An Experimental and Numerical Study on Pressure Drop Coefficient of Ball Valves

Transcription

1 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) An Expermental and Numercal Study on Pressure Drop Coeffcent of Ball Valves A. Ozdamar* 1, K. Turgut Gursel*, Y. Pekbey* and B. Celkag Abstract In ths study, a computatonal method to predct steady and sngle-phase flows nsde a ppe joned to a ball valve has been examned. Flow computatons have been performed usng the fnte volumes method. To ths am, governng equatons for contnuty and momentum are frst ntegrated over a control volume, and then the resultant algebrac equatons are numercally solved. Results obtaned ndcate the change of the flud velocty and pressure fluctuaton dependng on longtudnal drecton nsde the ppe. In addton to the computatonal study, results from the expermental study carred out under the same condtons were obtaned to compare wth the results of the computatonal method. Thus, the expermental study does not only confrm suffcent senstvty of the results obtaned from the computatonal model, but t also ndcates a relaton between the ball valve openng and the pressure drop coeffcent. Thus, the proposed computatonal model may be used as a tool to desgn better and effcent nstallaton systems wth dfferent ball valves. Keywords Ball valve, computatonal flud dynamcs, expermental flud dynamcs, fnte volumes method, mnor loss, pressure drop coeffcent, turbulence model. 1. INTRODUCTION Mnor loss values for ball valves ndcate averaged losses gven by varous manufacturers. However, t s well known that there s an uncertanty up to ± 50 percent [1, 2]. Due to the complex geometry of ball valves, manufacturers desgn detals nfluence almost all mnor losses of valves n dfferent flows, whch exactly can be determned only expermentally. Steady and sngle-phase flows are encountered n several engneerng applcatons from the smple flow nsde a ppe to the flow of a rver. Several studes have been performed n the past to analyze the characterstcs of such flows. Recent developments n computatonal flud dynamcs (CFD) enabled researchers to smulate almost all knds of problems that can occur n real stuatons as presented n [3]. In study of Larach et al. [4], a dfferent engneerng applcaton of CFD method n explorng bed pressure drop of sngle-phase gas flow n towers s avalable. Erdal [5] studed several parameters affectng turbulent mxng and fully developed flow condtonng downstream of a plate by usng CFD tools. Halupovch et al. [6], calculated the steady two-dmensonal vscous supersonc turbulent flow by usng a CFD code and the two-equaton k-ε turbulence model for the turbulent flow smulaton n nvestgatng turbulent supersonc flow. Erdal and Andersson [7] executed a full ppe smulaton to prmarly nvestgate varous grd effects, coordnate arrangements and turbulence models n order to predct more accurate flow values through an orfce n twodmensonal axsymmetrc flow. Smlar studes regardng turbulent and lamnar gas flows, whch use the CFD * Mechancal Engneerng Department, Faculty of Engneerng, Ege Unversty, Bornova Izmr, Turkey. 1 Correspondng author; Tel./Fax: E-mal: aydogan.ozdamar@ege.edu.tr method, were executed n [8, 9, and 10]. However, n the correspondng lterature, comparsons regardng mnor loss values of ball valves obtaned numercally and expermentally could not be found. Steady and sngle-phase flows occurrng as nternal flows partcularly are of great mportance. The flow nsde a ppe that s joned to a ball valve s an example of nternal free, steady and turbulent sngle-phase flow. The objectve of the present study was to develop a CFD model that can predct the steady free flows nsde a ppe controlled by a ball valve, n order to obtan the pressure drop coeffcent ( ζ ) by means of the CFD method [11]. Further, these numercal results were compared to those of the experments carred out under the same condtons. In agreement of these results, ths model could be used for desgnng nstallaton systems wth new types of ball valves wthout executng expensve experments, and uncontrolled pressure drop that causes blockages, nose and energy losses n ppng systems could be reduced wth the developed model, whch s usually the general am n engneerng applcatons. 2. EXPERIMENTAL DETERMINATION OF THE MINOR LOSS COEFFICIENT OF A BALL VALVE The measured mnor loss coeffcent s usually defned as a rato of the head loss along the setup to the head velocty of the flud [1]: 2gh ζ = (1) 2 u Where; Δp h = and (2) ( ρg) Δ p : Dfference between nlet and outlet pressure.

