shroud contour optimization for a … shroud contour optimization for a turbocharger centrifugal...

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SHROUD CONTOUR OPTIMIZATION FOR A TURBOCHARGER CENTRIFUGAL COMPRESSOR TRIM FAMILY

H.-P. Dickmann

ABB Turbo Systems Ltd, R&D Turbochargers/Fluid Mechanics, 5401 Baden, Switzerland, [email protected]

ABSTRACT A wide range of flow rates can only be covered by a family of compressors which are called

trims. In the compressor map trims differ by a horizontal shift of the speed lines. Designs for lower flow rates are achieved by reducing the passage area. The goal is to maintain efficiency and pressure ratio of the base design as far as possible. In this study, an optimizing tool has been used to design the axisymmetric impeller shroud contour for each trim. Only the best efficiency point of the 100% speed line for each trim was optimized. Afterwards two complete speed lines were computed with the new geometry and analyzed. Whereas smaller trims typically show considerably lower efficiency levels, this optimization resulted in a relative efficiency loss of 0.94% only for an almost 20% smaller geometry combined with the same absolute tip clearance as the one of the base design. The pressure ratio of the best point of the base design could be maintained for all trims.

NOMENCLATURE Cp [-] pressure recovery coefficient ζ [-] total pressure loss coefficient m& [kg s-1] mass flow ∆rel [-] (opt. value – start value) / (start value) N [revolution s-1] rotational shaft speed p [Pa] pressure Subscripts R [m] radial coordinate 1, 2 inlet and outlet of component or stage T [K] temperature 1-7 trim sizes from low to high V& [m3 s-1] volume flow (pt1=1 bar, Tt1=298 K) # arbitrary trim size y+ [-] wall distance in normal direction best best efficiency point on speed line Z [m] axial coordinate s, t static, total η [-] isentropic total to total efficiency Superscripts ρ [kg m-3] density * normalized with corresponding value Π [-] total to total pressure ratio of best point of base design INTRODUCTION Although probably all turbocharger and industrial compressor manufacturers use compressor trimming, there is surprisingly little published literature on this topic. Engeda (2007) lists the following methods to adjust an existing compressor design to a smaller flow range:

1 Varying the angle of the inlet guide vanes (if inlet guide vanes are existing) 2 Narrowing the impeller flow passage depth (impeller exit width trimming) 3 Varying the inlet angle of the diffuser vanes 4 Radial cropping of the impeller blades 5 Radial cropping of the diffuser vanes

A 6th method was introduced by Grigoriadis et al. (2012) where a conical nozzle-type element is

inserted into the casing upstream of the impeller of an automotive turbocharger compressor without changing the impeller geometry. This principle implies no flow into the inducer at higher radii.

Proceedings of

10th European Conference on Turbomachinery Fluid dynamics & Thermodynamics

ETC10, April 15-19, 2013, Lappeenranta, Finland

OPEN ACCESS

Downloaded from www.euroturbo.eu Copyright © by the Authors

As a reason to apply trimming Engeda process industry)modification of an existing impeller. to use trimming: Diesel engines. The flow range for the entire power classbut by a family of compressors. Tcapacity. Trims, tEvery member has to cover a certain flow range preferably maintaining efficiency and pressure ratio of the base design. that the entireAs the turbodesigns” takingjust by a horizontal shift of the speed lines.proportionalmembers have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the list above by varying the Engeda (2003) (2001) does not mention whether work also applies method 2trim resultinghad to be maintained for all trims. This is due tocause blade ruconstant for the smaller trims.“mm” while TRIM FAMILYIn the present case tand volume flow by a factor ofidea is that trim 2the flow cross sectionsand smallest trim

Figure 1: Compressor Map

NUMERICAL DISCRETIZATIONThe CFD model has been reduced to one 320’000 cells) have not been modeled.

As a reason to apply trimming Engeda process industry) have to respond instantly to new impeller designs or in an aftermarket situation to modification of an existing impeller. to use trimming: a turboDiesel engines. The flow range for the entire power classbut by a family of compressors. T

Trims, the smaller Every member has to cover a certain flow range preferably maintaining efficiency and pressure

o of the base design. that the entire family guarantees a gap free overlapping within a combined compressor map (FigAs the turbocharger shaft speed is the same for all trims,

” taking into account the rules of geometric similarity. In the compressor map trims differ just by a horizontal shift of the speed lines.proportional to the ratio of impeller (and diffuser) members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the list above by varying the Engeda (2003) for shrouded impellers (2001) does not mention whether work also applies method 2

resulting in blade height had to be maintained for all trims. This is due tocause blade rubbing. Blade rubbing is caused constant for the entire smaller trims. Absolute tip clearance“mm” while relative tip clearance

TRIM FAMILY In the present case two adjacent and volume flow by a factor ofidea is that trim 2 can

flow cross sectionsand smallest trim of this family

Compressor Map

NUMERICAL DISCRETIZATIONThe CFD model has been reduced to one

cells) with periodic boundary conditions. been modeled.

As a reason to apply trimming Engeda have to respond instantly to new impeller designs or in an aftermarket situation to

modification of an existing impeller. turbocharging system is usually designed for a typical power cl

Diesel engines. The flow range for the entire power classbut by a family of compressors. T

he smaller members Every member has to cover a certain flow range preferably maintaining efficiency and pressure

o of the base design. The so-family guarantees a gap free overlapping within a combined compressor map (Fig

charger shaft speed is the same for all trims, into account the rules of geometric similarity. In the compressor map trims differ

just by a horizontal shift of the speed lines.tio of impeller (and diffuser)

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the list above by varying the shrouded

for shrouded impellers (2001) does not mention whether work also applies method 2 where t

blade height reduction.had to be maintained for all trims. This is due to

. Blade rubbing is caused entire compressor

Absolute tip clearanceelative tip clearance

wo adjacent and volume flow by a factor of 1.0388

can handle 1/1.0388flow cross sections at the impeller inlet and exit and in the entire vaned diffuser

of this family is

Compressor Map with 6

NUMERICAL DISCRETIZATIONThe CFD model has been reduced to one

with periodic boundary conditions. been modeled. The mesh, consisting of structured blocks (

As a reason to apply trimming Engeda (2003)have to respond instantly to new impeller designs or in an aftermarket situation to

modification of an existing impeller. Turbocharger manufacturers charging system is usually designed for a typical power cl

