8 aDepartment of Mechanical Engineering Sciences, University of Surrey, Guildford GU2 7XH, UK 9 bSchool of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, C
Trang 18 aDepartment of Mechanical Engineering Sciences, University of Surrey, Guildford GU2 7XH, UK
9 bSchool of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
10 cSchool of Energy and Power Engineering, Beihang University, Beijing 100191, China
11 dLaboratoire de Me´canique des Fluides et d’Acoustique, E´cole Centrale de Lyon, E´cully 69134, France
12 Received 12 December 2015; revised 2 September 2016; accepted 2 September 2016
13
16
17 Corner separation;
18 Influencing parameter;
20 Linear compressor cascade;
Abstract Large-eddy simulation (LES) is compared with experiment and Reynolds-averaged Navier-Stokes (RANS), and LES is shown to be superior to RANS in reproducing corner separa-tion in the LMFA-NACA65 linear compressor cascade, in terms of surface limiting streamlines, blade pressure coefficient, total pressure losses and blade suction side boundary layer profiles How-ever, LES is too expensive to conduct an influencing parameter study of the corner separation RANS approach, despite over-predicting the corner separation, gives reasonable descriptions of the corner separated flow, and is thus selected to conduct a parametric study in this paper Two kinds of influencing parameters on corner separation, numerical and physical parameters, are ana-lyzed and discussed: second order spatial scheme is necessary for a RANS simulation; incidence angle and inflow boundary layer thickness are found to show the most significant influences on the corner separation among the parameters studied; unsteady RANS with the imposed inflow unsteadiness does not show any non-linear effect on the corner separation
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/ ) 22
23
1 Introduction
24
For the economic and ecological purpose, researchers work at
25
reducing the weight of turbomachines in aircrafts This leads
26
to an increase of compression ratio per compressor stage,
27
and thus of the blade loading However, the rise of the blade
28
loading results in the strengthening of three-dimensional
phe-29
nomena, e.g., corner separations, clearance flows, shock waves
* Corresponding author.
E-mail address: liuyangwei@126.com (Y Liu).
Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
Chinese Society of Aeronautics and Astronautics
& Beihang University
Chinese Journal of Aeronautics
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http://dx.doi.org/10.1016/j.cja.2016.09.015
Trang 230 and other secondary flows, which highly restrict the efficiency
31 and stability of compressor.1,2The corner separation has great
32 effect on compressor performance, such as passage blockage,
33 limiting on static pressure rise, total pressure loss, and
eventu-34 ally stall and surge especially for highly loaded compressor
35 Hence, recently the flow mechanism and flow control for
cor-36 ner separation have been investigated by many researchers
37 using experiment3–5and computational fluid dynamics.6–8
38 Associated with high pressure gradients and boundary layer
39 separations, corner separation is quite difficult to reproduce
40 with a conventional Reynolds-averaged Navier-Stokes
41 (RANS) approach.9,10 Large-eddy simulation (LES) and
42 hybrid RANS/LES have proven to be capable of simulating
43 turbomachinery flows,9,11–13 and are found to be superior to
44 RANS in simulating the corner separation Nevertheless,
45 LES is still too expensive to investigate the influencing
param-46 eters of the corner separation
47 In the present work, both LES and RANS are used to study
48 the corner separation and compared with the experimental
49 results RANS, despite over-estimating the extent and intensity
50 of the corner separation, can give a reasonable prediction, and
51 is an alternative to conduct the influencing parameter study In
52 this study, two kinds of influencing parameters on corner
sep-53 aration, numerical and physical parameters, are analyzed and
54 discussed based on RANS approach
55 2 Review of influencing parameters on corner separation
56 Corner separation has been investigated by many researchers,
57 and so do its influencing parameters Some known influencing
58
parameters are loading, inflow boundary layer, free-stream
59
turbulence intensity, clearance flow, Reynolds number, Mach
60
