the entire trajectory of seeding particle.
A. Liu, X. Shen, G. H. Smith, I. Grant
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F r o m direct observation of the particle orbits, the best beach configuration to minimise wave reflection was achieved. This was a short beach with vertical strips of b u o y a n t mesh in front• The u p p e r portion of the beach surface was c o v e r e d with mesh to allow current to pass through. Figure 6(a) and (b) show the particle orbitals achieved at the test section with using a long b e a c h with a curved surface and with the final configuration described above.
3.5 Production of current profile In order to p r o d u c e a shear current near the water surface with an acceptable level of turbulent fluctuation, a bronze wire mesh held on a flexible frame was installed in front of the test area. The mesh, which had variable grades, e x t e n d e d from a b o v e the water surface to the b o t t o m of the tank. The mesh was transparent to waves. A wave gauge
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was used to monitor the wave conditions in the test section; it was placed downstream of the mesh screen during experiments. The currents were characterised by their shear rates, 8V/Oy, and mean flow speeds. The mean flow speeds were obtained by averaging along the depth of the test section. In the experiments, three bulk rates at 10, 15 and 20 m3/h, were used to provide currents with mean flow speeds at 48, 62 and 72 mm/s respectively. The one-component L D A system described in Section 3.3 was used to obtain profiles of velocity and turbulence in the middle of the test section. It was found that the final configuration of louvers and mesh limited the turbulent fluctuations to be less than 5% in most areas.
P I V measurements o f wave-current interaction
249
3.6 Wave and shear current interaction The characteristics of the w a v e - s h e a r current interactions were obtained from a series of experiments featuring various combinations of wave and current conditions. The methodology used was as follows: (1)
(2)
(3)
Sinusoidal wave only: a variety of wave amplitudes were generated for each frequency of wave. This provided baseline measurements for comparison with the combined w a v e - c u r r e n t case. Current only: current profiles at three flow bulk rates--10, 15 and 20 m 3 / h - - w e r e measured to feature the current shear rates and profiles. Wave-current: in this case experiments were carried out to provide data (a) for a single current with several wave amplitudes and frequencies and (b) for a particular wave with several current magnitudes.
The PIV photographs or images were obtained in each case.
3.7 Image processing techniques The objective of the processing was to 'group' all the principal and tagging spots corresponding to the same particle and so enable measurement of the particle displacement between laser pulses and thus infer the particle velocity. The correct directional characteristics of each 'seed' were also required. These were obtained from the locations of tagging spots relative to their principal spot partners. A n automatic processing program was developed to identify particle images and their corresponding tagging spots. The computing time taken for the analysis of one image was less than 25 s on a PC. The details of the various processing steps are presented in Refs 14 and 16. Figure 7 shows a group of the initial velocity results obtained.
4 DATA ANALYSIS AND COMPARISON
4.1 Wave motion only A series of experiments was executed to investigate the velocity fields arising from sinusoidal gravity waves with frequency, Fw, and amplitude, Hw.
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The experimental results were also used to assess the validity of a second order wave model, which was used to build a linear addition model for the prediction of w a v e - c u r r e n t interaction. This second order model was introduced based on the linear wave theory with a second order correction from Stokes theory. In this model, each
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where constants bT and bB relate to the current shear, aT and aB relate to the mean velocity, and YT is the transition point between the two regions. The y-axis was defined as depicted in Fig. 10. In the present study, the point YT, =40 mm, was chosen in all three cases as the point at which the second derivative of the current profile was maximum. The detailed values of aT, aa, bT and bB were solved from eqn (3) using the least squares method. The constants aT, bT, as and bB, which varied with the flow rate Q, are listed in Table 1. The gradients for the upper region of the flow were seen to vary depending on the volumetric flow rates. In the case of the 10 m3/h rate it was relatively small, 0.27. However, the rate of shear for the higher flow rates used was somewhat greater, 0.34 and 0.39 for the 15 m3/h and 20m3/h flow, respectively. For y
Since the sinusoidal waves were progressed with currents, the extension of wave crest region and the reduction of wave trough region were straightforwardly demonstrated from PIV measurements. A whole field comparison of the wave-current flow vectors measured from PIV with those obtained from the addition of the second order wave particle velocity model (eqn (4)) and the measured current profile (eqn (3)) are shown in Fig. 11. The velocity differences are shown in Fig. 12. A comparison of the measurements of the combined wave-current interaction and the result of a linear addition of wave-alone and current-alone velocities was also carried out at different wave phases. That is, the variation of the horizontal velocity profiles with water depth from the wave-current data was compared with the result of a linear addition of wave-only and current-only velocity profiles. The PIV measurements from the wave-current interaction were compared to the result obtained from linear addition for the region of the wave crest. Figure 13 shows the variation in horizontal velocity component with depth measured by PIV. Also shown are the results of a linear addition of measured wave- and current-only flows. Finally, the velocity fields are depicted. It is clear that in the wave crest region (phase 0 °) the results obtained by adding the separate PIV measurements for wave-only and currentonly cases are close to those derived from the linear addition of the two