Diesel engines. The flow range for the entire power classbut by a family of compressors. The base design is applicable to the uppe

members of the compressor family Every member has to cover a certain flow range preferably maintaining efficiency and pressure

-called trim factor between two adjacent trims is defifamily guarantees a gap free overlapping within a combined compressor map (Fig


just by a horizontal shift of the speed lines.tio of impeller (and diffuser)

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the shrouded impeller tip diameter. Rodgers (2001)

for shrouded impellers have presented analog comparisons for method 2. (2001) does not mention whether tip clearance was

where the impeller shroudreduction. In addition

had to be maintained for all trims. This is due to. Blade rubbing is caused

compressor family and does not allow to reduce Absolute tip clearance is the real distance

elative tip clearance is a percentage of blade height.

wo adjacent trim family members 1.0388. Trim 7 i1.03885 = 1/1.21 = 82

impeller inlet and exit and in the entire vaned diffuseris 1.21. Figure 2 shows an overlay of the 6 compressor trims.

with 6 Trims

NUMERICAL DISCRETIZATION The CFD model has been reduced to one pitch per

with periodic boundary conditions. The mesh, consisting of structured blocks (

2

(2003) mentions have to respond instantly to new impeller designs or in an aftermarket situation to

Turbocharger manufacturers charging system is usually designed for a typical power cl

Diesel engines. The flow range for the entire power classe base design is applicable to the uppe

of the compressor family Every member has to cover a certain flow range preferably maintaining efficiency and pressure

called trim factor between two adjacent trims is defifamily guarantees a gap free overlapping within a combined compressor map (Fig


just by a horizontal shift of the speed lines. The ratio of ctio of impeller (and diffuser) inlet cros

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the impeller tip diameter. Rodgers (2001)

have presented analog comparisons for method 2. tip clearance was reduced

impeller shroudIn addition, the absolute tip clearance of the

had to be maintained for all trims. This is due to mechanical reasons. Blade rubbing is caused considerably

family and does not allow to reduce is the real distance

a percentage of blade height.

family members Trim 7 is the base design and trim 2 is the smallest trim. = 1/1.21 = 82.7

impeller inlet and exit and in the entire vaned diffuserFigure 2 shows an overlay of the 6 compressor trims.

Figure

pitch per componentwith periodic boundary conditions. The v

The mesh, consisting of structured blocks (

mentions that manufacturershave to respond instantly to new impeller designs or in an aftermarket situation to

Turbocharger manufacturers in contrastcharging system is usually designed for a typical power cl

Diesel engines. The flow range for the entire power class cannot be covered by just one compressor, e base design is applicable to the uppe

of the compressor family are derived from this base design. Every member has to cover a certain flow range preferably maintaining efficiency and pressure


charger shaft speed is the same for all trims, their designs into account the rules of geometric similarity. In the compressor map trims differ

The ratio of choke line volume flows inlet cross sections

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the impeller tip diameter. Rodgers (2001)

have presented analog comparisons for method 2. reduced while decreasing

impeller shroud contour was the absolute tip clearance of the

mechanical reasonsconsiderably by an impeller tilting moment

family and does not allow to reduce is the real distance between

a percentage of blade height.

family members of a turbocharger compressor s the base design and trim 2 is the smallest trim.

7% of the volume flow of trim 7impeller inlet and exit and in the entire vaned diffuser

Figure 2 shows an overlay of the 6 compressor trims.

Figure 2: Overlay of

component (impeller: The volute and

The mesh, consisting of structured blocks (

that manufacturers (i.e. have to respond instantly to new impeller designs or in an aftermarket situation to

in contrast have a different reason charging system is usually designed for a typical power cl

cannot be covered by just one compressor, e base design is applicable to the uppe

are derived from this base design. Every member has to cover a certain flow range preferably maintaining efficiency and pressure


designs are not “just scaledinto account the rules of geometric similarity. In the compressor map trims differ

hoke line volume flows s sections. Comparisons of trim family

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the impeller tip diameter. Rodgers (2001) for open i

have presented analog comparisons for method 2. while decreasing

was separately the absolute tip clearance of the

mechanical reasons, because simpeller tilting moment

family and does not allow to reduce the absolute between blade and casing

of a turbocharger compressor s the base design and trim 2 is the smallest trim.

of the volume flow of trim 7impeller inlet and exit and in the entire vaned diffuser


Overlay of 6

impeller: 1’400’000olute and the inducer casing bleed system

The mesh, consisting of structured blocks (y+ < 2 along walls),

i.e. of compressors for have to respond instantly to new impeller designs or in an aftermarket situation to

have a different reason charging system is usually designed for a typical power class of gas or

cannot be covered by just one compressor, e base design is applicable to the upper limit of swallowing


called trim factor between two adjacent trims is defined that way family guarantees a gap free overlapping within a combined compressor map (Fig

are not “just scaledinto account the rules of geometric similarity. In the compressor map trims differ

hoke line volume flows Comparisons of trim family

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the for open impellers

have presented analog comparisons for method 2. while decreasing trim size. The present

rately optimized the absolute tip clearance of the base design

because smaller impeller tilting moment

the absolute tip clearance for blade and casing with dimension

of a turbocharger compressor differ in size s the base design and trim 2 is the smallest trim.

of the volume flow of trim 7. The ratioimpeller inlet and exit and in the entire vaned diffuser between


Trims

1’400’000 cellsinducer casing bleed system

along walls), is a result of

of compressors for have to respond instantly to new impeller designs or in an aftermarket situation to

have a different reason ass of gas or

cannot be covered by just one compressor, r limit of swallowing


ned that way family guarantees a gap free overlapping within a combined compressor map (Fig. 1).

are not “just scaled base into account the rules of geometric similarity. In the compressor map trims differ

hoke line volume flows is ideally Comparisons of trim family

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the mpellers and

have presented analog comparisons for method 2. Rodgers The present

optimized for each base design

maller gaps could impeller tilting moment, which is

tip clearance for with dimension

differ in size s the base design and trim 2 is the smallest trim. The

. The ratio of between biggest


cells, diffuser: inducer casing bleed system

is a result of

of compressors for have to respond instantly to new impeller designs or in an aftermarket situation to

have a different reason ass of gas or

cannot be covered by just one compressor, r limit of swallowing


ned that way 1).

base into account the rules of geometric similarity. In the compressor map trims differ

is ideally Comparisons of trim family

members have been presented by Sapiro (1983) and Casey (1990), who applied method 4 from the and

Rodgers The present

for each base design

ould , which is

tip clearance for with dimension

differ in size The

of biggest

, diffuser: inducer casing bleed system

is a result of

3

mesh independence studies for a similar compressor stage. A CFD Solver from NUMECA (2010) has been applied. The Spalart-Allmaras turbulence model is used. The working fluid is air (ideal gas). Walls are assumed to be adiabatic. A central spatial discretization scheme of 2nd and 4th order of Jameson was used and an explicit 4-stage Runge Kutta discretization scheme in time. The mixing plane model is used for the rotor-stator interface. The relative error in mass flow balance is always less than 0.01%.

