Claudio
A. Fattor, Jorge D. Bacchiega
Hydraulic Structures Division, Laboratory of Hydraulic and Environment
National Institute of Water and Environment
Casilla Correo 21 – (1802) Aeropuerto Ezeiza, Argentina
Tel.:54-11-4480-0457, Fax:54-11-4480-0459
E-mail:clafat@feedback.net.ar
Abstract: The purpose of this paper is to make an analysis of the instabilities of the flow, whose apparition result commonly associated in the transition from a spillway regime to an orifice regime, in the special case of a Morning-Glory spillway. Even though these structures are usually designed to function at free surface, the analysis of the mentioned transition is important in order to quantify the loss of performance in the discharge and analyze the flow-induced solicitations regarding the pressure and frequency fields. The condition given by the beginning of the submergence is particularly analyzed, being this situation related to a condition where strong flow instabilities appear on the spillway profile.
Keywords: morning-glory spillways, flow pattern, flow instabilities, pressures field, frequency
Morning-Glory spillways are a particular case of spillway, being formed by a superior structure, a vertical bend and a tunnel that allows the discharge towards downstream (Figure 1). These structures are commonly designed for operating at free surface, even for discharges higher than the design discharge Qd, being important to avoid the change of regime because of the loss of performance in the discharge capacity. However, it would be feasible that this kind of structures might spill discharges higher than Qd. In this sense, the characterization of the flow conditions and the determination of pressures acting upon the structure in the beginning of the submergence need to be considered, being this condition particularly meaningful due to the strong instabilities of the free surface. Consequently, the stated topics will be considered in this article.
Fig. 1 Longitudinal section of a typical Morning-Glory spillway
Morning-Glory spillways are formed by a circular structure of diameter Dv, being the spillway profile developed from the crest. The downstream section of the profile reduces the cross section until reaching a diameter Dg, where the beginning of the vertical bends starts. The vertical bend has diameter Dg and radio R (Figure 1).
From the hydraulic behavior viewpoint, the variation of the discharge capacity can be summarized in Figure 2. Three different operation conditions can be observed:
Phase I: it is a free surface flow following a relation Q=f(H3/2).
Phase II: this phase is characterized for the beginning in the submergence of the spillway, which functions alternatively and partially under pressure. The control section moves gradually from the vertical bend to the throat (D=Dg), reaching finally a relation Q=f(H1/2).
Fig. 2 General analysis of the discharge in Morning-Glory spillways
Phase III: due to the increase of the reservoir elevation, a situation characterized for its total submergence is reached, and consequently the whole structure (spillway, bend and tunnel) is under pressure, being the discharge a function of the energy losses in the conduction (Q=f(J)).
Once the layout of the spillway was defined, its condition of operation is strongly influenced for the surrounding area (topography, hillsides, dams, etc.). Constructive and economical aspects usually determine the need of locating these spillways close to dams or hillsides. The distance (Ra) from the spillway to a hillside or dam influences on the approach conditions of the flow and the discharge that will establish the beginning of the submergence. Though the perfect location would be that able to ensure a radial flow on the crest of the spillway, this is usually only possible in the upstream sector of the crest (in front of the reservoir). The flow on the remaining spillway crest presents tangential components of the velocity due to the interaction of two opposite currents. These currents are responsible for a slight increase of the free surface and the presence of a jet whose trajectory moves away from the spillway profile.
Most of these spillways were, in fact they are, designed to function with discharges into Phase I, mainly because of the good performance compared to other phases. Though there is a trend to move away the design condition from the beginning of the submergence, the structure could extraordinarily function with discharges into Phase II, being necessary that the spillway ensures the discharge without introducing risks of exceeding the dam. Besides, it is important to know how the beginning of the submergence develops, which is possible if the flow pattern as well as mean and fluctuating pressures are known. Then, the safety margin for the operation of the structure under this condition as well as the incidence of the flow in the rest of the structure can be determined.
The analysis of a singular condition given by the beginning of the submergence of a Morning-Glory spillway has been carried out. Even though this condition is influenced for the surrounding area and the spillway geometry, the beginning of the submergence is reached in this case for Q=1.34.Qd and H/Hd=1.17, in a spillway with relation Dv/Dg=2.37 and Ra/De=1.05. Even though the involved phenomenon can be found in the whole range of discharges from the beginning of the submergence until reaching a full orifice regime, the first condition was selected due to it represents the situation which makes evidence the instabilities characteristics of this phenomenon.
The studies were carried out in a physical model of a Morning-Glory spillway, representing all the structures and the surrounding topography at the spillway. The water supply system has a constant level tank that supplies an upper gaging channel where a thin vertical plate was installed, whereas the water head on the crest spillway was measured with limnimeters.
Taking into account the characteristics of the flow for the condition under study, a pressure measurement in two gage taps located at 3.Hd below the crest spillway was made during 30 minutes. The location of the gage taps (Figure 1) is related to the area affected by the jet (Gage A) and without incidence of the jet (Gage E). The record was made with an acquisition device including a 8 bits plate connected to a computer, selecting the sample period in 10 mseg. The post-processing of the records was focused on the pressure and frequency fields, in order to understand the phenomenon related to flow instabilities for this situation.
