TWO-PHASE FLOW APPROACH FOR THE EXPERIMENTAL INVESTIGATION OF SUSPENDED SEDIMENT TRANSPORT

Marian Muste

Research Engineer

Iowa Institute of Hydraulic Research

The University of Iowa

Iowa City, IA 52242-1585, U.S.A

E-mail:marian-muste@uiowa.edu 

Abstract: Extensive research efforts in the last few decades have only partially elucidated the complexities of suspended-sediment transport. Lacking an adequate formulation and quantification of the interaction between suspended particles and the carrier liquid, it is common practice to combine sediment mechanics theory and empiricism to obtain predictive formulations. Flume data for suspended sediment transport, however, is incomplete and often inconsistent with respect to insights into sediment effects on water flow. Improvement of the data quality/reliability for future experiments requires thorough evaluation of the current experimental investigative approaches and identification of new research paths. The present paper reveals several limitations of the existing flume investigations of suspended-sediment transport. Considered next are the benefits resulting from the adoption of a two-phase flow approach in the investigation of this flow process. Emphasis is placed on illustrating the potential of the new generation of non-intrusive measurement instruments for increasing the reliability of the experimental results. 

Keywords: suspended-sediment transport, two-phase flows, non-intrusive instruments

1    INTRODUCTION

Investigation of suspended-sediment transport is not a trivial task, even for the simple case of a uniform channel flow, because of the complex interaction between the two flow phases. This interaction is sensitive to sediment concentration and velocity gradients across the flow depth, non-homogeneous open-channel turbulence, the irregularity of sediment particle geometry, and simultaneous presence a range of particle sizes.

Extensive research efforts in the last few decades have only partially elucidated the complexities of suspended-sediment transport. Lacking an adequate formulation and quantification of the interaction between suspended particles and the carrier liquid, there remains heavy reliance of laboratory flume experiments to reveal the problems associated with suspended-sediment transport. Flume data for suspended sediment transport, however, is incomplete and often inconsistent with respect to insights into sediment effects on water flow. Some of the inconsistencies are evident in Table 1. These inconsistencies are for essentially same flow conditions, thereby making it difficult to interpret the findings.

Table    1

The present paper identifies several significant sources of conceptual bias errors in flume investigations of suspended-sediment transport.  Conceptual bias errors are defined herein as errors that might stand between concept and measurement.  Most of these errors are generated through idealizations (assumptions) in the data interpretation equations, use of equations which are incomplete and do not acknowledge all the significant factors, or by not measuring the variable which is assumed.  Considered next are the benefits resulting from the adoption of a two-phase flow approach in the investigation of this flow process.

2    TRADITIONAL APPROACH

The main quantities of practical interest in suspended-sediment transport in alluvial channels are the mean suspended concentration of sediment C_ss, and the mean flow streamwise velocity U. The mean suspended sediment concentration for a steady, two-dimensional, uniform open channel flow is determined using the advection-diffusion equation, which integrated over the flow depth provides C_ss

                            (1)

Where C_sa is the mean sediment concentration at a conventional elevation a, h is the flow depth, v_ss is the settling velocity of the sediment particles, e_ss is the sediment diffusion coefficient, k is the Karman constant, and u_* is the bed friction velocity.  The coefficient b, defined as

                            (2)

relates the sediment diffusion coefficient e_ss and momentum diffusion coefficient e_m .

A general form for the distribution of the mean velocity, U, in sediment-laden flows is given using a modified Coles’law

                     (3)

where, k_s is the equivalent sand roughness, n is the kinematic water velocity, B and  B_r are additive constants associated with smooth rough walls, respectively, P is the Coles’ wake parameter, and X(C_ss) is a parameter related to the sediment concentration profile.

Use of these equations as governing equations for suspended-sediment transport and of the assumptions traditionally attached to them, do not rule out the findings obtained from the previous experimental investigations. What is needed, though, to increase the reliability and usefulness of the experimental results, is thorough estimation of the conceptual bias errors affecting the equations governing the flow and errors impact on the experimental findings.

3    RECENT FINDINGS

Recent experimental findings reveal that some of the traditional assumptions associated with equations (1) to (3) are not accurate and that further insights can be obtained using a two-phase flow investigative approach (see Table 2). This approach implies that both particle and fluid motions be simultaneous measured.

Assumption 1 (Table 2) is valid only if particles are small enough to follow closely the smallest temporal and spatial turbulence scales. For this to be true the particle relaxation time of suspended particles (defined as t_p = v_ss/g) should be smaller than the turbulence time scales and sediment particle sizes should be smaller than the turbulence macro scales. Recent measurements using instruments capable of distinguishing flow phases such as laser-Doppler velocimentry (LDV), illustrate consistently that, in the outer region of flow, the average fluid velocities are higher than those for suspended-sediment particles, whether the fluid is air or water (see Figure 1). Velocity lag is larger near the bed, where larger velocity gradient and sediment concentration exist.

