J. of Thermal Science Vol.15, No.1

Rotating Stall and Stall-Controlled Performance of a Single Stage Subsonic Axial Compressor Eisuke OUTA Department of Mechanical Engineering, Waseda University, Tokyo, Japan Activities by various authors on aerodynamics and control dynamics of rotating stall in axial compressor are first traced. Then, a process of stall cell evolution in a subsonic stage is discussed based on a 2-D CFD. A few numbers of vortices grow ahead of the rotor accumulating vorticity ejected from lightly stalled blades, and eventually organize a cell of circumferentially aligned huge vortices, which merge and recess repeatedly during the rotation. Such stall disturbance is intensified on trailing side of a circumferential inlet distortion and decays on the leading side. Considering these features, a new algorithm for stall warning is developed based on a correlation between pressure waveforms at each passing of a fixed blade. A remarkable change in the correlation level at near-stall provides a warning signal prior to the stall onset with sufficiently large time margin. This scheme is applied to achieve rotating stall prevention by actuating flaps installed on the hub. The last issue is on characteristics of forward swept blade which has much increased throttle margin with decreased tip loss. A 3-D computation shows that a secondary vortex generated in suction surface mid span interacts to reduce the tip leakage vortex that initiates the stall.

Keywords: rotating stall, stall warning sensing, stall control, forward swept blade, two- and three-dimensional unsteady CFD, stall cell structure, tip leakage flow. CLC number: TK474.8+1 Document code: A Article ID: 1003-2169(2006)01-0001-13

Introduction Technology for extending stable operation range of axial compressor by suppressing rotating stall onset, or by recovering swiftly from rotating stall, is one of the main subjects in improving aeroengine performance. Engines experience severe load increase in their acceleration process, and are often exposed to inlet distortion. Hence, the compressors are more likely to be forced into unstable operations than compressors of industrial gas turbines. Furthermore, the components are arranged forming an extremely compact system with small fluid inertia and plenum element, and the type of flow instability is thought to tend to be rotating stall rather than system surge. The basic non-linear mechanisms of the compressor instability can be traced back to the works of Emmons et al[1], and systematic treatment has a basis of theoretical studies of Greitzer on a dynamic model[2]. For rotating stall model, Takata and Nagano[3] assumed a time lag due to fluid inertia as produced in the stage pressure rise, and determined the stall cell behavior so as to give a balance Received September 30, 2005 Eisuke OUTA: Professor

between circumferential distribution of the pressure rise and the perturbation which may be generated on both sides of the stage. Through precise measurement in a multistage compressor, Day and Cumpsty[4] showed that the pressure rise across the cascade traversing the stall cell do not change stage by stage. It was also found that the cell speed could be predicted by considering a linear sum of the stage pressure rise at the trailing side of the cell, and some essentials of rotating stall in multi-stage machines became clear[5]. Based on such background, Moore[6] determined a condition for stall inception and the cell speed by solving an eigenvalue problem for small perturbation in the axial flow velocity. Moore and Greitzer[7] analyzed post stall surge introducing both of the circumferential and axial modes of disturbance, and the process was confirmed in a test[8]. To improve the stability of the compressor, Epstein, Ffowcs Williams and Greitzer proposed an innovative concept of active feedback control in Ref. [9]. The main idea was that adding of artificial perturbation on the axial velocity fluctuation that appears prior to the stall has an

2

effect of damping the system instability. In the theory, a long-scale wave with a harmonic mode in the compressor circumference was treated as the pre-stall fluctuation. To realize the long wave control, hardware systems activating inlet guide vanes and assessment of control capability were systematically developed at MIT (Paduano et al[10], Haynes et al[11]). In the meantime, stall control by jet injection at the blade leading edge was studied at Cambridge University, in order to suppress the short length-scale perturbation that causes the compressor to fall abruptly into stall (Day[8,12]). A very compact system was developed using autonomic flow regulation valves providing an aero-mechanical feedback control by Gysling and Greitzer[13]. More recently, Suder, et al[14] demonstrated the impact of wall jet injection to the stability enhancement and a mechanism of stall recovery, based on a 3-D CFD verified by experiment for a transonic isolated rotor flow. As for the unsteady structure of the rotating stall flow, various difficulties are encountered in the study because the phenomena extend in both circumferential and spanwise directions in an asynchronous manner to the rotor motion. Larguire[15] suggested a vortical flow pattern of the stall cell based on Laser Doppler velocimetry, and Jackson[16] showed a transient process of the stall growth. Poensgen and Gallus[17] precisely discussed a development process of a part-span stall based on hot-wire anemometry. Computer analyses at the beginning of the author’s study period were limited to discrete vortex methods such as by Nishizawa and Takata[18]. The first activity specifying the deep rotating stall cell as composed of multiple vortices fluctuating with time was made by the author’s group through a 2D. analysis covering half circumference of a rotor and stator stage[19~22]. However, the mechanism of the vortex evolution must be three dimensional interacting with the tip-leakage flow as suggested by Hoying et al[23]. The first study employing three dimensional analysis of an entire blade row was made by Hah et al[24] for an isolated subsonic rotor flow, in which twin vortices were identified ahead of the blade. A very clear computational vortex evolving a short length-scale rotating stall is presented in a skilful experimental study of Inoue, et al, in which the processes of rotating stall evolution is demonstrated on wavelet representation[25,26]. Apart from these fluid mechanics investigations, a reliable technique of stability enhancement must be realized in highly loaded modern compressors. In active controls, the key technology is to sense the stall warning in a real time manner. An algorithm based on FFT processing on pressure fluctuation was applied for surge monitoring in industrial compressors[27]. Tahara et al[28,29]

