Effect of bed form evolution on sediment erosion and suspended load transport in an impinging jet

Transcription

1 th 17 International Symposium on Applications of Laser Techniques to Fluid Mechanics Effect of bed form evolution on sediment erosion and suspended load transport in an impinging jet Ken T Kiger1,*, Kyle Corfman1, Rahul Mulinti1 1: Department of Mechanical Engineering, University of Maryland, College Park, Maryland, USA * correspondent author: kkiger@umd.edu Abstract Two-phase flow experiments have been conducted to study particle suspension and sedimentation within coupled particle-laden flows relevant to rotorcraft brownout conditions. Specifically, a downward facing strongly forced jet was impinged upon a mobile sediment bed consisting of nominally uniform glass spheres. The evolution of the eroded bed and the suspended flux of particles were measured using a combination of calibration photogrammetry and two-phase PIV under repeated, but separate tests. The results show that the initially flat bed quickly erodes into radial bed forms, initiated near the point of closest approach of the coherent vortex within the forced jet. The region of strongest erosion is found to correlate to the peak in coherent Reynolds stress produced by the primary vortex. With subsequent development to larger bed forms, the peak erosion rates move to the stoss slope of the first and second dune, with similar erosion rates on both faces. The suspended load observed in the early flat bed conditions is shown to be spatially evolving with a monotonic increase with downstream location, while the eroded bed conditions show a much larger (approximately 10x) magnitude with very little evolution within the field of measurement. 1. Introduction Rotorcraft brownout is characterized by dust suspension that is uplifted during rotorcraft operations such as landing, takeoff or hover in a dusty environment. The downwash from the main rotor is strong enough to suspend large amounts of dust and sand and the resulting dust cloud can severely impair pilot s visibility (Figure 1). One of the main flow features within the rotor wake are intense vortices shed from the tips of the rotor blades, which are advected in the downwash in a helical path and subsequently interact with the ground plane in a turbulent stagnation point flow (Johnson et al 2009). Mitigation of brownout requires a thorough understanding of the particle suspension behavior under brownout conditions as a function of wall/vortex interaction parameters and the initiation mechanisms of events like saltation and scouring. Most sediment suspension models are based upon assumptions of a quasi- equilibrium development, which are inadequate in predicting the suspension process in this highly transient flow. Furthermore, quantification of particle/turbulence interaction is necessary to examine the nature of a potentially strong coupling that may Fig.1 Dust cloud formation around landing zone -1-

2 alter vortex dissipation process. Rapid erosion of sediment and formation of topographic structures on comparatively short time-scales can potentially alter the boundary conditions from a nominally planar surface in significant ways, leading to a coupling between the evolution of the air and sediment phases. To this end, experiments have been conducted with a sediment bed to assess the effects of evolving bed topography (i.e., possible valley or ripple formation by scouring) on the evolution of the near-wall vortex structures. 2. Experimental Test Conditions To understand the coupled two-phase fluid mechanics of the sediment entrainment process, a simpler prototype model of a forced impinging jet has been constructed (see Fig. 2). This facility is capable of generating repeatable coherent vortex rings superimposed within an axisymmetric stagnation point flow in the presence of a mobile sediment bed. This captures the essential features of a strong and highly organized blade tip vortex undergoing a transient interaction with the surface, while providing a limited lifespan to moderate the amount of particulates that are extensively suspended in the chamber. The jet diameter was D j = 10 cm, and located a distance of H = 10 cm above the mobile bed. The mean exit velocity U j = 4.1, 6.2 or 7.9 m/s, and was force with a frequency of f = 35, 55 or 75 Hz to maintain a nominally similar Strouhal number of S = fd j /U j = 0.85, 0.89 and 0.95 and an increasing Reynolds number of Re = D j U j /ν = 27,000, 40,700 and 52,700, respectively. The amplitude of the forcing was reduced to keep similar circulation strengths in the three cases, which was nominally 0.59, 0.52 and 0.63 m 2 /s, respectively. Fig. 2 Schematic of test facility and measurement regions. Experiments were conducted using a 1.5 cm thick sediment bed made of 45 < d < 63 µm or 120 < d < 180 µm particles (sieved). All tests were started from a nominally flat and smooth bed, produced by drawing a screed plate (situated on guide rails positioned over the solid bottom of the test chamber) across a loosely placed bed. The minimum test velocity was selected by determining those conditions that produced incipient motion of the smallest particles when the jet was unforced. The Stokes number (St = ρ p d 2 f/18ν, based on the mean particle size and jet forcing frequency) varied from 0.8 at the lowest speed for the small particles to 13.5 for the largest size at the highest speed condition. Quantitative imaging of the sediment bed profile and suspended sediment were recorded in separate experiments using several different fields of view, as shown in Figure 2. The flow was illuminated with dual cavity Nd:YAG laser (Litron nanopiv, capable of 200 mj per pulse, 15 Hz repetition rate) with a light sheet formed in a vertical plane with a nominal thickness of 1.5 mm, as measured by the sheet half-width thickness determined from a beam profile camera. The thickness varied by no more than 15% over the field of view. Two frame-straddling CMOS cameras (LaVision, Imager ProX4M, 14-bit, 2048x2048 pixels) were used to acquire the images. For the bed erosion profiles, the light sheet was directed downward from above the bed to minimize the - 2 -

