Unsteady flow in a turbocharger centrifugal compressor

Transcription

1 Value Paper Authors: Hans-Peter Dickmann, Thomas Secall Wimmel *, Jaroslaw Szwedowicz #, Janpeter Kühnel, Uwe Essig Unsteady flow in a turbocharger centrifugal compressor Abstract Experimental investigations on a single stage centrifugal compressor with radial inlet duct showed that measured alternating strains of the rotating blades depend considerably on the circumferential position of the diffuser ring to the volute tongue. By modeling of the entire turbocharger compressor stage with volute and inducer casing bleed system included, 3D unsteady flow simulations provided comprehensive insight into the excitation mechanism. A part load operating point was investigated experimentally and numerically. For operating conditions due to resonance transient CFD was employed, since only then a meaningful prediction of the blade excitation, induced by the unsteady air flow, is expected. The CFD results show primarily the interaction between the volute tongue and the two different vaned diffuser ring positions. It is shown that pressure and flow angle vary significantly due to the circumferential position of the flow entering the volute and the turning impeller blades. The geometrical arrangement of the volute and suction elbow imposes a nonaxisymmetric flow field, which excites rotating blades periodically. These vibrations depend on the circumferential assembly position of the vaned diffuser. Outflow and reverse flow at the tongue region also differ with respect to the vaned diffuser ring position. The time dependent pressure distribution on the impeller blades resulting from the CFD calculation was transformed into the frequency domain by Fourier decomposition. The complex modal pressure data were imposed as exciting load on the structure which was simulated by the FEM. By applying a fine FE mesh the measured resonant frequencies for the lower modes were reproduced very well by FEM. After determining the 3D mode shapes of the impeller by means of a free vibration calculation, forced response simulations without considering transient vibration effects were carried out for predicting the resonance strain amplitudes which were computed for both minimum and maximum experimental modal damping ratios. Comparisons with the experimental results at the strain gauges demonstrate that this employed methodology is capable of predicting the 3D impeller s vibration behavior under real engine conditions up to 8 khz. Considering strong influence of mistuning on real impeller vibrations, a new method for the comparison of experi-mental and numerical data has been successfully introduced. In general, this approach is based on the resonance sensitivity assessment, which takes into account the excitation, damping and mistuning parameters. Then, the measured resonance strain amplitudes of all experimental tests match very well the predicted scatter range of numerical results. Nomenclature 5 Index for volute cylindrical inlet plane (figs. 2 and 5) CFD Computational Fluid Dynamics EO (=k) engine order FE(M) Finite Element (Method) - for structural mechanics FFT Fast Fourier Transformation FSI Fluid Structure Interaction F O resulting excitation amplitude HCF High Cycle Fatigue N number of symmetrical sectors of the impeller hub ND=j nodal diameter number (0, 1, 2,, N/2) P Blade blade power V volume flow X r esonance displacement amplitude c rad5 absolute radial velocity entering the volute absolute tangential velocity entering the volute c tan5

2 s,s 0,(s E ) stimulus, (scaled) reference stimulus in the FE analysis a acceleration of the turbocharger f 1...f 4 frequencies (multiples of nop) i eigenfrequency number i, j/k blade mode, # of nodal diameters/engine order k (=EO) engine order k modal stiffness m modal mass m mass flow n op operational rotational speed p static pressure p 1D area averaged static pressure at volute inlet t time a 5 volute inflow angle = atan (crad5/ctan5) ε r measured resonance strain amplitude ε A,gauge, FE FE strain amplitude at the strain gauge σ resonance stress of the blade σ 0, (σ E ) (scaled) reference stimulus used in the FE analysis ω,ω r excitation frequency, resonance frequency ξ modal damping ratio ξ 0,(ξ E ) (scaled) modal damping ratio Θ amplification response factor due to mistuning tot-tot total-to-total compressor pressure ratio Ω rotational speed of the turbocharger Introduction Centrifugal compressors of turbochargers operate in a wide range of rotational speeds, which depends on the load of the supercharged engine. Consequently, there are, according to the dispersion curve (Figure 1), a number of possible intersections between the excitation and the natural frequencies of the impeller with the potential for resonant vibration. Therefore, it is of great importance for a safe design of centrifugal compressors, to determine the structure s vibration behavior of the turbocharger so that it can be properly accounted for operation under resonance conditions. Current designs of turbocharger compressors exhibit high efficiencies accompanied by high flow capacities [1]. Consequences of aerodynamic optimization are high mean stress values in the blades due to centrifugal loading as well as dynamic stresses due to blade vibrations. Blade vibrations in a turbocharger compressor are assumed to be predominantly excited by unsteady aerodynamic forces. These forces are caused by a variety of sources influencing the flow. Examples include the geometry of the flow channel, elbows, the diffuser vanes or struts. Therefore, an understanding of FSI is essential for further design optimizations. A unidirectional FSI simulation performed on a turbocharger compressor concerning different amplitudes for operating points close to choke and close to surge on an off-design speedline [2] could verify what was observed during the measurements: a difference of factor 3 in the amplitudes. The CFD simulation was done on a coarse mesh (700,000 cells) for the entire compressor and the volute was substituted by a circumferentially asymmetric pressure distribution behind the vaned diffuser with respect to the location of the volute tongue. Encouraged by that result and having been aware that a geometric representation of the volute is advantagous for at least two reasons: more realistic geometry model of the compressor as the component volute exists as a 3D-model and more realistic flow model and outlet boundary condition, because a steady state boundary condition at the volute exit is closer to reality than a steady state boundary condition behind a vaned diffuser. A similar simulation was performed for a new prototype with different and more ambitious goals: Power Distribution on two splitter blade types A new impeller design with two different splitter blades per segment was tested. What does a load distribution on these three blade types look like? Investigation of a higher mode Besides mode 1,4/4 one higher mode (3,3/11) was investigated. Higher modes are more difficult to simulate, because they are more complex and consist of more node lines. Different amplitudes due to different geometries: Measurements showed significant differences for each mode in amplitude corresponding to the circumferential position of the vaned diffuser ring. Will it be possible to reproduce these differences for the two modes marked in Figure 1 with the help of FS simulations? Unsteady nature of the flow entering the volute It is well known that the flow entering the volute is circumferentially asymmetric. This has been shown for typical flow variables like pressure and flow angle in many publications (i.e. [3], [4]). To the knowledge of the authors there is no information available about the variation in space and time concerning the typical volute inlet plane. Centrifugal compressor stage The compressor stage can be seen in Figure 2. The compressor wheel consists of eight main blades, accompanied 2 Unsteady flow in a turbocharger ABB Value Paper