Journal of Thermal Science, Vol.15, No.1, 2006

have developed a fast correlation algorithm to capture the warning, and applied for a single stage research compressor to avoid a short length-scale stall by inducing artificial hub side stall. Another scheme of stability enhancement that has been proved practically effective is provided by casing treatments such as by circumferential and skewed grooves[30]. In this scheme, the recirculation of flow reduces the compressor efficiency and raises casing temperature. Forward sweep profile of blade is expected to provide a wide throttle margin that meets a recent trend of aeroengine design to increase compressor stage load. While the advantage for transonic operation is already recognized[31], subsonic performance still remains to be assessed. In the present paper, axial compressor behaviors related to rotating stall are discussed based on experiments and unsteady flow analyses on research compressors. The first issue is concerned with an overall behavior of developed rotating stall cell based on a two-dimensional computation. The inception of the rotating stall is usually triggered by tip leakage flow as one of the most critical three dimensional features. Nevertheless, since the developed cell is thought to be constituted with vortices ahead of the rotor, then a two dimensional consideration will give an essential in assessing the stall cell behaviors. The original intent of the analysis is to know how rotating stall can take place without interactions of the tip leakage flow and to know how the stall cell vortex is maintained. The complicated process supported by main flow can be analyzed while the rotor revolves considerable times. In the second place, a new scheme of rotating stall control actuated by a signal of stall warning is introduced. In a test on a low subsonic single stage compressor, the flow disturbance toward the rotating stall induced by an artificially posed inlet distortion can be sensed at previous several tens rotor revolutions prior to the stall, and the signal is applied to actuate a hardware of preventing rotating stall. Despite that the scheme should be still studied for applications to multi stage transonic compressors, the stall sensing algorithm is expected as practically valuable. Finally, pressure-rise performances and the throttle margin of a forward sweep blade are discussed in compared with those of radially stacked blade by a single stage subsonic compressor test and three-dimensional unsteady Navier-Stokes analysis. The throttle margin is considerably expanded because of the reduction in the tip leakage flow loss.

To Which Extent Can Two-Dimensional Analysis Asses Rotating Stall Feature? Experimental compressor and numerical analysis

Rotating Stall and Stall-Controlled Performance of a Single Stage Subsonic Axial Compressor

The rotating stall study has been conducted on a single stage compressor as shown in Fig.1. Although the stage is originally designed for a transonic aeroengine compressor, the test to validate the computation was conducted at 6000 r/min, which is about one-third of the design speed. The rotating stall takes place prior to the system surge. Pitot rake φ i

Rotor

Stator

Domain of 2-D. analysis

Inlet flow 363

180

Compressor- I

Strut

Rotor I-A

Design φ I

0.38

Profile

DCA

Total pressure rise

4 kPa

Number of blade

37

0.35 m

Chord length

41 mm

0.74

Solidity

1.46

Stagger

55 deg

Tip diameter Hub/Tip ratio (rotor)

6000 r/min

Inlet angle

57 deg

Rotor speed

0.33 (tip)

Outlet angle

53 deg

Blade M number

3×105 (tip)

Blade Re number

Fig.1 Specifications of test compressor I and the installed rotor blade I-A

The performance curve is shown in Fig.2 in terms of stage total pressure rise ψ T −T versus inlet flow coefficient φ i measured ahead of the rotor blade, respectively defined as:

ψ T −T ≡ ( p Td − p Ti ) / ρ aVb2,tip and φ i ≡ C xi / Vb,tip (1) where, p Td and p Ti are respectively total pressures averaged at sections downstream of the stator and ahead of rotor. Cxi is averaged axial flow velocity ahead of the rotor. Vb and ρa denote blade tip speed and atmospheric air density. In Fig.2, the pressure-rise measured in stable operation range is indicated by open circles and time averaged pressure-rise during rotating stall operation by filled circles. In this compressor, a two-cell rotating stall is induced at a flow rate below φi =0.3. The dark and broken line traces show computed results of the two dimensional analysis for the rotor and stator system. Cascade geometry at a radial section of 68% span from the hub has been applied for the analysis and the axial extent of the computational domain is shown in Fig.1. The analysis is constituted as follows: Governing equation system: Two-dimensional unsteady compressible Navier-Stokes system, modified through a

Weak stall

0.4 Rotating stall U5

0.3

Unstall flow (throttle close)

R2

0.2 U3

R3

0.1 U2

0 264 mm

3

0.5 Total-to-total pressure rise ψ T-T

Eisuke OUTA

0

To unstall

0.1

0.2

0.3

0.4

Rig test Unstall Stall

0.5

0.6

Inlet flow coefficient φ i

spanwise averaging to incorporate the contraction of the passage. Turbulence model is not applied. Fig.2 Pressure rise characteristic of test compressor I (Rotor blade I-A) , compared with result of the present two-dimensional computation