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semi-empirical flow models. The differences are mostly less than 5 % . H o w e v e r , the m e a s u r e m e n t s of w a v e - c u r r e n t interaction, Vwcp, are smaller than linear superposition results o b t a i n e d from either theoretical or experimental results. T h e difference b e t w e e n m e a s u r e m e n t s of w a v e - c u r r e n t interaction and the results from the linear addition of wave-only and current-only is m o r e significant in the region close to the still water level (approximately 1 5 - 2 5 % ) , and decreases with water depth. Further comparisons of P I V m e a s u r e m e n t s of w a v e - c u r r e n t interaction and the predictions from linear addition were m a d e in which either the wave amplitude, wave frequency or current rate were varied. This was to highlight the effect that each flow characteristic has on the w a v e - c u r r e n t interaction. Figure 14(a) and (b) show the P I V m e a s u r e m e n t s of w a v e - c u r r e n t interaction and results from the two linear addition m e t h o d s at the wave crest region (phase 0°). T h e results were obtained at the same current rate Q = 15 m3/h with two different waves having a frequency Fw = 2 H z b u t with different amplitudes Hw = 25 m m and Hw = 36 mm. It was f o u n d that with the increase of wave amplitude from 25 m m to 3 6 m m , the difference b e t w e e n m e a s u r e d velocities and the results predicted from linear addition was greater. In the region close to the still w a t e r surface, the difference increased approximately from 17% to 30% as w a v e amplitude increased from 25 m m to 36 mm. The effect of
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wave amplitudes on w a v e - c u r r e n t interaction has also been investigated by Peregrine and J o n s s o n . t9 A similar conclusion was reached. In Fig. 15(a), (b) and (c), profiles obtained for the same wave conditions but three current rates, in the wave crest region are compared. In this case the PIV and L D A measurements of w a v e current interaction are c o m p a r e d with results from adding the semiempirical wave-only model and current-only profiles. The data obtained by P I V and L D A are in very good agreement for each of the various current rates. The magnitude of the measured combined velocity profiles is still less than that predicted by linear addition. The departure between profiles decreases as measurements were made at greater depths below the still water level. It was found that a higher shear rate increases the profile departure between the measured and linear addition profiles. Referring to Table 1, the current shear rate at Q = 15 and 20 m3/h were much higher than that for Q = 10 m3/h. This increased the difference between measured and predicted profiles, as illustrated in Fig. 15(a)-(c). In the region close to the still water surface, differences between measured and predicted velocities were approximately 20%, 25% and 27%, corresponding to current rates Q = 10, 15 and 20 m3/h. The influence of current shear rate is also evident from the results for a single shear current. The difference between measured and predicted velocity field is large in the high shear b-r region of the current profile.
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For example, at Q = 20 m3/h at a depth below the still water surface of 4 0 m m for which the current shear bB was m u c h less than bT, the d e p a r t u r e was u n d e r 10%. In the w o r k of Iwagaki and A s a n o , 2° the influence of the current profile on w a v e - c u r r e n t interaction was also emphasised. It is shown that in the region close to the still water surface, the differences b e t w e e n the predicted results for the parabolic c u r r e n t case and m e a s u r e d results are m u c h larger than those b e t w e e n the predicted results for the uniform current case. In other words, when the gradient of the current profile was less, the differences between m e a s u r e d and predicted results was less in the region close to the still water surface. Figure 16 shows how the differences e n h a n c e w h e n the c u r r e n t shear rates increase.
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A. Liu, X. Shen, G. H. Smith, I. Grant
262
5 SUMMARY In summary, the velocities measured in the crest region for the combined wave-current interaction were less than those predicted by a linear addition of the wave-only and current-only velocity fields. The difference between measured and calculated profiles became more significant with an increase of wave amplitude and current shear rate. In the present flow conditions, the difference in the region near the still water surface varied from 15% to 25%. In the wave trough region where the particle velocities were against the currents, a rapid attenuation in velocity and trough region size was undergone with an increase of the current rate. However, the difference between the PIV measurements of wave-current interaction and results from linear addition was not as significant as that found in the crest region, as shown in Fig. 17. Consequently, if the velocities derived from a linear addition of wave-only and current-only profiles were employed in Morrison's equation to estimate fluid loading, the resulting estimated drag force (which was proportional to velocity squared) in the wave crest region would be overestimated.
