Turbine performance improvement by the multi-objective optimization for variable nozzle vanes of turbocharger

This paper focuses on improving the turbine efficiency of a variable geometry system (VGS) of turbochargers for internal combustion engines. The study investigates the shape optimization of the turbine nozzle vane and impeller of VGS through a meta-model-assisted multi-objective optimization. The design parameters of the optimal solution were compared with the baseline model for data and internal flow field analysis to explore which parameters have an impact on performance improvement. It was found that the optimized trailing edge angle of the nozzle vanes allows the exhaust airflow to reach the impeller with the minimum traveling path, and it contributes to mitigating the mixing loss of the flow to the impeller blade. The optimized impeller blade angle leads to an increase in torque and a higher turbine efficiency (> 5%) with the narrow opening, also ensuring a high mass flow in the wide opening. This outcome can contribute to the design and development of high-performance and low-emission turbocharger systems by optimizing the performance of turbine design parameters simultaneously.


Introduction
The variable geometry system (VGS) of turbochargers enables automotive engines to satisfy power demand while ensuring extremely high transmission efficiency and making exhaust emissions cleaner.The turbocharger consists of a coaxially connected turbine and a compressor, which utilizes the combustion exhaust from the internal combustion engine passing into the turbine to drive the impeller, which then drives the coaxial compressor to draw in fresh air and compress it into the engine [1].This work cycle and the increase in the engine air intake is the basic principle of the turbocharger.Since the performance of the compressor is closely related to the turbine, when the performance of the turbine decreases, the power and air intake of the compressor will also be affected.Improving turbine performance is an important objective of turbine optimization design.
For this reason, the optimization of VGS has attracted the interest of both academia and industry.
Hatami [2] conducted a comparison of turbine performance under different pressure ratios and nozzle vanes' shapes for different combinations of blade height, thickness, length, and angle based on the experimental design method combined with the central composite design method.It was finally concluded that the blade angle has the greatest effect on turbine efficiency.Lei [3] conducted a CFD numerical study of the variation in VNT's (The variable nozzle turbines which is the same as VGS) performance due to the clearance between the nozzle blade and rotor.Several cases differ in gap size, rotation speed, and expansion rate conditions.It was found that the nozzle blade clearance was the main factor leading to the variation of VNT performance compared to the rotor clearance.Ota [4] carried out numerical simulations of different blade openings to obtain the location and opening of the main excitation of the blade.The analysis of the internal flow field state showed that the nozzle blade opening also affects the pressure distribution around the impeller and the stability of the impeller.Yamagata [5] conducted CFD calculations on a variable nozzle turbine to investigate the effect of the clearance around movable nozzle blades on the turbine performance and concluded that the nozzle blade clearance has a bigger impact on the turbine efficiency loss when the nozzle is closed.The results confirmed the consistency between the simulation and experiments.In order to get a high-performance turbocharger turbine, Fukaya [6] did research on the area around the nozzle vanes and the spacers by complex flow and designed a new vane shape that can improve the turbine efficiency.Based on the ordinary VNT section, Zhang [7] compared the aerodynamic performance inside the turbine and also made an analysis about the leakage loss by special variation.To avoid the leakage loss of the narrow opening of the vanes, a new blade design scheme that can partially rotate is proposed, which can improve the turbine efficiency under small opening conditions.Practical engineering design involves making optimal decisions with a balance between two or more conflicting objectives.For a mechanical design, a component will have many dimensions, and different combinations of design parameters will affect the shape change of the component, thus affecting the overall effect.In the process of optimal design, there will not be a single solution that optimizes each objective simultaneously.At the same time, the objective functions will have mutual interference.
Therefore, a set of optimal design solutions is usually found based on the optimization objectives what the designer requires.
In this context, this paper uses a multi-objective optimization system that combines a genetic algorithm (GA) and an artificial neural network (ANN) developed by the Von Karman Institute (VKI) [8] .This system uses artificial neural algorithms to analyze shapes and explore the best combination of shape data.In this optimization process, every candidate geometry is evaluated in terms of turbine/turbocharger efficiency for low-speed flows and Mass Flow Parameter (MFP) for high-speed flows.The research focus of this question is to optimize and redesign the nozzle blade position and shape, using the multi-objective optimization method, to seek the optimal solution under the combination of narrow opening and high performance and wide opening and high flow conditions.

