CFD Computational Fluid Dynamics is a well-established method of modelling fluid flows and can cope with very complex fluid flows. The technique is widely used in the turbomachinery industry and skills in this area are in demand in industry. OpenFOAM is an open source CFD code, which means that it is available for anyone to use at no cost, subject to certain conditions. The advantages of using OpenFOAM as opposed to using conventional commercial codes are:
Customisation. The open source code means that the user can potentially customise the code for their own specific requirements.
Cost effectiveness. As OpenFOAM is free of charge it could offer a more effective way of computing complex flow, or quickly modelling many variations of a design. Commercial codes usually require a licensing fee per processor used, therefore to compute complex problems on many processors the cost would be high.
This projects aim is to investigate the usefulness of OpenFOAM for modelling turbomachinery flows at Queens University Belfast. The project will undertake modelling of an existing turbine geometry using OpenFOAM and the results will be compared by using the commercially available CFD code, ANSYS CFX. ANSYS CFX is currently used at Queens University Belfast to model turbomachinery flows. The project should also be able to act as a guide for future students who show an interest in CFD.
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1 Introduction 1
2 Technological Review 6
3 Development of System Model 9
Appendix A: Project Management 11
Wx Total shaft work (J/sec)
Mass flow rate (kg/s)
C Absolute velocity (m/s)
U Blade speed (m/s)
p pressure (Pa)
T Temperature (K)
V Relative Velocity (m/s)
Î± Absolute flow angle (deg)
Î² Relative flow angle (deg)
Î¸ Turning angle (deg)
h Specific enthalpy; height (j/kg K)
W Relative velocity; diffuser throat width (m/s)
Cm Axial Velocity (m/s)
0 stagnation condition
0, 1, 2.. Stations in the stage
CFD Computational Fluid Dynamics
CSA Cross-Sectional Area
1.1CFD; an overview
Traditional modelling in engineering is heavily based on empirical or semi-empirical models. These models often work very well for well-known unit operations, but are not reliable for new process conditions. Developing new processes and equipment can be expensive both in terms of time consumption and usage of man power. This is also the case when trying to take the step from the experimental stage to real life stage. In order to overcome this problem engineers are increasingly turning to Computational Fluid Dynamics, CFD. CFD is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyse problems that involve fluid flows. Design equations are in place but only for existing equipment and only for a limited range of process conditions. Therefore when there are no accurate predictions available, CFD simulations are run to obtain solutions to the problem. A big advantage of this is that the simulation can be repeated with changes to the parameters implemented so that an optimum solution can be found.
1.1.1 History of CFD
CFD is a tool that has only been developed recently, almost simultaneously with electronic digital computers. It has been in the past 40 years that it has made spectacular progress and several powerful computational methods have come up during this period, the most significant among them being the finite difference method, the finite element method and the finite volume method.
1.1.2 Mathematics of CFD
The fundamental basis of almost all CFD problems are the Navier-Stokes equations, (Andersson, 2001). These are the set of equations that describe the processes of momentum, heat and mass transfer. These partial differential equations have no known general analytical solution but can be discretized and solved numerically. Equations describing other processes, such as combustion, can be solved in conjunction with the Navier-Stokes equations. Often an approximating model is used to derive these additional equations e.g. a turbulence model.
1.1.3 Applications of CFD
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In the last several decades the dramatic growth of CFD has led it to becoming a widely applied technique in the engineering industry. Its techniques have been applied in a broad scale in the process industry to gain insight into various flow phenomena, examine different equipment designs or compare performance under different operating conditions. Presently, CFD is being increasingly employed by many industries either to reduce manufacturing design cycles or to provide an insight into existing technologies so that they may be analysed and improved, (Leeds 2012). CFD is used across many areas in industry including Aerospace; wing design, Automotive; internal combustion, Environmental; fire management, Mechanical; pumps, Sports Equipment; golf balls, Water; wave loading, Wind; wind loading and Turbomachinery; turbines.
Turbomachinery; an overview
A turbomachine is classed as a machine having the characteristic to transfer energy between a continuous stream of fluid and an element rotating about a fixed axis. Machines that fall in to this category would include pumps, compressors and turbines. Turbomachines are categorized by their flow path and function. These can include axial, centrifugal and radial. In all turbomachine cases the defining essential equation that must be understood is the Euler turbomachinery equation (Baines, 1997):
This relates the work delivered to the flow, , per unit mass flow rate , to the change in important velocities leaving at stage 2 (outlet) with respect to those entering at stage 1 (inlet). The flow gives a change in temperature and pressure. The work input in each type of turbomachine is affected differently. For example in an axial machine the work input is affected by changes in flow angle which in turn affects the pressure and temperature change. However in a radial machine the work input is also affected by changes in radii at the inlet and outlet which in turn affects the pressure and temperature change. In axial turbines the radii of the inlet and outlet are approximately constant therefore this has no effect on the work input.
