Blade excitation in pulse-charged mixed-flow turbocharger turbines

Value Paper Authors: Stephan M. Senn, Martin Seiler, Ottmar Schaefer

IntroductionAerodynamic blade design and thermodynamic stage optimi- zation are always subject to mechanical constraints [1,2]. Among the various constraints, high cycle fatigue is an important constraint which in general significantly limits thermo-dynamic optimization. Aerodynamic excitation forces are the main reason for high cycle fatigue in turbocharger turbines. A fundamental understanding and accurate numerical prediction of fluid-structure interactions [3] is therefore of key importance.

In contrast to previous two-dimensional and quasi-three dimensional numerical studies in the field [4-7], this paper presents a fully three-dimensional computational modeling approach in the time and frequency domain that allows to accurately and efficiently (with respect to computational time and resources) predict fluid-structure interactions in turbocharger turbines subject to transient pulse-charged and stationary turbine inlet conditions. For stationary inlet boundary conditions, a three-dimensional analysis of a radial turbine 2wheel neglecting the effects of inlet casings has been recentlypublished [8]. Existing studies mainly focus on single-stageaxial turbines subject to stationary (instead of transient) inletboundary conditions neglecting also the effect of inlet casingson aerodynamic excitation of the rotor assembly. In this study,the modeling approach is demonstrated and validated withexperimental results based on two different mixed-flow turbine

AbstractIn this article, a fully three-dimensional computationalmodeling approach in the time and frequency domain ispresented which allows to accurately predicting fluid-structure interactions (FSI) in pulse-charged mixed-flow turbocharger turbines. As part of the approach, a transient computational fluid mechanics analysis is performed based on the compressible inviscid Euler equations covering an entire engine cycle. The resulting harmonic orders of aerodynamic excitation are imposed in a forced response analysis of the respective eigenvector to determine effective stress amplitudes. The modeling approach is validated with experimental results based on various mixed-flow turbine designs. It is shown that the numerical results accurately predict the measured stress levels. The numerical approach can be used in the turbine design and optimization process. Aerodynamic excitation forces are the main reason for high cycle fatigue in turbocharger turbines and therefore, a fundamental understanding is of key importance.

NomenclatureA motor blade surface area [m2]F resulting rotor blade force [N]k stiffness matrix [kg s-2]m mass matrix [kg]m number of stator bladesn surface normal vectornEN engine speed [s-1]nTC turbocharger speed [s-1]p static pressure [Pa]Δp total pressure difference between inlets [bar]s pulsation ordert time [s]u,v,w velocity [m s-1]x eigenvectorx,y,z coordinates [m]μ generalized mass [kg]ρ density [kg m-3]σ reference stress amplitude [MPa]ω eigenfrequency [s-1]ξ amplitude [m]

Φ excitation amplitude [kg m s-2]Θ excitation phase [rad]Ω forcing frequency [rad s-1]RD rotor designRS resonance

-

2 Blade excitation | ABB Value Paper

designs. The computational domain of the stage is extendedincluding also a twin volute at the inlet hence allowing capturing the related aerodynamic excitation effects. The modeling approach consists of two main steps: In a first step, a three-dimensional computational fluid mechanics analysis isperformed based on the inviscid Euler equations subject totransient pulse-charged inlet conditions covering an entireengine cycle. Note that an engine cycle itself typically includesin the order of 102 turbocharger revolutions. In a second step,the resulting harmonic orders of aerodynamic excitation areimposed in forced response analyses of the respectiveeigenvectors to determine effective stress amplitudes based an empirically-defined damping parameter.

In addition to numerical investigations, strain gage and optical measurements are performed for both stationary-charged and transient pulse-charged turbine inlet conditions to experimentally quantify effective stress amplitudes. Numerical results are validated with experimental results by comparing stress amplitudes under resonance conditions. Computations are performed at measured operating points.

Mathmetical formulationThe computational modeling approach accounts for sequential coupling between the fluid and solid phase according to the methodology introduced by Filsinger et al. [4,5]. A computational fluid mechanics analysis is performed in a first step based on the assumption of a non-vibrating solid structure. In a second step, the resulting aerodynamic excitation forces are imposed in a steady state forced response analysis of the respective eigenvector to determine effective stress amplitudes. Concerning the damping parameter, an empirically-defined constant value is used in this study. In accordance with related studies in the field [4-7], blade deformations are assumed to be sufficiently small, such that aerodynamic excitation forces can

1 Computational domain and discretization of the mixedflow turbine stage,

including a twin-volute with two separate gas inlets, stator, and rotor.

be calculated based on the assumption of a non-vibrating solid structure. It should be noted that for typical mixed flow turbine rotors manufacturing deviations can be in the same order asmaximum vibration amplitudes.

