© Strojni{ki vestnik 46(2000)9,595-606 © Journal of Mechanical Engineering 46(2000)9,595-606 ISSN 0039-2480 ISSN 0039-2480 UDK 621.646.5:004.94 UDC 621.646.5:004.94 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Razsipanje mo~i curka vode v umirjevalni posodi z iglastim zasunom Dissipation in a Vertical Needle Valve Induced Jet in a Pressure Chamber Nikola Jeli} - Toma` Kol{ek - Anton Bergant - Jo`e Duhovnik V tem prispevku prikazujemo rezultate raziskave disipacije moči in vzbujenih nihanj vodnega curka v umirjevalni posodi valjaste oblike. Namen raziskave je bil ugotoviti nestacinarno tokovno polje, ki povzroča močne vibracije okrova posode ter telesa iglastega zasuna. Raziskava je temeljila na uporabi RST metode (računalniška simulacija toka fluida), ki je bila uporabljena na pomanjšanem modelu in skaliranem prototipu konstrukcije. Izkazalo se je, da je mogoče rezultate z modela uporabiti tudi na prototipu z uporabo preprostih skalirnih faktorjev. Pokazali smo, da je mogoče rezultate numerične metode primerjati z eksperimentalnimi rezultati z natančnostjo, ki je uporabna tako za inženirske kakor za znanstvene namene. © 2000 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: simuliranje toka, simuliranje računalniško, modeliranje numerično, curek vodni) In this paper we present the results of a study of power dissipation and induced oscillations in a water jet in a pressure chamber. The purpose of the study was to detect transient flow causing extensive structure oscillations on the chamber and valve body. The study was performed by applying the CFD code to the model and prototype scales and comparing the results. It turned out that the results obtained at the model scale could be applied to the prototype by applying simple scaling rules. It has been shown that the numerical method yielded results that fit reasonably with experiments and might be applied with confidence for both engineering and scientific purposes. © 2000 Journal of Mechanical Engineering. All rights reserved. (Keywords: flow simulations, computer simulations, numerical modelling, water jets) 0 UVOD Raziskava tokovnega polja za izbrano geometrijsko obliko in robne pogoje je pomembna inženirska in raziskovalna naloga, navadno jo je treba rešiti za različne pogoje toka, ki nas zanimajo. Meritve so v splošnem drage in se po navadi izvajajo le na pomanjšanih modelih. Vrednosti na prototipu konstrukcije so navadno predpostavljene z uporabo ustreznih podobnostnih kriterijev, ki pa žal pogosto ne morejo biti izpolnjeni vsi hkrati. To velja še posebno za zapletene geometrijske oblike, pri katerih se pojavlja večje število lokalnih karakterističnih velikosti in s tem povezanih časovnih skal. V takih primerih se zdi najbolj obetajoča metoda računalniško simuliranje toka (RST - CFD), povezana z računalniškim simuliranjem mehanike konstrukcij (RSK - CSM), ki lahko identificirata inženirske in znanstvene probleme. Žal pa so rezultati (podobno kakor pri 0 INTRODUCTION Investigating fluid flow field distribution for a particular geometry under particular boundary condi-tions is an important engineering and scientific task that has to be solved for a large number of various complex fluid flow conditions that might be of interest. The experimental method is in general an expensive one and is frequently applied only at laboratory model scale. Results at the prototype scale are usually predicted by using appropriate similarity criteria which, unfortunately, might not all be satisfied simultaneously. This is espe-cially true for complex geometries in which a large num-ber of local characteristic lengths and related time scales play a role. In this situation Computational Fluid Dynamics (CFD) coupled with Computational Structural Mechanics (CSM) appears to be most promising method for finding appropriate engineering solutions and iden-tifying engineering and scientific problems. However, as in experiments, the underlying physics in CFD and gfin^OtJJlMlSCSD 00-9 stran 595 |^BSSITIMIGC N. Jeli} - T. Kol{ek - A. Bergant - J. Duhovnik: Razsipanje mo~i curka - Dissipation meritvah), dobljeni na temelju metod CFD in CSM, pogosto napačno interpretirani. Mnogokrat je to posledica uporabe neprimernih matematičnih modelov ali uporabljenih predpostavk in aproksimacij pri numeričnem modelu kakor tudi morebitnih numeričnih nestabilnosti. Zato mora biti postopek računanja ne samo pazljivo načrtovan in izveden, temveč morata biti primernost in natančnost rezultatov preverjena za vsako novo geometrijsko obliko. Primer geometrijske oblike, ki ga opisuje