Master thesisInner flow structures of turbidity currents based on applied ultrasonic techniques

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Master thesis

Inner flow structures of turbidity currents based on applied ultrasonic techniques

Jumpei HITOMI

Laboratory for Flow Control,

Division of Energy and Environmental Systems, Graduate School of Engineering,

Hokkaido University.

1st February 2019

Abstract

The flow behavior of experimental turbidity currents is evaluated quantitatively in order to reveal their long-distance propagation mechanism. Turbidity currents occurring in nature have complicated and large-scale of flow structures, so it is difficult to obtain sufficient knowledge about their flow behaviors from currents with a limited occurrence observed by a field research. Our research group, therefore, thinks that it is important to obtain basic knowledge that can be extended to actual phenomena from experimental turbidity currents. The test section is an inclined rectangle flume with 4,548 mm in length, 210 mm in height and 143 mm in width. The gate, which separates a heavier fluid and an ambient fluid, is positioned at roughly half length of the flume. It is revealed that the gravity currents generated by the lock-exchange method in such a high-volume release propagate with almost constant values of front velocity Uf. As the heavier fluids, three kinds of fluids are examined; quartz-suspended fluid, opalin-suspended fluid, and saline-dissolved fluids. The center diameters d50 of quartz particles and opalin particles are 12.2 and 18.9 m, respectively. Such small particles have been not used for UVP measurement basically, because the intensity of reflected waves from the particle is too small to be detected by an ultrasonic transducer. In this study, however, a supplemental experiment reveals that the volume fraction () range of quartz particles 0.1 ≤  ≤ 5% shows reasonable velocity distributions obtained by UVP with 4 MHz transducer. Total twenty-five cases of experiments are carried out changing the kind and initial density of the heavier fluids H. In the seven cases of them, two-layer turbidity currents are generated, and the experimental results are discussed. The details about the experimental facility, sediment materials, and initial conditions are summarized in chapter 2.

In chapter 3, analysis method is mentioned. To evaluate the flow behaviors of the gravity

currents quantitatively, it is essential to extend the use range of ultrasonic velocity profiler (UVP), which can be applied to opaque flows. In this study, the measurement by a pair of UVPs makes it possible to obtain horizontal and vertical velocity components (u and v) along the whole measurement line of the ultrasonic beam using time correction method based on Uf. Additionally, the particle concentration is estimated by the calculation using the spatio-temporal echo distribution. In case of Rayleigh scattering, the echo values vary with the particle concentration existing in a unit volume. In this study, the boundary condition at the bottom is set to solve the non-linear integral equation between the echo amplitude and the particle concentration. Besides, the scattering intensity is varying depending on the diameter of particles. Appling this characteristic to echo intensity distributions, it makes possible to detect interfaces in the cases of two-layer turbidity currents.

In chapter 4.1., the flow structures between the quartz-suspended currents and the saline density currents are compared. The initial density of all heavier fluids mentioned in this chapter is

H = 1008 kg/m3. Appling pattern matching method to sequential experimental images, it is revealed

that the Uf values of the turbidity currents are greater on average 19.0% than the density currents. The

wall shear stress W is calculated by the least square fitting method for the time-averaged u distributions. The W of the turbidity current is larger than the density current. Therefore, it is revealed that the turbidity current propagates with larger values of Uf than the density current, although the turbidity currents have larger friction coefficient Cf about wall shear stress on the bed. In the body region of the two types of currents, the maximum velocity of horizontal component (umax) is also larger in the turbidity current than the density current. On the other hand, both values of the height hm that

takes the maximum velocity umax and the thickness of the flows are smaller in case of the turbidity current. From these results, the existence of the suspended particles with heavier density than water suppresses the influence of the diffusion, which is predominant factor in the density currents, and helps the continuous supply of driving force due to the density difference.

In chapter 4.2., the turbulent flow structures of the quartz-suspended turbidity current as solid–liquid two–phase flow is discussed. The momentum conservation equation based on two-fluid model is applied to the distributions of the body region. The computed results indicate that the viscous stress and Reynolds shear stress among the five shear stress components are dominant like single– phase channel flows, but the distribution in the height direction of the shear stresses shows a different shape from that. The values of the viscous stress and Reynolds shear stress get canceled out in the outer region (hm < y < ht, where the u reaches zero), so it is revealed that the pressure gradient is working just in the inner region (0 < y < hm) of the current. Such a phenomenon shows a negative momentum transfer against the mean velocity gradient, which is working to keep a stable stratification. In chapter 4.3., the flow behaviors of several kinds of currents are discussed. These experimental cases show that the turbidity currents containing quartz particles propagates 38.5% faster than turbidity currents containing opalin particles. The analysis results about two-layer turbidity currents show that the kind of the particles suspended in the lower layer determines the front velocity Uf, when the bulk density H in initial condition is equal. In the two-layer turbidity currents composed of different kinds of particle-suspended fluid, it is confirmed that the lower layer is rolled up in the head region and the upper layer is covered with the fluid forming the lower layer. According to such a flow structure of the lower layer, not only the friction with the bed but also the interaction with the ambient fluid in the vicinity of the head region are dominated by the kind of lower layer, which means that the value of Uf can be almost estimated by the friction at the bottom and the interaction at the head region regardless the influence of the shear flow at the upper boundary. In addition to the comparison about Uf, the friction velocity u* is estimated from the distribution of the horizontal velocity component u in the body region. The relationship between the friction velocity u* and the maximum velocity umax in the body region is confirmed as u*/umax ≈ 0.114 in every experimental case. It is also

confirmed that the friction coefficient Cf =2(u*/umax)2 ≈ 0.0260 is obtained using the relationship.

