Flow Measurement and Instrumentation Volume 28 Issue None 2012 [Doi 10.1016_j.flowmeasinst.2012.07.006] Stefano Malavasi; Gianandrea Messa; Umberto Fratino; Alessandro -- On the Pressure Losses Thro

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On the pressure loss through Orifice
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  On the pressure losses through perforated plates Stefano Malavasi a , Gianandrea Messa a, n , Umberto Fratino b , Alessandro Pagano b a Dip. IIAR, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy b Dip. Ingegneria delle Acque e di Chimica, Politecnico di Bari, Via Orabona, 4-70125 Bari, Italy a r t i c l e i n f o  Article history: Received 22 February 2012Received in revised form18 July 2012Accepted 22 July 2012Available online 17 August 2012 Keywords: Perforated platesPressure loss coefficientParameters a b s t r a c t Perforated plates are widely used in pipeline systems either to reduce flow nonuniformities or toattenuate the onset and the development of cavitation. This experimental work aims at investigatingthe dependence of the pressure losses through sharp-edged perforated plates with respect to thegeometrical and flow key parameters. The data, collected in two large experimental campaigns carriedout on different pilot plants, are reported and discussed. Several plates with different geometricalcharacteristics were tested. More precisely, perforated plates whose equivalent diameter ratio variesbetween 0.20 and 0.72; relative hole thickness between 0.20 and 1.44; and number of holes between3 and 52. Experimental data from literature are also considered in order to ensure the reliability of theparametric investigation. The dependence of the pressure loss coefficient upon the Reynolds number,the equivalent diameter ratio, the relative thickness, and the number and disposition of the holes isstudied. A comparison to different empirical equations, as available by the technical literature, and tothe standard ISO 5167-2 single-hole orifice is also provided. &  2012 Elsevier Ltd. All rights reserved. 1. Introduction Perforated plates are commonly used for the control and themaintenance of the efficiency of pressurized systems, beingpreferred over other hydraulic devices for their simple geometryand low cost. Generally, perforated plates are installed upstreamto flowmeters to remove swirl and correct a distorted flow profileor, coupled with a control valve, used for preventing cavitationphenomena, assuring safe operating conditions (Tullis and DiSanto et al. [1,2]).The hydraulics of perforated plates was largely investigated inthe technical literature, and most of the researches were aimed atinvestigating their functionality as flow conditioners. Laws andOuazzane [3] focused their attention on the use of such devicesfor pre-conditioning a disturbed flow, whereas Schluter andMerzkirch [4] measured, by means of PIV techniques, the time-averaged axial velocities downstream perforated plates for opti-mizing their geometry. A similar analysis was recently carried outby Xiong et al. [5].Few investigations deal with the dissipation characteristics of perforated plates, being mostly focused on the occurrence anddevelopment of the cavitation phenomena (Govindarajan [6];Tullis and Govindarajan [7]; Kim et al. [8]; and Testud et al. [9]). Tullis [1] investigated the pressure losses through differentperforated plates and the pressure profile downstream them.Gan and Riffat [10] determined the pressure drop through aperforated plate in a square pipe by means of experimental testsand numerical simulations. Erdal [11] performed a numericalinvestigation of the parameters affecting the performance of amulti-hole plate used as flow conditioner, and discussed about itsdissipation characteristics. Weber et al. [12] made a review of literature data about the pressure losses through perforated platesin circular and rectangular pipes, reporting data from differentauthors (Dannenberg; Kolodzie and Van Winkle; Wang et al.). Inaddition,some experimental tests on perforated plates andflat