Influence of coupled boundary layer suction and ...

CJA 756 24 December 2016 Chinese Journal of Aeronautics, (2016), xxx(xx): xxx–xxx

No. of Pages 16

1

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics [email protected] www.sciencedirect.com

5

Influence of coupled boundary layer suction and bowed blade on flow field and performance of a diffusion cascade

6

Cao Zhiyuan a,*, Liu Bo b, Zhang Ting c, Yang Xiqiong b, Chen Pingping b

3

4

7 8 9

10

a

College of Engineering, Peking University, Beijing 100871, China School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China c AECC Xi’an Aero-engine Controls Co., LTD, Xi’an 710077, China b

Received 10 December 2015; revised 9 May 2016; accepted 19 October 2016

11

13 14

KEYWORDS

15

Axial compressor; Boundary layer suction; Bowed blade; Corner separation; Coupled method; Passage vortex

16 17 18 19 20

21

Abstract Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance of a highly loaded diffusion cascade with less suction slot. The effectiveness of the coupled method under different inlet boundary layers is also investigated. Results show that mid-span local boundary layer suction can effectively remove trailing edge separation, but deteriorate the flow fields near the endwall. The positive bowed cascade is beneficial for reducing open corner separation, but is detrimental to mid-span flow fields. The coupled method can further improve the performance and flow field of the cascade. The mid-span trailing edge separation and open corner separation are eliminated. Compared with linear cascade with suction, the coupled method reduces overall loss of the cascade by 31.4% at most. The mid-span loss of the cascade decreases as the suction coefficient increases, but increases as bow angle increases. The endwall loss increases as the suction coefficient increases. By contrast, the endwall loss decreases significantly as the bow angle increases. The endwall loss of coupled controlled cascade is higher than that of bowed cascade with the same bow angle because of the spanwise inverse ‘‘C” shaped static pressure distribution. Under different inlet boundary layer conditions, the coupled method can also improve the cascade effectively. Ó 2016 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

* Corresponding author. E-mail address: [email protected] (Z. Cao). Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

1. Introduction

22

Boundary layer suction, or aspiration, was first introduced by Kerrebrock et al. in 1997 with the purpose of increasing aerodynamic loading and avoiding severe flow separation of axial flow compressors in the meanwhile.1–3

23

http://dx.doi.org/10.1016/j.cja.2016.12.023 1000-9361 Ó 2016 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Cao Z et al. Influence of coupled boundary layer suction and bowed blade on flow field and performance of a diffusion cascade, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.023

24 25 26

CJA 756 24 December 2016

No. of Pages 16

2 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88

A transonic aspirated compressor stage and an aspirated fan stage are designed and experimentally investigated to validate the application of boundary layer suction in axial flow compressor.4,5 The transonic aspirated compressor stage has a design tip speed of 457 m/s, and it achieved a maximum pressure ratio of 1.58 and efficiency of 90% under the design conditions. The design tip speed of the fan stage is 229 m/s, and it achieved a total pressure ratio of more than 3.0 at the design rotation speed in the experiment. Gbadebo et al. first investigated the nature of three-dimensional (3D) separations in axial compressors.6,7 Then, with the application of boundary layer suction, he eliminated the typical compressor stator hub corner 3D separation.8 Chen et al.9 performed active control of corner separation in a linear cascade by boundary layer suction, and investigated the influence of the location of the endwall suction slot. Wang, Chen, Song et al.10–13 also investigated the application of boundary layer suction in compressors. In their investigations on the control of corner separation, the optimum slot is the endwall slot, which is sufficiently long to remove the limiting streamline. However, the suction slot on the blade surface cannot effectively eliminate the corner separation. In a highly loaded compressor, the suction surface boundary layer suction and endwall suction are combined to eliminate trailing edge separation and corner separation.5 However, suction slots on the suction surface and endwall lead to the complexity of the suction system. Investigation on the possibility to control the corner separation and trailing edge separation by a single suction slot is rarely seen in published literatures. In the 1960s, Deich et al. adopted 3D blade to reduce the loss of turbines.14 In the 1980s, Wang Zhongqi et al. reported that it was the spanwise redistribution of static pressure that reduced the loss of cascade.15 Breugelmans16 and Shang et al.17 investigated the leaned and bowed cascade in a wind tunnel. The results showed that the corner separation was eliminated by bowed blade, but the loss of mid-span increased as low momentum fluid migrated to the region. The increment of mid-span loss may exceed the decrement of endwall loss. Thus, the overall loss of cascade may be more than that of the linear cascade. Bogod18 investigated five different bowed stators in a multi-stage compressor. In his investigation, positive bowed stators could increase stage efficiency by 1.0–1.5%, whereas negative bowed stators could increase stage efficiency by 2.0– 3.0% at most. Positive bowed stator overloads the mid-span and improves the near endwall flow field. Fischer et al.19 investigated the influence of strongly bowed stator on the performance of a four-stage axial flow compressor. The efficiency and total pressure ratio between design and blocking conditions decreased as the increased surface area increased the fraction loss. The efficiency and total pressure ratio between maximum total pressure ratio and stall conditions increased as the corner separation was eliminated. As the bowed blade can effectively improve the endwall flow field and control the corner separation, bowed cascade is appropriate for coupling with mid-span boundary layer suction to control the trailing edge separation and corner separation. In this study, a highly loaded compressor cascade, which has both corner separation and trailing edge separation, is investigated. First, mid-span local boundary layer suction and bowed blade are adopted in the cascade separately, and four different bow angles are investigated. Then, coupled

Z. Cao et al. mid-span local boundary layer suction and bowed blade is adopted to further improve the performance of the cascade. Moreover, the length effect of the suction slot is also investigated. Corner separation and trailing edge separation are effectively controlled by the coupling method with a single suction slot.

