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September 2011
The Flow
CFD Insights for the Turbomachinery Designer

INSIGHT: Techniques for Gaining Unsteady Flow Insight During Design
Capturing unsteady flow insight is a must for advancing turbomachinery durability and performance during design. Several techniques are available to obtain these insights, each with strengths and limitations.  In this month's issue of The Flow, we sit down with Steven Allmaras to discuss these techniques and their relative merits.  Steve is the Vice President of CFD at ADS.  Prior to joining ADS, Steve spent 22 years at the Boeing Company, where he was a key member of the CFD methods group and a co-author of the Spalart-Allmaras turbulence model.

FLOW: Welcome to ADS, Steven!  Let's start by identifying the most common techniques used to capture unsteady flow insights.
STEVE: Thanks.  Generally speaking, there are four approaches: fully unsteady, phase lag, harmonic balance and domain scaling.  Setting aside turbulence and transition modeling issues, fully unsteady represents "nirvana", while the other three approaches are simplifications employed to reduce computational cost and turnaround time with acceptable tradeoffs in accuracy.
FLOW: Let's explore each of these options.  What do you mean by "fully unsteady" and what are its strengths and weaknesses?
STEVE: By fully unsteady" we refer to the use of unsteady simulation on a full wheel.  In this approach, a series of modified steady states are marched in pseudo time for each physical time step in order to develop a time accurate picture of flow behavior.  For fully unsteady simulations, all airfoils in each row of a multistage machine are included in the computation.
This approach offers high fidelity because it captures both linear and non-linear disturbances on the full wheel. However, this comes at a very high computational cost, due to the high passage counts for each row and the need for a large number of small time steps to ensure accuracy and stability.
[Note: in the rare situation where blade counts for each row share a common multiple, the computational domain can be reduced to a corresponding sector.  For example, if the blade counts for a 1.5 stage turbine are 24, 36 and 24 respectively, the full wheel analysis can be reduced to 2, 3, and 2, translating to a 12x reduction in computational domain and cost.]

FLOW: So fully unsteady simulation remains out of reach due to excessive computational cost?
STEVE: Yes and no. Fully unsteady calculations are definitely expensive—probably about 100-1,000 times the cost of a corresponding average-passage steady calculation, so it’s not likely to be a technique you employ early and often in a design cycle. On the flip side, a 100x increase in computational cost does not translate into a 100x increase in turnaround time or hardware investment. The availability of cloud computing from vendors like Amazon Web Services makes it possible to rent large amounts of computing capacity on a pay as you go basis. Since it makes no difference whether you use 50 processors for 4 days or 200 processors for 1 day, you have the ability to scale up capacity to produce a turnaround time feasible for your design cycle. The net impact could be a 1-3 day turnaround time on this type of analysis—far less than the 1-2 weeks it might take a typical company to carry out on an internal cluster. If full scale unsteady helps you to get in front of rotating stall, forced response or adverse secondary flow, the simulation cost will seem cheap in comparison to a redesign cycle or field failure.     

FLOW: Makes sense.  Please describe the "phase lag" approach.
STEVE:   The phase lag approach assumes the unsteady flow is periodic and provides a numerical method to account for the time lag between the periodicities of a stator and rotor blade (in the case of a turbine stage).
The phase lag approach is computationally less expensive due to its assumption of periodicity and since only one passage from each blade row is required for the computation. This approach can also capture discontinuous effects such as shock flow. On the downside, this technique requires that you know the periodicity and phase lag between adjacent blade rows a priori. While this may be straightforward for single stage analysis—blade row interaction effects, for example—these assumptions are more difficult to identify for multistage unsteady computations.

FLOW: And how does this compare with the "harmonic balance" technique?
STEVE:   The harmonic balance technique also assumes the flow is periodic, but represents the unsteady flow with a Fourier series in time with frequencies that are integer multiples of either a fundamental excitation frequency, blade passing frequency or blade vibratory frequency. Like the phase lag approach, the harmonic balance technique simulates the true geometry using only one passage per row.
This approach is also computationally less expensive because of the single passage per blade row requirement and its intrinsic periodicity. However, this advantage is also its weakness: it assumes a priori knowledge of the frequencies, and it cannot model discontinuous-in-time features such as shock flow. Furthermore, as more rows are added to the analysis, more frequencies will need to be introduced which increases computational cost and blurs the distinction between harmonic balance and fully unsteady. 

FLOW: What is "domain scaling"?
STEVE: Domain scaling is yet another simplification of the fully unsteady approach.  This simplification comes in the form of explicit or implicit geometric scaling that enables a periodic sector of the full wheel to be analyzed.  For example, say you have a 1.5 stage turbine with 19 first vanes, 24 first blades and 19 second vanes.  To run full scale unsteady, you would need to simulate 62 passages (19+24+19).  Alternatively, by scaling the blade count for the first and second vanes to 18 you would end up with an 18/24/18 passage ratio which could then be reduced down to 3/4/3 => 10 passages.

Thus, the scaled unsteady approach gives you the opportunity to reduce the computational domain—by a factor of 6 in the example above—but it comes with a corresponding penalty on accuracy since the geometry is being modified to get there.  It's also more difficult to identify and quantify the modeling errors with domain scaling compared to either the phase lag or harmonic balance methods. 

FLOW: What is the difference between explicit and implicit scaling?
STEVE: The difference relates to how the domain scaling is carried out.  With explicit scaling, the actual geometry is modified in the x and theta directions; with implicit scaling, the interface boundary between adjacent blade rows is scaled to create a similar result without the need for man-in-the-middle modifications to geometry.  Please refer to the May 2011 edition of this newsletter for more information and a supporting case study. 
FLOW: What are your recommendations for when to use each of these methods?
STEVE: All of these approaches can be useful in certain situations.  For example, we think harmonic balance can be quite effective for single stage calculations where the dominant frequency is known, such as blade passing without strong vortex shedding.  This can be useful for high cycle fatigue analysis for cases of this type.  The phase lag approach can also be used in this fashion with the added benefit of being able to capture discontinuous shocks.   

On the other hand, if you need to assess multistage turbine/compressor performance, the need to model more frequencies will significantly increase computational cost. In these situations it may be more prudent to utilize domain scaling for unsteady analysis. And if the objective is to fully capture nonlinearities such as rotating stall, shocks and vortex shedding, we also believe it may be more prudent to invest a few thousand dollars on a cloud-based fully unsteady computation.

FLOW: What are the relative computational costs between the various unsteady approaches?
STEVE: Assuming 3D multistage steady has an index of 1, we'd roughly estimate harmonic balance to be 10-50, phase lag at 10-100, fully unsteady at 100-1,000 and scaled unsteady at 10-50 depending on the scaling factor.

FLOW: Any final thoughts?
STEVE: Three comments.  First, unsteady analysis really has the potential to advance turbomachinery durability and performance during design, so give it serious consideration. Second, be sure to understand the strengths and limitations of each unsteady techniques to gauge how they can be applied to your situation.  Finally, the best way to build confidence in these techniques is to put them to use and compare to your experimental results.  Most commercial CFD vendors offer evaluation programs to support this need.

FLOW: Thanks Steve.
STEVE: You're welcome.
CASE STUDY: Conjugate Heat Transfer of a Film Cooled Turbine Vane   
Under an SBIR Phase II award from the U.S. Air Force, a conjugate heat transfer capability has been developed for the ADS solver Code Leo.  In this recent paper from Turbo Expo 2011 (GT2011-45920), the conjugate heat transfer analysis methodology is defined and applied to a modern film cooled turbine vane consisting of 648 cooling holes.  <more>
TECHTIPS: Initializing a New Simulation with an Old Solution   
When running many cases with similar geometries, the number of iterations to convergence can be reduced by using a previous solution as an initial condition for the new geometry using ADS-FCOOL. <more>
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