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doi:10.1016/j.jfluidstructs.2006.08.010 ARTICLE IN PRESS 0889-9746/$ - se doi:10.1016/j.jfl �Correspond E-mail addr Journal of Fluids and Structures 23 (2007) 163–189 www.elsevier.com/locate/jfs Noise generated by cavitating single-hole and multi-hole orifices in a water pipe P. Testuda,�, P. Moussoua, A. Hirschbergb, Y. Auréganc aLaboratoire de Mécanique des Structures Industrielles Durables, UMR CNRS-EDF 2832, 1 Avenue du Général De Gaulle, F-92141 Clamart, France bFluid Dynamics Laboratory, Department of Applied Physics, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands cLaboratoire d’Acoustique de l’Université du Maine, UMR CNRS 6613, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France Received 13 December 2005; accepted 5 August 2006 Available online 27 October 2006 Abstract This paper presents an experimental study of the acoustical effects of cavitation caused by a water flow through an orifice. A circular-centered single-hole orifice and a multi-hole orifice are tested. Experiments are performed under industrial conditions: the pressure drop across the orifice varies from 3 to 30 bar, corresponding to cavitation numbers from 0.74 to 0.03. Two regimes of cavitation are discerned. In each regime, the broadband noise spectra obtained far downstream of the orifice are presented. A nondimensional representation is proposed: in the intermediate ‘developed cavitation’ regime, spectra collapse reasonably well; in the more intense ‘super cavitation’ regime, spectra depend strongly on the quantity of air remaining in the water downstream of the orifice, which is revealed by the measure of the speed of sound at the downstream transducers. In the ‘developed cavitation’ regime, whistling associated with periodic vortex shedding is observed. The corresponding Strouhal number agrees reasonably well with literature for single-phase flows. In the ’super cavitation’ regime, the whistling disappears. r 2006 Elsevier Ltd. All rights reserved. Keywords: Confined flow; Orifice; Cavitation; Broadband noise; Whistling 1. Introduction 1.1. Motivations In industrial processes, cavitating flows are known to sometimes generate significant levels of noise and high vibrations of structures. Some papers have been published in the last years on this topic: Au-Yang (2001), Weaver et al. (2000), Moussou (2004). In particular, fatigue issues have been reported recently for the configurations of a cavitating valve (Moussou et al., 2001) and a cavitating orifice (Moussou et al., 2003). The examination of the noise generated by a cavitating device, in e front matter r 2006 Elsevier Ltd. All rights reserved. uidstructs.2006.08.010 ing author. ess:
[email protected] (P. Testud). www.elsevier.com/locate/jfs dx.doi.org/10.1016/j.jfluidstructs.2006.08.010 mailto:
[email protected] ARTICLE IN PRESS Nomenclature c speed of sound measured downstream of the orifice (in m s�1) cw speed of sound in pure water (in m s �1) cmin minimum speed of sound (in m s �1) d diameter of the single-hole orifice ðd ¼ 2:2� 10�2 mÞ deq single-hole equivalent diameter of the multi- hole orifice ðdeq ¼ 2:1� 10�2 m) dmulti diameter of the holes of the multi-hole orifice ðdmulti ¼ 3� 10�3 mÞ f 0 whistling frequency (in Hz) D pipe diameter ðD ¼ 7:4� 10�2 mÞ Sj cross section of the jet (in m 2) St Strouhal number for the whistling frequency t orifice thickness, ðt ¼ 14� 10�3 mÞ tp pipe wall thickness ðtp ¼ 8� 10�3 mÞ U volume flux divided by pipe cross-sectional area (in m s�1) Ud volume flux divided by orifice cross-sec- tional area (in m s�1) Uj volume flux divided by orifice jet cross- sectional area (in m s�1) Gpp Power spectrum density of the pressure (in Pa2=Hz) Nholes number of holes for the multi-hole orifice ðNholes ¼ 47Þ pþ; p� forward, backward propagating plane wave spectra (in Pa= ffiffiffiffiffiffiffi Hz p ) P1;P2 static pressure, respectively, upstream and far downstream of the orifice Pj static pressure at the jet (vena contracta) Pv vapor pressure (Pvð310KÞ ¼ 5:65� 103 Pa (Tullis, 1989)) S cross-section of the pipe (in m2) DP static pressure difference across the orifice (in Pa) nwater kinematic viscosity of water [nwaterð310KÞ ¼ 7:2� 10�7 m2 s�1 (Idel’cik, 1969)] b volume fraction of gas in the water rw density of water ðrwð310KÞ ¼ 994kgm�3) s cavitation number si incipient cavitation number sch choked cavitation number P. Testud et al. / Journal of Fluids and Structures 23 (2007) 163–189164 this study a cavitating orifice, is typically an industrial issue. It provides information which is a basis for a safer design in terms of pipe vibrations. 