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Simultaneous Velocity and Pressure Measurements using PIV and Multi Layer Pressure Sensor Arrays in Gravel Bed Flows M. Detert, V. Weitbrecht & G.H. Jirka Institute for Hydromechanics (IfH), University of Karlsruhe, Germany

HMEM 2007, ASCE-Conference in Lake Placid, 2007/09/12, final version at September 4, 2007

To investigate hydrodynamic processes above and within river beds, laboratory experiments have been performed to quantify the interaction between turbulent flow and pressure fluctuations at a porous gravel bed. A 2-D Particle Image Velocimetry (PIV) system measuring in streamwise vertical or horizontal planes above the gravel layer was used, synchronized with a pressure sensor array of 16 miniaturized piezoelectric pressure sensors (MPPS). This setup enables the visualization and quantification of instantaneous, simultaneous velocity and pressure fields. Results under stable bed conditions show alternating large-scale wedge-like structures of uniform momentum, inclined at an angle of 10 − 25° to the bed in flow direction. The measurements show a significant pressure drop in regions where fluid with high speed interacts with fluid of lower velocity in the sense of a sweep event. This characteristic pressure drop can lead to the initial lift that is needed for the entrainment of single grains.

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Adrian et al. (2000)a proposed an extended model that also describes coherent structures in the outer flow: individual packets with uniform momentum flow exist under fluid packages of hairpin vortices. These hairpin vortex packages (HVP) originate from the smooth bed and incline along straight lines, generally with an angle of 12° to the smooth wall. Tomkins (2001) showed that large scale structures angled upwards at ∼ 10 − 20° are also common over rough walls generated by hemispherical elements. Both Adrian et al. (2000)a and Tomkins (2001) did wind tunnel experiments with a 2-D PIV setup.

INTRODUCTION

Fluctuating forces at a river bed are the result of a complex interaction. On the one hand there are the dynamics of the free surface flow interacting with the interstitial flow. On the other hand there are eddygenerating mechanisms near the wall. These eddies emerge from both, wakes behind single roughness elements and unrolling-processes at free shear layers. The latter eddy-generating mechanism was first described by Kline et al. (1967) as the bursting phenomenon with well organized turbulence structures in the vicinity of the boundary layer of a smooth impermeable wall. Based on wind tunnel experiments with hot wire probes and piezoelectric pressure transducers, Thomas and Bull (1983) identificated a characteristic wall-pressure pattern associated with the burstsweep cycle and the inclined shear layer between two large organized flow structures, respectively. Grass et al. (1991) evidenced that streaky, coherent structures are also present near rough walls. Defina (1996) showed experimentally, that the lateral spacing between these structures is λz ∼ = 3.8ks , with ks being the equivalent sand-roughness. Lately, St¨osser et al. (2005) confirmed this criterion using a LargeEddy Simulation (LES) of flow over a channel bed, roughened with one layer of spheres.

Roy et al. (2004) measured large scale wedge-like flow structures in natural, gravel-bed rivers by electromagnetic current meters. The structures are narrow and elongated, with either increased or decreased velocity over most of the water depth h. The average angle in the streamwise direction was estimated to be inclined at 25° to the bed. The average longitudinal length scales were determined to be 3 − 5 h, the width was between 0.5 − 1 h. Hofland (2005) observed the flow field during the entrainment of a single stone using 2-D PIV technique and piezoelectric pressure sensors that were housed in artificial stones. He showed by conditionally sampled flow fields, that two structures are responsible 1