Table of contents

Introduction 6
Experimental method 15
Development of analysis method 21
Results and discussions 39
Conclusion 86
Bibliography 89

Acknowledgements Appendix

‌Introduction
1. ‌Turbidity currentsGravity currents can be observed in many places, for instance in the seas, rivers, and so on. Turbidity currents, a kind of gravity currents driven by density difference between particle-suspended fluid and ambient fluid, are strongly related to the transportation or the deposition of fine particles. Consequently, they play important roles not only for a general understanding of global sediment transport process, but also for estimating the potential environmental hazards which they cause (reservoir sedimentation, trigger of Tsunami, cutting of submarine pipeline systems and cables, effluent dispersal and volcanic hazard (Middleton,1993)). Chamoun et al. (2016) suggested the problem about reservoir sedimentation and a solution for the efficient discharge by the venting. In order to settle the reservoir sedimentation problem, Oehy et al. (2010) evaluated the effect of inclined jet screen on turbidity currents. The result of their study indicates that in certain configurations turbidity currents can be partially stopped by the jet screen and the deposits downstream of the screen may be reduced up to a factor of two as compared with deposits of a free-flowing turbidity current. In addition, there is also the theory that the specific deposition formed by turbidity currents is related to the production or the melting process of fossil fuels such as methane hydrate. The reason why turbidity currents have been payed attention as an important subject is not limited in the field of civil engineering, and the interest for the long-distance propagation mechanism is attracting much attention with a view toward multi- phase fluid dynamics or Earth science.Actually, turbidity currents have been reported to propagate several thousand or hundred kilometers in the seas or rivers by field researches. For example, Azpiroz-Zabala et al. (2017) reported the measurement results by acoustic Doppler current profiler (ADCP) of actual turbidity currents occurring in Congo Canyon (see Table 1-1). In that research, turbidity currents are reported to have occurred six times in the period of seven months, and their thicknesses are from 48 to 77 m and the duration time of the currents is from 5.2 to 10.1 days. Additionally, Symons et al. (2017) also reported the field measurement results in Monterey Bay obtained by ADCP. In the study, the evolution of flow structure and composition are discussed as shown in Fig. 1-1.Contrary to such field researches, many laboratory experiments and numerical simulations have been conducted to collect detailed knowledge of the velocity and turbulent flow structures in the turbidity currents. Paker et al. (1986) suggested the self-acceleration mechanism of turbidity currents from numerical simulation. In the study, it is reported that the sediment entrainment from the bed resupplies potential energy, and it makes possible the acceleration and the long-distance propagation of turbidity currents. Cesare et al. (2001) established a novel numerical model for computational fluid dynamics of the turbidity current, which takes into account the interaction between the current and the deposited sediment. That three-dimensional (3D) numerical model can simulate the balance between deposition and erosion, and the currents provides good agreement with the turbidity currents in alaboratory flume as well as field measurements at the Luzzone Reservoir in swiss Alps. In the study by Gladstone et al. (2004), the multi-layer saline density currents were examined in the lock-exchange flume. It was revealed that the flow behaviors of those currents depend on a dimensionless densityratio between the layers * and dimensionless difference in the driving buoyancy B* (see Fig. 1-2);   g'*  U W  U , ( 1-1 )   g'andL W LB h g ' MB*  U  U U  U , ( 1-2 )U WU U L LU LB  B h g '  h g '  M  Mwhere U, L, and W denote the density of the upper layer, lower layer, and water, respectively. In the study by Longo et al. (2016), the saline density currents produced in a circular cross-section channel were focused on, and then they established a theoretical model which coincides well with the experimental results.‌Table 1-1 Summary of flow properties of the turbidity currents observed in Congo Canyons (Azpiroz-Zabala et al., 2017)
  ‌Fig. 1-1 Schematic of evolution of flow structure and composition of the turbidity current observed in Monterey Bay (Symons et al., 2017)
  ‌Fig. 1-2 Experimental images of the developing two-layer saline density current in case of * = 0.55 and B* = 0.36 (Gladstone et al., 2004)
2. ‌Ultrasonic measurement techniques and multi-phase flowsIn some laboratory experiments and industries, acoustic measurement techniques have been widely used, because they have strong advantages of (i) utility to apply to opaque fluids and inside the opaque materials (e.g. metal pipeline), (ii) non-invasive measurement, and (iii) wide measurable velocity range. Ultrasonic velocity profiler (UVP) (Takeda, 2012) is one of the most used devices in the field of fluid measurement, and UVP made it possible to measure the spatio-temporal velocity distributions along the ultrasonic beam, using frequency veering based on Doppler effects of ultrasonic waves. Along with the advance in ultrasonic measurement technique, the needs for ultrasonic measurement have also diversified and become complicated. In order to obtain such complicated flow fields, some advanced techniques have been established. One example is ultrasonic imaging velocimetry (UIV) or echo-PIV using array transducers (e.g. Poelma, 2017). In this method, two-dimensional echo image is generated by converting echo amplitude values received by each transducer element to gray scale values. Then, the cross-correlation method used in particle imaging velocimetry (PIV) is applied for two consecutive echo images, and vector fields can be obtained. In the study by Zheng et al. (2006), the results measured by UIV provided good agreement with the vector fields measured by optical-PIV (see Fig. 1-3).