3 by two splitter blades per section. The diffuser has 18 meridionally leaned vanes. In order to improve the operation range an inducer casing bleed system (described in [2]) is used. For blade vibration tests two different diffuser positions relative to the volute have been examined. For this purpose the diffuser has been turned by 10 in circumferential direction (maximum possible change for 18 identical vanes, which cause a pitch angle of 20 ). These positions are called 0 and caused lower vibration amplitudes. No additional positions between 0 and +10 were investigated. Comparison of measured and calculated operating points Vibration analyses were done at two different operating points (green and red in Figure 3). The computed operating point for both cases is located in between: (yellow in Figure 3). The difference in total pressure ratios and volume flows relative to the two measured points lies in the range of +/- 3%. Test facility The blade vibration measurements were performed on a turbocharger test rig at the OEM s test center. The test stand is equipped for mass flow, pressure and temperature measurements. It provides the means for the thermodynamic evaluation of the turbocharger performance and its components. The measurement uncertainty of the mass flow is 1.0%. The uncertainty of the measured turbocharger efficiency is 0.4% or better depending on the operating point of the turbocharger. The state-of-the-art test rig monitoring and control system 1 The calculated dispersion curve for the rotational speed n op at the operation point of interest allows to identify excitable modes (in this case modes i,j/ k=1,4/4 and i,j/k=3,3/11). 3 Compressor performance map excerpt. CFD simulations were done for an identical operating point for both vaned diffuser ring positions. 2 Investigated turbocharger compressor stage. 4 Geometry model for CFD with highlighted area of interest: volute tongue vaned diffuser interaction (sketchy snapshot of Mach number distribution between 0 and 1 at diffuser midspan). ABB Value Paper Unsteady flow in a turbocharger 3

4 enables the turbocharger to be operated under all possible conditions of a piston engine. In the test facility the turbocharger is operated like a gas turbine by the use of a combustion chamber. The test rig is equipped for performance map measurement as well as for blade vibration measurements. Blade vibration measurements were performed by means of strain gauges. The application is designed to evaluate the vibration level of the relevant mode shapes of the compressor blades. The strain signals are transferred by telemetry to the acquisition system. CFD model and simulation Geometry The entire compressor has been modeled as mounted at the test facility taking into account (Figure 4): upstream pipe suction elbow, inducer casing bleed system, impeller including tip gap, vaned diffuser and volute. Discretization CFD simulations have been performed with the CFX10 code from ANSYS on a mesh with 7 million cells. As this time the volute was modeled as well an estimation of memory, storage and runtime did not allow more than 2 million cells for the impeller and 1.5 million cells for the diffuser. One impeller revolution needed 2.5 days on 10 processors of a LINUX cluster. One impeller revolution has been resolved by 256=2 8 time steps. On this way the Nyquist-Shannon sampling theorem is fulfilled and all required excitation orders can be analysed by FFT. One timestep corresponds to 1.4 turning of the impeller per time step or a resolution about 11 states per pitch between a main and adjacent splitter blade or between two splitter blades of different size. The k-ε turbulence model with scalable wall functions has been applied. High order resolution in space has been used. This adaptive numeric scheme locally adjusts the discretisation to be as close to second order as possible, while ensuring the physical boundedness of the solution [5]. A conclusion of [2] was that 3 internal loops per time step were sufficient for convergence in time of the data of interest, namely the online monitored blade powers: 10 internal loops, necessary to arrive at maximum residuals of 10-3 for the conservation equations, arrived at the same blade power values. Simulations were stopped when the transient solutions of the main blade powers were periodic in time and the ratio of inlet to outlet mass flow remained at almost identical values for more than 3 revolutions: in out m in / m out = for the 0 position and for +10 position when the computations were stopped. Boundary conditions Average values for total temperature and total pressure, a turbulence intensity of 5 % and flow vertical to the inlet boundary have been applied to the inlet boundary. The upstream circumferential bypass bleed slot and the interface vaned diffuser / volute have been treated as general grid interfaces without one-to-one connections. The downstream slot and the interfaces impeller/suction elbow and impeller / vaned diffuser have been treated as transient rotor/stator interfaces. At the volute exit an average static pressure was imposed. The two measured points corresponding to the two vaned diffuser ring positions are not identical in the compressor map In order to have comparable CFD results for different geometries which are not influenced by slightly different operating points just one CFD operating point was chosen to represent both measured operating points. Figure 3 shows a section of the compressor performance map including the two measured (different) and two computed (identical) operating points on a part load speed line. Vaned diffuser - volute - interaction It is well known that the flow distribution at volute inlets of centrifugal compressors varies significantly along the circumference. A typical volute inlet plane is located behind the vaned diffuser or at the end of a vaneless diffuser. Following typical centrifugal compressor balancing plane numbering this is referred to plane 5 (Figures 2 and 5). Volute performance evaluations therefore use plane 5 as inlet and planes 7 or 8 as outlet depending whether the exit cone is included or evaluated separately ([6], [7]). As these simulations were the first unsteady ones performed at the OEM including the volute and as no unsteady flow measurements at compressor volute inlets could be found in literature, this was the first chance to find out how the circumferentially asymmetric flow distribution aries in time at all and how 1D-values, variations along the circumference and variations along the circumference and in time differ from each other. 4 Unsteady flow in a turbocharger ABB Value Paper