The computational domain of the fluid mechanics analysisis fully three-dimensional and consists of the entire mixed-flowturbine stage, including rotor, stator, and a twin volute with two separate gas inlets, as shown in Fig. 1. In this study, twodifferent mixed-flow turbine designs are investigated, referredto as rotor design (RD) A and RD B, with 12 and 11 blades,respectively, where the stator includes 24 blades and is the same for both designs. The inner volute encloses the firstcircumferential half of the stator, and the outer volute covers the second half.

More specifically, the approach includes a transient fluidmechanics analysis to determine the time-dependent staticpressure field at the rotor blade surfaces. The time-dependentthree-dimensional Euler equations for inviscid and compressible flow, given as

are numerically solved subject to stationary and transient boundary conditions at the inner and outer inlets of the twin volutes. Heat transfer between the solid and fluid phase is neglected and adiabatic boundary conditions are used at thewalls. At the rotor outlet plane, a static pressure boundary condition is imposed. A discrete Fourier transformation of thestatic pressure solution, given as

ABB Value Paper | Blade excitation 3

is performed to determine the variation of the aerodynamicexcitation amplitude and phase at the rotor blade surfaces. The resulting harmonic orders of aerodynamic excitation are interpolated from the structured fluid mechanics discretizationto the unstructured structural discretization and imposed in aforced response analysis,

of the respective eigenvectors, resulting from the eigen value problem

to determine effective stress amplitudes based on an empirically-defined damping parameter which is assumed to be constant in this study. In this article, first resonance frequencies are investigated that are excited by the global pressure differences between the two inlets. These effects are expected to be sufficiently accurately captured by the inviscid Euler method.

Numerical solutionThe governing equations are numerically solved based on the finite volume method using the ABB inhouse code HT206, which is a multiblock Euler/Navier-Stokes solver [9]. The governing equations are solved subject to total pressure and total temperature boundary conditions at the inlet, a static pressure boundary condition at the outlet, and adiabatic boundary conditions at the walls and blade surfaces. Note that an engine cycle typically includes in the order of 102 turbocharger revolutions, and therefore, numerical solutionconsidering also the Nyquist criterion for sufficient resolution in time presents a major challenge in terms of computational time. Code parallelization based on the message passing interface allows achieving acceptable computational times. A structured grid with 2x105, 2x105, and 105 cells for the twin-volute, stator, and rotor, respectively, is used in this study. The mesh size used in this study corresponds to mesh sizes used in earlier studies in the field [4-7]. A number of 1536 time steps are used per rotor revolution. For pulse-charged conditions, a computation in parallel using 8 CPUs takes 3.5 days. The computations are run on 64 Intel XEON EM 64T 3.6 GHz CPUs. The ABB inhouse code FACET [10] is used for interpolation between the CFD and FE mesh. ABAQUS [11] is used for the static analysis of the structure, the computation of eigenvectors and eigenvalues, and the steady state forced response analysis.

Numerical resultsStationary boundary conditionsTwo different rotor designs (RD) are investigated, referred to as RD A and RD B, where RD A includes 12 blades and RD B 11 blades. Note that RD A and RD B are also different with respect to the blade designs. Computations are performed at different resonance conditions of the rotor and different total pressure differences Δp between the outer and inner inlet of the twin volute, subject to stationary inlet boundary conditions. For RD A, 7 different computations are performed, referred to as cases A1-A7, as indicated in Table 1. For RD B, 4 different computations are performed, referred to as cases B1-B4, see Table 1.

Note that the operating points in computations A1-A7 andB1-B4 are chosen such that the rotor is operated at resonance conditions. In cases A1-A4, the RD A is operated in resonance f1.6 (first frequency and sixth excitation order). In cases A5-A7, the RD A is operated in resonance f1.7. In cases B1-B4, the RD B is operated in resonance f1.5. These orders correspond to the highest 1st frequency orders within the operating range of the respective design. In all computational cases described in Table 1, stationary inlet boundary conditions, i.e., total pressure and total temperature, are imposed at the inner and outer inlet of the twin volute. The difference between the total pressure imposed at the outer and inner inlet of the twin volute is indicated in Table 1.