  ‌Fig. 1-3 Validation of echo-PIV using a vertical flow: (a) B-mode particle image of the flow; (b) velocity field measured by echo-PIV; and (c) echo-PIV and optical PIV velocities along one radial line within the flow field (Zheng et al., 2006)Another one is phased-array transducer system (e.g. Kikura et al., 2016; Kang et al., 2016). In this method, adding a phase difference to the emitted ultrasonic waves from each element, spatial two- or three-dimensional echo images as well as measurement line can be generated. Murakawa et al. (2008) established unique ultrasonic measurement device using a dual-frequency Doppler transducer for bubbly flows, which makes it possible to measure both velocity distributions of tracer particles (liquid phase) and bubbles (gas phase) (see Fig. 1-4).
  ‌Fig. 1-4 Schematic image of measurement principle using ultrasonic multi-wave method (Murakawa et al., 2008)In addition to the contraption for the arrangement of ultrasonic transducers, another approach has been conducted, which is utilizing echo intensities information termed echo intensity method. Echo intensity, which is the strength of reflected ultrasonic waves scattered on interfaces between two media having different acoustic impedance, gives us beneficial information. In past studies, echo intensity obtained from UVP could be used to detect moving interfaces of air-water bubbly channel flow by Murai et al. (2010). Hitomi et al. (2017) used echo intensity of pulse repetition method to detect and monitor the air-oil-water three-layer pipe flows (see Fig. 1-5). Su et al. (2017) revealed the relationship between the attenuation coefficient and the phase fraction in oil-water two- phase pipe flows. Shi et al. (2019) established the method to characterize oil-gas-water three-phase flow using time-frequency decomposition. Dong et al. (2015) measured velocity distributions of oil- water two-phase flows using continuous ultrasonic waves. Additionally, echo intensity method was applied to obtain the profiles of suspended sediment concentration mentioned below and to measure the profiles of void fraction in bubbly flows (Murai et al., 2009).
  ‌Fig. 1-5 Samples of interface detection: (a) optical visualization, (b) echo intensity distribution,(c) phase distribution, and (d) Doppler velocity distribution (Hitomi et al., 2017)
3. ‌Final goal and objective of this studyAs mentioned above, the final goal of this study is to elucidate the long-distance propagation mechanism of turbidity currents occurring in nature under rivers, seas, and so on. In order to achieve this purpose, it is required to reveal the inner flow structures and the condition determining the flow behaviors of turbidity currents. The turbidity currents in nature, however, have huge flow structures, so it seems difficult to obtain sufficient and quantitative detailed data from field researches. Additionally, these have complicated flow structures due to turbulence and complex interaction caused between each particle. The turbidity currents show local mixture density fluctuation accompanying clusters and clouds of particles, which is hardly investigated by optical approaches and numerical simulations. Our research group, therefore, has ascribe experimental studies as a suitable option to take not only basic but also advanced knowledge to estimate the behavior of turbidity currents.To evaluate the flow behaviors of such experimental turbidity currents quantitatively, the measurement techniques, which can be applied to opaque flows with high resolutions, is required. Therefore, it is necessary to expand the utility of ultrasonic measurement techniques for solid–liquid two–phase flows. Based on the above discussions, the objective of this study is written below.
  - To elucidate the long-distance propagation mechanism of turbidity currents fromexperimental results by the lock-exchange technique
  - To expand the utility of ultrasonic measurement techniques, which can be applied to solid–liquid two–phase flows
  Experiments, analysis and discussions along the above objectives are described from the next chapter.
4. ‌Nomenclature
‌Experimental method
1. ‌Experimental facilitySeveral types of gravity currents were generated in a flume by means of the lock-exchange technique, which has been widely used to investigate unsteady currents in laboratory experiments (e.g. Theiler and Franca, 2016). Schematic diagram of the experimental facility is shown in Fig. 2-1 and the picture of the facility is shown in Fig. 2-2. The test section is an inclined rectangle flume with 4,548 mm in length, 210 mm in height and 143 mm in width. Surface on side and bottom walls of the flume walls is lubricated, and top boundary of the fluid layer is free surface. One of the walls is transparent whereas the other is coated with a non-reflective black film, producing a dark uniform and contrasting background for flow visualization. The region surrounded by a dotted square in Fig. 2-1 indicates the area for optical visualizations. A lock gate 1 made of plastic plate is positioned at roughly half length of the flume. As an initial condition, the left-side region of the flume separated by the gate 1 is occupied by a heavier fluid with bulk density H while the right-side region is filled with tap water with densityW as the ambient fluid. As experimental conditions of ambient fluid summarized in Table 2-1,temperature and density of tap water were almost constant, 8.0°C and 999.9 kg/m3, respectively. When the gate 1 is released, the heavier fluid invades under the ambient fluid with front velocity Uf according to the density difference between both fluids. The horizontal displacement from the gate in the right region is defined as x axis and y axis denotes the height from the bed. For one-layer turbidity currents, which are examined in laboratory experiments normally, one separation gate (gate 1 only) is enough as shown in Fig. 2-1(a). In this study, in addition to the one-layer currents, two-layer currents were examined using two separation gates (gate 1 and gate 2) as shown in Fig. 2-1(b) to observe the difference of flow behaviors depending on the initial conditions or variation of sediment particles. In cases of two-layer currents, the gate 2 was firstly released to generate density difference between heavier particle-suspended fluid in the tank A and lighter particle-suspended fluid in the tank B. Then, the gate 1 was barely released before the head of heavier particle-suspended fluid reached the gate 1, and two-layer currents propagated in the right-side region.
