INVESTIGATION OF AERATED SIPHON

Transcription

1 INVETIGATION OF AERATED IPHON Detlef Aigner, Hans-B. Horlacher Institute for Hydraulic Engineering and Alied Hydromechanics, Dresden Uniersity of Technology, 006 Dresden, Germany, hone: ; fax: ; ABTRACT ihon is the name gien to ressure conduits whose highest oint (the crest is situated aboe the water leel of the reseroir (Figure. hen the air inside them is eacuated either automatically or artificially, the sihon begins to work. Due to the low ressure at the crest, by regulating the aeration ia air inlets the discharge can be regulated or stoed altogether. ihons are tyically emloyed as flood discharge. Non-aerated sihons are somewhat controersial due to the fact that, in a ery short time, their maximum discharge is attained which then causes the reseroir water leel to suddenly rise. The main objectie of an aerated sihon is to hae a regulating effect on the sihon discharge erformance. In this aer we roose a simle method for the calculation and management of such a regulatory rocess. Keywords: sillway, flood, sihon, air induction, water/air mixture THEORY A sihon for use in flood relief at reseroirs is usually constructed with a rectangular cross section area A, with a breadth b and a height a. The inlet is rounded off so as to cause little energy loss. Contraction is to be found in the icinity of the sihon exit which reent the utake of air and, in so doing, facilitate riming. taggered sihons are ositioned at different heights so that they in the case of an eer increasing water leel can begin to function at differing times. z l A A b a H g Δ ρg r G g E l D G Figure : The rinciles of an aerated sihon

2 ituated in the crest of an aerated sihon there is a ale for regulating the air intake. hen exerimenting with hysical models, the air inflow is often wrongly interreted due to the fact that insufficient attention is aid to the relationshi between the sihon s air requirements and the actual air suly aailable. f(a 4 f(a3 f(a f(a Δ HK BK oerating oint _Max Figure : ihon (HK and air inlet (BK characteristics. Oerating oint as function of the air inlet ale oening (A Figure shows the tyical characteristics for the calculation of the air flow in a sihon. The sihon characteristic demonstrates the rogressie reduction of the low ressure in the sihon crest with increasing air intake. The aeration characteristics define the degree of air intake in deendence of low ressure and the effectie degree of oenness µ. A of the aeration ale including the energy losses incurred in the aeration canal. The intersection of the lines is the oerating oint for a secific degree of oening of air ale.. DEFINITION AND AUMPTION Our calculations were the basis for the following definitions and assumtions: ater discharge[m 3 /s], Air flow [m 3 /s], m& ρ Mass olume flow of the air [kg/s], G + Air and water discharge [m 3 /s], ß Degree of aeration [-], Aerage elocity [m/s] in the sihon front of air ale, A Velocity in the crest of the sihon bend [m/s], G G aerage, sliless elocity [m/s] of the mixture, A

3 3 G ß + relati elocity [-] of the mixture, A b a Cross section of the sihon [m ], rectangular cross section, crest alue, z Distance between the sihon crest and the water leel [m], H Energy head of the sihon [m], r ihon radius [m], K Influence of the bend [-], A Cross section of the aeration [m ], µ Inflow coefficient of the air flow including energy losses [-], Absolute atmosheric ressure in the sihon crest [Pa], Air ressure, Outside ressure [Pa], ength of the sihon u to the aeration slots [m], ength of the sihon after the aeration slots [m], ρ G Density of the mixture [kg/m 3 ], ρ Air density [kg/m 3 ], ρ ater density [kg/m 3 ], R Gas constants of air [87, m /s /K], T Temerature in Kelin [K], d hy A b a 4 rhy 4 hydraulic diameter of A in [m], l b + a U k λ f (Re, Friction coefficient deending on the Reynolds-number and roughness [-], d hy ζ um of the local energy losses [-], R l λ + ζ Energy loss coefficients of the sihon u to the aeration ale [-], d hy R l λ + ζ Energy loss coefficients of the sihon after the aeration ale [-], d hy ρ Air density calculated ia the gas equation [kg/m 3 ], R T ρg ρ ρ + ß ρ Density ratio between the mixture and the water [-], ß + ß +