1.2. Literature In single-phase flow, an orifice generates a free jet surrounded by a dead water pressure region of uniform pressure, cf. Fig. 1. The static pressure reaches its minimum value Pj in the jet region, also called the vena contracta, and large eddies are generated in the shear layer separating the jet from the dead water region. Two-phase flow transition occurs when the lowest static pressure in the fluid falls below the vapor pressure (Brennen, 1995). The level of cavitation is usually correlated with the help of a so-called cavitation number. Different definitions exist of the cavitation number for cavitation in a flowing stream (also called hydrodynamic cavitation). They correspond to different cavitation configurations, and are usually chosen for convenience, so that they can easily be determined in practice: (i) For wake cavitation, that is cavitation round a body (i.e. an hydrofoil) or generated by a slit, the cavitation number is commonly defined as function of the upstream conditions (Young, 1999; Brennen, 1995; Franc et al., 1999; Lecoffre, 1994): s ¼ P0 � Pv ð1=2ÞrLU20 , (1) where U0 is the infinite upstream flow velocity, P0 the ambient static pressure, Pv the vapor pressure of the liquid and rL the density of the liquid. (ii) For mixing cavitation, that is cavitation formed in a jet (i.e. in pumps, valves, orifices), a similar cavitation number, as in the wake cavitation, can be used (Young, 1999; Brennen, 1995): s ¼ Pref � Pv ð1=2ÞrLU20 , (2) where Pref is very often defined as the downstream static pressure. ARTICLE IN PRESS Fig. 1. Flow through an orifice and corresponding evolution of the static pressure. P. Testud et al. / Journal of Fluids and Structures 23 (2007) 163–189 165 We prefer to use the cavitation number, based on the pressure drop across the singularity generating the jet: s ¼ P2 � Pv DP , (3) where DP ¼ P1 � P2 is the pressure drop across the orifice, with P1 the static pressure upstream of the orifice and P2 the downstream static pressure far away from the orifice. In this choice, we follow common practice in industry (Tullis, 1989; Franc et al., 1999; Lecoffre, 1994). One should note that both those cavitation numbers lead to very similar classifications as they are related to each other by the pressure drop coefficient of the singularity. When the pressure Pj has a sufficiently low value, intermittent tiny cavitation bubbles are produced in the heart of the turbulent eddies along the shear layer of the jet. This flow regime transition is called cavitation inception, and it appears at a cavitation number of the order of 1 (when d=D ¼ 0:30) according to the data of Tullis (1989). Other references (Numachi et al., 1960; Tullis and Govindajaran, 1973; Ball et al., 1975; Yan and Thorpe, 1990; Kugou et al., 1996; Sato and Saito, 2001; Pan et al., 2001) are in good agreement with the values and scale effects given by Tullis (1989). Some differences result from the influence of the variation in the dissolved gas content and in the viscosity (Keller, 1994). As the jet pressure decreases further, more bubbles with larger radii are generated, forming a white cloud. The pressure fluctuations increase and a characteristic shot noise can be heard. A further decrease in jet pressure induces the formation of a large vapor pocket just downstream of the orifice, surrounding the liquid jet. The regime occurring after this transition is called super cavitation and it exhibits the largest noise and vibration levels. In the super cavitation regime, noise is known [see, for example, Van Wijngaarden (1972)], to be mainly generated in a shock transition between the cavitation region and the pipe flow, at some distance downstream of the orifice. Downstream of the shock, some residual gas (air) bubbles can persist but pure vapor bubbles have disappeared. Cavitation indicators are used to predict the occurrence of cavitation regimes. The use of two of them has seemed relevant, in view of our experimental results. First, a so-called incipient cavitation indicator, noted si, which predicts the transition from a noncavitating flow to a moderately cavitating flow, that is called developed cavitation regime. Second, a so-called choked cavitation indicator, noted sch, which predicts the transition from a moderately cavitating flow to a super cavitating flow, with the formation and continuous presence of a vapor pocket downstream of the orifice around the liquid jet. To calculate both those incipient and the choked cavitation indicators, scaling laws are given by Tullis (1989). They take into account the various pressure effects and size scale effects, by means of extensive experiments on single-hole orifices in water pipe flow. For multi-hole orifices, as mentioned in the same work, less data are available but identical values are expected to hold. Only a few studies provide downstream noise spectra generated by cavitating orifices (Yan et al., 1988; Bistafa et al., 1989; Kim et al., 1997; Pan et al., 2001). A few complementary studies give the noise spectra created by cavitating valves ARTICLE IN PRESS P. Testud et al. / Journal of Fluids and Structures 23 (2007) 163–189166 (Hassis, 1999; Martin et al., 1981). In fact, it appears that far more research has been developed on submerged water jets (Jorgensen, 1961; Esipov and Naugol’nykh, 1975; Franklin and McMillan, 1984; Brennen, 1995; Latorre, 1997). A comprehensive overview of the state of the art in this domain is given in Brennen (1995). 2. Experimental set-up 2.1. Tested orifices In the piping system of French nuclear power plants, a basic configuration to obtain a pressure discharge can be realized with a single-hole orifice. The maximum flow velocity can reach about 10m s�1 and the pressure drop 100 bar across the orifice. This can induce high vibration levels. The orifices used are chosen in order to reduce the pipe vibration to acceptable levels (Caillaud et al., 2006). In our study, two orifices have been tested (see Fig. 2), as follows: (i) A single-hole orifice, circular, centered, with right angles and sharp edges. It has a thickness of t ¼ 14mm ðt=d ¼ 0:64Þ and a diameter of d ¼ 22mm ðd=D ¼ 0:30Þ, for a pipe diameter of D ¼ 74mm. It is considered as a ‘thin’ orifice as t=dt2 (Idel’cik, 1969). In