prispevek, je sestavljen iz navpičnega regulacijskega iglastega zasuna, ki je povezan z valjasto umirjevalno posodo z dodano izhodno cevjo. Tak sistem določa več različnih parametrov, ki jih je treba določiti preden se izvede ekonomsko upravičena, varna in zanesljiva konstrukcija. Med temi parametri so višina posode glede na moč disipacije, kavitacijske karakteristike, pretočni koeficient in spekter ter amplituda nihanja tlaka na stenah. V tem prispevku predstavljamo rezultate, ki utegnejo biti pomembni za bodoča računalniška simuliranja toka v zapletenih sistemih podobnega tipa. Raziskava je bila osredotočena na: a) raziskavo višine umirjevalne posode glede na optimalno disipacijo moči ter nihanja tlaka, b) določanje nihanj na pomanjšanem modelu kakor tudi na prototipu (podobnostni zakoni), c) ugotavljanje pretočnega koeficienta za različna odprtja zasuna, d) primerjavo z orientacijskimi meritvami na pomanjšanem modelu. 1 OPIS SISTEMA Slika 1 prikazuje obravnavani sistem. Taka postavitev je značilna in se pogosto uporablja za disipacijo moči ([1] do [4]). Eden od možnih postopkov v numerični analizi je modeliranje le polovice simetričnega sistema, toda tokovno polje bi utegnilo biti asimetrično iz več razlogov, npr. kot posledica “izmenične nestabilnosti” [5]. Namen iglastega zasuna je sprememba potencialne energije vode v kinetično, ki se v obliki vodnega curka s hitrostjo več deset metrov na sekundo vbrizga v umirjevalno posodo. Ta energija se nato disipira v turbulenci, ki jo popisuje v splošnem neznani spekter k-a>, ki končno pojenja na mikroskopskem nivoju v toploto zaradi nelinearnih pojavov. Območje projektne višine AH prototipa je bilo med 100 in 200 metri. Projektna moč, ki jo je bilo treba sipati, je bila 60 MW. Premer umirjevalne posode je bil d = 7 m in projektna višina umirjevalne posode h = 17 m (20 m od dna umirjevalne pososde do zgornjega roba zasuna). Navpični iglasti zasun (sl. 2) je bil postavljen na vrhu v osi posode. Dovod vode v zasun je bil speljan skozi cevno koleno. Notranji premer zasuna na spoju zasun - posoda je znašal 0,7 m (nominalni premer zasuna d = 1,4m). Raziskan je bil primer s t.i. “nenadno razširitvijo“ ^BSfiTTMlliC | stran 596 CSM might still remain unclear and largely misinter-preted. This is usually due to effects that arise from improper use of mathematical models or particularly adopted solver assumptions and implemented approxi-mations, as well as due to possible numerical instabili-ties. Therefore the computational procedure should not only be carefully planned and prepared but the relevancy of the results should be investigated for every new particular geometry. Such a geometry is presented in this paper by a vertical regulating needle valve connected to a dissipation pressure chamber with an outflow pipe. This system is characterized by a variety of fixed and variable parameters that have to be determined before cost-effective design and proper safe and reliable operation can be implemented. Such parameters are chamber height for the predicted water power to be dissipated, cavitation characteristics, discharge coefficient and flow-induced wall pressure os-cillations. In this paper we present some of the results that might be relevant for future CFD investigations of complex systems of similar type. These results include: a) study of chamber height in order to determine the most favorable conditions regarding both power dissipation and pressure oscillations b) assessing oscillations at both model and proto-type scales (similarity rules) c) determining the discharge coefficient for various valve openings d) comparison with preliminary measurements at the model scale 1 DESCRIPTION OF THE SYSTEM The system in question is shown in Fig 1. It represents one of common arrangements used for water power dissipation ([1] to [4]). One approach in nu-merical analysis could be to model only half of the sym-metric system, but we supposed that the flow might not be symmetric for many reasons, e.g., due to a so-called “exchange of instabilities” [5]. The role of the needle valve (Fig. 2) is to transform the potential energy of the water column into kinetic energy in order to be further injected by a high speed of several tens of meters per second into the chamber. This energy is then dissi-pated into a generally unknown three-dimensional k-w spectrum that finally decays due to nonlinear phenom-ena at microscopic level into thermal energy. The interval of the design head DH of the selected prototype valve was between 100 and 200 m. The nominal power which was dissipated was 60 