4 4. CACUATION OF THE ATER FO UP TO THE AERATION As is the case with normal ressure conduits, the hydraulic calculation of a sihon is done with an energy equation. If the cross section is not circular, the equialent or hydraulic diameter d hy is emloyed instead of the normal diameter. The energy equilibrium existing between the inlet and the aeration ale in the crest of the sihon results in the following equation (. Δ ρ g (z + h V + ρ ρ g z + ρ ( R + K ( The ure water flow in the first section of the sihon defines the relationshi between the distance z of the water leel from the aeration oening (situated in the crest, the degree of low ressure at this oint and, thirdly, the discharge. The elocity at the crest of the sihon bend is somewhat less than the aerage elocity in the sihon. Their squared relationshi defines the influence of the bend K. The friction coefficient R considers not only the friction and local energy losses but also cross sectional differences within the sihon..3 VEOCITY DITRIBUTION DUE TO THE BEND If the ressure and elocity distribution in the bend are considered within the crest cross section (Bollrich, 000, the elocity head at the extreme boundary decreases in accordance with equation (. The ratio between the reduced elocity head and the aerage elocity head is defined as the bend influence K. At the extreme edge of the crest the oint where the aeration takes lace K will always hae a alue lesser than. K ( ( (r / a + ln( + a / r Turbulent ressure changes caused by changes in elocity can lead to the sihon closing down earlier than exected. In such a situation the ressure can fluctuate of the size of dynamic ressure (elocity head. ith assuming K 0, this influence can be considered in calculations for determining the cut-off oint of flow..4 CACUATION OF THE MA FO RATE OF THE AIR Due to the comressibility of the air, the air intake is calculated according to the equation (6 as mass flow rate (ill, tröhl, 990: m& μ A Ψ ρ (6 with Ψ κ ( κ κ ( κ + κ 3,5 ( 0 7 ( 7 (6a As is the case with normal ressure conduits, the hydraulic calculation of a sihon is done with an energy equation. If the cross section is not circular, the equialent or hydraulic Ψ is the out-flow function for comressible gases, calculated with the adiabatic exonent κ,4 for air. The inflow coefficient µ comrises the contraction and the energy losses of the in-coming air. The air density and the air olume flow are now different deending on

5 5 whether they are at the sihon crest with ery low ressure or at the sihon out flow with normal atmosheric ressure. This has an influence on the ß-alue and also affects the elocity of the mixture flow. For a gien ressure in the sihon crest, the density of the sucked in air is calculated by the gas equation gien in oint.. The air olume flow and thus also the degree of aeration ß in the crest then becomes: ß m& ρ m& R T (7a and for the exit at the end of the sihon at atmosheric ressure to: ß m& ρ m& R T (7b For calculating the energy losses in the mixture along second section of the sihon, we calculated the aeraged alue ß m of the two air roerties with: ß ß ( (7c m +.5 INFO COEFFICIENT OF THE AIR The inflow coefficient µ comrises the energy losses and the contraction of the air flow. It is affected by the geometry of the inlet and also by the water flow itself within the crest of the sihon. The elocity of the water in the sihon causes a lateral deflection and contraction of the inflowing air. Aigner (000 inestigated how far the main stream influences the contraction of the water inflow. This influence would hae the same effect for inflowing air, although the influencing role layed by the density difference is unknown. The aeration ale used in the model was assigned an inflow coefficient of µ 0,85 by its manufacturers. A comarison between the measured in the model and calculated air inflow resulted in a inflow coefficient of µ 0,4 + 0/3.z/H..6 ENERGY EUATION FOR THE MIXTURE As the air olume flow is ressure deendent, this leads to the air in the sihon crest occuying more sace due to the low ressure than at the sihon exit where normal atmosheric ressure exists. On the assumtion that there is a uniform distribution of the water and the air - in an attemt to simlify the rocedure - the friction alue is calculated on the basis of a mixture elocity which, itself, is deried from the aeraged air density. It is only the elocity head at the sihon exit which is calculated with the mixture density for normal atmosheric ressure. For the friction in the turbulent mixture, the same coefficient of flow resistance was used as is alid for ure water flows. Comarable calculations for sihons without air can be used to determine the amount of the local energy losses. The additional energy losses due to mixing with the air (combination losses and due to sliing (sliing losses can be determined with the hel of comarable calculations with measurements taken either from models or from nature. The energy balance between the sihon crest and the exit roides:

6 6 G GE ρ G g (H + z ρ g z + ρ R + ρg R + ρge (8 The transforming of equation (8 with the definitions in oint. roides an equation for calculating the elocity head with the elocity of the water flow. The discharge is determined from the continuity-equation. g H z ß m (9 (ß + (R + (ß + R + ß + m m It was quite a comlicated matter to determine the loss of mixing between water and air as art of the friction losses R in sihon. e tried to quantify these losses with the hel of other comarable calculations. For this energy loss coefficient we emloyed: ζ 7 (0 V ß m Due to the fact that the equation system is deendent uon many influencing factors, this equation is only alid for the stated assumtions and stated examles. EXAMPE The transfer and alication of the results arising from exeriments with modelled aerated sihons on to real life size sihons can become extremely comlicated. Their scale u alication to life-size sihons can only be successful if a comarison is made with measurements carried out on the original (see Bollrich/Aigner 000. The different results achieed between the model and the life size sihon are a consequence of the limiting restrictions inoled when scaling u or down to any great extent. These limits exist, for examle, a due to the resectie atmosheric ressure at the reseroir which can t be realistically modelled, b due to the unaoidable difference in the size of the air bubbles between real size and model sihons, c due to the turbulence related differences with resect to the times when air utake begins, d due to the non-identical surface tension and the differing air comressibility and d due to the non-identical energy losses between real size and model sihon. During 994 and 995 at Dresden Uniersity s Institute for Hydraulic Engineering and Alied Hydromechanics modelled ersions of the aerated sihons installed at the Oker dam were used in exeriments for the Harz aterworks (Horlacher, Dornack, Müller, 995. They were based on modelling exeriments which were carried out by Prof. Press in Berlin during in rearation for the construction of the reseroir. Unfortunately at that time, the results of the (somewhat simlified modelling trials caused the aeration ale to hae been built far too small. Een the results of the modelling trails in 994 and 995 roided alues which were still unrealistically small. Based on comarisons with life size data it was then roosed to aly a u scaling factor of 300% for the aeration cross section. For the sihon a constant energy loss coefficient of ζ,9 was determined for the flow of ure water and this was allocated ractically comletely to the nd section of the sihon. It comrises the local energy losses occurring in the inlet, within the bend, due to local obstacles and also includes the effects of the cross sectional differences within the sihon channel (a0,65,8m, b,3,5m. As for the friction alue, an hydraulic roughness of k mm was assumed for life size sihons and k 0,mm for models.