BOUNDARY CONDITIONS All computations were run with pt = 1 bar and Tt = 298 K at the inlet. The inflow direction is normal to the inlet boundary, here axial. For each speed line the procedure was as follows: starting at the choke line the averaged static pressure ps at the outlet has been increased until it was impossible to arrive at a converged solution. In a second step, the mass flow at the best efficiency point computed with the previous technique was reduced until, again, no converged solution could be reached. For each trim all data base samples and optimization samples were calculated for one operating point only: the best efficiency point with a mass flow prescribed at the outlet.

OPTIMIZATION PROCESS The trim optimization process, the geometry generation and parameterization followed by the grid generation were conducted with modules from NUMECA (2010). Figures 3 and 4 describe the optimization process at the parameterized geometry and with a flow chart. For each trim the best efficiency point on the 100% speed line had to be improved. Before the optimization process was started, it had to be checked whether the base design (trim 7) could be improved as well. Based on this design first guesses for trims 6,5,4,3 and 2 had to be created, followed by the actual optimization. Each trim was optimized separately. The axisymmetric flow path for the first guess per trim geometry is achieved as follows (right part of figure 3): - the hub contour (B1+B2) is kept constant for all trims - the shroud contour has to be adjusted to get lower cross sections than for the base design:

� C1 is shifted to lower R values � C3 and C4 are shifted to higher Z values

- C2 is changed manually with Bezier points to fit in between Before starting the optimization process, for each trim the first guess or base design geometry has to be parameterized to be able to generate the basic mesh. According to Figure 3 all coordinates are kept constant except the majority of points which define curve C2 on top of the blades’ tip contours. These points are allowed to change within a given reasonable interval. The blade geometry (main & splitter, each defined by 5 cuts) and the vane geometry input data never change. The vaned diffuser downstream of the interface remains “untouched” during the entire optimization process. This implies that its mesh is identical for all samples. The impeller blades have to be cut off due to the current shroud contour shape maintaining the absolute tip clearance of the base design. This is reached by the fact that only the shroud contour is exchanged in the input data for the impeller mesh generation process which adjusts the tip clearance automatically. It is important to mention that no point on C2 should have a radial coordinate lower than on line C1. Otherwise the impeller cannot be inserted into the “one part” casing. The number of the so-called free parameters to describe a new geometry is 11. There are 6 axial and 5 radial coordinates to define the shroud contour. The parameterization of the first guess (start solu-tion) is called fitting. For all trims the genuine geometry and the fitted geometry match very well. The computation of two speed lines (N*=100% and N*=70%) is repeated for the solution of the first guess for two reasons. First, one has to make sure that the parameterized geometry provides the same results as the previously non-parameterized geometry. Second, the solution of the first guess will be compared to the speed lines for the optimized geometry later on.

Fig. 3: Definition of Parameterized Geometry

Figure 4: Flow Chart of the Optimization Process The optimization procdata base was generated and calculated with CFD. The postprocessing was previously defined in order to osamples around three times the number of


: Flow Chart of the Optimization Process

The optimization procdata base was generated and calculated with CFD. The postprocessing was previously defined in order to obtain 1D parameters and typical turbomachinery CFD plots. Typically a number of samples around three times the number of



The optimization process is based on a surrogated method. For the data base was generated and calculated with CFD. The postprocessing was previously defined in

1D parameters and typical turbomachinery CFD plots. Typically a number of samples around three times the number of



sed on a surrogated method. For the data base was generated and calculated with CFD. The postprocessing was previously defined in

1D parameters and typical turbomachinery CFD plots. Typically a number of samples around three times the number of free parameters is sufficient (Hildebrandt et al. (2009)).

4




1D parameters and typical turbomachinery CFD plots. Typically a number of free parameters is sufficient (Hildebrandt et al. (2009)).



sed on a surrogated method. For the design of experiments (DOE), a data base was generated and calculated with CFD. The postprocessing was previously defined in


design of experiments (DOE), a data base was generated and calculated with CFD. The postprocessing was previously defined in





1D parameters and typical turbomachinery CFD plots. Typically a number of

5

Based on the DOE data base, the optimization is started with one objective function only: η, the total-to-total isentropic efficiency of the stage, should be maximized. Concerning all 6 optimiza-tions after 50 samples maximum the process was stopped. It was observed that as some kind of rule η did not improve significantly after the first 25 samples. To close the process, for each trim the computation of two speed lines had to be repeated with the optimized geometry to see the influence on other operating points of the N*=100% speed line, especially on the ones close to surge and at the choke line and on the N*=70% speed line. The right part of figure 5 shows the results in form of optimized shroud contours for 6 trims in comparison to the start contours on the left part (base design for trim 7, first guesses for trims 6,5,4,3 and 2). Direct comparisons (before vs. after) of the contours of trim 7 and trim 4 are shown later on. The specialty of the first guesses of trims 3 and 2 are discussed in a later chapter (“Splitter blade choke as a result of a bad first guess”).