  ‌Fig. 2-1 Experimental facility of lock-exchange technique
  ‌Fig. 2-2 Picture of the experimental facility‌Table 2-1 Experimental conditions of the ambient fluids
2. ‌Sediment particles
  ‌Fig. 2-3 Pictures of sediment particles, left-side is the quartz particles and right-side is the opalin particles
  ‌Fig. 2-4 Particle images taken by electron microscopeAs suspended materials, two kinds of particles, quartz (Cario Bernasconi S.A., K-13) and oplain (Opalit AG Holderbank, Opalit), were examined (see Fig. 2-3), and their microscope photographs are shown in Fig. 2-4. Particle seize distributions of them measured by MasterSizer 3.0 (Malvern S. A., 2013) are shown in Fig. 2-5. In these distributions, a dispersion of the particle size distribution in case of the quartz particles is smaller than case of the opalin particles. The calculated center diameter and other physical properties mentioned in their specifications are summarized in Table 2-2. The calculated center diameters of quartz and opalin are 12.2 and 18.9 m, respectively. The quartz particles are almost composed of SiO2, while the opalin are composed of not only SiO2 but also Al2O3, Fe2O3, and so on. From these results, each particle-suspended fluid is expected to have different rheological characteristic and it would cause the change of their flow structures.
  ‌Fig. 2-5 Particle size distributions of (a) quartz particle and (b) opalin particles‌Table 2-2 Basic information about suspended particles
  As mentioned above, the specific weights of quartz and opalin particles are larger than 1.0, so the settling of the particles occurs in a still-water. Such a settling velocity vs is estimated by Stokes’ law written asd 2     gvs p p W18, ( 2-1 )Wwhere dp and g indicate the diameter of the particle and gravitational acceleration, respectively. The values of vs in case of quartz and opalin calculated based on each center diameter d50 are 0.0965 and0.244 mm/s, respectively. This law can be applied only for the particle Reynolds number Rep shown below is smaller than 2,Rep dpvs W . ( 2-2 )WAs the result of the calculation, the values of Rep for each particle were confirmed to be much smaller than 2, so the Stokes’ law works.
3. ‌Experimental casesTotally, twenty-five series of experiments using some kinds of different heavier fluids and initial conditions were performed, and experimental conditions about heavier fluids are summarized in Table 2-3. In the table, capitalized alphabet denotes the kind of heavier fluids, that is Q, S, and O show quartz-suspended fluid, saline-dissolved fluid, and opalin-suspended fluid, respectively. In Case 1–8, quartz-suspended turbidity currents, which are water containing quartz particles with 0.5% in volume fraction, were performed, and bulk density of heavier fluids H in those cases is 1008 kg/m3. In case 9and Case 10–12, heavier fluid contains quartz particles with 1.0% in volume fraction(H = 1016 kg/m3) and 2.0% (H = 1032 kg/m3), respectively. In case 13–15, saline density currents colored with white ink were examined for H fixed at 1008 kg/m3 in these three cases. In Case 16–18, opalin-suspended turbidity currents, which are water containing opalin particles, and H is differentfrom each other between 1008 to 1032 kg/m3. In Case 19–25, two–layer turbidity currents were performed. In Case 19–22, the density in the lower layer is 1032 kg/m3 and that in the upper layer is 1016 kg/m3. In Case 23–25 the density in the upper layer is 1032 kg/m3. The densities of each lower layer are 1016 kg/m3 in the Case 22 and 25, and 1032 kg/m3 in the Case 24.In this study, there are two types of the ultrasonic transducers arrangements as shown as Ⅰ orⅡ in Table 2-3, then the details of the arrangement and principle of velocity measurement by UVP are explained in next section.‌Table 2-3 Experimental conditions of heavier fluids
‌Development of analysis method
1. ‌Velocity measurementUltrasonic velocity profiler (UVP) (Takeda, 2012), which measures instantaneous profiles of velocity component along the propagation line of ultrasonic wave and is applicable to opaque fluids was adopted for the measurement of velocity profiles in the currents. In this method, using the frequency veering according to Doppler effect, spatio-temporal velocity distributions can be measured.‌
  Supplemental experiments by stirring flowAs mentioned above, quartz and opalin particles with order of 10 m in the central diameter are examined. This range of particle diameter is less than one-tenth the ultrasonic wavelength of central frequency 4 MHz in water, so Rayleigh scattering, which is almost isotropic scattering, occurs. Such small particles are not used for UVP measurement basically, because the intensity of reflected waves from a quartz particle is too small to be detected by ultrasonic transducers. In ordinary UVP measurements, it is considered that the adequate diameter of the tracer particles as reflector is appropriately quarter to half of the ultrasonic wave length. Fig. 3-1 shows the schematic diagram of those scattering patterns. In this part, therefore, a series of supplemental experiments was conducted by the stirring flows shown in Fig. 3-3 to elucidate the flow conditions and the volume fractions of the quartz particles that UVP can measure reasonable velocity distributions of particle-laden flows. The experiments were conducted in a cylindrical container with 100 mm in outer diameter, and 3 mm in thickness of lateral wall and 120 mm in height. The cylinder is made of acrylic resin and filled with test fluids containing the fine particles. The cylinder does not have a lid and thus top of fluid layer is free surface. The cylinder was mounted inside the water jacket to keep uniform temperature and allow transmission of ultrasonic wave from the outside of the cylinder. The flow was driven by a stirrer with 60 r.p.m. in the rotational speed, and a stirring bar dipped into the bottom of the cylinder. An ultrasonic transducer was fixed in the jacket with a horizontal displacement 10 mm from the center line. This