numerical investigation of the superimposed effects on stator wake oscillation in an axial-radial...

Journal of Thermal Science Vol.23, No.1 (2014) 2235

Received: October 2013 YANG Ce: Professor. Financially supported by National Natural Science Foundation of China (No. 51176013) and Chinese Specialized Research Fund for the Doctoral Program of Higher Education (No. 20091101110014).

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DOI: 10.1007/s11630-014-0673-y Article ID: 1003-2169(2014)01-0022-14

Numerical Investigation of the Superimposed Effects on Stator Wake Oscillation in an Axial-radial Combined Compressor

ZHAO Ben 1, YANG Ce 1, HU Liangjun1, ZHOU Mi2, ZHANG Jizhong3

1. School of Mechanical Engineering, Beijing Institute of Technology, 100081 Beijing, China

2. Basic Subject Department, Bohai Shipbuilding Vocational College, 125000 Huludao, China

3. Science and Technology on Diesel Engine Turbocharging Laboratory, China North Engine Research Institute, 037036

Datong, China

© Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2014

The superimposed influences of the blade rows in a multistage compressor are important because different matches

of upstream and downstream blades can result in significant differences in the stator wake oscillation. Numerical inves-

tigation of the axial stator wake oscillation, which is affected upstream by the axial rotor and downstream by the radial

rotor, was performed in an axial-radial combined compressor. Many configurations with different blade numbers and

locations, which influence axial stator wake oscillation were investigated. When rotors have equal blade numbers, the

axial stator wake oscillates periodically versus time within time T (moving blade passing 1/3 revolution). In contrast,

stator wake oscillates irregularly within T when rotors have different blade numbers. A model-split subtraction method is

presented in order to separate the influences of the individual blade rows on the wake oscillation of the axial stator.

Analysis from the rotor-stator configuration showed that the unsteady flow angle fluctuation response is caused by the

upstream rotor. For the rotor-stator-rotor configuration, the unsteady flow angle fluctuations are influenced by up- and

downstream blade rows. With the model-split subtraction method, the up- and downstream influences on the flow angle

fluctuation could be clearly separated and quantified. Low amplitudes could be observed when the influences from up-

and downstream moving rows were superimposed with the “positive peak- negative peak” type wave. Clocking investi-

gations were carried out to change the relative superimposed phase of influences from the surrounding blade rows in or-

der to modulate the amplitudes of the axial stator wake oscillation. However, the amplitudes did not reach the maximum

when they were superimposed with “positive peak-positive peak” type wave due to the impact of the interaction between

the two moving blade rows.

Keywords: axial-radial combined compressor; wake oscillation; superimposed effect; absolute flow angle;

clocking

Introduction

The blade wake oscillation phenomenon in a multi-stage compressor has been a crucial research topic for a

long time. Because of the interaction between the wake and the free stream, blade wake oscillation introduces variations of velocity deficit in upstream row wakes, and thus induces periodic variations in incidence and inlet

Ben Zhao et al. Investigation of Superimposed Effects on Stator Wake Oscillation in an Axial-radial Combined Compressor 23

Nomenclature

α absolute flow angle () d Downstream

steady time-average flow angle that is not disturbed by up- and downstream influences ()

g Geometry

time-average absolute angle () ud upstream and downstream

unsteady part of the absolute flow angle () ― time-average value

g absolute flow angle variation caused by the geometry of the trailing edge of the axial sta-tor ()

~ unsteady fluctuation part

,u u i absolute flow angle variation caused by the upstream rotor ()

RMS root mean square

,d d i absolute flow angle variation caused by the downstream rotor ()

Original- compressor

12 axial rotor blades- 17 axial stator blades – 9 radial rotor blades

,ud ud i flow angle variation induced by the ro-tor-rotor interaction (the potential field of the radial rotor is influenced by the axial rotor wakes) and clocking ()

Config 1 4 axial rotor blades- 6 axial stator blades – 3 radial rotor blades (after scaling)

T four axial rotor blades passing periodicity Config 2 4 axial rotor blades- 6 axial stator blades (after scaling)

rotational speed (rad/s) Config 3 4 axial rotor blades- 6 axial stator blades – 4 radial rotor blades (after scaling)

N time step CP 1\2\3\4\5 clocking position 1\2\3\4\5

i order of time step,1,2,3,…… R axial rotor or radial rotor

u Upstream S axial stator

Mach number to downstream blade rows. As a result, the interaction noises, flow/structure interactions and com-pressor performance are influenced by this phenomenon. Therefore, it is very important to account for the un-steady wake oscillation in order to improve the perform-ance and life of a multistage compressor. This requires a detailed physical understanding of blade wake oscillation in a multistage compressor.

Thus far, there are a little experimental and computa-tional data available about blade wake oscillation in tur-bomachinery. Oro[1] used hot-wire anemometry to obtain the phase averaged velocity and discovered that the defi-cit of velocity is modified by potential effects and wake’s position changes over time. Rotor wake variability in a multistage compressor was studied by Key[2]. Time- re-solved flow angle data are acquired with a cross-film sensor. In downstream rotors, ensemble-averaged revolu-tions of data show an amplitude modulation caused by interactions with the rotor wakes from the upstream blades rows. Standers and Fleeter[3] investigated the mul-tistage interaction effects on rotor blade-to-blade wake variability. Strazisar[4] investigated the blade-to-blade periodicity of the flow in a transonic fan rotor using laser anemometry. Analysis of rotor wake data in the tip region indicated that at peak efficiency the wakes oscillated about their mean positions with amplitudes of approxi-mately 4-6% of the blade pitch. Thus, the unsteady blade

wake oscillation is influenced by the incoming wakes as well as by the potential effects of the surrounding blade rows.