for the entrainment. Small-scale vertical fluctuations, rms(v), initiate the motion of the stone and a largescale sweep, (u0 > 0, v 0 < 0), moves the stone further over its pivot point. This result was roughly confirmed by high speed 2-D PIV results Cameron et al. (2006), who found a sweep structure over and around a target particle to be the cause of entrainment. Breugem (2005) studied the influence of wall permeability on turbulent flows both theoretically and by direct numeric simulations (DNS) of flow on top and through a porous medium of cubes. He showed that turbulence near a highly permeable wall is dominated by relatively large vortical structures, which originate possibly from a Kelvin-Helmholtz instability of the inflexional mean velocity profile. Wall permeability causes a large increase in the pressure fluctuations rms(p). A validation of these results by experimental data is missing. Lately, Flores and Jim´enez (2006) and Hurther et al. (2007) did intensive investigations of flow over rough walls; the former by DNS over artificial roughness, the latter used Acoustic Doppler velocity profiler (ADVP). Both studies support close similarities of coherent structures over smooth and rough walls, although the scaling laws are different. To sum up, much research has been done concerning coherent structures in flow over rough walls, especially within the last decade. Most of the studies focus on the velocity field in a streamwise vertical plane, disregarding its lateral extension as well as the permeability of the wall and closely connected pressure fields. A comprehensive measurement campaign is missing to close the lack of a synoptic understanding. This paper shows exemplarily, how advanced measurement techniques can be used synchronously to get insight into the whole flow regime on top and and within a gravel bed.

the distribution was very uniform. A roughness geometry parameter was determined to be Φ = Vf /Vo = 0.38 − 0.40, with Vf as volume of fluid within the total volume Vo . In loose package, the density was ρ = 2, 460 kg/m3 . As the bottom of the flume had a slight declination of Sb = 0.5‰, this also roughly holds for the mean slope of the porous bed. However, due to a slight inevitable erosion that started at the outlet, the slope increased up to Sb ' 0.8‰ downstream of the measurement area. Fig. 1 illustrates the measurement setup, which consisted of up to 16 miniaturised piezometric pressure sensors (MPPS) located within the gravel layer, and a 2-D Particle Image Velocimetry (PIV) system. The latter technique was used for measuring velocities both in a centerlined plane perpendicular to the bed (xy-plane: setup A) and in a horizontal plane directly above the gravel layer at y = +7.5 mm (xzplane: setup B). Additional insight into the velocity regime was gained by Acoustic Doppler Current Profilers (ADCP) in order to double-check the PIV results. The data acquisition was carried out simultaneously for the 2-D PIV system, 16 MPPS and one single ADCP probe for 205 s. Hereinafter, only one flow condition will be considered, where the provided flow rate was Q = 0.120 m3 /s at a water depth h = 0.20 m. The bulk velocity was determined by Ubulk = Q/(Bh) = 0.667 m/s. With the kinematic viscosity of water ν = 10−6 m2 /s at 20°C, the Reynolds number is

2 EXPERIMENTS 2.1 SETUP The experiments were carried out in a flume with an effective length of L = 16.5 m and a width of B = 0.9 m. The inlet was located at x1 = −10.5 m, the outlet at x = +6.5 m was controlled by a lamellaeweir (vertical arrangement). Hence influences of inlet (fully developed boundary layer) and outlet were negligible. A porous gravel layer of hP = 0.10 m was inserted. The grain sizes quantiles were d10 = 7.7 mm and d85 = 13.2 mm, and the weighted mean of the whole grain size distribution was d = 10.2 mm. Thus, 1 A right-handed coordinate system is implied, where x is orientated positive in streamwise, y in upwards vertical and z in transverse direction. The origin of the global x = 0 is located in the measurement area, y = 0 is below 0.25d of the uppermost gravel tops (±1 mm) and z = 0 in the centerline of the flume. The velocity components u, v and w correspond to x, y and z.

Figure 1: Sketch of experimental setup, dimensions in [m], not to scale. (a) view in streamwise direction, with both 2-D PIV arrangements setup A and B. b) side view.

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Reh = U h/ν = 133, 000. The equivalent sand roughness of ks = 26.5 ± 2 mm resulted from a logarithmic fit of the double averaged velocity profile hu(y)ix for y/h < 0.2, gained by PIV and was confirmed by u(y) from ADCP. The shear velocity was calculated in the same manner as ks to u∗log = 0.064 ± 0.002 m/s, roughly validated by an estimation of the bed shear stress τb = f(∆h/∆x, Sb ). In contrast to this, the maximal Reynolds stress component from PIV gave 1/2 u0 v 0 = 0.055 m/s, indicating the presence of secondary currents due to an aspect ratio of B/h = 4.5 (Nezu and Nakagawa (1993)).