off-axis measurement makes it possible to obtain the velocity component including not only radial but also azimuthal velocity component. The transducer was set at 25 mm from the bottom of the cylinder to avoid the blind of ultrasonic propagation due to the free surface. In Table 3-1, the setting parameters of UVP measurement for supplemental experiments are summarized. Each value of spatial resolution, number of cycles, and number of repetitions is same value in the measurements for the gravity currents in this study. The velocity range of the stirring flows is larger than that of the gravity currents, so temporal resolution is higher. The cylinder was filled with 500 mL of tap water and the quartz particleswere added based on each volume fraction . Total seven cases with different volume fractions,  =0, 0.01, 0.1, 1.0, 5.0, 10, and 15%, were conducted, and the sample images of the fluids for  = 0.01, 1.0, and 10% are shown in Fig. 3-2. As you can see, in cases of  > 1%, the test fluid becomes completely opaque, so the inner flow structures cannot be observed by optical approaches.
  ‌Fig. 3-1 Schematic diagram of scattering patterns reflected by each particle
  ‌Fig. 3-3 Schematic diagram of experimental setup for stirring flow‌Table 3-1 Setting parameters for supplemental experiments
  ‌Fig. 3-2 Sample images of test fluidsFrom these experiments, we tried to comprehend the trends of velocity profiles measured in this setup. Fig. 3-4 shows velocity distributions obtained from UVP in each experimental case. These velocities show the components of the measurement direction, that contain the azimuthal and radial velocity components. The measurements and the time-averaging were conducted for 40 s after the flows reached adequate developed states, so the corresponding number of the velocity profiles for time-averaging is 4000. In this figure, x axis donates the distance from the center of the cylinder and the ultrasonic measurement direction is from left to right side. In the cases of 0.1 ≤  ≤ 5%, reasonable velocity distributions can be observed. In this study, the velocity profiles measured with usual tracer particles (Mitsubishi Chemical, DIAION HP20SS, diameter 60–150 m, density 1020 kg/m3),which are indicated as orange dotted line in Fig. 3-4, is assumed as correct distribution, and “reasonable velocity distribution” means having good agreement with the correct distribution. The velocity profiles of 0.1 ≤  ≤ 5% have an accuracy that has a high cross-correlation value exceeding0.95 for the correct distribution. The cases of  = 10 and 15%, however, do not show the reasonablevelocity distributions. It seems that the influence of the scattering attenuation of ultrasonic waves occurring in cases of Rayleigh scattering becomes large and that prevents the ultrasonic transducer from detecting the echo signals. In addition, the case of  = 0.01% shows a notable result. The velocity values of this case drop irregularly near the center of the cylinder. This phenomenon implies that the amount of quartz particles is much fewer than wall side due to the centrifugal force. As known from the velocity distribution, high velocity values can be observed near the center. As the distance from the center becomes longer, the velocity values are getting smaller. From these distributions, the existence of a free vortex seems to be confirmed. The density of the quartz particles is about 2.65 times higher than that of water, so it is possible that the particles are blown from the center to near the wall sides by the centrifugal force.‌Fig. 3-4 Profiles of time-averaged value of Doppler velocity
  In addition to the velocity distributions, time-averaged echo amplitude profiles are also shown in Fig. 3-5. These echo amplitudes were calculated as the absolute values of difference from UVP echo intensity in case of background ( = 0%). As the volume fraction becomes larger in the cases of  = 0.01, 0.1, and 1%, echo amplitude values are also getting lager. In the case of0.01 <  < 1%, on the opposite side from the ultrasonic transducer, an extremely large value of echoamplitude is observed because of the reflection from the wall. In contrast, the reflected waves from the opposite wall disappears under the conditions  ≥ 5% due to the attenuation of ultrasonic waves, and the attenuation is getting larger depending on their volume fractions.
  ‌Fig. 3-5 Profiles of time-averaged value of echo amplitudeBasically, UVP measurements are applied to flows containing tracer particles with adequate size, density, and concentration to reflect ultrasonic waves. However, the concentrations of particles in these experiments are relatively larger in comparison with the flows which UVP measurements are applied to normally. The experimental results for 0.1 ≤  ≤ 5% show reasonable velocity distributions. This range of particle concentration, therefore, might be useful to detect integral echo signals obeying Rayleigh scattering. That is why UVP can obtain velocity distribution, although quartz diameter is much smaller than tracer particles (Hitomi et al., 2018).‌
  Velocity measurements for gravity currents
  ‌Fig. 3-6 Schematic image of arrangement of ultrasonic transducersAs mentioned above, there are two types of the ultrasonic transducer arrangements in this study. In more than half of the experiments, as shown in Fig. 3-6(Ⅰ), a pair of ultrasonic transducers was used for the measurement. Such a symmetric arrangement of two measurement lines has been used in some studies, because that makes it possible to obtain instantaneous profiles of both horizontal and vertical velocity components (u and v) at their crossing point using following equations (Jamshidnia and Takeda, 2010; Kitaura et al., 2010 (in Japanese)),u  y,t   , ( 3-1 )u1  y,t   u2  y,t 2sinv  y,t   . ( 3-2 )u1  y,t   u2  y,t 2cos‌In many cases of the previous studies, the relationship shown by these equations has been extended in the entire height direction to estimate multi-component or multidimensional flow field assuming that the tilted angle  is sufficiently small. In this study, two ultrasonic transducers with 4 MHz in basic‌frequency connected to each equipment of UVP model Duo (Met-Flow S.A., Switzerland) were installed with tilt angle of 25° from the y axis. Those two measurement lines of the transducers intersect at (xI, yI) = (1005 mm, 15 mm), where yI is the height expected roughly that the horizontal velocity takes the maximum value umax according to previous researches. For instance, in the study by Keller et al., (1999), the height hm taking velocity maximum within the body region of the saline density currents is reported to occur at hm/d ≈ 0.2 in the rectangular lock-exchange flume using Laser-Doppler anemometry, where d is the flow thickness of the currents. The start time of the two-UVP measurement was synchronized with the release of the gate 1, continuing sufficiently long measurement time to analyze flow structures from head to body of the currents.