The numerical model and information
A turbine with the same structure shown in Figure 1 is selected as the study model.In the numerical simulation, the nozzle vane, and impeller of the turbine are taken as the main study objects and regions.On the contrary, the scroll and inlet/outlet pipes of the turbine are not included in this study.The aim of this study is to improve the efficiency of the turbine.The main optimization objectives in this paper are the efficiency improvement at the narrow opening condition and the maintenance of high flow in the turbine at the wide opening condition.The main parameters of the model are shown in Table 1 and Table 2

Numerical analysis and constraints
The three-dimensional viscous flow calculations are carried out for the Reynolds Averaged Navier-stokes solver by the professional analysis CFD software ANSYS-CFX 20.2.The turbulence model is the SST (Share Stress Transport) model.The boundary conditions of inlet are set by total temperature and total pressure.In the process of numerical calculation, the gas from the engine with high pressure and temperature to the turbine, the total pressure is given at 257kPa, the total temperature is given at 873.15K.A static pressure of 101.325kPa is set as the outlet boundary condition.
Y + is the dimensionless distance from the wall to the first grid point.The flow near the boundary is divided into a viscous bottom layer, a transition layer, and a logarithmic layer.According to which layer the first lattice belongs, the turbulence model is determined.However, in this study, regardless of the layer of the first lattice, the turbulence model is automatically changed for calculation, and the SST model is used for analysis.In the calculation, Y + will take the value 6.In the computational simulation, the inlet flow channel, the scroll channel, the outlet flow channel, and the nozzle vanes' parts are taken by the numerical analysis validation.The nodes division of the main parts include the nozzle vanes and impeller that is shown in Figure 3 and the number of nodes is shown in Table 3.The entire computational model was divided into 24 million nodes, of which about 1.08 million nodes per Figure 4 shows the design pressure ratios of optimization on the characteristic curve.For the performance requirements of the VGS turbine, the turbine efficiency needs to be maximized at narrow openings at a low speed with the engine; and the quantity of flow also needs to be improved at a high speed with wide openings.
Therefore, as a function of the purpose of this optimization, the turbine efficiency at narrow openings and the modified flow rate (also called MFP: mass flow parameter) at wide openings are set in the design pressure ratio shown in Figure 4. To evaluate the turbine efficiency at the narrow opening, it is necessary to ensure that the turbine maintains a high flow rate at the wide opening.Therefore, the turbine efficiency was evaluated under the condition that the opening of the variable nozzle vane can make the MFP constant as shown in   Efficiency @Narrow Opening (4) MFP @Wide Opening The constraint conditions are presented in equation 5. First, the efficiency should be higher than the baseline, thus the dimensionless ratio calculated by dividing the efficiency of the optimized geometry by the efficiency of the baseline geometry (hereafter Optimized Efficiency) must be higher than the value 1.
Furthermore, regarding the RMS residuals of RANS analysis, the RMS residual in the narrow opening should be under 10 -4 , and in the wide opening should be under 10 -3 .The design parameters of the variable nozzle vane and turbine impeller set by this optimization are represented in Table 4 and Table 5.

Multi-objective optimization system
An ANN-GA (Artificial Neural Network -Genetic Algorithm) optimization approach was used in this research.The flowchart of this method, developed by the von Karman Institute (VKI) of Fluid Dynamics, is presented in Figure 6.The optimization process starts with a DOE (Design of Experiment) to randomly generate 64 (128 in VGS) geometries.Flow conditions using these geometries are simulated by CFD calculations and the performance results are used to generate a database file.Based on the information available in this database, the ANN-based meta-model can produce estimations for the performance of new geometries with less accuracy than CFD models, however with much lower computational requirements.At this point, the optimization loop (Level 1 in Figure 6) is initialized.Using the information provided by the meta-model results, the differential evolution algorithm generates a new candidate geometry, whose performance is again estimated and predicted by the ANN-based meta-model.Among all the geometries generated and evaluated through this optimization loop, a short number (six in the case of the present study) of promising candidates is simulated with high-accuracy CFD models.Through this, the meta-model is validated, and six more cases are added to the database (Level 2 in Figure 6) in every generation until the best optimization shape appeared.Then, the meta-model is re-trained with the enlarged database and the optimization loop is invoked again.

The shape comparison of the nozzle vanes
The result of optimization can make better efficiency than the baseline.And the output files by CFD can be used to confirm some changes inter the turbine.The shape of nozzle vanes and impeller were drawn by the profile data file that is based on points.Therefore, shape comparison between baseline and optimum can be made through graph reproduction.
Figure 8 (a) shows the shape of the optimum and baseline in the narrow opening and the wide opening.
To compare the nozzle vane easily, make a simple curve comparison for shape in Figure 8 (b).And putting the trailing edge point of two curves in the common original point, it can be found that the chord length of the optimum is shorter than the baseline.In Figure 8 (b) the middle camber line of the optimum is larger than the baseline as a smooth and fusiform shape.The camber can guide the direction of the air flow to impeller and also will impact the flow energy of the turbine.It is well known that the angle of the blade affects the wake trajectory.But this time we will only discuss the impact of the overall shape.In this part of the optimization, the new streamlining shape can reduce the air resistance.As can be seen from the comparison in Figure 8, the chord length of the optimum is shorter than the baseline.To make a sensitivity graph by collating the data about the relationship between efficiency and chord length in Figure 9, the coordinate axis is set in dimensionless, the efficiency is processed in minimizes for finding extreme value conveniently.By CFD analysis, the graphic of sensitivity can extrapolate a conclusion that the optimum with high efficiency matching to short chord length.