MW. The diameter of the pressure chamber was dch = 7 m and the nominal height was h = 17 m (20 m from the chamber bottom up to the valve top). The vertical needle valve (Fig. 2) was positioned at the top of the chamber. The water was supplied to the needle valve through a pipe elbow. The inner diameter of the needle valve at the valve-chamber interface was 0.7 m (nominal valve diameter dv = 1.4 m). The study was performed for a N. Jeli} - T. Kol{ek - A. Bergant - J. Duhovnik: Razsipanje mo~i curka - Dissipation iglasti zasun needle valve dv izstopna cev outlet pipe Sl. 1. Umirjevalna posoda z iglastim zasunom Fig. 1. Dissipation chamber with needle valve izhoda ([6] in [7]), ki ga ponazarja slika 2. Odprtje zasuna smo spreminjali med 10% in 100% pri različnih vhodnih tlakih. Na voljo smo imeli meritve na modelu, pomanjšanem za faktor = 14 glede na prototip. Glede na Froudov podobnostni zakon morajo veljati naslednji skalirni faktorji: - dolžina, tlak Ä - prerez, površina X - prostornina, masa, sila A3 - hrapavost sten v ceveh X1/6 - hitrost, čas A1/2 - Reynoldsovo število 23/2 - pretok X5/2 valve with a “sudden expansion” exit ([6] and [7]), see Fig. 2. The valve opening was adjusted continually between 10% and 100% for various pressure heads. Experimental results were available for a model scaled down by a factor of l = 14. The follow-ing scale factors resulting from Froude’s similarity law should hold: - length, pressure l - cross sectional area l2 - volume, mass, forces l3 - pipe wall roughness l1/6 - velocity, time l1/2 - Reynolds number l3/2 - discharge l5/2 odprtje zasuna Av valve opening Av Sl. 2. Iglasti zasun Fig 2. Needle valve stran 597 glTMDDC h N. Jeli} - T. Kol{ek - A. Bergant - J. Duhovnik: Razsipanje mo~i curka - Dissipation 2 METODA Uporabljeno je bilo računalniško simuliranje toka s programsko kodo ICCM-Comet enačbah [8], ki temelji na Reynolds-povprecenih Navier-Stokesovih (RPNS) enačbah [9]. Predpostavljen je bil viskozen in turbulenten tok. Sistem enačb RPNS je bil sklenjen z znanim modelom k-s. Geometrijski model, kakor tudi diskretizacija, sta bila pripravljena s programskim orodjem I-DEAS [10], ki je bil poleg tega uporabljen še za trdnostno analizo zasuna in posode. Računsko območje smo razdelili v več podobmočij, kar je omogočilo izdelavo blok-strukturirane mreže kontrolnih prostornin (elementov, celic) kvadraste oblike, ki jo je bilo mogoče uporabiti za pripravo izračuna v različnih izračunalnikih toka. Kombinirali smo večje število O in H topoloških shem ter število kontrolnih prostornin postopoma povečevali, da smo dosegli neodvisnost rezultatov od topologije in gostote mreže [9]. Tipično število elementov, nad katerim opazovane količine niso več bile odvisne od gostote mreže, je bilo 100.000 za celoten sistem. Zaradi velikih vibracij plašča umirjevalne posode, ki je bila predmet meritev, smo se odločili za časovno odvisno (neustaljeno) simuliranje. Kadar curek vode zapusti cev z nenadno razširitvijo, se lahko pojavijo samovzbujana nihanja ([11] in [12]). Pri meritvah smo opazovali statični tlak na več značilnih mestih v posodi (na vrhu, na cilindrični steni, na dnu). Najbolj značilne rezultate smo dobili v merilnih točkah na dnu posode. 3 NUMERIČNI REZULTATI 3.1 Višina posode Višino posode smo spreminjali, da bi našli najboljšo vrednost glede na največjo moč disipacije pri še sprejemljivih amplitudah nihanja tlaka. Nihanje statičnega tlaka v osi na dnu posode za različne višine posode prikazuje slika 3. Slika 4 prikazuje odvisnost razlike statičnega tlaka »od vrha do vrha« glede na višino posode. Poudariti je treba, da se dinamična komponenta tlaka prl =pv2/2 v vseh merilnih točkah ni kaj dosti spreminjala v času, torej je bila glavna nihajoča količina statični tlak. Količnik disipacije je bil definiran kot razmerje med disipirano močjo in vstopno močjo. Izkazalo se je, da se je 93 ± 0,2% vstopne moči (0,2% je v glavnem posledica nihanja) sipalo neodvisno od višine posode. Presenetljivo se je izkazalo, da je rezultat postal odvisen od začetnih pogojev pri višinah pod 11 m. Ta pojav bo predmet prihodnjih raziskav. ^BSfiTTMlliC | stran 598 2 METHOD CFD calculations were performed using ICCM-Comet computer codes [8] based on Reynolds averaged Navier-Stokes (RANS) equations [9]. The flow was assumed to be viscous and turbulent. The system of RANS equations was closed using the well-known^turbulence model. Geometry modeling and grid generation were performed using SDRC I-DEAS software [10], which was also used for additional structural investigations of the mechanical valve and