Figure 5: Shroud Contours: First Guesses (left) and optimized (right)

INFLUENCE ON THE BEST POINT OF 100% SPEED LINE PER TRIM The efficiency gain per trim on the best point of the N*=100% speed line is shown in figure 6 and table 1. η* is normed by η of the base design’s best point on the N*=100% speed line. The relative gain of η* and Π is defined as “(optimized value – start value) / start value” in percent. All 6 optimizations were successful. The relatively low gain in η* for the base design can be explained by the fact that the base design was developed by experienced engineers and was already improved during several iterations. As the derived smaller trims of the base design had been created primarily to produce a start solution of the optimization process, it is not surprising that the gain in efficiency is comparatively higher here. The first guesses of trims 3 and 2 can be regarded as either “bad on purpose” or as “not checked well enough” especially in comparison to the previous trims (geometry and speed lines) before starting the optimization. But even these incidentally bad guesses did not prevent the optimization module to arrive at an optimum that fits onto a linear regression line for a “rule of thumb” which indicates the efficiency for smaller trims in the present case. The specialty of trims 3 and 2 in figure 6 are explained as follows:

1) For trims 4 to 7 there were no better efficiencies for lower or higher mass flows than for the one which was kept constant through the optimization process.

2) As the first guesses for trims 3 and 2 were choked (see later on) and the mass flow was kept constant during optimization, it turned out that the optimized shroud contour provided better efficiencies for slightly lower mass flows than for the one which was kept constant. Therefore these two points were inserted as well into figure 6 and used to compute the linear regression line.

This line indicates for the present case that between two trims the smaller one loosesnormalizedis the difference efficiencies

Fig 6: Efficiency Gain per Trim Optimization Table 1 shows efficiency and pressure ratio at relative changes optimized one (1.008It was of interest what could be gained if the for a smallerto suction side of scaled tip clearance. compressor stage

INFLUENCE ON REST OF 100%As the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not mentioned in Rodgers (2trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled andsquares per trim).Tt1= 298K is applied. The optimized shroud contours allowed to compute more converged results for points in the direction of small volume flow. This by an experiment)The left part of figure 7have been a lucky coincidence to achieve an improved part load speed line by optimizing with respect to the best point oif shifted slightly downward in case of the base design. For trim 4 it is even worse: It was impossible to compute converged operating pointas for the base design.efficiencies than higher trims do (filled and empty squares in left part of even measured for a different trim fam

This line indicates for the present case that between two trims the smaller one loosesnormalized efficiency is the difference between the efficiencies η (both values < 100%) are even smaller, of course.

: Efficiency Gain per Trim Optimization

shows efficiency and pressure ratio at relative changes for all trimoptimized one (1.008) It was of interest what could be gained if the for a smaller trim. Smaller tip clearance minimizes losses caused by the flow from to suction side of a blade. Therefore the optimized shroud contour scaled tip clearance. It was possible to increase compressor stage. Π∗

INFLUENCE ON REST OF 100%As the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not mentioned in Rodgers (2trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled andsquares per trim). For turbocharger compressor maps usually a volume flow relating to p

= 298K is applied. optimized shroud contours allowed to compute more converged results for points in the

n of small volume flow. This by an experiment) which is positive as well as in addition to the gainThe left part of figure 7have been a lucky coincidence to achieve an improved part load speed line by optimizing with respect to the best point oif shifted slightly downward in case of the base design. For trim 4 it is even worse: It was

possible to compute converged operating pointas for the base design.efficiencies than higher trims do (filled and empty squares in left part of even measured for a different trim fam

This line indicates for the present case that between two trims the smaller one loosesency η* compared to

between the (both values < 100%) are even smaller, of course.


shows efficiency and pressure ratio at for all trim optimization

) could be maintIt was of interest what could be gained if the

trim. Smaller tip clearance minimizes losses caused by the flow from blade. Therefore the optimized shroud contour It was possible to increase changes from 1.016 to 1.

INFLUENCE ON REST OF 100%As the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not mentioned in Rodgers (2003) and Engeda (2007). Figure 7trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled and

For turbocharger compressor maps usually a volume flow relating to p= 298K is applied. Therefore it is directly proportional to mass flow via

optimized shroud contours allowed to compute more converged results for points in the n of small volume flow. This

which is positive as well as in addition to the gainThe left part of figure 7 shows the influence of the optimized shroud contour on part load. It would have been a lucky coincidence to achieve an improved part load speed line by optimizing with respect to the best point of the design speed line. Except for the choking part the if shifted slightly downward in case of the base design. For trim 4 it is even worse: It was

possible to compute converged operating pointas for the base design. Counterintuetively, in part load it can happen that smaller trims show better efficiencies than higher trims do (filled and empty squares in left part of even measured for a different trim fam

This line indicates for the present case that between two trims the smaller one loosescompared to the higher one or 0.973

between the computed (both values < 100%) are even smaller, of course.


shows efficiency and pressure ratio at optimizations.

could be maintained for all trims in theirIt was of interest what could be gained if the

trim. Smaller tip clearance minimizes losses caused by the flow from blade. Therefore the optimized shroud contour It was possible to increase changes from 1.016 to 1.

INFLUENCE ON REST OF 100%-SPEED LINE AND ON ENTIRE 70%As the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not

003) and Engeda (2007). Figure 7trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled and

For turbocharger compressor maps usually a volume flow relating to pTherefore it is directly proportional to mass flow via

optimized shroud contours allowed to compute more converged results for points in the n of small volume flow. This could be interpreted with a gain in surge margin

which is positive as well as in addition to the gainshows the influence of the optimized shroud contour on part load. It would

have been a lucky coincidence to achieve an improved part load speed line by optimizing with f the design speed line. Except for the choking part the

if shifted slightly downward in case of the base design. For trim 4 it is even worse: It was possible to compute converged operating point

nterintuetively, in part load it can happen that smaller trims show better efficiencies than higher trims do (filled and empty squares in left part of even measured for a different trim family at the OEM. The source of this behaviour has not been

6

This line indicates for the present case that between two trims the smaller one loosesthe higher one or 0.973

d optimized points)(both values < 100%) are even smaller, of course.

: Efficiency Gain per Trim Optimization Table 1: Efficiency and Pressure Ratio per Trim Optimization

shows efficiency and pressure ratio at the beginning . The base design pressure ratio

ained for all trims in theirIt was of interest what could be gained if the relative tip clearance

trim. Smaller tip clearance minimizes losses caused by the flow from blade. Therefore the optimized shroud contour It was possible to increase η* from changes from 1.016 to 1.020.

