Danxun Li

Velocity profile of sediment suspensions and comparison of log-law and wake-law

The log-law and wake-law of velocity profile of open channel flow of sediment suspensions are discussed and compared in the paper. Data from 9 literatures are employed for comparison of the two laws and regression analyses are conducted on the main factors affecting velocity profile. Empirical formulas are obtained for estimation of the factors from the flow conditions. The elevation of the maximum velocity and the deviation of velocity from the logarithmic formula at the water surface are functions of the aspect ratio of the channel. The log-law is developed into Eq. (20) applicable to the whole flow including the region near the water surface for various boundary conditions. The wake law describes the velocity distribution below the maximum velocity point. The relative error of wake-law (11%) is larger than that of log-law (6%). Moreover, the wake coefficient must be determined by using the measured velocity profile because there is no reliable formula to estimate its value from the flow conditions.

Three-dimensional unstructured-mesh eutrophication model and its application to the Xiangxi River, China.

The Xiangxi River is one of the main tributaries in the Three Gorges reservoir, with the shortest distance to the Three Gorges Project Dam. Severe and frequent algal bloom events have occurred frequently in the Xiangxi River in recent years. Therefore, the current study develops a three-dimensional unstructured-mesh model to investigate the dynamic process of algal bloom. The developed model comprises three modules, namely, hydrodynamics, nutrient cycles, and phytoplankton ecological dynamics. A number of factors, including hydrodynamic condition, nutrient concentration, temperature, and light illumination, that would affect the evolution of phytoplankton were considered. Moreover, the wave equation was used to solve the free surface fluctuations and vertical Z-coordinates with adjustable layered thicknesses. These values, in turn, are suitable for solving the algal bloom problems that occurred in the river style reservoir that has a complex boundary and dramatically changing hydrodynamic conditions. The comparisons between the modeling results and field data of years 2007 and 2008 indicate that the developed model is capable of simulating the algal bloom process in the Xiangxi River with reasonable accuracy. However, hydrodynamic force and external pollution loads affect the concentrations of nutrients, which, along with the underwater light intensity, could consequently affect phytoplankton evolution. Thus, flow velocity cannot be ignored in the analysis of river algal bloom. Based on the modeling results, building an impounding reservoir and increasing the releasing discharge at appropriate times are effective ways for controlling algal bloom.

Coherent structures and their interactions in smooth open channel flows

The study presents experimental results of coherent structures and their interactions in a smooth open channel flow based on measurement of instantaneous two-dimensional velocity vectors with particle image velocimetry. The sampled data were analyzed through techniques of ensemble average, vortex extraction, and proper orthogonal decomposition (POD). Redistribution of turbulent kinetic energy is observed in the near-surface region. The spanwise vortices, which are closely related to hairpin vortices, exhibit a clear dependence on Reynolds number of the flow. Hairpin vortex packets and long streamwise vortices are identified as typical large-scale and super-scale coherent structures, respectively, and their interaction is revealed by examining the relationship between the population density of spanwise vortices and the coefficient functions of the first POD mode. Interactions between large-scale and super-scale structures have been recognized to support the hypothesis of closed-loop feedback cycle.

An improved swirling-strength criterion for identifying spanwise vortices in wall turbulence

Swirling strength, λci, is an effective vortex indicator in wall turbulence, and existing vortex extraction methods introduce normalisation of λci with its root mean square as the basis for defining a universal threshold. This study presents an improved criterion by normalising the vortex indicator for prograde and retrograde vortices, respectively, with its conditional mean. Finally, a single, universal threshold is selected for extracting prograde and retrograde vortices simultaneously. The improved method was compared with the previous method based on open channel flow data measured with particle image velocimetry. Results show that while the two methods are basically equivalent in extracting prograde vortices, the improved method extracts a higher fraction of retrograde vortices. The approach of separately normalising vortex indicators associated with prograde and retrograde vortices can also be applied to other vortex extraction criteria.

Experimental study on the role of spanwise vorticity and vortex filaments in the outer region of open-channel flow

ABSTRACT The dynamic importance of spanwise vorticity and vortex filaments has been assessed in steady, uniform open-channel flows by means of particle image velocimetry. By expressing the net force due to Reynolds’ turbulent shear stress, , in terms of two velocity–vorticity correlations, and , the results show that both spanwise vorticity and the portion of it that is due to spanwise filaments make important contributions to the net force and hence the shape of the mean flow profile. Using the swirling strength to identify spanwise vortex filaments, it is found that they account for about 45% of , the remainder coming from non-filamentary spanwise vorticity, i.e. shear. The mechanism underlying this contribution is the movement of vortex filaments away from the wall. The contribution of spanwise vortex filaments to the Reynolds stress is small because they occupy a small fraction of the flow. The contribution of the induced motion of the spanwise vortex filaments is significant.

Experimental study on the multimodal dynamics of the turbulent horseshoe vortex system around a circular cylinder

A turbulent horseshoe vortex (HV) system is generated around a wall-normal cylinder when the approaching boundary layer separates from the wall. This study investigates the dynamics of the turbulent HV system around a circular cylinder in open channel flows with cylinder Reynolds numbers ranging from 8600 to 13900. The velocity fields in the upstream symmetry plane of the cylinder are measured using time-resolved particle image velocimetry. The joint probability density function of the streamwise and vertical velocities in the HV system region is found to exhibit three peaks, indicating that three major types of flow events are induced by the turbulent HV system. The conditional averaged velocity fields based on the characteristic velocity vectors of these events are obtained by using the method of linear stochastic estimation. The estimated flow fields reveal that the turbulent HV system interplays mainly among the back-flow, intermediate, and zero-flow modes. These modes are present for the smallest, mo...

