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L6-1 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Modeling Rotating
Machinery using
ANSYS FLUENT
Customer Training Material
Lecture 6
滑移网格 Sliding Mesh Model
(SMM)
Modeling Rotating Machinery using ANSYS FLUENT
L6-2 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Outline
•滑移网格介绍
• N-S方程: 动网格形式
•设置要点 – 交接面Grid Interfaces
– 预览网格Mesh Preview
– 时间步Choosing a Time Step
•常见问题及求解策略
• Summary
• Appendix
Modeling Rotating Machinery using ANSYS FLUENT
L6-3 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Introduction
• 精确的瞬态求解方式:
– Potential interactions - flow unsteadiness due to pressure waves which propagate both upstream and downstream
– Wake interactions - flow unsteadiness due to wakes from upstream blade rows advecting downstream
– Shock interactions - for transonic/supersonic flows, unsteadiness due to shocks waves striking downstream blade row
• 弱交互可简化用 MRF and Mixing Plane
Modeling Rotating Machinery using ANSYS FLUENT
L6-4 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Illustration of Unsteady Interactions
wake interaction
shock interaction
potential interaction
stator rotor
Modeling Rotating Machinery using ANSYS FLUENT
L6-5 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material What is the Sliding Mesh Model?
•多个域
•非共节点interface
– interfaces must be surfaces of revolution about the
axis of rotation
– interfaces can be rotationally periodic, but adjacent
zones must have equal periodic angles
•绝对位移unsteady
– For each time step, the meshes are moved and the
fluxes at the sliding interfaces are recomputed
Modeling Rotating Machinery using ANSYS FLUENT
L6-6 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Navier-Stokes Equations: Moving Mesh Formulation
• In the sliding mesh (or moving mesh) formulation , the motions of
moving zones are tracked relative to the stationary frame
– No moving reference frames are attached to the computational
domain, which simplifies the flux transfers across the interfaces
• The motion of any point in the domain is given by a time rate of
change of the position vector ( )
– is also known as the grid speed
– Note that for rigid body rotation at constant speed
r
r
Urr
Modeling Rotating Machinery using ANSYS FLUENT
L6-7 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Moving Mesh Illustration
x
y
z
stationary
frame
axis of
rotation
Δt)(tr
Moving CFD domain
)(tr
Modeling Rotating Machinery using ANSYS FLUENT
L6-8 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Navier-Stokes Equations for a Moving Mesh (1)
gb Q
0)(
VF
VVpTkeUVdt
ed
FpVUVdt
Vd
UVdt
d
tt
b
(Continuity)
(Momentum)
(Energy)
Modeling Rotating Machinery using ANSYS FLUENT
L6-9 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pros and Cons of the Sliding Mesh Model
• Advantages
– 更精确结果
– 可用于多运动区域
– 交接面类型灵活
• Disadvantages
– 瞬态求解
– 时间长、数据多
Modeling Rotating Machinery using ANSYS FLUENT
L6-10 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Sliding Interfaces
• 交接面要求圆周
“warped” interfaces aligned
at initial time level...
…become misaligned at a
subsequent time level!
Modeling Rotating Machinery using ANSYS FLUENT
L6-11 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Sliding Mesh Setup [1]
• 瞬态项.
• interface zone pair.
• “Mesh Motion”选项. – Enter rotational speed, axis, etc. in
the same manner as SRF.
• 边界类似SRF, MRF models.
• 插值格式discretizations – 时间First order time discretization.
– 空间Second order spatial discretizations.
– 压力基PRESTO! for pressure-based solver pressure discretization.
Modeling Rotating Machinery using ANSYS FLUENT
L6-12 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Sliding Mesh Setup [2]
•设置Solution controls – 默认选项
•监控Monitors – 时间相关.
– 可以做FFT.
•时间步长和子步.
Modeling Rotating Machinery using ANSYS FLUENT
L6-13 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Sliding Mesh Preview
• Fluent provides a sliding mesh preview option for checking sliding mesh motion before beginning the calculation
• To use this facility:
– Specify the time step and number of time steps
– Click on Preview
• You can display the grid motion and optionally save hardcopy images of the grid motion for later animation
• NOTE: Save your initial case and data files prior to running Mesh Preview so you can start from your original mesh positions
Modeling Rotating Machinery using ANSYS FLUENT
L6-14 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Solving SMM Problems
• Choose appropriate time step and
Max Iterations Per Time step to
ensure good convergence with each
time step
• Advance the solution until the flow
becomes time-periodic (pressures,
velocities etc. oscillate with a
repeating time variation)
– Usually requires several
revolutions of the grid
• Good initial conditions can reduce
the number of time steps needed to
achieve time-periodicity
– You can use either an MRF or
mixing plane solution as an
initial condition
• Data Sampling for Time Statistics
can be enabled to have Fluent save
time-averaged flow field variables.