The shape comparison of the turbine impeller
The shape of the turbine impeller also has been changed in the optimization.

The internal analysis of the nozzle
Figure 12 shows the circumferential averaged entropy graph with the radius change in the turbine.All over the turbine radius from the inlet to the outlet, the baseline (blue) entropy increased largely.The entropy of the optimum (orange) from the nozzle inlet to the nozzle outlet gets larger than the baseline.And then in the part of the impeller from the inlet to the final outlet, the baseline entropy is bigger.Therefore, the entropy increase should be analyzed and confirm what can impact the efficiency of the turbine in the optimization.
Figure 13 is the chart of velocity with radius from inlet to outlet.It can be concluded that the velocity in the optimum accelerated greatly at the nozzle area.There is an effect about the optimum shape, it will give a larger pressure for increasing airflow rate.The Mach number contour was set on a plane that at span 50% of the hub to the shroud of the nozzle.To confirm with Figure 12, the entropy curve of optimum became lower after the nozzle throat to the impeller.
And in the contour of the Mach number, the velocity distribution can be seen in Figure 15.After analyzing the shape comparison, the different shapes will impact the internal flow of the turbine.At the same time, the longer flow path increases the frictional resistance between the airflow and the blades, and also generates shocks and friction between the airflows when mixing with the airflows coming out of the other nozzle flow paths and generating energy consumption.In this way, we can know the optimized shape of the nozzle vane can reduce the entropy increasing between the area of the nozzle vane and the impeller.

The internal analysis of the impeller
In section 4.1, it's known that the optimized shape can make a shorter flow path to the impeller.While doing the internal flow analysis in the area of nozzle, the Mach number distribution around the trailing edge has a difference which gives a larger velocity at the throat of the nozzle as shown in Figure 15.In Figure 16, a new surface that set as the boundary for the inlet of the impeller.This surface splits to two parts of the turbine.Figure 17 is the hub-to-shroud chart of the pressure with different spans, comparing the pressure with the hub side to the shroud side, the inlet pressure of optimum is bigger than the baseline on the hub side.From the hub to shroud side, the pressure at the beginning of airflow entering into the impeller has a very high initial value.Then the pressure in the area from the hub to the shroud becomes smaller but the optimum pressure is always larger than baseline invariably.To sum up the velocity and pressure of the result comparison, the part of turbine impeller can be given a larger energy by optimized nozzle vanes.
Figure 18 depicts the blade loading graph of pressure with streamwise at the span of 20% and span 70% from the hub of the impeller.The pressure of optimum is larger than the baseline from the leading edge.In Figure 18 (a) on the pressure side of the impeller blade, the pressure of the selected optimum model has consistently maintained values above the baseline.As known in the part of the analysis of the nozzle part, the air flowed out from the nozzle gives the impeller a larger kinetic energy by optimization.Therefore, the pressure at the impeller inlet can be kept at a larger value.
Figure 5 (b) has already explained the shape difference of the impeller.Because the rake angle has been changed that made the impeller blade is bent inward.From the Figure 18 (a) of the span 20%, it can be seen the pressure difference of the optimum between the pressure side and suction side is larger than the baseline in the whole range of the streamwise.The thrust force which can push the impeller rotating will be produced by this pressure difference.With the relationship between the thrust force and rotation rate, finally, the efficiency will also be improved by this positive pressure difference.In Figure 18 (b) of the span 70%, the pressure of optimum is also larger than baseline with pressure loading.The impeller blade has trended inward with the rake angle turned to the rotational direction side.

Conclusion and prospect
By using VKI multi-objective optimization, the impeller and nozzle vanes of the turbine inside the variable geometry turbocharger are optimized.The optimization objectives were aimed at achieving the goal of maintaining a high flow rate at the wide opening while enabling the improvement in the efficiency of the turbine by approximately 5% at the narrow opening.In summary, the following conclusions can be obtained from this research: 1. Using the multi-purpose optimization method, the efficiency performance of the optimized turbine can be improved by more than 5.2% at the narrow opening of nozzle blades while maintaining a high flow rate.The design parameters of the appropriate shape are finally obtained.
. The number of nozzle vanes is 11 and the number of impeller blades is 12.The turbine dimensions are written in Figure 2. In this paper, the dimension parameters are presented as dimensionless ratios in comparison with the baseline geometry.The VGS performance evaluation indexes are shown in equations (1) to (3).