Solution procedure: Implicit time-marching is processed by applying an Euler backward scheme and a secondorder accurate TVD scheme respectively for the unsteady and convective terms. At each time step, a Newton- Raphson iteration is applied in treating the interaction between rotor flow and stator flow across the sliding boundary. Grid System: The computational grids covers 18 rotor blades and 30 stator vanes with a nearly same pitch ratio as in the compressor. Very dense O-type grids are generated around the blades and vanes, and a H-type grid system covers the flow passage. Boundary conditions: On the inflow boundary, total temperature and total pressure are posed, together with Riemann invariant of one-dimensional characteristic waves to provide a non-reflecting condition. On the outflow boundary, in addition to the Riemann invariant, a throttle resistance with a load coefficient ζ is assumed between the boundary and the outside atmosphere so as to determine the boundary pressure in relation to the through flow rate. Across the sliding boundary separating the rotor and stator region, the latest data on one side are transferred pointwise to the other side, and iterations are processed at each time step. As a whole, flow condition is set continuously by specifying only the rotor blade speed Vb,tip and the load coefficient ζ as in a compressor test. Evolution of developed rotating stall cell and its unsteady structure By closing the throttle posed at the outflow boundary, the computed flow rate decreases and the operation point traces a stationary locus slightly higher than the rig test result. As ζ is increased beyond 2, the operation point moves superposed with a large amplitude fluctuation as shown by the light dark traces. In this weak stall process,

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Journal of Thermal Science, Vol.15, No.1, 2006

STAz82016

STRz82316 STRz82316

Rotor stall vortex VR

VR

Stage stall cell

Stator blockage

STRz82106

Rotor Stator (a) Uncoupled propagation of rotor and stator stall vortices, t /Tbp = 213.1; φi = 0.167, ΨT-T=0.225

(c) Developed rotating stall cell at t /Tbp = 267.1; φi = 0.129, ΨT-T=0.151

A process of forming a developed rotating stall cell through coupling of weak stall blockages in rotor and stator passages. t /Tbp indicates time relative to the blade passing period.

VR4

VR3

VR4

VR21

VR4

extent of the stage is much expanded, and the pressure-rise takes the highest level at a high flow rate. A process to recover a stable clean flow is indicated by broken line trace in Fig.2[22]. Multiple vortices cell reduces to a cell of recessing single vortex, and clean flow passages formed with almost ideal incidence expand to occupy the whole circumference.

VR21

the flow pattern proceeds as shown in Fig.3 to attain a developed rotating stall stage. At the stage of (a), weak stall vortex VR appearing in a rotor passage moves almost attached to the rotor blade. The separate movements of the rotor vortex VR and the distributed stator flow blockage become coupled at the stage of (b). After several times of rotor revolution, a developed stall cell is formed propagating with a speed of roughly half the blade speed as shown in the stage (c), and the operation point traces as the thick dark locus shown in Fig.2. In the present case of two-dimensional flow, such stall vortex and stator blockage are formed due to separation bubbles on the blade suction surface. The developed rotating stall takes place at a much lower flow rate of φ i = 0.2 than the rig test flow rate of φi = 0.3 , since a triggering by the tip leakage flow is absent, and since the flow blockage is assumed to span the entire height of the passage in contrast to the part span blockage in the real flow. The pressure rise also fluctuates with remarkably large amplitude, even though the average is close to the measured rotating stall pressure rise. Despite of these exaggerated appearance, the computed results suggest that the rotating stall cell is composed of vortices and that the configuration changes significantly with time as shown in Fig.4. At the stage of U2, the rotating stall cell is constituted with a leading vortex VR3 and developing vortices VR21 and VR4. Since the extent of unstalled passage is significantly reduced, the stage pressure-rise and the flow rate take the minimum levels as marked in Fig.2. At the stage of U3, VR21 and VR4 grow up and a three vortices composition is formed. After a while, a single vortex cell is formed through a recession of VR3 and merging of VR21 into VR4. The unstalled

VR3

Fig.3

(b) Locked-in-phase propagation of rotor and stator vortices, t /Tbp = 221.1; φi = 0.16, ΨT-T=0.17

U2: φ I = 0.085 ψT-T = 0.057

U3: φ I = 0.096 ψT-T = 0.135

U5: φ I = 0.147 ψT-T = 0.273

Fig.4 Streamline and vorticity contours indicating typical change of rotating cell structure composed of huge vortices during the propagation

In Fig.5, force and moment are indicated for each of the blades momentarily located inside the rotating stall cell region. Blades 6 and 7 are passing through unstall flow region in the leading side of the cell. Blade 4 entering the cell receives an extremely high level force and a clockwise moment, while blade 1 receives a counter clockwise high moment. In leaving the cell region, a high

Rotating Stall and Stall-Controlled Performance of a Single Stage Subsonic Axial Compressor

negative force is applied as indicated for blades 12 and 13. The amplitude of such force fluctuation is computed as more than five times the fluctuation amplitude in the design flow range. This complicated feature of aerodynamic unsteady load is caused by a remarkable change of flow incidence inside of the cell and by a presence of retarded high pressure passage where vortex driven incident flow merges with stator back flow. A significantly high level force is also applied to the stator vane located at the trailing side of the cell. High pressure passage

Jet on T.E.

Blade leaving

High incidence Blade entering

LP Leading side: L.S.

5

T.S.

0-1 0-2 3 blade -pitches

Recession of vortex Merging of vortex L.S. Growth of vortex 1

Cell-1

Cell-2

Cell-2

Cell-1

0 0-1

1 0 T.S.

0

LP

Trailing side: T.S.

Cell-1

Tangential velocity Cθ / Vb

Eisuke OUTA

20

0-2

L.S.

80 40 60 100 Dimensionless time t / tbp

120

140

Fig.6 Tangential velocity traces measured ahead of the rotor. The change of local peak indicates the modification of vortex system Table 1 Summary of rotatig stall cell configurations Vortex configuration

Fig.5 Force and moment loaded to blades located inside a deep rotating stall cell

Experimental features of rotating stall cell Temporal change of recession, grow of vortex and merging of vortices are also observed in compressor test. Typical time traces of tangential flow velocity Cθ measured at location 0-1 and 0-2 ahead of the rotor are shown in Fig.6. In this case two-cell rotating stall takes place, and Cθ increases by passing of the cell from the unstall level to blade speed level superposed with irregular multiple peaks. The respective peaks indicate the vortices constituting the cell, and the changes during the movement are shown by arrows. In general, the leader vortex at the trailing side T.S. recesses, and the vortex at the leading side L.S. grows and merges into the preceding vortex. Typical configurations of the cell are summarized in Table 1. Double vortices and triple vortices appear most frequently, and sometimes the cell is formed by a single vortex. The cell speed is slightly altered by the number of vortices and the single vortex cell takes the highest speed. Quite similarly, the computed cell speed changes with the cell configuration. Suggestive model of rotating stall cell structure By taking into account the computed features and flow velocity profiles measured by traversing the hotfilm probes in spanwise direction, it is suggested that the

Single

Double

Triple

Multipl

15 %

40~50 %

30~50 %

~5 %

Cell speed / Vb 55~70 % 53~58 % - measured

50~57 %

50 %

Ct trace - hot film Appearance frequency

Cell speed / Vb - computed

65 %

56 %

54 %

rotating stall cell in developed stage takes such configurations as schematically shown in Figs.7 and 8. The cell is essentially composed of a rotor-driven vortex VR and counter vortex VS as indicated in Fig.7. This twin system induces light separation vortices in the follower blade passages. Due to a significant reverse flow driven by VS, the separation vortices is ejected upstream, and the leader vortex VR maintains the strength by accumulating the ejected vorticity. Such developed vortex forces the high incidence flow to turn with low incidence, and almost an ideal blade flow is recovered in blade passages approaching the cell region. In the real compressor flow, strength of the rotating stall cell weakens towards the hub side, and the span-wise configuration will take a configuration as shown in Fig.8 for a triple vortices cell. It should be noted that the most part of the hub side flow still keeps high axial flow velocity, so that the stage flow rate of rotating stall is

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Journal of Thermal Science, Vol.15, No.1, 2006

considerably higher than the flow rate of 2-D analysis. Interaction between the stall vortex and tip leakage flow is the most serious problem to be discussed. High incidence flow

~ qv VR

Rotor

Vs

Stator

Ejection of vorticity Reduced incidence

-Vb

Low pressure

High pressure

Fig.7 Schematic of computed two-dimensional stall cell structure in a frame relative to the blade motion

Accumulation of vorticity

Reverse and high tangential flow

Ejection of vorticity

Leading side

High axial flow

(2-3) blade-pitches

Trailing side

Rotor revolution

Fig.8 Three-dimensional aspect of developed rotating stall cell aligned ahead of rotor[20,21]

In Which Way is a Stall Warning Signal Processed in a System of Rotating Stall Control? Sensing of rotating stall warning and fast processing for warning index In either case that the rotating stall is triggered by a tip leakage vortex or by blade stall vortex, disturbances growing to the rotating stall will first appear at the leading edge of a certain rotor blade. To know in what timing in advance of the rotating stall onset a warning signal is assured, a preliminary test has been conducted on a small scale compressor II, see Fig.12, in a single stage set up to avoid a confusion arising by stage interactions. By mounting pressure transducers on the casing wall at various locations along the blade chord as shown in the top picture in Fig.9, chord-wise distribution of blade passing pressure waveform is obtained. The waveforms measured at a leading edge location F:LE are shown overlaid for several times of passing of an arbitrary fixed blade. It is seen that each passing wave form almost coincides at the design point operation, while that a

significant deviation between the waveforms becomes remarkable as the near stall condition is approached. Then a correlation between waveforms of the current passing and the previous passing is processed by introducing the following coefficient R[29]: R=

∫ [ P(t ) − Pavn ][ P(t − τ ) − Pavn−1 ]dt ∫ ( P(t ) − Pavn ) 2 dt ∫ ( P(t − τ ) − Pavn−1 ) 2 dt

(2)

where, τ is the time period of one rotor revolution, Pavn and Pavn−1 denote averaged pressure respectively over one blade pitch at the current and the previous revolutions, and the integration is taken for waveform of one blade pitch. At a stable operation where deviation in pressure waveform is absent, the coefficient is unity; i.e. R = 1. In the extreme case of rotating stall range, there is no correlation between the waveforms; i.e. R = 0. Signal processing algorithm introduced here has various advantages in application to a real time control of rotating stall: e.g. (1) computation is simple and fast, (2) the system is robust against geometrical differences among the blades, and (3) signal noise affects on the fail-safe side from a viewpoint of stall preventing system. The time trace shown in Fig.9 indicates the correlation coefficient processed for each of the sensor outputs that is growing as the compressor operation point approaches a rotating stall limit. The rotating stall onset, taken as the time origin, is marked by almost discontinuous increase in the level of (1-R). At sensor position D of the blade upstream, no indication is found until the near stall is reached. In contrary, the correlation coefficients at positions I and J show significant changes at about previous three- to two-hundred revolutions prior to the rotating stall. However, the blade receives at such positions various disturbances caused by tip leakage flow and flow separation on the suction surface. These disturbances could not be taken as a stall warning. The position F:LE has been selected as the most appropriate among them, since the most critical flow reversal of the rotating stall onset first takes place around the leading edge. By setting a threshold level, the rotating stall will be predicted with a margin of more than fifty times rotor revolution. In the presence of an inlet distortion, the breakdown of the correlation appears in different manner in respect of the circumferential location as shown in Fig.10. At location B, where the blade has left the distorted zone, the correlation has broken down insignificantly long time before the rotating stall. At location E, where the blade is approaching the distorted zone, the rotating stall takes place about fifty times rotor revolution after the correlation break down is detected. Such feature is due to

EisukeOUTA

Rotating Stall and Stall-Controlled Performance of a Single Stage Subsonic Axial Compressor

D F: LE

Wall pressure at F:LE

I

Design point

J

0.2

Sensor: spacing 4 mm

0 0.2

R.-Stall Near stall

0 0.4

0 0.4 Sensor F:LE

0.2

1-R

Sensor D

Stall detection

0 0.4 Sensor I

0.2

0.2

Distortion plate F

Location F

A

E

B D

C

Location A

Location B

0 0.4 0.2

Location C

0 0.4 0.2

Location D

0 0.4

0 0.4 Sensor J

0.2 0

Correlation coefficient

Correlation coefficient

1-R

0.4 0.2

R-Stall

0.4

0.4

Design point

Throttling under inlet distortion

7

0.2

Location E

0 -800

-600 -400 -200 0 Non-dimensional time prior to stall t / Trev

Fig.9 Measurement of blade passing disturbance leading to rotating stall. The process is expressed by time change of correlation coefficient

that the blade is passing through a high incidence flow in leaving the distorted zone and through a negative incidence flow in approaching the distorted zone[22]. Inside the distortion wake, the breakdown takes place immediately before the rotating stall onset. Thus, the stall warning sensing responding to the inlet distortion must be done by collecting correlation signals at all locations around the compressor circumference. Preliminary experiment of stall preventing scheme of a hub-flap operation It is thought that a rapid increase of pressure loss in a particular region of blade passage versus a decrease in the flow rate leads to a system instability. Then, if the loss concentrated in such a region as usually a tip region is shared by a blade region of low loss generation, e.g. hub-side region, the instability may be prevented to a lower flow rate than the flow rate in original loss distribution. Based on such a simple concept, a scheme of active control of the rotating stall has been presented by the research group in which the author is involved[28].

-600 -400 -200 0 Non-dimensional time prior to stall t / Trev Fig.10 Growing blade passing disturbance toward rotating stall at various circumferential position in presence of inlet distortion

As shown schematically in Fig.11, wall pressure data measured at the blade leading edge section is transferred to a high speed DSP unit, and the stall warning signal is processed as described in the previous section. Responding to this signal, a controller actuates flaps installed around the hub circumference so as to partially close the compressor inlet passage. The wake of the flap covers the lower part of the blade span, and the loss is much increased there. Meanwhile, the upper part toward the tip recovers a high flow rate with a decrease of pressure loss. By such an arrangement of loss distribution, the rotating stall onset may be prevented, and the stall flow rate is shifted to a lower value. Response of the flap motion to an imposed inlet distortion is shown in the figure. By sensing the stall warning signal at t/Trev ≈50, the flap moves to an angle of 15 deg. with a response time of about 50 times the rotor revolution. When the disturbance is removed, the stall warning level becomes very low and the flap gradually moves to open the passage. This operation data is obtained by a test using a small scale compressor II set as

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Journal of Thermal Science, Vol.15, No.1, 2006

Stall signal Flap controller

DSP unit

Actuator

Pressure

Air flow

Stall detection

Toward unstall at R

Distortionremoved

R

1 0.5

Correlation Closing

Flap angle: 0 deg

Flap

Opening 15 deg

0 deg

Rotor

0

20

40

60 80 100 400 600 800 Dimensionless time t / Trev

1000

Fig.11 Scheme of rotating stall control by hub-flap and response of hub-flap motion to breakdown of correlation due to an imposed inlet distortion

Compressor- II Flow rate 0.37 kg/s 1.5 kPa Pressure rise 0.13 m Tip diameter 0.62 Hub/Tip ratio 12000 Rotor speed r/min Parallel passage

Rotor Profile Blade number Chord length Solidity Stagger Inlet angle Outlet angle

NACA65 12 30 mm 1.76 29.2 deg 63.9 deg 44.5 deg

Fig.12 Test compressor used for rotating stall control by hub-flap actuation

Pressure-rise coefficient ΨT-T ( Total to Total )

0.4 Opening of flap

0.35

D : impose distortion

R : stable operation with closed flap

Flap: open

0.3 Flap: 15 deg.

0.25

On What Reason is the Throttle Margin Expanded by Blade Profile of Forward Sweep?

S : operation with (flap+plate) R- stall without control

0.2 0.1

0.15

0.2

0.25

0.3

Flow coefficient φ i Fig.13 Compressor performance controlled by hubflap device responding to an inlet distortion

a single stage configuration, see Fig.12. The locus of the pressure-rise versus the flow rate recovering from the rotating stall is presented in Fig.13. The performance in a normal condition indicated by a thick black curve is stable until φ i ≈0.22, while in an operation with a flap angle set at 15 deg., the stall takes place at a flow rate lower than φ i ≈0.21 as indicated by a gray curve. The present scheme of rotating stall control works in the compressor test as follows: (1) At point D, a distortion plate is installed at the compressor inlet. (2) The operation point once moves to the point S, where a light stall is temporarily in presence disturbed by the distortion plate. However, the flow rate is considerably higher than the flow rate of rotating stall operation. (3) By removing the distortion, a stable point R is reached on the performance curve with the flap angle of 15 deg. (4) Then, the flap opens the passage and the compressor recovers the original performance at D. Such intriguing result of the rotating stall control is probably the first trial as far as the author knows. However, further study must be required in applying to the multistage compressor. There arises a question: Can the hub-flap located at the inlet affect the last stage when the last stage is reaching rotating stall?

0.35

Gain of throttle margin by a forward swept profile of rotor blade The forward swept rotor blade I-SWEPT installed in the test compressor-I is shown in Fig.14. The sweep profile is conventionally generated by shifting the stacking line of a non-swept blade I-RADIAL in the

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Rotating Stall and Stall-Controlled Performance of a Single Stage Subsonic Axial Compressor

Swept blade

ε≡

Radial blade 0.5 %chd 1.6 %chd 2.2 %chd

0.5 %chd 1.6 %chd 2.2 %chd

(Tip clearance) (Blade chord)

9

0.2

Rotor: I-Radial

Rotor

I-Swept

I-Radial

Sweep angle (tip)

30 deg

0 deg

Design φ I Rotor speed Profile Number of blades Chord length Solidity Stagger Inlet angle Outlet angle Aspect ratio Tip clearance

Total-to-static pressure rise ψ T-S

Rotor: I-Swept

0.45 6000 1/m DCA 33 50.2 mm 1.47 60.4 deg 67.9deg 52.9 deg 0.93 0.25-1.1 mm

Design point

0.15

0.1 Rotating stall

0.05

0 0.1

0.2

0.3

0.4

0.5

0.6

Inlet flow coefficient φ i = C xi / V b,tip

Fig.14 Specification and pressure-rise performances of swept and radial blade rotors

chord-wise direction. The sweep angle takes 30 deg. at the blade tip. The profiles of the respective blades at spanwise sections are identical, and the profile data at the blade tip are listed in the figure. The pressure-rise (total-to-total) is by 40% higher than the pressure-rise of Rotor I-A shown in Fig.1. The pressure-rise ψ T − S is compared in Fig.14 for various tip clearance ε ranging between 0.5% and 2.2%; where:

ψ T − S ≡ ( p sbr − p Ti ) / ρ aVb2,tip psbr is averaged static pressure behind the rotor.

blade rotor. (5) With a wider stall margin, the swept blade provides slightly higher pressure-rise performance than the radial blade. By introducing a throttle margin TM, a performance gain of the swept blade for the rotating stall is compared: ⎛k ⎞ φ TM ≡ ⎜⎜ DP − 1⎟⎟ × 100, k = i k ⎝ SP ⎠ ψ'

(3)

Particular features in respect to the rotating stall onset provided by sweeping the blade are summarized as: (1) Rotating stall flow rate is much reduced for the swept blade, in compared with the flow rate for the radial blade. (2) Stable operation is possible by the forward swept blade even in a range of flow rate of positive pressurerise gradient. The radial blade flow comes into the rotating stall while the pressure-rise gradient is negative. (3) If a criteria presented by Camp and Day[32] is applied to such distinctive features, a modal stall inception arises in case of the swept blade rotor, and a spike stall inception in case of the radial blade rotor. (4) However, at a wide tip clearance of ε = 2.2%, the swept blade rotor falls into rotating stall before the pressure-rise reaches the peak level. This suggests that the flow pattern becomes similar to that of the radial

ψ' =

(γ −1) / γ ⎤ C p Ti ⎡⎛ ΔPS − S ⎞ ⎢⎜⎜ ⎟ + − 1⎥ 1 ⎟ 2 1 / 2Vb ⎢⎝ Pi ⎥ ⎠ ⎣ ⎦

(4)

where, kDP and kSP denote flow coefficients of throttle at the design point DS and the stall point SP. ψ’ expresses coefficient for isentropic static pressure rise ΔPS-S, where Cp, Ti and γ denote specific heat at constant pressure, inlet temperature and ratio of specific heats. The throttle margin data for the blade I-Swept and I-Radial are compared in Fig.15. The margin of I-Swept is by 20% higher than the value of I-Radial at a moderate tip clearance of ε = 1.6% , and by 15% at the extremely narrow clearance of ε = 0.5% . A weak hysteretic delay appears in the flow rate of recovering the stable performance, as indicated by the plots of “to unstall”. This delay disappears at ε = 1.6% in case of I-Radial, suggesting that the rotating stall is weaker than the rotating stall of I-Swept in this range of low tip clearance. In the figure, the throttle margin obtained by