5 These pieces of information could be obtained using the following procedure: Only 32 (=256/8) time steps need to be taken into account, because these are sufficient to represent the periodically repeating states per revolution (8 impeller segments with 3 different adjacent blade types). Plane 5 was divided in 120 elements (3 per element) and area averaged flow angles and static pressures were computed for each element. All computed values were plotted along the circumference in the same diagram using the convention in Figure 5: 0 on top close to the exit cone inlet turning anti-clockwise to arrive at the same location after 360. The flow angle at the volute inlet is defined as in Figure 6 with tangential velocity regarded as positive in anti-clockwise direction. The unsteady effects can be detected as local fluctuations with respect to the red curve, which only takes into account spatial variation and represents the arithmetic mean curve of the 32 time varying black curves. The green line is the arithmetic mean value = 1D value for plane 5. The static pressure has been plotted non-dimensionally and therefore the percentage of fluctuation is directly visible (Figure 5). Values vary in time up to +/- 3.5 % around the time averaged values depending on the circumferential position. Concerning the maximum and minimum peaks (close to the tongue at 30 and 60 ) of the pure spatial variation: The 0 configuration shows generally higher variations and the pressure distortion is higher as well (Pressure distortion at plane 5 is defined as the difference between the maximum and minimum value non-dimensional pressure. In case of 0 it is 10% 5 Static pressure variation at volute inlet. 32 (black curves) of 256 states per revolution are shown, because they repeat per pitch (8 sets with 3 blades). 6 Flow Angle variation at volute inlet. 32 (black curves) of 256 states per revolution are shown, because they repeat per pitch (8 sets with 3 blades). ABB Value Paper Unsteady flow in a turbocharger 5

6 higher than for +10. The circumferential extension of 30 in the tongue region is the same in both cases, only shifted by 6.5 due to the turning of the diffuser ring. The absolute 1D values for the static pressure were almost identical in both cases (relative difference = 0.14%). The spatial variation (red) differs between +6 (+5.25)% and -3.5 (-3) % from the 1D-value (=1 / green) for the positions 0 (+10 ). The variation in space and time (black) differs correspondingly between 7 (7)% and 5.5 (5)%. The shapes of the pressure fluctuations for both diffuser vane ring positions look similar, but differ apart from the min-max-values in the shape of the spatial min-max peaks close to the tongue. The unsteady flow angles (black, Figure 6) vary between +5 and -7 around the 1D-value in time along the circumference for both cases (0 and +10 ), which is quite a lot for operating points regarded as stationary in the compressor map. Locally it varies up to +/-3 (0 ) and +5 /- 4 (+10 ) around the time averaged values (red curve). The 1D-values are identical: 27.4 due to identical mass flows for both CFD simulations. The mass flows are identical, because it was decided to apply identical boundary conditions for both operating points and the 10 -rotation of the diffuser ring did not change the incidence angles of the diffuser vanes and no severe flow separation occurred due to different tongue vs. adjacent diffuser vanes configurations. FFT Analyses of the computed pressure signals The computed static pressure signals vary in time around the average pressure distribution, which is indicated with red curves in Figure 5. Considering the discrete nature of the impeller excitation based on its eigenfrequency spectrum, these varying static pressure signals are decomposed by FFT to determine the discrete excitation spectrum. For separating the pulsation excitation from the engine (order) excitation, the novel double FFT analysis is proposed here. In the first FFT step, the static pressure signal of every CFD time step is split up with respect to the circumferential position. Then, the obtained spectrum of every engine order is again analyzed with FFT, which provide the excitation amplitudes of the engine order k E at harmonic 0 depending on the rotational speed and the pulsation order at harmonics k P = {±1, ±2, }, which can appear because of the signal pulsation or acoustic resonances. The results of this FFT analysis of the CFD pressure signals given in Figure 5 are presented in Figure 7 for the diffuser s position at 0 deg. The same is determined for the diffuser s position at 10 deg, however the resulting excitation amplitudes are respectively 10% and 28% smaller for excitation (k E =4, k P =0) and (k E =4, k P =±8) of interest. For the excitation resulting amplitudes at (k E =11, k P =0) and (k E =11, k P =±8), these difference are lower by 47% and higher by 75%, respectively for the diffuser position 10 than that for 0. These amplitude differences for all considered engine and pulsation orders clarify why both time signals for diffuser positions of 0 and 10 differ to each other as presented in Figure 5. Based on the results in Figure 7 it can be claimed that the FFT analysis, which is performed at one radius along the circumferential direction (see plane 5 in Figure 5), cannot identify the excitation changes in the system, in which the position of the diffuser ring is changed. These changes can be found by using the spatial single FFT analysis of the pressure signals distributed on the rotating blades in the time domain. Then, the excitation amplitudes of the engine and pulsation order are superimposed to each other. Therefore, the pulsation excitation is not treated independently in further analysis. 7 The resulting excitation amplitudes for the engine and pulsation order of the CFD static pressure signal for the diffuser s position at 0 deg (Figure 5) For engine orders of 4 and 11, the results of the spatial FFT analysis are presented in Figures 8 and 9, which clearly detect the excitation differences between diffuser positions of 0 and 10. These local amplitude differences have an impact on the blade excitation, due to its excitability, which depends on the mode shapes obtained from the FE free vibration calculation. For an engine order of 4, the main vane shows small amplitude differences in the blade zones of its high excitability 6 Unsteady flow in a turbocharger ABB Value Paper

7 in the resonance excitation. In case of an engine order of 11, differences in the excitation amplitudes occur in the airfoil areas, which have less excitability. Therefore, for an engine order of 11 the resonance response of the blade with diffuser positions of 0 and 10 do not differ to each other, as it is confirmed further by the FE steady state resonance simulation. Typical snapshots of the transient simulation (top of Figure 10) document the different flow structures in the volute tongue region with respect to the two different positions of the diffuser vanes. For better identification the differences in circumferential position these vanes have been numbered. Diffuser mid span planes have been chosen for comparison in Figure 10. The view description in the lower part emphasizes that these planes are not located in the middle of the exit cone. Two phenomena are visible: 10 : a separation zone at the exit cone inlet is visible, while there is none existing for 0 (red circles). 0 : a distinctive stagnation area below the tongue underneath the exit cone only for the 0 case (red ellipses). A better resolution of the separation area can be seen on 3D snapshots in Appendix 1. The different vibration behavior of the impeller blades is influenced by the interaction of the volute tongue and the circumferential position of the adjacent diffuser vanes: Combined with a volute it is important to take into account the exact circumferential position of the vaned diffuser for impeller blade vibration investigations. 8 Different views of the normalized pressure amplitude difference between the 0 and the 10 diffuser ring position for engine order k=k E of 4 with a pulsation order k P of 0. 9 Different views of the normalized pressure amplitude difference between the 0 and the 10 diffuser ring position for excitation order k=k E of 11 with a pulsation order k P of 0. Blade powers Blade power is equivalent to blade torque times rotations per second. Blade torque is computed via the area integrals of pressures plus the area integrals of the corresponding shear stress components on the wetted surface of one main blade taking into account the distances to the axis of rotation. Pressures and temperatures on all (3*8=24) blades for the last two computed revolutions (2*256=512 time steps) were stored and transferred for FFT- and forced response analyses. Figures 11, 12, and 13 demonstrate the loads of the three different impeller blade types: main blade, long and short splitter blades. Figure 11 shows that a state periodic in time has been reached with the help of cyclic repeating minimum and maximum peaks for 4 of the 8 impeller main blades in series and 4 impeller revolutions in series. 10 Vectors colored by Mach numbers between 0 and 1 in the area around the volute tongue at diffuser mid span plane. Note: different diffuser vane positions. ABB Value Paper Unsteady flow in a turbocharger 7

8 Both, characteristic shapes and extreme values repeat. Comparing these plots for the investigated two circumferential positions of the vaned diffuser ring the following facts are observed: The difference between maximum and minimum values differs by about 7% (10.25 vs kw). The characteristic peak shape differs per configuration: The configuration, which causes higher exciting amplitudes (+10 ) shows double peak maxima and single peak minima (black ellipses). The configuration, which causes lower exciting amplitudes (0 ) shows one peak more on each side: triple peak maxima and double peak minima (black ellipses). The triple peak type consists of one high peak followed by two slightly smaller peaks. 11 Powers of 4 main blades (4 revs., ). An explanation for the different peak shapes per configuration has not been found yet. One (obvious) conclusion, which can be deduced from this observation, is that the 18 diffuser vanes act differently on the impeller main blades depending on their circumferential positions. This can be explained by different interactions of the volute tongue with the closest diffuser vanes. Figure 10 shows these two different configurations and figures 12 and 13 show the principal load distributions on the three different blade types of the impeller. From top to bottom the blade powers for two impeller revolutions are shown for two adjacent main blades, shorter and longer splitter blades. Obviously blade powers are not proportional to blade lengths in the present case: The shorter splitter blades show higher blade powers than the longer ones. 12 Powers of 2 main + splitter blades(2 revs, 0 pos.). 13 Powers of 2 main + splitter blades (2 revs, 10 pos.) 8 Unsteady flow in a turbocharger ABB Value Paper

9 The reason for this can be explained as follows: density and pressure in the main blade s bow wave is that high that the pressure integral on the (smaller) faces of the shorter splitter blade is higher than the pressure integral on the (bigger) faces of the longer splitter blade. Besides that the longer splitter blade is located in the suction/wake area of the (always ahead the impeller turning direction) main blade suction side. Each blade type sees 18 diffuser vanes / channels per impeller revolution. These 18 peaks have been numbered for one revolution on top of Figures 12 and 13 (main blades). The 18 changes from maximum to minimum peaks can be seen as well for the two splitter blade types below at the same relative scale. The principal load distributions per blade type are very similar in both configuration cases. Power levels per blade types are identical and the different peak types described due to Figure 11 above less visible due to the smaller scale in Figures 12 and 13. Damping evaluation from measured resonances At the set-up, the experimental validation of the performance map (Figure 3) provided many blade resonances measured for different flow conditions. These data, given in form of resonance response functions (Figure 14), were valuable experimental source for the identification of the overall damping capabilities of the rotating compressor blades. Due to the measuring methodology used for testing compressor performance, each resonance function was measured under transient conditions. The transient resonance amplitude mainly depends on a value of the acceleration +a or deceleration -a of the turbocharger where the blades pass their resonances with the rotational speed Ω(t) in the time domain t, expressed by Ω(t) = Ω 0 + at, where Ω o is the initial rotational speed of the measurement. The CFD and centrifugal FE analyses were performed for the constant rotational speed Ω. Also the FE vibration results corresponded to steady-state vibrations of the radial blade rotating with the constant rotational speed Ω. Therefore, the velocity Ω(t) = at of the turbocharger shaft in experiments, for which blades passing their resonances, was minimized so far that the transient vibration behavior was almost eliminated from the measured resonance response function of the tested impeller. Then, the damping blade capabilities were able to be evaluated from the measured resonance response functions by using the steady-state vibration method. Every measured resonance frequency ω i,j of mode shape (i,j) is represented by the resonance response function (RRF) as given in Figure 14. For unknown damping value ξ i,j and the resulting excitation amplitude F o acting on the blade, the experimental resonance response amplitude X of mode shape i,j is obtained from the measurement. To evaluate the damping property of the measured resonance, single degree of freedom (SDOF) model is used as m a t + ξ ω v t + k x t F exp jωt ( ) ( ) ( ) ( ) i, j 2 i, j i, j i, j = o 14 The experimental resonance response functions measured by passing blade resonances with rotational speed Ω(t), where a denotes acceleration or deceleration of the turbocharger by passing the blade resonances. where for the mass-normalized mode shape (i,j), the modal mass m i,j = 1 and modal stiffness k i,j = (ω i,j ) 2 whereby ω and t are the excitation frequency and time, respectively. In SDOF equation a, v, and x are the vibratory acceleration, velocity and displacement, respectively. For the linear blade excitation F(t) = F o exp(jωt), the harmonic blade response is then characterized by a = -ω 2 X exp(jωt), v = jωx exp(jωt) and x = X exp(jωt), where j = (-1) 1/2 and X denotes the response amplitude at excitation frequency ω of interest. In terms of the modal damping ratio ξ i,j and the measured resonance response amplitude X exp (see the maximum response amplitude in Figure 14), SDOF response analysis is being ABB Value Paper Unsteady flow in a turbocharger 9

10 performed as long as both measured and simulated RRFs adjust to each other. The adjusted experimental and SDOF resonance response functions are illustrated in Figure 14, where green and red colors correspond to the experimental and numerical data, respectively. The adjustment process of the numerical RRF to the measured ones provides the required modal damping ratio ξ i,j. The described process is done automatically by using an inhouse code (see Figure 14). For all measured resonances, the scatter of the modal damping ratios varied from 0.07% up to 0.21%, as it is presented in Figures 25 and 26. The found minimum damping value is about 2 times higher than the material damping and the all experimental damping results create a relationship of the normal (Gauss) distribution in terms of the number of the evaluated resonances. These damping values are in very good agreements with Kammerer s and Abhari s results [8], who also investigated the impeller made of aluminum. Based on this evaluation, the reference modal damping ratio of 0.12 % is taken into consideration for the FE resonance simulation of the tuned compressor hub. Resonance blade analysis For determining the dynamic behavior of the tuned compressor wheel a cyclic symmetric finite element model including the main blade, the two splitter-blades and the corresponding hub sector was built with parabolic brick and wedge elements as shown in Figure 16. The static and vibration analyses of the rotating impeller were performed using the commercial ABAQUS FE software [9]. For the validation of the simulation results blade vibration measurements were carried out with strain gauges. Figure 17 shows the experimental Campbell diagram obtained by 15 The numerical evaluation (red curve) of the experimental modal damping ratio from the measured vibrations at strain gauge (green curves), where ε r and ω r are measured strain resonance amplitude and resonance frequency, respectively. 16 Cyclic symmetric finite element sector model (left) for simulating the impeller of interest (right). 10 Unsteady flow in a turbocharger ABB Value Paper

11 sweeping the rotational speed over the part load operation point to be analyzed. In the diagram on the left side the resonances i,j/k=1,4/4 and i,j/k=3,3/11 can be identified close to the considered operation point at the rotational speed n op. Mode i,j/k=1,4/4 splits into two contiguous peaks, which indicate the presence of mistuning effects in the compressor hub. Mistuning in bladed discs usually can be attributed to slight manufacturing differences among the blade geometries coupled elastically by a disc. For the assessment of the static load on the compressor wheel the centrifugal force at operation speed n op and the corresponding non-uniform temperature distribution were applied on the FE model. The static aerodynamic load for both circumferential positions of the diffuser vanes was calculated by Fourier decomposition of the time dependent pressure signal resulting from CFD calculation (the aerodynamic pressure corresponding to the 0th harmonic of the Fourier decomposition) and mapped on the FE model with the in house interface tool FACET. The resulting static stress distribution and static pressure load shown in Figure 18 are identical for both angular positions of the diffuser vanes. the analysis of the tuned blades was possible due to the restriction of the cyclic FE modeling. On the other hand, the deterministic quantification of mistuning in the conventional design process is difficult due to its random nature. Static and unsteady flow loads acting on the compressor blades were determined with the FFT of the computed unsteady pressure. Due to the revolution-periodicity of the unsteady CFD-pressure signal in form of 256 time increments, a Fourier decomposition was performed at each CFD-node, to get the static pressure and harmonic excitation amplitudes with respect to the rotational speed [10, 11]. With applied static load a modal analysis was run by means of FE. The resulting Campbell diagram (Figure 19) is coincident with the experimental diagram in Figure 17. The eigen frequencies of the modes i,j/k=1,4/4 and i,j/k=3,3/11 differ by less than 1% from the measured frequencies. Figure 20 illustrates the calculated mode shapes for both modes. In the FE results, each computed resonance is represented by one peak, because only 17 Campbell diagram obtained by blade vibration measurements with strain gauges. In the diagram the resonances i,j/k=1,4/4 and i,j/k=3,3/11 can be identified. The double peak for mode i,j/k=1,4/4 is a typical sign of mistuning. 17 Campbell diagram obtained by blade vibration measurements with strain gauges. In the diagram the resonances i,j/k=1,4/4 and i,j/k=3,3/11 can be identified. The double peak for mode i,j/k=1,4/4 is a typical sign of mistuning. 19 Numerical Campbell diagram representing the eigenfrequency in dependency of the rotational speed of the compressor wheel for the 8 lowest blade modes. The eigenfrequency of the modes i,j/k=1,4/4 and i,j/k=3,3/11 differs by less than 1% from the measured frequencies in the experimental Campbell diagram. ABB Value Paper Unsteady flow in a turbocharger 11

12 In literature, numerical tools for the interaction of CFD data with the FE mesh are well described for axial turbine blades (e.g. [10], [11], [12]). For a radial 3D blade that has a more complicated geometry than an axial one, a description of the computational process in the literature limited (e.g. [13]). For the spatial extrapolation of the CFD data onto the contour of the cyclic FE mesh of one sector of the radial impeller (Figure 21) the numerical formulation of the in-house FACET code [2,11] was generalized to be also used for radial disc assemblies. For the association of points of the CFD-mesh with single element faces on the FE contour, a weight function was defined using the distance tolerance based on the characteristic element size of the blade and hub contour. It is beyond the scope of this paper to give more details of the CFD-FE interaction process being extensively described in [2,11]. As result the FACET output gives the weighted CFD static and excitation amplitudes, which are associated with the appropriate element face of the FE mesh. 20 FE mode shapes of modes i,j/k=1,4/4 (left) and i,j/k = 3,3/11 (right). The contour plot represents displacement amplitudes. Red color denotes maximum amplitudes. The FACET output conforms to the format of the standard FEcode ABAQUS and defines the static and complex excitation pressure distribution on FE-element faces. Then the forced response calculation under resonance conditions was carried out by applying the complex excitation pressure for the 4th and the 11th excitation order respectively on the impeller s FE-mesh. For the simulation the experience value of 0.12% was assumed for the damping ratio of the compressor wheel. The resulting contour plots of the normalized dynamic equivalent stress (Figures 22 and 23) shows differences for both circumferential diffuser vane positions. Verification of the numerical results with experimental data In the typical design process, the static pressure load on the impeller is known from the steady-state flow simulation. In the worst case, the resulting static force Fo is given for the dynamic analysis. Usually the characteristic stimulus s and the modal damping ratio ξ are acquainted with the experimental data of previous investigation of similar blades. Then, the resonance stresses and strains can be computed from the FE simulation and the maximum resonance strain ξa,gauge,fe at the strain gauge is obtained for the assumed stimulus so and modal method. Then the measured stress amplitude was plotted as a function of the damping ratio (Figures 25 and 26). The wide scatter of the damping ratio demonstrates the sensitivity of the damping properties. The forced response calculation of the impeller was made for the tuned system under resonance condition. For a damped system the resonance displacement amplitude X is given by (see details in Szwedowicz, 2008 [16]). details in Szwedowicz, 2008 [16]). Fo X = m ( ω ) ( ) 2 i. j ω + 2ξωi. jω where m denotes the modal mass, which equals 1 for the where denotes the modal mass, which equals 1 for the massnormalized FE mode shapes, Fo is the exciting force amplitude, k the system s stiffness, w the excitation frequency and ξn the blade eigenfrequency. 21 Mesh resolutions: CFD (blue) and FEM (green). 12 Unsteady flow in a turbocharger ABB Value Paper

13 From the FEM-analysis considering the steady state, the resonance stress amplitude σ o is obtained for the constant excitation amplitude F o and the constant damping ratio ξ o, being the stress amplitude σ o proportional to the displacement amplitude X. With respect to the given minimum ξ e,min and maximum ξ e,max modal damping ratio, this FE stress amplitude σ o can be scaled to another resonance stress σ relating to the e damping ratio ξ e. Assuming the constant excitation amplitude F o, the stress σ is calculated with the hyperbolical function e given as given as ξ σ o e = σo ξe On the other hand, a higher stimulus s e than s o used in the FE analysis needs to be considered in the design process. Then, assuming the constant damping ratio σ o, the resonance stress response σ for stimulus s e stress response is determined linearly from o σ e for stimulus s o is determined linearl s σ e e = σ o so In Figure 24, these variations of the resonance In Figure 24, these variations of the resonance stresses of the tuned blades are summarized in the sensitivity diagram of the resonance responses, which is a novel diagram in the literature. In this diagram, the computed stresses can be compared straightforwardly with the experimental stresses at their evaluated damping values, as it is shown for experimental data (referring to the resonances in Figure 15) in Figures 25 and 26. These equations are used for calculating the vibration amplitude for any arbitrary damping ratio and for extrapolating the calculation results (red curve in Figures 25 and 26). To determine the possible maximum forced response of the mistuned impeller with N=8 cyclic sectors, the amplitude of the tuned system can be amplified by Θ=1.9 (for N sectors in the disc assembly Θ=(1+(N) 1/2 )/2, as it is given by Whitehead in [14]) (green curve in Figures 25 and 26). A more conservative approach for determining the vibration amplitude of a mistuned bladed disc was determined by Han et al. [15], who suggests an amplification equal Θ=(N) 1/2. The violet curve in Figures 25 and 26 shows the amplified values for 8 cyclic sectors with Θ= Normalized equivalent stress for mode i,j/k = 1,4/4 resulting from aerodynamic excitation with 4 th EO for 0 (left) and 10 (right) vaned diffuser position. 23 Normalized equivalent stress for mode i,j/k = 3,3/11 resulting from aerodynamic excitation with 11 th order for 0 (left) and 10 (right) vaned diffuser position. ABB Value Paper Unsteady flow in a turbocharger 13

