A powerful two‐color Laser Doppler Anemometer (LDA) system, with direct digital signal processing has been used to measure accurately the longitudinal and vertical velocity components in two‐dimensional, fully‐developed open‐channel flow over smooth beds. The law of the wall and the velocity defect law were re‐examined because the log‐law has been often applied to open channels without detailed verification. It was found that the log‐law can be applied strictly only to the near‐wall region. In this region, the von K´rm´n constant κ and the integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number. As the Reynolds number becomes larger, the deviation from the log‐law cannot be neglected in the outer region. This deviation can be expressed well by Coles' wake function which involves a Reynolds‐number dependent parameter Π. The distributions of eddy viscosity and mixing length were evaluated and found to depend on Π. All the data including the...

Open‐channel Flow Measurements with a Laser Doppler Anemometer

Localized fluid flow measurements with an He-Ne laser spectrometer

The axial and radial velocity components w and u, and the concentration c of a Rhodamine 6G dye were measured simultaneously in a turbulent buoyant jet, using laser-Doppler anemometry combined with a recently developed laser-induced-fluorescence concentration measurement technique. These non-intrusive techniques enable measurements in a region of plume motion where conventional probe-based techniques have had difficulties. The results of the study show that the asymptotic decay laws for velocity and concentration of a tracer transported by the flow are verified experimentally in both jets and plumes. The momentum and volume fluxes and the mean dilution factor are determined in dimensionless form as a function of the normalized distance from the flow source. Contradictory results from earlier experimental plume investigations concerning the decay laws of w and c and the plume width ratio b_c/b_w are discussed. The turbulence properties and the transition from momentum-driven jets to buoyancy-driven plumes are presented. The turbulence is found to scale with the mean flow as predicted by dimensional analysis and self-similarity. Buoyancy-produced turbulence is found to transport twice as much tracer as jet turbulence. Although velocity statistics in jets and plumes are found to be highly self-similar there is a strong disparity in the distribution of tracer concentration in the two flows. This occurs in the time-average mean flows as well as the r.m.s. turbulent quantities. Instantaneous concentration fluctuations are found to exceed time averages by as much as a factor of 3. The experimental results should provide a reasonable basis for validation of computer models of axisymmetric plumes.

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Investigations of round vertical turbulent buoyant jets

Certain mathematical models for predicting the flow and mixing processes in stratified fluids are reviewed, with particular focus on stratified lakes and reservoirs. The various types of prediction methods are introduced briefly, from one-dimensional integral methods to direct simulations of the Navier-Stokes equations. The paper concentrates on turbulence models for simulating the turbulent momentum, heat, and mass transport terms appearing in the statistical methods employing averaged equations. Models ranging from the simple Prandtl mixing length theory to second-order-closure schemes are discussed. To illustrate the predictive capabilities of the methods, examples are presented of applications of the method covered to a variety of stratified flow situations.

Examples of calculation methods for flow and mixing in stratified fluids

Computational flow modelling and design of bubble column reactors

The effects of stable stratification on turbulence structure have been experimentally investigated in stratified open-channel flow and a theoretical spectral-equation model has been applied to the stably stratified flow. The measurements were made in the outer layer of open-channel flow with strongly stable density gradient, where the wall effect was small. Velocity and temperature fluctuations were simultaneously measured by a laser-Doppler velocimeter and a cold-film probe. Measurements include turbulent intensities, correlation coefficients of turbulent fluxes and coherence–phase relationships. These turbulent quantities were correlated with the local gradient Richardson number and compared with the values calculated using a spectral-equation model and with other laboratory measurements. In stable conditions, turbulent motions approach wavelike motions, and negative heat and momentum transfer against the mean temperature and velocity gradient occurs in strongly stable stratification.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112083000944

Turbulence structure in stably stratified open-channel flow

Eddy diffusivity near the free surface of open channel flow

The velocity profile, longitudinal turbulent intensity profile, and bursting period in drag reducing pipe flow were measured using a laser Doppler technique. The temperature distribution and heat transfer coefficient were measured with thermocouples in the same system. The results of the decrease in eddy diffusivities of momentum and heat near the wall, the gross flow measurements, and the velocity distribution were shown to be in a good agreement with the predictions of the eddy diffusivity model for viscoelastic fluids previously proposed. A simple method based on the eddy diffusivity model to calculate the rate of heat transfer in the fully developed pipe flow of viscoelastic fluids is proposed, and is ascertained to be effective by the previous experiments.

Reduction of eddy diffusion for momentum and heat in viscoelastic fluid flow in a circular tube

Pulsating turbulent flow in a tube was studied experimentally. Measured instantaneous profiles of the velocity and the intensity of turbulence can be clearly classified into two groups by means of a certain critical period of pulsation. At longer periods of pulsation, the shapes of the velocity profiles are similar to those for steady flow, while the intensity of turbulent fluctuation does not pulsate ; whereas at shorter periods, the velocity profiles are not similar to those for steady flow, while the intensity of turbulent fluctuation pulsates oppositely to the velocity. From measuring the time intervals between bursts in both steady and pulsating turbulent flows, it was clarified that the range of burst periods occurring in pulsating flow was the same as the preferred range of burst periods in steady flow. If the pulsation period is longer than the upper limit of this range, the mean burst period is equal to that of steady flow, but if the pulsation period is included in the range of burst periods for steady flow, the bursting of the same period as the pulsation period dominates.

Pulsating turbulent flow in a tube

The flow transition from uniform bubbling regime to liquid circulation regime was studied in a vertical two-dimensional bubble column with no net liquid flow. A regular two-loop liquid circulation was observed to occur as a result of violent interactions of unsteady liquid circulation and large bubbles. A critical superficial gas velocity was defined as the velocity at the point of incipient regular circulation and was obtained from the gas velocity at maximum gas hold-up. Under a uniform stable gas distribution the critical gas velocity depends on the ungassed liquid height and is independent of sparger geometry, i.e., the diameter and pitch of holes. When the pressure drop through the sparger is insufficient or inlet gas is distributed in the narrow central region of the sparger, interactions of large-scale liquid motions and large bubbles in the bulk section is suppressed by depleting the growth of large bubbles at the base. This makes the critical gas velocity larger than that under the uniformly sparged condition. A similar dependence of critical gas velocity on ungassed liquid height was confirmed with literature data for three-dimensional bubble columns.

Tokuro Mizushina

Papers

Turbulence structure in stably stratified open-channel flow

Eddy diffusivity near the free surface of open channel flow

Reduction of eddy diffusion for momentum and heat in viscoelastic fluid flow in a circular tube

Pulsating turbulent flow in a tube

The flow transition in a bubble column.