GATE LIP HYDRAULICS
B.T.A. SAGAR Chief Hydromechanical Engineer, ECI, a division of Frederic R. Harris, Inc., 5660 Greenwood Plaza Boulevard, Englewood, CO 80111, U.S.A. e-mail:
[email protected]
ABSTRACT ABSTRACT Gate lip angle is defined as the angle whose tangent is given by the ratio of vertical distance as measured between the gate bottom edge (skinplate bottom edge) and the bottom edge of gate bottom beam, to the depth or thickness of gate (depth of gate as measured from the upstream face of gate bottom beam to the upstream edge of skinplate bottom. Gate lip angle has a profound influence on (a) gate vibrations, (b) cavitation of the gate members, and (c) downpull. The paper provides guidelines for lip angles, especially when modifying old gates. Historically, the laboratory experiments addressed all three problems with predominant preoccupation on evaluating downpull forces and minimizing downpull. The writer points out that, in general, the lip angles required to minimize vibrations and cavitation are much less than required for substantial reduction in downpull forces. INTRODUCTION Gate designers, the world over, are aware that the gate bottom geometry -- usually referred to as the "gate lip" -- plays a vital role in determining the satisfactory gate performance. The gate lip has profound influence with regard to the following hydraulic aspects: 1.
Cavitation damage to the gate.
2.
Gate vibrations.
3.
Downpull on gate.
4.
Uplift on gate.
5.
Discharge coefficient.
Historically, hydraulic model studies have been conducted in the past in various institutions of the world to study some of the above aspect either individually or in combination. Majority of such studies were intended for new gate designs to develop an optimum geometry where the objectives were to: •
Eliminate cavitation damage.
•
Eliminate vibrations.
•
Minimize downpull.
•
Avoid uplift.
•
Maximize the discharge coefficient.
A large number of model studies and publications were predominantly preoccupied with downpull. Such studies, therefore, invariably resulted in adopting conservative lip angles in new gate designs. Thus, Davis' "Handbook of Applied Hydraulics" showed an example lip angle (see Section 3.0) of 35 o for gate with upstream skinplate and upstream seal. Some designers adopt larger conservative lip angles with e/d ratio of 0.6 (see paragraph 3.0) for upstream skinplate gates with upstream seals without substantial justification. It is unfortunate that inspite of many hydraulic model studies over the years by eminent researchers on a variety of practical and impractical gate bottom lips, no guidance is available to the practical gate designer to determine gate lip geometry especially when confronted with the task of remodelling existing old gate experiencing specific problems. To illustrate this point, consider the case of an existing gate installation, where the gate is known to have vibration problems without any evidence of cavitation. Reducing downpull is of no concern, as the hoist has safely withstood it. Vibration problems in this installation led to frequent failure of roller bearings in the gate wheel assemblies contributing to the non-closure of the gates under gravity. To what minimum extent the bottom beam should be cut to eliminate vibrations without creating net uplift is the question to be resolved from hydraulic considerations. From structural considerations, it is obviously not desirable to cut the bottom beam depth excessively and induce excessive shear stresses in the welded connections of the webs at the beam ends, which are already in uncertain state of deterioration and corrosion. Maintaining the structural integrity of such old gates should be a paramount consideration. The aim of this paper is to focus on the lip angle influence on the hydraulic aspects considered individually so as to provide guidelines to the designer in selecting minimum lip angle useful in remodelling the gate bottoms of existing gates. INFLUENCING FACTORS Factors that have significant influence on the gate lip hydraulics are: •
Submerged or free flow downstream of gate.
•
Aeration downstream of gate.
•
Upstream or downstream skinplate.
•
Upstream or downstream seals.
In studying the influence of the gate bottom geometry, one should not forget that the flow conditions downstream of the gate have a significant impact. Thus the gate bottom geometry should be carefully studied in the separate context of free flow or submerged flow conditions immediately downstream of the gate. Another important factor which also has a significant impact on the performance of the gate and the gate bottom geometry is aeration, not only in the vicinity immediately downstream of the gate but also in the zones beneath the gate, in the gate lip areas. As high velocity flows beneath the gate have a tendency to carry away the air with them, thus creating low pressure zones often with fluctuating air pressures in these zones, the availability of air and access for aeration to such zones, thus becomes a very significant factor impacting the successful hydraulic performance of gate lip geometry. Other obvious factors that have influence on the hydraulics of gate bottom geometry include: •
Head on the gate during operation.
•
Shape of the upstream bellmouth and its proximity to the gate.
•
Gate slot geometry.
•
Bottom seal shape.
•
Downstream conduit slope.
•
Conduit geometry downstream and upstream.