89

2. Diffusion cascade description and experimental procedure

95

A highly loaded compressor linear cascade is investigated in the study. The details of the cascade are given in Table 1. Design inlet Mach number is 0.6, and design incidence angle is 0.5°. Airfoil of the cascade is shown in Fig. 1. The baseline linear cascade was experimentally investigated in a high subsonic cascade wind tunnel at inlet Mach number of 0.6, incidence angle of 0.5° and 5.0°, and Reynolds number (Re) of 8.02 105 under the design conditions based on the chord. Fig. 2 shows the test region of the linear cascade wind tunnel. This study assessed blade surface static pressure coefficient (Cp) of baseline linear cascade. Blade surface static pressure was measured from static pressure holes, located at the midspan of the suction surface and pressure surface.

96

3. Computational method and validations

109

3.1. Computational method

110

The 3D numerical simulation is performed on a single cascade passage with the assumption of periodicity. The structure grid is created by AUTOGRID in NUMECA FINE/TURBO. The ‘‘O-type” mesh is created around the blade to achieve a high quality. The total grid number of the baseline linear cascade is approximately 1,030,000. The mesh on the blade surface and endwall is shown in Fig. 3. The ‘‘H-type” mesh is created for the suction slot by IGG of NUMECA FINE/TURBO. The simulation code employed is FINE/TURBO. The SpalartAllmaras turbulence model is utilized in the simulations. Inlet total pressure, inlet total temperature, inlet flow angle, and outlet static pressure are presented at the boundary according to the experimental data. The investigation is conducted at an incidence angle of 0.5°. In the experiment, the endwall boundary layer is removed by boundary layer suction at one chord upstream the inlet of the cascade, and thus the simulations in most of the study are conducted with clean inlet conditions. With the purpose of validating the effectiveness of coupled method under different inlet endwall boundary layer characteristics, two different inlet endwall boundary layers are defined and investigated in Section 4.5.

111

Table 1

Main geometric parameters of cascade.

Parameter

Data

Chord (m) Inlet blade angle Outlet blade angle Setting angle Solidity Blade height (m) Maximum thickness/chord Relative position of maximum thickness

0.063 40.17° 13.21° 15.40° 1.66 0.10 0.08 0.61

Please cite this article in press as: Cao Z et al. Influence of coupled boundary layer suction and bowed blade on flow field and performance of a diffusion cascade, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.023

90 91 92 93 94

97 98 99 100 101 102 103 104 105 106 107 108

112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131


No. of Pages 16

Influence of coupled boundary layer suction and bowed blade

3 the experimental results of NACA 65 cascade from DLR20 are utilized in this study to validate the capability of the numerical code on capturing the separation structure and near-wall flow filed. The cascade features approximate diffusion factor and similar corner separation with the cascade investigated in this study. Thus, it is appropriate for validation. Fig. 5 compares the suction surface flow field of the experimental and numerical results. The numerical results show excellent agreement with the experimental results.

Fig. 1

Fig. 2

Fig. 3

132

133 134 135 136 137 138 139 140 141 142 143 144 145 146

Airfoil of the cascade.

Wind tunnel test region.

Mesh near blade surface and endwall.

3.2. Validations Fig. 4 compares Cp of the experimental and numerical results at the mid-span of the baseline linear cascade at the inlet Mach number of 0.6 and incidence angles(i) of 0.5° and 5.0°. In the figure, PS is pressure surface, and SS is suction surface. Cp is the ratio of the local static pressure to the inlet total pressure. The numerical results show excellent agreement with the experimental results. From approximately 60% axial chord position to the trailing edge, where the camber angle is larger than that of the front segment of the blade, the Cp on the suction surface increases abruptly. At the trailing edge, a weak separation is evident. Since there is no experimental data of surface visualization for the investigated cascade, and rarely any published experimental data for highly loaded compressor cascade is found,