The situation of beginning of the submergence is characterized for the abrupt change from a free surface regime to a unstable condition, with alternative states of submergence. Under these circumstances it is possible to see that the jet formed by the two opposite currents impinges on the spillway profile and generates a local recirculation of the flow around the impact area. This flow condition tends to decrease the free cross section, until that a slight movement of the jet submerges temporary the flow and a succession of non periodical instabilities starts, which can be characterized for semi-permanent conditions of submergence that changes alternatively for free surface and intermediate instabilities.
With the purpose of relating the flow pattern with the flow-induced solicitations, two randomly selected parts of the whole records will be analyzed, being able to see their outputs in Figures 3 and 4.
The figures show the variation of the pressure as a function of the time, being able to see the unsteady behavior of the flow, with submerged flows, free surface flows and unstable flows. The records show that there is not periodicity in the appearance and duration of the phenomena involved (non periodical and unsteady behavior), where the turbulence inherent at the flow has to be add to the semi-permanent stages previously mentioned.
Even though the main purpose is to analyze the whole behavior, three different stages could be considered:
Free surface temporary flow: this situation is characterized for pressures (p/g)/Hd»0, with pressure fluctuations by turbulence above and below this value.
Temporary instability: this zone presents, for a random period of time, a wide variation going from a free surface regime of short duration to a partially submerged discharge of short duration, not being possible to establish a tendency towards one or another condition. The pressures field shows the most meaningful variations, being –0.20<(p/g)/Hd<1.20. It is possible to see strong variations in the free surface elevation close to the shaft of the spillway.
Fig. 3 Unstable behavior at the beginning of the submergence – Q=1.34.Qd
Fig. 4 Unstable behavior at the beginning of the submergence – Q=1.34.Qd
Submerged temporary flow: this situation presents positive values of the pressure, with (p/g)/Hd»0.70, and pressure fluctuations by turbulence above and below this value.
Figures 3 and 4 also show that the change from a particular condition to another one does not always follow the same pattern. For instance, Figure 4 shows the change from temporary free surface to temporary submerged regime passing or not for a temporary instability stage.
As regards the flow-induced solicitations, and taking especially into account pressures and frequencies fields, this is one the most important aspects from the viewpoint of the structure.
The intensity of solicitations of the whole phenomenon can be estimated by computing the root mean square of the pressure amplitudes (RMS). Complementary, and only to quantify the relative influence of each stage (free surface temporary flow, temporary instability and submerged temporary flow) respect to the whole, it is feasible to make a similar analysis for them. The first analysis throws as result RMS/Hd=0.315, whereas the partial analysis of each stage throw more reduced values of RMS. Figure 5 shows the relation between the values obtained from partial records and those obtained from the whole record. It is important to see that the relation tends towards 1 when a temporary instability is analyzed, and it reaches the minimum value if a comparison with a free surface regime is made.
Fig. 5 Relationship between RMS partial records related to RMS of the whole record
In relation to the extreme values analysis, values of pressure p/g related to occurrence probability of 99.9% (p/g99.9%) and 0.1% (p/g0.1%) were calculated. Figures 3 and 4 show that the partial consideration of some of the temporary regimes tends to sub-value p/g99.9% and p/g0.1%, which characterize the phenomenon as a whole.
The difference between p/g99.9% and p/g0.1% is an indicator of the solicitation acting upon the structure due to the flow instabilities for the beginning of the submergence. The analysis of the values presented in Figures 3 and 4 show differences, especially for p/g0.1%, which emphasizes the complexity of the phenomenon. The compute of the total record throw (p/g99.9%)/Hd»1.10 and (p/g0.1%)/Hd»-0.38, being the amplitude p/g»1.48*Hd.
In relation to the frequency field (Figure 6), the analysis of the whole record, where different stages are included, shows a power density spectrum with a peak frequency less than 1 Hz, without secondary peaks that could eventually make evident the incidence of the instabilities. A secondary peak in the power density spectrum can just be observed when a temporary submerged flow is analyzed, being this frequency around 3 Hz.
Fig. 6 Power density spectrum
l The objective of the study was focused on the analysis of the flow pattern in a situation given by the beginning of the submergence of a Morning-Glory spillway, which is reached in this case for Q=1.34*Qd.
l The records of pressures, in a location with incidence of flow instabilities, allowed to verify the unsteady of the phenomenon, and the presence of temporary free surface, submerged and instability regimes. Parameters that may suggest some kind of periodicity were not observed.
l The variation of the pressures field as consequence of this phenomenon show that the variation of extreme values, which is expressed as the difference between (p/g99.9%)/Hd and (p/g0.1%)/Hd, is around 1.48.
l The partial analysis of each record, that is taking only into account a period during the structure functions submerged or at free surface, tends to sub-value the intensity of the phenomenon.
l As regards the frequency field, the integral analysis permits to see the presence of a peak frequency around 0.7 Hz, without observing secondary peaks. The analysis carried out for a condition with temporary submergence shows a power density spectrum with a peak frequency in 0.7 Hz and a secondary peak around 3 Hz.
l The total comprehension of the phenomenon could be reached if other discharges were analyzed, going from the beginning of the submergence to the discharge where a relation Q=f(H1/2) is reached. In this sense, INA is working in this line.
Acknowledgements
The authors thanks to Eng. Julio C. De Lío, Director of Laboratory of Hydraulic – INA, for his contribution in the discussion of the results presented in this paper.
References
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