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PIV measurements of waoe-current interaction
263
REFERENCES 1. Ismail, N. M., Wave-current models for design of marine structures. J. of Waterway, Port, Coastal and Ocean Engineering, 110(4) (1984) 432-47. 2. Kemp, P. H. & Simons, R. R., The interaction of waves and a turbulent current: waves propagating against the current. J. Fluid Mech., 130 (1983) 73-89. 3. Hedges, T. S., Anastasiou, K. & Gabriel, D., Interaction of random waves and currents. J. of Waterway, Port, Coastal and Ocean Engineering, 111(2) (1985) 275-88. 4. Hales, L. Z. & Herbich, J. B., Tidal inlet current-ocean wave interaction. In Proc. of Coastal Eng., Vol. 1. American Society of Civil Engineers, 1972, pp. 669-88. 5. Kaplan, P., Analysis of the effect of currents on wave forces measured on an offshore structure at sea. Offshore Technology Conf., 0TC5143. Offshore Technology Conference, 1986, 527-32. 6. Eastwood, J. W., Townend, I. H. & Watson, C. J. H., The modeling of wave-current velocity profiles in the offshore design process. Advances in Underwater Technology, Ocean Science and Offshore Engineering, 12 (1987) 327-42. 7. Fenton, J. D., Some results for surface gravity waves on shear flows. J. Inst. Maths Applics., 12 (1973) 1-20. 8. Dalrymple, R. A., A finite amplitude wave on a linear shear current. J. of Geophysical Research, 79(30) (1974) 4498-504. 9. Christoffersen, J. B., Skovgaard, O. & Jonsson, I. G., A numerical model for current depth refraction of dissipative waves. Int. Symp. on Hydrodynamics in Ocean Engineering, 1981, pp. 425-45. 10. Gaillard, P., Numerical modeling of wave-currents in the presence of coastal structures. Coastal Eng., 12 (1988) 63-81. 11. Kemp, P. H. & Simons, R. R., The interaction of waves and a turbulent current: waves propagating with the current. J. Fluid Mech., 116 (1982) 227-50. 12. Koop, C. G. & McGee, B., Measurements of internal gravity waves in a continuously stratified shear flow. J. Fluid Mech., 172 (1986) 453-80. 13. Grant, I. & Smith, G. H., Modern developments in Particle Image Velocimetry. Optics and Laser in Engineering, 9 (1988) 245-64. 14. Grant, I. & Liu, A., Directional ambiguity resolution in Particle Image Velocimetry by pulse tagging. Exps. in Fluids, 10 (1990) 71-6. 15. Adrian, R. J., Multi-point optical measurements of simultaneous vectors in unsteady flow--a review. Int. J. Heat & Fluid Flow, 7(2) (1986) 127-45. 16. Liu, A., The development of image processing techniques and their applications in Particle Image Velocimetry. PhD thesis, Heriot-Watt University, Edinburgh, UK, 1990. 17. Pickering, C. J. D. & Halliwell, N. A., Particle image velocimetry
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improving fringe signal-to-noise ratio with a two-step photographic process. J. Opt. Soc. Am., A:2(4) (1985) 610-15. 18. Grant, I. & Owens, E. H., Confidence interval estimates in PIV measurements of turbulent flows. Applied Optics, 29(10) (1990) 1400-02. 19. Peregrine, D. H. & Jonsson, J. G., Interaction of waves and currents. Miscellaneous Report No. 83-6, 1983. 20. lwagaki, Y. & Asano, T., Water particle velocity in wave-current system. Coastal Engineering in Japan, 23 (1980) 1-14.
