STUDY OF VORTEX CHAMBER TYPE SEDIMENT EXTRACTOR

Abstract

When a canal takes off from the head works on an alluvial river, water flowing in the canal also carries considerable sediment load with it unless special measures are taken to reduce the same. The sediment load entering into the canal may deposit in it thus causing silting of the canal that results in a reduction of discharge carrying capacity of the canal. In case of power canals a part of the sediment load reaching the power plant passes through the turbines and damages the turbine runner blades/bucket Thus the success of any canal system greatly depends on the control achieved in stopping the entry of excess sediment into it. The measures for control of sediment entry into a canal can be applied either at canal head works or in canal downstream. In exceptional cases they can be applied at both locations. The measures adopted for this purpose at canal head works are known as excluding devices while the devices used in the canal are known as sediment ejectors or sediment extractors. Sediment ejectors only are studied in the present thesis. Various ejectors such as tunnel type, vortex tube, settling basins and vortex chamber type extractor have been used in practice. The chambers of vortex type extractors are found to be smaller in size, particularly, with respect to the settling basins and the tunnel type extractors handling same amount of water. The flow mechanism in a vortex chamber type sediment extractor is similar to the Rankine vortex in which a forced vortex core is surrounded by an irrotational or free vortex zone. Experimental studies have been conducted by several investigators for studying the flow structure and similarity in the vortex chambers. Using the theory of free vortex, the expressions for tangential velocity and water surface elevation in a vortex flow at the entrance of an outlet pipe were derived by the previous investigators Investigations for the flow pattern in a vortex chamber type sediment extractor using the dye injection method have also been made. It has been seen that the radial flow towards the orifice is mainly supplied by the fluid layers near the floor of the chamber. The sediment particles entering the chamber at the periphery were observed to move towards the outlet at the centre along a helicoidal path. Some investigators have studied the variation of concentration of fine sediment particles in a Rankine vortex system Detailed investigations are also available about the trajectory and distribution of radial and tangential velocities in a vortex type settling basin The helicoidal trajectories were observed to be followed by sediment particles in a vortex chamber Tangential velocities were found to follow the Rankine vortex system except near the periphery of the chamber and also near the inlets and outlets of the vortex chamber. Radial velocities were found to remain constant across a vertical while they varied in the radial direction A comprehensive review indicated that detailed studies have been made concerning the flow development in vortex chambers by mainly observing the tangential velocities. A smaller number of studies are, however, available in which both the radial and the tangential velocities were measured for study of flow pattern in the vortex chambers. The equation governing the variation of sediment mass concentration in the chamber of a vortex type sediment extractor is derived in the present investigation in polar cylindrical co-ordinate system. This is given as below: ' a rod dz r a \ a) ,• d0\ 36) ct\ dz) dz where v,., vg and v. are the radial, tangential and axial velocities and £•,.,% and ez are the diffusion coefficients along radial (/•), tangential (8) and vertical (z) directions respectively, /'is the radial spacing, co0 is the fall velocity of the sediment particle and c is the sediment concentration. Effectiveness of vortex type sediment extractors in removing the sediment from the flow can be evaluated mathematically by obtaining the solution of the above equation. For simplified cases this equation can be solved analytically. However, simplified solutions would not hold good for flow in the chamber of a vortex type sediment extractors due to complex flow and geometric configurations. Numerical methods, therefore, can be used for solving the above mentioned equation. The review of literature indicated that complex flow conditions occur in the chamber of the vortex type sediment extractors particularly near the inlets and the outlets This aspect is carefully studied herein. The governing equation for variation of sediment concentration in the chamber of the vortex type extractor is solved numerically to obtain sediment concentration also. The available relations for sediment removal efficiencv of these extractors are validated and modified by using data having wide range of hydraulic variables Information on the velocity components is required while making the computations regarding suspended sediment concentration within the chamber ol" the vortex type sediment extractor. Velocity distributions in axi-symmetric vortex flows are derived in literature by approximating the turbulence by mixing length model. Indeed, it is not easy to model the turbulence even in the simplest of the flow conditions, whereas the vortex flow as it occurs in the chamber of an extractor, is quite complex. Keeping these points in mind, the velocity distributions in the chambers of vortex type sediment extractors studied herein are derived using experimental observations. Details of the experiment conducted are included later in the present text. The following conclusions are derived regarding the distribution of velocity components from analysis of the experimental data, (i) The radial and tangential velocity components can be considered to remain uni - form over the flow depth (ii) The chamber of the extractor can be sub-divided into different sub-zones for the purpose of computation of velocity components. The following functional relationships are assumed to hold good for the radial and tangential velocity components. "• =/ coj- RL k1^ ' V 0*, and —2— = / (Or Rf r 0 £/, Qu Rl l>r Qi Here co f is the reciprocal of the characteristic time (also called characteristic