number, rotating effect, surface roughness and real blade
61
geometry A literature review of these parameters is listed in
62 Table 1
63
3 Experimental and numerical configuration
64
3.1 Experimental configuration
65
The experiments have been made in the LMFA-NACA65
lin-66
ear compressor cascade wind tunnel.36,37A schematic of the
67
test section and the blade geometry is drawn inFig 1 Thirteen
68
NACA65 blades are installed to ensure the periodicity in the
69
middle passage The free stream velocity is set to 40 m/s,
yield-70
ing a chord-based Reynolds number Rec= 3.82 10.5
In
71
order to force the boundary layers as turbulent on the blade
72
surface (as expected in real compressors), two pieces of
sand-73
paper are pasted near the blade leading edge on both the
pres-74
sure and suction sides In this paper, particular attention is
75
paid to the incidence angle 4°, considered as a reference, where
76
a three-dimensional corner separation has been clearly
77
observed More information about the compressor cascade
78
and experimental details could be found in Ref.36
79
3.2 Numerical setup
80
Two different solvers have been used to conduct the numerical
81
studies: an in-house code Turb’Flow developed in the
Nomenclature
Roman symbols
B characteristic point of blade pressure coefficient
ca axial chord length
CL blade lift coefficient
CP static pressure coefficient
CPt total pressure loss coefficient
CP
t pitchwise-mass-averaged total pressure loss
coeffi-cient
k turbulent kinetic energy
Pt absolute total pressure
Rec chord-based Reynolds number
s* arc length from leading edge
Tu turbulence intensity
us tangential velocity component to blade suction
side
un wall normal velocity component to blade suction
side
x, y, z coordinates
Greek symbols
d1 displacement boundary layer thickness
Dy+
wall distance of the 1st grid layer, in wall unit
e4 fourth-order artificial viscosity coefficient
x specific turbulent dissipation rate Subscript
Acronyms AUSM advection upstream splitting method
DRSM differential Reynolds stress model LES large-eddy simulation
LMFA Laboratoire de Me´canique des Fluides et
d’Ac-oustique MUSCL monotone upwind schemes for conservation law-s RANS Reynolds-averaged Navier-Stokes
SISM shear-improved Smagorinsky model SLAU simple low-dissipation AUSM TKE turbulent kinetic energy URANS unsteady RANS
Trang 3Table 1 Review of influencing parameters on corner separation.
Parameter References Description
Loading 14, 15 Increasing the blade loading, a corner separation developed into a full-span separation on the rotor In
the second-stage stator, increasing the blade loading resulted in a dramatic growth of the stator corner separation, and the blockage due to the corner separation reached nearly 40% with an extension of nearly 70% of the span
16–19 The same trends were observed: increasing compressor loading generally increases the spread and the
intensity of corner separation Inflow boundary layer 20, 21 The size of corner separation and the losses increase when the incoming boundary layer is thickened
20 Through RANS simulations with mixing length model, Gbadebo presumed that increasing the
turbulence level within the thickened inlet boundary layer brought high momentum fluid from the free-stream into the boundary layer, thus suppressing the further growth of separation, and the extra losses were generated by the turbulent mixing within the boundary layer
22 It is observed that the size of the corner separation decreases when the incoming boundary layer
skewness increases Free-stream turbulence
intensity
16, 23 The high turbulence intensity suppressed the laminar-turbulent transition bubble on the blade suction
side The massive corner separation and the losses near the hub significantly decreased, mostly owing to the wakes-induced transition at the blade leading edge which suppressed the transition bubble
24 When turbulence intensity increased, the laminar-turbulent transition bubble was removed, and the
bypass transition became dominant At the same time, the transition location moved upstream The authors of the present paper observed in the figures of Ref 24 that the upstream movement of the laminar-turbulent transition can reduce the corner separation and the losses
Clearance flow 25 The stator corner separation was significantly reduced by a hub clearance (the hub is not rotating),