PEED LINE AND ON ENTIRE 70%As the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not

003) and Engeda (2007). Figure 7trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled and


optimized shroud contours allowed to compute more converged results for points in the be interpreted with a gain in surge margin



if shifted slightly downward in case of the base design. For trim 4 it is even worse: It was possible to compute converged operating points for the optimized shroud contour as far

nterintuetively, in part load it can happen that smaller trims show better efficiencies than higher trims do (filled and empty squares in left part of

ily at the OEM. The source of this behaviour has not been

η∗η∗η∗η∗ [%]

trimstart

optimizedlower m

∆η∆η∆η∆η rel

trimoptimizedlower m

ΠΠΠΠ [%]

trimstart

optimizedlower m

∆Π∗∆Π∗∆Π∗∆Π∗

trimoptimizedlower m

This line indicates for the present case that between two trims the smaller one loosesthe higher one or 0.973 % between trim 7 and trim 2

ed points). The(both values < 100%) are even smaller, of course.

Table 1: Efficiency and Pressure Ratio per Trim Optimization

the beginning and e design pressure ratio

ained for all trims in their best efficiency pointstip clearance

trim. Smaller tip clearance minimizes losses caused by the flow from blade. Therefore the optimized shroud contour

* from 99.70% (table 1) to 99.79%


003) and Engeda (2007). Figure 7 shows these influences for trim 4 and trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled and





if shifted slightly downward in case of the base design. For trim 4 it is even worse: It was s for the optimized shroud contour as far

nterintuetively, in part load it can happen that smaller trims show better efficiencies than higher trims do (filled and empty squares in left part of


[%]

trim 2start 97.27

optimized 98.97lower m 99.20

rel∗∗∗∗ [%]

trim 2optimized 1.74lower m 1.99

[%]

trim 2start 0.975

optimized 1.022lower m 1.014

∆Π∗∆Π∗∆Π∗∆Π∗ [%]

trim 2optimized 4.80lower m 4.00

This line indicates for the present case that between two trims the smaller one loosesbetween trim 7 and trim 2he differences between absolute

Table 1: Efficiency and Pressure Ratio per Trim Optimization

and of the optimized design e design pressure ratio Π

best efficiency pointstip clearance of the base design

trim. Smaller tip clearance minimizes losses caused by the flow from blade. Therefore the optimized shroud contour of trim 4 was combined with the

99.70% (table 1) to 99.79%


shows these influences for trim 4 and trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled and

For turbocharger compressor maps usually a volume flow relating to pTherefore it is directly proportional to mass flow via ρt1=constant


which is positive as well as in addition to the gain in efficiency for the best shows the influence of the optimized shroud contour on part load. It would



nterintuetively, in part load it can happen that smaller trims show better efficiencies than higher trims do (filled and empty squares in left part of figure 7


3 496.91 99.0399.04 99.7099.37

3 42.20 0.682.53

3 40.976 0.9900.988 1.0161.008

3 41.16 2.593.28

This line indicates for the present case that between two trims the smaller one loosesbetween trim 7 and trim 2

differences between absolute

Table 1: Efficiency and Pressure Ratio

of the optimized design Π* of 1.000 or even the

best efficiency points. of the base design is maintained

trim. Smaller tip clearance minimizes losses caused by the flow from the pressure side was combined with the

99.70% (table 1) to 99.79% for the trim 4

PEED LINE AND ON ENTIRE 70% -SPEED LINEAs the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not

shows these influences for trim 4 and trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled and

For turbocharger compressor maps usually a volume flow relating to p=constant: V

optimized shroud contours allowed to compute more converged results for points in the be interpreted with a gain in surge margin (to be proved

in efficiency for the best shows the influence of the optimized shroud contour on part load. It would

have been a lucky coincidence to achieve an improved part load speed line by optimizing with f the design speed line. Except for the choking part the η* curve looks as


nterintuetively, in part load it can happen that smaller trims show better figure 7). This effect was


5 699.64 99.8699.87 100.07

5 60.23 0.21

5 60.996 0.9961.013 1.008

5 61.71 1.20

This line indicates for the present case that between two trims the smaller one looses 0.195 % between trim 7 and trim 2 (0.94%


Table 1: Efficiency and Pressure Ratio

of the optimized design and their or even the

is maintained pressure side

was combined with the for the trim 4

SPEED LINE As the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not

shows these influences for trim 4 and trim 7 (base design). The right side (100%) shows again that the base design did not experience very much change compared to a first guess of a small trim (difference between filled and empty

For turbocharger compressor maps usually a volume flow relating to pt1=1bar and V& = m& /ρt1.

optimized shroud contours allowed to compute more converged results for points in the (to be proved

in efficiency for the best point. shows the influence of the optimized shroud contour on part load. It would

have been a lucky coincidence to achieve an improved part load speed line by optimizing with * curve looks as

if shifted slightly downward in case of the base design. For trim 4 it is even worse: It was s for the optimized shroud contour as far to the left

nterintuetively, in part load it can happen that smaller trims show better ). This effect was


799.86 100.00100.07 100.14

70.21 0.14

70.996 1.0001.008 1.008

71.20 0.78

% 94%


and their or even the

is maintained pressure side

was combined with the for the trim 4

As the optimization was applied to the best point of the N*=100% speed line only, the influence on the rest of this speed line and on part load (N*=70%) had to be investigated. This is i.e. not

shows these influences for trim 4 and trim 7 (base design). The right side (100%) shows again that the base design did not experience

empty =1bar and

optimized shroud contours allowed to compute more converged results for points in the

(to be proved point.

shows the influence of the optimized shroud contour on part load. It would have been a lucky coincidence to achieve an improved part load speed line by optimizing with

* curve looks as if shifted slightly downward in case of the base design. For trim 4 it is even worse: It was

to the left nterintuetively, in part load it can happen that smaller trims show better

). This effect was ily at the OEM. The source of this behaviour has not been

investigated yet. In the work of Rodgers (2001) the same behavior is even visible for a design speed line of a Π

Figure 7: Compressor Map

REASON FOR PERFORMANCE IMPROVEMENTTable 2 shows the characteristic 1D p4. ∆rel is “(optimized value total efficiencies „+0.06%“ changed the downstream component: the vaned diffuser.Comparisons of flow variables like , S2 and S3 planes did not show any significant change between the two characteristic 1D parameters for diffusers like pressure recloss coefficient and ζ∗ decreases and 95% diffuser heighvelocities in the trailing edge region(wakes). The flow of the optimized design is better attached to the vanes. Summarized: The impeller shroud contour optimization did not improve the impeller performance but did improve The ζ∗-distribution confirms this higher total pressurebalancing planes are inlet and impeller/impeller/diffuser interface and outlet of the computational domain.

investigated yet. In the work of Rodgers (2001) the same behavior is even visible for a design speed Π=1.5 compressor.