2 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) In ths study, a steady-state turbulent ar flow wth an nlet temperature of 293 K and an nlet pressure of 2500 Pa has been consdered. To avod dsturbances before and after the openng due to the present valve, the nlet and outlet straght ppe sectons were joned to the valve as shown n Fgure 1. Fg. 1. Ball valve joned to straght ppe Fg. 2. Experment faclty As seen n Fgure 2, the system conssts of a ball valve of DN 32 (5), regulaton valves at the nlet and outlet sectons (1,2,6), a flow meter measurng the flow rate of ar passng through the system (7), a manometer measurng nlet pressure (3) and an electronc panel measurng pressure dfference between the nlet and the outlet sectons (4). The compressed ar flows nto the system through the plug valve (2). The nlet pressure of the ar s set to 2500 Pa by the pressure regulator as shown n the manometer (3). When the ball valve (5) s at fullyopened poston, outlet pressure s set to 2400 Pa by means of the valve (6). The dfference between nlet and outlet pressure can be observed on the dgtal panel (4) as 100 Pa durng the experment process. Under these crcumstances, the volume flow rate of the ar s measured per mnute. When the handle of the ball valve s turned towards ts fully-opened poston, change n the flow rate s also measured. Frst, the am of the experment was to determne the response of the system when the ncrease of pressure dfference reaches 100 Pa for the fully-opened poston of the ball valve. The valve nlet pressure was gradually ncreased up to 3500 Pa, whereas the outlet pressure was kept constant at 2400 Pa, and volumetrc flow rates (Q) were measured by a flow meter. In the next steps, the handle of the ball valve was turned towards ts closed poston 10 once agan, after volumetrc flow rates (Q) were measured. The mnor loss coeffcents were determned by Equaton 1 wth measured pressure dfferences Δ p and respectve veloctes that were calculated from the volumetrc flow rates. 3. NUMERICAL DETERMINATION OF THE MINOR LOSS COEFFICIENT OF A BALL VALVE In prncple, two dfferent classes of numerc soluton methods exst, whch complement each other n practcal applcaton. In the frst class, one proceeds from a soluton assumpton for a sought-after varable already before the executon of the approxmaton calculaton. Ths varable s approxmated n form of a fnte seres, n whch the seres elements after a certan number are to be neglected accordng to the needed accuracy. For nstance, Galerkn s method belongs to ths class of methods wth the specal advantage that the ndvdual assumpton functon accurately fulflls the boundary condtons of the flow problem examned. The dsadvantage of these otherwse exact soluton methods les n the fact that n some cases no sutable assumpton functons can be found. Hence, for the mentoned flow problems, such numerc soluton methods are generally used, whch drectly solve the partal dfferental equatons approxmately after dscretsaton of the ntegraton area wthout any assumpton functons selected beforehand. The fnte volumes method belongs to ths numerc soluton one [12]. CFD codes contan dfferent numerc soluton methods of partal dfferental equatons of flud flows such as the Naver-Stokes and Euler equatons. For

3 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) solvng these dfferental equatons, the fnte volumes method s developed that t satsfes the conservaton equatons (contnuty, momentum and energy) dscretzed over each volume element n the computatonal doman wth better accuracy. Governng Equatons The cornerstone of computatonal flud dynamcs s the fundamental governng equatons of flud dynamcs; namely the contnuty, momentum and energy equatons. In the present study, the Eddy-Vscosty Model was appled for solvng the Reynolds Averaged Naver-Stokes equatons (RANS), and Reynolds stresses were modeled by usng an Eddy-Vscosty μ t [13]. The contnuty equaton and the unsteady ncompressble RANS equaton are respectvely wrtten as follows: U x = 0 U p R (3) 2 j ρ U k = + μ + (4) xk x x j x j x j In Equatons 3 and 4, mean velocty components U and Reynolds stresses R j are gven as: r U ( x, t) r u ( x, t) u ' U r ( x, t) = (5) ' u In Equaton 5, u and denote flud velocty and velocty fluctuaton, respectvely. The Reynolds stresses n Equaton 4 obtaned from Equaton 6 nclude addtonal unknowns ntroduced by the averagng procedure; hence they must be added n order to complete the equatons. In Equaton 6, μ t s calculated n Standard k-ε Model that s defned as: 2 k μt = 0.09ρ (7) ε In Equaton 7, k and ε respectvely denote turbulent knetc energy and the dsspaton rate. Representatve flud veloctes are obtaned by solvng the Equatons 3 and 4 through the doman n FLUENT 6.0 wth respect to boundary condtons, whch are explaned n the followng sectons [14, 15]. Soluton Methodology n Fluent 6.0. Grd generaton In the present study, a two-dmensonal geometrcal system wth szes of 476 mm x Ø36 mm s consdered for numercal analyss of the problem as shown n Fgure 3. The modeled system possesses the same external dmensons as the testng faclty of the commercal ball valve. A computatonal grd of hex/wedge elements s generated usng the preprocessor of the commercal software GAMBIT as gven n Fgure 4. R = ρu j ' u ' j U xj =μ t + Uj x (6) Fg. 3. Geometrcal szes of the experment faclty Fg. 4. Typcal grd used n CFD analyss