because the high momentum leakage flow through the gap from the pressure side to the suction side re-energized the low-momentum flow on the suction side and thus decreased corner separation
18 A stator hub clearance provides great impact on the corner separation, and the losses It helps increase
the flow turning and decrease the diffusion factor near the hub, therefore leading to a reduction of the corner separation
26 With a small clearance of about 0.2% of chord length, the losses were predicted to be the highest, which
could be also associated to the increase of the critical points When the clearance is increased to about 0.58%, which is comparable to the displacement thickness of the inlet boundary layer, the losses are significantly reduced, and the critical points as well as the horseshoe vortex are found to disappear As the clearance is increased well beyond 0.58%, a strong tip-leakage vortex is formed, which prevents the end-wall low momentum fluid from interacting with the blade suction surface and thereby inhibits the corner separation
Reynolds number 27 Within a range of Reynolds number from 50,000 to 200,000, there is no significant effect of Reynolds
number on the cascade performance for fully separated configurations Above a critical Reynolds number in the neighborhood of 200,000, the losses and the flow deflection (i.e., the cascade performance) are constant for a cascade that is not separated
28 The losses are insensitive to the Reynolds number for the smoothing blades, while for the rough blades,
the losses increase when the Reynolds number is augmented Mach number 29 In a numerical study on a stator row of a high loading core compressor with a subsonic design inlet
Mach number distribution around 0.72, a corner separation was formed close to the leading edge at high attack angle due to the shock that follows the leading edge local acceleration zone When the inlet Mach number was reduced, the exit losses were reduced, and the leading edge corner separation was eliminated
as well
30 A violent corner separation induced by a strong 3D shock system was identified experimentally and
numerically in a compressor cascade at an inlet Mach number of 1.09 and a Reynolds number of 1.9 10 6
Rotating effect 14 Under low rotating speed condition, low total pressure fluid accumulates at blade-hub corner due to the
passage vortex, which leads to a big corner separation However, under high rotating speed condition, a large spanwise redistribution of fluid occurs, and low energy fluid is centrifuged radially outward, which results in a smaller corner separation
Surface roughness 31 The blade roughness induces an earlier laminar-turbulent transition, as well as a considerable frictional
drag into the flow, which leads to the premature thickened boundary layer on the blade suction side This thickened boundary layer encounters the passage adverse pressure gradient, and finally leads to the increase of the corner separation and the losses
28 The decrease of the compressor cascade performance depends mostly on the blade suction surface
roughness For Reynolds number above 500,000, increasing the blade roughness will further increase losses and blockage
(continued on next page)
Trang 482 LMFA,12,38and a commercial solver ANSYS FLUENT The
83 reason is that only two k-x turbulence models are currently
84 available in Turb’Flow, and ANSYS FLUENT is thereby used
85 as a complement to provide more results with other turbulence
87 A large-eddy simulation,39consisting of 3 108
grid points
88 (the grid size isDx+6 60, Dy+6 1 and Dz+6 30), has been
89 carried out with Turb’Flow A flat plate simulation was
run-90 ning with the simulation of the compressor cascade domain,
91 in order to feed the inflow condition of the latter The
92 approach is depicted inFig 2 The blade surface sandpaper
93 used in the experiment is reproduced by removing some grid
94 points at the same position A 4-point Jameson centered
spa-95 tial scheme with an artificial viscosity coefficient40,41of 0.002
96 is implemented for the inviscid fluxes interpolation, while the
97 viscous fluxes are discretized by a two-point centered scheme
98 A three-step Runge-Kutta scheme is used for temporal
dis-99 cretization with a fixed time step of 2.5 108s,
101
condition) of 0.95 Finally, the shear-improved Smagorinsky
102
model (SISM)42 is utilized to represent the subgrid-scale
103
motions
104
Similar configurations are applied to the RANS simulations
105
with Turb’Flow, where the grid-point number is reduced to