Transient boundary conditionsIn addition to computations subject to stationary boundaryconditions, two computations, referred to as A8 and A9 in Table 2, are performed subject to transient inlet boundary conditions. In both cases, the RD A is investigated at different resonance

Table 1

Computations subject to stationary inlet boundary conditions

Case RD RS Δp [bar]

A1 A f1.6 0.0

A2 A f1.6 0.5

A3 A f1.6 0.8

A4 A f1.6 1.1

A5 A f1.7 0.0

A6 A f1.7 0.5

A7 A f1.7 1.1

B1 B f1.5 0.0

B2 B f1.5 0.5

B3 B f1.5 0.8

B4 B f1.5 1.1

4 Blade excitation | ABB Value Paper

conditions, i.e., resonance f1.6 and f1.7. The time-dependent inlet boundary conditions are calculated for an entire engine cycle using the ABB inhouse code SiSy [12]. In this code, a sophisticated transient one-dimensional model of the entire thermodynamic system including engine and turbocharger is numerically solved to predict the variation of the total pressure and total temperature at the inner and outer inlet of the twin volute during an entire engine cycle. The resulting transient boundary conditions for RD A are shown in Fig. 2.

In Fig. 3., the variation of the local excitation amplitude on the suction side and pressure side of the rotor blade of rotor design A is shown for cases A1 and A4. The variation of the excitation amplitude is rather complex, indicating especially high excitation amplitudes near the leading edge on the suction side close to the hub. High excitation amplitudes near the leading edge are caused by the effect of local flow incidence. The complex variation of the excitation amplitude shown in Fig. 3 clearly demonstrates that it is imperative that aerodynamic excitation amplitudes be computed based on a fully threedimensional modeling approach. Based on these results it seems to be obvious that two-dimensional and even quasi threedimensional modeling approaches may significantly fail to predict excitation amplitudes with the required accuracy.

In Fig. 4, numerical results are exemplified by case A8 (rotor design A), indicating the aerodynamic excitation force at the rotor blade surface under pulse-charged conditions. The time-dependent rotor blade force is shown for an entire engine cycle [see Fig. 4(a)], for 1/16 engine cycle [see Fig. 4(b)], and one single turbocharger revolution [see Fig. 4(c)]. The corresponding excitation amplitudes are shown in Fig. 5. Note that the resulting rotor blade force F(t) is obtained byintegration of the local static pressure p at the rotor bladesurface, i.e., F(t) = |F(t)| where dF(t) = pndA. Discrete Fourier transformation of the resulting rotor blade force leads to theexcitation amplitudes shown in Fig. 5. The resulting rotor blade force signal includes three intrinsic frequencies, given (1) by variations at low frequencies (order of snen) due to engine pulsations [see Fig. 4(a)], (2) by variations at mediumfrequencies (2nTC) due to the imposed pressure differencebetween the inlet of the inner volute and the inlet of the outervolute [see Figs. 4(b), 5(a), 5(c)], and (3) by variations at highfrequencies (order of mnTC) due to the impact of the statorblades [see Figs. 4(c), 5(a), 5(b)]. Note that nEN is the enginespeed, s is the pulsation order, nTC is the turbocharger speed, and m is the number of stator blades.

Experimental validationIn Fig. 6(a), measured maximum stress amplitudes are shown for rotor design A and resonance f1.6 (cases A1-A4). In Fig. 6(b), measured maximum stress amplitudes are shown for rotor design A and resonance f1.7 (cases A5-A7). In Fig. 6(c), measured maximum stress amplitudes are shown for rotor design B and resonance f1.5 (cases B1-B4). Maximum stress amplitudes are scaled with a reference stress amplitude σ. Maximum stress amplitudes are measured on each single blade using strain gage and optical measurement technique. A total number of 8 strain gages positioned on different blades and 8 optical sensors have been used for the measurement. Strong blade-to-blade variations of the maximum stress amplitude can be identified which is due to the effect of structural mistuning of the blade assemblies [13].

In Fig. 7, comparisons between computed maximum stressamplitudes (red circles) and measured maximum stressamplitudes (blue lines) are shown. Note that the numericalresults refer to a perfectly tuned blade assembly. Experimentaldata for the mistuned system are given in terms of ranges,indicating the maximum, average, and minimum of the blade-toblade maximum stress amplitudes. Fig. 7(a) shows a validation of numerical results with experimental result for rotor design A, resonance f1.6, cases A1-A4. Fig. 7(b) shows a validation for rotor design A, resonance f1.7, cases A5-A7. Fig. 7(c) shows a validation for rotor design B, resonance f1.5, cases B1-B4. Except for cases A3 and A5, excellent agreement between numerical and experimental results is found.

