NUMECA is now Cadence
Robust Design Optimization of a turbocharger impeller
This case focuses on a multidisciplinary multipoint robust design optimization (RDO) of a turbocharger compressor from FORD Motor Company.
The goal is to extend the compressor flow capacity and improve the surge margin. To reach this goal an active selfrecirculation casing treatment is used.
The standard deviation of the objectives choke mass flow and efficiency are reduced by 33% and nearly 48% respectively, leading to significantly more performance stability. Yannick Baux, Head of Turbomachinery, NUMECA International. 
Two different meshes are used for points close to choke and stall respectively given the varying geometry.
SIMULATION DOMAIN
The simulation domain consists of the impeller, a vaneless diffuser, the selfrecirculation casing and the volute for fluid flow simulation (CFD) and the solid blade with back plate for structural simulations (CSM).
 All parts are simulated (CFD and CSM)
 The impeller shape is optimized
Mesh size is 6.6 million points:
 Wheel and diffuser 2.7 million
 Casing 2.0 million
 Volute 1.5 million
 Solid blade 0.4 million
FINE™/Design3D is used to run the optimization:
 The CFD domain is meshed with a full hexahedral structural mesh in AutoGrid5™.
 The solid domain is meshed with a full hexahedral unstructured mesh in Hexpress™.
DESIGN SPACE
The design space consists of a total of 19 design variables and optimizations are performed as multipoint optimization accounting for the following design points:
 2 parameters for the hub line
 3 parameters for the camber line in two sections, i.e. a total of 6 parameters
 3 parameters for the camber line of the splitter in two sections, i.e. a total of 6 parameters
 1 parameter for the meridional location of the splitter
 2 parameters for the tangential location of the splitter
 2 parameters for the tangential stacking
Three different operating points on two different speed lines:
 Choke conditions at 120000rpm
 Stall conditions at 120000rpm
 Stall conditions at 40000rpm
 Mechanical stresses at 135000rpm
The robust optimization and the UQ study on the deterministic design accounts for the following uncertainties:
 Tip gap height ±25% (symmetric betaPDF)
 Blade thickness ±1% (symmetric betaPDF)
 ±1% (symmetric betaPDF) of the total pressure at the inlet or static pressure at the outlet respectively
 Boundary condition for choke and stall conditions are different
DESIGN OPTIMIZATION FORMULATION
The design optimization formulations for the standard (deterministic) and robust optimization are:
Deterministic formulation  Robust formulation 
Maximize efficiency in the two stall points (2 objectives)

Maximize the mean value of the efficiency in the two stall points (2 objectives) Minimize the standard deviation of the fficiency in the two stall points (2 objectives) 
Maximise choke mass flow (1 objective)

Maximize the mean value of the choke mass flow (1 objective) Minimize the standard deviation of the choke mass flow (1 objective) 
Maintain level pressure ratio in the two stall points (2 constraints) 
Maintain the level of the mean value of the pressure ratio in the two stall points (2 constraints) 
Maintain level of von Mises Stresses (1 constraint) 
Maintain the level of the mean value of von Mises Stresses (1 constraint) 
The number of objectives/constraints increases for the robust optimization. At the example of the efficiency, the deterministic optimization maximizes the efficiency in two stall points, while the robust optimization maximizes the mean value of efficiencies in the two stall points and minimizes at the same time the standard deviation of the efficiency.
COMPARISON: ORIGINAL DESIGN VS ROBUST DESIGN
If the performances of design 1 are compared with robust design 1, it can be seen the mean values of choke mass flow and efficiency vary in a similar range, but the standard deviations of these objectives are drastically reduced by the robust design formulation only. It is also to be noted that the resulting blade designs are notably different.
 Mean Choke mass flow: +6,7%
 Std. Dev. Choke mass flow: 7,2%
 Mean Efficiency at 120k rpm: 2,8%
 Std. Dev. Efficiency at 120k rpm: +36,85%
 Mean Choke mass flow: 10,9%
 Std. Dev. Choke mass flow: +80,8%
 Mean Efficiency at 120k rpm: 5,4%
 Std. Dev. Efficiency at 120k rpm: +53,8%
 Mean Choke mass flow: +4,2%
 Std. Dev. Choke mass flow: 33,0%
 Mean Efficiency at 120k rpm: 3,8%
 Std. Dev. Efficiency at 120k rpm: 47,9%
CONCLUSIONS
A multidisciplinary multipoint robust design optimization is performed and compared to a standard design optimization. Accounting for uncertainties in the optimization process allows to find optimal designs that are less sensitive to these uncertainties. The standard deviation of the objectives choke mass flow and efficiency are reduced by 33% and nearly 48% respectively, leading to significantly more performance stability.