Yan Zhan Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794 Foluso Ladeinde Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794 Harold G. Kirk Department of Physics, Brookhaven National Laboratory, Upton, NY 11973 Kirk T. McDonald Department of Physics, Princeton University, Princeton, NJ 08544 The Effects of Pipe Geometry on Fluid Flow in a Muon Collider Particle Production System Liquid mercury has been investigated as a potential high-Z target for the production of muon particles for the Muon Collider project. This paper investigates the dynamics of mercury ﬂow in a design of the target delivery system, with the objective of determining pipe conﬁgurations that yield weak turbulence intensities at the exit of the pipe. Eight curved pipe geometries with various half-bend angles and with/without nozzles in the exit region are studied. A theoretical analysis is carried out for steady laminar incompressi- ble ﬂow, whereby the terms representing the curvature effects are examined. Subsequent simulations of the turbulent ﬂow regime in the pipes are based on a realizable k  e Reynolds-Averaged Navier–Stokes (RANS) equations approach. The effects of half-bend angles and the presence of a nozzle on the momentum thickness and turbulence intensity at the exit plane of the curved pipe are discussed, as are the implications for the target delivery pipe designs. [DOI: 10.1115/1.4027176] 1 Introduction The MERIT experiment at CERN [1,2] is a proof-of-principle test for a target system that converts a 4MW proton beam into a high-intensity muon beam for either a neutrino factory complex or a muon collider (see Fig. 1). The mercury jet issues from the nozzle at the end of a delivery pipe to form a target that intercepts an intense proton beam inside a 15T solenoid magnet. The use of liquid targets overcomes the problematic effects of solid targets such as the melting/vaporization of components, damage by beam-induced pressure waves for pulsed beams, and extensive radiation damage. Additionally, liquid target systems offer the advantage of the continuous regeneration of the target volume. However, the design of the mercury delivery pipe introduces new challenges. The MERIT experiment uses a 180 deg bend, which has half- bend angles of 90 deg in the shape of a “U” for the delivery of the mercury. This geometry complicates the ﬂow relative to that in a straight pipe and, arguably, affects the quality of the jet. Since the quality of the jet greatly inﬂuences the production of muon par- ticles, it is pertinent to investigate the dynamics of the ﬂow of mercury in the 180 deg bend, with a focus on the exit-ﬂow results. Furthermore, for optimum muon particle production, the mercury ﬂow should be near laminar. Four half-bend angles of 0 deg 30 deg 60 deg, and 90 deg have been chosen for investigation in this paper. For each conﬁguration, a pipe with/without a nozzle is studied. Eustice [3,4] is among the ﬁrst to demonstrate the existence of a secondary ﬂow in a curved pipe, an observation he made from injecting ink into water ﬂowing through a pipe. Dean [5,6] introduces a parameter which bears his name (Dean number, De  Red 1=2 , where Re is the Reynolds number based on the area-averaged mean velocity through a pipe of diameter 2a and d is the curvature ratio (d  a=R, where R is radius of curvature) used to characterize the magnitude and shape of the secondary motion inside a loosely coiled pipe (d  1). Subsequent work by others have investigated curved pipes with different values of R. Adler [7] presents the experimental results of laminar and turbulent ﬂows in three pipes with different R values. Rowe [8] investigates turbulent water ﬂows for a curvature ratio of d ¼ 1=24 in a circular 180 deg bend. The total pressure and yaw angle relative to the bend axis are measured for the Reynolds number Re ¼ 236; 000. Enayat et al. [9] reports on the axial com- ponents of the mean and ﬂuctuating velocities for the turbulent water ﬂow in a circular 90 deg bend for a d value of 1=5:6 and for a wide range of Reynolds numbers. Azzola et al. [10] computes and measures the developed turbulent ﬂow in a 180 deg bend for d ¼ 1=6.75 and Re ¼ 57; 400 and 110,000, using the standard k  e model. Answer et al. [11] measures the Reynolds stresses and mean velocity components in vertical and horizontal planes containing the pipe axis for air ﬂow in a 180 deg bend, with d ¼ 1=13 and Re ¼ 50; 000. Sudo et al. [12] reports on the meas- urements of the turbulent ﬂow through a circular 90 deg bend with d ¼ 1=4. Sudo and co-workers [13] also measure turbulent air ﬂow in a 180 deg circular bend for the same d value, but with Re ¼ 60; 000. The axial, radial, and circumferential components of the mean velocity and the corresponding components of the Reynolds stress tensor are reported. H€ uttl et al. [14] investigate the inﬂuence of curvature and torsion on the turbulent ﬂow in helically-coiled pipes for Re s ¼ 230, where Re s is the mean fric- tion velocity (u s )-based Reynolds number. The pipe curvature is found to induce a secondary ﬂow with a strong effect on the ﬂuid dynamics. Rudolf et al. [15] study the ﬂow characteristics in sev- eral curved ducts: a single elbow to coupled elbows in the shapes of “U,” “S.” and the spatial right angle position, for a ﬁxed value of d ¼ 1=4 and Re ¼ 60; 000. Fig. 1 Sectional view of the target supply pipe of the MERIT experiment. The mercury jet generated at the end of the nozzle is on top of the nominal beam trajectory (both the mercury jet and proton beam move from right to left in this ﬁgure). Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 8, 2013; ﬁnal manuscript received February 9, 2014; published online July 24, 2014. Assoc. Editor: Ye Zhou. Journal of Fluids Engineering OCTOBER 2014, Vol. 136 / 101203-1 Copyright V C 2014 by ASME Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 11/05/2014 Terms of Use: http://asme.org/terms