3 obscuration by evolving bed forms. Two overlapping camera views (Region IIa and IIb) were used to obtain profiles from 0.8 < r/r j < 4.6 (105 mm lens, f# = 11, image resolution = 50 µm/pixel). The profiles were measured with the jet turned off to prevent suspended load from contaminating the bed elevation measurement. Scattering from the bed produced a bright band where the light sheet intersected the bed. The static images were smoothed with a Gaussian filter in the vertical direction, and the peak scattering intensity was used to mark the nominal bed height. Changes in bed elevation relative to the initial profile were discernable to better than 1 pixel. Separate single-phase PIV tests with a glass plate in place of the mobile bed were also conducted with a similar field-of-view to the bed profile imaging (Region IIa and IIb) to get a measure of the vortex strength and trajectory within the domain. A standard multi-pass algorithm (LaVision Davis, ver. 8.1) was used in the interrogation (5-frame sliding minimum subtraction applied to images, initial window = 64x64 pixels, final window = 32x32 pixels with 50% overlap). In addition to the above bed erosion and single-phase observation tests, phase-resolved particle imaging velocimetry (PIV) was conducted to obtain a measure of the suspended particle concentration, velocity and flux, in conjunction with the corresponding unsteady fluid structure and statistics. Two overlapping camera views (Region IIIa and IIIb) were used with a field of view covering 3 < r/r < 5 (200 mm lens, f# = 8, image resolution = 25 µm/pixel). The laser and camera were synchronized with the forcing applied to the jet speaker, allowing for ensemble-averaging of the flow characteristics at a given phase within the forcing cycle. Ensembles of 500 image pairs were used to accumulate statistics for the flow. Two conditions were selected for detailed examination: 1) a nominally flat bed case where data was accumulated from repeated trials sampled over a period of 3 < t < 9 seconds after the flow was initiated and 2) an eroded bed case where visible bed forms were established over the time range from 80 < t < 86 seconds after the flow was initiated. Ensembles were created from groups of 16 different tests (35 image pairs in each group, 560 total samples), each of which were checked for consistency in terms of nominal erosion rates. For the two-phase PIV, data processing steps involve image processing to separate the carrier and dispersed phase (Kiger & Pan, 2000; Khalitov & Longmire, 2002), followed by standard cross-correlation PIV on carrier phase and particle tracking on the dispersed phase. Particle tracking becomes non-trivial in this flow field due to large concentration and velocity gradients. A hybrid PIV/PTV algorithm has been implemented (Keane et al 1995) to improve the performance in high concentration regions, while still retaining the flexibility inherent to PTV to resolve multi-valued velocity displacements within a given interrogation window, as reported previously (Mulinti and Kiger, 2012). A coarse PIV pass is carried out on dispersed phase images when the number of particle images in an interrogation window (64 64 pixels) is higher than a nominal threshold value to ensure that the cross-correlation information obtained is reliable. If the particle image concentration is low, this step is skipped and the displacement estimate at this window location is set to zero. The second image sub-window is shifted by this displacement in the appropriate direction and crosscorrelation analysis is performed again. This process is repeated until the nearest integer value of the displacement goes to zero but if the value does not converge in three passes, the displacement estimate at that window is set to zero (Cowen et al 1997). At the end of each PIV pass, spurious vectors are identified using a median test as outlined by Westerweel (1994). In the subsequent PTV step, particles in the first image are paired with particles in the second image and the position of particle in the second image is estimated using the mean interpolated displacement obtained from the PIV pass. A sub-window is centered on each particle location and a correlation analysis is done to estimate the final displacement. 3. Results The time averaged flow field of the single phase flow (sampled over a glass plate with no mobile bed) is shown for the low- and high-speed cases in Fig. 3, along with the trajectory of the primary and secondary vorticies of the flow. The non-dimensional velocity magnitudes in the jet and near the wall are larger for the low-speed case due to the stronger forcing amplitude and resulting circulation strength relative to the exit flow. The trajectories of the vorticies are also slightly different, with the point of closest approach by the primary vortex delayed to r/r ~ 2.4 for the high-speed case, in comparison to r/r ~ 2 for the low-speed case. Formation and lift-off of the secondary vortex is also delayed, and does not rise as highly into the flow before losing coherence

