DEVELOPING FINITE ELEMENT MESHES FOR THE ACOUSTIC SIMULATION OF JET ENGINES
by
Karl Kowallis
Submitted to Brigham Young University in Partial fulfilment of graduation requirements for University Honors
Advisor: Dr. Scott Sommerfeldt Honors Dean:
Signature: ____________________ Signature: _____________________
ABSTRACT
CAD software, which enables quick modeling, is now available, allowing advanced study of jet engine acoustics. Using I-DEAS computer software, finite element models of a turbofan gas-turbine engine have been created that are themselves instructive and provide preparation to use I-DEAS in other research. The steps of mesh creation are explained so that others may use this work as a guide for experimental research. These models are only a preliminary effort to study jet engines analytically, and although the models are finished, the analysis for this research project is ongoing.
CHAPTER 1
INTRODUCTION
Little has changed with the modern jet engine since its invention of in the 1930's. An engine's life span can be several decades, and many of today's commercial engines trace their origin to the 1970's. The methods available for analysis in the early history of aircraft engine design included analytical calculations and modeling. Simplifying assumptions were necessary in the geometry of analytical models to make analysis feasible. The development of computer design applications bridges the barrier of human computational ability and relaxes the need for drastic assumptions thereby allowing more accurate creation and modeling of jet engines.
This finite element work is part of Dr. Scott Sommerfeldt's research and a beginning for the dissertation work of Laralee Ireland. Due to the breadth of the problem, the focus of this paper is on mesh creation and the preparation for analysis of the engine models. When referring to "us" or "our" in the collective, I refer to Dr. Sommerfeldt, Laralee Ireland and myself.
Using CAD (Computer-Aided Design) FEM (Finite Element Mesh) software, we create models for studying the acoustic field in a jet engine, using a numerical acoustics package called SYSNOISE. The objective of this research is to finish the models that other project members will use in continuing analysis. Modeling and eventual simulation will provide insights into the acoustic field that may give guidance to future design alterations.
CHAPTER 2
HISTORY
2.1 Jet Engine Development
The most challenging task in jet engine development was compressing the incoming air. In the 1930's, Frank Whittle solved the problem using a centrifugal type compressor such as those used in some supercharged automobiles today (Borden 1967). The power needed to drive this compressor is high compared with the total power produced. About three fourths of the power produced in a gas turbine engine drives the compressor, leaving the remainder as aircraft thrust (Borden). Most calculations involving jet engine performance required simplifying assumptions and only basic algebra. Because jet engines have so few parts, they are much simpler than automotive piston engines. The small number of design parameters permitted trial and error development of the gas turbine, culminating in today's versatile source of thrust.
To compare the variety of engines and designs, the Society for Automotive Engineers (SAE) developed performance standards and is still responsible for the standards of commercial aircraft engines. These standards include comparisons of thrust and performance.
Engine references refer to the station designation. These are reference measurements along the axis of the engine beginning from the ambient air head (Borden 1967 p. 37). This ambient air head is ahead of station one, which is the entrance to the air duct, and in front of the engine (Borden).
2.2 Analytical Study of Engines
In 1947, Heins and Feshbach used numerical techniques to study sound reflection on duct walls without airflow consideration (as cited in Joshi et al 1982). Computer development made computation less costly and allowed models with more variables and greater accuracy. Early techniques used approximations to the desired geometry and then formed sets of equations to fit the scenarios. These equations formed large matrix equations that were solved using algebraic methods complicated mainly by the number of variables and the sizes of the matrices.
In 1982, M.C. Joshi, R.E. Kraft, and S.Y Son published a paper on sound propagation in annular ducts. In their introduction they surveyed the development of duct analysis:
The method presented in this study has been developed previously for ducts of rectangular and cylindrical geometry. The rectangular geometry applies approximately to the case of high radius ratio exhaust ducts, while the cylindrical geometry finds primary application to inlet ducts. What follows is the extension of the problem to annular geometry which will have direct application to engine exhaust ducts. Although the basic theory for all three geometries is similar, the increasing complexity of the fundamental solutions for the wave propagation in each case dictated that they be taken in this order; a primary emphasis of this paper will be to describe methods developed to handle the annular geometry eigenvalue problems. (Joshi 1982)
The method they employed involved mode matching, which "uses the modal analysis approach to obtain the infinite duct solution and extends it to the segmented duct by accounting for the acoustic coupling between the various sections" (Joshi 1982).
Disadvantages arise in applying the method to variable geometry ducts, for which the finite difference and finite element schemes are more suitable (Joshi 1982). Approximations, such as assuming a duct is infinite, allow the equations to reflect this symmetry which makes the matrix equations more sparse (lots of zeros) and speeds computation. Assumptions of symmetry also make the boundary conditions more mathematical and therefore easier to calculate.
An additional disadvantage of this early development was that every bit of research involving theoretical calculations then required the development of programmed methods to do the mathematics. Our aim was to use CAD programs to simplify and speed up the model production. I-DEAS would build the mesh and SYSNOISE would create the equations and implement the algorithms, freeing us from the need to develop our own mathematical procedures and allowing us to concentrate on creating appropriate boundary conditions.
Finite elements allow the approximation of one mathematical object for another. A numerical solution for real world problems requires approximations. These approximations can be either nodal or elemental.
Nodal approximation uses the values of a function at discrete points. Values between data points are interpolated. Finite elements, as opposed to the discrete point approximation, use an element, such as a line, in the initial approximation. Take a topographical example. To describe the shape of a mountain, one could have a table of values with latitude and longitude and the elevation. This tabular set of data would be the discrete point method. We could estimate elevations between data points using the surrounding data.
The element method incorporates the interpolation into the initial step rather than placing it at the end. One could list several approximate equations, one for each longitude, that would give the elevation as a function of latitude. This method is discrete in one direction and elemental in the other. To make the example even more like finite element modeling, we would give the equation for a surface at each rectangular section. FEM analysis is harder to set up initially, but when the data and results are to be used repeatedly, it is more powerful and flexible.
Other current efforts continue to use simple tubes as models for engines. The NASA Lewis Research Center in Cleveland, Ohio has a cylindrical fan duct used in acoustic research. D.L. Sutlif's dual research efforts, one in association with Z. Hu, F.G. Pla, and L.J. Heidelberg, and the other with James Bridges and Edmane Envia, used NASA's fan for active noise control research (Sutlif et al. 1997a) and for modal interaction studies (Sutlif, et al. 1997b) respectfully. Active noise control, which involves the introduction of out-of-phase noise to decrease the sound pressure level (Lp), is on the forefront of current acoustics research and is difficult to achieve without a proper understanding of the environmental parameters.
CHAPTER 3
OBJECTIVE
I-DEAS is an integrated computer modeling package designed by SDRC (Structural Dynamics Research Corporation) with the ability to create basic three-dimensional models. Meshes based on these created models can be studied in IDEAS or exported to a file for postprocessing in another program. The objective of this project is to create several meshes of various sizes for use in continuing research on modeling the acoustic field in a jet engine.
CHAPTER 4
MESH DEVELOPMENT
4.1 Introduction to IDEAS
SYSNOISE is a powerful acoustics package, but has poor mesh creation abilities. Thus the BYU Physics Department needed a way to develop meshes for use in the SYSNOISE package. I-DEAS, by SDRC, is well suited to the task of mesh creation. I-DEAS stands for Integrated Design Engineering Analysis Software and is a graphical modeling package with capabilities to create models and analyze them internally or export them for analysis in another program.
Once we define a part in I-DEAS, it can be used to generate a mesh. A mesh consists of an ordered grid laid out on a part. We call these points nodes. Connecting the nodes are lines that, in geometric groups, form "elements." Common shapes for elements are triangles and rectangles. These shapes may be either flat with straight lines between nodes, or curved. The notation for the element type often reflects the shape and number of nodes. A quad4 element is a rectangle with straight lines connecting four nodes at the corners. A quad8 element has nodes at the corners of a rectangle and also at the midpoint of each line segment. The sides of the rectangle therefore may have a parabolic curvature. The mathematical calculations can depend on the nodes as the fundamental values or on the elements as a whole depending on the procedure being done.