147 148 149 150 151 152 153 154 155

4. Results and discussion

156

4.1. Boundary layer suction in linear cascade

157

The position and suction coefficient of the suction slot have an important effect on the suction effectiveness. In order to select appropriate slot position and suction coefficient for further investigation, four different suction slot schemes for the linear cascade are designed and investigated. The positions of the four suction slot schemes are at 53.9% (Slot-A), 67.5% (Slot-B), 76.6% (Slot-C) and 87.7% (Slot-D) axial chords; they are 1 mm in width and distribute from 20% to 80% spans. Fig. 6 illustrates the configurations of the four suction schemes. The comparison for the mid-span loss coefficient of the four suction schemes is shown in Fig. 7. The mid-span loss is defined as the mass flow averaged loss coefficient of 60% mass flow in the mid-span. It is indicated that the mid-span loss of the four suction schemes all reduces as the suction coefficient increases. Slot-C exhibits the lowest mid-span loss. However, as the mid-span loss of Slot-B is just slightly higher than that of Slot-C, and the blade thickness near Slot-B is greater than that near Slot-C, the slot position of Slot-B is adopted in the subsequent investigation for better blade strength. The mid-span loss coefficient of Slot-B and Slot-C almost does not change as the suction coefficient approaches 1.92%. Therefore, in order to compare the flow fields and the performance of different suction schemes at the same suction coefficient, the suction coefficient of 1.92% is adopted for the following analysis. Fig. 8 compares limiting streamlines/static pressure contours on the suction surface of the baseline linear cascade and linear cascade with suction. The suction coefficient is 1.92%. After boundary layer suction, the trailing edge separation line (TSL) vanishes completely. With suction, the corner separation line (CSL) does not joint with the TSL, but ends at a focus point (F) near the trailing edge. Moreover, static pressure at the trailing edge of the mid-span increases significantly, which indicates that the diffusion ability of the cascade increases. However, the corner separation enlarges significantly after mid-span boundary layer suction. Saddle point & focus point (S&F) structure in the suction surface corner indicates that the cascade exhibits an open corner separation. The streamlines in the suction corner are reversed by the streamwise gradient. After mid-span boundary layer suction, the reverse flow region in the suction surface corner increases. Moreover, the S&F points move closer to the endwall. Fig. 9 shows the pitchwise mass flow averaged loss coefficient at the outlet of cascade. After mid-span boundary layer suction, the loss coefficient at the mid-span decreases signifi-

158


159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204


No. of Pages 16

4

Z. Cao et al.

Fig. 4

Comparison between numerical and experimental results (baseline linear cascade).

Fig. 5

Suction surface limiting streamlines of NACA 65 cascade.20

Fig. 7

Fig. 6

205 206 207 208 209 210 211

Different suction slot schemes.

cantly as the suction coefficient increases. However, the loss coefficient of 0–28% spans increases remarkably because of the increase in corner separation. Fig. 10 compares the loss coefficient (Cp*) contours at different axial sections and 3D corner streamlines of the baseline linear cascade and the linear cascade with suction. The high loss coefficient region mainly distributes in the suction corner.

Comparison of loss coefficients.

The 3D streamlines show severe reverse flow in the corner and further prove that the cascade exhibits an open corner separation. The corner separation region enlarges after mid-span boundary layer suction because of the spanwise inverse ‘C’ shaped static pressure distribution after mid-span suction prevents the migration of low energy fluid towards the mid-span. More low energy fluid concentrates to the suction surface/endwall corner. The spanwise static pressure distribution is shown in Fig. 20 together with other schemes.


212 213 214 215 216 217 218 219 220


No. of Pages 16


5 224

Fig. 8 Suction surface limiting streamlines/static pressure contours (linear cascade).

redistributes the spanwise static pressure. So the bowed blade is combined with the mid-span boundary layer suction to improve the corner flow filed of the cascade. The stacking curve of the bowed blade is defined as an arc that goes through the endpoints of the baseline stacking line (straight line). The stacking curve is shown in Fig. 11. The bow angle is defined as the angle between bowed stacking curve and baseline stacking line. Four bowed cascades are investigated in this study. The bow angles are 10°, 20°, 30° and 40°. Fig. 12 shows the surface mesh of 40° bowed cascade. The bowed cascade is investigated first before being combined with boundary layer suction. Fig. 13 shows the suction surface limiting streamlines and static pressure contours of the bowed cascade. Compared with the baseline linear cascade, the S&F points in the suction corner of the 10° bowed cascade move towards the mid-span, and the limiting streamlines migrate to the mid-span. As bow angle increases, the open corner separation is replaced by closed corner separation. Meanwhile, static pressure near the endwall increases with the bow angle. However, the mid-span trailing edge separation line of the bowed cascade moves upstream, and mid-span static pressure decreases, indicating that the flow field in the mid-span is deteriorated. Spanwise static pressure distribution of the bowed cascade is shown in Fig. 20. The ‘C’ shaped distribution of the bowed cascade is beneficial for improving the endwall flow field. Therefore, the mid-span boundary layer suction combined with the bowed cascade is a promising method to improve the flow field of the cascade, which includes both the flow field of mid-span and that near the endwall. Then, combined midspan local boundary layer suction and bowed blade is applied in the cascade. The position, width and length as well as suction coefficients of the suction slot are the same as those of the linear cascade with suction. 4.3. Application of coupled local boundary layer suction and bowed bade in diffusion cascade

258

In bowed cascades, if the absolute length is equal to the suction slot in the linear cascade, the projected length will be shorter; if the projected length is equal to the suction slot of the linear cascade, its absolute length will be longer. The selection of absolute length or the projected length will influence the

260

Fig. 9 Pitchwise mass averaged loss coefficient at outlet of cascade (linear cascade).

221

222 223

4.2. Application of bowed blade in diffusion cascade The spanwise inverse ‘C’ shaped static pressure distribution enlarges the corner separation, and the bowed blade

Fig. 10

Loss coefficient contours at different axial sections/3D corner streamlines (linear cascade).


225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257

259

261 262 263 264


No. of Pages 16

6

Z. Cao et al.

Fig. 11

Definition of bowed blade.

Fig. 13 Suction surface limiting streamlines/static pressure contours (bowed cascade).