  ‌Fig. 3-7 Schematic diagram of concept of the time correction method ()In addition, since the positions of two ultrasonic transducers in this arrangement have a certain displacement outside the intersection point, our research group suggests the time correction method of velocity distributions using front velocity Uf (Nomua et al., 2018a; Nomua et al., 2018b). Although the details about Uf will be described in another section, the currents in experimental cases of high-volume release like this study propagate with almost constant front velocity. The high-volume release means that the initial volume of the heavier fluids is relatively similar to that of ambient fluid in this study. The schematic diagram of this method is described in Fig. 3-7. Using this concept, Eq.( 3-1 ) and Eq.( 3-2 ) are modified as follows,‌u  y,t   , ( 3-3 )u1  y,t  t   u2  y,t  t 2sin‌v  y,t   , ( 3-4 )u1  y,t  t   u2  y,t  t 2coswheret   y  yI  tan . ( 3-5 )U fIn the remaining several experiments, in order to observe the temporal and spatial development of the currents, three ultrasonic transducers connected to one UVP equipment were arranged in parallel as shown in Fig. 3-6(Ⅱ), and the measurement by the multiplexer mode was performed. The positions of each transducer were x = 500, 1000, 1500 mm, respectively. The setting parameters for UVP measurement are specified in Table 3-2.‌Table 3-2 Setting parameters for UVP measurement
2. ‌Concentration profilesIn addition to the velocity profiles using frequency veering based on Doppler effects, echo amplitude distributions reflecting waves scattered by suspended particles give us beneficial information on particle concentrations. The size of sediment material used in this study is much smaller than ultrasonic wave length  (100 m) with 4 MHz frequency in water, that causes Rayleigh scattering. For such conditions, Thone and Hanes (2002) suggested the relationship between the mean-square amplitude of echo signal <V2> received by the ultrasonic transducer and mass concentration M in kg/m3 as following.M  4 a3 N , ( 3-6 )3 S Pwhere, aS denotes the equivalent radius of suspended particles (≈ d50/2) and N is the number of particles per unit volume.2 2 4 r  rM r dr 2   r 4r2   r  W 0 ‌M r   V   e  V   e   , ( 3-7 ) Ks Kt   Ks Kt where, W is the clear water attenuation which is a function of the temperature only expressed as (Fisher and Simmons, 1977)W  1015 55.9  2.37T  4.477 102T 2  3.48104T3 F2 , ( 3-8 )with T in Celsius degrees and F is the sound frequency in 1/s. Then  is sediment attenuation constant.  3 4aSp , ( 3-9 )where,  is the normalized total scattering cross-section, and it is described as (Thone and Hanes, 2002)1.1  4  0.18kaS 4  31  1.3kaS 2   4  0.18kaS 43, ( 3-10 )where k is the wave number of the sound in water (k = 2/,  are the wavelength of ultrasonic wave, respectively).Additionally, Ks is a function of the scattering properties of the suspended sediment, Kt is a constant for the ultrasound system, and (r) accounts for the effect of the oscillating backscattered signal from the spherical spreading in the near field. Furthermore, Pedocchi and Garicía (2012) applied this relationship to the echo distributions obtained from UVP. Their study indicated that the echo signal displayed by the UVP software is result of the passing signal through AD converter. That divides echo signals into voltage variation with 14 bits, and the measurable range is in ±2.5 V (2.5 V = 8191; - 2.5 V = -8191). The echo signals are amplified by the “gain factors” (as “gain start” and “gain end” in the software). To amplify the echo values, it is reported that time variable gain (TVG) is used and unamplified echo signal can be obtained following this equation using absolute gain values of start Gs and end Ge. The details of amplification by UVP software are written in Table 3-3 and Fig. 3-8.r rs   V  Vamp   Gs  re rs , ( 3-11 )G  G s  e where, Vamp is amplified echo signal, and rs and re are the minimum and maximum measurable distance from the transducer.
  ‌Table 3-3 Gain factors to amplify UVP echo signals (Oliver Mariette from Met-Flow, personal communication 2018)
  ‌Fig. 3-8 Gain factors for UVP echo signals monitored by the ultrasonic transducers with 2 or 4 MHz in basic frequency (Oliver Mariette from Met-Flow, personal communication 2018)V 2
  Here, a non-linearly is contained in the Eq.( 3-7 ), because the s is also a function of M. To overcome this problem, Lee and Hanes (1995) established an explicit method to invert the equation by substituting the concentration at an initial point MI. The procedure for the deformation of the formula is described below. Firstly, on the both sides of Eq.( 3-7 ) are taken by logarithm. r 2      r ln M r   ln V 2‌  e4r  2ln r   2ln   4lnWr   M r dr  . ( 3-12 ) Ks Kt     Ks Kt   0 Next, it takes the derivative with respect to r on both sides of the equation,dV 2
          dr            rdM r   V 2 
     dr     2   4W  M r  , ( 3-13 )M  r V 2    where (r) can be treated as constant in case of the measurement for far field from the ultrasonic transducer not a near field (Downing et al., 1995). Therefore, the second term on the right side of Eq.( 3-12 ) is handled as a constant, and it became zero by differentiating with respect to r.dV 2
   dM r  dr  2rV 2V 2