Particle Image Velocimetry Measurements of W a v e Current Interaction in a Laboratory Flume A. Liu,* X. Shen,** G. H. Smith & I. Grant The Fluid Loading Instrumentation Centre, Heriot-Watt University, Riccarton, Edinburgh, UK EH14 4AS (Received 1 February 1991; revised version received 1 April 1991; accepted 31 August 1991)
ABSTRACT The hydrodynamics of wave-current interaction is of interest to those concerned with marine and offshore structures. In particular the fluid loading characteristic may be radically altered in a sea state consisting of a mean current flow mixed with freely propagating gravity waves. The present paper describes water flume experiments, using Particle Image Velocimetry (PIV), executed to examine hydrodynamics of wave-current interaction. A variety of wave and current conditions were investigated to determine the major influences on the combined
flOW. This paper describes the experimental procedures used to obtain simultaneous measurements of the resulting wave velocity vectors over an extended region of the wave. It also describes how the directional ambiguity inherent in the basic PIV method was resolved by 'pulse tagging' technique. Velocity vectors under waves at various phase points for different current and wave conditions are presented and compared in some cases with measurements derived using Laser Doppler Anemometry ( LDA). The resulting velocity vectors are used to estimate how the mutual interaction, between wave and current, effect the calculation of structural loads using Morrison's equation. * To whom correspondence should be addressed at: Schlumberger Industries, Flow Measurement, P.O. Box 3, Talbot Road, Stretford, Manchester, UK M32 0XX. **Present address: Department of Engineering Mechanics, Tsinghua University, Beijing, People's Republic of China. 239 Optics and Lasers in Engineering 0143-8166/92/$05-00 t~) 1992 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
240
A. Liu, X. Shen, G. H. Smith, 1. Grant
1 INTRODUCTION Wave-current interaction is a significant element defining the marine and offshore environment.~ The presence of a uniform or shear current superimposed on gravity water waves will modify the characteristics of the wave-induced particle motions near the water surface. 2'3 When gravity waves propagate in the same direction as the current, both the wave length and the maximum fluid velocity increase. When waves travel against a current, there is an increase in wave steepness with a corresponding greater probability of wave breaking? In either case the fluid loading on marine and offshore structures will increase over that calculated assuming a wave only sea state. The normal practice in estimating wave-loading is to use the Morrison equation. s'6 This calculates the loading on a structure as the sum of a drag force proportional to velocity squared and the inertial force, proportional to acceleration of the fluid as dF
dy
parD 2 8 V
CM
4
Ot + CD
V IVI
(1)
where CM and Co are the inertia and the drag coefficients respectively. Hence, a clear knowledge and accurate assessment of how the presence of a current will modify the wave only fluid velocity is required. Any improvement in the description of the water particle motions will lead to a more accurate estimate of the induced fluid loading on marine and offshore structures. The evolution of improved design relies on this process. Many studies of wave-current interaction have been made. The complexity of the motion and concomitant experimental difficulties, however, have meant that a great reliance is placed on analytical or numerical modeling, v-m Most experimental investigations reported have provided particle motion measurements as a time series at a particular point in the flow. Laser Doppler A n e m o m e t e r s (LDAs) 2'3"~1 or hot-film gauges and conductivity probes, ~2 have been most commonly used. The measurement over large regions by such methods is time consuming, and more importantly, the instantaneous relationship between flows in disparate regions would be lost. In practice, the wave-current loading is frequently obtained from Morrison's equation using a velocity/acceleration field derived from linear wave theory and the superimposition principle. This is because of the lack of experimental data describing wave-current interaction.
P I V measurements o f wave-current interaction
241
The present paper describes how Particle Image Velocimetry (PIV) was used to provide simultaneous velocity data at many stations over an extended region. The work was concentrated on the wave-current interaction in the case of current travelling with waves and at the region near the still water level. A variety of wave and current conditions were investigated to determine the major influences on the combined flow. The difficulty of resolving directional ambiguity in the particle, inherent in the investigation of wave-current interaction, was solved using a 'pulse tagging' method. The validity of the common practice of estimating fluid loading from Morrison's equation assuming a velocity field calculated from a linear addition of wave-only and current-only velocity fields is discussed. 2 BASIC T E C H N I Q U E
2.1 Particle image velocimetry PIV is an optical velocimetry technique which enables two, in-plane, velocity components to be instantaneously measured over an extended area of flow. The area of flow under investigation is illuminated with a thin 'sheet' of laser light. The flow following seed particles are photographed. The light source is pulsed during an exposure to provide stroboscopic illumination producing multiple images of each seed particle. A knowledge of the time between light pulses and the optical magnification of the imaging system enables an estimate of the local 'in-sheet' component of the flow velocity vector to be obtained, x3
2.2 Resolution of directional ambiguity using pulse 'tagging' The directional ambiguity experienced in the basic PIV image interpretation was overcome in the present study by inserting extra 'tagging pulses' into the principal laser pulse train. 14 The tagging pulses were of different duration from the principal illuminating pulses. The image size of a seed particle was proportional to the pulse duration and the flow velocity. 15 Hence, each principal image was partnered by a small tag image. The relative times of occurrence of the principal and tagging pulses were known and therefore the placing of the corresponding image gave an unambiguous measure of direction. Since the flow trajectory produced when a surface gravity wave interacted with a current was trochoidal, the identification of local flow direction was of great importance. For example, around the wave zero crossing point region, even for the particles located very close to each
242
A. Liu, X. Shen, G. H. Smith, 1. Grant
other, the direction of the horizontal velocity component could differ by 180 °. The use of the pulse tagging methods meant that unambiguous measurements of flow velocity could be obtained over the whole field under investigation. 2.3 The wave-current experiment Velocity measurements from the combined wave-current flows were compared with results obtained by adding wave-only and current-only velocity fields. The velocity field arising from the linear addition was calculated in two ways. Firstly, the PIV measurements of waves alone, Vwp, and currents alone, Vcv, were added together as Vwcp. = V~,v + Vcv
(2)
where subscript a indicates the linear addition and p denotes a measurement using PIV. Secondly, a semi-empirical wave-only model, Vwm, and an empirical current-only model, Vcm, provided velocity information for the addition as, Vwcma= Vwm + Vcm
(3)
where m defines model values. In this comparison, firstly, the differences between the PIV measurements of combined flow and the results found from linear addition of the two isolated flows were highlighted. Any measured difference could then be used to determine the validity of the linear addition model when applied to Morrison's equation. Secondly, measurements of the flow fields arising from a variety of wave and current combinations were compared. From these, the relative contribution of wave and current parameters could be investigated. These 'base-line' measurements were used to draw general conclusions regarding wave-current interaction. Additionally, a number of velocity measurements obtained using PIV were compared with those obtained using a Laser Doppler Anemometer. This gave additional confirmation of the validity of PIV as a measurement technique. The detailed experiments and data analysis are discussed below.