Fig. 12

265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290

Surface mesh of bowed blade.

performance of the cascade. In order to investigate the influence of the selection, the disparity of absolute length and projected length and the overall loss coefficients of the bowed cascades with different slots are compared in Figs. 14 and 15. It is indicated in Fig. 14 that the disparity of absolute length and projected length is rather small; at 20° bow angle, which is the optimal bow angle shown in the following part of this section, the disparity is 0.7% of the absolute length. Fig. 15 provides the comparison of overall loss coefficient for the same absolute length and projected length of suction slot at 20° bow angle. It shows that the two loss curves almost overlap with each other. Thus the selection of the slot length does not affect the bowed cascade much at the optimal bow angle. The same projected length is selected in the paper for the following investigation. Fig. 16 compares the suction surface limiting streamlines and static pressure contours of the bowed cascade at the suction coefficient of 1.92%. After mid-span boundary layer suction, mid-span separations of the four bowed cascades are removed. The trailing edge shows a significant increase in static pressure. The mid-span flow field is similar to the linear cascade after suction. Compared with the linear cascade with suction, the corner separation of the bowed cascade shows remarkable variations. The S&F structure of the 10° bowed cascade is farther from the endwall, which indicates the increase of spanwise static

Fig. 14

Disparity of absolute length and projected length.

pressure gradient. The low energy fluid has more driving force to migrate towards the mid-span. The S&F structure vanishes as the bow angle increases to more than 10°, which indicates that the open corner separation is replaced by the closed corner separation. Streamlines in the corner separation region still flow in reverse under the streamwise pressure gradient. Compared with the bowed cascade without boundary layer suction in Fig. 13, the reversed flow trend increases because of the increase in mid-span static pressure after boundary layer suc-


291 292 293 294 295 296 297 298 299 300


No. of Pages 16


Fig. 15 Comparison of loss coefficient for different length of suction slot.

7 the bow angle increases, which indicates that endwall loss reduces. However, compared with the bowed cascade without boundary layer suction, the corner shape factor increases after boundary layer suction, which indicates that the near endwall flow field is deteriorated. Variations similar to that of the linear cascade after boundary layer suction are observed. Fig. 18 shows the endwall limiting streamlines and static pressure contours of the bowed cascade with suction coefficient of 1.92%. Endwall static pressure increases steadily as the bow angle increases. On the endwall, the most important flow structure is the horseshoe vortex system which originates from the leading edge saddle point. The suction leg of the horseshoe vortex (HS) flows around the leading edge of the blade and then crosses the suction surface at the driving force of the pressure gradient. The pressure leg of the horseshoe vortex (HP) flows towards the suction surface of the adjacent blade at the driving force of the static pressure gradient and crosses the rear part of the suction surface. As bow angle increases, the intersection position of the HS and HP with suction surface moves upstream, which indicates the increase of endwall static pressure gradient. Variations of HS and HP can be further explained by the static pressure distribution near the endwall, which is shown in Fig. 19(a). Endwall static pressure of the bowed cascade is higher than that of the baseline linear cascade and linear cascade with suction, and static pressure increases with bow angle. Near the leading edge of suction surface, the static pressure of the baseline linear cascade decreases after the leading edge peak. As the bow angle increases to more than 20°, static pressure no longer decreases near the leading edge. Therefore, the local static pressure gradient near the leading edge of the bowed cascade is higher than baseline linear cascade, which leads to the earlier intersection of HS with suction surface. HP flows towards the suction surface under the transverse gradient and streamwise static pressure gradient of the endwall. Endwall streamwise overall static pressure gradient from inlet to outlet increases with the bow angle. Therefore, the intersection position of HP with the suction surface moves upstream. Meanwhile, corner separation is reduced. For linear cascade, static pressure near the trailing edge of the suction surface remains the same, which indicates a corner stall. As bow angle increases, the static pressure also increases steadily from the leading edge to the trailing edge, and the corner stall is reduced. Fig. 19(b) shows the mid-span static pressure coefficient distribution. Static pressure at the front section of the pressure surface decreases slightly. From 5% axial chord to the suction slot of the suction surface, static pressure decreases

Fig. 16 Suction surface limiting streamlines/static pressure contours (bowed cascade with suction).

301 302 303 304 305 306 307

tion, as shown in Fig. 20. As bow angle increases, the streamline curvature of the corner separation region also increases. Taylor and Miller21 defined the corner shape factor as the angle between forward facing flow vector (V1) and reversed flow vector (V2), as shown in Fig. 17. The corner shape factor varies between 0 and p. The endwall loss increases with the corner shape factor. In Fig. 16, the shape factor decreases as

Fig. 17

Definition of corner shape factor.


308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355


No. of Pages 16

8

Z. Cao et al.

Fig. 18 Endwall limiting streamlines/static pressure contours (bowed cascade with suction).

356 357 358 359 360 361 362 363 364 365 366 367 368 369

significantly after boundary layer suction; static pressure decreases as bow angle increases. Near the suction slot, static pressure shows a sudden change. Then, static pressure increases steadily to the trailing edge. Boundary layer separation of the mid-span is removed completely. Fig. 20 shows the spanwise static pressure distribution for the trailing edge of the suction surface. The baseline linear cascade, linear cascade with suction and bowed cascades with and without suction are all shown in the figure. The suction coefficient is 1.92%. Mid-span static pressure of the linear cascade increases significantly after mid-span suction, whereas the static pressure near the endwall decreases slightly. Therefore, a spanwise inverse ‘C’ shaped static pressure is established. The low energy fluid near the endwall concentrates to the suc-

Fig. 19

tion surface/endwall corner, and can hardly migrate to the mid-span. Bowed cascade without suction increases the static pressure near the endwall. However, the static pressure in the mid-span decreases. Thus, a spanwise ‘C’ shaped static pressure is established. The ‘C’ shaped distribution of static pressure is beneficial for the migration of low energy fluid towards the midspan. Therefore, endwall loss decreases, but mid-span loss increases. After mid-span boundary layer suction on the bowed cascades, mid-span static pressure increases remarkably. Static pressure near the endwall increases as well, but the increment is much smaller than that of the mid-span. An inverse ‘C’ shaped static pressure distribution forms for each bowed cascade with boundary layer suction. The inverse ‘C’ shaped static pressure distribution leads to the increase in endwall loss after mid-span boundary layer suction. However, the static pressure gradient is much smaller than the linear cascade with suction. Thus, the increment of endwall loss is smaller than the linear cascade with suction. Fig. 21 shows the loss coefficient contours at different axial sections and 3D corner streamlines of bowed cascades with suction. The figure shows that the high loss region decreases as the bow angle of the cascade increases, and that it is smaller than the linear cascade with suction. This result indicates that the endwall loss decreases. In the corner of 10° bowed cascade, 3D streamlines form a vortex, which further proves the open corner separation in 10° bowed cascade. The corner separation is smaller than the linear cascade with suction. As the bow angle increases up to 20°, 3D streamlines flow smoothly downstream, and no severe corner vortex is observed, which indicates that the open corner separation is removed by the bowed cascade. Fig. 22 compares the overall loss, mid-span loss, and endwall loss of the linear cascade with suction and bowed cascades at different suction coefficients. Fig. 23 shows the pitchwise averaged loss of different cascades at the suction coefficient of 1.92%. The endwall loss is defined as the mass flow averaged loss coefficient of 20% mass flow near the endwall. Mid-span loss is defined as the mass flow averaged loss coefficient of 60% mass flow in the mid-span.

Static pressure coefficient distribution of different blade spans.


370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410


No. of Pages 16


Fig. 20 411 412 413 414 415 416 417 418 419 420 421

Spanwise distribution of static pressure coefficient.

Without boundary layer suction, the overall loss of the cascade first decreases and then increases as the bow angle of the cascade increases. The 10° bowed cascade has the lowest overall loss because the bowed blade improves the flow filed near the endwall, but deteriorates the mid-span flow filed. The reduction of endwall loss is more than the increment of midspan loss. The mid-span loss increases with the bow angle, and the endwall loss decreases as bow angle increases to 30°. The reduction of endwall loss from 20° to 30° bow angle is much smaller than that from 0° to 10°. The endwall loss of 40° bow angle is more than that of 30° bow angle.

Fig. 21

9 As suction coefficient increases, the overall loss of linear cascade with suction and 10° bowed cascade first decreases and then increases slightly. The overall loss of the cascade with larger bow angle keeps decreasing at the suction coefficient range in this study. The cascade with 20° bow angle exhibits the minimum loss of all the cascades at most of the suction coefficient ranges. Mid-span loss of the linear cascade with suction and the cascade with 10° bow angle first decreases and then remains unchanged as the suction coefficient increases. Meanwhile, mid-span losses of 20–40° bow angles keep decreasing at the mass flow range in this study. Mid-span losses of the linear cascade with suction and 40° bowed cascade are the minimum and maximum of all the cascades respectively, because the bowed cascade transfers the low energy fluid to the mid-span. The endwall loss of all the cascades increases with the suction coefficient. At the same suction coefficient, the endwall loss of the bowed cascade is smaller than that of the linear cascade with suction. The cascade with 40° bow angle has the smallest endwall loss. Moreover, the growth rate of the endwall loss of bowed cascade is lower than that of the linear cascade with suction because the bowed cascade decreases the spanwise static pressure gradient. Fig. 23 shows the same trend as Fig. 22(b) and (c). From 0% to approximately 20% span, the loss coefficient decreases as the bow angle increases. From 20% to approximately 40% span, the loss coefficient increases with the bow angle because the bowed cascade moves the low energy fluid towards the

Loss coefficient contours at different axial sections/3D corner streamlines (bowed cascade with suction).


422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449


No. of Pages 16

10

Z. Cao et al.

Fig. 23

Fig. 22 Linear cascade with suction and bowed cascades at different suction coefficients.

450 451 452 453 454 455 456 457 458 459

mid-span. From approximately 40% to 50% spans, the loss coefficient remains unchanged as bow angle increases. Fig. 24 shows the velocity vectors and Mach number contours at the cascade outlet. The figures show only the lower half of the cascade outlet. Fig. 24(a) shows a passage vortex near the endwall and a concentration shedding vortex (CSV) above the passage vortex (PV). After boundary layer suction of the baseline linear cascade, the passage vortex nearly disappears, as shown in Fig. 24(b). The concentration shedding vortex enlarges, and the center

Pitchwise averaged loss coefficient.

of the vortex moves towards the endwall because the inverse ‘C’ shaped static pressure reduces the migration of low energy fluid towards the mid-span. The low Mach number region near the endwall increases, which indicates the increase of low energy fluid at the suction surface/endwall corner. Bowed cascade increases the static pressure gradient near the endwall, leading to the enlargement of the passage vortex. The low Mach number region near the endwall decreases as bow angle increases. The low Mach number region close to the endwall of 40° bowed cascade almost vanishes; it migrates towards the mid-span.