The effect of the wakes and the potential effects on the unsteady blade loading and the excited aerodynamic blade forces were investigated by Hsu and Wo[5]. More-over, they discussed the influence of rotor clocking on the unsteady force excitation. Numerical results of the clocking influence on the unsteady blade forces are also presented by Lee[6]. However, few researchers have dis-cussed the clocking influence on the blade wake oscilla-tion phenomenon.

Up to now, one important thing ignored by most of these investigations is the aerodynamic coupling interac-tion on the blade wake oscillation in a multistage com-pressor. Therefore, the superimposed effects acting on wake oscillation cannot be best organized and utilized. In fact, if a new method is provided to separate all of the influence into several sets, it would promote better un-derstanding about these effects, which could then be su-perimposed to each other in the blade wake flow field and the unsteady flow will be organized and utilized eas-ily in the design process. Similar method was provided firstly by Zhao and Yang[7,8] and used to investigate the pressure fluctuation on the blade surface in multistage compressor. Now, it was developed and then used to re-search wake oscillation.

24 J. Therm. Sci., Vol.23, No.1, 2014

This paper has two goals: One is to develop a useful method, named the model-split subtraction method, to separate all of the components that influence the blade wake oscillation into two groups and then determine the relative superimposed phases; the other is to introduce the clocking modulation method, which is used to modu-late the amplitude of the stator wake oscillation, and ex-plain the physical mechanism of this method by using the model-split subtraction method.

Compressor description

The investigation object, an axial-radial combined compressor, consists of an axial rotor, axial stator, radial rotor, a vaneless diffuser and volute from inlet to outlet. The major geometry parameters are listed in Table 1. The upstream axial rotor and the downstream radial rotor are coaxially connected on a shaft and rotate at the same speed. The compressor numerical model is illustrated in Fig. 1.

The investigation was carried out in the following steps: first, the performance of the compressor with vo-lute, as showed in Fig. 1, was numerically simulated and validated against test data; then the unsteady simulation of the compressor with different blade counts and clock-ing positions were carried out. In the unsteady simulation, the volute wasn’t included and the domain scaling method was applied. The blades were scaled in the fol-lowing configurations and listed in Table 2:

Config 1: The axial stator blades were scaled from 17 to 18 and a model with 4 axial rotor blades-6 axial stator blades-3 radial impeller blades was investigated.

Table 1 Axial-radial combined compressor parameters

Items Axial Rotor Axial Stator Radial Rotor

Main blade 12 17 9

Split blade - - 9

Outlet radius 52 mm - 75 mm

Tip clearance 0.3 mm - 0.6 mm

Design speed 60000 r/min

Design mass 1.15 kg/s

Fig. 1 Numerical model of the axial-radial combined com-pressor

Config 2: The axial stator blades were scaled from 17 to 18 and the radial rotor was removed. In this case, the model was changed into a one stage axial compressor.

Config 3: The axial stator blades and radial rotor blades were scaled from 17 to 18 and 9 to 12, respec-tively. A model with 4 axial rotor blades-6 axial stator blades-4 radial impeller blades was investigated. Five different clocking positions (CPs) of the axial rotor, comprised of rotating the axial blades from 0° (CP1) to 6° (CP2)/12° (CP3)/18° (CP4)/24° (CP5) in the counter rotation direction of the rotor, were also investigated.

Table 2 Model introduction

Name Clocking Position

Blade Number (R-S-R) (R-S)

Position of radial Rotor /

Config 1 12-18-9 0

Config 2 12-18

CP1 12-18-12 0

CP2 12-18-12 6

CP3 12-18-12 12

CP4 12-18-12 18

Config 3

CP5 12-18-12 24

Computation mesh

The volute mesh was manually generated, using the butterfly technique to improve the mesh quality. The blade row mesh was automatically created with O4H topological structure. Periodic boundaries were applied and multi-blocked structured grids were developed to achieve the required mesh quality. H-type grids were used for the inlet and diffuser blocks. An O-type block was used around the blade surface. There were 13 grid nodes in the rotor clearance region in the spanwise direc-tion. For the computational grids in blade rows, the minimum skew angles of grid cells were greater than 18°, the maximum expansion ratio were less than 2.7 and the maximum aspect ratios were less than 560. Y+ values of less than 3 were achieved in most areas with a maximum y+ value of 13 located on the surface of the centrifugal rotor near the trailing edge. The small area where y+ was greater locates near the trailing edge of centrifugal rotor and is far away from the stator. On the other hand, a transonic condition was formed at the inlet of the cen-trifugal rotor. Therefore the effect of larger Y+ value on the embedded stator can be ignored. The number of grid nodes in each section is listed in Table 3.

Numerical scheme

The steady calculation was simulated by solving the 3-D Reynolds Averaged Navier-Stokes (RANS) equa-tions with Spalart-Allmaras turbulence model. The dis-


crete N-S equations are solved by using a cell-centered finite volume scheme and the steady-state flow solution is achieved at the convergence of a 4-stage explicit Runge-Kutta integration scheme. The steady calculation field includes one axial rotor blade, one stator blade, one radial rotor blade, a vaneless diffuser and volute. Total pressure, total temperature and direction of the absolute velocity were specified at the inlet boundary. Static pres-sure was specified at the outlet boundary. The conserva-tive coupling by pitchwise rows was used at the ro-tor/stator interface, which guaranteed an exact conserva-tion of mass flow, momentum and energy through the interface. This approach adopts the same coupling pro-cedure for all the nodes along the circumferential direc-tion, even if the local flow direction is different from the average one. It shows to be very robust and is therefore used in this research. Table 3 Number of grids for single passage

Block Number Block Number

Inlet 39729 Radial-rotor 662250

Axial-rotor 323663 Diffuser 100450

Stator 203389 Volute 749438

To study the physical mechanism of the superimposi-

tion, an unsteady simulation was performed at the same speed and flow rate. Fig. 2 shows the numerical model of Config 1. At each computational field, 60 physical time steps were applied and a sufficient convergence was achieved after dozens of cycles of the simulation at the design operation point (1.15 kg/s, 60000 r/min). At the rotor-stator interface, a direct interpolation on sliding meshes was employed for the unsteady calculations. Pe-riodical repeat of the static pressure from many monitor-ing points indicate that the size of time step can satisfy the need of study.

Fig. 2 Numerical model for computation, including four axial rotor blades, six stator blades and three radial rotor blades (1/3 of a whole revolution)

To eliminate the simulation error caused by the mesh,

a grid independence study was conducted. The different

levels of the mesh were created by changing the distribu-tion of nodes along the span-wise, chord-wise and stream-wise direction. Table 4 includes the descriptions of the mesh as well as their corresponding performance (steady calculation, the computational field including one axial rotor blade, one stator blade and one radial rotor blade). A notable elevation appears with the coarse grid through to a medium level grid. As for the fine level mesh, the rows’ performance increases insignificantly from the medium grid based on almost the same total nodes number growth. Therefore, the medium grid is adequate enough for the simulation, and it is adopted for the following studies of unsteadiness. Table 4 Simulation performances with different mesh at de-sign point

Level Total number

of nodes Pressure ratio(t-t)

Isentropic efficiency(t-t)

Coarse 741789 3.7254 0.76335

Medium 1176321 3.9302 0.79298

Fine 2005501 3.9574 0.7956

Unsteady simulation was performed with a central

spatial discretization scheme and dual time stepping technique. Convergence criteria and maximum inner it-erations were set at -4 and 50, respectively, for dual time steps. The total number of grid nodes used for the un-steady simulation was approximately 4,460,000. The y+ value is within 3-8 for most flow-fields.

Performance testing

The compressor performance was measured in a stan-dard turbocharger test rig in the China North Engine Re-search Institute. The compressor was driven by the tur-bine with a supply of high pressure hot air, which was controlled by a valve. At the compressor inlet, a plenum chamber was fitted with two nozzles; the first for mass flow measurement and the second to ensure that the air entered the compressor intake pipe smoothly without a sudden contraction. At the compressor exit, a throttle valve was used to control the air flow rate and, hence, the operating point of the turbocharger.

The overall performance of the axial-radial combined compressor was calculated through the measured inlet and discharge static pressures together, as well as the total pressures and total temperatures, at 60000 r/min. Its uncertainty is 0.2 percent point.

Validation of numerical simulation

Fig. 3 presents the experimental (Exp) and computa-tional (Cal) comparison of the compressor performance. The mass flow was normalized by the design flow rate. It

26 J. Therm. Sci., Vol.23, No.1, 2014

can be seen that the curve tendency shows good agree-ment, although a certain amount of distinction exists. The discrepancy is in an acceptable range.

Fig. 3 Numerical and experimental comparison of the com-pressor performance at 60000 r/min

Data processing

As the study purpose is to investigate the physical mechanism of superposition, which happens in the stator exit, the focus of the analysis is on the stator wake oscil-lation at the stator exit and the absolute flow angle fluc-tuation at the central location of the stator wake at the 50% span. The research data used to investigate the su-perposition phenomenon were obtained from simulation results. The monitoring position of the entropy value was marked with a red line on the stator exit, and the absolute flow angle was monitored at the central location of stator wake and marked with point in Fig. 4.

T is the time for the four axial rotor blades passing pe-riods. The angle equals to 2/3π in magnitude (1/3 of a whole revolution).

2

3

(1)

Ω represents the rotational speed in the previous equa-tion.

The absolute flow angle α was determined by adding the time-averaged value and the unsteady part of the

absolute flow angle .

(2)

Fig. 4 Investigated location, entropy and absolute flow angle obtained at the stator exit; locations marked, respec-tively with a red line and a point, at a 50% span, 1/3 of the whole revolution

Results and discussion

Axial Rotor(12)-Axial Stator(18)-Radial Rotor(9) Re-sults: Stator wake oscillation driven by all influences with different frequencies

The stator blade row of Config 1 (Axial Rotor(12)- Axial Stator(18)-Radial Rotor(9)) is embedded into the up and downstream rotor blade rows with different blade numbers. This is why the unsteady stator wake oscillation is affected by the wake of upstream blade row and the potential effect of the downstream blade row. The fol-lowing results on the stator wake oscillation for the de-sign point will be discussed (Figs. 5 and 6).

Fig. 5 shows the unsteady response of the stator wake oscillation at a 50% span with respect to the influences of the up and downstream rotor blade rows for the design point. This figure reveals information about the stator wake oscillation and the axial rotor wake transportation with respect to the relative position of the axial rotor. The vertical axis shows time, normalized by the four axial rotor blades passing period (T, calculated by equation (1)), while the horizontal axis corresponds to the stator pitch (location marked with the red line in Fig. 4). The vertical band of high entropy corresponds to the stator wake and cannot be fixed at a particular tangential posi-tion while the wakes oscillated about their mean position with variable amplitude in time T. As seen in Fig. 5, the maximum value is up to 7.5 percent of the vane pitch. The transversal bands running diagonally to the plot rep-resent the axial rotor wakes; obviously, they are diagonal because the axial rotor is moving tangentially over time. Thus, the spill of these bands depends upon the passing axial rotor blades. Fig. 6 shows the time trace of the ab-solute flow angle at the central position of the stator wake (position designated with a point in Fig. 4). The variable fluctuation amplitudes within time T are the most noticeable feature in Fig. 6. In other words, the ab-


solute flow angle fluctuated with the variable amplitudes within T. In addition, three peaks can be obviously ob-served in Fig. 6, which is identical to the number of passing radial rotor blades within T.

To determine the reason for the absolute flow angle fluctuated with the variable amplitudes, the frequency spectra of the absolute flow angle is presented in Fig. 7. In the frequency spectra, different periodic influences can be clearly separated from each other. The highest ampli-

Fig. 5 Entropy fluctuation at the stator exit, 50% span, Config 1 (Axial Rotor(12)-Axial Stator(18)-Radial Rotor(9))

Fig. 6 Time trace of the absolute flow angle at the central position of stator wake, 50% span, Config 1 (Axial Rotor(12)-Axial Stator(18)-Radial Rotor(9))

Fig. 7 Frequency spectra of the absolute flow angle at the central position of stator wake, 50% span, Config 1 (Axial Rotor(12)-Axial Stator(18)-Radial Rotor(9))

tude occurs at 9 kHz, which is identical with the blade passing frequency of the radial rotor. The axial rotor wake influence is clearly visible in Fig. 7 as well. These results indicate that the stator wake oscillation was driven collectively by the wake of the upstream axial rotor and the potential field of the downstream radial rotor blade row. Sanders[3] carried out the rotor blade-to-blade wake variability in a multistage compressor. He indicated that the waveforms of velocity exhibit small differences in one rotor revolution due to the unequal number of blades and vanes. Another similar phenomenon was also pre-sented in reference[9].

The interaction-driven rotor wake variability charac-teristics for a multistage compressor were investigated by Key[2]. In the downstream rotors, the ensemble-averaged revolutions of the absolute flow angle show an amplitude modulation caused by interactions with the rotor wakes from the upstream blade rows, which increase the levels of blade-to-blade wake variability. Oro[1] used hot-wire anemometry to obtain the phase averaged velocity and discovered that the deficit of velocity in the IGV’s wake is modified and its positions change over time. He indi-cated that these phenomena are caused by the potential field of the downstream rotor. Interaction-driven wake variability refers to the changes in the wake structures due to the forcing effects from the upstream and down-stream blade rows. Blade-to-blade wake variability refers to the changes in the wake structures emanating from discrete rotor blades with slight differences in geometry. It is also possible that the interaction variations can cou-ple to the geometry driven blade-to-blade variations to provide a more complex forcing function [10]. Fig. 8 shows an illustration that indicates some of the com-plexities associated with the flow-field at the axial stator exit. The axial rotor and the axial stator wakes are shown with a wake centerline. The wakes from the axial rotor will be chopped into segments by the axial stator leading

Fig. 8 Illustration of some of the complexities associated with the flow-field at the axial stator exit, 50% span, Config 1 (Axial Rotor(12)-Axial Stator(18)-Radial Rotor(9), 1/3 of the whole revolution)

28 J. Therm. Sci., Vol.23, No.1, 2014

edge. The wake segments will then turn and diffuse as they undergo convection through the axial stator passage. After passing the axial stator passage, these axial rotor wake segments will interact with the axial stator wakes, labeled “R-S Wake Interaction”. The interacted field be-tween the wakes, at the axial stator exit, will transport downstream and then interact with the potential field of the radial rotor. Moreover, there are also the interactions between the axial stator wakes and the potential field of the radial rotor. The characteristics of these interactions can be shown and analyzed by the absolute flow angle variability. Thus, a simple hypothesis is proposed that the absolute flow angle of the axial stator wake can be sepa-rated into several terms:

steady : the time-average flow angle, which is not dis-

turbed by the up- and downstream influences;

g : the absolute flow angle variation caused by the

geometry of the trailing edge of the axial stator;

,u u i : the absolute flow angle variation caused by

the upstream rotor;

,d d i : the absolute flow angle variation caused by

downstream rotor;

,ud ud i : the absolute flow angle variation induced

by the axial rotor-radial rotor interaction (the potential field of the radial rotor is influenced by the axial rotor wakes), which can be changed by clocking.

Then, for Config 1 (Axial Rotor(12)-Axial Stator(18)- Radial Rotor(9)), which has the axial rotor and the radial rotor in the up- and downstream of the axial stator, the unsteady aerodynamic response on the stator wake can be quantified by equation (3), according to superposition.

, 1 ,

, ,

i Config steady g u u i

d d i ud ud i

(3)

Axial Rotor(12)-Axial Stator(18) Results: Stator Wake Oscillation driven by part of Influences

The axial stator wake is influenced collectively by both the wakes from the upstream axial rotor and the potential field of the downstream radial rotor. Because of the superimposed effect, it is difficult to separate and quantify the individual influence from the upstream axial rotor wake. To solve this problem, the axial-radial com-bined compressor was modified into a one stage axial compressor by wiping off the radial rotor and the volute. This approach to separating the configurations has been used by Hsu[5]. In the one stage axial compressor, the stator wake is influenced by both the stator trailing edge geometry and the axial rotor blade row’s wakes. Fig. 9 shows the interaction model. Equation (4) describes the superimposed effect. Notice that the fluctuation parts ( ,g u i ) can be separated and obtained by equations

(2 ) and (3).

, 1 ,i Config steady g u u i

(4)

Fig. 10 shows the time trace of the absolute flow angle in the central position of the axial stator wake field. It can be observed that the absolute flow angle fluctuated peri-odically in time within time T. Four peaks are represented in Fig. 10, which is identical to the passing blade number of the axial rotor within T. The frequency spectrum of the absolute flow angle is shown in Fig. 11. The blade pass-ing frequencies of the axial rotor and harmonics could be found, but the axial rotor blade passing frequency (12 kHz) is dominant and significant. The magnitude of 12 kHz in Fig. 10 is decreased by 12% compared to what is seen in Fig. 6. This is because the ,ud ud i value dis-

appears in Config 2 (Axial Rotor(12)-Axial Stator(18)). In Config 2, the axial stator wake oscillation is driven

collectively by the axial rotor wake and the geometry of the stator trailing edge. Because of the lack of influence from the radial rotor, a periodical fluctuation of entropy in time within T is shown in Fig. 12. The amplitude of

Fig. 9 Illustration of some of the complexities associated with the flow-field at the axial stator exit, 50% span, Config 2 (Axial Rotor(12)-Axial Stator(18), 1/3 of the whole revolution)

Fig. 10 Time trace of the absolute flow angle at the central position of the stator wake, 50% span, Config 2 (Ax-ial Rotor(12)-Axial Stator(18))


Fig. 11 Frequency spectra of the absolute flow angle at the central position of the stator wake, 50% span, Config 2 (Axial Rotor(12)-Axial Stator(18))

Fig. 12 Entropy fluctuation at the stator exit, 50% span, Con-fig 2 (Axial Rotor(12)-Axial Stator(18))

the axial stator wake oscillation reaches up to 3.3% of the pitch range of the axial stator in Config 2, which is far less than what is seen in Config 1. In addition, another obvious distinction is periodicity or non-periodicity within time T by comparing Fig. 5 and Fig. 12.

Model-split subtraction method

Based on the above analysis, the stator wake oscilla-tion was influenced by the blade trailing geometry, the upstream and the downstream moving blade rows. The influences can be distinguished by Fourier transformation, but the individual influence component cannot be sepa-rated by this method. Therefore, the superimposed effect of the periodic wake passing effect and the potential field influence from the downstream rotor cannot be best or-ganized and utilized in the design process. In fact, in a multistage compressor, a detailed understanding of the superimposed effect on the blade wake field, such as separating the individual influence component from all other factors, which would provide insight into the physical mechanism of the superimposition, could help designers to further improve the performance and the life of the blade by organizing and utilizing the unsteady flow.

To solve the problem of separating the individual in-fluence component, a model-split subtraction method is provided in this paper, according to theory of separating configurations. This method is able to separate the influ-ences into two parts. The calculated method was shown in equation (5).

, 1 , 2 , ,i Config i Config d d i ud ud i

(5)

The , ,d i ud i value, included in equation (5), could

be separated by equations (2) and (3) from equation (5). Moreover, the ,g u i value has been obtained in a pre-

vious section. Thus their time traces are shown in Fig. 13. The periodical fluctuation within T time is the most ob-vious feature for the ,g u i value. In contrast, the

, ,d i ud i value fluctuated irregularly in time within T

time. This is due to the ,ud i value, which has an effect on

the waveform of , ,d i ud i . Because the impact of the

parameter ,ud i is far weaker, the amount of the amplitude

variability caused by the parameter ,ud i is substantially

smaller than that of the , ,d i ud i value fluctuation.

The four peaks corresponding to the waveform marked with ,g u i , could be found in the time T, and

there are three peaks for another curve in T. The different relative superimposed phases, such as the typical “posi-tive peak – negative peak” type wave in the range of time from t/T=0.2 to t/T=0.5, the typical “positive peak – positive peak” type wave in range of time from t/T=0.5 to t/T=0.7 and other atypical superimposed phases, could be observed in Fig. 13. Thus, it is why the absolute flow angle fluctuated irregularly with time within T in Fig. 6.

The , ,d i ud i fluctuation amplitude is more than

three times larger than that of ,g u i in Fig. 13. This

indicates that the impact of , ,d i ud i is dominant in

two parts of the influences which drive the stator wake oscillation.

Fig. 13 Time traces of ,g u i and , ,d i ud i , at 50%

span, Config 1 (axial rotor(12)-axial stator(18)-radial rotor(9))

30 J. Therm. Sci., Vol.23, No.1, 2014

If the , ,d i ud i and ,g u i are superimposed with

the same superimposed phases in time T, the absolute flow angle must fluctuate periodically in time and its frequency is equal to that of , ,d i ud i plus ,g u i .

However, the relative superimposed phase can stay about the same only when , ,d i ud i

plus ,g u i

fluctu-

ates in time with the same frequency, which will be fur-ther discussed in the next section.

Axial Rotor(12)-Axial Stator(18)-Radial Rotor(12) Results: Stator wake oscillated driven by all influ-ences with the same frequency

The stator wake oscillates irregularly with time when it is driven by different frequency influences, such as the irregular waveform in Fig. 5 and Fig. 6. According to the logic inference, when the stator wake is influenced by the same frequency factors, periodic waveforms must be obtained. To verify this logical deduction, the radial rotor is scaled to have 12 blades instead of 9 as Config 3 (axial rotor(12)-axial stator(18)-radial rotor(12)). After scaling, the upstream and downstream rotor rows have identical blade numbers (see Fig. 14, 1/3 of the whole revolution). The stator wake is influenced by the axial and radial rotor with the same frequency as they are connected in the same shaft and rotate at the same speed.

Fig. 14 Illustration of some of the complexities associated with the flow-field at the axial stator exit, 50% span, Config 3 (axial rotor(12)-axial stator(18)- radial ro-tor(12), 1/3 of the whole revolution)

The evolution of entropy on the stator outlet at the

mid-span is represented in Fig. 15. This plot shows that the stator wake oscillates periodically in time within time T, with the amplitude reaching up to 7% of the stator pitch. This means that the above logical deduction is true. Moreover, the amplitude of the stator wake oscillation is larger than what is seen in Fig. 12, but smaller than the maximum amplitude in Fig. 5.

The time trace of the absolute flow angle in the stator wake flow-field is shown in Fig. 16. The time is also re-lated to the four axial rotor blades passing period T. In

every T, the absolute flow angle periodically repeats. The fluctuation amplitude of the absolute flow angle in Fig. 15 is higher than that in Fig. 10, but smaller than the maximum fluctuation amplitude in Fig. 6. Thus the am-plitude and the waveform of the absolute flow angle in the stator wake flow field is determined by the superim-posed effect of the incoming wake of the axial rotor, the potential effect of the downstream stator blade rows and other minor influence components. The wake-wake in-teraction phenomena and wake-potential field interaction were already discussed with experiments by Oro[1] and Key[2],respectively. Thus this paper will no longer ana-lyze the phenomenon, but focus on the superimposed effect.

Fig. 15 Entropy fluctuation at the stator exit, 50% span, Con-fig 3 (Axial Rotor(12)-Axial Stator(18)-radial rotor (2))

Fig. 16 Time trace of the absolute flow angle in the stator wake, 50% span, Config 3 (axial rotor(12)-axial sta-tor(18)-radial rotor(12))

The frequency spectrum of the absolute flow angle is

shown in Fig. 17. The highest amplitude occurs at 12 kHz and the higher frequency component, located at 24 kHz, possesses lower amplitude than that of 12 kHz. Therefore, the fluctuation frequency (12 kHz) of the ab-solute flow angle in Fig. 16 is equal to the blade passing frequency (12 kHz). However, the existence of 24 kHz


harmonic means that the two distinct peaks are superim-posed on the wave-like absolute flow angle traces for the passing time of one rotor blade, visible in Fig. 18, which will be introduced in the following section.

Fig. 17 Frequency spectrum of the absolute flow angle at the central position of the stator wake, 50% span, Config 3 (axial rotor(12)-axial stator(18)-radial rotor(12))

By comparing Fig. 6 and Fig. 16, it can be found that

the absolute flow angle fluctuated periodically in time within time T when the influence’s frequencies in the compressor are equal (in Config 3). The waveforms of the time traces of the absolute flow angle are non-periodical within T when it is driven by influences with different frequencies (in Config 1).

For Config 3, which has the axial rotor and the radial rotor in the up- and downstream of the axial stator, the unsteady aerodynamic response on the stator wake can also be quantified by equation (6).

, 3 ,

, ,

i Config steady g u u i

d d i ud ud i

(6)

The downstream influence components, such as

, ,d d i ud ud i , are separated by the model-split

subtraction method, and the resulting equation is as fol-lows:

, 3 , 2 , ,i Config i Config d d i ud ud i (7)

The unsteady fluctuation part component, such as

, ,d i ud i , is separated by equations (2,3) from equa-

tion(7). Fig. 18 shows the time traces of the unsteady fluctua-

tion parts ,g u i and , ,d i ud i . The two distinct

peaks are superimposed on the wave-like absolute flow angle traces for the passing time of one rotor blade. In other words, the four peaks corresponding to ,g u i are

superimposed with the four peaks corresponding to

, ,d i ud i

in T time. This is why the absolute flow

angle fluctuates periodically in time within T time in Fig. 16. It should be noted that the relative superimposed phase is - one of the factors in determining the fluctua-

Fig. 18 Time traces of ,g u i and , ,d i ud i , at 50%

span, Config 3 (axial rotor(12)-axial stator(18)-radial rotor(9)-radial rotor(12))

tion amplitude of the absolute flow angle. Notice that the amplitude and the shape of the unsteady aerodynamic blade force can be changed by clocking[11~13]]. Therefore, a detailed discussion about the clocking influences on the stator wake oscillation will be performed in the next sec-tion.

Clocking modulation method

The time differences of the arrival of the influence from the upstream axial rotor at the stator trailing edge and the potential flow field of the downstream blade rows at the same location of the stator can be modulated by clocking. Therefore, five different clocking positions (CPs) of the rotor in Config 3 (4 axial rotor blades-6 ax-ial stator blades-4 radial impeller blades model, 1/3 of the whole revolution), created by rotating one moving blade row from 0° (CP1) to 6° (CP2)/12° (CP3)/18° (CP4)/24° (CP5) relative to another rotor in the counter rotation direction of the rotor, as shown in Fig. 19, were investi-gated.

Fig. 19 Illustration of the clocking positions, 50% span, Con-fig 3 (axial rotor(12)-axial stator(18)- radial rotor(12)), 1/3 of the whole revolution

32 J. Therm. Sci., Vol.23, No.1, 2014

Fig. 20 shows the root mean square value of the abso-lute flow angle (RMS(α)) for the five clocking positions. The maximum RMS(α) occurs when the moving blade rows are located at clocking position 2 (CP2), while the minimum value could be observed when the rotor is lo-cated at clocking position 5 (CP5). The maximum RMS(α) is approximately twice as large as the minimum value in the five clocking positions. In other words, the largest and smallest amplitudes of the stator oscillation correspond to the rotor clocking position 2 (CP2) and clocking position 5 (CP5), respectively. The maximum deviation of the stator wake oscillation in the five clock-ing positions approaches 50% of the largest amplitude. This indicates that clocking has a great effect on the am-plitude of the absolute flow angle fluctuation and the stator wake oscillation.

Fig. 20 Root mean square value of the absolute flow angle (RMS(α)) for five clocking positions

The time-average axial velocity, at the stator exit, was

represented in Fig. 21 for the five clocking positions. The vertical axis shows the axial velocity, while the horizon-tal axis corresponds to the dimensionless stator pitch (lo-cation marked with a red line in Fig. 4). The most obvi-ous deviation among the five clocking positions can be observed in the low velocity field, which corresponds to the stator wake flow field. The minimum values of veloc-ity for each curve in Fig. 21 are listed in Table 5. The stator wake oscillation with a large amplitude can reduce the velocity deficit of the wake, such as the minimum time-average axial velocity is 112.07 m/s when the mov-ing blade rows were located at clocking position 2 (CP2). In contrast, the velocity deficit of the stator wake is en-hanced and the minimum value reduced to 109.05 m/s when the moving blade rows were located at clocking position 5 (CP5). These phenomena can be explained by a mixture variable between the stator wake and the free stream. As indicated in Fig. 21, the stator wake oscilla-tion can enhance the mixture between the stator wake and the free stream at the stator exit, and an increasing am-plitude of stator wake oscillation leads to more intensive mixing, and as a result, the velocity deficit is weakened to a greater extent.

Fig. 22 and Fig. 23 show the fluctuation of entropy at

the stator exit for the clocking positions 5 and 2, respec-tively. The stator wake oscillation phenomena with dif-ferent amplitudes for the different clocking positions were represented visually with time bars.

Fig. 21 Time-average axial velocity at the stator exit, 50% span, Config 3 (axial rotor(12)-axial stator(18)- ra-dial rotor(12))

Table 5 Minimum time-average axial velocity for the 5 clocking positions

CP CP1 CP2 CP3 CP4 CP5

Vz (m/s) 110.56 112.07 112.06 110.40 109.50

An obvious deviation of the oscillation amplitude can

be found by comparing Fig. 22 and Fig. 23, which means that the stator wake oscillation amplitude can be modu-lated significantly by the clocking. A similar clocking modulation method was investigated by Schennach[14]. In his paper, the secondary flows of the second vane are modified for different clocking positions. Reference [5] shows a 60 percent reduction in the stator unsteady force by clocking the downstream rotor. However, this is the first time, the authors believe, that the clocking modu-lation method (beneficial in the use of flow unsteadiness) is definitively demonstrated to reduce the stator wake oscillation amplitude in a multistage compressor.

The stator wake oscillation variability has been dis-cussed above, but the mechanism, changing the stator wake oscillation amplitudes, is unclear. Therefore the theory of the superimposed effect will be introduced to explain the stator wake oscillation variability.

Superimposed Effect: Relative superimposed phase influence on the stator wake oscillation amplitude

The time traces of the unsteady fluctuation parts, such as ,g ui and , ,d i ud i , are shown in Fig. 24 for CP5.

At first, the two groups of the unsteady fluctuation com-ponents, separated by the model-split subtraction method, are superimposed with a typical “positive peak-negative peak” type wave in Fig. 24. As a result, the fluctuation amplitude must be reduced by this superimposed effect with “positive peak-negative peak” type wave. This


Fig. 22 Fluctuation of entropy on the downstream of stator at 50% span for CP5, Config 3 (axial rotor(12)-axial sta-tor(18)- radial rotor(12))

Fig. 23 Fluctuation of entropy on the downstream of the sta-tor at 50% span for CP2, Config 3 (axial rotor(12)- axial stator(18)- radial rotor(12))

Fig. 24 Time traces of ,g u i and , ,d i ud i for clock-

ing position 5 (CP5), at 50% span, Config 3(axial ro-tor(12)-axial stator(18)-radial rotor(12))

mechanism may explain that the stator wake oscillation amplitude and the root mean square value of the absolute flow angle (RMS(α)) are at the minimum among the five clocking positions when the moving blade rows are lo-cated at clocking position 5.

The superimposed phases have a great effect on the amplitudes of the absolute flow angle fluctuation and the stator wake oscillation. In other words, the time differ-

ences between the arrival of the influence from the up-stream axial rotor at the stator trailing edge and the po-tential flow field of the downstream blade rows at the same location of the considerable stator determine the waveforms of the absolute flow angle fluctuation and the amplitude of the stator wake oscillation.

According to the superimposed phase theory, the typi-cal “positive peak-positive peak” type wave should be found only when the moving blade rows are located at clocking position 2 (CP2). Two individual components that are separated by the model-split subtraction method are shown in Fig. 25. This plot thus provides a further justification for the above theoretical reasoning. It is im-portant to note that the relative phase is not a typical “positive peak-positive peak” type wave when the mov-ing blade rows are located at clocking position 2. This fact, represented in Fig. 25, is in conflict with the logical inference. Only five clocking positions were investigated in this paper; therefore, the limitation of clocking posi-tions is the reason for that lack of a typical “positive peak – positive peak” type wave, which has not occurred in the five clocking positions. However, there are other reasons for why the stator wake oscillation amplitude reaches up to a maximum value when the moving blade rows are located at clocking position 2 (CP2). The fol-lowing work tries to answer this question.

Fig. 25 Time traces of ,g u i and , ,d i ud i for clock-

ing position 2, at 50% span, Config 3 (axial ro-tor(12)-axial stator(18)-radial rotor(12))

The time traces of two sets of the fluctuation compo-

nents separated by the model-split subtraction method are shown in Fig. 26 for the other two clocking positions (i.e., CP3 and CP4). Notice that when the upstream and down-stream moving blade rows are located at clocking posi-tion 3 (CP3), two groups of influence components were superimposed with typical “positive peak – positive peak” type wave. Therefore, this phenomenon excluded the idea that the limited clocking positions caused no typical “positive peak – positive peak” type wave to oc-cur among the five clocking positions. Thus, there must be other factors that interact with the amplitude of the stator wake oscillation or the root mean square of the absolute flow angle (RMS(α)).

34 J. Therm. Sci., Vol.23, No.1, 2014

Fig. 26 Time traces of ,g u i and , ,d i ud i for three

clocking positions (CPs), at 50% span, Config 3 (ax-ial rotor(12)-axial stator(18)-radial rotor(9)-radial rotor(12))

Superimposed Effect: Interaction between up- and downstream rotor influenced on the stator wake os-cillation amplitude

Notice that the fluctuation amplitude of the g

,u i component is constant for the five clocking positions,

but the amplitudes corresponding to , ,d i ud i vary

with the different clocking positions, as seen by compar-ing Fig. 18, Fig. 24, Fig. 25 and Fig. 26. The fluctuation amplitudes of , ,d i ud i were shown for the five

clocking positions in Fig. 27. The fluctuation amplitude, when moving blade rows are located at clocking position 2, is larger than that for clocking position 3. This devia-tion makes up for the lack of a relative superimposed phase when the moving blade rows are located at clock-ing position 2. Therefore, the maximum amplitude of the stator wake oscillation and the root mean square of abso-lute flow angle (RMS(α)) occur when the moving blade rows located at clocking position 2.

An important fact is that the ,ud i value can be modi-

fied by clocking. Thus the ,ud i value is a variable for the

different clocking positions. As a result, the fluctuation amplitudes of , ,d i ud i are changed by clocking. Thus,

the interaction between the moving blades rows is also one of the factors determining the stator wake oscillation amplitudes.

Fig. 27 Fluctuation amplitudes of , ,d i ud i value sepa-

rated by model-split subtraction method for five locking positions

Conclusions

In the present paper, a model-split subtraction method and a clocking modulation method were studied in order to separate and organize the unsteady flow in an axial stator wake field and were verified by numerical simula-tions in an axial-radial combined compressor. Unsteady 3-D Reynolds Averaged Navier-Stokes simulations for the 7 modified configurations and the performance test for the original model were conducted. The steady com-putational prediction was compared with the experimen-tal results to validate the numerical simulation, and they showed good overall agreement.

The waveforms of the absolute flow angle fluctuation and the patterns of the axial stator wake oscillation, within T time, are determined by the frequencies of the influences. The frequency is equal to the blade passing frequency. The absolute flow angle fluctuated periodi-cally in time when the influence’s frequencies are equal (in Config 3). The shapes of the time traces of the abso-lute flow angle are non-periodical within time T, when stator wake is driven by the influences with different frequencies (in Config 1). The axial stator wake oscilla-tion phenomena are also similar.

A new idea, named the model-split subtraction method, was presented in order to separate the influences of the partial factors on the wake oscillation of a stator vane and applied in the axial-radial combined compressor. After employing the equations presented in this study (equa-tions 2, 3, 6, 7, 8 and 9), the two parts of the influences on the axial stator wake oscillation could be clearly separated and quantified by the absolute flow angle fluc-tuation. With the suggested model-split method, the rela-tive superimposed phase of the two parts of the influ-ences can be clearly shown.

A clocking modulation method was presented to modulate the axial stator wake oscillation amplitude through the adjusting of the rotor clocking in Config 3. After analyzing the numerical simulations for the five clocking positions, it was found that the axial stator wake oscillated with different amplitudes for each clocking


position. The physical mechanism of the clocking modu-lation method could be obtained by the model-split sub-traction method. Moreover, the axial stator wake oscilla-tion phenomenon has an effect on enhancing the mixing between the axial stator wake and the free stream. The higher the amplitude that the axial stator wake oscillates at, the more rapidly the wake mixes. As a result, the ve-locity deficit of the axial stator wake can be reduced.

Two reasons were concluded for why the amplitude of the absolute flow angle fluctuation and the stator wake oscillation could be adjusted by clocking. One of the reasons is due to the relative superimposed phase. For instance, the lowest amplitude is obtained when the rotor clocking located at clocking position 5 (CP5), where the influences are superimposed with opposite phases (typi-cal “positive peak-negative peak” type wave).

Another reason for the physical mechanism of clock-ing modulation method is the interaction between the moving blade rows. In other words, the ,ud ud i value

has some influence on the amplitudes of the stator wake oscillation (absolute flow angle fluctuation). Because the

,ud ud i value could be adjusted by clocking, the am-

plitudes corresponding with , ,d i ud i vary with dif-

ferent clocking positions. This is why the stator wake oscillation amplitude is not up to a maximum value in the five clocking positions when the moving blade rows are located at clocking position 3(CP3). CP3 is where the two parts of the influences were superimposed with a typical “positive peak-positive peak” type wave.

Acknowledgments

The authors are grateful for the financial support of National Natural Science Foundation of China (No. 51176013) and the Chinese Specialized Research Fund for the Doctoral Program of Higher Education (No. 20091101110014).

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numerical investigation of the superimposed effects on stator wake oscillation in an axial-radial...

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