In Table 3, comparisons between computed maximum stress amplitudes and measured maximum stress amplitudes are

Table 2

Computations subject to transient inlet boundary conditions

Case RD RS Δp [bar]

A8 A f1.6 see Fig. 2(a)

A9 A f1.7 see Fig. 2(b)

Table 3

Maximum stress amplitudes (scaled with σ ):

Computed vs. measured values under pulse-charged conditions

Exp. Results Num.

Case RD RS Min. Avg. Max. Results

A8 A f1.6 0.10 0.18 0.30 0.30

A9 A f1.7 0.054 0.072 0.11 0.15

ABB Value Paper | Blade excitation 5

shown for cases A8 and A9. Note that the validation results in Fig. 7 all refer to cases subject to stationary boundary conditions, whereas the results in Table 3 refer to cases subject to transient boundary conditions. In cases A8 and A9, maximum stress amplitudes were measured directly on the engine. In case A8, the numerical prediction of the maximum stress amplitude equals the measured maximum bound of the stress amplitude range. In case A9, rather small maximum stress amplitudes are identified by both, the numerical prediction and the measurement. However, the numerical results over-predict the measurement.

Due to the complex modeling approach and sophisticated measurement technique, a variety of reasons exists for differences between numerical and experimental results. It should be recognized that the computational model always refers to a perfectly tuned blade assembly, which in reality does not exist. In fact, the investigated rotor blade assemblies are strongly mistuned structures, being reflected by the strong blade-to-blade variations of the maximum stress amplitudes (see Fig. 6). Consequently, numerical results need to be compared rather to a range of measured values than to a single experimental value. In addition, experimental results depend on the quality of strain gage positions [14] and amplification factors, which in turn are also determined on a computational basis.

2 Transient total pressure and temperature boundary conditions at the outer inlet (full line) and inner inlet (dashed line) of the twin volute of rotor design A for

an entire engine cycle. (a) Boundary conditions of case A8 (resonance f1.6). (b) Boundary conditions of case A9 (resonance f1.7).

(A)

(A)

(B)

(B)

6 Blade excitation | ABB Value Paper

Concerning the numerical side, boundary conditions mayappear more complex in reality than they need to be assumed in the modeling approach. In addition, the damping parameter, which was assumed to be constant in this study, may vary between different operating points and rotor designs.

(A)

(A)

(B)

(B)

3 Variation of the local excitation amplitude on the suction side and pressure side of the rotor blade of turbine design A. Amplitudes are scaled with the

maximum amplitude of case A4. (a) Case A1. (b) Case A4.

Generally, it can be stated that the numerical results accurately predict the measured stress levels as well as their intrinsic pressure-dependent variations. It is expected that the most important reason for local disagreement between numerical and experimental results is due to the strong effect of mistuning.

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4 Resulting rotor blade force for (a) an entire engine cycle, (b) 1/16 engine

cycle, and (c) one single turbocharger revolution, exemplified by case A8

(rotor design A).

(B)

(C)

5 Aerodynamic excitation amplitudes at the rotor blade surface under

pulse-charged conditions, exemplified by case A8 (rotor design A).

(A)

(B)

(C)

24th turbocharger order

6th turbocharger order

(A)

24th turbocharger order

6th turbocharger order

6th turbocharger order

8 Blade excitation | ABB Value Paper

6 Measured maximum stress amplitudes for each rotor blade (scaled with

σ). (a) Rotor design A, resonance f1.6. (b) Rotor design A, resonance f1.7. (c)

Rotor design B, resonance f1.5.

7 Maximum stress amplitudes (scaled with σ): computed (red circles) vs.

measured (blue lines) values. Ranges of experimental results indicate

maximum, average, and minimum blade-to-blade maximum stress amplitudes.

(a) RD A, RS f1.6, A1-A4. (b) RD A, RS f1.7, A5-A7. (c) RD B, RS f1.5, B1-B4.

