FLOW DEVELOPMENT IN RECTANGULAR CHANNELS AND DUCTS

Abstract

Laboratory experiments related to open channel hydraulics are generally intended to be carried out in fully developed flow regions of a rectangular flume. Thus it is customary to exclude arbitrarily, in such cases, the initial length of the flume from experimental observations. This distance may or may not be adequate for the establishment of fully developed flow. While considerable amount of information is available regarding development of flow In a circular pipe, there is limited information available in this respect for open channels which would enable one to decide the length required for the establishment of fully developed turbulent flow in channels. Thus, there exists a need to investigate the establishment of fully developed turbulent flow in ^rectangular open channels of various aspect ratios and different surface r and flow conditions, so as to evolve a satisfactory criterion for accurate prediction of the establishment length in open channels. The present study was undertaken with the foregoing objective. An exhaustive review of the available literature on the methods for computation of turbulent boundary layers indicated that the computer program of Crawford and Kays (1976) is the most promising for the problem in hand. This program in its original form is applicable to twodimensional smooth rectangular ducts only. In the present investigation this model has been shown to be applicable to three-dimensional developing flows in channels and ducts, if modifications as suggested in the present study are accommodated in the model to account for the following three aspects: (II) (a) The effect of surface roughness, (b) The effect of secondary currents and side wall boundary layers and, (c) Different empirical constants (from those suggested by Crawford and Kays) to account for the changed structure of the mid-width velocity distribution due to (a) and (b) above. The necessary changes required to accommodate these aspects in the program of Crawford and Kays [1976] were made. The continuity and momentum equations were modified for three-dimensional effects by considering a variable width of flow. The zero equation model of turbulence with Boussinesq's eddy viscosity concept was adopted for the solution of these equations. The experimental program was designed to obtain empirical information regarding the variation of bulk mean velocity along the streamwise direction (for the computation of variable width of flow to be used in the mathematical model) and the structure of the mid-width boundary layers in channels and ducts and also for calibrating the computer model. The experiments related to channel flow were carried out in a rectangular flume having a test section 15m long, 0.75m wide and 0.5m deep. The data in the flume included the measurement of mean velocity profiles (along the centre line of the flume) at different locations in the streamwise direction, in the developing and the developed flow regions for different depths of flow (which means different aspect ratios) and different discharges. These velocity profiles were measured by using an assembly of a static tube and a total head tube and a pressure transducer (PD1 and KWS/3S-5 system of HBM) for smooth as well as rough bed conditions (15mm diameter spherical glass beads in closely (ill) packed formation). An open circuit wind tunnel having a test section 9m long, 0.46m wide and 0.15m deep (adjustable ceiling to vary the depth of the tunnel) was used for the experiments related to the duct flow. The data In the wind tunnel included the measurements of mean velocity profiles, longitudinal turbulence intensity profiles (at the centre line of the tunnel) and axial pressure distribution at different locations in the streamwise direction for different aspect ratios. These data were taken for the cases of smooth as well as rough boundaries. For rough boundary runs the top and the bottom walls of the wind tunnel were roughened with (1) spherical glass beads of 15mm diameter, in closely packed formation and (ii) hemispherical elements made of plaster of paris and of size 40mm diameter, in closely packed formation. The mean velocity profiles and the longitudinal turbulence Intensity profiles were measured by using a constant temperature hot wire anemometer system (55M system of DANTEC). The axial pressure distribution was measured with the help of an inductance-type pressure transducer (MKS-Baratron). The developing flow in a channel is shown to be different from that in ducts. This difference is reflected in the different predictor curves for bulk mean velocity for the above two cases. The observed mid-width velocity distribution along the streamwise direction has been subjected to a two-dimensional treatment for the purpose of analysis. The defect law for the velocity distribution in developing channel flows is shown to be similar to that in ducts. The longitudinal turbulence intensity profiles for both smooth and rough ducts are shown to follow an exponential law given by Eq.(5.22), with 0^2.428 and X^O.699 in smooth ducts, and with D =2.423 and X=0.902 in (lv) rough ducts. The proposed mathematical model is shown to be capable of predicting the developing and fully developed mean velocity profiles and other boundary layer parameters and also the length of flow establishment. Satisfactory agreement is shown between the predictions of the model and the experimental observations. The ratio of the length of flow establishment to the depth of flow as computed from the model is shown to be dependent upon the aspect ratio and Reynolds number in smooth channels. In case of rough channels it depends upon the aspect ratio and the relative roughness. For 99.% development of mid-width velocity profiles the length of flow establishment is shown to be varying between 60h and 120h in smooth channel and between 44h and lOOh in rough channels, within the range of parameters investigated. The length of establishment reduces considerably if the criterion is changed from 99% to 95%. Based on 95% criterion the length of establishment varies between 40h and 64h for smooth channels and remains approximately constant at 34h for rough channels.