A turbocharger is a forced induction device, driven by the engine's exhaust gas turbine, used to allow more power to be produced for an engine of a given size. In 1905 Swiss engineer Alfred Bchi received a patent for using a compressor driven by exhaust gases to force air into a diesel engine to increase power output. However it wasn't until 1924 that the first turbocharged engine was commercialised and back then the applications were applied to large ships and locomotives. The development of turbocharged automobile applications progressed slowly until in 1978 the first turbocharged diesel passenger car was produced. Today turbocharged engines are very common for automobile applications in any size range. Turbochargers have many other applications ranging from small motorcycle engines to large ship engines.
The function of an Axial Turbine
There are two basic types of turbine; radial flow and axial flow turbines. The vast majority of gas turbines employ the axial flow turbine and this project is going to focus solely on that type. The axial flow turbine is normally the more efficient of the two. The axial flow turbine consists of one or more stages located immediately to the rear of the engine combustion chamber. The turbine extracts kinetic energy from the expanding gases as the gases come from the burner, converting this kinetic energy into shaft power to drive the compressor and engine accessories. The gas, which is restricted by the turbine's flow cross-sectional area, results in a pressure and temperature drop between the inlet and outlet. This pressure drop is converted into the kinetic energy to drive the turbine wheel, (BorgWarner 2012). As the pressure drop between the inlet and outlet increases so does the turbine performance.
Axial Turbine Theory
A turbine converts the energy of a fluid into the energy of a rotating shaft. The connection is made clear by the first law of thermodynamics (Baines, 1997) in which the fluid internal energy is measured by the total enthalpy ho (where stage 1 refers to the inlet, stage 2 refers to the stator outlet/rotor inlet and stage 3 refers to the exit):
The actual mechanism for this transfer is, however, via an exchange of angular momentum across the rotor, expressed in the Euler turbomachinery equation. For an axial stage there is little or no change in radius therefore it is assumed that the blade speed is constant so the equation becomes:
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It can be seen that the work transfer is achieved by arranging the fluid to turn in the blade passage, thus changing the tangential component of the velocity appropriately, and usually by accelerating the fluid. This fact can be appreciated if this equation is fully developed using velocity triangles at the inlet and rotor stage. The resulting equation is:
This equation shows the need to maximize the rotor inlet velocity C2 by accelerating the fluid through the stator, minimize the exit velocity C3 by a suitable choice of velocity triangle and arrange the fluid to accelerate through the blade passage so that W3>W2. The turning is achieved by applying a suitable curvature to the turbine blades, and the expansion by arranging that the blade passages have a decreasing CSA in the direction of flow in order to accelerate fluid, (Baines 1997).
The preliminary analysis of a turbine stage proceeds from velocity triangles. Velocity triangles (Figure. 1) can be used to calculate the basic performance of a turbine stage. Gas enters the stationary turbine stator at absolute velocity C1 and angle Î±1 and accelerates to an absolute velocity C2 and angle Î±2. The rotor rotates at velocity U. Relative to the rotor, the velocity of the gas as it impinges on the rotor entrance is W2. The gas is turned by the rotor and exits, relative to the rotor, at velocity W3. However, in absolute terms the rotor exit velocity is C3, (Saravanamuttoo 2001). The velocity triangles are constructed using these various velocity vectors. Velocity triangles can be constructed at any section through the blading.
Figure 1. Velocity triangles for a turbine stage (courtesy of Saravanamuttoo, 2001)
Velocity triangles at rotor inlet and exit give:
The Euler turbomachinery equation is:
( (Eqn. 7)
This can be combined with Eqn. 5 to give:
( (Eqn. 8)
From these equations the important factors which influence the axial turbine design stage can be seen therefore it can be stated that maximizing the blade speed, U, increasing the axial velocity, Cm, and increasing the amount of turning, , will increase the specific work output (Baines, 1997 and Saravanamuttoo, 2001).
2.1 CFD Methodology
Before starting a new simulation for any application of CFD it is wise to think carefully of what it is that should be predicted and what physical phenomena affect the results. There are many steps that have to be defined.
