NUMECA is now Cadence

Blade Design Optimization

FINE™/Design3D is used to optimize the aerodynamics performances of a centrifugal compressor wheel pre-designed with FINE/Agile™.

The blades count and shape are automatically varied to maximize the total-to-total efficiency.

 

The compressor efficiency has increased by almost 2% without re-fitting or conversion of the preliminary design geometry. All this in less than 4 hours on a standard workstation. 

Yannick Baux, Head of Turbomachinery, NUMECA International.

 

 

OPTIMIZATION SETUP DEFINITION

  • 500k cells – Mixing plane – CPU Booster
  • CPU time   = 0.6 CPU.h/MPts
  • Turnaround time =4 min⁡on 4 cores

Constraints:

  • Lower bound on Mass flow
  • Lower bound on TT Efficiency

22 parameters:

  • Hub curve x8
  • Beta angles x6
  • Blade thickness x6
  • Inlet Theta angle x1
  • Blade count x1

 

 

 

DESIGN OF EXPERIMENTS POPULATION

The number of samples computed to build the DoE is kept minimal, one CFD run per free parameter. The full database computation requires no more than half an hour on a standard workstation (12 cores). Advanced data analysis tools allow verifying the accuracy of the surrogate model.

 

Fill the Design of Experiments

  • Only 22 samples (= nb of parameters)
  • Can be processed in parallel
  • Turnaround time = 8 min on 44 cores (or 3h 20min on 4 cores)

Evaluate the accuracy of the surrogate model: Leave-One-Out

  • For each point, build a surrogate model with all others and compare the predicted value with the accurate value from the CFD run.

        

 

OPTIMUM SEARCH (SEQUENTIAL)

Sequential search: minimum number of runs to reach the optimum design.

 

One candidate per design iteration

Best design 93:

  • EFFTT = 0.8816
  • MF = 2.052 kg/s
  • PR = 1.179

78 sequential runs in the search

 

CPU time = 27.8 CPU.h

Turnaround time = 7h on 4 cores

 

 

 

OPTIMUM SEARCH (PARALLEL)

Parallel search: one point evaluate the optimum while the others explore the design space to minimize the turnaround time.

 

Three candidates per design iteration

One point evaluate the optimum, the others explore.

Best Design 137:

  • EFFTT = 0.8826
  • MF = 2.050 kg/s
  • PR = 1.179

128 runs in the search
3 processed in parallel

 

CPU time = 41.7 CPU.h

Turnaround time = 3h30min
on a workstation with 12 cores

 

 

 

 

ANALYSIS OF VARIANCE ANOVA

Which parameters have the most influence?

  • Beta angles are the most influential parameters
  • Blade count is second in terms of influence
  • Thickness has almost no influence

 

 

OPTIMIZATION RESULTS

Efficiency raise of +1,8%

 

   

 

 

          

 

CONCLUSION

In less than 4 hours on a standard workstation, you have increased the efficiency of your preliminary design by almost 2%.