3 EXPERIMENTAL PROCEDURES 3.1 The wave flume The experiments on w a v e / s h e a r - c u r r e n t interaction were carried out in a wave flume which was 7 m long, 0.3 m wide and 1 m deep. The water
243
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stood at a depth of 0-66 m, as shown in Fig. 1. A dry-back, flap-type wave maker was used to produce small amplitude gravity water waves. A short beach was employed to minimise wave reflection, which is detailed in Section 3.4. Shear currents, with different mean flow speeds were generated using a centrifugal p u m p with associated pipework. 3.2 PIV instrumentation The optical arrangement is shown in Fig. 2. An 18 W, cw, argon-ion laser was used as a light source. A mechanical chopper was used to produce a train of principal and 'tagging' light pulses. The pencil beam was shaped into a light sheet by passing it through a solid glass rod before illuminating the fluid. The thickness of the light sheet was approximately 2 mm. The area viewed by camera was near the water surface with a size of approximately 300 m m (wide) × 200 m m (depth) as shown in Fig. 2. The fluid was seeded with neutrally buoyant particles of specific gravity approximately 0-98-1.02. The particles were of an inert material used in industrial coating processes with an average diameter, by volume, of 60 # m . The density of the seeding particles ensured they did not drop out during testing. The likely error caused by using the particle velocity to infer the fluid velocity was estimated from the motion of a seeding particle relative to the fluid. The result showed that
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this error was under 35/~m/s. C o m p a r e d with the amplitude of flow velocity measured ( > m m / s ) , the uncertainty was not significant. 14'~6 The PIV photographs or images were recorded using a Nikon 35 m m camera and Ilford HP5 film. A contact printing technique was employed to improve the quality of the recorded images.17 The images recorded on the photographic negative were analysed using the arrangement shown in Fig. 3. The photographic negative was mounted on a X - Y transversing carriage which was driven, independently in either direction, by two stepper motors under computer control. Each step of the m o t o r moved the negative 5 × 10-6m. Repeated traversing over the whole area of the negative was found to introduce negligible additive error in positioning. A small area of the negative was imaged onto a JVC video camera using a fiat field microscope lens. The output from the video camera was digitised and held in a Seescan RD257 framestore. The video image
245
P I V measurements o f wave-current interaction
CARR lAG E
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IT"AVE~SIN?I I Fig. 3. PIV image processing system. area was divided into a matrix of 256 x 256 divisions or pixels. The light intensity at each pixel was represented by one of 256 grey levels. The matrix was transferred to the computer for further processing and could be viewed on a monitor as a digital picture. The spatial resolution was defined by the overall magnification of the imaging system. Typically, 15-30 pixels per m m (in the object plane) was obtained. 3.3 L D A system Measurements of the flow were also made using a single c o m p o n e n t L D A which could be traversed in the vertical direction. The system incorporated a 15 mw h e l i u m - n e o n laser in a forward scatter mode, with frequency shifting, to measure the horizontal velocity c o m p o n e n t at 15 points along one vertical section. Figure 4 shows the optical arrangement and traversing system used in the L D A measurements. Figure 5 is a plan view which demonstrates the simultaneous use of the PIV and L D A at a particular section of the water flume. The L D A measurements were made only at phase 0 ° and 180 °, i.e. at the crest and trough. 3.4 Wave motion and reflection Sinusoidal gravity waves were generated using a signal generator to drive the wave paddle. Considering the limitation of the flume length, a series of experiments were performed to study and minimise the wave reflection problem. This was done, photographically, by using a high laser pulse repetition rate with a long camera exposure time. W h e n the camera exposure was equal to the wave period, the entire trajectory (orbit) of a seeding particle could be observed. The wave motion state could then be judged from an analysis of the entire trajectory of seeding particle.