4 Fig. 3 Time-averaged velocity magnitude and streamlines for the single-phase flow of the forced jet for the low-speed (U j = 4.1 m/s) and high-speed (U j = 7.9 m/s) conditions. The average trajectory of the primary (o) and secondary (+) vortex is shown by the white lines. The periodic component of the Reynolds stress, u v, extracted 1 mm above the ground plane (y/r = 0.02) is plotted in the lower half of the figure for different times in periodic cycle. Fig. 4 Bed profile evolution and denudation rate for the smaller size particle (50 µm) for a jet exit velocity of 4.1 m/s

5 The strong forcing of this flow produces a coherent (periodic) structure that dominates the flow behavior. To study this effect in detail, it is useful to use ensemble averaging and a triple decomposition to describe the flow: θ = θ + θ + θ (1) Where overbar represents the time-average, represent the coherent periodic fluctuations, and ( ) represents the random or stochastic fluctuations. The latter two components by definition have a zero time average. Note that a net ensemble mean value can be defined that combines the effects of the time-average and coherent fluctuation: θ = θ + θ where θ = θ + θ The periodic fluctuation component of the Reynolds stress, u v, sampled 1 mm (y/r = 0.02) above the ground is shown in the bottom portion of Fig. 3, along with an estimate of the critical threshold stress required to initiate motion of the smaller particle size class (d = 50 µm). The critical stress was estimated as the maximum value of the time-average value of the Reynolds stress of the minimum flow rate conditions, uv, as the minimum velocity condition was selected such the unforced flow was just below the mobilization threshold for the small size particles. We realize that using the time-average of the forced flow is therefore an overestimate, and plan to make single-phase flow measurements of the unforced conditions to improve the precision of our estimate. Nevertheless, one can clearly see the large increase in the surface stress caused by the coherent primary and secondary vortex, with the periodic component exceeding the maximum timeaveraged value by 3 to 4 times. Note also that the peak periodic stresses are slightly larger in the low-speed case than the high-speed case, likely due to the greater coherence (reduced variability within the ensemble) of the lower speed flow despite the slightly lower circulation values. The erosion of the mobile bed is shown in detail for the small-particle low-speed case in Fig. 4, with end-run profiles for repeated trails under all of the tested conditions are shown in Figure 5. Tests were halted after a maximum scour depth of 10 mm to prevent breakthrough of the 15 mm thick bed. In general, the erosion starts just upstream of the point of closest approach of the primary vortex (r/r = 2.0 is the point of closest approach for the low-speed case, Fig. 3), with a crest and second shallower trough forming downstream of the first. The wavelength of the bedform is approximately λ/r = 1.2, and varies little throughout the development of the bed profile. A third trough appears to be forming beyond the second, but with a greatly reduced depth. The reduction in depth with radial distance is to be expected due to both the reduced coherence of the primary vortex as it interacts with the ground surface (becoming highly three-dimensional and rapid dissipation), as well as due to the deceleration of the wall jet due to the axisymmetric expanding flow. Once the initial trough begins to form, scouring occurs progressively, and moves the troughs and crest downstream while keeping the lee slope profile into the first trough approximately constant. The denudation rate