2.1.1 Creating the Geometry and Mesh
The body about which flow is to be analysed requires modelling. This generally involves modelling the geometry with a CAD software package. Most commercial CFD programmes include a CAD software package for their system but the geometry can usually be imported into the grid-generation programme. Concurrently, decisions are made as to the extent of the finite flow domain in which the flow is to be simulated. Grid generation specifies the physical configuration to be simulated and divides it up into a three-dimensional grid containing a sufficient number of small regions known as control volume cells so that the Navier-Stokes equations can be solved iteratively. Obtaining an accurate mesh of the computational domain is as important as defining the physical model. So the mesh quality must be evaluated prior to the simulation. Typically the cell size of a mesh should not change with more than a factor of 1.25 between neighbouring cells.
Setting Physical Properties
All the physical properties of the fluids must be defined, e.g. the viscosity and density and their temperature, composition and pressure dependence.
Turbulent flows are characterized by fluctuating velocity fields in which there exist small-scale and high frequency fluctuations. At high Reynolds numbers, turbulent fluctuations cause a much greater net momentum transfer than viscous forces throughout most of the flow. This then means that for turbulent flows the Navier-Stokes equations cannot be solved directly. Thus, accurate modelling of the Reynolds stresses is vital. A turbulence model is a means of approximating the Reynolds stresses in order to close the mean-flow equations.
Boundary Conditions and Initial Conditions
For a CFD simulation to produce a result, the environment around the design must be defined. This environment is described by the boundary conditions. These conditions are the inputs for the simulation and so using them properly is necessary for good simulation results. Conditions at the inlet, the outlet and the walls must all be defined. Boundary conditions due to simplifications of a computational domain may be introduced i.e. symmetry boundary conditions. And advanced conditions can be applied for rotating equipment which are known as periodic boundary conditions.
Solving the CFD Problem
Once the problem definition is completed, it is submitted to the solver for the computation of a solution. This is the solution step. The governing equations are coupled and nonlinear in nature.
Therefore, a guess-and-correct, iterative strategy is adopted to compute the solution. Although the solution method is automated, user intervention frequently is required to obtain a stable converged solution.
Post processing is the stage at which CFD results are analysed. A CFD solution provides full-field data; flow variables at thousands of locations depending on the mesh. Analysis of results will give local information about flow, concentrations, pressures, temperatures etc. However a key value of CFD is its ability to provide accurate predictions of integrated quantities such as heat transfer rates and mass transfer rates. The post processing stage should also be used to analyse the quality of the solution.
CFD in turbomachinery
CFD now forms an integral part of the design process for many fluid machines including compressors, turbines, aero-engines, gas turbines and turbochargers. Simulation of multi-bladed machines brings challenges beyond those encountered in simple wall bounded turbulent flows. And for a successful simulation it is the following problems that have to be overcome:
The geometrical complexity of, multi-bladed, multi-stage rotating equipment coupled to the physical complexity of unsteady rotating flow.
The performance prediction of a rotating machine requires accurate simulation of attached or detached boundary layers.
Rotation makes it necessary to account for relative motion of multiple rotors and stators.
The cost of simulation needs to be sufficiently low to allow detailed studies of varying input parameters, geometric shape optimisation etc.
2.2.1 OpenFOAM software
OpenFOAM is an abbreviation which stands for "Open source Field Operation And Manipulation", and is an open source numerical simulation software with extensive capabilities in solving
fluid flows and other multi-physics problems. The software is first and foremost a C++ library for the development of numerical solvers, and utilities for pre and post-processing the solution of continuum mechanics. The code is released as free and open source software under the GNU General Public License. It was developed by OpenCFD Ltd and distributed by the OpenFOAM Foundation.
OpenFOAM is ever developing as a useful tool for modelling flows in turbomachinery. Its general purpose capabilities are enhanced with turbo-specific features in order to overcome the aforementioned problems in modelling turbomachinery flows. These features include moving mesh calculations, single rotating frame of reference and multiple rotating frame. There are then interface handling techniques for overcoming the problem at the interface between stationary and rotating parts. These include the frozen rotor technique, a General Grid Interference (GGI) and a cyclic GGI.
ANSYS CFX is a commercial CFD program used to simulate fluid flow in a variety of applications. ANSYS CFX combines advanced solver technology with a modern user interface and an adaptive architecture to make CFD highly accessible to engineers who require in-depth modelling of complex fluid dynamic problems.
ANSYS CFX provides a suite of special-purpose tools for tasks such as blade row geometry definition, flow path meshing, 1-D performance estimation, accelerated case setup, design of experiment analysis and component-specific post-processing. More specifically for solving fluid flows in turbomachinery ANSYS CFX provides general interfaces such as incompressible and compressible flow, rotating machinery with stage interfaces, frozen rotor technique. When these are used in conjunction with the customizable physics and user interface, and solved, an accurate model can be produced. A real in depth analysis can be achieved with the blade-row specific post-processing tool provided by ANSYS CFX.