: Compressor Map

REASON FOR PERFORMANCE IMPROVEMENTshows the characteristic 1D p

is “(optimized value ciencies η* points already to the fact that the optimized impeller shroud contour has primarily

changed the downstream component: the vaned diffuser.Comparisons of flow variables like , S2 and S3 planes did not show any significant change between the two characteristic 1D parameters for diffusers like pressure recloss coefficient ζ account for the improvement of the diffuser performance.

decreases by 1and 95% diffuser heigh

cities in the trailing edge region(wakes). The flow of the optimized design is better attached to the vanes. Summarized: The impeller shroud contour optimization did not improve the impeller performance

improve the diffuser performance due to more favorable inlet flow conditionsdistribution confirms this

higher total pressure values at the diffuser exit are not balancing planes are

impeller/diffuserimpeller/diffuser interface and outlet of the computational domain.

investigated yet. In the work of Rodgers (2001) the same behavior is even visible for a design speed =1.5 compressor.

: Compressor Map – Off

REASON FOR PERFORMANCE IMPROVEMENTshows the characteristic 1D p

is “(optimized value - start value)/ start value”. for the entire

points already to the fact that the optimized impeller shroud contour has primarily changed the downstream component: the vaned diffuser.Comparisons of flow variables like , S2 and S3 planes did not show any significant change between the two characteristic 1D parameters for diffusers like pressure rec

account for the improvement of the diffuser performance.10.0%. Figures 8 and 9 show the change of these values in S1

and 95% diffuser height. The source of the favorable change of Ccities in the trailing edge region

(wakes). The flow of the optimized design is better attached to the vanes. Summarized: The impeller shroud contour optimization did not improve the impeller performance

the diffuser performance due to more favorable inlet flow conditionsdistribution confirms this

values at the diffuser exit are not balancing planes are inlet and outlet

diffuser interface impeller/diffuser interface and outlet of the computational domain.

investigated yet. In the work of Rodgers (2001) the same behavior is even visible for a design speed

Off -Design Speed (left)

REASON FOR PERFORMANCE IMPROVEMENTshows the characteristic 1D parameters for the first guess and the optimized design of trim

start value)/ start value”. entire stage

points already to the fact that the optimized impeller shroud contour has primarily changed the downstream component: the vaned diffuser.Comparisons of flow variables like static or total pressure, Mach number and e, S2 and S3 planes did not show any significant change between the two characteristic 1D parameters for diffusers like pressure rec

account for the improvement of the diffuser performance.Figures 8 and 9 show the change of these values in S1

t. The source of the favorable change of Ccities in the trailing edge region at the suction side of the diffuser vane and


the diffuser performance due to more favorable inlet flow conditionsdistribution confirms this effect and is also an explana

values at the diffuser exit are not outlet of the

interface of the impeller/diffuser interface and outlet of the computational domain.

7


Design Speed (left)

REASON FOR PERFORMANCE IMPROVEMENTarameters for the first guess and the optimized design of trim

start value)/ start value”. stage „+0.67%“

points already to the fact that the optimized impeller shroud contour has primarily changed the downstream component: the vaned diffuser.

static or total pressure, Mach number and e, S2 and S3 planes did not show any significant change between the two characteristic 1D parameters for diffusers like pressure rec


t. The source of the favorable change of Cat the suction side of the diffuser vane and


the diffuser performance due to more favorable inlet flow conditionsand is also an explana

values at the diffuser exit are not of the computation

of the computationimpeller/diffuser interface and outlet of the computational domain.


Design Speed (left)– Design Speed

REASON FOR PERFORMANCE IMPROVEMENT arameters for the first guess and the optimized design of trim

start value)/ start value”. The comparison in changes of the total„+0.67%“ (impeller+diffuser)

points already to the fact that the optimized impeller shroud contour has primarily changed the downstream component: the vaned diffuser.

static or total pressure, Mach number and e, S2 and S3 planes did not show any significant change between the two characteristic 1D parameters for diffusers like pressure recovery


t. The source of the favorable change of Cp

at the suction side of the diffuser vane and (wakes). The flow of the optimized design is better attached to the vanes. Summarized: The impeller shroud contour optimization did not improve the impeller performance

the diffuser performance due to more favorable inlet flow conditionsand is also an explanation for the r

values at the diffuser exit are not taken into account in the Ccomputational domain. computational domain.

impeller/diffuser interface and outlet of the computational domain.


Design Speed (right)

arameters for the first guess and the optimized design of trim The comparison in changes of the total(impeller+diffuser) and the impeller only

points already to the fact that the optimized impeller shroud contour has primarily

static or total pressure, Mach number and e, S2 and S3 planes did not show any significant change between the two impeller

overy coefficient account for the improvement of the diffuser performance. C

Figures 8 and 9 show the change of these values in S1p* and ζ∗ is the reduct

at the suction side of the diffuser vane and (wakes). The flow of the optimized design is better attached to the vanes. Summarized: The impeller shroud contour optimization did not improve the impeller performance

the diffuser performance due to more favorable inlet flow conditionstion for the r

taken into account in the Cdomain. Impeller balancing planes aredomain. Diffuser balancing planes are

impeller/diffuser interface and outlet of the computational domain.


