Enquête sur la formation de vortex et autres anomalies d'écoulement dans une enceinte avec ou sans surface libre

A study of vortex formation and other abnormal flow in a tank with and without a free surface

Electricité de France.

Résumé

1. introduction. Quite pronounced eddy motion is apt to occur in certain hydraulic structures when a transition occurs from free-surface to pressure flow, and other abnormal flow effects. (especially vortex "streamers') are also observed, even in pressure flows. Eddies on a free surface sometimes grow to the point of forming a kind of "funnel" or vortex at one point. Air is sometimes entrained in the central depression, and when this happens, rotational speeds increase very sharply towards the vortex centre. Such phenomena can be observed in orifice flows (tank drains, lock chambers, power tunnel intakes, flow under a gate, reservoir or river intakes, etc.) or in pumping plant, irrespective of the pump intake orifice design (Fig. 1). 2. Aims of this study. In the absence of precise theories whereby the likelihood of vortex formation might be predicted for each particular case, many manufacturers and research laboratories undertake several research programmes every year in an attempt to find a way of preventing vortex formation in dam water intakes in rivers or in pump intake chambers. Conditions governing vortex formation not only depend on the hydraulic flow conditions (depth or head of water, rate of flow, etc.) and ambient conditions (especially fluid temperatures) but also on the chamber design (shaped intake or suction chamber). Ideal intake or suction chamber outlines cannot always be achieved, for civil engineering and imperative cost requirements almost invariably make it necessary to put up with considerable misalignment of the supply canal centre line and the intake or pump position, resulting in an appreciable kinetic moment and vortex formation. The same types of test are repeated over and over again with the same imperfect devices such as floating rafts, strainers, deflecting panels at various angles, etc., until satisfactory results are finally obtained. An attempt has now been made by "Société Hydrotechnique de France" ("Machines Section") to collate the experience of various manufacturers and laboratories for the common good. The three main points retained for consideration in this study were the following: (i) Vortex formation conditions (and conditions for other abnormal flow effects, where applicable) ; (ii) Anti-vortex devices; (iii) Vortex similitude. The most characteristic special cases have been retained out of the replies received (they are summed up in "card-index" fashion in an appendix hereto) so that manufacturers and laboratories may acquaint themselves not only with the vortex formation conditions for such cases, but also with successful counter-measures. It is a good thing to thus be able to avoid the considerable amount of costly trial-and-error work associated with the search for a solution, which may not even then be entirely satisfactory. It is also thought the attached reference list to the principal current research into the subject may be of interest. 3. Vortex formation conditions. Vortex formation depends on numerous parameters, notably hydraulic conditions (depth or head of water, rate of flow, etc.) and the geometry of the installation. By analysing information obtained, experimental data from the Chatou Test Centre, and published data (see bibliographical reference list herewith) it has been possible to determine the critical head or depth of water above the bellmouth intake beyond which vortices no longer entrain air. Especially in the case of vortices formed by vertical rising suction flow, the tests have shown up the effect of chamber geometry and-for example-variation of any of the following (Fig. 2) : (i) Distance from bellmouth to floor ; (ii) Distance from the walls ; (iii) Pump position in the sump ; (iv) Bellmouth diameter ; (v) Pipe diameter ; (vi) Chamber intake width. Other forms of abnormal now liable to appear in a water intake are also worth noting, for instance the formation of a vortex "streamer" underneath the bellmouth, with large quantities of bubbles (Fig. 3 and 4). 4. Anti-vortex devices. Contributors have drawn attention to numerous such devices, and references to others are found in published material (see bibliographical reference list herewith). Most are designed to prevent air entrainment and do not eliminate eddies near the intake orifice, as would strictly speaking be desirable for ideal pump intake conditions. This has led to the development of a special device consisting of lateral vertical expanded metal screens by the Chatou Research Centre, which are positioned in the suction chamber parallel to the flow and symmetrically to either side of the pump (or of the suction orifice in the case of a drain) (see sketches, Figs 5 a-b). An expanded metal screen comprises a large number of identical diamond-shaped meshes which, seen in cross-section, appear as a series of parallel blades ; to ensure efficient flow deflection, the "strap" of each such "blade" must be fairly wide. In addition, the longer mesh diagonal must lie parallel to the eddy vector, i.e. nearly always vertical. The lack of symmetry of this metal device thus enables lateral frictional resistance to any flow to be reduced to practically nothing in the normal direction of flow, i.e. from the intake sluice towards the suction orifice. This resistance becomes very great (and the flow may be deflected) with the flow occurring in the reverse direction, as is invariably associated with eddy formation (Fig. 5 c). This being so, experience