CHAPTER 5 AERODYNAMIC DATA AT ONE CLOCKING POSITION
5.4 MODELING UNSTEADY PRESSURE DATA WITH UNSFLO-2D
The focus of this part of the chapter is to show an example of how this complex data set can be used for model verification. The term “model” is a relatively broad term.
For some it means all Computational Fluid Dynamics (CFD). For others it is any type of analytic or computational approach that attempts to explain reality by some
approximation. It is the latter definition that is implied in this work.
Models come in various forms. There are analytic model that describe boundary layer behavior. There are empirical models used in design that build on past hardware successes and failures to help designers in estimating life expectancy of parts. And there are computational models that attempt to solve problems that do not yield to analytical solutions. Over the last several decades the promise of CFD has been that computational
“models” could help sort out many of the intractable problems of earlier decades, and in many cases these efforts have had at least some level of success. However, the measure of success if often hard to define for the simple reason that the main arbitrators of the successfulness of an approach are often the engineering design team that has little interest in reporting the results in a timely fashion.
This has led to an interesting schism in the gas turbine community. As start-up costs have continued to decrease for computational work, many more research efforts have been started in various computational approaches at the academic level, with little connection to the needs of the design community. This is easily seen in the great amount of work done in non-rotating turbine tip flows. On the industrial side, the efforts seem to
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have moved (at least at the research level) towards brute force solving of the equations, given the relatively limitless supply of computer power. This has tended towards increased solution accuracy, but the problem is how to move these types of algorithms into design tools.
The OSU Gas Turbine Laboratory has historically focused on the experimental aspects of aeropropulsion research, but has wanted some type of capability for modeling the unsteady vane/blade interaction that occurs in the turbine stage. The interest has not been in developing code, but rather in the use of an existing system. Some work had been done with commercially available codes such as Star-CD. And while that particular code has undergone a great deal of development and has been widely used in the
industry, it was relatively complicated to use requiring a great deal of experience in order to grid the solution and to actually get it to converge (and this was for steady solutions).
Our attention was drawn to a simpler model originally conceived at MIT by Prof. Giles [35] called UNSFLO and since then renamed UNSFLO-2D. The OSU GTL has
permission from Rolls Royce England to use this code for research studies performed at the GTL.
UNSFLO-2D is both an analytic model and a numeric implementation of this model. The analytic part can be easily described, although the numerical approaches to implement this were novel, and most of the key insights of Giles and co-workers have been incorporated into later codes. Analytically, Giles hypothesized that the core
problem in vane/blade interaction was obtaining the unsteady, periodic solution, and that could be done by separating the region into the area immediately around the blade where the full viscous equations are solved, and an area over most of the passage where the entropy generated in the immediate blade area is convected inviscidly. This
simplification required two different grids to be created and two different solutions run, but this became manageable on computers of the 1980’s. Giles’ work built upon four main pieces of work in the early 1980’s [36], [37], [38], and [39]. Giles intentionally used his computing resources on the unsteady part of the problem instead of proceeding with trying to calculate a full 3-D passage.
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It is beyond the scope of this work to go into the details of the code. The main components can be summarized in the following fashion.
1) The code operates over two regimes
a. In the viscous region, the equations are unsteady Reynolds averaged Navier-Stokes equations, using an implicit scheme. One has a choice of turbulence model and can several different types such as algebraic or K- epsilon
b. In the inviscid region, an unstructured grid is used, solving the unsteady Euler equations along a stream-tube using an explicit solution
2) The code has the ability to handle unsteady boundary conditions of four different forms:
a. Unsteadiness in a single blade row due to unsteady inlet conditions such as wake/blade or potential/blade interactions
b. Rotor/Stator interaction
c. Single blade row unsteadiness due to blade vibration
d. Natural unsteadiness due to flow phenomenon such as vortex shedding 3) The code can handle arbitrary pitch ratios (number of blades in each row)
The three main numerical innovations were the hybrid grid used for the solution, the ability to use arbitrary pitch ratios (which led to the development of the time-tilting algorithm used widely today), and the variety of boundary conditions. In fact, it was this variety of boundary conditions that attracted us to this code, since most of our current research problems could be modeled and it could generate unsteady heat-flux predictions (something very few codes can do, design or research codes).
Several papers were published during the development of UNSFLO-2D, which cover the time from 1988 to 1991 [40] and [41]. Over the period of 1989 to 1992, the code was validated using data from the MIT blowdown turbine. Two papers dealt specifically with rotor heat transfer and compared the data to the numerical predictions and to cascade data [42] and [43]. Two other papers were done in conjunction with this
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work by Giles’ student Korakianitis [44], [45]. A literature review turned up two other reports where UNSFLO was listed (other than the work done at the OSU GTL), both 1998 reports done by Singh from Pyestock in England [46], [47]
This raises the question as to why UNSFLO-2D has not become more widely used, and the answer has a few components to it.
1) First, the code was and has been used widely, just not in the academic
environment. The code was originally developed for Rolls-Royce (sponsor of the work at the MIT GTL), and after a relatively few number of published papers it was taken over by the Rolls-Royce design group.
2) Secondly, it was a code ahead of its time in terms of data validation. The early MIT data was extremely limited, having no published pressure data on the
rotating airfoil and only limited heat-transfer data. While the OSU group (then at Calspan) had access to a significant rotating airfoil data base, it was not until the mid 1990’s that the code became available for use at the OSU GTL [48].
3) Actually, while the academic world has not seen a large amount of verification papers written with UNSFLO-2D, in the 1990’s a great deal of work has been done with similar types of codes. One has to remember that UNSFLO-2D was part of a family of codes that were developed in the late 1980’s (Allison’s VBI code [49], Pratt’s Ni code [50], and Mississippi State Universities TURBO code (created in conjunction with NASA) [51] are all similar in concept). All were used extensively by their respective companies in the design process in the
1990’s. In the academic world, the problems had shifted away from the 2D codes onto the problems associated with doing full 3-D calculations. Currently, some of the most promising research codes that may actually make the transition to design codes are 3-D codes that have a model similar to UNSFLO-2D in the generation of entropy and inviscid propagation.
As a final statement, there was also a fundamental question of how well the UNSFLO-2D model worked in the computational environment. We understand that we are making
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some simplifying assumptions about the flow, and as a comparison, full 3-D unsteady Navier-Stokes codes needed to be developed to compare against the UNSFLO-2D solution to see how important some of these issues are in real flows. This has been done in the past with a model which is more 2D in nature [1] with good results. With this data set, most of the pieces to revisit the applicability of the UNSFLO-2D model are in place.
We have a full 3-D data set of both pressure and heat-flux over three blade rows, and industrial design codes and research codes to compare against.
Getting UNSFLO-2D to run is not an easy task. The main code is relatively robust, although the operation of it is very unclear for those who have not previously run the system. Unfortunately, the code requires some extra I/O libraries that are not strictly Fortran 77 compliant and were only able to run off an old SGI complier because of the relative looseness of the compilers. The main code was recompiled on a very old SGI and run, although some effort was put into porting the code to a Macintosh computer, which was mostly successful. The effort was stopped after the main code was able to be recompiled on the SGI, but in the future the code will probably be run on either a Linux based system or a Mac, once the code has been brought into more strict F77 compliance.
Getting the code to work actually required a great deal of front-end processing of the geometry files (which was done in LabView) to get the proper file formats. However, once the operation of the program was learned, essentially the first geometry attempt converged, without requiring any change in the input conditions. The results are shown in Figure 5.17 for the HPV and HPB at 50% span locations compared to the data and industrial codes.
Detailed specifics of the code and how it was run will not be discussed, since it is not that relevant to the work. No attempt was made at grid refinement. The goal was to see if the code could be used as a prediction tool, once it was compiled and the proper input geometry was applied and a converged solution obtained, without a lot of modification of the input conditions. Probably the only relevant material is that the solution shown below was done with a K-epsilon turbulence model using a freestream turbulence level between 5 and 10%, (which did not alter the aerodynamic solution). For
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these solutions only the first two blade rows were modeled, and the streamtube thickness variation for 2% span location (49 to 51% span) was provided from an inviscid
streamtube code used by industry.
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0 0.2 0.4 0.6 0.8 1 1.2
-100 -50 0 50 100
HPV 50% Span
Comparision of Data with Unsflo-2D and Industrial Predictions Bars on Data are Average Max and Min for a passage
Data averaged over one Revolution
DataUNSFLO-2D Avg Press UNSFLO-2D Min Press UNSFLO-2D Max press
Industrial Design Code (Steady)
Industrial Research Code (3 row, Unsteady) P Local/P Total
% WETTED DISTANCE
0 0.1 0.2 0.3 0.4 0.5 0.6
-100 -50 0 50 100
HPB 50% Span
Comparision of Data with Unsflo-2D and Industrial Predictions Bars on Data are Average Max and Min for a passage
Data averaged over one Revolution
DataUnsflo-2D Avg Press Unsflo-2D Min Press Unsflo-2D Max press
Industrial Design Code (Steady)
Industrial Reseach Code (3-Row Unsteady) P Local/P Total
% WETTED DISTANCE
Figure 5.17 UNSFLO Predictions HPV and HPB 50%
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As seen in the figures, all three codes do a very good job predicting the time- average values at the midspan location. At the vane trailing edge on the suction surface and on the blade leading edge area of the pressure surface the data aligns a little better with UNSFLO-2D than with the industrial design codes. The reason for this is due to the fact that the UNSFLO-2D solution is first done on the vane and then the rotor, and then combined, and thus the pressure ratio across the vane was matched to the data, and then the pressure ratio across the entire stage. For the industrial codes, only the pressure ratio across the entire stage was matched. Another interesting point is that the unsteady bands predicted by UNSFLO-2D match the data passage envelopes quite well. This
information was not immediately available from the industrial codes. It is also interesting that the influence of the low vane is not great on the time-averaged pressure for the blade as shown at the trailing edge of the blade, since all three codes predict similar values.
To reiterate, the main goal in using UNSFLO-2D for predictions was to see if that code specifically could be used to generate reasonably accurate predictions of the time- resolved pressure as an engineering design tool. It is not surprising that both the
industrial design code would reproduce the time-average values, or that the research code would also function to get similar answers. What is different is the scale of effort that goes into running each code. The industrial design code will not generate the periodic information that UNSFLO-2D or the research code generates. However, UNSFLO-2D will run on a Macintosh or PC, and the research code takes several large machines running in parallel to reproduce similar answers. To be fair, the research codes will handle the strong 3-D effects and provides information over the entire blade surface, including the tip and platform regions of the airfoil. However, in the present state the code does not provide an estimate of the heat-flux. UNSFLO-2D has that possibility, although for this work, it was found that the temperature normalization was not working properly and the heat-flux answers were similar in shape to the data but the scale was off dramatically. This was left to another day to examine.
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Returning to the main principles of UNSFLO-2D, we see that at least at the 50%
span location, the basic idea of convecting the entropy generating wakes downstream invisicidly works well in terms of reproducing the pressure fields. The influence of the third blade row on the upstream rows (potential effect) is not critical and that is probably due more to the design of this particular machine than any other issue. While a lot of time was spent trying to get the code compiled and run, very little was actually needed to run the solutions (once the particulars of how a solution is generated in UNSFLO-2D became understood). The time has probably passed for this version of UNSFLO-2D to become important to the industry. Computer power has increased, and the problems have changed to the point where the 3-D unsteady Navier-stokes codes that can handle the entire airfoil surface are receiving much more attention. However, UNSFLO-2D
remains a very powerful tool for use in the upcoming film cooling measurement program.
In order to formulate a macro model for film effectiveness on the blade, one will have to have an unsteady code that can calculate heat flux to deal with the secondary flow effects.
Assuming the airfoil is not too 3-D, one should be able to get a good start on the macro model formulation using the UNSFLO-2D code as a computational tool. In addition, the promising results presented above suggest that with a little extra work one would expect to get the heat-flux data correct, and an ability to run three blade rows. Codes with similar ideas to UNSFLO-2d, but which examine the entire passage are currently being investigated as possible candidates for unsteady design tools instead of the much more complex full 3D Navier-Stokes codes.