(right)

arameters for the first guess and the optimized design of trim The comparison in changes of the total

and the impeller onlypoints already to the fact that the optimized impeller shroud contour has primarily

static or total pressure, Mach number and entropy on several S1impeller designs.

coefficient Cp and total pressure Cp

* increases Figures 8 and 9 show the change of these values in S1-planes at 50%

is the reduction of lower at the suction side of the diffuser vane and further downstream

Summarized: The impeller shroud contour optimization did not improve the impeller performance the diffuser performance due to more favorable inlet flow conditions did

tion for the rise of η∗, because the taken into account in the Cp

* formula. Stage Impeller balancing planes areDiffuser balancing planes are


arameters for the first guess and the optimized design of trim The comparison in changes of the total-to-

and the impeller onlypoints already to the fact that the optimized impeller shroud contour has primarily

ntropy on several S1-designs. Typical

and total pressure increases by 11.1%

planes at 50% on of lower downstream

Summarized: The impeller shroud contour optimization did not improve the impeller performance did improve. , because the

formula. Stage Impeller balancing planes areDiffuser balancing planes are


arameters for the first guess and the optimized design of trim -

and the impeller only points already to the fact that the optimized impeller shroud contour has primarily

-Typical

and total pressure %

planes at 50% on of lower downstream

Summarized: The impeller shroud contour optimization did not improve the impeller performance .

, because the formula. Stage

Impeller balancing planes are Diffuser balancing planes are

Table 2: Characteristic

Figure

: Characteristic

ure 8: Diffuser:

: Characteristic Numbers

Diffuser: Pressure Recovery Coefficient at 50% Channel Height

Numbers to evaluate

Pressure Recovery Coefficient at 50% Channel Height

8

to evaluate the Optimization Success


Optimization Success


Optimization Success for Trim 4


for Trim 4


Figure 9

Figure 10

Figure 9: Diffuser:

Figure 10: Set of 2 Speed Lines

Diffuser: Total Pressure Loss Coefficient at 95% Channel Height

: Set of 2 Speed Lines

Total Pressure Loss Coefficient at 95% Channel Height

: Set of 2 Speed Lines – Base Design+1

9


Base Design+1


Base Design+1st Guesses (left)


Guesses (left) – Optimized (right)


Optimized (right)


Optimized (right)

SPLITTER BLADE The “bad” can be detected by just one glance when they are combined with the other four shroud contours or when all speed lines are combined in one compshapes are completely different than the ones of the other trims anof trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of trim 3 leads to choking at smaller volume flows than intended11 shows that in case which of course does not exist in case of trim 7 = base desigthat the optimized shroud contours avoid choking in the splitter channel aspeed lines for full load and part load.

Fig 11: Corresponding Operating Pointoptimized Shroud C

APPEARANCE

Operating

Point

peak η

Rel. to Trim Factor

choke line

Rel. to Trim Factor

Tabl

SPLITTER BLADE “bad” first guesses concerning the shroud contours for trim 2 and trim 3 as shown in

can be detected by just one glance when they are combined with the other four shroud contours or when all speed lines are combined in one compshapes are completely different than the ones of the other trims anof trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of trim 3 leads to choking at smaller volume flows than intended

shows that in case which of course does not exist in case of trim 7 = base desigthat the optimized shroud contours avoid choking in the splitter channel aspeed lines for full load and part load.

: Corresponding Operating Pointoptimized Shroud Contours, circumferen

APPEARANCE OF

V& Trim+1/V& Trim

Rel. to Trim Factor

V& Trim+1/V& Trim

Rel. to Trim Factor

Table 3: Ratio of Volume Flows of

SPLITTER BLADE CHOKE AS RESULT OF A BAD FIRST GUESSfirst guesses concerning the shroud contours for trim 2 and trim 3 as shown in


shows that in case of trim 3 choking takes place already in the inlet region of the splitter blades which of course does not exist in case of trim 7 = base desigthat the optimized shroud contours avoid choking in the splitter channel aspeed lines for full load and part load.

: Corresponding Operating Pointontours, circumferen

F THE OPTIMIZED

7 (Base Design)

Trim No Trim 8

Rel. to Trim Factor

Trim No Trim 8

Rel. to Trim Factor

: Ratio of Volume Flows of

CHOKE AS RESULT OF A BAD FIRST GUESSfirst guesses concerning the shroud contours for trim 2 and trim 3 as shown in


of trim 3 choking takes place already in the inlet region of the splitter blades which of course does not exist in case of trim 7 = base desigthat the optimized shroud contours avoid choking in the splitter channel aspeed lines for full load and part load.

: Corresponding Operating Points on Choking Line for Trimontours, circumferentially averaged Mach number in Meridional P

OPTIMIZED T

7 (Base Design)

Trim 6

No Trim 8

./. -No Trim 8

./. +0.06

: Ratio of Volume Flows of Adjacent

10


can be detected by just one glance when they are combined with the other four shroud contours or when all speed lines are combined in one compressor map as shown in figure 10shapes are completely different than the ones of the other trims anof trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of trim 3 leads to choking at smaller volume flows than intended

of trim 3 choking takes place already in the inlet region of the splitter blades which of course does not exist in case of trim 7 = base desigthat the optimized shroud contours avoid choking in the splitter channel a

s on Choking Line for Trimtially averaged Mach number in Meridional P

TRIM FAMILY

Trim 6

1.037

-0.17% 1.0391

+0.06%

Adjacent optimized


can be detected by just one glance when they are combined with the other four shroud contours or ressor map as shown in figure 10

shapes are completely different than the ones of the other trims anof trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of trim 3 leads to choking at smaller volume flows than intended – as

of trim 3 choking takes place already in the inlet region of the splitter blades which of course does not exist in case of trim 7 = base design. It is obvious from figures 10 and 11that the optimized shroud contours avoid choking in the splitter channel a

s on Choking Line for Trimtially averaged Mach number in Meridional P

RIM FAMILY

Trim 5

1.044

+0.5% 1.0389

+0.03%

optimized Trims

CHOKE AS RESULT OF A BAD FIRST GUESS first guesses concerning the shroud contours for trim 2 and trim 3 as shown in

can be detected by just one glance when they are combined with the other four shroud contours or ressor map as shown in figure 10

shapes are completely different than the ones of the other trims and the gap between the speed lines of trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of

as one could have of trim 3 choking takes place already in the inlet region of the splitter blades

n. It is obvious from figures 10 and 11that the optimized shroud contours avoid choking in the splitter channel a

s on Choking Line for Trims 7 andtially averaged Mach number in Meridional P

Trim 4

1.046

+0.7% 1.038

-0.05%

Trims at Design Speed

first guesses concerning the shroud contours for trim 2 and trim 3 as shown in can be detected by just one glance when they are combined with the other four shroud contours or

ressor map as shown in figure 10. The contour d the gap between the speed lines

of trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of one could have expected

of trim 3 choking takes place already in the inlet region of the splitter blades n. It is obvious from figures 10 and 11

that the optimized shroud contours avoid choking in the splitter channel and lead to equidistant

s 7 and 3 – for tially averaged Mach number in Meridional P

Trim 3

1.055

+1.6% 1.048

+0.90%

at Design Speed

first guesses concerning the shroud contours for trim 2 and trim 3 as shown in Figure 5can be detected by just one glance when they are combined with the other four shroud contours or