Statistical analysis of turbulent super‐streamwise vortices based on observations of streaky structures near the free surface in the smooth open channel flow

Long streamwise-elongated high- and low-speed streaks are repeatedly observed near the free surface in open channel flows in natural rivers and lab experiments. Super-streamwise vortex model has been proposed to explain this widespread phenomenon for quite some time. However, statistical evidence of the existence of the super-streamwise vortices as one type of coherent structures is still insufficient. Correlation and proper orthogonal decomposition (POD) analysis based on PIV experimental data in the streamwise-spanwise plane near the free surface in a smooth open channel flow are employed to investigate this topic. Correlation analysis revealed that the streaky structures appear frequently near the free surface and their occurrence probability at any spanwise position is equal. The spanwise velocity fluctuation usually flows from low-speed streaks toward high-speed streaks. The average spanwise width and spacing between neighboring low (or high) speed streaks are approximately h and 2h respectively. POD analysis reveals that there are streaks with different spanwise width in the instantaneous flow fields. Typical streamwise rotational movement can be sketched out directly based on the results from statistical analyses. Point-by-point analysis indicates that this pattern is consistent everywhere in the measurement window and is without any inhomogeneity in the spanwise direction, which reveals the essential difference between coherent structures and secondary flow cells. The pattern found by statistical analysis is consistent with the notion that the super-streamwise vortices exist universally as one type of coherent structure in open channel flows.

Bias errors induced by cross-talk in two-phase flow measurements

Cross-talk was identified as an important elemental uncertainty source in dispersed two-phase flow measurement with laser-Doppler anemometry or particle tracking velocimetry. Analytical formulations are presented to quantify the cross-talk bias errors introduced to the ensemble-averaged mean and root-mean-square (rms) velocities. Experimental data available in the literature were used to demonstrate the possible unintended consequences of these errors. It was found that these cross-talk errors are closely related to the slip velocity between the two phases. The error in the mean velocity is proportional to the cross-talk ratio times the slip velocity. The error in the rms velocity depends on the rms velocities of each phase, the cross-talk ratio, and the slip velocity. In practice, the presence of cross-talk may lead to either under- or overestimation of the true velocities.

Influence of the time interval on image-based measurement of bed-load transport

ABSTRACT The influence of the time interval (Δt) between two successive images on measurement of bed-load dynamics has been investigated both analytically and experimentally. The analytical approach is based on simplifying bed-load motion to follow a “flight-rest” pattern. The experimental work involves measuring bed-load transport in a closed channel with a particle imaging technique. The two approaches are consistent in revealing the influence of Δt on measurement results. It is shown that an increase in Δt leads to reduction in measured particle velocity and increase in the measured number of moving particles as well as the flight time. The measured flight length and bed-load transport rate are not directly affected by Δt. The influence of Δt needs to be fully addressed in image-based measurement of bed-load transport.

Comparison of swirling strengths derived from two- and three-dimensional velocity fields in channel flow

Swirling strength is an effective vortex indicator in wall turbulence, and it can be determined based on either two-dimensional (2D) or three-dimensional (3D) velocity fields, written as λci2D and λci3D, respectively. A comparison between λci2D and λci3D has been made in this paper in sliced XY, YZ, and XZ planes by using 3D DNS data of channel flow. The magnitude of λci2D in three orthogonal planes differs in the inner region, but the difference tends to diminish in the outer flow. The magnitude of λci3D exceeds each λci2D, and the square of λci3D is greater than the summation of squares of three λci2D. Extraction with λci2D in XY, YZ, and XZ planes yields different population densities and vortex sizes, i.e., in XZ plane, the vortices display the largest population density and the smallest size, and in XY and YZ planes the vortices are similar in size but fewer vortices are extracted in the XY plane in the inner layer. Vortex size increases inversely with the threshold used for growing the vortex region from background turbulence. When identical thresholds are used, the λci3D approach leads to a slightly smaller population density and a greater vortex radius than the λci2D approach. A threshold of 0.8 for the λci3D approach is approximately equivalent to a threshold of 1.5 for the λci2D approach.Swirling strength is an effective vortex indicator in wall turbulence, and it can be determined based on either two-dimensional (2D) or three-dimensional (3D) velocity fields, written as λci2D and λci3D, respectively. A comparison between λci2D and λci3D has been made in this paper in sliced XY, YZ, and XZ planes by using 3D DNS data of channel flow. The magnitude of λci2D in three orthogonal planes differs in the inner region, but the difference tends to diminish in the outer flow. The magnitude of λci3D exceeds each λci2D, and the square of λci3D is greater than the summation of squares of three λci2D. Extraction with λci2D in XY, YZ, and XZ planes yields different population densities and vortex sizes, i.e., in XZ plane, the vortices display the largest population density and the smallest size, and in XY and YZ planes the vortices are similar in size but fewer vortices are extracted in the XY plane in the inner layer. Vortex size increases inversely with the threshold used for growing the vortex region...