460

4.4. Influence of slot length on effectiveness of coupled local suction and bowed blade

471

In addition, in order to investigate the influence of slot length on the effectiveness of coupled local suction and bowed blade, two suction slots with different lengths are designed and investigated. The suction slots distribute from 25% to 75% and 15% to 85% spans. The slot distributing from 25% to 75% span is a bit far from the suction corner. Considering that a slot distributing throughout the whole blade span will weaken the strength of the blade significantly, we do not investigate longer slot in the study, e.g., Brian et al.4 utilized part span slot for both the rotor and stator of an aspirated compressor in the experiment. Fig. 25 compares the suction surface limiting streamlines of bowed cascades with the suction slot distributing from 25% to 75% span; the suction coefficient is 1.92%. Compared with Fig. 13, the mid-span separations are all removed. However, the flow field in the corner is deteriorated obviously. The open corner separation enlarges at the bow angle of 10°. The open corner separation remains at the bow angle of 30°. As the bow angle approaches 40°, the open corner separation is replaced by a closed corner separation. The corner shape factor is larger than that in Fig. 16(d). In Fig. 26, the limiting streamlines on the suction surface of bowed cascades with the suction slot distributing from 15% to 85% span are provided; the suction coefficient is also 1.92%. Local boundary layer suction effectively removes the midspan separations. The open corner separation of all the cascades in Fig. 26 vanishes; moreover, compared with the bowed cascade with the suction slot distributing from 20% to 80%

473


461 462 463 464 465 466 467 468 469 470

472

474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500


No. of Pages 16


Fig. 24

501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524

11

Velocity vector/Mach number contours at cascade outlet.

span as shown in Fig. 16, the corner shape factor decreases, indicating lower endwall loss. Figs. 27 and 28 provide the variations of overall loss with the increase of suction coefficient. With the suction slot distributing from 25% to 75% span, the overall losses of the bowed cascades are lower than those of the linear cascade with suction. The optimal bow angle is 20°. The minimum loss is lower than that of the linear cascade with the suction slot distributing from 15% to 85% and 20% to 80% spans. Therefore, a shorter suction slot coupled with bowed blade is able to achieve the effect of a longer suction slot in the linear cascade. However, as the open corner separation exists even at the optimal bow angle, the reduction of overall loss coefficient is lower than the coupled suction schemes with longer suction slots. As the coupled suction scheme with the suction slot distributing from 15% to 85% span effectively eliminates the open corner separation, the overall loss of the cascade reduces significantly. The optimal bow angle is also 20°. The minimum overall loss is lower than that of the coupled suction schemes with the suction slot distributing from 25% to 75% and 20% to 80% spans. Figs. 29 and 30 provide the variations of endwall loss and mid-span loss with the increase of bow angle for different suction slots. The suction coefficient is 1.92% for each condition.

The coupled suction scheme with the shortest suction slot exhibits the highest endwall loss and mid-span loss because of the open corner separation under most conditions. In conclusion, shorter suction slot far from the suction corner tends to induce open corner separation, which deteriorates the near endwall flow field, whereas longer suction slot that extends to the suction corner is apt to avoid open corner separation, which deteriorates the near endwall flow filed less. Therefore, longer suction slot is easier to balance the suction technique and bowed blade, and exhibits lower overall loss coefficient. In the design process of coupled mid-span suction and bowed blade, the slot length should be sufficiently long to eliminate the open corner separation at the optimal bow angle; the strength of the blade is also to be considered, so a suction slot distributing throughout the whole span is not suggested. In this study, a suction slot distributing from 20% to 80% span can effectively eliminate the mid-span trailing edge separation and the open corner separation at the optimal bow angle. In Fig. 29, the slop of endwall loss curve for 20–80% span suction is approximately the same before 20° bow angle; the decrement is much smaller while the bow angle is higher than 20°, and the endwall loss almost does not change from 30° to 40° bow angle. The variations of endwall loss for 15–85% span


525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548


No. of Pages 16

12

549 550 551

Z. Cao et al.

Fig. 25

Suction surface limiting streamlines of bowed cascade with suction (25–75% span suction).

Fig. 26

Suction surface limiting streamlines of bowed cascade with suction (15–85% span suction).

suction are similar with those for 20–80% span suction. The variations are related to the forms of corner separation. At low bow angles, as there is much low energy fluid in the open

corner separation region, bowed blade decreases the endwall loss obviously, whereas at high bow angles, as there is little low energy fluid in the closed corner separation region, the


552 553 554


No. of Pages 16


Fig. 27

Overall loss with 25–75% span suction.

Fig. 28

Overall loss with 15–85% span suction.

13

Fig. 30

Fig. 31

Fig. 29

Variation of endwall loss.

556 557 558 559 560

increase of bow angle does not improve the endwall flow filed much. However, as the bowed blade increases the loading of mid-span, and enlarged surface area increases the fraction loss19, the mid-span loss keeps increasing. Moreover, the magnitude of the slop of the mid-span loss curves increases with the bow angle. Therefore, in the design process of coupled suc-

Schematic of inlet boundary layer.

tion cascade, the bow angle should be sufficiently high to eliminate the low energy fluid near the endwall, but it should also be not so high as to avoid excessive mid-span loss. For the cascade in the study, 20° is the optimal bow angle.

561

4.5. Validity of coupled method under different inlet boundary layer characteristics

565

This study presents the total pressure boundary layer on the cascade inlet to validate the effectiveness of coupled method under different inlet boundary layer characteristics. The definition of the total pressure boundary layer is expressed as follows

567

P ¼ P0

555

Variation of mid-span loss.