A. Liu, X. Shen, G. H. Smith, I. Grant
246
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F r o m direct observation of the particle orbits, the best beach configuration to minimise wave reflection was achieved. This was a short beach with vertical strips of b u o y a n t mesh in front• The u p p e r portion of the beach surface was c o v e r e d with mesh to allow current to pass through. Figure 6(a) and (b) show the particle orbitals achieved at the test section with using a long b e a c h with a curved surface and with the final configuration described above.
3.5 Production of current profile In order to p r o d u c e a shear current near the water surface with an acceptable level of turbulent fluctuation, a bronze wire mesh held on a flexible frame was installed in front of the test area. The mesh, which had variable grades, e x t e n d e d from a b o v e the water surface to the b o t t o m of the tank. The mesh was transparent to waves. A wave gauge
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was used to monitor the wave conditions in the test section; it was placed downstream of the mesh screen during experiments. The currents were characterised by their shear rates, 8V/Oy, and mean flow speeds. The mean flow speeds were obtained by averaging along the depth of the test section. In the experiments, three bulk rates at 10, 15 and 20 m3/h, were used to provide currents with mean flow speeds at 48, 62 and 72 mm/s respectively. The one-component L D A system described in Section 3.3 was used to obtain profiles of velocity and turbulence in the middle of the test section. It was found that the final configuration of louvers and mesh limited the turbulent fluctuations to be less than 5% in most areas.
P I V measurements o f wave-current interaction
249
3.6 Wave and shear current interaction The characteristics of the w a v e - s h e a r current interactions were obtained from a series of experiments featuring various combinations of wave and current conditions. The methodology used was as follows: (1)
(2)
(3)
Sinusoidal wave only: a variety of wave amplitudes were generated for each frequency of wave. This provided baseline measurements for comparison with the combined w a v e - c u r r e n t case. Current only: current profiles at three flow bulk rates--10, 15 and 20 m 3 / h - - w e r e measured to feature the current shear rates and profiles. Wave-current: in this case experiments were carried out to provide data (a) for a single current with several wave amplitudes and frequencies and (b) for a particular wave with several current magnitudes.
The PIV photographs or images were obtained in each case.
3.7 Image processing techniques The objective of the processing was to 'group' all the principal and tagging spots corresponding to the same particle and so enable measurement of the particle displacement between laser pulses and thus infer the particle velocity. The correct directional characteristics of each 'seed' were also required. These were obtained from the locations of tagging spots relative to their principal spot partners. A n automatic processing program was developed to identify particle images and their corresponding tagging spots. The computing time taken for the analysis of one image was less than 25 s on a PC. The details of the various processing steps are presented in Refs 14 and 16. Figure 7 shows a group of the initial velocity results obtained.
4 DATA ANALYSIS AND COMPARISON
4.1 Wave motion only A series of experiments was executed to investigate the velocity fields arising from sinusoidal gravity waves with frequency, Fw, and amplitude, Hw.
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The experimental results were also used to assess the validity of a second order wave model, which was used to build a linear addition model for the prediction of w a v e - c u r r e n t interaction. This second order model was introduced based on the linear wave theory with a second order correction from Stokes theory. In this model, each
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Fig. 8. Comparison of wave profiles (F. = 2 Hz, Hw = 36mm): (a) trough (180°); (b) crest (0°). 4.2 Current flow only The current profiles m e a s u r e d by the PIV technique were c o m p a r e d with the results m e a s u r e d using a one-dimensional L D A system to ensure their accuracy and reliability. ~8 As depicted in Fig. 10 the a g r e e m e n t b e t w e e n the results derived from the two techniques was good; the difference errors b e t w e e n the two techniques were normally less than 2%. It was found that the current profile could be separated into two regions: a region of high shear close to the water surface, with a region of lower shear in the middle and lower portion. The two higher volumetric flow rates, 15 m3/h and 20 m3/h exhibited larger shear rates in the region close to the m e a n water level than that shown at a volumetric flow rate of 10 m3/h. The experimental currents were idealised into two linear regions, i.e. a high shear region and a low shear region, for comparison with the results obtained from the combined w a v e - c u r r e n t m e a s u r e m e n t s . The idealised current profiles were obtained by fitting experimental results with linear equations, f a t + b r y,
vc [ aB +
bBy,
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(5)
253
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254
A. Liu, X. Shen, G. H. Smith, I. Grant
where constants bT and bB relate to the current shear, aT and aB relate to the mean velocity, and YT is the transition point between the two regions. The y-axis was defined as depicted in Fig. 10. In the present study, the point YT, =40 mm, was chosen in all three cases as the point at which the second derivative of the current profile was maximum. The detailed values of aT, aa, bT and bB were solved from eqn (3) using the least squares method. The constants aT, bT, as and bB, which varied with the flow rate Q, are listed in Table 1. The gradients for the upper region of the flow were seen to vary depending on the volumetric flow rates. In the case of the 10 m3/h rate it was relatively small, 0.27. However, the rate of shear for the higher flow rates used was somewhat greater, 0.34 and 0.39 for the 15 m3/h and 20m3/h flow, respectively. For y