14 24 Sensitivity diagram of the resonance response for the tuned and mistuned blades, where N is the number of blades in the disc assembly and ξ m is the material modal damping ratio treated as the minimum damping for the dynamic analysis (Szwedowicz, 2008 [16]). 25 For 0 (top) and +10 (bottom) vaned diffuser ring positions, the sensitivity diagram of the measured and numerical equivalent stresses of mode i,j/k=1,4/4 in terms of possible damping ratio variation and mistuning amplification. Measuring points refer to the resonances in Figure For 0 (top) and +10 (bottom) vaned diffuser ring positions, the sensitivity diagram of the measured and numerical equivalent stresses of mode i,j/k=3,3/11 in terms of possible damping ratio variation and mistuning amplification. Measuring points refer to the resonances in Figure Unsteady flow in a turbocharger ABB Value Paper

15 The assessment of the mistuned compressor wheel is not possible by using a cyclic symmetric sector model, because in reality all blades randomly differ from each other in different manner as it occurs in the mass-production of impellers. Mistuning occurs due to slight differences in the geometry of all blades and disc in the range of manufacturing tolerances. Those geometrical dissimilarities could be proved for individual impellers by a three-dimensional (3D) scanning. However, its measuring accuracy, which also depends on the scanning time, and usually is above a few hundredth millimeter of the typical mistuning range for 3D thin impeller blades. In spite of the numerically controlled impeller manufacturing within the allowable tolerance band, a number of mistuning combinations based on slight local geometrical differences on the blade contours exceeds the computational capability of the conventional design process. In addition, for the assessment of mistuning a full 3D numerical model of the wheel including mistuned blades would have to be built. Then a large number of simulations would have to be made by varying the geometry of the mistuned blades to acquire statistic data of the tolerance variation that would provide the possible maximum response amplitude of the mistuned disc assembly. Because this time consuming study was not relevant for the fluid structure interaction process, the described Whitehead [14] and Han et al. [15] criteria were used for a realistic estimation of the maximum vibration response amplitudes of the mistuned impeller. Their studies are based on the simplified N-disc assemblies, in which every blade is represented by one degree of freedom attached to the elastic disc. By using the Monte-Carlo approach, these simplified disc assemblies allow for around one hundred thousand simulations of different possible sequences of all mistuned blades in one stage. Based on this analysis, Whitehead and Han found criteria (1+(N) 1/2 )/2 and (N) 1/2, respectively, are used for prediction of the possible maximum response amplitudes of the disc assembly with N=8 mistuned blades. In the applied computational process, the FE steady-state response of the tuned disc assembly is calculated for the CFD pressure, which is defined with 3D complex Fourier amplitudes acting on every elemental face of the blade. Multiplying this FE result by both Whitehead and Han criteria, the possible scatter of the maximum vibration amplitudes at the strain gauge positions of the measured mistuned impeller are computed and compared to strain gauge measurements. In the diagrams it can be recognized that the values resulting from numerical simulations are in very good agreement with the measured ones. Any of the measured points exceeds the limit that was calculated for the mistuned impeller. This way of representing calculation data is a useful design tool that helps to estimate vibration amplitudes for any arbitrary damping ratio and to avoid HCF damages in bladed discs. When analyzing the amplitude difference between 0 and +10 diffuser ring position in the diagrams of Figures 25 and 26 an increase of the stress by 18% can be observed for mode 1.4/4. This tendency is confirmed by the measurement results. 26 For 0 (top) and +10 (bottom) vaned diffuser ring positions, the sensitivity diagram of the measured and numerical equivalent stresses of mode i,j/k=3,3/11 in terms of possible damping ratio variation and mistuning amplification. Measuring points refer to the resonances in Figure 14. ABB Value Paper Unsteady flow in a turbocharger 15

16 For mode 3.3/11 the difference between the calculated stresses for both diffuser ring positions is insignificant with an amplitude decrease of 1%. A comparison with the experimental values is not possible for this mode due to the large scatter band of the stress amplitudes for the +10 diffuser ring position. Conclusions The influence of two different circumferential vaned diffuser ring positions on the compressor flow and the impeller blade excitation mechanism for an off-design operating point have been investigated. With the help of flow visualisations two different phenomena could be detected per circumferential ring position: An alternating separation zone in the volute tongue / exit cone region (+10 ) and a stagnation area below the tongue underneath the exit cone (0 ). A novel double FFT analysis, which provides detailed information about the engine order and pulsation excitation and clarifies the investigated excitation phenomena, has been successfully applied. For the first time time varying states of flow variables were presented at the volute inlet plane: Static pressure and volute inlet flow angle differ significantly from stationary mean values for each circumferential position. An impeller with two splitter blades per pitch has been used and the power (load) distribution on these splitter blades has been shown: The load distribution on the shorter splitter blade is considerably higher than on the long one. The load distribution on different splitter blades is not due to blade length, but to relative position with respect to the main blade. Using the described numerical procedure, the simulation results satisfactorily reproduce the vibration measurement for the lower excitation frequency. This demonstrates that a coupled CFD-FEsimulation (here applied in series only and not simultaneously) is a useful tool for doing fluid and structural assessment of operation conditions of the analysed impeller. It allows the comparison of different systems with each other. Also the influence of different operating conditions on the impeller lifetime can be estimated and HCF assessments can be performed. A new manner for representing the results of an FSI simulation is proposed in the form of a sensitivity response diagram. In general, this approach is based on the resonance sensitivity assessment, which takes into account the excitation, damping and mistuning effects as key parameters affecting real blade responses. It allows extrapolating the calculated values for an arbitrary damping ratio and to estimate the enlargement of resonance amplitudes of the mistuned system. The measured resonance strain amplitudes of all experimental tests match very well the predicted scatter range of numerical results. This comparison demonstrates that the employed methodology is capable of predicting the 3D impeller s vibration behavior under real engine conditions up to 8 khz. Acknowledgements The authors would like to thank ABB Turbo Systems Ltd for the permission to publish this work. Several colleagues have contributed to the success of this project, particularly Manfred Kissel and Niklas Sievers. 16 Unsteady flow in a turbocharger ABB Value Paper

