0
Research Papers: Fundamental Issues and Canonical Flows

# The Effects of Pipe Geometry on Fluid Flow in a Muon Collider Particle Production System

[+] Author and Article Information

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

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.

J. Fluids Eng 136(10), 101203 (Jul 24, 2014) (12 pages) Paper No: FE-13-1227; doi: 10.1115/1.4027176 History: Received April 08, 2013; Revised February 09, 2014

## Abstract

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 incompressible 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 $k-ɛ$ 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.

<>

## References

Efthymiopoulos, I., 2008, “MERIT—The High Intensity Liquid Mercury Target Experiment at the CERN PS,” Proceedings of the IEEE NSS'08, p. 3302.
Kirk, H. G., Tsang, T., EfthymiopoulosI., FabichA., HaugF., LettryJ., PalmM., PereiraH., MokhovN., StriganovS., CarrolA. J., GravesV. B., SpampinatoP. T., McDonaldK. T., BennettJ. R. J., CarettaO., LoveridgeP., and ParkH., 2007, “The MERIT High-Power Target Experiment at the CERN-PS,” Proc. of the EPAC08.
Eustice, J., 1910, “Flow of Water in Curved Pipes,” Proc. R. Soc.London, Ser. A, 84(568), p. 107.
Eustice, J., 1911, “Experiments on Stream-Line Motion in Curved Pipes,” Proc.R. Soc. London, Ser.A, 85(576), p. 119.
Dean, W. R., 1927, “Note on the Motion of Fluid in Curved Pipes,” Philos. Mag., 20, p. 208.
Dean, W. R., 1928, “The Streamline Motion of Fluid in a Sinuous Channel,” Philos. Mag., 30, p. 673.
Adler, M., and Angew, Z., 1934, “Perturbation by and Recovery From Bend Curvature of a Fully Developed Turbulent Pipe Flow,” J. Math. Mech., 14, p. 257.
Roew, M., 1970, “Measurements and Computations of Flow in Pipe Bends,” J. Fluid Mech., 43, p. 771.
Enayat, M. M., Gibson, M. M., Taylor, A. M. K. P., and Yianneskis, M., 1982, “Laser-Doppler Measurements of Laminar and Turbulent Flow in Pipe Bend,” Int. J. Heat Fluid Flow, 3, p. 213.
Azzola, J., Humphrey, J. A. C., Iacovides, H., and Launder, B. E., 1986, “Developing Turbulent Flow in a U-Bend of Circular Cross Section: Measurement and Computation,” ASME J. Fluids Eng., 108, p. 214.
Answer, M., So, R. M. C., and Lai, Y. G., 1986, “Perturbation by and Recovery From Bend Curvature of a Fully Developed Turbulent Pipe Flow,” Phys. Fluids A, 1, p. 1387.
Sudo, K., Sumida, M., and Hibara, H., 1998, “Experimental Investigation on Turbulent Flow in a Circular-Sectioned 90-Degree Bend,” Exp. Fluids, 25, p. 51.
Sudo, K., Sumida, M., and Hibara, H., 2000, “Experimental Investigation on Turbulent Flow in a Circular-Sectioned 180-Degree Bend,” Exp. Fluids, 28, p. 42.
Hüttl, T. J., and Friedrich, R., 2000, “Influence of Curvature and Torsion on Turbulent Flow in Helically Coiled Pipes,” Int. J. Heat Fluid Flow, 21, p. 345.
Rudolf, P., and Desova, M., 2007, “Flow Characteristics of Curved Ducts,” Appl. Comput. Mech.1, p. 255.
Batchelor, G. K., 1967, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, UK.
Murata, S., Miyake, Y., and Inaba, T., 1976, “Laminar Flow in a Curved Pipe With Varying Curvature,” J. Fluid Mech., 73, p. 735.
Berger, S. A., Talbot, L., and Yao, L. S., 1983, “Flow in Curved Pipes,” Annu. Rev. Fluid Mech., 15, p. 461.
Webster, D. R., and Humphrey, J. A. C., 1997, “Traveling Wave Instability in Helical Coil Flow,” Phys. Fluids, 9, p. 407.
Ladeinde, F., and Torrance, K. E., 1991, “Convection in a Rotating, Horizontal Cylinder With Radial and Normal Gravity Forces,” J. Fluid Mech., 228, p. 361.
Launder, B. E., Reece, G. J., and Rodi, W., 1975, “Modeling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach,” J. Fluid Mech., 68, p. 537.
Spalart, P. R., and Allmaras, S. R., 1992, “A One Equation Turbulence Model for Aerodynamic Flows,” Paper No. AIAA92-0439, p. 439.
Harlow, F. H., and Nakayama, P. I., 1968, “Transport of Turbulence Energy Decay Rate,” Los Alamos Scientific Laboratory, Report No. LA3854.
Shih, T. H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J., 1995, “A New k−ε Eddy Viscosity Model for High Reynolds Number Turbulent Flows–Model Development and Validation,” Comput. Fluids, 24(3), p. 227.
Michalke, A., 1965, “On Spatially Growing Disturbances in an Inviscid Shear Layer,” J. Fluid Mech., 23, p. 521.
Plaschko, P., 1979, “Helical Instabilities of Slowly Divergent Jets,” J. Fluid Mech., 92, p. 209.
Cohen, J., and Wygnanski, I., 1987, “The Evolution of Instabilities on the Axisymmetric Jet. Part 1. The Linear Growth of Disturbances Near the Nozzle,” J. Fluid Mech., 176, p. 191.
Corke, T. C., Shakib, F., and Nagib, H., 1991, “Mode Selection and Resonant Phase Locking in Unstable Axisymmetric Jets,” J. Fluid Mech., 223, p. 253.
Corke, T. C., and Kusek, S. M., 1993, “Resonance in Axisymmetric Jets With Controlled Helical-Mode Input,” J. Fluid Mech., 249, p. 307.

