Statistical Properties of Distribution of Solid Particles at the Bottom Setting in Turbulent Shear Flow

In this paper the behaviors of settling particles in turbulent shear flow are investigated and the statistical properties of distribution of the particles at the bottom are obtained experimentally and theoretically. For the properties of distribution of the particles, the mean settling length of the particle, that is, the mean value of the streamwisely transporte length of the particle, and the standard deviation of the settling length are considered. These statistical properties are obtained by experiment and the trajectories of the settling particles are photographed by storoboscopic light. Then, on the basis of these experimental results, the stochastic models for the behaviors of the settling particles are developed. These models can explain well the actual phenomena, and it is found that these stochastic models are to be pertinent. Problems to be solved in the future are discussed

Structure of Instantaneous Reynolds Stress over a Permeable Open-channel with Suction or Injection

In the present study, we investigate experimentally the structure of the instantaneous Reynolds stress in open-channel flow over a permeable bed with suction or injection. Then, the fluctuating signals obtained from the X-type hot-films are conditionally analyzed in order to examine the effect of suction or injection on the turbulence production mechanism or the bursting phenomenon. We can then obtain the following results. The absolute magnitudes of the turbulence intensities and the Reynolds stress near the wall increase with an enlargement of the injection, while they decrease with an enlargement of the suction. However, the fraction of time occupied by each bursting event and the contributions of its event to the Reynolds stress against any hole size are almost the same, irrespective of suction or injection. The promotion of turbulence by injection or its suppression by suction may be caused by similar variations of three parameters of the bursting intensity, the bursting period and the bursting duration time. To sum up, the internal structure of the turbulence or the bursting mechanism is not essentially influenced by suction or injection, as long as the flow is still turbulent

Numerical Calculation of Turbulent Open-Channel Flows in Consideration of Free-Surface Effect

Numerical calculation techniques of turbulent shear flows are classified into two categories : one is the k-ε turbulence model, and the other is the large eddy simulation (LES). The standard k-ε model has been established at present to predict a turbulent structure in jets, boundary layers and closed channel flows, while LES is being developed to predict a coherent eddy structure in simpler channel flows. The standard k-ε model cannot be, however, easily applied to open channel surface flows, because the turbulence near the free surface is more depressed than the closed channel flows. In the present study, a new modified k-ε model is proposed to predict reasonably a turbulent structure in open channel flows with both the low and high Reynolds numbers. The numerical calculations indicate a good agreement with the experimental data which were obtained by making use of hot-film and Laser Doppler anemometers

Bursting Phenomenon near the Wall in Open-channel Flows and its Simple Mathematical Model

In this paper we propose a new evaluation method for the bursting period, on the basis of the phenomenological consideration that the number of the occurrences of interaction-like motions should be removed from those of the ejection or the sweep events in the sorted Reynolds-stress fluctuating signals. Then, it is confirmed by this method that the mean bursting period in open-channel flows may be universally expressed by outer rather than inner parameters, and that its probability distribution becomes log-normal, irrespective of the Reynolds and the Froude numbers, as well as the wall roughness. Next, in order to explain even quantitatively the bursting process or the turbulent structure in the wall region, we propose a simple mathematical model on the basis of the Einstein-Li model and also the knowledge of the bursting-period characteristics obtained above. Though the present model is inherently quasi-two-dimensional and quasi-linear, this model can describe fairly well some distributions of mean-velocity, turbulence intensities and Reynolds stress. In particular, it can satisfactorily explain a sequence of the bursting process