106
about 2.8 106
The near wall grid size is Dy+
= 1 Two
107
available turbulence models are tested: the Wilcox k-x model43
108
and the Kok k-x model.44To complement the RANS results
109
with different turbulence models, and to assess the sensitivity
110
to the numerical solver, ANSYS FLUENT is used to carry
111
out two simulations with the Spalart-Allmaras (SA) model45
112
and the differential Reynolds stress model (DRSM).46 The
113
mesh used in these two simulations consists of 1.6106
grid
114
points, and the grid sizeDy+
is set to 1 A standard scheme
115
is applied to the pressure term discretization, while second
116
order upwind schemes are used for modified turbulent
viscos-117
ity and energy term interpolation Another two FLUENT
118
RANS simulations on the same mesh are conducted with
119
two spatial interpolation schemes of two different scheme
Table 1 (continued)
Parameter References Description
Real blade geometry 32–34 In the investigation of Friedrichs et al., a stator was designed with advanced conception rules, i.e., an
aft-swept leading edge with increasing sweep angle near hub and shroud It was observed that this modern design tends to reduce cross-passage pressure gradient, and therefore reduces the corner separation and losses by an induced new secondary flow
35 Corner separation and its corresponding losses are very sensitive to the turbulent transition process
between 5% and 30% span near the leading edge Blade geometric changes which cause suction surface transition to move toward the leading edge in this region will result in a large growth of the corner separation and its impact on losses
Fig 1 Schematic of experimental test section and blade geometry
Fig 2 Sketch map of LES inflow feeding
Trang 5120 orders to check the influence of the spatial scheme order on
121 corner separation
122 More details about the computational settings involved in
123 this paper are listed inTable 2
124 4 Influencing parameters of corner separation
125 The influencing parameters of the corner separation are
classi-126 fied into two categories: (1) numerical parameters, which
con-127 cern the numerical resolution, such as turbulence model,
128 numerical scheme and boundary condition type; (2) physical
129 parameters, e.g., incidence angle, inflow turbulent kinetic
130 energy, inflow perturbations and inflow boundary layer
131 thickness
132 Before the investigation on the influencing parameters of
133 the corner separation, a subsection on the mean aerodynamics
134 comparison will be firstly presented In this subsection, results
135 are compared among the experiment, LES and RANS in order
136 to make a sense on the capacity of the different numerical
137
methods and turbulence models for predicting the corner
sep-138
aration in the reference configuration (incidence angle: 4°)
139
Comparisons are made on the wall static pressure coefficient
140
and the total pressure losses, which are good indicators of
141
the separation Surface flow visualizations and blade suction
142
side boundary layer profiles are also presented for the
experi-143
ment, LES and reference RANS in order to emphasize the
144
computational accuracy Apparently, the influence of
turbu-145
lence model will also be included in this part It will be
fol-146
lowed by a small synthesis Then, the other influencing
147
parameters will be discussed
148
4.1 Mean aerodynamics comparison (influence of turbulence
149
model)
150
Surface flow visualizations are usually used to qualitatively
151
identify the corner separation that occurs in compressor
cas-152
cades As illustrated inFig 3, the LES and reference RANS
153
surface limiting streamlines are compared with the
experimen-Table 2 List of computations
Code Incidence
angle
Trip Spatial scheme Artificial
viscosity
Turbulence model
center
outlet RANS
reference
Turb’Flow 4 ° Yes 4-pt Jameson
center
RANS
DRSM
DRSM
1st-order
DRSM
3rd-order
MUSCL
AUSM + -up Turb’Flow 4 ° Yes 3rd-order
AUSM+-up
Viscosity 0.01 Turb’Flow 4 ° Yes 4-pt Jameson
center
Mixed outlet Turb’Flow 4 ° Yes 4-pt Jameson
center
outlet
center
center
center
center
center
center
center
center
Inflow
fluctuation
Turb’Flow 4 ° Yes 4-pt Jameson
center
0.020 Wilcox k-x d 1(Exp.) with inflow
fluctuations
P outlet
Trang 6154 tal oil visualization, on both the endwall and blade suction
sur-155 face On the endwall, a good qualitative agreement is achieved
156 among the experiment, LES and RANS, in terms of the reverse