LIP ANGLE The gate bottom geometry is usually defined by the lip angle θ which is determined as below for the gate with upstream skinplate and upstream seals. If, e
=
the vertical distance between the gate bottom (usually skinplate) edge and the downstream bottom edge of the bottom beam downstream flange.
d
=
the thickness or depth of gate measured from the downstream edge of skinplate to the downstream face of the bottom bearing then
In the case of gates with downstream skinplate and downstream seal: e
=
the vertical distance between the gate bottom edge (skinplate edge) and the upstream bottom edge of the bottom beam upstream flange.
d
=
the thickness or depth of gate measured from the upstream face of
the bottom beam U/S flange and the upstream edge of skinplate. tan θ = e/d
In both cases, lip angle
θ
is defined by:
FLOW HYDRAULICS The influence of the gate lip geometry on the hydraulic aspects listed in Paragraph 1.0 is now briefly examined based on historical model and prototype data available to the gate designer; and listed in bibliography at the end of this paper. CAVITATION DAMAGE Significant or excessive cavitation damage was observed in some high head gate installations. Cavitation damage is usually observed on: (a) the gate members especially at the bottom and/or (b) to the conduit downstream of the gate and the gate slot areas. It is a well-known fact that a gate with flat bottom (or with e/d = 0) has the maximum potential for cavitation, regardless of the fact whether the gate has upstream skinplate or downstream. This is because the flow jet springs from the upstream bottom edge and frequently reattaches to the gate bottom near the downstream bottom edge, thus creating a low pressure zone under the gate without access to aeration. Increasing e/d ratio or the lip angle obviously reduces the cavitation damage potential. In the gates with upstream skinplates and upstream seals (U/S gates) where the flow under the gate is divergent, the increase in lip angle prevents the reattachment of jet to the gate bottom member and the cavitation potential is reduced as more and more access becomes available for aeration into the low pressure zones, under free discharge conditions. In the case of gates with downstream skinplate and downstream sealing gates where the flow under the gate is convergent, increasing e/d ratio creates a stagnation zone under the gate with positive pressure thus eliminating cavitation potential. Based upon the available data, the following minimum values of e/d ratios or lip angles can be assumed for minimizing cavitation potential to a reasonable degree.
Diverging Flow U/S Gates
Converging Flow D/S Gates
Free Discharge Condition
±
20o
45o
Submerged Condition
±
20o
45o
VIBRATION OF GATES One of the main contributing factors for gate vibrations is the impingement of high velocity flow by shifting control point alternately from the gate upstream bottom edge to the downstream bottom edge. Other contributing factors include pressure fluctuations in the low-pressure zones at gate bottom, (Naudascher 1991) and downstream of the gate, excessive variation of hydrodynamic forces for small vertical movements of the gate and shear flow under the gate (Sagar, 1977). As can be expected, gates with flat bottoms
exhibit significant potential for vibrations due to control point shifting, as well as large downpull variations for small vertical travel. Vibrations can be significantly reduced in the upstream sealing gates with divergent flows with a lip angle of 25 o, when the issuing water jet normally can be expected to clear the downstream bottom edge of the gate beam. It is noteworthy to mention that Japanese standards permit 20 o lip angle for such gates with upstream skinplate and upstream seals, as the jet flare in the upward direction seldom exceeds this angle (although they confined their recommendation to large span gates in order to avoid the uncertainty of gate slot influence on flow patterns under the gate which becomes significant in narrower gates). DOWNPULL Downpull is the net downward hydraulic force on the gate under hydrodynamic conditions (Sagar, 1977). To minimize downpull so as to reduce the hoist capacity was the primary objective of many gate designers and researchers until the recent past. Various gate lip shapes and the corresponding downpull coefficients were studied in the hydraulic laboratories (Naudascher, 1991). But two main considerations need to be noted in this regard: 1. The maximum downpull does not necessarily occur at the small openings of the gate where maximum friction demands maximum hoist pull. Provision of conservative hoist capacity is advisable in any case as the hoist costs do not significantly increase by the increased hoist capacity. Thus, downpull has no significant influence with gates in modern designs, which use proper lip angles. 2. Downpull is not a disease to be cured or eliminated. Downpull serves as a very useful tool for the gate designer to ensure self closure of the gates, if skillfully developed to provide static or dependable downpull. In downstream sealing gates, a static or "dependable" downpull can be created by offsetting the flow control point at the bottom gate seat and seal sufficiently upstream of the top and side seals, to ensure gate closure under gravity. As the dynamic downpull on the gate varies with the gate opening being minimum at small openings, it cannot be depended upon for gate closure. Minimizing downpull should not, therefore, be the primary objective of a gate designer, provided the gate is otherwise satisfactory with regard to cavitation and vibration. While increasing lip angle reduces the magnitude of downpull, it can also create sufficient uplift as to prevent gate closure with upstream sealing gates. Therefore, a lip angle of about 25 o or e/d ratio of 0.45 is considered adequate to avoid net uplift on the upstream sealing gate. For downstream sealing gate, a lip angle of 45 o, with a sloping bottom plate, is preferable to minimize downpull as such slope ensures positive water pressures on the sloping plate at all gate positions, which plays a desirable role to reduce vibration potential. UPLIFT FORCES Local uplift forces can exist under hydrodynamic conditions on the gate bottom. In fact, it is desirable that positive pressures exist on the gate bottom to prevent cavitation potential. A 45 o lip with a sloping bottom plate in downstream sealing gates with convergent flow under the gate is proposed because such local uplift or positive pressures exist throughout gate bottom. However, "net uplift" on the gate which is