Table    2

A recent study conducted by Cellino and Graf (1999) regarding assumption 2 (Table 2) shows that b ranges from 0.565 to 4.269 in sediment-laden flows with and without bedforms.  This large variation in b raises a question about the current interpretation of the relationship between the water momentum diffusion coefficient (directly connected to the shear stress, ) and sediment diffusion coefficient. Investigation of this important suspended-sediment transport parameter using a two-phase flow approach can better capture the sediment-flow interaction, by separately measuring the characteristics of the two flow phases.  This approach could also clarify the validity of the alternative mechanism for sediment entrainment and suspension, suggested by Diplas and Parker (1992), Nelson et al. (1995), and Papanicolaou et al. (1998).  Their experiments showed that the normal stresses and  (where , the root mean square values of the velocity fluctuations in the streamwise and vertical directions) correlate better with sediment motion than with the shear stress.

The Karman coefficient k in assumption 3 (Table 2) was established as a constant from universal correlations for turbulent fluctuation in boundary-layer, homogeneous turbulent fluid flows. Consequently, discussion of the k values in sediment-laden flows is directly connected with the modulation of water turbulence by the suspended-sediment particles.  Recent experiments using a two-phase flow approach (e.g., Rashidi et al., 1990; Kaftori et al., 1995; Muste and Patel, 1997; Best et al., 1997; and Taniere et al., 1997) found that turbulence intensities for fluid and particles may increase or decrease. Gore and Crowe (1991) compiled experimental evidence for gas-solid, gas-liquid, and liquid-gas flows spanning a large range of density ratio, concentration and Reynolds number to document these effects. Their study suggests that threshold values for the ratio D₅₀/l (where l is the size of the most energetic turbulence scales) and for Stokes number ( , where  is a representative time scale of the flow) can be defined to quantify turbulence modulation by sediment. Without here providing an exhaustive argument, but mentioning recent experimental work (e.g., Coleman, 1981; Cellino and Graf, 1998), and theoretical arguments (Cao et al., 1995), and, bearing in mind the need for an unified method for data analysis, a constant value for Karman constant is considered appropriate for sediment-laden flows involving only small suspended sediment concentrations ( < 0.05). 

4    DISCUSSION

Conceptual bias errors generated by use of the assumptions for equations (1) to (3) are not easily detected, because experimental evidence for them is still scarce. Recent experimental evidence on flows carrying suspended sediment shows that the hydrodynamic characteristics of the flow phases are closely coupled, but remain distinct, and that a feedback mechanism relates the two phases in the flow. Consequently, the current approach of treating the flow as a mixture of water and suspended matter is not adequate.

Initial experiments on sediment-laden flows involved the use of intrusive (conventional) techniques for measuring of mean velocity mixture of water and sediment (e.g., Pitot-static tube, Prandtl-tube, hot-wire anemometer) and mean sediment concentration (e.g., sediment samplers of different configurations). Due to their intrusive nature, these instruments are subject to sediment-probe interactions leading to measurement bias errors. In general, relevant aspects such as uncertainty estimates, calibration of the instrumentation, and determination of what was measured (liquid or particle velocity) were documented only in few cases. 

With the advent of optical and acoustic Doppler velocimetry, non-intrusive methods have become favored for velocity measurements in sediment-laden flows (e.g., Muller, 1973; Tsuji and Morikawa, 1982; Lyn, 1986; Best et al., 1997). Much effort presently is going into developing non-intrusive instrumentation for documenting complete flow-field diagnostics including velocity measurements for the underlying flow simultaneously with velocity, concentration, and particle size measurements for the suspended fraction of the flow (e.g., Kaftori et al., 1995; Tanniere et al., 1997; Kiger and Pan, 1999). These measurements show that, even for dilute sediment concentrations, the velocity of the sediment is smaller than that of the water. The magnitude of this difference is strongly dependent on local dynamic conditions. Measurements in the sediment-laden jet show that the shift in the mean axial velocities varied between 11% and 88% (Muste and Patel, 1997).

The additional insights provided by the non-intrusive, two-phase flow measurements, in comparison with measurements obtained with conventional velocity instruments can be inferred by a closer look at the velocity profiles shown in Figure 1.  It can be assumed that, in the near-bed region, conventional velocity measurement techniques measure reduced velocities of the sand-water mixture (due to particle-particle and particle-transducer collisions). In the upper region of the flow, they mainly measure water velocity because here the sediment concentration is drastically reduced. This inference also suggests that previous conclusions about the variation of the Karman constant in sediment-laden flows may partially be attributed to the limitations of the measurements without distinction between flow phases.

5    CONCLUSIONS

It can be concluded that the measurement techniques that would considerably minimize the conceptual bias errors in sediment-laden experiments are the non-intrusive instruments capable of measuring both flow phases. This alternative, however, increases the cost and complexity of the experiments. The utility of the two-phase flow investigative approach for the suspended-sediment transport experiments has been already pondered in several studies.  For example, Aziz (1996) shows that computation methods that do not distinguish the flow phases might overestimate suspended-sediment load by up to 40%. Cao et al. (1995) argue that the two-phase flow approach is particularly important when the sediment concentration is significant. One of the major tasks for the future experiments in sediment transport would be to establish thresholds for sediment concentration and sizes delineating the utility of the two-phase flow approach versus analyzing the sediment transport as a mixture of water and sand.

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Fig.    1  Comparison of the fluid velocities in the outer region flow and for suspended sediment particles