V (m/s) V (m/s) Fluid Motion Between Rotating Concentric Cylinders Using COMSOL Multiphysics® K. Barman, S. Mothupally, A. Sonejee and P. L. Mills Department of Chemical and Natural Gas Engineering Texas A&M University - Kingsville, Kingsville, TX, USA Introduction Flow in annular regions occur in many practical applications, such as: • Production of oil and gases • Centrifugal separation process • Fluid viscometers • Electrochemical cells • Tribology Understanding the flow behavior in annular regions whose outer wall is stationary while inner wall rotates is important for interpretation of data & system modeling. Objectives Develop solutions to the fluid momentum transport equations for annular laminar flows of a Newtonian fluid in a 3-D control volume where the outer wall is stationary and the inner wall is rotating with an angular velocity Ω. Results Conclusions • The 3-D model captures the variation of velocity in the entry and exit regions, which is not the case for the 1-D model. • The pressure gradient increases with increasing Ω. • A foundation has been established for extension to non-Newtonian fluids, e.g. drilling muds and other fluids. References 1. R. B. Bird and C. F. Curtiss. Tangential Newtonian flow in annuli-I. Chem. Eng. Sci. (1959)11, pp.108-113. 2. R. B. Bird et al., Transport Phenomena, 2 nd Edn., Wiley, New York (2006) Effect of Cylinder Inner Radius (R i ) on Fluid Velocity Profiles Velocity Profiles in the Annulus at Various Rotational Speeds 0.035 0.028 0.025 0.023 0.02 Ω = 555 rpm 5 rpm t = 0.5 to 5 s (overlapping) Parameter: t Parameter: Ω Parameter: R i Figure 2. Transparent Geometry of Concentric Rotating Cylinder. Figure 1. Rotating Concentric Cylinder. Model Equations 1-D Equations 3-D Equations =0 + . = − + + + − 2 =− . =0 1 =0 − − =0 Figure 4. Pressure Profiles COMSOL CFD Module Meshed Geometry Fluid Pressure Profiles t = 5 s t = 5 s 555 rpm Figure 5: Velocity Profiles Figure 3. Meshed Geometry Here = for 1-D and = , , for 3-D. the parameters varied include Ω, μ, and R i . Ω=55 rpm, t= 5 s Ω=555 rpm, t= 5 s V (m/s) V (m/s) Radius, r (m) Radius, r (m) t = 0 s 0.035 0.028 0.025 0.023 0.02 Radius, r (m) Radius, r (m) Parameter: R i Height at which these readings were recorded in the annular region (0.05 m) Figure 6: Reynolds Number Developing Velocity Profiles During Cylinder Startup Velocity Profiles and Reynolds Number Ω=555 rpm, t= 5 s Ω=555 rpm, t= 5 s Ω=555 rpm, t= 5 s 0.038 0.038 Excerpt from the Proceedings of the 2015 COMSOL Conference in Boston
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V (
m/s
)
V (
m/s
)
Fluid Motion Between Rotating Concentric Cylinders
Using COMSOL Multiphysics® K. Barman, S. Mothupally, A. Sonejee and P. L. Mills
Department of Chemical and Natural Gas Engineering
Texas A&M University - Kingsville, Kingsville, TX, USA
Introduction Flow in annular regions occur in many practical applications,
such as:
• Production of oil and gases
• Centrifugal separation process
• Fluid viscometers
• Electrochemical cells
• Tribology
Understanding the flow behavior in
annular regions whose outer wall is stationary while inner wall
rotates is important for interpretation of data & system modeling.
Objectives Develop solutions to the fluid momentum transport equations for
annular laminar flows of a Newtonian fluid in a 3-D control
volume where the outer wall is stationary and the inner wall is
rotating with an angular velocity Ω.
Results
Conclusions • The 3-D model captures the variation of velocity in the entry
and exit regions, which is not the case for the 1-D model.
• The pressure gradient increases with increasing Ω.
• A foundation has been established for extension to
non-Newtonian fluids, e.g. drilling muds and other fluids.
References 1. R. B. Bird and C. F. Curtiss. Tangential Newtonian flow in
annuli-I. Chem. Eng. Sci. (1959)11, pp.108-113.
2. R. B. Bird et al., Transport Phenomena, 2nd Edn., Wiley, New
York (2006)
Effect of Cylinder Inner Radius (Ri) on Fluid Velocity Profiles
Velocity Profiles in the Annulus
at Various Rotational Speeds
0.035 0.028 0.025 0.023 0.02
Ω = 555 rpm
5 rpm
t = 0.5 to 5 s
(overlapping)
Parameter: t Parameter: Ω
Parameter: Ri
Figure 2. Transparent Geometry of
Concentric Rotating Cylinder.
Figure 1. Rotating Concentric Cylinder.
Model Equations
1-D Equations 3-D Equations
𝜕 𝜈𝜃
𝜕𝜃= 0 𝜌
𝜕𝜈
𝜕𝑡+ 𝜌 𝜈. 𝛻 𝜈 = 𝛻 −𝑝 + 𝜇 𝛻𝜈 + 𝛻𝜈 𝑇 + 𝐹
−𝜌𝜈𝜃2
𝑟= −
𝜕𝑝
𝜕𝑟 𝜌. 𝛻 𝑢 = 0
𝜕
𝜕𝑟
1
𝑟
𝜕 𝑟𝜈𝜃
𝜕𝑟= 0
−𝜕𝑝
𝜕𝑧− 𝜌𝑔𝑧 = 0
Figure 4. Pressure Profiles
COMSOL CFD Module
Meshed Geometry Fluid Pressure Profiles
t = 5 s
t = 5 s
555 rpm
Figure 5: Velocity Profiles
Figure 3. Meshed Geometry
Here 𝜈𝜃 = 𝜈𝜃 𝑟 for 1-D and 𝜈𝜃 = 𝜈𝜃 , 𝜈𝑟 , 𝜈𝑧
for 3-D. the parameters varied include Ω, μ,
and Ri.
Ω=55 rpm, t= 5 s Ω=555 rpm, t= 5 s
V (
m/s
)
V (
m/s
)
Radius, r (m) Radius, r (m)
t = 0 s
0.035 0.028 0.025 0.023 0.02
Radius, r (m) Radius, r (m)
Parameter: Ri
Height at which these
readings were recorded
in the annular region
(0.05 m)
Figure 6: Reynolds Number
Developing Velocity Profiles
During Cylinder Startup
Velocity Profiles and Reynolds Number
Ω=555 rpm, t= 5 s Ω=555 rpm, t= 5 s Ω=555 rpm, t= 5 s
0.038 0.038
Excerpt from the Proceedings of the 2015 COMSOL Conference in Boston
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