DP ðx DLÞ2 DL2

ð1Þ P0

where P is local total pressure; the baseline inlet total pressure and total pressure of the inlet bulk flow in the cascade with inlet boundary layer; DP the difference between the total pressure of the bulk flow and the endwall; DL the thickness of the boundary layer; x the position of the blade span. The study investigates the influence of two different schemes of the inlet boundary layer, as shown in Fig. 31. Boundary-05 scheme has a total pressure boundary layer


562 563 564

566

568 569 570 571 572 574 575 576 577 578 579 580 581 582


No. of Pages 16

14 583 584 585 586 587 588 589 590 591 592

Z. Cao et al.

thickness of 5% span, whereas Boundary-10 scheme has a thickness of 10% span. The inlet mass flow averaged Mach number stays the same as the baseline linear cascade. The suction slot is the same as that of Sections 4.1 and 4.3. Fig. 32 shows the overall loss coefficient, mid-span loss coefficient and endwall loss coefficient of Boundary-05 scheme, respectively. Fig. 33 shows the loss coefficients of Boundary-10 scheme. The loss coefficients of the Boundary-05 and Boundary-10 schemes show similar variations as the suction coefficient increases.

Fig. 33

Fig. 32

Loss coefficient of Boundary-05 scheme.

Loss coefficient of Boundary-10 scheme.

For the Boundary-05 scheme, the overall loss shows similar variations as the clean inlet cascade. The overall loss of the linear cascade of the Boundary-05 scheme first decreases and then increases slightly as the suction coefficient increases. The overall loss of the 10° bowed cascade and other bowed cascades keeps decreasing in the suction coefficient region, which indicates more low energy fluid migrating to the mid-span. At the highest suction coefficient, the losses of all the bowed cascades are lower than the linear cascade. The 20° bowed cascade has the lowest overall loss at the highest suction coefficient. Compared with the linear cascade at the same suction coefficient, the 20° bowed cascade decreases by 22.6%.


593 594 595 596 597 598 599 600 601 602 603 604


605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621

622

624 623 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657


15

Mid-span loss variations are similar to the clean inlet cascade. Endwall loss of the cascades increases with the suction coefficient, but with a smaller increment. For the Boundary-10 scheme, the bowed cascades still improve the performance of the cascade effectively. The overall loss of the linear cascade of Boundary-10 scheme first decreases and then increases significantly. The overall loss of the linear cascade is lower than the clean inlet and Boundary-05 scheme, and keeps reducing until the suction coefficient reaches 1.44%. The overall loss of the bowed cascade keeps decreasing at the suction coefficient range in the study. The overall loss of 10°, 20° and 30° bowed cascades is lower than that of the linear cascade in most of the suction coefficient regions. The variation of mid-span loss is similar to that of the clean inlet cascade. The endwall loss of the linear cascade shows more difference than that of the clean inlet cascade, and increases slightly with the suction coefficient.

to thank Dr. Zhou Chao for the help during the writing of the paper.

663

References

665

1. Keerebrock JL, Reijnen DP, Ziminsky WS, Smilg LM. Aspirated compressors. In: Proceedings of ASME Turbo Expo; 1997 June 2– 5; Orlando, USA. New York: ASME; 1997. Paper No.: 97-GT525. 2. Keerebrock JL. The prospects for aspirated compressors. In: Proceedings of AIAA Fluids 2000 Conference and Exhibit; 2000 June 19–22; Denver, USA. Reston: AIAA; 2000. Paper No.: AIAA 2000–2472. 3. Merchant AA, Kerrebrock JL, Epstein AH. Compressors with aspirated flow control and counter-ratation. In: Proceedings of 2nd AIAA Flow Control Conference; 2004 June 28-July 1; Portland, USA. Reston: AIAA; 2004. Paper No.: AIAA 2004– 2514. 4. Brian JS, Kerrebrock JL, Merchant AA. Experimental investigation of a transonic aspirated compressor. ASME J Turbomachinery 2005;127(2):340–8. 5. Merchant AA, Kerrebrock JL, Adamczyk JJ, Braunscheidel E. Experimental investigation of a high pressure ratio aspirated fan stage. ASME J Turbomachinery 2005;127(1):43–51. 6. Gbadebo SA, Cumpsty NA, Hynes TP. Three-dimensional separations in axial compressors. ASME J Turbomachinery 2005;127 (2):331–9. 7. Gbadebo SA. Three-dimensional separations in compressors [dissertation]. Cambridge: University of Cambridge; 2003. 8. Gbadebo SA, Cumpsty NA, Hynes TP. Control of three-dimensional separations in axial compressors by tailored boundary layer suction. ASME J Turbomachinery 2008;130(1):011004. 9. Chen PP, Qiao WY, Liesner K, Meyer R. Location effect of boundary layer suction on compressor hub-corner separation. In: Proceedings of ASME Turbo Expo; 2014 June 16–20; Dusseldorf, Germany. New York: ASME; 2014. Paper No.: GT2014-25043. 10. Wang ST, Qiang XQ, Lin WC, Feng GT, Wang ZQ. Highlyloaded low-reaction boundary layer suction axial flow compressor. In: Proceedings of ASME Turbo Expo; 2007 May 14–17; Montreal, Canada. New York: ASME; 2007. Paper No.: GT2007-28191. 11. Qiang XQ, Wang ST, Lin WC, Wang ZQ. A new design concept of highly-loaded axial flow compressor by applying boundary layer suction and 3D blade technique. In: Proceedings of ASME 2008 International Mechanical Engineering Congress and Exposition; 2008 October 31-Novenber 6; Boston, USA. New York: ASME; 2008. Paper No.: IMECE2008-66899. 12. Chen F, Song YP, Chen HL, Wang ZQ. Effects of boundary layer suction on the performance of compressor cascades. In: Proceedings of ASME Turbo Expo; 2006 May 8–11; Barcelona, Spain. New York: ASME; 2006. Paper No.: GT2006-90082. 13. Song YP, Chen F, Yang J, Wang ZQ. A numerical investigation of boundary layer suction in compound lean compressor cascade. In: Proceedings of ASME Turbo Expo; 2006 May 8–11; Barcelona, Spain. New York: ASME; 2006. Paper No.: GT2005-68441. 14. Deich ME, Gubalev AB, Filippov GA, Wang ZQ. A new method of profiling the guide vane cascade of stage with small ratios diameter to length. Teplienergetika 1962;8:42–6. 15. Wang ZQ, Lai SK, Xu WY. Aerodynamic calculation of turbine stator cascades with curvilinear leaned blades and some experimental resultsProceedings of symposium of 5th international symposium on air breathing engines; Bangalore, India. Bedfordshire: International Society of Air Breathing Engines; 1981. 16. Breugelmans FAE. Influence of incidence angle on the secondary flow in compressor cascade with different dihedral distributionProceedings of 7th international symposium on air breathing

