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                Tich Thien TRUONG, Eng. Duy Khuong NGUYEN, Eng. Thanh Nha NGUYEN
                      Department of Engineering Mechanics, Faculty of Applied Science
                                    University of Technology, NU-HCM

                                                            pressure are used for blades design and optimization
A turbomachine is a device in which energy transfer
                                                            The turbomachine as described above covers a wide
occurs between a flowing fluid and a rotating element
                                                            range of machines, such as gas turbines, steam turbines,
due to dynamic action, and results in a change in
                                                            centrifugal pumps, centrifugal and axial flow
pressure and momentum of the fluid. Mechanical
                                                            compressors, windmills, water wheels, and hydraulic
energy transfer occurs inside or outside of the
                                                            turbines. Basing on this simulation method,
turbomachine, usually in a steady-flow process.
                                                            turbomachine applications can be analyzed and applied
Turbomachines include all those machines that produce
                                                            for design optimization.
power, such as turbines, as well as those types that
produce a head or pressure, such as centrifugal pumps
and compressors. The turbomachine extracts energy
from or imparts energy to a continuously moving             2. Description
stream of fluid. However in a positive displacement         2.1. Turbomachines Introduction
machine, it is intermittent.
                                                            There are different types of turbomachines. They can be
The turbomachine as described above covers a wide           classified as:
range of machines, such as gas turbines, steam turbines,
centrifugal pumps, centrifugal and axial flow               • Turbomachines in which (i) work is done by the fluid
compressors, windmills, water wheels, and hydraulic           and (ii) work is done on the fluid.
turbines. In this text, we shall deal with incompressible   • Turbomachines in which fluid moves through the
and compressible fluid flow machines.                         rotating member in axial direction with no radial
In turbomachine problems (that its part rotates with          movement of the streamlines. Such machines are
high velocity in fluid domain), pressure, force values of     called axial flow machines whereas if the flow is
fluid flow on blades are so important for design. When        essentially radial, it is called a radial flow or
designers have a model of turbine blade, they want to         centrifugal flow machine. Some of these machines
know how it will work, specially the moment and               are shown in Fig. 1.1. Two primary points will be
propulsive force values supplied by it in fluid               observed: first, that the main element is a rotor or
environment. More, they also want to learn the                runner carrying blades or vanes; and secondly, that
behaviour of these turbine blades in fluid for their          the path of the fluid in the rotor may be substantially
optimal design. Normally, engineers often do many             axial, substantially radial, or in some cases a
experiments with some blade models for testing.               combination of both. Turbomachines can further be
Nowadays, with the development of numerical methods           classified as follows:
and digital computer, we can simulate this kind of              o    Turbines: Machines that produce power by
problem so fast and comfortably.                                     expansion of a continuously flowing fluid to a
                                                                     lower pressure or head.
KEY WORDS                                                       o    Pumps: Machines that increase the pressure or
                                                                     head of flowing fluid.
Propeller, turbomachine, fan, pump, turbine.
                                                                o    Fans: Machines that impart only a small
                                                                     pressure-rise to a continuously flowing gas;
BODY TEXT                                                            usually the gas may be considered to be
1. Introduction
                                                                o    Compressors: Machines that impart kinetic
In this paper, we want to present a problem that                     energy to a gas by compressing it and then
simulates the behaviour of a propeller in fluid                      allowing it to rapidly expand. Compressors can
environment. For this purpose, finite element method                 be axial flow, centrifugal, or a combination of
(FEM) be used to analyse. With ANSYS/CFX software,                   both types, in order to produce the highly
the results obtained such as velocities, forces, moments,            compressed air. In a dynamic compressor, this
                                                                     is achieved by imparting kinetic energy to the
         air in the impeller and then this kinetic energy      Newton’s Second Law states that the sum of all the
         is converted into pressure energy in the              forces acting on a control volume in a particular
         diffuser.                                             direction is equal to the rate of change of momentum of
                                                               the fluid across the control volume. For a control
                                                               volume with fluid entering with uniform velocity C1
                                                               and leaving with uniform velocity C2, then

                                                               ∑ F = m (C
                                                                     &      2   − C1 )

                                                               •      NAVIER-STOCKES EQUATION

                                                                      1 ∂p 1 ∂ ⎡ ⎛ ∂ui ∂uk               ⎞ ⎤ 2 1 ∂ ⎡ ∂u j ⎤
                                                               Fi −        +      ⎢μ     +               ⎟⎥ −        ⎢μ       ⎥
                                                                      ρ ∂xi ρ ∂xk ⎣ ⎜ ∂xk ∂xi
                                                                                     ⎝                   ⎠ ⎦ 3 ρ ∂xi ⎢ ∂x j ⎥
                                                                                                                     ⎣        ⎦
                                                                                                               ∂ui   ∂
                                                                                                             =     +    ( ui uk )
                                                                                                               ∂t ∂xk