is defined simply as the rate of removal of the bed surface, and is calculated locally by subtracting the difference in elevation of the bed at successive times (see Fig. 4). This clearly reveals two maxima in surface erosion rate located about the center of the nacent forming troughs at the earliest times (r/r ~ 2.3 and r/r ~ 3.5). Although it seems clear that the forcing by the primary vortex is responsible for the initiation of the bed forms, due to the correlation of the periodic Reynolds stress with the initial erosion maxima, it is not yet clear from the evidence we have as to what causes the second erosion maxima. It may possibly that this results from an increase in the stochastic component of the turbulent stresses caused by the breakdown and three-dimensionalization of the primary vortex, which occurs in this region. Soon after formation of the bedforms, the peak erosion rates shift to the stoss slope with similar erosion rates on both dunes, in contrast to the marked asymmetry shown between the two dunes in the intial erosion conditions. Minimal erosion (or even deposition) is evident on the lee slopes. The effect of increasing the jet velocity and particle size can be observed in Fig. 5. For increasing jet velocity, the erosion is typically initiated further upstream, and the wavelength of the bedform seems to increase. This later point can only be inferred from the two cases where the second trough is clearly visible within the measurement region, and so is somewhat speculative. The fact that the first trough is much further downstream for the highest-speed case is consistent with the delayed approach of the primary vortex (point of closest approach is at r/r = 2.3). The impact of this different trajectory of the vortex is also visible in the periodic Reynolds stress, which has a peak amplitude near r/r ~ 2.4 (see Fig. 3). For increasing particle size, the position of the first trough is also further downstream in comparison to the same conditions for the - 5 -

6 smaller particle case. Fig. 5 End-of-run bed elevation profiles for 3 repeated tests for each condition examined. Columns correspond to particle size (small on left, larger on right) and rows correspond to jet velocity. Fig. 6 Net erosion rate averaged over the entire field of view. Dimensional quantities shown on the left, and same quantities scaled by the number of vortex passage events on the right. Vertical gray lines demark sampling region for the flat bed and eroded bed conditions, respectively. The integral of the erosion rate over the entire field of view gives the net erosion results depicted in Fig. 6. The dimensional plots show a generally increasing erosion rate with jet velocity for the smaller size class, and also initially for the larger size class. Although the earliest times are not resolved with the coarse temporal resolution of the current measurements, the erosion rate for all cases shows peak values at the first measured interval. This rate rapidly declines and plateaus to a constant rate, before gradually increasing reaching a maximum again near the termination of the test (the low-speed cases decreased again to the plateau value). Given the dominant role played by the primary vortex for these conditions, and similar work investigating sediment transport by single vortex rings (Bethke & Dalziel, 2012), the erosion rate is also plotted in Figure 6 with the temporal component scaled by the vortex frequency. This has the effect of a much-increased - 6 -

7 similarity in the shape of the temporal evolution of the net erosion rate, with the initial maxima occurring in the range from 500 to 1500 vortex passings, and the second maxima occurring around The amplitude - 7 -

