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FLUID DYNAMIC SIMULATION FOR PROPELLER Tich Thien TRUONG, Eng. Duy Khuong NGUYEN, Eng. Thanh Nha NGUYEN Department of Engineering Mechanics, Faculty of Applied Science University of Technology, NU-HCM Email: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org pressure are used for blades design and optimization ABSTRACT work. 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 incompressible. 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. • THE FIRST LAW OF THERMODYNAMICS 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 where ∫ 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. 2 U 2 − U1 = ∫ δ Q − δ W o Rotate axial 1 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. 2 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 elements 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  Department of Fluid Mechanics, Fluid Mechanics Lecture (HCM City University of Technology).  Rama S. R. Gorla, Aijaz A. Khan, Turbomachinery Design and Theory, (Marcel Dekker, Inc, 2003).  ANSYS Inc, ANSYS-CFX Release 10 Documentation, Reference Guide.
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