                                                               Where u is velocity
                      Figure 1. Turbomachines

2.2. Fundamental equations for dynamics fluid                  2.3. Procedure for                   solving         turbomachinery
problem                                                        simulation problems
•   CONTINUITY EQUATION                                        To perform turbomachinery simulation problems,
For steady flow through a turbomachine, m remains              engineer has to prepare files of rotor and stator model
constant. If A1 and A2 are the flow areas at secs. 1 and 2     designed in some CAD softwares. Because this is a
along a passage respectively, then                             periodic model, a sector of rotor and stator can be used
                                                               for full model computation for time saving.
m = ρ1 A1C1 = ρ 2 A2C2 = constant

where ρ1 , is the density at section 1, ρ 2 , the density at
section 2, C1, the velocity at section 1, and C2, is the
velocity at section 2.
According to the First Law of Thermodynamics, if a
system is taken through a complete cycle during which
heat is supplied and work is done, then

∫ (δ Q − δ W ) = 0
        ∫ δQ    represents the heat supplied to the system                               Figure 2. Periodic model

during this cycle and
                              ∫ δW     the work done by the
                                                               These files are imported into ANSYS CFX-Mesh
system during the cycle. The units of heat and work are        program. After meshing, finite element models are
taken to be the same. During a change of state from 1 to       transferred to CFX-Pre (Turbo Mode).
2, there is a change in the internal energy of the system
                                                               • Set up parameters for analysis.
U 2 − U1 = ∫ δ Q − δ W                                                o   Rotate axial

For an infinitesimal change of state                                  o   Angular velocity for rotor
dU = δ Q − δ W                                                        o   Physics parameters for environment.

•   THE STEADY FLOW ENERGY EQUATION                            • Define interface.
The energy equation at the inlet and outlet of any device             o   Connect the two meshes (stator and rotor)
may be written                                                            together.

                    m(C2 − C12 )
                       2                                              o   Specify the periodic interfaces on the stator
Q1−2 = U 2 − U1 +                + mg ( Z 2 − Z1 ) + W1−2                 and rotor.
NEWTON’S SECOND LAW OF MOTION                                  • Applied boundary conditions.
                                                               • Set solver parameters
    o     Determine convergence control parameter.
• Start the solver (CFX-Solver) with one of these
  solving mode:
    o     Serial Mode
    o     Local Parallel Mode
    o     Distributed Parallel Mode
• View results (CFX-Post).

2.4. A simulation example
A propeller works in water with an angular velocity
about 3000 RPM. Determine the pressure distribution
on propeller, velocity distribution of water, total axial                    Figure 2. Pressure Distribution
force on propeller...
Solution summary:

                        Rotor           Stator     Total
                       domain           domain    domain

   Number of           687375           109990    797365

Solution time: 90 minutes (Local Parallel Mode)

                                                                    Figure 5. Velocity streamline Result Distribution

                                                                             Figure 6. Velocity vector result
                    Figure 3. Propeller model
                                                            With results exported from CFX-Post, we can calculate
                                                            the total moment and propulsive force values.
                                                            Results table:

                                                                       Sum of Fx (N)               6.11e4

                                                                       Sum of Mx (Nm)              1.442e3

                                                            3. Conclusion
                                                            Because of limit working conditions, these results in
                      Figure 4. FEM model                   this paper can not be verified by experiments. However,
                                                            the demo problem in this paper can severed as useful
                                                            information for engineers who are interest in
turbomachine problem. The simulation in fluid dynamic
problem can be performed so quickly and exactly by
using finite element method. Results of axial force and
total moment are so useful for boat design problem.
Nowadays, this simulation method gradually becomes a
powerful tool that helps designer and producer save
much time and money for performing experiments.

4. Acknowledgements
The authors are grateful for the support provided by
Department of Engineering Mechanics, Faculty of
Applied Sciences, Ho Chi Minh city University of
Technology. Thank the Faculty of Applied Sciences for
this conference and congratulate to the 5th year of
faculty’s foundation.

5. References
[1] Department of Fluid Mechanics, Fluid Mechanics
Lecture (HCM City University of Technology).
[2] Rama S. R. Gorla, Aijaz A. Khan, Turbomachinery
Design and Theory, (Marcel Dekker, Inc, 2003).
[3] ANSYS Inc, ANSYS-CFX                 Release    10
Documentation, Reference Guide.

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