(A)

(B)

(C)

Blade number

Blade number

Blade number

(C)

(B)

(A)

ABB Value Paper | Blade excitation 9

ConclusionsA fully three-dimensional computational modeling approach in the time and frequency domain has been presented in this article, which allows to accurately predicting fluidstructure interactions in pulse-charged mixed-flow turbocharger turbines. Transient computational fluid mechanics analyses were performed based on the inviscid Euler equations for bothstationary and time-dependent pulse-charged boundary conditions. The resulting harmonic orders of aerodynamicexcitation were imposed in forced response analyses of therespective eigenvectors to determine effective stress ampli-tudes. The modeling approach has been validated with experimental results based on two different mixed-flow turbine designs. It has been demonstrated that it is imperative that aerodynamic excitation amplitudes be computed based on a fully threedimensional modeling approach. It is shown that the numerical results accurately predict the measured stress levels. Structural mistuning effects cannot be predicted by the numerical approach, since a perfectly tuned structure is investigated in the simulation. The numerical approach can be used in the turbine design and optimization process, hence allowing reducing development time and cost.

AcknowledgmentsThe authors would like to thank ABB Turbo Systems Ltdfor the permission to publish this work.

References[1] Rajoo, S., Martinez-Botas, R., 2008, “Mixed Flow Turbine Research: A Review,” Journal of Turbomachinery, Vol. 130, No. 4, pp. 1-12.[2] Copeland, C. D., Martinez-Botas, R., Seiler, M., 2008, “Unsteady Performance of a Double Entry Turbocharger Turbine With a Comparison to Steady Flow Conditions,” Proceedings ASME Turbo Expo, GT2008-50827.[3] Dowell, E. H., and Hall, K. C., 2001, “Modeling of Fluid- Structure Interaction,” Annu. Rev. Fluid Mech., Vol. 33, pp. 445-490.[4] Filsinger, D., Szwedowicz, J., and Schaefer, O., 2001, “Approach to Unidirectional Coupled CFD-FEM Analysis of Axial Turbocharger Turbine Blades,” Proceedings of ASME Turbo Expo, 2001-GT-0288.

[5] Filsinger, D., Szwedowicz, J., and Schaefer, O., 2002, “Approach to Unidirectional Coupled CFD-FEM Analysis of Axial Turbocharger Turbine Blades,” Journal of Turbomachinery, Vol. 124, No. 1, pp. 125-131.[6] Filsinger, D., and Schaefer, O., 2003, “Numerical Calculation of Low Order Blade Excitation in Pulse Charged Axial Turbocharger Turbines and its Experimental Assessment,” Proceedings ASME Turbo Expo, GT2003-38182.[7] Filsinger, D., Frank, C., and Schaefer, O., 2005, „Parctical Use of Unsteady CFD and FEM Forced Response Calculation in the Design of Axial Turbocharger Turbines,” Proceedings ASME Turbo Expo, GT2005-68439.[8] Kulkarni, A., and LaRue, G., 2008, “Vibratory Response Characterization of a Radial Turbine Wheel for Automotive Turbocharger Application,“ Proceedings ASME Turbo Expo, GT2008-51355.[9] Rembold, B., Schaefer, O., “HT206 User Guide,” Technical Report, ABB Turbo Systems, 2008.[10] Dickmann, H. P., Secall Wimmel, T., Szwedowicz, J., Filsinger, D., and Roduner, C. H., 2005, „Unsteady Flow in a Turbocharger Centrifugal Compressor 3D CFD Simulation and Numerical and Experimental Analysis of Impeller Blade Vibration,“ Proceedings ASME Turbo Expo, GT2005-68235.[11] ABAQUS/CAE User‘s Manual, Version 6.8, West Lafayette, IN 47906-1000, USA, 2008.[12] Bulaty, T., Codan, E., Skopil, M., „Flexible System for the Simulation of Turbocharged Diesel Engines and Turbocharging Systems, Spring Technical Conference of the ASME, Youngstown, Ohio, USA, ICE Vol. 26-3, pp. 57-63, 1996.[13] Kenyon, J. A., and Griffin, J. H., 2001, “Forced Response of Turbine Bladed Disks and Sensitivity to Harmonic Mistuning,” Proceedings ASME Turbo Expo, 2001-GT- 0274.[14] Szwedowicz, J., Senn, S. M., and Abhari, R. S., 2002, “Optimum Strain Gage Application to Bladed Assemblies,” ASME Journal of Turbomachinery, Vol. 124, pp. 606-612

Proceedings of ASME Turbo Expo 2009: Power for Land, Sea and AirGT2009June 8-12, 2009, Orlando, Florida, USA

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