. The contour d the gap between the speed lines

of trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of expected. Figure


nd lead to equidistant

for start and tially averaged Mach number in Meridional Plane

Trim 2

1.037

-0.17% 1.037

-0.16%

Line

Figure 5 can be detected by just one glance when they are combined with the other four shroud contours or

. The contour d the gap between the speed lines

of trim 4 and trim 3 is almost double the size than between trim 5 and trim 4. The shroud contour of Figure


nd lead to equidistant

start and

11

Volume ratios of the best efficiency points and points on the choke line of adjacent trims are listed in table 3 for comparison with the intended trim factor (1.0388). The relative deviations of these volume flow ratios to the constant intended trim factor are very low. They are lower for operating points on the choke line than for those of peak efficiencies. Besides the accuracy of the simulation it is supposed that the reason why these ratios differ from the exact trim factor is that the optimization was done for peak efficiency points only and that the ratio of cross sections at inlet and outlet of the impeller and in the diffuser correspond to the exact trim factor only. The applied procedure should be improved for future optimization processes: Instead of optimizing the best efficiency point of the first guess with fixed mass flow it might be better to optimize the efficiency of a trim at the mass flow corresponding to the scaled powers of the trim factor corresponding to the base design, i.e. the fixed mass flow for trim 2 is 1/1.03885 of the mass flow of the best efficiency point of the base design (trim 7). Even if the base design has successfully passed blade vibration tests the blade vibration situation for the smaller trims has to be assessed again. Rodgers (2001) reminds that due to blade trimming there are also mechanical design concerns such as inducer blade thickness and vibrational frequency, the ratio of tip clearance height and axial thrust changes.

CONCLUSIONS AND OUTLOOK A process to optimize the shroud contours of a 6 member trim family has been presented. The optimization was limited to the curved part of the impeller shroud contour which automatically implied that main and splitter blade tips were adjusted. The absolute tip clearance of the base design had to be maintained for all smaller trims. All optimizations succeded in arriving at better efficiencies. A linear regression could be found that tells approximately how much loss in efficiency can be assumed for a trim family member com-pared to the base design. The difference between normalized efficiencies η* for the optimized trims 7 and 2 (size ratio 1.21) is 0.94%. The difference between absolute efficiencies η is even smaller. The base design pressure ratio could be maintained for all trims in their best efficiency points. In some cases even the (numerical) surge margin could be improved. The source of the stage efficiency improvement are better inflow conditions into the diffuser. The impeller efficiency was not influenced significantly by the change of the shroud contour – if the shroud contour was not a too bad guess. The diffuser performance however was improved, verified by higher pressure recovery and lower total pressure loss coefficients. The flow around the diffuser vanes is more attached than it is in the first guess geometry. An optimization of the best efficiency point on the 100% speed line does not simultanously improve the entire speed line as well and can even worsen the efficiencies for an entire part load speed line. It depends on the field of compressor application whether this can be accepted or not. A multi-point-optimization for 3 operating points on one speed line, as done by Hildebrandt et al. (2009), or even for 6 points distributed on the two speed lines of the presented case could be performed to obtain a shroud contour that improves definitely more than just one operating point. The quality of a “first guess shroud contour” depends on the experience of the designer and on the time and effort spent to arrive at it. It is recommended, not to rely on just one operating point improvement, but to compute entire speed lines with a shroud geometry optimized for just one operating point. The compressor model itself was reduced to one pitch of the impeller and one pitch of the diffuser. An inlet duct systems, inducer casing bleed system and volute have not been modelled. Therefore it is of big interest to know the improvement which can be gained in comparative runs on the test facility. Such a test is planned for one of the trims to evaluate the optimization results.

12

ACKNOWLEDGMENTS The author thanks ABB Turbo Systems Ltd for the permission to publish this work and gratefully appreciates all kinds of support from his colleagues from the compressor design team and the fluid mechanics team during discussions about the subject. Furthermore he is thankful to the personel from NUMECA Ingenieurbüro in Altdorf, Germany, for support concerning the optimization software.

REFERENCES Casey, M. V., Dalbert, P., and Schurter, E., (1990). Radial compressor stages for low flow coefficients, Paper C403/004, I Mech E International Conference, Machinery for the Oil and Gas Industries, Amsterdam 1990. Engeda, A. (2007). Effect of Impeller Exit Width Trimming on Compressor Performance, Proceedings of the 8th International Symposium, on Experimental and Computational Aerothermodynamics of Internal Flows, Lyon, ISAIF8-00135 Grigoriadis, P., Müller, S., Benz. A., Sens, M. (2012). Variable trim compressor – a new approach to variable compressor geometry, Proceedings of 10th International Conference on Turbochargers and Turbocharging, London Hildebrandt, T., Thiel, P., Lehmann, I. (2009). Entwicklung eines leistungsgesteigerten Radialver-dichters für Abgasturbolader: Von der CFD basierten Optimierung mit FINETM/Turbo bis zum serienreifen Prototyp im Hause KBB, Proceedings of 14. Aufladetechnische Konferenz, Dresden NUMECA INTERNATIONAL (2010). User Manuals: AutoGrid5TMv8, Automated Grid Generator for Turbomachinery + IGGTM v8.7 + Interactive Grid Generator, FINETM/Turbo v8.7, Flow Int. Environment + AutoBladeTM v8.7 + FINETM/Design3D v8.7 + Blade Modeler and Addenda: FINETM/Turbo v8.8 and FINETM/Turbo v8.8, Optimization Kernel Rodgers, C. (2001). Centrifugal Compressor Blade Trimming for a Range of Flows, Proceedings of ASME Turbo Expo 2011, New Orleans, Louisiana, 2001-GT-0316. Sapiro, L (1983). Effect of Extended Shrouds on Centrifugal Compressor Performance as a Function of Specific Speed, Trans ASME Jnl Eng for Power 105(3)

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