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VMFL001: Flow Between Rotating and Stationary Concentric Cylinders
Overview
F. M.White,“Viscous Fluid Flow”, McGraw-Hill Book Co., Inc., New York, NY,
1991, Section 3-2.3.
Reference
FLUENT, CFXSolver
Laminar flow, rotating wallPhysics/Models
rot_conc_cyl.cas for FLUENT
rotating_cylinder.def for CFX
Input Files
Test Case
Steady laminar flow between two concentric cylinders is modeled. The flow is induced by rotation of the
inner cylinder with a constant angular velocity, while the outer cylinder is held stationary. Due to periodicity
only a section of the domain needs to be modeled. In the present simulation a 180° segment (half of the
domain shown in Figure 1 (p. 5)) is modeled. The sketch is not to scale.
Figure 1 Flow Domain
Boundary ConditionsGeometryMaterial Properties
Angular velocity of the inner wall = 1
rad/s
Radius of the Inner Cylinder = 17.8
mmDensity = 1 kg/m
3
Viscosity = 0.002 kg/m-sRadius of the outer Cylinder = 46.8
mm
Analysis Assumptions and Modeling Notes
The flow is steady. The tangential velocity at various sections can be calculated using analytical equations
for laminar flow. These values are used for comparison with simulation results.
5Release 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information
of ANSYS, Inc. and its subsidiaries and affiliates.
Results Comparison for FLUENT
Table 1 Comparison of Tangential Velocity in the Annulus at Various Radial Locations
RatioFLUENT, m/sTarget Calculation, m/sTangential Velocity at
0.9990.015120.01514r = 20 mm
0.9960.010550.01059r = 25 mm
0.9900.007200.00727r = 30 mm
0.9790.004560.00466r = 35 mm
Results Comparison for CFX
Table 2 Comparison of Tangential Velocity in the Annulus at Various Radial Locations
RatioCFX, m/sTarget Calculation, m/sLocation
0.9910.01500.015139r = 20 mm
0.9980.010530.010589r = 25 mm
0.9880.0071880.007274r = 30 mm
0.9760.0045510.004664r = 35mm
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VMFL001
VMFL002: Laminar Flow Through a Pipe with Uniform Heat Flux
Overview
Reference 1. F. M. White, Fluid Mechanics, McGraw-Hill Book Co., Inc., New York,
NY, 1979
2. F. P. Incropera, D. P. DeWitt, Fundamentals of Heat Transfer, John Wiley
& Sons, 1981
FLUENTSolver
Laminar flow with heat transferPhysics/Models
laminar-pipe-hotflow.casInput File
Test Case
Laminar flow of Mercury through a circular pipe is modeled, with uniform heat flux across the wall. A fully
developed laminar velocity profile is prescribed at the inlet. The resulting pressure drop and exit temperature
are compared with analytical calculations for Laminar flow. Only half of the 2–D domain is modeled due to
symmetry.
Figure 1 Flow Domain
Boundary ConditionsGeometryMaterial Properties
Fully developed velocity profile at inlet.
Inlet temperature = 300 K
Length of the pipe = 0.1 m
Radius of the pipe = 0.0025 m
Fluid: Mercury
• Density = 13529 kg/m3
Heat Flux across wall = 5000 W/m2• Viscosity = 0.001523
kg/m-s
• Specific Heat = 139.3
J/kg-K
• Thermal Conductivity =
8.54 W/m-K
Analysis Assumptions and Modeling Notes
The flow is steady and incompressible. Pressure drop can be calculated from the theoretical expression for
laminar flow given in Ref. 1. Correlations for temperature calculations are given in Ref. 2.
7Release 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information
of ANSYS, Inc. and its subsidiaries and affiliates.
Results Comparison
Table 1 Comparison of Pressure Drop and Outlet Temperature
RatioFLUENTTarget Calculation
1.0010.9990 Pa0.9976 PaPressure Drop
1.000340.56 K340.39 KCenterline Temperature
at the Outlet
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VMFL002
VMFL003: Pressure Drop in Turbulent Flow through a Pipe
Overview
R. C. Binder, Fluid Mechanics, 3rd Edition, 3rd Printing, Prentice-Hall, Inc.,
Englewood Cliffs, NJ, 1956, pg. 118, article 8-6.