Since the sinusoidal waves were progressed with currents, the extension of wave crest region and the reduction of wave trough region were straightforwardly demonstrated from PIV measurements. A whole field comparison of the wave-current flow vectors measured from PIV with those obtained from the addition of the second order wave particle velocity model (eqn (4)) and the measured current profile (eqn (3)) are shown in Fig. 11. The velocity differences are shown in Fig. 12. A comparison of the measurements of the combined wave-current interaction and the result of a linear addition of wave-alone and current-alone velocities was also carried out at different wave phases. That is, the variation of the horizontal velocity profiles with water depth from the wave-current data was compared with the result of a linear addition of wave-only and current-only velocity profiles. The PIV measurements from the wave-current interaction were compared to the result obtained from linear addition for the region of the wave crest. Figure 13 shows the variation in horizontal velocity component with depth measured by PIV. Also shown are the results of a linear addition of measured wave- and current-only flows. Finally, the velocity fields are depicted. It is clear that in the wave crest region (phase 0 °) the results obtained by adding the separate PIV measurements for wave-only and currentonly cases are close to those derived from the linear addition of the two
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A. Liu, X. Shen, G. H. Smith, 1. Grant TABLE 1 Variation of Constants with Flow Rate
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P I V measurements of wave-current interaction -20-
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semi-empirical flow models. The differences are mostly less than 5 % . H o w e v e r , the m e a s u r e m e n t s of w a v e - c u r r e n t interaction, Vwcp, are smaller than linear superposition results o b t a i n e d from either theoretical or experimental results. T h e difference b e t w e e n m e a s u r e m e n t s of w a v e - c u r r e n t interaction and the results from the linear addition of wave-only and current-only is m o r e significant in the region close to the still water level (approximately 1 5 - 2 5 % ) , and decreases with water depth. Further comparisons of P I V m e a s u r e m e n t s of w a v e - c u r r e n t interaction and the predictions from linear addition were m a d e in which either the wave amplitude, wave frequency or current rate were varied. This was to highlight the effect that each flow characteristic has on the w a v e - c u r r e n t interaction. Figure 14(a) and (b) show the P I V m e a s u r e m e n t s of w a v e - c u r r e n t interaction and results from the two linear addition m e t h o d s at the wave crest region (phase 0°). T h e results were obtained at the same current rate Q = 15 m3/h with two different waves having a frequency Fw = 2 H z b u t with different amplitudes Hw = 25 m m and Hw = 36 mm. It was f o u n d that with the increase of wave amplitude from 25 m m to 3 6 m m , the difference b e t w e e n m e a s u r e d velocities and the results predicted from linear addition was greater. In the region close to the still w a t e r surface, the difference increased approximately from 17% to 30% as w a v e amplitude increased from 25 m m to 36 mm. The effect of
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wave amplitudes on w a v e - c u r r e n t interaction has also been investigated by Peregrine and J o n s s o n . t9 A similar conclusion was reached. In Fig. 15(a), (b) and (c), profiles obtained for the same wave conditions but three current rates, in the wave crest region are compared. In this case the PIV and L D A measurements of w a v e current interaction are c o m p a r e d with results from adding the semiempirical wave-only model and current-only profiles. The data obtained by P I V and L D A are in very good agreement for each of the various current rates. The magnitude of the measured combined velocity profiles is still less than that predicted by linear addition. The departure between profiles decreases as measurements were made at greater depths below the still water level. It was found that a higher shear rate increases the profile departure between the measured and linear addition profiles. Referring to Table 1, the current shear rate at Q = 15 and 20 m3/h were much higher than that for Q = 10 m3/h. This increased the difference between measured and predicted profiles, as illustrated in Fig. 15(a)-(c). In the region close to the still water surface, differences between measured and predicted velocities were approximately 20%, 25% and 27%, corresponding to current rates Q = 10, 15 and 20 m3/h. The influence of current shear rate is also evident from the results for a single shear current. The difference between measured and predicted velocity field is large in the high shear b-r region of the current profile.
260
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For example, at Q = 20 m3/h at a depth below the still water surface of 4 0 m m for which the current shear bB was m u c h less than bT, the d e p a r t u r e was u n d e r 10%. In the w o r k of Iwagaki and A s a n o , 2° the influence of the current profile on w a v e - c u r r e n t interaction was also emphasised. It is shown that in the region close to the still water surface, the differences b e t w e e n the predicted results for the parabolic c u r r e n t case and m e a s u r e d results are m u c h larger than those b e t w e e n the predicted results for the uniform current case. In other words, when the gradient of the current profile was less, the differences between m e a s u r e d and predicted results was less in the region close to the still water surface. Figure 16 shows how the differences e n h a n c e w h e n the c u r r e n t shear rates increase.