Modeling Rotating Machinery using ANSYS FLUENT
L6-15 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Time Periodic Flow
Flow unsteadiness becomes
periodic after initial transient
Modeling Rotating Machinery using ANSYS FLUENT
L6-16 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Choosing a Time Step for the SMM
• Recommended time step size is based on the principal
that the time step should be no larger than the time it
takes for a moving cell to advance past a stationary point
• An estimate for the time step can thus be calculated as:
movingV
st
s = mesh spacing at sliding interface
Vmoving = velocity of the moving zone
cells at time t cells at time t+t
moving mesh zone s
Modeling Rotating Machinery using ANSYS FLUENT
L6-17 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 常见问题及求解策略Troubleshooting
• 交接面位置问题
– interface网格质量尽量高
– 分解交接面(多个简单面)
• Some other things to consider for troublesome cases
– 网格质量要求 (max cell skewness < 0.9 – 0.95)
• 双精度(网格高长宽比)
– MRF初始化
– 减小松弛因子或 Courant numbers
– 减小时间步或增大迭代步
Modeling Rotating Machinery using ANSYS FLUENT
L6-18 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 快速设置Accelerating Sliding Mesh Cases
•旋转参数设置moving mesh parameters.
– Rotational axes, velocity
– Translational velocity
•扩展设置 profile file or UDF. – The Zone Motion Function
can be employed to permit
all inputs to be defined in a
single UDF function.
Modeling Rotating Machinery using ANSYS FLUENT
L6-19 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Example: Flapping Airfoil
Oscillating inner zone
Stationary outer zone
Modeling Rotating Machinery using ANSYS FLUENT
L6-20 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Flapping Airfoil UDF
• UDF uses the TRANSIENT
_PROFILE macro to
prescribe the sinusoidal
oscillation of the domain.
/**********************************************/
/* flap.c */
/* UDF for specifying a time-varying omega */
/* */
/* Simulates +/- 8 deg flapping with cycle of */
/* of 1 sec. */
/* */
/* Version 13.0 */
/* */
/**********************************************/
#include "udf.h"
#define PI 3.141592654
DEFINE_TRANSIENT_PROFILE(speed, time)
{
real ampl = 2.0*PI/15.0;
real freq = 2.*PI;
real omega;
omega = 2.0*PI*ampl*cos(freq*time);
return omega;
}
Modeling Rotating Machinery using ANSYS FLUENT
L6-21 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Flapping Airfoil Animation
Velocity magnitude contours
Modeling Rotating Machinery using ANSYS FLUENT
L6-22 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Summary
• 真实更精确的仿真方式(包含动静域)
– 交接面位置非稳态模拟
• 计算时间长
• 设置与MRF类似
– MRF作为初步计算
• 预览网格特征The mesh preview option allows you the check the mesh motion prior to run the calculation
• Accelerating reference frames can also be handled using sliding mesh – See Appendix B for mode details.
Modeling Rotating Machinery using ANSYS FLUENT
L6-23 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Appendix A: Sliding Mesh Examples
•2-D turbine stage
•2-D blower
•1.5 stage research turbine (ERCOFTAC U1)
Modeling Rotating Machinery using ANSYS FLUENT
L6-24 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Turbine Stage
• 2-D subsonic turbine stage test case
• Planar geometry simulates midspan stream surface
• Equal blade counts for stator and rotor
• Motion of rotor modeled using linear y-velocity (29.445
m/s)
• Boundary conditions
– Stage Inlet
• Ptotal = 1 atm, Ttotal = 300 K, TU = 5%
– Stage Exit
• Pstatic = 0.963 atm
Modeling Rotating Machinery using ANSYS FLUENT
L6-25 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Turbine Stage (2)
• Numerical model
– Coupled-implicit solver, steady-state, compressible flow (air)
– mesh (total): 7917 tri cells
– Realizable k-e turbulence model
• Two cases examined
– Mixing plane model (with mass conserving mixing plane)
– Sliding mesh model
• MPM results used as initial condition for SMM
Modeling Rotating Machinery using ANSYS FLUENT
L6-26 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Turbine Stage: Mesh
Modeling Rotating Machinery using ANSYS FLUENT
L6-27 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pressure Contours - Mixing Plane Solution
Modeling Rotating Machinery using ANSYS FLUENT
L6-28 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Mach No. Contours - Mixing Plane Solution
Modeling Rotating Machinery using ANSYS FLUENT
L6-29 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Stator Pressure Distribution Comparison
Modeling Rotating Machinery using ANSYS FLUENT
L6-30 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Rotor Pressure Distribution Comparison
Modeling Rotating Machinery using ANSYS FLUENT
L6-31 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Blower