666

5. Conclusions (1) A coupled local tailored boundary layer suction and positive bowed blade method is developed based on the investigation of the mid-span local boundary layer suction and bowed blade separately. (2) Mid-span local boundary layer suction can effectively eliminate mid-span trailing edge separation. However, the open corner separation is more severe than baseline linear cascade because of the spanwise inverse ‘‘C” shaped static pressure distribution. The positive bowed cascades exhibit an opposite characteristic; they effectively improve the near endwall flow field, but enlarge the mid-span separation because of the spanwise ‘‘C” shaped static pressure distribution. (3) The coupled method can effectively improve the near endwall flow field and the mid-span flow fields. The open corner separation is replaced by closed corner separation at 20° or higher bow angles. The corner shape factor decreases as the bow angle increases. Mid-span trailing edge separation is removed by local boundary layer suction. The static pressure near the trailing edge increases significantly. The 20° bowed cascade has the lowest overall loss at the maximum suction coefficient. (4) For the linear cascade with suction and coupled controlled cascades, mid-span loss decreases as the suction coefficient increases, whereas mid-span loss increases with the bow angle. Endwall loss increases in different degrees as the suction coefficient increases. As bow angle increases, endwall loss decreases significantly. The endwall loss of coupled cascade is higher than that of the bowed cascade without boundary layer suction because of the weak spanwise inverse ‘‘C” shaped static pressure distribution. The coupled method can also improve the flow field of the cascade effectively under different inlet boundary layer conditions.

658

659

Acknowledgements

660

This study was supported by China Postdoctoral Science Foundation and a key project of the National Natural Science Foundation of China (No. 51236006). The authors would like

661 662

No. of Pages 16


664

667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726


16

Z. Cao et al.

746

engines; Beijing, China. Bedfordshire: Internal Society of Air Breathing Engines. p. 663–8. Shang EB, Wang ZQ, Su JX. The experimental investigation on the compressor cascade with leaned and curved blade. In: Proceedings of ASME Turbo Expo; 1993 May 24–27; Cincinnati, USA. New York: ASME; 1993. Paper No.: 93-GT-050. Bogod AB. Direct and inverted calculation of 2D axisymmetric and 3D flows in axial compressor blade rows. Revue Francaise de Mecanique 1992;4:351–9. Fischer A, Riess W, Seume JR. Performance of strongly bowed stators in a four-stage high-speed compressor. ASME J Turbomachinery 2004;126(3):333–8. Meyer R, Bechert DW, Hage W. Secondary flow control on compressor blades to improve the performance of axial turbomachinesProceedings of 5th European conference on turbomachineryfluid dynamics and thermodynamics; Prague, Czechoslovakia. Florence: European Turbomachinery Society; 2003. p. 1–8, March 18–21. Taylor JV, Miller RJ. Competing 3D mechanisms in compressor flows. ASME J Turbomachinery 2016;139(2):021009.

747 748

Cao Zhiyuan is a postdoctoral researcher at Peking University. He

727 728 729

17.

730 731 732 733

18.

734 735 736

19.

737 738 739

20.

740 741 742 743 744 745

21.

No. of Pages 16

received his Ph.D. degree from Northwestern Polytechnical University in 2014. His current research interests are flow control and aerodynamic design of highly loaded axial compressors.

749

Liu Bo is a professor at School of Power and Energy, Northwestern Polytechnical University. His area of research includes aerodynamic design and flow control of axial compressors.

753

Zhang Ting is an engineer and designer at AECC Xi’an Aero-engine Controls Co., LTD. She received the master’s degree from Northwestern Polytechnical University. Her current research interests include design and optimization of fluid machinery.

757

Yang Xiqiong is a postgraduate student at Northwestern Polytechnical University. Her current research interests include design and optimization of axial compressors.

762

Chen Pingping is a postdoctoral researcher at Kuang-Chi Institute of Advanced Technology. She received the Ph.D. degree from Northwestern Polytechnical University. Her current research interests are aerodynamics and flow control of axial compressors.

766


750 751 752 754 755 756 758 759 760 761 763 764 765 767 768 769 770