based on the piezoresistive effect. The initial point is an element of silicon, with implanted resistances in its bending panel. The differential pressure is measured with reference to atmospheric pressure, with compensation of temperature errors. The components for the MPPS were obtained from Aktiv Sensor GmbH, Berlin (sensor element ATD 0.040-G00-BG-K1408 and AU blank PGA-V0-D18A). The components were assembled at the IfH to adapt them to their application within the experimental flume. To miniaturize the pressure pick-up the amplifying blankets had to be arranged in an external box. Unfortunately, the length of the flexible cables to the external amplifying board could not be shorter than 2.5 m. Thus, the possibility of a slight antenna effect had to be accepted. Flexible PVC tubes were used to provide atmospheric pressure in the pick-up, also with a length of 2.5 m. The heads of the MPPS were encapsulated with slowly hardening epoxy resin and sealed up with clear varnish to make them water resistant. Thus, the mean diameter of one sensor head was 15 mm. The readybuilt sensors were point-calibrated by Aktiv Sensor GmbH to 1 − 9 V according to 0 − 4 kPa with a tolerance in accuracy of less than 1.0% full scale. The response time guaranteed by the manufacturer was < 10 ms, limited due to signal conditioning by the amplifying blankets. Test under flume conditions showed, that the MPPSs even were able to react on the laser double pulse of 2 ms, as the sensors were aligned within the laser sheet. This unforeseen effect was used to validate the synchronization of the PIV and the MPPS. To avoid aliasing effects due to high frequency noise > 2 kHz, the recording was made at f = 2125.7 Hz, additionally supported by a 4th order Butterworth low-pass filter with a cut-off frequency of 500 Hz (DT SAK 52-150-501-10). The sensors had an absolute range of 0 − 4 kPa. A 16-bit AD-Card (DT 321) allowed a theoretical resolution corresponding to a LSB = 20/8 · 4000/216 = 0.15 Pa.

2.2 PIV The PIV system is a 2-D PIV LaVision system. Measurements were based upon seeding the flow with neutrally buoyant tracer particles (Vestosint polyamide powder, d = 80 − 200 µm) and illuminating the flow field with a double-pulsed Nd:Yag laser with a pulse energy of up to 25 mJ per pulse. The laser sheet was enlarged by a tophead lens and a had thickness of 1 − 2 mm. For setup A, the laser sheet was guided through the water surface by a streamlined boat construction. For measuring a horizontal plane in setup B, a similar construction for the camera was inserted. An interval time of 2 ms was used to acquire one double frame. When the laser sheet sliced through the flow, light was scattered by the seeding material and detected by a 1280x1024 pixel CCD camera (Flowmaster 3S). At setup A (B), the size of the camera frames were vertically (laterally) reduced to 1280x384 (1280x800) pixel to increase the read out time. Thus, constant double frame rates of f = 8.5(4.9) Hz were reached, leading to 1740 (1003) double frames within 205 s. The data were directly written to a RAID system. The image processing was done by a multipass cross-correlation method with discrete window offset, where the intermediate vector fields were smoothed by a 3x3 Gaussian filter. A final window size of 16x16 pixel with 50% overlap was chosen. This led to a spacial resolution of 2.52(2.06) mm and a vector spacing of 1.26(1.03) mm. The resulting vectors were checked by a median filter, an absolute allowed vector range and the distinctiveness of the highest correlation peak. Typically 75-80% of all vectors were validated. The final vector fields were smoothed by a 2x2 moving average filter. Thus, the velocities were large-eddy filtered to a kernel of 2.52(2.06) mm. 2.3 MPPS Fig. 2 shows the sensor array in a top view, as it was mounted on a grid for setup B (similar to A). The sensors were locally fixed on a grid to keep them on an accurately defined position. The principle of the miniaturized piezoelectric pressure sensors (MPPS) is

Figure 2: Top view of the MPPSs mounted in the gravel layer, setup B. The white circle highlights the ’target’ sensor head at (x, y, z) = (−6.0, −1.5, 0.2) [mm] (see ch. 3).