7 Model Oker Dam _ - measurement _ - measurement _ with K0,76 and µ0,47 _ with K0,76 and µ0,47 _ with K0 and µ0,85 _ with K0 and µ0, aeration oening in % Figure 3: A comarison calculation with model alues for a dynamic head of 47,03 m aboe for the Oker Dam Assumtions and alues of the examle calculation for the model: 0,03 m 3 A 0,05 m R 0,36 K 0,76 A /A 0,07 z 0,047 m H,5 m R 4,38 The measured alues of the hydraulic model were ery satisfactorily reroduced for K 0,76 and µ 0,4 + 0/3. z/h. The interrution of flow was better simulated with K 0 (see Figure 3. Figure 4 reresents calculations of flow with ruture of the riming rocess with K0 and a constant inflow coefficient µ 0,84 in deendence of relatie water leel z/h. [m3/s] z/h 0,0089 z/h 0,033 z/h 0,078 z/h 0,009 z/h 0,03 z/h 0,0400 z/h 0,0489 z/h 0, A / A [%] Figure 4: Verification calculation of the ruture rocess of the sihon model in deendence of the aeration cross section and the dynamic water leel of the Oker Dam

8 8 3 CONCUION hen considering the comressibility factor of air, the resented equations for calculating the correct dimensions of an aerated sihon ermit an analysis of the influencing factors and roide calculations for the aroriate degree of aeration required for controlling an aerated sihon. A comarison of the results from the model exeriments and from the real size data of the Oker Dam sihon underlines the alidity of these calculations. The examle calculations that we carried out show that the required degree of aeration greatly deends on the height of the water leel in the reseroir. hen alying the results of the model exeriments on to the real life scale, these arious influences can also be identified. The arious assumtions in the equations such as, for examle, the energy loss coefficients due to the utake of air, the flow coefficient of the air flow and how this is affected by the water flow, or the influence of the water flow turbulence on the ruture rocess, all highlight the comlexities inoled when u scaling model results for the alication to other tyes of sihon systems. For such alications additional comaratie measurements and / or modelling exeriments are indisensable. REFERENCE Aigner, D. (000: Hydraulik der asserbehandlungsanlagen und industrieller Prozesse. In Technische Hydromechanik, Band 4, Verlag für Bauwesen Berlin 000, Horlacher, H.-B.; Dornack,.; Müller, U. (995: Hydraulische Untersuchungen für die Heberanlage der Okertalserre. Institut für asserbau und THM der TU Dresden, Forschungsbericht FO 95/ om , uneröffentlicht Bollrich, G. (994: Hydraulische Untersuchung der Heberüberfälle des Ausgleichsbeckens Burgkhammer. Internationaler Talserrenkongress in Duban/üdafrika, Noember 994, in IT Heft, eimar, Oktober 994 Bollrich, G.; Aigner, D. (000: Hydraulisches Versuchswesen. In Technische Hydromechanik, Band 4, Verlag für Bauwesen Berlin 000, Bollrich, G. (000: Technische Hydromechanik, Band, 5. Auflage, Verlag für Bauwesen Berlin 000, Volkart, P. (978: Hydraulische Bemessung steiler Kanalisationsleitungen unter Berücksichtigung der uftmitnahme. Mitteilungen der Versuchsanstalt für asserbau ETH Zürich, Heft 30, Zürich, 978 ill, D..; tröhl, H. (990: Einführung in die Hydraulik und Pneumatik, 5. Auflage, VEB Verlag Technik Berlin, 990 Horlacher, H.-B.; üdecke, H.-J. (006: trömungsberechnung für Rohrsysteme,. Auflage, Exert Verlag, Renningen, 006 AUTOR: al. Prof. Dr.-Ing. habil. Detlef Aigner Prof. Dr.-Ing. habil Hans.-B. Horlacher Institut of Hydraulic Engineering and Alied Hydromechanics Uniersity of Technology Dresden Helmholtzstrasse 0, 006 Dresden Tel.: Fax: detlef.aigner@tu-dresden.de