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Research Papers: Flows in Complex Systems

# Computational Investigation of Torque on Coaxial Rotating Cones

[+] Author and Article Information
Steve Rapley, Kathy Simmons

University Technology Centre for Gas Turbine Transmission Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

Carol Eastwick

University Technology Centre for Gas Turbine Transmission Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdomcarol.eastwick@nottingham.ac.uk

A “right” cylinder is one where the angle between the sides of the cylinder is $90deg$, a right angle.

J. Fluids Eng 130(6), 061102 (Jun 06, 2008) (14 pages) doi:10.1115/1.2903518 History: Received April 16, 2007; Revised November 04, 2007; Published June 06, 2008

## Abstract

This article looks at a modification of Taylor–Couette flow, presenting a numerical investigation of the flow around a shrouded rotating cone, with and without throughflow, using the commercial computational fluid dynamics code FLUENT 6.2 and FLUENT 6.3 . The effects of varying the cone vertex angle and the gap width on the torque seen by the rotating cone are considered, as well as the effect of a forced throughflow. The performance of various turbulence models are considered, as well as the ability of common wall treatments/functions to capture the near-wall behavior. Close agreement is found between the numerical predictions and previous experimental work, carried out by Yamada and Ito (1979, “Frictional Resistance of Enclosed Rotating Cones With Superposed Throughflow  ,” ASME J. Fluids Eng., 101, pp. 259–264; 1975, “On the Frictional Resistance of Enclosed Rotating Cones (1st Report, Frictional Moment and Observation of Flow With a Smooth Surface)  ,” Bull. JSME, 18, pp. 1026–1034; 1976, “On the Frictional Resistance of Enclosed Rotating Cones (2nd Report, Effects of Surface Roughness)  ,” Bull. JSME, 19, pp. 943–950). Limitations in the models are considered, and comparisons between two-dimensional axisymmetric models and three-dimensional models are made, with the three-dimensional models showing greater accuracy. The work leads to a methodology for modeling similar flow conditions to Taylor–Couette.

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## Figures

Figure 1

Schematic of rotating cone geometry

Figure 2

Schematic diagram, showing a cross section of the model

Figure 3

Close up of mesh structure near cone vertex

Figure 4

Graph of rotating Reynolds number (Re) against moment coefficient (CM), for a vertex angle of ϕ=120deg, nondimensional gap width s=0.016, and no throughflow (Cq=0)

Figure 5

Graph of rotating Reynolds number (Re) against moment coefficient (CM), for a vertex angle of ϕ=90deg, nondimensional gap width s=0.008, and no throughflow (CQ=0)

Figure 6

Graph of rotating Reynolds number against moment coefficient, for a vertex angle of ϕ=90deg, nondimensional gap width s=0.016, and no throughflow (CQ=0)

Figure 7

Graph of moment coefficient (CM) against rotating Reynolds number (Re), for a vertex angle of ϕ=90deg, nondimensional gap width s=0.008 and nondimensional throughflow CQ=1500

Figure 8

Graph of moment coefficient (CM) against rotating Reynolds number (Re), for a vertex angle of ϕ=90deg, nondimensional gap width s=0.016, and nondimensional throughflow CQ=1500

Figure 9

Graph of moment coefficient (CM) against rotating Reynolds number (Re), for a vertex angle of ϕ=90deg, a nondimensional gap width of s=0.016, and a nondimensional throughflow of CQ=1500, showing the effect of using different turbulence models

Figure 10

Graph of moment coefficient (CM) against rotating Reynolds number (Re), for a vertex angle of ϕ=90deg, a nondimensional gap width of s=0.016, and a nondimensional throughflow of CQ=1500, showing the effect of using different turbulence models

Figure 11

Graph of percentage difference between standard and RNG k-ϵ turbulence models, for a vertex angle of ϕ=90deg, nondimensional gap width s=0.016, and nondimensional throughflow CQ=1500

Figure 12

Graph of moment coefficient (CM) against rotating Reynolds number (Re), to show the performance of the three-dimensional model (Mesh 6), for a vertex angle of ϕ=90deg, nondimensional gap width s=0.016, and nondimensional throughflow CQ=1500

Figure 13

Graph of rotating Reynolds number against percentage error, to show the performance of the three-dimensional model, relative to that of the two-dimensional model, using the RNG k-ϵ turbulence model, with standard wall function

Figure 14

Graph of rotating Reynolds number against percentage error, to show the performance of the three-dimensional model relative to that of the two-dimensional model, using the RNG k-ϵ turbulence model, with enhanced wall treatment

Figure 15

Graph of rotating Reynolds number against moment coefficient, to show the performance of the three-dimensional model

Figure 16

Streamlines, between the shroud and the cone, colored by velocity magnitude, to show vortex. Computed using Mesh 3, Ω=28rads−1, CQ=1500.

Figure 17

Figure 18

Graphs of velocity components against chordal length (along a chord situated in the middle of the annulus) for a variety of rotational speeds (rads−1)

Figure 19

Graph of moment coefficient (CM) against rotating Reynolds number (Re), for a vertex angle of ϕ=90deg and a nondimensional gap width s=0.016, for increasing nondimensional throughflow rates (CQ)

Figure 20

Graph of moment coefficient (CM) against rotating Reynolds number (Re), to show the effect of increasing vertex angle (ϕ) for a constant, nondimensional gap width (s=0.016)

Figure 21

Graph of moment coefficient (CM) against rotating Reynolds number (Re), to show the effect of increasing gap width (s), for a constant vertex angle (ϕ=90deg), and a constant, nondimensional throughflow (CQ=0)

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