10

Journal of Thermal Science, Vol.15, No.1, 2006

GE Aircraft Engines[33] is shown. The design flow rate and sweep angle are close to those of I-Swept and I-Radial. It is worth notice that the respective swept blades shows almost same level of the throttle margin. Among them, the GE-conf.2 is the best profile in view of the tip-clearance sensitivity. 80

Throttle margin TM %

I-Swept

to stall to unstall

60

GE- conf.2 -swept -radial

40 to stall

GE-conf.1

I-Radial

20

-swept

to unstall

-radial

0

0

0.5

1 1.5 2 Tip clearance / Chord

2.5

3

ε%

Fig.15 Throttle margin of various blade configurations

Spanwise loss distributions of forward swept and non-swept radial blades Characteristic flow patterns of the swept blade and radial blade are described in terms of span-wise distribution of total-pressure loss shown in Fig.16. The loss coefficient ω is computed based on total pressure distributions measured in both sides of the rotor blade by the expression of: ri + 5% flowrate

rbr + 5% flowrate

− P Tbr ,rel P Ti ,rel ri rbr ω≡ ri + 5% flowrate ri + 5% flowrate − P Si P Ti ,rel ri ri

φ I = 0.45 (DP) ε = 0.5%

0.33 0.5%

0.33 (nS) 2.2%

0.29 0.5%

(5)

where, the passages ahead “i “ and behind “ br “of the blade are divided with an interval of 5% of the through flow rate, and averaged total pressure PTi ,rel and PTbr ,rel are calculated in relative frame of the blade motion, as well as the static pressure PSi ahead of the blade. Span-wise location ri and rbr indicate the bounds of the integration. As the flow rate decreases, the loss increases in the upper part of the blade span, and the rotating stall takes place at a flow rate slightly lower than φi = 0.25 in case of the swept blade with ε = 0.5% and φi = 0.30 in case of the radial blade. With a tip clearance of ε = 2.2%, these limits increase respectively to 0.33 and 0.36. In the radial blade flow, the loss due to the tip leakage flow constitute the major part of the loss causing the rotating stall, while in the swept blade the tip leakage flow loss is not significant in compared with the loss produced in the mid span indicated by shaded zone. In other words, the loss concentrated in the tip region is shared by the mid span region as similarly as stated in the concept of the hub-flap stall control. Further interesting feature is that in case of wide tip clearance of ε = 2.2% the loss in the swept blade takes a similar profile of distribution as in the radial blade. As the computed loss agrees well with the measured, the three-dimensional flow computation will reveal the related flow structure. Three-dimensional computation of flow structures leading to rotating stall Time dependent compressible three dimensional Navier-Stokes equation system with a turbulence closure of Spalart-Allmaras one equation model[34] is analyzed for the isolated rotor flow in an explicit time marching mode. The solution is advanced applying a three stage Runge-Kutta scheme combined with a residual smoothing algorithm of Jameson, and the convection terms are

φ I = 0.45 (DP) ε = 0.5%

0.25 (nS) 0.5%

20 40 60

R.-stall I-Swept

80 100 -0.1

0.36 (nS) 2.2%

0.30 (nS) 0.5%

0 %-span from tip

%-span from tip

0

0.35 0.5%

0

0.1 0.2 0.3 Loss coefficient

ω

0.4

0.5

20 R.-stall

40 60

I-Radial

80 100 -0.1

0

0.1 0.2 0.3 Loss coefficient

ω

0.4

Fig.16 Span-wise distribution of total-pressure loss at various operation flow rate between the design point DP and the near stall point nS. Thick curves are obtained by N.S. computation

0.5

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Rotating Stall and Stall-Controlled Performance of a Single Stage Subsonic Axial Compressor

Reversed tip leakage flow

I-Swept

11

I-Radial

Trailing edge

Low flow from hub

Fig.17 Flow configurations produced by I-Swept and I-Radial at design flow rate: φ i = 0.45 (ζ =1), ε = 0.7%. Streamlines: incident flow (Black), low energy flow from hub (Red), and tip leakage flow (Yellow/ Green)

I-Swept

Thin tip leakage

Reversed leakage flow extends to the follower blade

I-Radial

Trailing edge Secondary vortex separated from pressure surface

Moderate flow separation

(a) Stable flow with ε = 0.7%, φ i = 0.35 (ζ =2) I-Swept

Induced lateral vortex

Tip leakage vortex

(Single passage analysis)

I-Radial Broken down tip vortex

(3-passages analysis)

(b) Near stall flow with ε = 2.2%, φ i ≈ 0.35 (ζ =2) Fig.18 Stable and near-stall flow configurations of I-Swept and I-Radial with narrow and wide tip clearances. Streamlines are indicated for incident flow (Black), low energy flow from hub (Red), and tip leakage flow (mixed)

expressed by a third order accurate TVD scheme of Chakravathy-Osher. The boundary conditions at the compressor inlet and exit are similar to the conditions applied for the two-dimensional cascade flow analysis presented in the previous chapter, except that a conventional turbulent boundary layer profiles are posed on the casing and hub walls at the inlet section. The finest mesh size are selected so as to take a y+ value

less than 0.5 on the blade surface surrounded by an O-type grid and less than 2 on the casing and hub walls of the compressor passage filled with a H-type grid. The highest turbulence eddy viscosity is restricted to less than 500 times the molecular viscosity. At the present stage, the computation has been conducted for an isolate blade and three blades system. The computed velocity distributions agree well with