Reference
FLUENTSolver
Turbulent flow, standard k-ε ModelPhysics/Models
turb_pipe_flow.casInput File
Test Case
Air flows through a horizontal pipe with smooth walls. The flow Reynolds number is 1.37 X 104. Only half
of the axisymmetrical domain is modeled.
Figure 1 Flow Domain
The figure is not to scale.
Boundary ConditionsGeometryMaterial Properties
Inlet velocity = 50 m/sLength of the pipe = 2 mDensity = 1.225 kg/m3
Outlet pressure = 0 PaRadius of the pipe =
Analysis Assumptions and Modeling Notes
The flow is steady. Pressure drop can be calculated from analytical formula using friction factor f which can
be determined for the given Reynolds number from Moody chart. The calculated pressure drop is compared
with the simulation results (pressure difference between inlet and outlet).
Results Comparison
Table 1 Comparison of Pressure Drop in the Pipe
RatioFLUENTTarget Calculation
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of ANSYS, Inc. and its subsidiaries and affiliates.
Viscosity = 1.7883 e-5 kg/m-s0.002 m
1.00021480 Pa21489 PaPressure Drop
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VMFL003
VMFL004: Plain Couette Flow with Pressure Gradient
Overview
“Fundamentals of Fluid Mechanics” (5th Edition), Munon,Young, OkiishiReference
FLUENT, CFXSolver
Laminar flow, moving wall, periodic boundariesPhysics/Models
couette_flow.cas for FLUENT
Couette_Flow.def for CFX
Input Files
Test Case
Viscous flow between two parallel plates is modeled. The top plate moves with a uniform velocity while the
lower plate is fixed. A pressure gradient is imposed in a direction parallel to the plates.
Figure 1 Flow Domain
Boundary ConditionsGeometryMaterial Properties
Velocity of the moving wall = 3 m/s
in X-direction
Length of the domain = 1.5 m
Width of the domain = 1 m
Density = 1 kg/m3
Viscosity = 1 kg/m-sFor FLUENT, pressure gradient across
periodic boundaries = 12 Pa/m
For CFX, pressure gradient across
periodic boundaries = 12 Pa/m
(pressure change = –18 Pa)
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of ANSYS, Inc. and its subsidiaries and affiliates.
Analysis Assumptions and Modeling Notes
The flow is steady and laminar. Periodic conditions with specified pressure drop are applied across the flux
boundaries.
Results Comparison for FLUENT
Figure 2 Comparison of X-Velocity (m/s) at a Section Where X = 0.75 m
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VMFL004
Results Comparison for CFX
Figure 3 Comparison of X-Velocity (m/s) at a Section Where X = 0.75 m
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of ANSYS, Inc. and its subsidiaries and affiliates.
VMFL004
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VMFL005: Poiseuille Flow in a Pipe
Overview
S.W.Yuan, Foundations of Fluid Mechanics, Prentice-Hall of India Private Limited, 1976,
sec. 8.36.
Reference
FLUENTSolver
Steady laminar flowPhysics/Models
poiseuille-flow.casInput File
Test Case
Fully developed laminar flow in a circular tube is modeled. Reynolds number based on the tube diameter
is 500. Only half of the axisymmetric domain is modeled.
Figure 1 Flow Domain
Boundary ConditionsGeometryMaterial Properties
Fully developed laminar velocity profile
at inlet with an average velocity of 2.15
m/s
Length of the pipe = 0.1 m
Radius of the pipe = 0.00125
m
Density = 1 kg/m3
Viscosity = 1e-5 kg/m-s
Analysis Assumptions and Modeling Notes
The flow is steady. A fully developed laminar velocity profile is prescribed at the inlet. Hagen-Poiseuille
equation is used to determine the pressure drop analytically.
Results Comparison
Table 1 Comparison of Pressure Drop in the Pipe
RatioFLUENTTarget Calculation
0.99810.22 Pa10. 24 PaPressure Drop
15Release 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information
of ANSYS, Inc. and its subsidiaries and affiliates.
Release 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.16