( a )Figure 3 .
Figure 3. Computational mesh for the steady flow.

Figure 4 .
Figure 4. Location of optimization points on the characteristics curve.

Figure 5 .
Figure 5. Definition of the geometric parameters of the nozzle vane and impeller in the turbine.

Figure 6 .
Figure 6.The general layout of the VKI optimization system.

Figure 7
Figure 7 describes the result data of the variable nozzle vanes calculation.After the optimization of the VKI system described in Section 2.3, the results of the CFD calculations are presented in the form of graphs for visualization.The graphs represent the results obtained through optimization and shape searching, the two axes represent the objective function.The horizontal axis represents the turbine efficiency at the narrow opening and the vertical axis represents the MFP at a wide opening.The database generated is first combined and constructed based on the Design of Experiments (DOE) method with a design range of extreme values.The database is utilized as the input layer of the artificial neural network (ANN), which is trained and computed iteratively using the back-propagation algorithm, and the objective function is used as the output layer for the search of the eligible shapes.This is why called the IT point.During ANN learning and computation, the results of each generation are summarized in a Pareto chart until the optimization process is concluded by obtaining the best shape on the Pareto front.In the Pareto chart, gray indicates DOE data combination points and dark indicates data combination points that meet the constraints.The points on the Pareto Front located in the lower left of the graph are the results of the optimization that meets the objective function, while the target combination of the optimum is the best result under the trade-off choice.And the table.6shows the performance comparison of baseline and optimum with good advance.

Figure 7 .
Figure 7.The result of the Pareto solution by calculation.

8 .
(a) The shape of the baseline and optimum (left: baseline; right: optimum) (b) The shape comparison in same coordinate system The shape comparison of baseline and optimum.

Figure 9 .
Figure 9.The sensitivity graph of Chord length with efficiency.
Figure 10 presents both baseline and optimized geometries, showing different meridian planes of the impeller in the two cases.The TE (Trailing Edge) sideline (as the parameter deltatheta3) is moved to the rotational axis direction as a whole and with a larger inclination.The control point B on the hub side of the outlet portion of the impeller is longer than the control point A on the shroud side.Therefore, the meridian shape of the optimum impeller blade is The 17th Asian International Conference on Fluid Machinery (AICFM 17 2023) Journal of Physics: Conference Series 2707 (2024) 012156 smaller than the baseline.The actual outline of the turbine blades can be seen from the 3D model in Figure 11.The curvature of the impeller blade has increased the design parameter deltatheta1 has been bent to the rotational direction and changed from a curve to a straight-line shape in red line.The curvature for the degree of blade (deltatheta2) has been shown in Figure 5.The optimization impeller blades are shown to be inwardly curved in Figure 11.

Figure 10 .
Figure 10.The meridian plane of baseline and optimum.

Figure 11 .
Figure 11.The 3D model of impeller of baseline and optimum.

Figure 12 .
Figure 12.The inlet-to-outlet chart of the entropy with radius in narrow opening.

Figure 13 .
Figure 13.The inlet-to-outlet chart of the velocity with radius in the narrow opening.The streamlines for the narrow opening from the scroll outlet to the impeller inlet range are shown in Figure14.Comparing the streamline of the baseline and optimum, it can be found that the fluid passed the nozzle throat to the impeller inlet has made as a bundle of streamlines.In the ring channel area from the nozzle throat outlet to the impeller inlet, it can be seen that the streamline of optimum arriving at the impeller inlet takes a short distance.The air flows in baseline with a long path by rotating around the axis will impact

Figure 14 .Figure 15 .
Figure 14.The streamline of baseline and optimum with one pitch in narrow opening.(left: baseline; right: optimum)

Figure 16 .
Figure 16.The surface on the impeller inlet.

Figure 17 .
Figure 17.The hub-to-shroud chart of the pressure on the impeller inlet in narrow opening.

Figure 18 .
Figure 18.The blade loading of pressure and streamwise in narrow opening.

2 .
By exploring the internal flow distribution of the turbine, the optimized nozzle blade can shorten the airflow distance to the impeller and concentrate the flow to the turbine blade.It proves that the optimized shape of the nozzle blade has a positive influence on the performance of the turbine.It is also found that the chord length can impact the efficiency of the turbine.3.Analyzed the pressure loading of the impeller, the optimized impeller can load larger pressure and kinetic energy by high-speed airflow accelerated by nozzles.Moreover, the optimized rake angle of the turbine impeller blades increases thrust force by pressure difference from the pressure side to the suction

Table 1 .
The design size of the nozzle blade.

Table 2 .
The design size of the turbine impeller blade.

Table 4 .
Design parameters for nozzle blades optimization.

Table 5 .
Design parameters for turbine impeller blades optimization.

Table 6 .
Performance comparison of baseline and selected optimum.