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A. Liu, X. Shen, G. H. Smith, I. Grant
262
5 SUMMARY In summary, the velocities measured in the crest region for the combined wave-current interaction were less than those predicted by a linear addition of the wave-only and current-only velocity fields. The difference between measured and calculated profiles became more significant with an increase of wave amplitude and current shear rate. In the present flow conditions, the difference in the region near the still water surface varied from 15% to 25%. In the wave trough region where the particle velocities were against the currents, a rapid attenuation in velocity and trough region size was undergone with an increase of the current rate. However, the difference between the PIV measurements of wave-current interaction and results from linear addition was not as significant as that found in the crest region, as shown in Fig. 17. Consequently, if the velocities derived from a linear addition of wave-only and current-only profiles were employed in Morrison's equation to estimate fluid loading, the resulting estimated drag force (which was proportional to velocity squared) in the wave crest region would be overestimated.
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PIV measurements of waoe-current interaction
263
REFERENCES 1. Ismail, N. M., Wave-current models for design of marine structures. J. of Waterway, Port, Coastal and Ocean Engineering, 110(4) (1984) 432-47. 2. Kemp, P. H. & Simons, R. R., The interaction of waves and a turbulent current: waves propagating against the current. J. Fluid Mech., 130 (1983) 73-89. 3. Hedges, T. S., Anastasiou, K. & Gabriel, D., Interaction of random waves and currents. J. of Waterway, Port, Coastal and Ocean Engineering, 111(2) (1985) 275-88. 4. Hales, L. Z. & Herbich, J. B., Tidal inlet current-ocean wave interaction. In Proc. of Coastal Eng., Vol. 1. American Society of Civil Engineers, 1972, pp. 669-88. 5. Kaplan, P., Analysis of the effect of currents on wave forces measured on an offshore structure at sea. Offshore Technology Conf., 0TC5143. Offshore Technology Conference, 1986, 527-32. 6. Eastwood, J. W., Townend, I. H. & Watson, C. J. H., The modeling of wave-current velocity profiles in the offshore design process. Advances in Underwater Technology, Ocean Science and Offshore Engineering, 12 (1987) 327-42. 7. Fenton, J. D., Some results for surface gravity waves on shear flows. J. Inst. Maths Applics., 12 (1973) 1-20. 8. Dalrymple, R. A., A finite amplitude wave on a linear shear current. J. of Geophysical Research, 79(30) (1974) 4498-504. 9. Christoffersen, J. B., Skovgaard, O. & Jonsson, I. G., A numerical model for current depth refraction of dissipative waves. Int. Symp. on Hydrodynamics in Ocean Engineering, 1981, pp. 425-45. 10. Gaillard, P., Numerical modeling of wave-currents in the presence of coastal structures. Coastal Eng., 12 (1988) 63-81. 11. Kemp, P. H. & Simons, R. R., The interaction of waves and a turbulent current: waves propagating with the current. J. Fluid Mech., 116 (1982) 227-50. 12. Koop, C. G. & McGee, B., Measurements of internal gravity waves in a continuously stratified shear flow. J. Fluid Mech., 172 (1986) 453-80. 13. Grant, I. & Smith, G. H., Modern developments in Particle Image Velocimetry. Optics and Laser in Engineering, 9 (1988) 245-64. 14. Grant, I. & Liu, A., Directional ambiguity resolution in Particle Image Velocimetry by pulse tagging. Exps. in Fluids, 10 (1990) 71-6. 15. Adrian, R. J., Multi-point optical measurements of simultaneous vectors in unsteady flow--a review. Int. J. Heat & Fluid Flow, 7(2) (1986) 127-45. 16. Liu, A., The development of image processing techniques and their applications in Particle Image Velocimetry. PhD thesis, Heriot-Watt University, Edinburgh, UK, 1990. 17. Pickering, C. J. D. & Halliwell, N. A., Particle image velocimetry
264
A. Liu, X. Shen, G. H. Smith, I. Grant
improving fringe signal-to-noise ratio with a two-step photographic process. J. Opt. Soc. Am., A:2(4) (1985) 610-15. 18. Grant, I. & Owens, E. H., Confidence interval estimates in PIV measurements of turbulent flows. Applied Optics, 29(10) (1990) 1400-02. 19. Peregrine, D. H. & Jonsson, J. G., Interaction of waves and currents. Miscellaneous Report No. 83-6, 1983. 20. lwagaki, Y. & Asano, T., Water particle velocity in wave-current system. Coastal Engineering in Japan, 23 (1980) 1-14.