17 References [1] Rodgers C., 2003, High Specific Speed, High Inducer Tip Mach Number, Centrifugal Compressor, ASME Paper No. GT [2] Dickmann, H.-P., Secall Wimmel, T., Szwedowicz, J., Filsinger, D., Roduner, C.H., 2006, Unsteady Flow in a Turbocharger Centrifugal Compressor 3D-CFD-Simulation and Numerical and Experimental analysis of Impeller Blade Vibration, ASME Journal of Turbomachinery, Vol. 128, July 2006, pp [3] Sorokes, J.M., Borer, C.J., Koch, J. M., 1998, Investigation of the Circumferential Static Pressure Non- Uniformity Caused by a Centrifugal Compressor Discharge Volute, ASME 98-GT-326 [4] Sorokes, J.M., Koch, J., 2000, The Influence of Low Solidity Vaned Diffusers on the Static Pressure Non- Uniformity by a Centrifugal Compressor Discharge Volute, ASME 2000-GT-0454 [5] ANSYS, Inc. 2005, CFX-10 User Manual [6] Japikse, D., Centrifugal Compressor Design and Performance, Concepts NREC, 1996 [7] Aungier, R.H., Centrifugal Compressors A Strategy for Aerodynamic Design and Analysis, ASME Press, 2000 [8] Kammerer, A. and Abhari, S. R., 2008, Experimental Study on Impeller Blade Vibration During Resonance, Part 2: Blade Damping, ASME paper GT [9] ABAQUS User s manual Version 6.7, 2008 [10] Filsinger, D.; Frank, Ch.; Schäfer, O.; 2005, Practical Use of Unsteady CFD and FEM Forced Response Calculation in the Design of Axial Turbocharger Turbines, ASME GT [11] Schmitz, M. B., Schäfer, O., Szwedowicz, J., Secall Wimmel, T., Sommer, T. P., 2003, Axial Turbine Blade Vibrations by Stator Flow Comparison of Calculations and Experiment, ISUAAAT [12] Moyroud, F., Cosme, N., Jöcker, M., Fransson, T. H., Lornage, D., Jacquet-Richardet, G., 2000, A Fluid- Structure Interfacing Technique of Computational Aeroelastic Simulations, 9th International Symposium on Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines and First Legendre Lecture Series, Lyon, France [13] Filsinger, D., Sekavcnik, M., Ihli, T., Schulz, A., Wittig, S., 2002, Vibration Characteristics of a Radial Turbocharger Impeller, Proceedings of the 7th Int. Conference on Turbochargers and Turbocharging, London [14] Whitehead, D. S., 1988, The Maximum Factor by Which Forced Vibration of Blades Can Increase Due to Mistuning, J. of Eng. For Gas Turbines and Power, Vol. 120, pp [15] Han, Y., Xiao, B. and Mignolet, M. P., 2007, Expedient Estimation of the Maximum Amplification Factor in Damped Mistuned Bladed Disks, ASME Paper GT , Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May [16] Szwedowicz, J., 2008, High Cyclic Fatigue, VKI Lecture Series Structural Design of Aircraft Engines: Key Objectives and Techniques edited by E. Seinturier and G. Paniagua, ISBN , von Karman Institute for Fluid Dynamics, Rhode Saint Genese, Belgium ABB Value Paper Unsteady flow in a turbocharger 17

18 Appendix1 Two video snapshots of the flow structure in the volute tongue region for both vaned diffuser ring positions are shown. Flow visualization has been done by wall streamlines. Note: The same vane trailing edge has been marked in the black circles. It has just been turned by 10 in clockwise direction. The impeller circumferential positions are identical for the two snapshots on the top and the two snapshots on the bottom. The difference between the snapshots on top and bottom correspond to half main blade pitch of the impeller or 256/8/2 = 16 time steps. The view is from the exit cone on the tongue and on the trailing edges of the diffuser vanes. The two unsteady flow states differ especially at the exit cone inlet / tongue region (blue ellipse). While there is no separation visible for the 0 position, a moving separation (for moving direction see red double arrow) can be observed for the 10 position. The dark blue streamlines move between left and right during one impeller pitch pass or 8 times during one impeller revolution. This separation can be seen as well in figure 10 on cut plane A-A at 50% vaned diffuser channel height. This instability due to the different circumferential positions of the vaned diffuser is an indication for different blade vibrations of the impeller and demonstrates the importance of a fixed vaned diffuser ring position. 18 Unsteady flow in a turbocharger ABB Value Paper