## Figures

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).

Fig. 2

Coordinates along a curved pipe

Fig. 3

Configurations of the pipes investigated: without nozzles (ϕ1/ϕ2 =  (a-1) 0 deg/0 deg, (b-1) 30 deg/30 deg, (c-1) 60 deg/60 deg, and (d-1) 90 deg/90 deg); with nozzles (ϕ1/ϕ2 =  (a-2) 0 deg/0 deg, (b-2) 30 deg/30 deg, (c-3) 60 deg/60 deg, and (d-2) 90 deg/90 deg)

Fig. 4

Curvilinear coordinates for the periodically-curved pipe

Fig. 5

Contour plots of (a) u*, and (b) v* at x = 60 of the periodically-curved pipe (Re = 1000) and contour plots of (c) Dr*, and (d) Dθ* based on the straight pipe velocity field. Here, CV implies “convex (inner) side,” CC is the “concave (outer) side.”

Fig. 6

The sketch of a curved pipe with a 90 deg bend. Here, CV implies “convex (inner) side,” CC is the “concave (outer) side,” (xc,yc) denotes the curvature center, and R is the radius of curvature.

Fig. 7

Longitudinal distribution of static pressure at the convex (θ = −90 deg), concave (θ = 90 deg), and bottom (θ = 0 deg) regions of the 90 deg bend (Re = 60,000)

Fig. 8

Fully developed normalized velocity profile at the pipe inlet

Fig. 16

Radial distribution of U* in the 0 deg/0 deg pipe without (squares) and with (triangles) a nozzle at the following 3 locations along the pipe: (a) s = 0-, (b) s = 4.032, and (c) s = 8.3375

Fig. 15

Radial distribution of U* in the 90 deg/90 deg pipe

Fig. 14

Radial distribution of U* in the 60 deg/60 deg pipe

Fig. 13

Radial distribution of U* in the 30 deg/30 deg pipe

Fig. 12

Radial distribution of the U* in the 0 deg/0 deg pipe

Fig. 11

The horizontal distribution of the turbulence intensity at the exit plane. The subscripts “nzl” and “nnzl” denote the presence or absence of a nozzle at the pipe exit.

Fig. 9

Momentum thickness distribution at the exit plane of the pipes with half-bend angles of: (a) 0 deg/0 deg, (b) 30 deg/30 deg, (c) 60 deg/60 deg, and (d) 90 deg/90 deg. These pipes have nozzles and θ = 180 deg, 0 deg correspond to the convex and concave sides of the pipes, respectively.

Fig. 10

Momentum thickness distribution at the exit plane of the pipes with half-bend angles of: (a) 0 deg/0 deg, (b) 30 deg/30 deg, (c) 60 deg/60 deg, and (d) 90 deg/90 deg. These pipes have nozzles and θ = 180 deg, 0 deg correspond to the convex and concave sides of the pipes, respectively.

Fig. 17

Radial distribution of U* in the 30 deg/30 deg pipe without (squares) and with (triangles) a nozzle at the following five locations along the pipe: (a) s = 0-, (b) ϕ1 = 30 deg, (c) ϕ2 = 30 deg, (d) s = 4.032, and (e) s = 8.3375

Fig. 18

Radial distribution of U* between the 60 deg/60 deg pipe without (squares) and with (triangles) a nozzle at the following five locations along the pipe: (a) s = 0-, (b) ϕ1 = 60 deg, (c) ϕ2 = 60 deg, (d) s = 4.032, and (e) s = 8.3375

Fig. 19

Radial distribution of U* between the 90 deg/90 deg pipe without (squares) and with (triangles) a nozzle at the following five locations along the pipe: (a) s = 0-, (b) ϕ1 = 30 deg, (c) ϕ1 = 60 deg, (d) ϕ1 = 90 deg, and (e) ϕ2 = 0 deg

Fig. 20

Radial distribution of U* between the 90 deg/90 deg pipe without (squares) and with (triangles) a nozzle at the following four locations along the pipe: (f) ϕ2 = 30 deg, (g) ϕ2 = 90 deg, (h) s = 4.032, and (i) s = 8.3375

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections