Gas Turbine Industrial Fellowship Program 2006 CFD Post-Processing of Rampressor Rotor Compressor Curtis Memory, Brigham Young niversity Ramgen Power Systems Mentor: Rob Steele
I. Introduction Recent movements toward using relatively inexpensive Linux clusters for high performance computing has enhanced the capability of small companies to perform high quality CFD simulations. Extraction of pertinent flow variables from these simulations is a necessary step in the design of future gas turbine components. Ramgen Power Systems currently employs Numeca Inc s FINE/Turbo suite for their simulations of the Rampressor single stage compressor. This package consists of a structured mesh flow solver specializing in gas turbine applications, and the CFView post processing program to analyze solution results. Because of the number of CFD models required to properly analyze a design change, an automated process for extracting flow data is useful for maintaining employee efficiency. Data file size and the time required to process a data set is also a driving factor in the push to automating the post processing system. During my three month TSR Fellowship, a Matlab script was created that improves the automation procedure and calculates additional variables not available in the previously existing process. This paper will summarize the improvements and additions made to the process. Common variables of interest to the gas turbine design process consist of, but are not limited to Mach number, total temperature and pressure, and flow angle in both relative and absolute reference frames. These variables are usually presented in tabular form or color contour plots and are calculated at various locations in the domain of a component simulation. Previously, Ramgen utilized a system that employed an object oriented GI-based programming language similar to Labview called VEE, in conjunction with CFView linked through Python macro scripts, to extract flow variables and contour plots. These values and plots were automatically compiled into an HTML report for analysis. In addition to enhancing automation, it was desired to add to the current list of variables extracted from the data sets: mass flows through arbitrarily positioned planes or surfaces, blockage factor, and kinetic energy correction factor. In this paper, the latter two are referred to as theta cut variables because they are calculated from data extracted along constant-θ, cylindrical coordinate cuts. Also, because viscous models of the compressor are employed, a method to calculate various reduced boundary layer values such as displacement thickness, momentum thickness, shape factor, and coefficient of friction along the compressor hub and shroud was implemented. II. Automation Before discussion of the new variables, a description of the automation process is useful. Midway through the three month term it was realized that VEE was an overly complex framework for the process it was required to perform and work began on creating a replacement code entirely in Matlab. A functional beta version of the code was achieved in 3-4 days, borrowing from the basic VEE framework and the existing CFView macro script. There were various benefits to this switch. In addition to simplification of the original process, the capability to process large data sets on the Linux machines (increased system resources) was achieved, since VEE is a PC-only program.
The complex geometry meshes used in FINE/Turbo are generally made up of hundreds and potentially thousands of structured mesh blocks. Figure 1 shows mesh blocks constructing the trailing edge of two blades from a typical centrifugal compressor. 1 These blocks are then used by the FINE/Turbo solver for load balancing between processors when running on a parallel system (a Linux cluster for example). Figure 1. Mesh block divisions, denoted by yellow lines. Analysis requires that variables be calculated from data extracted or plotted along a cutting plane (meridional, cross sectional, or otherwise) at the desired flow-path location. Examples of cutting planes and contour plots on the example compressor are shown in Figure 2. Because of the number and locations of the mesh blocks, an arbitrary cutting plane in the domain can intersect blocks that are not wanted in the calculation. This would occur for example, if values were to be calculated on one of the two horizontal cutting planes shown below but only between two specific blades (note that the cutting plane intersects all blade flow paths). Two methods are used to overcome this problem: manual selection and geometric recognition. Figure 2. Velocity magnitude contours on various cutting planes.
Manual selection is performed by opening the solved mesh in CFView and noting the block names (the meshing package uses an indexing integer by default) for each plane that are to be included in the calculations. These block names are entered into a Matlab input file and included in the main process. This step adds approximately 5-10 minutes to the process and is required to calculate all the variables described below. The geometric definition function utilizes geometric limits found in the input file to identify specific sections of the rotor to be analyzed. The process is constrained to simple geometric definitions, such as radial limits, and adds 3-5 minutes to the process. Because of this issue, the current code is not fully automatic and requires prior knowledge of mesh block names and basic geometry definitions. A solution to the automation problem that would replace both the above methods was possibly discovered a few weeks before the end of the Fellowship. The code developed here will be used to process existing data sets and can be used on future data sets until the new method is fully investigated. III. Mass Flows The method of calculating mass flows utilizes a simple density weighted integration of the velocity field across a given plane or surface. However, because of the manner in which CFView handles directions normal to the mesh cell faces, it was required to first calculate a custom variable of the product of density with the normal velocity magnitudes and use normalized cylindrical velocity components to give the scalar field a direction and account for reversed flow through the cutting plane. The equation used is shown below: m = cyl abs( cyl ) ρ mag, n da where cyl is the cylindrical velocity component whose direction is most perpendicular to the cutting plane where the mass flow is calculated. The surfaces where mass flow calculations are performed must be known beforehand and entered into the input file before running the post processor. IV. Theta Cut Variables The theta cut variables are calculated at cross sections defined by creating constant theta cuts across the inter-blade flow path. The following equation was used to calculate blockage factor: β τ 1 = 1 da A
where is the free stream velocity and A is the cross section area. Blockage factor is generally used in diffuser design analysis and in three dimensions, is similar to that of a boundary layer displacement thickness in two dimensions. The kinetic energy correction factor is defined as: α 3 1 = da A KE 3 Where is the average velocity of the cross section and A the cross section area. Kinetic energy correction is the ratio of the actual kinetic energy flux to the ideal flux at a given flow rate through a cross section. The ideal flux condition would exist if the velocity profile were uniform across the section. Velocity non-uniformity (separation for example) increases this value above unity. Similar to blockage factor, this is a useful variable for diffuser design. 2 Other variables extracted at these theta cuts are average relative Mach number, and total temperature and pressure. Identical to the mass flow calculations, prior knowledge of the block names making up the flow path is required and is included in the input file before processing. Also, special provisions were added for a new meshing technique to be used in the future that will drastically reduce the time required to produce a mesh. The geometry currently included in meshes contains sections of two neighboring blades. Theta cut variables can be easily calculated from surfaces in a single domain cut. The new method however will mesh a single blade and the calculations will then require a second cut at a specific angular interval, to account for the full flow path geometry. To the end user this simply doubles the number of cuts required in the input file. Displacement thickness is defined as momentum thickness as shape factor as and coefficient of friction as V. Boundary Layer Values 0 * δ = 1 da, ϑ = dy 1, 0 δ * H =, ϑ
Cf = τw. 1 / 2 ρ 2 The shear stress, τw =µdu/dy, is calculated from the first node off the wall surface on the normal line. The normalizing velocity, in all cases was taken as the maximum velocity in the cutting plane. The boundary layer values and plots are extracted by Matlab after CFView has exported the appropriate cutting plane data sets. Figure 3 shows an example cutting plane and corresponding near-wall velocity field. Figure 3. Mid-pitch cutting plane and boundary layer velocity distribution. Boundary layer values are then calculated by parsing the data file and performing simple geometric modifications (rotation and translation) in order to accurately interpolate the velocity field. Wall surfaces are then identified and lines normal to wall surfaces are calculated. A line mesh is created on each line, also to improve interpolation quality. Figure 4 shows an example wall and corresponding normal lines. Figure 4. Wall (red line) with actual mesh points (blue circle) and normal line meshes (black X).
Interpolated velocity components obtained from these line meshes are then used to calculate velocities in the wall-tangent direction, resulting in profiles similar to those shown below in Figure 5. Figure 5. Sample boundary layer velocity profiles. Each profile is then integrated using the above boundary layer equations and reduced quantities are plotted versus their theta locations in the cylindrical coordinate system. An example plot of displacement thickness along a section of the example compressor hub is shown in Figure 6. It should be noted that the geometry modifications mentioned above are customized to the Rampressor shape and the plot is merely a sample; not an accurate representation of flow conditions. Figure 6. Example displacement thickness plot. Spikes are due to problems related to using zero velocity condition to acquire wall points. A boundary layer is defined as the region next to a wall where the flow velocity is 99% or less than the free stream velocity. Gas turbine component flows generally consist of complex flow phenomena such as adverse pressure gradients, centrifugal forces, and
shockwave interactions. This makes identification of a specific free stream velocity and boundary layer height difficult. The selection of a boundary layer height was arbitrarily based on the thickness of the boundary layer mesh or the refined mesh region close to the wall. This height was used at all points in the cutting plane at which these variables were calculated. Though not extensively tested, a method of finding the boundary layer thickness by calculating the percentage change in the velocity distribution did not yield satisfactory results. It was noted that minor variations in this height altered the scale of the plots but did little to change the overall shape and trends of the curves. Because of the above reasons, the function described above provides a good feel for what the boundary layer is doing but is not a definitive measure of its behavior. From a design stand point, it provides the analyst with a general view of where in the flow losses are occurring. When data calculations have finished, a custom Matlab function is automatically invoked to write an HTML report. This involves reading a data file containing values to be displayed in tabular form and creating links to the contour plots created by CFView. The capability exists to create both a single-data set report and a comparison report for two different sets. The dual HTML report displays contour plots side by side and calculates percentage changes between the sets for the tabular data. VI. Conclusion In conclusion, an improved CFD post-processing script was developed that is more reliable and automated than the previous system, calculates more variables, and hopefully improves upon Ramgen s ability to make design changes to the Rampressor rotor currently in development. This Fellowship has brought to light important requirements of the modern gas turbine industry spanning from the obvious need for accurate CFD modeling, to the rising need for rapid and inexpensive data mining methods. The latter consisting not only of extracting data from a single simulation but being able to then compare results to previously solved simulations. I would like to specially thank Rob Steele and Allan Grosvenor at Ramgen who were excellent mentors during the Fellowship and the TSR organization for providing the opportunity to learn and observe the industry first hand. References [1] McKain T., Holbrook G., 1997, Coordinates for a High Performance 4:1 Presure Ratio Centrifugal Compressor, NASA CR-204134 [2] Sovran, G.,Klomp, E., 1967, "Experimentally Determined Optimum Geometries for Rectilinear Diffusers with Rectuangular, Conical or Annular Cross-Section," Proceedings of the Symposium on the Fluid Mechanics of Internal Flow, pp. 270-319