chamber properties. The computational domain was divided into several sub-domains to enable block-structured hexahedral grid generation, which could easily be input to various fluid flow solver computer codes. A variety of different combinations of O and H topology types of grids were combined and the number of control volumes gradually increased to achieve independence of the results on grid density and the chosen combination of grid topology [9]. The typical number of elements above which the results of interest were not sensitive to the grid density was 100 000 for the entire system. Due to excessive vibrations of the chamber used in the experiment we decided to perform transient calculations. When a water jet exits a pipe with sudden expansion, self-sustaining oscillations can be expected ([11] and [12]). The static pressure was observed both in numerical and laboratory experiments at several characteristic locations inside the chamber (top, cylindrical wall, bottom). The most rep-resentative results were obtained at the measuring points at the bottom of the chamber. 3 NUMERICAL RESULTS 3.1 Height of the chamber The chamber height was varied in order to find an optimum value that gives maximum power dissipation at an acceptable amplitude of pressure oscillations. The static pressure oscillations at the bottom of the chamber for different chamber heights are shown in Fig 3. Figure 4 shows the dependence of peak to peak pressure variation as a function of chamber height. It should be pointed out that the dynamic component of the pressure p =pv2/2 at any diagnostic point inside the chamber did not change considerably over time, i.e., the main oscillating quantity was the static pressure. Calculation of the dissipation rate was defined as the ratio of dissipated power over input power. It turned out that 93 ± 0.2% of the inflow energy (the ± 0.2% was mainly related to the oscillations when present) was dissipated independently of the height of the chamber. This conclusion holds in the range 7 to 19 m of the chamber height. However, for heights below 11m the solution became sensitive to initial conditions. This phenomenon will be the subject of future studies. N. Jeli} - T. Kol{ek - A. Bergant - J. Duhovnik: Razsipanje mo~i curka - Dissipation 220 kPa 200 180 160 140 120 100 80 h=12m h=13m h=15m e h=19m 20 40 60 čas time 80 100 Sl. 3. Nihanje statičnega tlaka na dnu posode za različne višine posode Fig. 3. Oscillation of static pressure at the bottom of the chamber for different chamber heights 160 kPa 140 120 100 80 60 40 20 0 12 18 20 m 14 16 višina posode - h hight of the chamber - h Sl. 4. Razlika statičnega tlaka »od vrha do vrha« v odvisnosti od višine posode Fig. 4. Peak to peak pressure variation as a function of chamber height Iz inženirskega vidika je bilo treba določiti višino, nad katero se niso več pojavile velike mehanske obremenitve. Osredotočili smo se na ugotavljanje veljavnosti podobnostnih zakonov pri neustaljenem stanju. Zato smo raziskali tokovna polja pri tistih višinah posod, pri katerih so se pojavljala nihanja. Ugotavljali smo tudi povezavo med amplitudami nihanj ter padcem tlaka med vstopom in izstopom, izraženim v obliki DH=Dp / rg (Dp pomeni razliko totalnega tlaka (p = p+p ot ) med vstopom in izstopom, r je gostota vode in g je težnostni pospešek). Slika 5 ponazarja nihanje tlaka na dnu posode pri različnih padcih tlaka med vstopom in izstopom za izbrano višino posode h = 12 m. Slika 6 pa prikazuje razliko tlaka od vrha do vrha v odvisnosti od padca tlaka DH med vstopom in izstopom. From the engineering point of view it was important to determine the chamber height above which there were no excessive mechanical loads. We focused our attention on the validation of similarity laws under transient conditions. Therefore we inves-tigated chamber heights with expressed oscillations. We also determined the relation between oscillation amplitudes and the pressure head DH=Dptot/rg (where Dptot is the difference of the total pressure (ptot = p+pdyn) between the inlet and outlet, r is the water density and g represents acceleration due to gravity). In Figure 5 the time dependence of the cham-ber pressure for different head drops is illustrated for the case of constant chamber height h = 12m. Figure 6 shows the quantitative dependence of peak to peak pressure variation on the pressure drop DH for the same chamber height. stran 599 glTMDDC s N. Jeli} - T. Kol{ek - A. Bergant - J. Duhovnik: Razsipanje mo~i curka - Dissipation 220 kPa 200 180 160 140 120 100 80 -« H=20m e H=60m m H=140m ^\y