8 Fig. 7 Ensemble-averaged horizontal flux of particles for the eroded bed case (small particle size, low-speed jet) shown at 4 different times within the periodic forcing. The black lines show fluid velocity streamlines. Line plot depicts the depth-averaged horizontal flux of particles, normalized by the time-average flux of particles for the eroded bed case. Fig. 8 Depth averaged horizontal flux of particles (suspended load) for the flat bed (top) and eroded bed (bottom) conditions. The flux is normalized in both cases by the time-averaged flux measured in the eroded bed case. Note that the eroded bed flux is approximately 10 times greater than that measured in the flat bed conditions. is not entirely similar, but this is to be expected as a role is expected to be played by the co-flow of the jet, and not just the vortex by itself as though it were in isolation. A next step in the current work is to determine the critical Shields stress for the particles and develop a model that would combine the effects of the vortex with the co-flow. In addition to the particle transport evident from the erosion of the bed surface, we also made direct measurement of the suspended load transport through the use of two-phase PIV (see Fig. 7 and 8). Fig. 7 depicts the ensemble average of the horizontal particle flux, as calculated by nu!, where n is the number density of the particles and u p is the horizontal particle velocity component. Also shown in Fig. 7 is the total (depth integrated) horizontal particle flux, defined by:! φ r, t/t = nu!! Δz dy (2) These conditions correspond to the formation of the first crest near r/r ~ 3.3 and the second crest near r/r ~ 4.5. Waves of suspended sediment are evident moving through the region, with significant fluxes as high as y/r = 0.25, occupying more than half the thickness of the wall-jet at this point. The phasing of the sediment cloud corresponds directly to the presence of the primary vortex, with a maximum flux slightly downstream of the primary vortex core. Although there are strong temporal and spatial variations in the instantaneous flux, the time-averaged suspended transport shows a fairly constant value over the measurement region, - 8 -

9 increasing only 25% as one approaches the second crest (Fig. 8). In contrast to this, the flat bed conditions in the early flow evolution show a strongly evolving suspended flux rate, increasing continually from values near zero to approximately 10% of the eroded bed conditions by r/r = 5. This would seem to imply that the flat bed case is still evolving towards its equilibrium conditions, with the rate of particles coming into suspension continually exceeding those falling back to the wall during their saltation events. Review of the ensemble averaged suspended flux for the flat bed conditions (not shown) indicates a much thinner particle transport layer (y/r < 0.1), and a much greater spatial uniformity. From the net horizontal flux, it appears that the event causing the early maximum in erosion rate around r/r ~ 2.5 has not yet occurred, or if it has, the particles are moving in small reptation hops that occurs close enough to the boundary that we cannot detect them as suspended load using PIV. Further measurements are needed of the erosion rates to quantify this early behavior and to help determine what causes this dramatic shift in the suspended load transport mechanism. 4. Acknowledgements The authors would like to acknowledge the support of the Air Force Office of Sponsored Research under grant FA which enabled this work to be conducted. The authors are also grateful to colleagues Dr. Gordon Leishman, Dr. Anya Jones for their collaborative discussions throughout the work. 4. References Bethke, N. and S. B. Dalziel (2012) Resuspension onset and crater ersosion by a vortex ring interacting with a particle layer, Phys Fluids, 24, Cowen, E. A. and Monismith, S. G. (1997) A hybrid digital particle tracking velocimetry technique. Expts in Fluids 22: phase, high- Johnson, B., Leishman, J. G. and Sydney, A. (2010) Investigation of sediment entrainment using dual speed particle image velocimetry. J. Am. Helicopter Society 55: Kiger, K. T. and C. Pan (2000) PIV technique for the simultaneous measurement of dilute two-phase flows. J. Fluids Eng., 122: Keane, R. D., Adrian R. J. and Zhang. Y. (1995) Super-resolution particle image velocimetry. Meas Sci Technol 6: Khalitov, D. A. and E. K. Longmire. (2002) Simultanous two-phase PIV by two- parameter phase discrimination. Exp. Fluids, 32(2): Mulinti, R and K. T. Kiger. (2012) Particle Suspension by a Forced Impinging Jet on a Mobile Sediment Bed, 16th Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 2012 Westerweel, J. (1994) Efficient detection of spurious vectors in particle image velocimetry data sets. Exp. Fluids 16: