MULTIPOINT VANED DIFFUSER DISCRETE ADJOINT SHAPE OPTIMIZATION WITH SU2 OPEN-SOURCE SOFTWARE

Lorenzo Fabris¹, Altug M. Basol¹, Bob Mischo², Sebastiano Mauri², Philipp Jenny²

¹ Ozyegin University, Graduate School of Science and Engineering, Dep. Of Mechanical Engineering – Cekmekoy, Istanbul (TR)

² MAN Energy Solutions Schweiz AG – Zurich (CH)

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OUTLINE

1. Introduction
2. Numerical solution of the flow field
3. Optimization Methodology
• Single Point discrete adjoint optimization
• Multi Point discrete adjoint optimization
4. Conclusions

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CENTRIFUGAL COMPRESSOR DEFINITION AND UTILIZATION

• Centrigual compressor is a type of turbomachinery.
• Through the impeller, it transfers energy to a compressible fluid increasing its pressure.
• Several applications fields: aerospace, automotive, energy, etc. etc.

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Three are the main components of a centrifugal compressor:

1. INLET: guides the flow into the impeller.
2. IMPELLER: transfers work to the fluid and increases its enthalpy.
3. DIFFUSER: decelerates the flow to increase static pressure.

Centrifugal compressor schematic diagram

Centrifugal compressor impeller and diffuser

DIFFUSER VANE

IMPELLER

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WHAT IS A DIFFUSER AND WHY DO WE NEED IT?

• Placed downstream of the impeller.
• It converts flow’s kinetic energy (high velocity) into potential energy (high pressure) by decelerating (diffusing) the gas.
• It can be vaned or vaneless.

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Types of diffusers schematic diagram, ‘’Effect of diffuser vane height and position on the performance of a centrifugal compressor’’, Sitaram N., Govardhan M., Proceedings of the Institution of Mechanical Engineers Part A Journal of Power and Energy, 2004

DIFFUSER VANE

IMPELLER

IMPELLER

VANELESS DIFFUSER

DIFFUSER VANE

VANELESS DIFFUSER

IMPELLER

IMPELLER

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IMPORTANCE OF DIFFUSER VANE OPTIMIZATION

• Vaned diffuser generates higher increase in outlet pressure.
• However, operating range is narrowed due to flow incidence angle with respect to the vanes.
• Diffuser optimization directly affects the compressor performances.
• Vane’s leading edge greatly affects performances.
• Optimizing with respect to a single operating point might negatively affect all the other points in the compressor chart. Hence, multi-point optimization is needed.

Casey M., Robinson C., ‘’Radial Flow Turbocompressors: Design, Analysis, and Applications’’, pp. 405 - 442

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AIM OF THE STUDY

Compressor chart for the selected test case with fixed rotational speed, Uzuner et Al. ‘’Analysis of a Radial Compressor with the Open-Source Software SU2’’ (2023)

OPERATING POINT 1

(CLOSE TO CHOCKING)

OPERATING POINT 2

(ZERO INCIDENCE)

The aim of this study is to perform a multi-operating point adjoint optimization with respect to the following operating points:

OPERATING POINT 1

OPERATING POINT 2

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COMPUTATIONAL FLOW DOMAIN

• A single passage of the vaned diffuser is selected as flow domain.
• The structured, multiblock mesh contains 300.000 elements.

INLET

PERIODIC 2

PERIODIC 1

BLADE

SHROUD

HUB

Flow scenario and boundary namings of KD22 Vaned Diffuser

Computational grid

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BOUNDARY CONDITIONS DEFINITION

OPERATING POINT 1

OPERATING POINT 2

• The SU2 solution presented in slide 6 is kept as reference for diffuser inlet boundary conditions.
• Outlet boundary conditions are experimental data.

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SOLVER SETTINGS

All simulations were carried out with SU2 v7.5.1 running on UBUNTU 20.0.4

• JST was proven unstable during the computation probably due to dispersive errors.
• For lower mesh density JST provided consistent solutions.
• ROE scheme with second order accuracy allowed to compute a stable solution.
• The solution is tightly converged with a drop of four orders of magnitude.

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BASELINE DESIGN MACH NUMBER CONTOUR AT MIDSPAN

Midspan section of 3D flow solution for operating point 1

Midspan section of 3D flow solution for operating point 2

FLOW SEPARATION DUE TO FLOW INCIDENCE WITH THE VANE

LOCALIZED LOSSES

OPERATING POINT 1 (CLOSE TO CHOKING)

OPERATING POINT 2 (ZERO INCIDENCE)

HIGH MASS FLOW RATE

DESIGN MASS FLOW RATE

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SINGLE POINT DISCRETE ADJOINT OPTIMIZATION

The following studies have been carried out:

• Single-operating point adjoint optimization for each operating point
• Multi-operating point adjoint optimization

FFD BOX and its control points visualization

Blade was parametrized with a FFD BOX:

• FFD degree = (2,2,2)

To avoid overlapping and meaningless shape deformation the following plane was fixed.

• FFD_FIX_K =(2,0,0)

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SINGLE POINT OPTIMIZATION CONVERGENCE

After the 4th iteration, the new design does not perform better than the baseline.

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BASELINE

OPTIMIZED

OP. POINT 1 OPTIMIZED DESIGN MACH NUMBER CONTOUR AT MIDSPAN

TOTAL PRESSURE LOSS VARIATION [%]: -13.61

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BASELINE

OPTIMIZED

OP. POINT 2 OPTIMIZED DESIGN MACH NUMBER CONTOUR AT MIDSPAN

TOTAL PRESSURE LOSS VARIATION [%]: -2.65

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OPERATING POINT 1 (FLOW SEPARATION)

OPERATING POINT 2 (ZERO INCIDENCE)

Midspan section of baseline and optimized blade for operating point 1

Midspan section of baseline and optimized blade for operating point 2

Optimized

Baseline

Optimized

Baseline

BLADE DEFORMATION AFTER SINGLE-OPERATING POINT OPTIMIZATION

BLADE DESIGN A

BLADE DESIGN B

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For multi-point gradient calculation, the following objective function was defined:

Derived from Kusch et Al. ‘’Multi-Point Optimization of a Venturi Mixer for Residential Heating’’, SU2 Conference 2022

MULTIPOINT DISCRETE ADJOINT OPTIMIZATION

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Satisfactory?

SHAPE

OPTIMIZED

MULTIPOINT DISCRETE ADJOINT OPTIMIZATION WORKFLOW

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Baseline

Single pt. (no incidence)

Multipoint

Single pt. (close to choking)

TRAILING EDGE

LEADING EDGE

MULTIPOINT VS SINGLE POINT OPTIMIZATION MIDSPAN BLADE SHAPE

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MULTIPOINT OPTIMIZATION LOSSES EVALUATION

• The optimization provides a loss decrease for both operating points.
• The magnitude of the improvement is lower – for each operating point – if compared to the single point optimization.

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CONCLUSIONS

• A multi-operating point optimization worflow was established sucessfully.
• The multi-point adjoint optimization successfully provided a three-dimenional blade geometry that led to a loss decrease for each of the selected operating points.
• Computational cost for multi-point optimization is higher given the necessity to compute two different direct and adjoint solutions to reach the combined gradient calculation.

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• Multizone simulation including inlet channel and impeller will be carried out.
• Validation of the study.

FUTURE OUTCOMES OF THE STUDY

OBSERVATIONS

• JST scheme was proven to be stable for coarser meshes. This scheme loses its consistency proportionally to the increase of mesh size.
• Instability of JST scheme could be traced back to spurious obscillations in the solution caused by dispersive errors.

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ACKNOWLEDGMENTS

• This study was carried out in partnership with MAN Energy Solutions Schweiz AG. Their intellectual support and experimental data sharing are greatly acknowledged.

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• We would like to thank Dr. Emre Ozkaya, Dr. Ole Burghardt, Dr. Matteo Pini and Dr. Tobias Kattmann that kindly helped in the realization of this study sharing their knowledge on SU2 and adjoint optimization.

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• Finally, we would like to thank Dr. Pedro Gomes for his overseas support and his incredible work on the source code, especially the one that allowed us to properly work on the FFD BOX parametrization.