             dr          r 4W  M r   4M r 2. ( 3-14 )   using the general solution of Bernoulli differential equations, the flowing equation can be obtained.V 2 r2e4WrC  4  V 2 r2e4W rdrM r  ‌, ( 3-15 )where C denotes the integral constant. To set the boundary condition M(r = rI) = MI, finally it becomesr 2 V 2 e4W rM r  1  r2 V 2e4W rI  4 r 2 V 2e4W rdr‌. ( 3-16 )IrMI I I rWhen the ideal condition on lock-exchange technique, the MI is counted as zero, which means that the Eq.( 3-16 ) will diverge. It is required to set other boundary condition to overcome this problem. On the initial condition like this study, where the initial volume of heavier fluid is relatively similar to that of ambient fluid, the flow near the bed keeps containing the initial concentration as reported in (Theiler and France, 2016). That study shows the concentration profiles of colored density currents obtained by the image processing based on grayscale values, which was established by Nogueira et al. (2013). Applying this flow characteristic in case of turbidity currents where the high-volume release to this study, we rearranged Eq.( 3-15 ) by setting the boundary condition, where the concentration at the bottom is MB. In that case, the equation becomesr2 V 2 e4WrBBBM r  r   .rB B rBC  4Ir2 V 2 e4W rdr( 3-17 )Therefore, the integral constant C is determined asBr2 V 2C e4WrBB 4 rB r 2 V 2‌e4W rdr . ( 3-18 )MB rISubstituting Eq.( 3-18 ) into Eq.( 3-15 ), the following equation is obtained,M r  .V 2 r2e4Wrr2 V 2 e4WrBBBMB4 r V e dr  4rB2 2 4 rWrI V 2 r2e4W rdrrrI( 3-19 )r 2 V 2 e4WrThen, the equation is modified as,M r  1 r 2 V 2re4W rB  4  Br2 V 2e4Wrdr. ( 3-20 )MBIt takes finally the discrete form,B B rMn rn2 V 2Ne4Wrnn, ( 3-21 )1r2 V 2e4W rB  4r r2 V 2e4Wri  r2V 2e4W ri1 B   i i1 Mb bin1i i1 where n represents the position number of a certain measurement point when discretized.
3. ‌Pattern matching method and front velocityOutline motions of the fluids with the particles invading into the ambient fluid are monitored as successive images from t = t0 (Fig. 3-9), where t0 is an arbitrary elapsed time from the gate 1 release and the details about t0 will be mentioned later. The images were taken by the digital camera (Nikon, D5300) installed in front of the flume with 20 f.p.s. in flame rate for Case 1 and the shooting area is around xI as shown in Fig. 2-1. The frame rate was set to the same value as the sampling rate of the UVP measurements in cases of arrangement Ⅰ. In those images, some complicated flow structures can be observed near the upper boundary and the front part, which is caused by turbulent flow structure or interactions between the current and ambient fluid. In the study by Simpson and Britter (1979), tracing the shape of the vortices at the upper boundary, it was confirmed that the ratio of vortex structure to wavelength was the same as for Kelvin-Helmholtz vortices. In the image at t = t0 + 7.5 s of this experiment too, some transverse vortices can be seen clearly.
  ‌Fig. 3-9 Snapshots of quartz-suspended turbidity currents of Case 1 from t = t0 to t0 + 10.5 s
  ‌Fig. 3-10 Schematic diagram of pattern matching methodIn order to measure the front velocity Uf which is the advection speed of the head region of gravity currents, pattern matching method is applied to the successive experimental images. The schematic diagram of the pattern matching method is shown in Fig. 3-10. Firstly, a template image with 451 × 451 pixels was prepared from the image at t = t0, where t0 is a variable arbitrary elapsed time for each experimental case. Because the values of Uf are different from each experiment depending on the initial conditions, it is difficult to use a constant value as t0. In addition, it was also confirmed that the obtained result of Uf hardly depended on how to choose t0. In this study, therefore, the smallest value among the elapsed times of the image showing sufficient flow structures of the head region to make the template image with more than 451 × 451 pixels was used as t0 in each experiment. For every five images (every 250 ms), the cross-correlation value at each pixel was calculated, and just one pixel with the maximum cross-correlation value was defined as the head position of the current at that time. This operation was applied to the results of the experiments from Case 1–25. The results are shown in Fig. 3-11. In this graph, horizontal axis indicates the elapsed time (t) from t = t0 and vertical axis indicates the displacement of the computed head position from the initial position at t = t0. The results of quartz-suspended turbidity currents with 1008 kg/m3 in bulk density are summarized in Fig. 3-11(a). As you can see, a similar trend is confirmed in all experimental Cases 1–8, because the initial conditions are the same in these cases. Those results roughly ensure the reproducibility of the currents in this experimental facility. In Fig. 3-11(b), the symbols of square, diamond, and triangleindicate the results of quartz-suspended currents, saline density currents, and opalin-suspended currents, respectively. Additionally, the results of the two–layer turbidity currents in the Case 19–25 are shown in Fig. 3-11(c) by cross marks. As you can guess, in the two–layer turbidity currents, the variation of the gray scale values is larger than that of the one–layer turbidity currents, because two kinds layers showing different color from each other are mixed. Hence, in the cases of two–layer currents, it is confirmed that the variations in the head position detected by the pattern matching are slightly larger than in the cases of one–layer currents.
  ‌Fig. 3-11 Time variation of the head position of the gravity currents, (a) quartz-laden currents with H = 1008 kg/m3, (b) the remaining cases of the one–layer currents (quartz, saline, and opalin currents), and (c) two–layer currentsIn all cases, the displacement of the head is increasing in almost direct proportion to the tfdue to the lock-exchange experiments with high-volume release, that means the sufficient driving force keeps supplied by the density difference between the heavier fluids and the ambient fluid. Therefore, the currents propagate with almost constant front velocity Uf without decay in these experimental time ranges. Using this characteristic, the front velocity of each experimental case was calculated from the slope of a regression line estimated by the least-squared method, and the result is shown in Fig. 3-12. In this graph, the vertical axis denotes the calculated front velocity Uf and the horizontal axis denotes