4 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) As seen n Fgure 3, the nlet and outlet dameters of the ppe are 36 mm, and the dameter of the ball valve, whch permts the passage of the flud through the ppe, s 31.5 mm. The pressure values p 1 and p 2 correspond to the manometers that were mounted onto the nlet and outlet sectons of the ppe.. Boundary Condtons In ths CFD analyss, the varous physcal boundary condtons were appled as gven n Table 1. The computatonal and expermental studes were carred out under pressure dfference of 100 Pa between the nlet and outlet sectons (Table 2). Table 1. Appled boundary condtons Nr Physcal Boundary Condtons Computatonal Boundary Condtons 1 Inlet Pressure Inlet 2 Axs Axsymmetrc 3 Flud Ar 4 Outlet Pressure Outlet Table 2. Boundary condtons values used Nr Parameter Value 1 Inlet Gauge Total Pressure 100 Pa 2 Outlet Gauge Total Pressure 0 Pa 3 Densty kg/m 3. Soluton Procedure Governng dfferental equatons are ntegrated over each control volume, whch yelds a set of algebrac equatons that are numercally solved. The pressure and velocty are obtaned by usng the approach algorthm of k-ε standard turbulence modelng by Spaldng, snce the flows are turbulent at Re>2,300 and Re>20,000 n nternal and external flows, respectvely, whch also apply n FLUENT software. Calculatons n ths study were performed wth usng mplct vscous model solver as post-processor. After obtanng the results of numercal analyss, velocty magntude changes and statc pressure changes through the ppe system for ball angle of openng θ = 90, 50, 20 are shown n Fg. 5, 7, 9 and Fg. 6, 8, 10, respectvely. 4. RESULTS AND DISCUSSION In ths study, a computatonal method to predct steady and sngle-phase flows nsde a ppe joned to a ball valve has been nvestgated. Addtonally, results obtaned from the experment performed under the same condtons have been compared to the results of the computatonal method. In the computatonal analyss of the present study, t s assumed that the flud nsde the ppe s contnuous and ncompressble due to the low Mach-number, although t s ar. Table 3 shows the veloctes n experment and smulaton for comparson. The outlet veloctes obtaned n the experment are slghtly lower than those n smulaton. Smlarly, pressure drop coeffcents of the smulaton model are slghtly lower than those of the expermental model. Fgure 11 shows pressure drop coeffcent relaton dependng on the openng angle of the ball valve. It can be clearly seen that the results obtaned from the experment and CFD analyss exactly agree wth each other especally n ball angles of openng between 90 and 30. Besdes, the agreement of the results between 30 and 0 s satsfactory. Whle the ball angle decreases, the pressure drop coeffcent ζ ncreases rapdly, ths reaches up to nfnte value at the angle from 13 and up to the fullyclosed poston. In addton, whle the pressure dfference between the nlet and outlet sectons ncreases, the pressure drop coeffcent ζ remans constant. Table 3. Change of the pressure drop vs. the outlet velocty D p [Pa] Outlet velocty n experment [m/s] Outlet velocty n CFD [m/s]

5 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) Fg. 5. Axal velocty magntude change through the ppe (Ball angle of openng θ =90 o ) Fg. 6. Statc pressure change through the ppe (Ball angle of openng θ =90 ) Fg. 7. Axal velocty magntude change through the ppe (Ball angle of openng θ =50 )

6 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) Fg. 8. Statc pressure change through the ppe (Ball angle of openng θ =50 ) Fg. 9. Axal velocty magntude change through the ppe (Ball angle of openng θ=20 ) Fg. 10. Statc pressure change through the ppe (Ball angle of openng θ=20 )

7 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) ζ 1000 ζcfd = 0,3084 e^(0,9658θ) R^2 = 0,9776 Mnor loss coeffcent (-) ζexperment = 0,3598 e^(0,9541θ) R^2 = 0,9798 experment CFD Ball Angle (Degree) θ Fg. 11. Relaton of pressure drop coeffcent ζ vs. ball angle of openng n comparson of experment and CFD analyss Q 0,04 Q CFD= -0,0001Δp^2+0,0043Δp+0,0085 R^2 = 0,996 Volumetrc flow rate (m 3 /s) 0,03 0,02 0,01 experment CFD 0 Qexperment= -0,0001Δp^2+0,004Δp+0,0077 R^2 = 0, Pressure Dfference(Pa) Δp Fg. 12. Relaton of pressure drop vs. flow rate u u CFD = -0,1405Δp^2+4,2035Δp+8,3998 R^2 = 0,996 Flud Velocty (m/s) experment CFD 5 u experment = -0,1337Δp^2+3,9508Δp+7, R^2 = 0,996 Δp Pressure Dfference (Pa) Fg. 13. Relaton of pressure drop vs. axal velocty