barscreens in a large rectangular pipe were discussed. Fratino [13]studied experimentally and numerically the flow through multi-hole orifices in circular pipes, and proposed a formula to estimatethe pressure drop. Similar investigations are reported in Malavasiet al. [14], Macchi [15], and Malavasi et al. [16], where the dependence of the pressure losses upon the most significantgeometrical and flow parameters is considered. Zhao et al. [17]studied the dissipation characteristics of several multi-hole ori-fices of 2 mm thickness, and reported an empirical formula forestimating the pressure drop. Holt et al. [18] analyzed thedissipation and cavitation efficiency of baffle plates in circularpipes, introducing a method for evaluating the pressure losses inno cavitating conditions.The dissipation characteristics of perforated plates are usuallyquantified by means of the pressure loss coefficient, defined as Eu ¼  P  U   P  D 1 = 2 r V  2  ð 1 Þ Contents lists available at SciVerse ScienceDirectjournal homepage: www.elsevier.com/locate/flowmeasinst Flow Measurement and Instrumentation 0955-5986/$-see front matter  &  2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.flowmeasinst.2012.07.006 n Corresponding author. Tel.:  þ 39 02 2399 6287. E-mail address:  gianandrea.messa@mail.polimi.it (G. Messa).Flow Measurement and Instrumentation 28 (2012) 57–66  where  P  U   and  P  D  are, respectively, the pressure upstream anddownstream of the device,  V   is the pipe bulk-mean velocity, and  r is the fluid density (Fig. 1). As it will be discussed later, thereference sections  U   and  D  are defined in different ways by theexisting standards.When no cavitation occurs, the pressure loss coefficient isinfluenced by the geometry of the plate, defined, for a square-edged plate with holes of uniform size, by the following char-acteristics: (1) the porosity of the screen, i.e. the ratio of the openarea to the overall pipe section, usually expressed by means of itssquare root  b  (equivalent diameter ratio); (2) the plate thickness  t  ,usually taken into account by the relative thickness  t  / d h ,  d h  beingthe hole diameter; (3) the number of holes  n h ; (4) the distributionof the holes, usually quantified by the pitch  P  , i.e. the minimumdistance between two adjacent holes. The dimensionless groups P  / d h  and  P  / D  are considered in Weber et al. [12] and Zhao et al.[17] respectively,  D  being the diameter of the circular pipe.The losses are also influenced by the friction factor of the holes l , but such dependence, in the present work, was found to beabsolutely negligible.An important role is played by the Reynolds number char-acteristic of the phenomenon, whose definition is still controver-sial. Some authors (Fratino [13]; Malavasi et al. [14]; Malavasi et al. [16]; Zhao et al. [17]) make reference to the pipe Reynolds number  R  p ¼ V   p D / n , defined in terms of pipe diameter  D  and pipebulk mean velocity  V   p ; other authors (Weber et al. [12]; Idelcick[19]) considered the hole Reynolds number  R h ¼ V  h d h / n , defined interms of hole diameter  d h  and hole bulk mean velocity  V  h  (there-fore,  R  p  ¼ R h  ffiffiffiffiffi n h p   b ); in Gan and Riffat [10] and Holt et al. [18] a Reynolds number  R ¼ DV  h / n  expressed in terms of pipe diameter D  and hole bulk-mean velocity  V  h  is introduced.  R  is linked to  R  p by the following relationship  R  p ¼ b 2 R . Whatever Reynolds num-ber is considered, the dependence between the pressure losscoefficient  Eu  and the Reynolds number is qualitatively sketchedin Fig. 2. Under no cavitating conditions, as Reynolds increasestwo different regions can be identified: a low-Reynolds region (1),in which  Eu  is affected by the Reynolds number; and a self-similarity region (2), in which  Eu  is almost constant with respectto the Reynolds number. The occurrence of cavitation causes  Eu  toincrease suddenly with the Reynolds number. The threshold valueof Reynolds number at which a given device is subjected tocavitation depends on the