• Simple 2-D model of a squirrel cage blower (44 blades)
• Pressure boundaries (inlet total pressure = 200 Pa), 2500
rpm
• Numerical Model
– Segregated solver, incompressible flow (air)
– Standard k-e turbulence model (TU = 5% at inlet)
– MRF solution computed first - used as initial condition for SMM
– time step = 0.0001333 sec (corresponds to 2 deg rotation of the
wheel)
– Calculation carried out for 10 revolutions
– Time averaged solution computed for one revolution
Modeling Rotating Machinery using ANSYS FLUENT
L6-32 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Blower: Grid
interfaces
inlet
outlet
Modeling Rotating Machinery using ANSYS FLUENT
L6-33 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Blower: Unsteady Total Pressure
time-periodic solution achieved
Modeling Rotating Machinery using ANSYS FLUENT
L6-34 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Blower - Static Pressure
MRF Solution SMM Solution
(time-averaged)
Modeling Rotating Machinery using ANSYS FLUENT
L6-35 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 2-D Blower Results
• MRF results show reasonable agreement with SMM for this
operating condition
• Other operating conditions may show larger discrepancies -
e.g. lower flowrates, where unsteadiness due to
separation/stall become more significant
Total Pressure
Rise (Pa)
Outlet Normal
Velocity (m/s)
MRF 532.0 23.8
SMM* 491.3 24.6
Error (%) 8.3 3.3
* time-averaged results
Modeling Rotating Machinery using ANSYS FLUENT
L6-36 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 1.5 Stage Research Turbine (1)
• Three blade row (stator-rotor-stator) turbine stage
– 36 stator blades, 41 rotor blades
• Rotor geometry modified to 40 blades to permit periodic
boundaries (9 stator blades, 10 rotor blades)
– Design conditions: speed = 3500 rpm, flowrate = 8.0
kg/s
• Numerical model
– Coupled solver, compressible flow (air), SMM
– 50 subiterations per time step, 4.3 time steps per
passing period
– tet mesh - 882,000 cells
– Spalart-Allmaras turbulence model
Modeling Rotating Machinery using ANSYS FLUENT
L6-37 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 1.5 Stage Research Turbine (2)
• Results
– Unsteady data time-averaged for comparison with
experiments
– Computed flowrate = 8.04 kg/s - agrees very well with
data
– Pitch-averaged profiles extracted from time-averaged
flowfield at
• 8.8 mm downstream of trailing edge of first stator blade row
(plane 1)
• 8.8 mm downstream of trailing edge of rotor blade row (plane 2)
• 8.8 mm downstream of trailing edge of second stator blade row
(plane 3)
– Profiles show good overall agreement with data
Modeling Rotating Machinery using ANSYS FLUENT
L6-38 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material 1.5 Stage Turbine: Geometry
Modeling Rotating Machinery using ANSYS FLUENT
L6-39 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Surface Pressure Coefficient Contours
Modeling Rotating Machinery using ANSYS FLUENT
L6-40 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pitch-Averaged Yaw Angles (1)
Yaw angle at plane 1
0
5
10
15
20
25
30
0.24 0.25 0.26 0.27 0.28 0.29 0.3
Radial position (m)
Yan
gle
Experiment
CFD
Modeling Rotating Machinery using ANSYS FLUENT
L6-41 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pitch-Averaged Yaw Angles (2)
Yaw angle comparisons at plane 2
60
65
70
75
80
85
90
95
0.24 0.25 0.26 0.27 0.28 0.29 0.3
Radial position (m)
Yaw
an
gle
CFD
Experiment
Modeling Rotating Machinery using ANSYS FLUENT
L6-42 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pitch-Averaged Yaw Angles (2)
Yaw angle at plane 3
0
5
10
15
20
25
30
35
0.24 0.25 0.26 0.27 0.28 0.29 0.3
Radial position (m)
Yaw
an
gle
CFD
Experiment
Modeling Rotating Machinery using ANSYS FLUENT
L6-43 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pitch-Averaged Mach Number Profiles (1)
Mach number comparison at plane 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.24 0.25 0.26 0.27 0.28 0.29 0.3
Radial position (m)
Mach
nu
mb
er
CFD
Experiment
Modeling Rotating Machinery using ANSYS FLUENT
L6-44 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pitch-Averaged Mach Number Profiles (2)
Mach number comparison at plane 2
0
0.05
0.1
0.15
0.2
0.25
0.24 0.25 0.26 0.27 0.28 0.29 0.3
Radial position (m)
Mach
nu
mb
er
CFD
Experiment
Modeling Rotating Machinery using ANSYS FLUENT
L6-45 ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved. Release 13.0
December 2010
Customer Training Material Pitch-Averaged Mach Number Profiles (2)
Mach number comparison at plane 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.24 0.25 0.26 0.27 0.28 0.29 0.3
Radial position (m)
Mach
nu
mb
er
CFD
Experiment