157 flow structure and the singular points LES gives better
predic-158 tion on the outset of the endwall separation line, which occurs
159 around 50% axial chord position on the blade suction side A
160 second pair of flow visualizations shows on the blade suction
161 surface It should be noticed that an excellent symmetry has
162 been achieved in the experiment Recirculation regions are
163 observed among experiment, LES and RANS near the trailing
164 edge of the blade suction sides beside the endwalls Again,
165 RANS shows a larger reverse flow area, but qualitatively
166 agrees with the experiment and LES
167 The mean static pressure coefficient CP= (P P1)/
168 (Pt, 1 P1) is a key parameter to determine the compressor
169 cascade performance The area enclosed by the static pressure
170 coefficient on the pressure and suction sides represents the
171 blade loading A comparison among the experimental, LES
172 and RANS results is shown inFig 4 The left figure shows
173 the static pressure coefficient at midspan, while the distribution
174 close to the endwall is plotted on the right figure At midspan
175 (inFig 4(a)), both LES and RANS match with the
experimen-176 tal data The numerical oscillations, which appear near the
177 leading edge on both the pressure and suction sides, are due
178 to the square meshing of the tripping bands By carefully
179 inspecting the results, it can be observed that the DRSM model
180 gives the best prediction of CP The slight over-estimate by
181 LES may relate to the difficulty in simulating transition using
182 tripping bands It is more interesting to investigate what
hap-183 pens close to the endwall inFig 4(b) The results are quite
dif-184 ferent among the different turbulence models Encouragingly,
185 LES provides a very good prediction near the endwall On the
186 suction side, a flat region (indicating the separation) begins at
187 about x/ca= 0.6 in both the experiment and the LES Among
188 the four RANS simulations, the DRSM model gives the best
189 prediction, though the onset of separation is located earlier
190 at about x/ca= 0.4 The largest corner separation is predicted
191
by the SA model The results with the Kok k-x model are very
192
close to those with the Wilcox k-x model, but Kok’s model
193
predicts a slightly lower blade loading than Wilcox’s model
194
It is observed that the earlier the corner separation occurs,
195
the lower the blade loading is
196
A second key indicator of the compressor cascade
perfor-197
mance is the total pressure loss coefficient CP t= (Pt, 1 Pt)/
198
(Pt, 1 P1) Contour maps of the total pressure loss
coeffi-199
cient are compared in Fig 5 The losses are associated with
200
the blade wake (around y/s = 1) and the corner separation
201
wake (below z/h = 0.2) LES is found quite powerful to
pre-202
dict both the strength and extent of the losses, while RANS
203
models fail in reproducing the experimental total pressure
204
losses Among the RANS results, the SA model is seen to
pre-205
dict the highest losses, and it is consistent with the early
sepa-206
ration observed on the static pressure coefficient CP
207
The total pressure losses are then weighted averaged by
208
mass flow along the pitchwise direction (CP
t), and comparison
209
is plotted inFig 6 A very good agreement is observed between
210
the LES and the experiment In contrast, the RANS models
211
over-estimate the losses downstream of the corner separation
212
This is consistent with the over-prediction of the separation
213
observed through CP A good prediction of the blade wake
214
losses is obtained by the RANS models Among the RANS
215
models, the DRSM model gives the best prediction on CP
t
216
Further, the boundary layer profiles along blade suction
217
side are compared among the experiment, LES and reference
218
RANS The measurement stations are depicted in Fig 7
219
The velocity vectorsV on those measurement stations are
pre-220
sented in tangential velocity components us and wall normal
221
velocity components un, and the velocity decomposition
222
method is drawn in Fig 7 as well The velocity profiles at
223
two different blade span positions, z/h = 48.6% and z/
224
h= 2.7%, are discussed here, and they are plotted in Fig 8
225
Excellent agreements are observed in Fig 8(a) and (b) at z/
226
h= 48.6% for both us and un At z/h = 2.7%, LES results