plant pressure.Different formulas for evaluating the pressure loss coefficientin the self-similarity region with respect to  R D  (region (2) in Fig. 2)are available. All of them express  Eu  as a function of theequivalent diameter ratio  b  and, in some cases, the relativethickness  t  / d h  and the friction factor  l , therefore assuming thatthe effect of number and disposition of the holes is negligible.Some of them are derived for the single-hole orifice case and saidto be applicable to the perforated plate case. Among them, moreattention is given to that of Idelcick [19], valid for  R h 4 10 5 and t  / d h 4 0.015: Eu ¼  0 : 5 ð 1  b 2 Þþ t ð 1  b 2 Þ 1 : 5 þð 1  b 2 Þ 2 þ l t  = d h b 4  ð 2 Þ in which is  t  is a tabular coefficient depending on  t  / d h , and to thatof Miller [20]: Eu ¼  C  0 ð 1  C  C  b 2 Þ 2 C  2 C  b 4  ð 3 Þ in which  C  0  is a coefficient depending on  t  / d h , while  C  C   is thecontraction coefficient of the jets. As reported in Fratino [13],  C  0 can be calculated by the following empirical expression, assumedvalid for 0.1 o t  / d h o 3: C  0  ¼ 0 : 5 þ  0 : 1784 ð t  = d h Þ 2 þ 0 : 355 ð 4 Þ while  C  C   can be evaluated by C  C   ¼ 0 : 596 þ 0 : 0031 e b = 0 : 206 ð 5 Þ Empirical equations for estimating the pressure loss coefficientthrough perforated plates are reported in ESDU [21], Zhao et al.[17], and Holt et al. [18]. The first, said to be valid for  R h 4 10 4 , is Eu ¼ K  0 b  4 l a  t  = d h o 0 : 8 K  0 : 8 b  4 l b  t  = d h 4 0 : 8 (  ð 6 Þ where  K  0  and  K  0.8  are given as function of   b  while  l a  and  l b depend on  b  and  t  / d h . All coefficients are provided in a graphicalform. Zhao et al. [17] expressed  Eu  as a function of   b  using thefollowing equation, valid for  b  ranging from 0.25 to 0.45: Eu ¼ P  m ð b  4 : 448  1 Þ ð 7 Þ where P  m  ¼ 160 : 325 ð 71 : 467 b 4  100 : 300 b 3 þ 52 : 021 b 2  11 : 801 b þ 1 Þ ð 8 Þ At the end, according to Holt et al. [18], the pressure losscoefficient  Eu  can be evaluated as Eu ¼ 2 : 9  3 : 79  t d h b 0 : 4 þ 1 : 79  t d h   2 b 0 : 8   K  LA t d h b 0 : 4 o 0 : 90 : 876 þ 0 : 069  t d h b 0 : 4   K  LA t d h b 0 : 4 4 0 : 9 8>><>>: ð 9 Þ where  K  LA  is the pressure loss coefficient of a single-hole orifice asestimated by means of a theoretical model for reattached flow: K  LA  ¼ 1   2 b 2  þ  2 b 4  1   1 C  C  þ  12 C  2 C   !  ð 10 Þ The authors suggest setting the contraction coefficient of the jets C  C   equal to 0.72.The purpose of the present work is to investigate the dissipa-tion characteristics of a multi-hole orifice under no cavitatingconditions. The results of experimental campaigns performed intwo different pilot plants are reported and discussed. Data from Fig. 1.  Geometrical sketch of the system and identification of the referencesections  U   and  D . Fig. 2.  Qualitative trend of   Eu  as a function of Reynolds number. For a givendevice, the Reynolds number at which cavitation occurs depends on the plantpressure. S. Malavasi et al. / Flow Measurement and Instrumentation 28 (2012) 57–66  58  literature are made comparable and primarily checked for theirconsistency. Afterwards, they are added to our experimental datato create a large database for achieving a better awareness aboutthe dependence of the pressure loss coefficient upon the mostsignificant geometrical and flow parameters. A comparison withthe above described formulas and to the standard ISO 5167-2 [25]orifice is also reported. 2. Experimental setup Tests were carried out by research groups of PolytechnicSchool of Milan and Polytechnic School of Bari.Experiments of the former group were conducted in a pilotplant located at Pibiviesse S.r.l, Nerviano, Italy. The rig, shown inFig. 