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May 2011
The Flow
CFD Insights for the Turbomachinery Designer

INSIGHT: Scaling Blade Row Passages for Unsteady Analysis
Turbomachinery flows are inherently unsteady, but full-scale unsteady analysis remains elusive for commercial design due to computational cost.  Several approximation techniques are available to reduce this cost while maintaining an acceptable level of accuracy.  In this month's issue of The Flow, we sit down with Bob Ni to discuss the value and limitations of one such approach, geometric scaling.  Prior to founding ADS, Bob spent nearly 30 years at Pratt & Whitney leading turbomachinery CFD development in support of turbine and compressor design.

FLOW: Bob, how is scaling used in unsteady analysis?
BOB: Scaling is a commonly used approximation technique when blade row counts in a configuration are chosen to avoid periodicity/resonance.  For example, say I had a 1.5 stage turbine with 18 vanes, 24 blades and 18 vanes.  If I had sufficient computing power and a good solver, I could execute the simulation full wheel.  Alternatively, I could model a sector since the blade rows are divisible by 6.  This would allow me to conduct unsteady analysis on a 3/4/3 configuration.
But what if the blade row counts were 17/24/15?  Short of conducting full wheel unsteady analysis, the other option is to scale.  With scaling, you adjust the blade counts up or down to enable sector analysis to be conducted, recognizing that accuracy is being traded off in favor of turnaround time.  In this scenario, we might choose to scale the first vane down to 16 and the second vane up from 15 to 16 in order to get a 16/24/16 passage configuration that can be reduced to 2/3/2.
FLOW: How is scaling typically carried out?
BOB: Scaling is typically an explicit, manual process involving three steps.  First, the designer must scale the airfoil geometry the desired amount in the x and theta directions, holding r constant (for an axial flow machine).  Second, because the airfoils are scaled axially, the axial gap between adjacent blade rows changes and can materially impact predictions.  Therefore, adjustments must be made between adjacent blade rows to keep the axial gap consistent with the original case. Third, further adjustments may be required if the scaled geometry does not fit within the constraints of the defined endwalls.

FLOW: Sounds like a lot of work.  Are there better ways to handle scaling these days?
BOB: Yes.  To minimize the manual labor involved with explicit scaling, we've developed an alternative technique that we call implicit scaling.  With implicit scaling there is no need to manually adjust geometries, blade row locations and endwalls.  One simply specifies the desired target configuration (e.g. 2/3/2) and the ADS CFD system automatically scales the configuration to match that target.  Better yet, the implicit scaling approach has been designed in such a way that does not involve any adjustments of axial gaps or endwall geometry.

FLOW: What are the benefits of the implicit scaling approach?
BOB: The biggest benefit is that implicit scaling saves time by removing the manual labor from the scaling process.  A second benefit is that this approach can be automated and incorporated easily into design systems because no manual intervention is required.  A third benefit is broad applicability--this approach can be used equally as well on multi-stage axial and radial designs.  

FLOW: How does implicit scaling impact results?
BOB: Scaling, whether explicit or implicit, remains an approximation to obtain results in less time and computational cost.  In our experience, implicit scaling performs no better or worse that explicit scaling--it's just must simpler to use.  For example, we recently conducted an analysis of a 1.5 stage turbine consisting of 17 vanes, 24 blades and 17 vanes and compared the results of explicit and implicit scaling.  We found little to no difference in the predictions--less than a 0.2% difference in efficiency--between these techniques but a significant savings in setup time.  Check out the case study in the next section for more information.
FLOW: A lot of attention has been directed towards harmonic balance techniques to approximate unsteady behaviors.  How does this compare to the scaling approach?
BOB: Like all approximation techniques, it has its strengths and limitations.  Harmonic balance can be effective for single stage calculations in the dominant frequency is known, such as a blade passing without strong vortex shedding.  It is faster than unsteady simulation because of the smaller computational domain needed as well as the transformation to an equivalent steady simulation of one or more harmonics.  However, for multi-stage flow with large numbers of harmonics, the speed advantage of the method starts to deteriorate.  In addition, unlike scaling, harmonic balance will not work for transient flow problems. 
FLOW: Thanks, Bob.
BOB: My pleasure.
CASE STUDY: Unsteady Analysis of a Multi Stage Turbine Using Implicit Scaling  
Unsteady analysis of a notional 1.5 stage turbine is conducted using an implicit scaling technique developed for Code Leo.  Results are compared to full wheel unsteady predictions as well as predictions from an explicitly scaled run.  <more>
TECHTIPS: How to Extend an Inlet/Outlet Far Upstream of an Airfoil in Code Wand
  In some cases a user will want to extend the inlet or outlet of a domain far upstream of the airfoil.  This can be accomplished easily in Code Wand with a duct mesh.   <more>
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