has shown that provided the expanded metal screen has the requisite characteristics, vortex formation and 'streamer' effects underneath the bellmouth can be prevented completely by such screens extending over the full depth of water in the chamber. Visual observation then shows completely calm, steady flow throughout the chamber. Suitable screen characteristics depend on hydraulic conditions (depth of water, rate of flow etc.) and the initial fluid circulation value at the chamber inlet. These can be determined accurately by scale model tests, but a rough solution to the problem can be based on established practical solutions along the lines listed in the "card-index" herewith. (Slips II B 4 to II B 7.) As no flow passes, through the screens during normal plane operation, loss of head due to the device is negligible ; it was found to be well within normal experimental error on all the models tested. Full panels in lieu of these screens do not eliminate the vortex, but if placed behind the screens (on the opposite side to the suction orifice) they do not affect their beneficial action, and all eddy motion is still eliminated as before. This being so, vertical expanded-metal screens are able to inhibit vortex formation in suction chambers of any shape. A set of vertical screens facing in the direction of flow can thus be arranged by each suction orifice of an intake or in a chamber of any shape (examples are given in the appendix with the article). In the particular case of tank-fed vertical pumps, an additional vertical screen is placed behind the pump and connecting to the two lateral screens, in order to prevent formation of an unlimited dead water area behind the pump. The meshes of the third screen face in a direction ensuring a total absence of eddy formation. The expanded metal characteristics (mesh pitch 'strap' width, etc.) and screen spacing depend on the intensity of the initial circulation at the basin inlet, also on head of water and rate of flow. Some care is required in placing the expanded metal screens on the model (and subsequantly also on the prototype). Vortex formation is not prevented if the mesh is positioned incorrectly or if the screens are unsymmetrical with respect to each other, by virtue of the very process whereby correctly installed screens prevent vortex formation. This system also eliminates non-aerated eddy motion (overall motion on the free surface, 'streamers', rotary motion underneath the bellmouth, etc.) while regulating the flow with negligible loss of head. A further advantage of these screens is that they cannot clog up with dirt in the water as there is no flow through them. They have already been fitted in numerous installations and have invariably given the same efficient service as on the model. 5. Vortex similitude. Though this very complicated problem is beyond the scope of this study, it was nevertheless considered interesting to approach it because of the importance of comparing model and prototype when designing an anti-vortex device. Similitude conditions depend on the criterion considered for the comparison, which could be one of the following : - (i) Conditions for the formation of the initial hyperbolic portion of the vortex "funnel" on the free surface ; (ii) Conditions for initial air entrainment ; (iii) Air-core vortex frequency and duration under given conditions. The choice of different comparative criteria can thus explain the numerous differences between the similitude criteria suggested by various laboratories and in published work. These criteria are analysed, followed by a description of the main results obtained at Chatou Research Centre (Figs 6 to 9). An experimental method was required whereby the characteristics of a vortex might accurately be determined at any given instant, from the moment of initial depression formation to that of air entrainment. The main difficulties in finding such a method were associated with vortex instability in both space and time. Direct methods of determining the vortex 'funnel' profile (point gauges, pressure pick-ups) could not he considered, as a vortex continually changes its position on the free surface, and also because of the upsetting effect of such instruments upon the flow-even if in miniaturized form. Only an optical method could be practicable, therefore, but straight photography of the vortex shape and length also had to he given up because of its very considerable error when applied to shallow vortices. The 'refracted ray' method developed at Chatou in 1960 gives the requisite results. It is based on the optical phenomenon whereby a caustic surface forms when light rays are diverted in passing through the dioptic air-water surface of revolution of the vortex 'funnel'. It is then merely necessary to mark out the chamber floor with a suitable scale and to measure the diameter of the dark circular patch formed by the intersection of the caustic surface and the chamber floor (see Fig. 7). The actual measurement can be done by an appropriate cinematographic recording method. The advantage of this method is that it enables an experimental relationship to be established between circulation strength around the vortex (determined from the patch dimensions) the depth of water in the chamber, and the pump intake flow. Tests are still in progress on the subject, but it is already quite clear from results so far that : - (i) Formation of the hyperbolic upper part of the vortex 'funnel' on the free surface definitely appears to comply with Froude similitude requirements ; (ii) Given equal velocities on the model and prototype, the initial air entrainment process would also comply with similitude requirements.