3, consists of 10 00  and 12 00  steel pipes, supplied by a pump ableto guarantee pressures up to 10 bar at the reference sectionupstream the orifice. Control valves placed upstream and down-stream the test area allow setting the proper fluid-dynamicconditions in each experimental test. Pressure drop was measuredwith a series of absolute and differential pressure transducers inreference sections located 2 D  upstream and 6 D  downstream thedevice, according to ISA-RP75.23 standard [22]. Other measure-ment points were placed at 1 D  upstream and 1 D , 2 D , 3 D , 4 D , 5 D ,6 D , and 7 D  downstream the plate. Flow rate was measured by a10 00  electromagnetic flow-meter, placed upstream the test section.During the tests, the water temperature was measured in order tomonitor values of density, viscosity and vapor pressure of thefluid. The tests have been performed maintaining constant pres-sure at the upstream reference section  P  U   and decreasing thedownstream pressure  P  D  in order to increase the discharge andconsequently the Reynolds number.Complementary experimental tests have been performed bythe research group of Bari in the Laboratory of the Department of Ingegneria delle Acquee Chimica at Polytechnic Schoolof Bari. Thelaboratory setup, sketched in Fig. 4, is composed by 100 mm and200 mm steel pipes, supplied by a pump able to guaranteepressures of about 9.0 bar and flow rates up to 100 l/s.The pressure taps for evaluating the gross head drop were located1 D  upstream and 10 D  downstream the device, but other measure-ment points were placed at 0.5 D , 1 D , 2 D , 3 D , 4 D , 5 D , 7 D  down-stream the device. The pressure drop was measured by a mercurydifferential manometer and by Burdon tube pressure gauges,whereas the flow rate was evaluated by a flow measuring pipeorifice and by a volumetric tank. Even during this experimentalcampaign, the water temperature was measured in order tomonitor the values of density, viscosity and vapor pressure of the fluid. Differentpressure values, generally equal to 0.25, 0.5 and1 bar, have been fixed downstream the plate to make the resultsindependent from possible uncertainties due to the pressure scaleeffects in case of cavitation occurrence (Fratino [13]).It is worth mentioning that the different positions of thepressure taps in the two experimental pilot plants is related tolaboratory constraints and arrangements and it can be verified thatit has no influence on the reliability of the experimental data. Inconfirmation of it, the ISA-S39.2 standard [23] on testing proce-dures for estimating control valve capacity states that the locationof the upstream pressure tap is between 0.5 D  and 2.5  D  upstreamthe device. On the other hand, the difference in the downstreampressure tap locations is negligible, as in both cases the pressurerecovery is completed and there are distributed friction losseswithout any significance over such a small pipe length.Considerations about the estimate of the uncertainty of mea-surements are reported in Appendix A.Several plates were tested in the two campaigns. Theirgeometrical characteristics, reported in Table 1, are different interms of equivalent diameter ratio  b  (from 0.20 to 0.72); relativethickness  t  / d h  (from 0.20 to 1.44); number of holes  n h  (from 3 to52); and distribution of the holes. 3. Results and discussion Comments on the influence of geometrical and flow para-meters on the dissipation characteristics of perforated plates are Fig. 3.  Sketch of the test rig (Polytechnic School of Milan research group). S. Malavasi et al. / Flow Measurement and Instrumentation 28 (2012) 57–66   59  Fig. 4.  Sketch of the test rig (Polytechnic School of Bari research group).  Table 1 Geometrical characteristics and result obtained for all the plates tested (M-Series: tests of Polytechnic School of Milan researchgroup; B-Series: tests of Polytechnic School of Bari research group).Plate label  b  [-]  t/d h  [-]  n h  [-] Distribution of the holes  Eu  [-]M1 0.40 0.24 13 53.6 7 1.0M2 0.40 0.45 13 72.8 7 2.0M3 0.40 0.73 13 38.8 7 0.8M4 0.40 0.73 13 42.1 7 2.1M5 0.40 1.00 13 50.7 7 2.7M6 0.40 1.00 26 35.4 7 0.7M7 0.40 1.40 13 37.8 7 1.2M8 0.51 0.73 13 15.3 7 0.7M9 0.51 1.00 26 15.8 7 0.8M10 0.72 1.00 52 2.25 7 0.11 S. Malavasi et al. / Flow Measurement and Instrumentation 28 (2012) 57–66  60
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