caused by local upward forces on the gate bottom exceeding the downward force on the gate is not desirable, as such "net uplift" forces can prevent the gate closure, especially in self-closing gates under gravity. A gate designer should, therefore, encourage the local upward or positive pressures along the gate bottom to avoid cavitation but must also be careful to avoid "net uplift" forces on the gate. In hydraulic model studies on Pondoh Baggi gate with upstream sealing and skinplate (Dhillion, 1978), with divergent flow under the gate, net uplift prevented the gate closure when e/d ratio exceeded 0.45. The original design was modified to reduce the lip angle to be below this limit. Intermittent secondary upward forces on the gate can be caused by the vertical vortex flow in the gate slots. Such upward vertical flow only occurs with upstream sealing gates. In some installations, flow arresters have been used in the gate slots to minimize these vertical flows. DISCHARGE COEFFICIENTS Although the gate bottom lip geometry has a profound influence on the discharge coefficient for flow under the gate, due to predominant importance of other hydraulic aspects like cavitation, vibration and downpull, the gate lip geometry, especially in high head gates is not primarily determined from the discharge coefficient point of view. Gates with upstream skinplate and sealing with divergent flows present more or less a sharp bottom edge under the gate, and no special modifications or provisions are usually made as they are not cost effective. Value of discharge coefficient varies from 0.6 ~ 0.7. Gates with downstream sealing with converging flows, however, are more amenable to provide a smooth bellmouth entrance, which is done in some cases, usually low head installations (example: Romaign Gates), In high head installations, however, a 45 o sloping bottom plate with a smooth radius at its upstream top corner, is satisfactory. In majority of cases, no special provisions are called for to increase the discharge coefficients. CONCLUSIONS AND RECOMMENDATIONS This paper briefly discusses the influence of the gate lip geometry on the hydraulic aspects of cavitation, vibration downpull and uplift individually. While larger lip angles may be sometimes justified due to various special considerations related to the installations, care should be taken while remodelling the existing gates to address individual problem peculiar to the installation so as to subject the old gates to minimum modifications required to eliminate the particular problem. Attempting large lip angles may endanger the structural integrity of the old gate with welded joints which are usually in a state of deterioration. The usefulness of hydraulic model studies for some installations to determine minimum lip angles cannot be under estimated, if time and budget permits for conducting such model studies. For better clarity and simplicity, the flow under the gate can be classified as converging or diverging instead of basing on skinplate and seal locations.
1. Converging Flow Under Gates In order to simplify the lip shape options, the author recommends a 45 degree lip angle with sloping bottom plate for the converging flows as this slope prevents cavitation by ensuring positive pressures on the sloping surface and also eliminates vibrations. A large lip angle with convergent flows and sloping bottom plates can sometimes cause flow separation and is not advisable. 2. Diverging Flow Under Gate For divergent flow conditions, a lip angle of about 20 degrees normally clears the jet from impinging on gate bottom and thus primarily satisfies functions (a) and (b). Hence, the Japanese Standard for Gates recommended this angle although the standard limited its application to long span gates due to uncertainty of flow disturbance caused by gate slots in narrower spans. The end vertical gate members and gate slots can be designed to mitigate cross flow and other undesirable flow patterns induced by slots with such narrow spans. In fact, there are many highhead installations with short span gates with lip angles below 25 degrees functioning satisfactorily under high heads although such angles may not achieve substantial reduction in downpull force which is otherwise possible with larger lip angles. The author wishes to emphasize that while functions (a) and (b) are of paramount importance, the reduction of downpull should not be the predominant aim of the modern gate designer due to the following factors: a Downpull is a useful engineering tool for self-closing gates requiring closure under gravity. b Downpull does not materially add to the hoist cost, especially with hydraulic hoists. Maximum downpull does not occur simultaneously with the maximum friction during gate operation with the above recomended gate lips. Where downpull reduction is not a predominant consideration, gates with diverging flow underneath normally perform satisfactorily with lip angles of about 25 degrees. ACKNOWLEDGEMENTS My special thanks are due to Dr. J. Purushottam and Mr. Y. A. N. Sastry, eminent engineers, whose discussions and arguments provided justification for this paper, and to Vasar Saraswati Devi for the guidance.
1. 2. 3.
4.
REFERENCES Naudascher, E. (1991), "Hydrodynamic Forces" IAHR Structures Design Manual, International Association of Hydro Research, Stockholm, Sweden. Sagar, B.T.A. (1977), "Downpull in Highhead Gate Installations, Parts 1, 2 and 3", Water Power and Dam Construction (3-5). U.S. Bureau of Reclamation (1957), "Model Studies of Hydraulic Downpull Forces That Act on Palisades Type Regulating Slide Gate and on the Glendo Fixed Wheel Gate", Hydraulic Laboratory Report M, Hyd-421. Dhillion, G.S. (1978), "Modern Trends in Design and Research of Highhead Gates With Reference to Downpull" , All India Seminar on Hydraulic Gates, Hyderabad.