8 A. Ozdomar, K. Turgut Gursel, Y. Pekbey, B. Celkag / Internatonal Energy Journal 8 (2007) Fgure 12 shows the relaton between the volumetrc flow rate and the pressure drop. The results exhbt that the pressure dfference between the nlet and the outlet sectons ncreases wth the ncreasng volumetrc flow rate. Addtonally, Fgure 12 represents a satsfactory agreement between the CFD analyss results and those of the experment as n Fgure 13 that smlarly exhbts the change of the ncreasng nlet pressure versus the axal velocty. In other words, after 13 of openng angle, the pressure drop coeffcent decreases down to When the ball valve s turned towards ts fully-opened poston, the pressure drop coeffcent reaches ts mnmal value, namely zero. Generally, the expermental veloctes were determned lower than smulaton results. Ths s due to the constructonal reasons such as fttngs that t was normally mpossble to measure the pressure values exactly on ponts where numercal calculatons were carred out. Addtonally measurng accuracy partally was derogated by any losses. 5. CONCLUSION The pressure drop coeffcent values of other valve types are much hgher than those of the ball valve, whch s the man reason why the ball valves are used when lowpressure drop s especally requred. The results obtaned n the experment and CFD analyss ndcate that the computatonal model adopted can be used as a tool to desgn better and effcent nstallaton systems wth dfferent ball valves subjected to smlar condtons such as those of ths experment. Addtonally, pressure drops n ppng systems cause blockages, nose and energy losses, whch have to be reduced as much as possble. By usng the fully-opened ball valve, by mnmzng the ppe length and maxmzng the nsde ppe dameter, and by avodng unnecessary valves, flters and bends along a ppe system, users may obtan trple savngs n energy consumpton, ppe and fttng costs. Symbols G h k p Q R j U u u v Δp θ ε μ t ζ Ρ NOMENCLATURE Explanaton Acceleraton of gravty Head Turbulent knetc energy Pressure Volumetrc flow rate Reynolds stresses Mean velocty Flud velocty Velocty fluctuaton Velocty component n drecton of radal axs Dfference between nlet and outlet pressure Ball angle Turbulent dsspaton rate Eddy vscosty Pressure drop coeffcent Densty REFERENCES [1] Whte, F.M Flud Mechancs, McGraw-Hll, 5. Ed., New York. [2] Skousen, P.L Valve Handbook, McGraw-Hll, New York. [3] Bhaskaran, R., and Collns, L Introducton to CFD Bascs. [4] Larach, F., Petre, C.F., Iluta, I., and Grandjean, B Talorng the pressure drop of structured packngs through CFD smulatons. Chemcal Engneerng and Processng 42, [5] Erdal, A A numercal nvestgaton of dfferent parameters that affect the performance of a flow condtoner. Flow. Meas. Instrum. 8/2, [6] Halupovch, Y., Natan, B., Rom, J Numercal soluton of the turbulent supersonc flow over a backward facng step. Flud Dynamcs Research 24, [7] Erdal, A., and Andersson, H.I Numercal aspects of flow computaton through orfces. Flow. Meas. Instrum. 8/1, [8] Fu, W.S., and Ger, J.S A concse method for determnng a valve flow coeffcent of a valve under compressble gas flow. Expermental Thermal and Flud Scence 18, [9] Amat, G., Succ, S. and Benz, R Turbulent channel flow smulatons usng a coarse-graned extenson of the lattce Boltzmann method. Flud Dynamcs Research 19, [10] Makarytchev, S.V., Langrsh, T.A.G., and Fletcher, D.F CFD analyss of spnnng cone columns: Predcton of unsteady gas flow and pressure drop n a dry column. Chemcal Engneerng Journal 87, [11] Ozdamar, A., Gursel, K.T., Pekbey, Y., and Celkag, B A prelmnary study on pressure drop coeffcent of ball valves, Ege Unversty Scentfc Research Project Report (02/MUH/024), Izmr, Turkey. (In Turksh). [12] H. Oertel, M. Böhle, Stroemungsmechank, Veweg Verlag, Braunschweg, [13] Pacorr, R., Bonfglol, A., D Masco, A., and Favn, B RANS smulatons of a juncton flow. Internatonal Journal of Computatonal Flud Dynamcs, Vol. 19, No. 2, [14] Fluent Software Tranng Notebook, Why model turbulence, TRN , Fluent Inc., [15] Fluent Software Tranng Notebook, Two equaton model, TRN , Fluent Inc., 2002.