frequency) and is defined as 0,•/ (Ac Rl). Ac is the cross sectional area ofthe inlet channel, R, is the reference length which is taken to be equal to the radius of the vortex chamber RT, Zh is the difference in the bed levels of the bottom of the chamber and the overflow outlet, h is the depth of flow at the periphery of the chamber, Qu is the discharge through the underflow outlet, 0/ is the inlet discharge and 0 is the angular spacing measured in clockwise direction with respect to the centre of the vortex chamber The governing equation for variation of sediment mass concentration was solved numerically by using an unconditionally stable second order Crank-Nicholson type of implicit finite difference scheme. The governing partial differential equation was converted \ iii to the equivalent partial difference equation, which was solved through the standard Double Sweep algorithm by making use of the boundary conditions The sediment diffusion coefficients in radial, tangential and vertical directions were required for the above solution These were empirically related to the velocity gradients in the respective directions. Information on variation of sediment concentration within the vortex chamber is useful in computation of the sediment removal efficiency A scrutiny of the relations for distribution of velocity components in the vortex chamber and the numerical scheme mentioned above indicated that the removal efficiency (//„ ) of the vortex chamber type extractor can be expressed by the following functional relationship: %=f [Qi> Qu,Qw, Zln V RT> J' <°o, ", g ) Here Rr is the radius of the vortex chamber, d is the diameter of the sediment particle, co0 is the fall velocity of particle, v is the kinematic viscosity andg is the gravitational acceleration, and Qw is the discharge which gets rotated within the chamber Its value is dependent on the geometrical configuration of the extractor and is such that Ou < Ow < Qj. Hence the following expression is hypothesized for Qw Q„ = Qu+ K(Q,.-o„) Here K is the factor, the value of which is governed by the geometric configuration of the extractor. The variables of the above equation forr\0 are arranged into the following dimensional form >J„ = ./' V J o: *KK Here (Qu/Q,) ]S t,ie water abstraction ratio, \Zh/hp\ represents the depth ratio, (oj0t//v) is the particle Reynolds number and (gJ/g/^Ap) represents the Froude number with respect to the flow in the vortex chamber and is an index of the centrifugal force of rotational flow. Such a functional relationship can be used to develop an expression for the removal efficiency of the vortex chamber type sediment extractor. The experiments were conducted in the Hydraulics Laboratory at Civil Engineering Department, University ofRoorkee, Roorkee by using two models of different geometric configurations of the extractor each having the diameter of the vortex chamber equal to 1 m In the first model the axes of the inlet and outlet channels were co-planar and these joined the vortex chamber tangentially while in the second model the outlet channel was provided at a distance equal to the chamber diameter. An electromagnetic liquid velocity meter was used for velocity measurements. It measured simultaneously the two mutually perpendicular velocity components at the location of its sensor. Variation of suspended sediment concentration within the vortex chamber was measured by systematically varying the water abstraction ratio, sediment size and other parameters. In addition all the laboratory and field data available in literature on above aspects were compiled and used herein. Close study of observed velocity distributions indicated these to follow the pattern of combined Rankine vortex in some segments of the vortex chamber However, the vortex system is greatly affected due to inflows and outflows of the chamber. Values of the radial and tangential velocities were computed by developing different empirical relations in different sub-zones of the vortex chamber. The computed velocities were found to be in good agreement with their corresponding observed values. Variation of suspended sediment concentration within the vortex chamber was computed using the numerical method of solution. Coefficients appearing in the relations for sediment diffusion coefficients were ascertained so as to obtain a close agreement between observed and computed values of sediment concentration A comparison Was made between observations and such computed values for all other runs and it revealed a satisfactory agreement between these two. Sediment removal efficiency computed by making use of computed sediment concentration compared well with the experimental observation A check on existing relations for 1](J was made and they were found not to produce satisfactory results. Re-analysis of available laboratory and field data was carried out and the following equation was derived for ij0 . V'-25 ( 1o = K 0 kQ, , to J 0 gRlh\ The value of the coefficient A.',, was 2.24 for the geometric configuration-! and 1.35 for both of the geometric configurations II and III respectively The above equation was found to produce results with a maximum of ± 40 per cent error This accuracy is considered as satisfactory because the data used herein are from vortex chamber type extractors having different type geometric configurations and included laboratory and field data of a number of investigators. The relations for ij0 developed here are expected to be used by the extractor designers in their day-to-day work Vortex chamber type sediment extractor is thus found to be a suitable alternative to conventional extractors due to their smaller dimensions, high sediment removal efficiency and smaller water abstraction ratio. In the present study, two different geometrical models of these extractors were studied in detail. Variation of suspended sediment concentration within the vortex chamber is computed by solving the governing partial differential equation by an unconditionally stable second order accurate finite difference scheme of Crank-Nicholson type. A general relationship is also developed for the computation of sediment removal efficiency of vortex chamber type sediment extractors having varying geometric configurations. VI