12

data measured by a three-hole yaw probe, as indicated by the total pressure loss curve. Computed flow fields of I-Swept and I-Radial at the design condition are compared in Fig.17. Any significant difference between the two flow features is not recognized at this stage, and the respective tip leakage flow and hub side loss flow appear very similarly. However, as the flow rate decreases to φ i = 0.35, see Fig.18, a secondary vortex appears in the trailing edge side of I-Swept and causes the totalpressure loss in the mid span region. As a particular feature of the forward sweep profile, an adverse pressure gradient exists in the trailing edge side, by which an upward low energy flow along the suction surface is retarded inducing the vortex. In the radial profile without such adverse pressure gradient, the upward flow is mixed with the tip leakage flow. Then, the tip leakage flow becomes of high loss, and the reversed flow reaches the follower blade. In case of a wide tip clearance of ε = 2.2% , the blade flow of I-Radial almost reaches rotating stall flow. The counter-clockwise tip leakage vortex breaks down and disturbs the tip leading edge of the follower blade. Furthermore, a clockwise lateral vortex rolling up with the stream from the hub is induced spanning over the passage. The total pressure loss is rather concentrated in the high span region. In the flow of I-Swept, the tip leakage vortex is still swept back and attaches the follower blade in the mid chord. Rotating stall is not seen liable to onset. The mid span vortex is much reduced so that the loss increases almost linearly towards the tip region.

Journal of Thermal Science, Vol.15, No.1, 2006

the rear part will be integrated to realize a compact aeroengine compressor of high stage load with wide throttle range in the near future. The most part of the activities presented here the author owes to Prof. Ohta, Y. of Waseda University, Dr. Kato, D. of Ishikawa-Harima Heavy Industries, and Mr. Tahara, N. of Ishikawa-Harima Heavy Industries. The author wishes to express his sincere thanks for their creative discussions and valuable suggestions in the research collaboration.

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Concluding Remarks [7]

Research activities by various authors concerning the compressor rotating stall have been shortly traced in such aspect of non-linear fluid mechanics, concepts of active stall control, experimental and computational flow structures, sensing of stall warning and geometry of expanding the throttle margin. The framework of dealing with rotating stall has been supplemented by short summaries of study results by the author’s research group. The two-dimensional feature of the rotating stall cell will contribute in imaging a fundamental aspect of the non-linear process, and the sensing algorithm of stall warning will be utilized in realizing active stall control. A simple concept to expand the throttle margin by reducing the loss concentration in the tip region is almost proved by means of a controlled artificial stall on hub side and by sweeping forward the blade profile. Other than these subsonic flow researches, transonic compressor researches have been conducted by various researchers through computations and rig tests. The author wishes that activities of transonic flow for the front part of the compressor stages and subsonic flow for

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Passage Flow Structures in Axial Compressor Rotating Stall Inception. J. of Turbomachinery, Trans. ASME, 1999, 121: 735―742 Hah, C, Schulze, R, Wagner, S, et al. Numerical and Experimental Study for Short Wavelength Stall Inception in a Low Speed Axial Compressor. In: Proc. of 14th ISABE, Florence, Italy, ISABE Paper No. 99-7033, 1999 Inoue, M, Kuromaru, M, Tanino, T, et al. Comparative Studies on Short and Long Length-Scale Stall Cell Propagating in an Axial Compressor Rotor. J. of Turbomachinery, Trans. ASME, 2001, 123: 24―32 Inoue, M, Kuromaru, M, Yoshida,.S, et al. Short and Long Length-Scale Disturbances Leading to Rotating Stall in an Axial Compressor Stage with Different Stator/Rotor Gaps. J. of Turbomachinery, Trans.ASME, 2002, 124: 376―384 Hoenen, H, Arnold, T. Development of a Surge Prediction System for Multi Stage Axial Compressors. In: Proc. of the International Gas Turbine Congress 2003 Tokyo, Paper No. IGTC2003Tokyo TS-040, 2003. 1―6 Tahara, N, Kurosaki, M, Ohta,Y, et al. Active Stall Control in Axial Flow Compressor Using Artificial Hub Stall. AIAA Paper 97-2656, 1997 Tahara, N, Kurosaki, M, Ohta,Y, et al. Early Stall Warning Technique for Axial Flow Compressors. In: Proceedings of ASME Turbo Expo 2004, Wien, Austria, Paper GT2004-53292, 2004 Takata, H, Tsukuda, Y. Stall Margin Improvement by Casing Treatment – Its Mechanism and Effectiveness. J. of Engineering for Power, Trans. ASME, 1977. 121―133 Hah, C, Wennerstrom, A J. Three-Dimensional Flowfields Inside a Transonic Compressor with Swept Blades. J. of Turbomachinery, Trans. ASME, 1991, 113: 241―251 Camp, T R, Day, I J. A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor. J. of Turbomachinery, Tran. ASME, 1998, 120: 393―401 Scott McNulty, Decker, J J, Beacher, B F, et al. The Impact of Forward Swept Rotors on Tip Clearance Flows in Subsonic Axial Compressors. J. of Turbomachinery, Trans. ASME, 2004, 126: 445―454 Spalart, P R, Allmaras, S R. A One-Equation Turbulence Model for Aerodynamics Flow. AIAA paper 92-0439, 1992