the initial bulk density of heavier fluids (H). In case of two–layer currents, the density is calculated with considering the volume difference between the tank A and the tank B. The corresponding values are 1023 kg/m³ in Case 19–22, 1012 kg/m³ in Case 23 and 24, and 1019 kg/m³ in Case 24. The symbol indicating each case is the same to that used in Fig. 3-11. In the past studies about saline density currents, the dimensionless velocity ( U * ) for lock-exchange method have been used to summarize thevalues of Uf, and it is defined asg'Hf‌U *  U f , ( 3-22 )where H is total fluid depth and g´ is reduced gravitational acceleration defined asg'  H  W g . ( 3-23 )WIn this study, however, the flume was inclined at 1.38° and the fluid depth varies with the distance from the gate. Here, the calculation was carried out using the fluid depth of H = 179 mm at x = xI asUfthe representative depth. Some values of * are reported in the previous studies about lock-exchange density currents, as 0.44 (Middlen, 1966), 0.46 (Keulegan, 1957; Barr, 1967), and 0.41 (Kneller et al., 1999). Therefore, the front velocity can be estimated using Eq.( 3-22 ) from each initial density of heavier fluids. In Fig. 3-12, the estimated front velocity is plotted by solid lines, the upperffone is the estimated velocity in case of U *  0.46 and the lower is in case of U *  0.41 . The valuesUfof experimental Uf and estimated by * have good agreement just in cases of quartz-suspendedcurrents and some two–layer currents of experimental Cases 19, 20, 23, and 24, where the lower fluids contain the quartz particles. Contrary to that, the saline density currents show a little bit lower values of Uf, that may be affected by the inclined experimental flume as a result of the balance between downward force of heavier fluid and upward force of counter flow by ambient fluid. Notable points are shown in the remaining experimental cases of opalin-suspended currents and two-layer currents whose lower layer contains opalin particles of the experimental Cases 21, 22, and 25. In those cases, the values of Uf are obviously lower than estimated values. These results suggest that the value of Uf cannot be estimated only by initial density of heavier fluids and depth, that seems to be attributed to the difference of rheological property between opalin-suspended fluids and quartz-suspended fluids. The details about it will be discussed later.
  ‌Fig. 3-12 Measured front velocity in experimental Case 1–25The spatio-temporal velocity distributions of the experimental Case 3 obtained from UVP are shown in Fig. 3-13, those distributions were measured at (a) x = 500, (b) 1000, and (c) 1500 mm, respectively. The axes denote the height from the bed (y) and the elapsed time from the release of the gate 1 (t). In the arrangement of transducers Ⅱ, the velocity components along the propagation line of ultrasonic wave (u) are obtained. The magnitude of u is shown as color contour. Comparing these three distributions, the head of the current can be observed clearly at the measurement line x = 1000 (b) and 1500 mm (c), but it cannot be done at x = 500 mm (a). Therefore, it is assumed that the current was developing between x = 500 to 1000 mm and reached stationary state before x = 1000 mm in this case. Here, in order to confirm the characteristic of Uf, the estimated arrival time t* is defined ast*  l ,xl U f( 3-24 )where, l is an arbitrary distance from the gate 1. The value of*txlrepresents the expected time ofarrival at each measurement line, assuming that the front velocity Uf calculated above will be constanteven if it reaches each measurement point. Each value of*txlat x = 500, 1000, and 1500 mm isshown in Fig. 3-13 as dotted line. From those results, it is confirmed that the turbidity current roughly reaches each measurement line at the estimated arrival time calculated from Uf. In this study, therefore, the calculated front velocity Uf in each experimental case cam be treated as constant value below.
  ‌Fig. 3-13 Spatio-temporal velocity distributions measured at (a) x = 500, (b) x = 1000, and (c)x = 1500 mm of experimental Case 3
‌Results and discussions
1. ‌Comparison of flow structures between quartz-suspended currents and saline density currentsIn this section, the differences of flow characteristics between quartz-suspended turbidity currents of Case 1–8 and saline density currents of Case 13–15 are discussed. The main driving force of the currents of this experimental facility is density difference between heavier fluids and ambient fluid, and all of the initial densities of heavier fluids discussed in this section are the same value ofH = 1008 kg/m3. In other words, it is the main target of this section to investigate how the flowbehavior of gravity currents vary with the presence or absence of quartz particles and to compare flow structures for the elucidation of the long-range propagation mechanism of the turbidity currents.‌
  Inner velocity structures of the currentsSpatio-temporal distributions of horizontal and vertical velocity components (u and v) obtained by two-UVP measurement are shown in Fig. 4-1, where (a) left and (b) right panels are from Case 1 (turbidity current) and Case 13 (density current). The axes denote the height from the bed (y) and the elapsed time from the release of the gate 1 (t). The V-shaped distributions seen in these graphs are the ultrasonic interference noise caused by the simultaneous measurement of the two UVPs. As the color scale corresponding to the velocity magnitude, horizontal velocity component u is dominant in the flow. Because lock-exchange flume is a closed system, counter flows of ambient fluid occur at the upper boundary of the currents. In the distributions of u, the increase and decrease of velocity due to the propagation of the currents are confirmed. Regarding the distribution of v, in spite of small velocity magnitude, strong rolling-up structure is observed near the head position in the turbidity current (20 < t < 25 s). Some pair of positive and negative values in v distributions near the upper boundary can indicate the existence of vortices attributed to Kelvin-Helmholtz (K-H) instability.

Master thesisInner flow structures of turbidity currents based on applied ultrasonic techniques​