4.2 Building a Model
4.2.1 Raw data from GE.
Dr. Scott Sommerfeldt contacted Dr. Robert Kraft at General Electric about using a real model to work on for an acoustics project in the Physics Department. GE sent drawings and data to allow us to create the models. This model creation is the aspect of the project that I took. As an overview, GE included a drawing of a turbofan engine (Figure 1) and sent data on the engine cross section. They listed the radius in tabular form with the axial position, also called a station number.
4.2.2 Creating the model.
Using the I-DEAS point modeling tool (Figure 2) we entered the
data in. Several points on the model were visibly off the smooth curve of the engine.
Because they did not label these points with any significance, we deleted them from the
included data points. The sharp edges would have been problematic in our analysis because
of their relative size compared with the wavelengths we intended to study.
We needed a spline to connect the data points and
provide a smooth frame for the engine's cross section. The options on I-DEAS' spline
creation tool (Figure 3) were set to constrain the spline to pass through all of the
indicated points. Without this change to the options, I-DEAS would often fit the data
linearly, leading to strange geometric shapes that seemed to ignore many of the data
points. My original efforts used a series of splines on groups of points which led to
problems of smoothness and continuity. We redefined the spline as two large curves on the
outer cowl, one line each for the outer and inner side, and several small connected curves
for the inner cowl. Once we created the spline, we no longer needed the data points, and
we removed them from the workplace to a bin for later use.
The
revolve tool (Figure 4) generates a three-dimensional model from a two-dimensional curve
and was used to finish the three-dimensional model. Our data was entered as inches, and to
prepare for export and for ease of use in SYSNOISE, we changed the units to SI (meter,
newton, Kg).
4.3 Generating a Mesh
4.3.1 Meshing.
Mesh generation is part of the simulation package of I-DEAS. According to I-DEAS' online help, "A finite element model includes a mesh of nodes and elements. The best way of creating a mesh is to create the part's geometry, then generate a mesh on the geometry." A part is selected to mesh from the bin, and then the various options for the mesh creation are selected.
4.3.2 Mesh types.
The choice of what type of mesh to create depends on the purpose of the mesh. We wanted to have two-dimensional meshes to analyze using a boundary element method (BEM) in SYSNOISE. This BEM objective dictated a two-dimensional mesh on all of the external surfaces of the engine. The other available types of mesh available in I-DEAS include a three-dimensional mesh, useful for FEM analysis in SYSNOISE, and beam elements which can be used by I-DEAS' built-in FEM processor.
Two methods of creating a mesh exist in I-DEAS: mapped mesh and free mesh. Mapped meshes allow the number of elements to be defined directly on curves, surfaces or volumes. Dividing the part into several partitions gives edges on which we can define these element sizes. Partitioning also gives greater freedom as long as the geometry is simple. As noted by Thomas Dong et al (1987), dividing the part to be modeled into several domains avoids the need for dense grids on simple sections thereby improving calculation time. For our purposes, using a free mesh was more advantageous. The online help for I-DEAS explains the benefits:
Free meshing automatically generates nodes and elements on surface and solid geometry. This mesh type allows you more flexibility than the mapped mesh type. The boundaries of surfaces and volumes for free meshing can be more complex. Free meshing can mesh surfaces including holes, and volumes including holes and interior voids. The free mesh generator uses an algorithm that tries to minimize element distortion. . . . Surfaces of a part can be meshed with two-dimensional elements such as thin shells (I-DEAS).
4.3.3 Mesh parameters.
Of the available options when defining a mesh, element length is the most self-explanatory. The chosen element length will largely determine the coarseness of the resulting grid. The acoustic frequencies to be studied must be considered when choosing the element size. The wavelength and the frequency are related by the equation v=f where v is the velocity of sound, f is the frequency and is the wavelength. To get accurate resolution in acoustic analysis, at least six nodes per wavelength are needed. For frequencies up to 150 Hz this corresponds with a wavelength larger than 2 meters and therefore an element length of 0.3 meters will suffice. For actual analysis frequencies up to 1500 Hz will be needed and the grids required will correspondingly be up to ten times finer.
The
element type refers to the shape of the element and orientation of the nodes. The quad4
element, the type I used in my meshing, has four nodes positioned at the corners of a
rectangle. Another common type is the quad8, which adds nodes on the midpoints of the
rectangle edges (Figure 6). For our acoustic use, the additional nodes of the quad8 were
unnecessary and the rectangular element geometry of the quad4 fit the cylindrical shape.
The absolute deviation is a measurement of the warping of the element shape from the curvature of the part being meshed. The deviation is the distance the element sides are away from the ideal rectangular sides. In Figure 6, this would be the distance from the line connecting nodes 1 and 3 to node number 2. Lowering the allowed deviation will increase the number of elements needed to mesh unusually-shaped objects. This "curvature-based length" prevents small details of a model from being ignored by a coarse mesh. We can enter the deviation either as a percent or as a definite distance (I-DEAS). (See Figure 7)
The
"Free Meshing Method" can be by maximum area plane or in parameter space.
(Figure 7) The parameter space method uses the equations defining the part to create
elements. The maximum area plane method uses a projection of the object to then map on the
elements. The parameter space method fails at parametric singularities such as the point
on a cone or at the pole of a sphere. Area projections do not work when the part has near
180 degrees of curvature. This level of curvature would mean that more than one part of
the surface would be projected too closely on the area plane. For shapes involving both
situations the part must be partitioned and meshed in the different ways for the different
situations (I-DEAS).
4.3.4 Problems encountered in meshing.
The greatest difficulty encountered in the mesh creation was on the inner cowl. The frontal cone would not mesh. The exact reasons for I-DEAS' inability to mesh the part was not explained, but the error message suggested partitioning of the part to an open surface. Partitioning the cone so that we did not include the very tip allowed success. After using this work-around, I discovered the possibility of meshing using the maximum area plane method. I recreated the meshes using the parameter/area split on the two partitioned sections and was successful.
4.3.5 Exporting a mesh.
Because of the strength of I-DEAS model generation abilities, it implements many
methods 
for
exporting models into other formats for use in other programs. Figure 8 lists the
available export options in I-DEAS.
When we were creating meshes using the ME department's computer resources, we had to be
careful of our file space use. ME accounts are limited to 30 MB 
and model
files in I-DEAS can be 5-10 MB with each mesh approximately an additional 1 MB. Unneeded
files had to be quickly discarded to make room for new data. Once I-DEAS was running on sabine,
the acoustics group workstation, the constant file erasures were no longer critical. Of
the meshes that will be used in calculations, the largest was 1624 Kb and the smallest was
56 Kb. One file had so many nodes that using it in SYSNOISE would have been impossible. It
had more than 50000 nodes and was 12,808 Kb. Tables 1 and 2 list the file names and
relevant information on the meshes I have generated. For all of my meshes, the number of
nodes and the number of elements were similar, and therefore only the number of nodes
appears in the tables.
CHAPTER 5
ANALYSIS
5.1 Introduction to SYSNOISE
SYSNOISE is an advanced numerical analysis engine. Its strength is its ability to analyze data with complex boundary conditions using a variety of methods. Its flexibility is also one of its greatest liabilities because the software will do so much, it is challenging to get it to do what you want. The developers of SYSNOISE, LMS Numerical Technologies, were aware of their software's strengths, and they concentrated on those aspects, leaving the mesh creation abilities intentionally undeveloped. We can create only models made of simple geometric shapes within SYSNOISE but SYSNOISE does recognize a variety of formats for import, and I-DEAS Universal files are one of those.
5.2 Software Layout
The layout of SYSNOISE can be confusing. Menus are all text based, and although the windows include a help button, understanding what is going on can be difficult. The technical level of the online help is much higher than in I-DEAS, with more equations and theory listed. To use the online help effectively requires understanding the relevant procedures and being adept enough to recognize the material sought when it is found.
5.3 Software Uses
Besides complex boundary conditions, SYSNOISE has options to do flow acoustics. As long as the fields are incompressible and non rotational, SYSNOISE can include the motion of the sound medium in its calculations. We have not yet determined if the flow options will be a benefit or a hindrance. Compression in the engine duct may negate the ability of SYSNOISE to do accurate simulations because of the incompressible flow assumption in the algorithms. The online help for SYSNOISE says concerning the flow acoustics, "Designers of mufflers, air intake systems and manufacturers of air-conditioning systems will certainly appreciate this new feature" (SYSNOISE). In discussing the situation with Dr. Scott Sommerfeldt, he indicated that the incompressible flow was a reasonable assumption up to mach 0.3 (personal communication, 13 November 1997). Even if the assumption of incompressible flow is invalid for our application to engine ducts the results will be valuable despite the introduced error.
SYSNOISE can calculate modes of vibration on FEM models as well as the frequency response of models with the imposed boundary conditions. The entire package is a powerful tool that can be very useful if used properly by a knowledgeable researcher.
CHAPTER 6
CONCLUSIONS
The use of I-DEAS has enabled rapid and efficient creation of meshes for use in SYSNOISE. The learning curve since our first introduction to the software was steep because we had so few resources available for instruction. We relied heavily on the users' manuals and the online help. The most frustrating aspect of the research was getting acquainted with the software's quirks and understanding how to use the software for our intended purpose of creating models.
The analysis has not yet been done. I had planned to begin the analysis, but time constraints have pushed back that work for the continuation of this project on the GE engine. The use of I-DEAS as a development tool has become clear. It is useful in modeling and preparing meshes for analysis. The more the software is used, the more intuitive and simple it seems. It will be a valuable addition to the Physics department's resources.
Using SYSNOISE for analysis may be more challenging. Lots of meticulous care is needed to do worthwhile calculations in SYSNOISE. For calculations such as the ones we will do on this project, calculation times may become extremely lengthy. Some models contain many thousands of nodes. Models this large require all the resources a workstation has available and can take hours or even days. I expect that we will need simplifications to make initial simulation acceptably quick.
My next step will be importing a mesh into SYSNOISE. With the help of Laralee Ireland, who has been working with SYSNOISE, we will begin the analysis. I think that a realistic prediction is that we will complete preliminary analysis by the summer of 1998.
As a tool, I-DEAS is effective. A determination as to the usefulness of this modeling approach to gas turbines must wait until that first analysis is complete. Even if these I-DEAS models are not suitable for analyzing a jet engine, the methods will be useful in other modeling scenarios yet to be considered.
REFERENCES=
Borden, N.E. (1967) Jet-Engine Fundamentals. New York: Hayden.
Dong, Thomas Z., Shih, S.H., Mankbadi, R.R., & Povinelli, L.A. (1997). A numerical study of duct geometry effect on radiation of engine internal noise. //3rd AIAA/CEAS Aeroacoustics Conference//. AIAA-97-1604.
I-DEAS Master Series 5m1 [Computer Software]. Milford, OH: Structural Dynamics Research Corporation (SDRC).
Joshi, M.C., Kraft, R.E., & Son, S.Y. (1982). Analysis of sound propagation in annular ducts with segmented treatment and sheared flow.// AIAA 20th Aerospace Sciences Meeting.// AIAA-82-0123.
Sutlif, D.L. Hu, Z., Pla, F.G., Heidelberg, L.J. (1997). Active noise control of low speed fan rotor-stator modes. 3rd AIAA/CEAS Aeroacoustic Conference. AIAA-97-1641.
Sutlif, D.L., Bridges, J., & Envia, E. (1997). Comparison of predicted low speed fan rotor/stator interaction modes to measured. //3rd AIAA/CEAS Aeroacoustic Conference//. AIAA-97-1609.
SYSNOISE Rev 5.3 [Computer Software]. Leuvan, Belgium: LMS Numerical Technologies.