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3 RESULTS Before looking at the PIV results we concentrate on the pressure signals. Fig. 3 shows a cutout of one time series where a significant pressure drop is visible, which is related to the occurrence of coherent structures that are shown later in this paper. In fig. 3, first the pressure increases slowly, here from −40 to +40 Pa within 0.25 s. Than an essential pressure drop can be observed. This drop is accompanied by increased small scale pressure fluctuations. In this example, p0 decreases within 0.12 s rapidly to an absolute minimum of −220 Pa. A simple estimate shows, how this pressure drop could have led to the entrainment of a single grain: A force balance considering buoyancy and neglecting friction and inertia shows, that in the case that −220 Pa acts on 23% of the surface of a single (sphere shaped) gravel grain, it can be lifted.

Figure 4: Wedge-like √ flow structure passing the measurement window. u2 + v 2 is indicated by shadings of 1/3 Ubulk . Dotted lines: λci = 2.5 · 10−4 [s−2 ]. From each vector 0.8 Ubulk has been subtracted. In x/y every 16th/2nd vector is plotted. x: position of target sensor. Figure 3: Times series of p0 (t), showing at a typical pressure drop, setup A. Position of the ’target’ sensor: fig. 2, but y = 0. Labels: raw signal (-) and FIR-filtered (-◦-).

A closer look back to Fig. 3 shows, that p0 drops significantly when the tail of the slower wedge-like fluid structure passes the location of the pressure sensor and the faster fluid zone runs upwards on the back of the slower moving fluid volume. Because of the increased velocity, the pressure sensor measures a strong pressure drop. Thus, there is a clear correlation of the interaction between the two fluid packets to a rapid decrease of the pressure fluctuations at the bed. Furthermore, the interaction of the coherent flow zones play an important role on the initial movement of a single grain in general. To prove this, a conditional sampling method was used as follows: First, the pressure signal of the ’target’ pressure sensor was FIR-filtered (see fig. 3). Using a dp/dt criteria the positive peaks of p0 just before the strongest pressure drops were detected. Then, the corresponding, nearest neighbor PIV frames were collected. Assuming frozen turbulence, the collected frames were additionally extended by their two neighbored frames using a splicing method similar to Hofland (2005). Fig. 5 gives the resulting flow structure where 10 events are conditionally averaged. The observed structure again shows the typical wedge-like shape and is correlated to a characteristic pressure drop. An angle of ∼ 12° formed by the top of the eddies within the shear

To correlate this pressure signal with the simultaneously measured PIV results, the frames V1, V2 and V3 are analyzed (see fig. 4). Starting at t = 126.24 s (V1), a slower fluid packet with an angle of approx. 20° inclined to streamwise direction is prominent for the flow near the bed. Keeping its wedge-like structure, the packet moves forward, followed by a second fluid area of higher momentum (t = 126.35 s, V2). Due to its faster propagation velocity, the second fluid packet ’overruns’ the first one. Within the shear layer between both zones, small eddies are generated. Here, the vortex cores are indicated by the swirling strength λci using dotted lines (definition: see Adrian et al. (2000)b.) At t = 126.47 s (V3), the structure with lower momentum has completely passed the measuring window. It was observed, that these structures are self similar, roughly repeating with a frequency of 0.5 − 2Hz. This agrees with the model of Adrian et al. (2000) for the organization of vortex structures in the outer boundary layer of smooth walls. The observed angles of inclination of 10 − 25° agree well with results from Roy et al. (2004). 4