Fig 3 Surface flow pattern visualizations (top: endwall; bottom: blade suction surface)
Trang 7227 agree with the available PIV measurements RANS predicts an
228 earlier separation outset: the first negative usvalues appear on
229 the measurement station s*= 0.41 The separation outset
pre-230 dicted by LES is observed on the measurement station
231 s*= 0.80 Although RANS predicts an earlier separation
out-232 set, it shows similar velocity profiles to LES on the last two
233 measurement stations within the separation region This builds
235 investigations
236
4.2 Synthesis
237
The comparison among the experiment, LES and RANS is
238
concluded as follows: (1) regarding the surface flow
visualiza-239
tions, both LES and RANS qualitatively match the
experi-240
ment; (2) a good prediction of the static pressure coefficient
241
and the total pressure losses is obtained by LES throughout
242
the half span; (3) RANS predicts an earlier separation outset
243
but shows similar velocity profiles on the measurement stations
Figure 4 Mean static pressure coefficient
Fig 5 Mean total pressure loss coefficient (x = 1.363ca)
Trang 8close to the blade trailing edge Among the four RANS
mod-245
els, the DRSM works better than the others Finally, the
lar-246
gest corner separation is given by the SA model
247
Although LES gives the best prediction of the corner
sepa-248
ration, it is still too expensive to conduct the influencing
249
parameter studies RANS over-predicts the corner separation,
250
but gives qualitatively reasonable trends Along with the
anal-251
ysis about incidence angle effect in Section4.4.1, the results in
252
this section heighten confidence in using RANS approach to
253
continue the parametric studies in the following sections
254
4.3 Numerical parameters
255
4.3.1 Spatial interpolation scheme
256
It is interesting to study if the spatial scheme influences the
pre-257
diction of the corner separation Four different upwind spatial
258
schemes are studied in comparison with the four-point
cen-259
tered scheme and artificial viscosity (Jameson33) chosen as
ref-260
erence in this work These four upwind schemes are Roe
261
scheme,47AUSM scheme,48AUSM+-up scheme49and simple
262
low-dissipation AUSM scheme (SLAU).50Besides, in order to
263
bring some insights into the influence of the spatial scheme
264
order, a 1st-order upwind scheme and a 3rd-order monotone
265
upwind scheme for conservation laws (MUSCL) scheme are
266
also compared with a 2nd-order upwind scheme (as reference),
267
using FLUENT with DRSM model
268
The comparison of the static pressure coefficient on the
269
blade is drawn inFig 9 The results of the first five different
270
spatial schemes are strictly superimposed InFig 10, the total
271
pressure loss coefficient CPt contours are illustrated on a plane
272
downstream of the compressor cascade Their
pitchwise-mass-273
averaged values CP
t are plotted inFig 11 Again, it shows no
274
discrepancy for the first five different spatial schemes In the
275
present RANS simulation, the corner separation is insensitive
276
to these first five spatial interpolation schemes Moreover, it is
277
believed that the spatial scheme is not the cause of the
over-278
predicting of the corner separation
Fig 8 Blade suction side velocity profiles
Fig 6 Pitchwise-mass-averaged total pressure loss coefficient
Fig 7 Schematic of boundary layer profile measurement
stations and velocity decomposition method
Trang 9279 The last three spatial schemes are compared using
FLU-280 ENT with DRSM model Differences between them and the
281 first five spatial schemes may be due to the different solvers
282 and different RANS models At midspan, as plotted in
283 Fig 9, the CPlines of the DRSM results are overlapping,
sug-284 gesting that all of the three orders of spatial scheme are able to
285 capture the flow physics However, some discrepancies appear
286 close to the endwall on the suction side (seeFig 9(b)) from x/
287 ca= 0.4 to the trailing edge The results of 2nd-order and
3rd-288 order schemes are superimposed, differing from the 1st-order
289 scheme It means that in this case, the 1st-order scheme is
290 insufficient, while the 3rd-order scheme is lavish as it uses more
291 resources and provides the same results compared with the
292
2nd-order scheme The same conclusion can be drawn through
293
the total pressure loss comparison The total pressure loss
coef-294
ficient contours are shown inFig 10 The 1st-order scheme’s