layer is in exact agreement with Adrian et al. (2000)a. To analyse the horizontal appearance of these coherent flow structures, similar measurements have been performed using a horizontal laser light sheet (setup B). The results shown in fig. 6 are not taken simultaneously with the results in fig. 3 and fig. 4, but the frames H1-3 belong to the same kind of an interacting flow-pressure pattern as in V1-3. Similar observations can be made that support the discussed findings: The rapid transition from a slow to a fast fluid zone leads to a significant pressure drop. In fig. 7 the results of 10 conditionally sampled and averaged flow fields were used to give an estimate of the horizontal dimensions of the coherent structures: The flow structures appear to be slender and scale with the water depth h. The pressure field in fig. 8 simultaneously recorded to V1-3 also confirms this estimate. Here, the time domain t of 11 MPPS, located at −7.5 < x < 7.5 mm was transformed to a longitudinal dimension λx = Uc t, where Uc denotes the mean transport velocity of the pressure fields. It was gained from signalcorrelation of the upstream to the downstream MPPS (see fig. 3), resulting in Uc = 0.71Ubulk . In this, the x-direction reflects the dimension ’sensed’ by a stationary observer (Eulerian view). However, in assuming a constant Uc , streamwise dimensions of faster pressure fields are underestimated, and x-dimensions of slower fields are overestimated, respectively. Focussing on the flow pattern shown before in fig. 6, the longitudinal dimension of the corresponding pressure field is 3h (λx = 3600 − 3000 mm) and the breadth ∼ 0.5h. Also slender structures with smaller sizes can be seen, e.g. at λx = 2900 − 2600 mm or λx = 2950 − 2850 mm. Figure 6: Top view at y = 7.5 mm (PIV). Shadings: u0xz = (0.125 : 0.175 : 0.2 :>√0.2) [m/s]. Dashed lines: λci = (2.5 · 10−4 ) [s−2 ], (–,–): u2 + v 2 = (0, 0.2) [m/s]. 0 ). In x/z every 16th/2nd vector > u Vectors: (u0xz , wxz xz is plotted. Black circle: position of the ’target’ sensor (fig. 2).

4 SUMMARY AND OUTLOOK Laboratory measurements combining 2-D velocity and 2-D pressure information to investigate hydrodynamic processes above and within porous gravel layers has been presented. PIV measurements in horizontal and vertical planes synchronized with with a pressure sensor array of 16 miniaturized piezoelectric pressure sensors (MPPS) allows the identification of bed destabilising flow processes in the vicinity of rough gravel beds. Significant pressure patterns including a strong pressure drop could be identified as the transition point from zones of low flow velocities over-rolled by zones of fast fluid. A simple force balance shows that this pressure drop can be the initial point of the entrainment of single grains. By conditional sampling, it was shown that these fast flow pattern are correlated to a strong acceleration of the fluid in the sense of a sweep event. The shape is inclining and wedge-like. A rough estimate of time and length scales of these flow structures support the

Figure 7: Top view of conditionally sampled flow structures at the 10 strongest pressure drops within 1003 PIV frames in 205 s. Shadings, labels, vectors: see fig. 6.

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Figure 5: Wedge-like flow structure, conditionally sampled from the 10 strongest pressure drops within 1740 PIV frames in 205 s, each spliced from a sequence of 3 PIV-frames. x: position of target sensor. The bold dashed line visualizes an angle of ∼ 12° of the top of the eddies, indicated by the swirling strength. Contour lines in steps of 1/6 Ubulk . Shadings, labels, vectors: see fig. 4.

Figure 8: Pressure fluctuations p0 (λx = Uc t, z) at a horizontal plane at y = −1.5 mm for setup B. ’Sensed’ flow direction from left to right. Uc = 0.71Ubulk results from signal-correlation of the upstream to the downstream sensor (see fig. 3). Each time series is FIR-filtered to 200 Hz and smoothed by a motion filter of (1/8 1/4 1/4 1/4 1/8) to achieve approx. equally spaced axes. Shadings are p0 = (−10 : −20 : −30 :> −30) [Pa], the contour line is p0 = (+10) [Pa]. The rectangles correspond to the 3 PIV frames in fig. 6.

results from Roy et al. (2004) measured in a natural gravel bed river: The typical flow structure is slender and scales with the water depth h. Further experiments will be performed over natural sediment and in case of spherical roughness elements to allow comparison with natural conditions and numerical simulations, respectively.

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ACKNOWLEDGEMENTS Support by the ”Baden-W¨urttemberg Research Program Securing a Sustainable Living Environment” (BWPLUS, project BWR 25003) with funds of the State BadenW¨urttemberg is gratefully acknowledged. Special thanks to B. Hofland and G. K¨uhn for their ingenious ideas.

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