295
results are observed different from the 2nd-order and
3rd-296
order ones The mixing process is slower for the 1st-order
297
scheme, which shows a gradual gradient across the high loss
298
region The plot of CP
t of the last three spatial schemes is
299
depicted inFig 11, and the 1st-order scheme is found to differ
300
from others throughout the spanwise direction
301
4.3.2 Artificial viscosity of centered spatial scheme
302
When a centered spatial scheme is used to simulate a flow for
303
the convection terms of each governing equation, it is
neces-Fig 9 Influence of spatial interpolation scheme on CP
Fig 10 Influence of spatial interpolation scheme on CP t
Trang 10304 sary to employ an artificial viscosity to stabilize the
calcula-305 tion The definition of the numerical dissipative flux Fdj, at
306 the face indexed j 0.5 for a conservative quantity q, can be
307 found in Ref.41:
308
Fdj ¼ Vðu a þ cskakÞ e 4ðqjþ1 3qjþ 3qj1 qj2Þ=8 ð1Þ
310
311 where e4is the 4th-order artificial viscosity coefficient, while V,
312 u, a, csand j are the cell volume, velocity vector, contravariant
313 vector, speed of sound and index of grid, respectively
314 Smati51 suggests to set e4 between 0.01 and 0.15 for a
315 RANS simulation Nevertheless, it is desirable to know how
316 the artificial viscosity influences the simulation of the corner
317 separation Two simulations, with e4= 0.02 (reference) and
318 0.01, are carried out to investigate the influence of the artificial
319 viscosity on the description of the corner separation The
com-320 parison of CP, CP tand CP
tis shown inFigs 12and13 No
dis-321 crepancy can be seen between the ‘‘RANS reference” case and
322 the ‘‘viscosity 0.01” case Within the present range of values of
323 e4, there is no sensitivity to the artificial viscosity
324
4.3.3 Outlet boundary condition
325
Outlets need to be carefully treated in numerical simulations
326
because the outlet boundary condition controls the
confine-327
ment of the waves Moreover, if the outlet region is not long
328
enough, it may impact the mixing process In the present
329
study, the computational domain extends over 2c downstream
330
of the blade trailing edge, and the mesh is stretched near the
331
outlet plane Two outlet boundary conditions are tested here:
332
one is a standard pressure outlet condition; the other is the
333
pressure outlet condition mixed with a non-reflection outlet
334
condition, which allows a partial evacuation of the waves
335
out of the computational domain The comparison between
336
these two outlet boundary conditions is available inFigs 12
337
and 13 No difference is observed between the results This
338
implies that there is no spurious confinement effect in the
sim-339
ulations, since it would be influenced by the change of the
out-340
let condition
341
4.4 Physical parameters
342
4.4.1 Incidence angle
343
Incidence angle is an important physical parameter of corner
344
separation Numerical results for five incidence angles are
345
investigated in comparison with the experimental results The
346
static pressure coefficient around the blade, at midspan and
347
near the endwall is plotted inFig 14 The evolution of the
sta-348
tic pressure coefficient at midspan is fairly predicted by RANS
349
As proposed by Ma,52a characteristic point is identified on the
350
blade suction side near the leading edge, denoted by B in
351 Fig 14(a) at x/ca= 0.2 CPat this point never varies whatever
352
the incidence angle changes Upstream of the point B, CP
353
decreases with the incidence angle, while CP increases with
354
the incidence angle downstream of this point The location
355
of B is fairly well identified by RANS These good results at
356
midspan suggest that the incidence angle in the experiment,
357
which is rather difficult to precisely evaluate, is indeed the
358
same as that in the simulations The distribution of CPnear
359
the endwall is shown inFig 14(b) When the incidence angle
360
increases, the outset of the constant CPregion on the blade
361
suction side moves upstream, suggesting an earlier outset of
362
the corner separation The extent of the separation region is
363
thus increased by augmenting the incidence angle The
charac-364
teristic point B is again identified on the blade suction side;
Fig 11 Influence of spatial interpolation scheme on CPt
Fig 12 Influences of artificial viscosity and outlet boundary condition on CP