Investigation of the Shear Flow Effect on Secondary Flow and

Losses in a Low Speed Axial Flow Compressor Cascade

Mahesh K. Varpe and A. M. Pradeep

Department of Aerospace Engineering

Indian Institute of Technology, Bombay

Mumbai, India 400 076

Email: maheshvarpe@aero.iitb.ac.

ABSTRACT

This paper explores the effect of a prescribed intense shear flow

on the flow structures in an axial flow compressor cascade. An

approximate shear flow is generated in the test section of an open

circuit cascade wind tunnel by using a planar grid of parallel rods

with varying solidity. To study only the effect of shear, a

compressor cascade based on NACA65 series with a relatively low

camber was chosen. The cascade was analysed experimentally as

well as computationally (using ANSYS Fluent). The computational

results of the cascade were compared with the available measured

data. The results agreed well with the experimental data. Detailed

analysis of the numerical results was then carried out to explore the

complex flow features caused by the shear flow in a cascade. With

uniform flow, the secondary flow was found to be negligible from

experiments as well as from the computations. Therefore, in an

attempt to amplify secondary flow, a shear flow generator was

placed upstream of the cascade. Experiments showed quite

contrasting results with shear flow, as compared to the uniform flow,

in terms of the wake loss. Numerical analysis revealed the

formation of vortices in the wake of the cascade due to secondary

flows caused by the incoming shear flow and other interesting flow

features.

Keywords: Shear flow, Low-camber, Secondary flow, Endwall loss,

Deviation.

NOMENCLATURE

a Mean-line designation, fraction of the chord from

leading edge over which loading is uniform at the

ideal angle of attack

Cp Static pressure coefficient, = (P2 - P1) / (1/2*ρ*U2)

Cp0 Total pressure loss coefficient, = (P01 - P02)/(1/2*ρ*U2)

H Blade span, m

h semi-blade span/ height of shear generator, m, =H/2

i Incidence angle, degrees

K0 Grid resistance

P.S Pressure surface of the blade

P1, P2 Upstream and downstream static pressure respectively,

Pa

P01, P02 Upstream and downstream stagnation pressure

respectively, Pa

Re Reynolds number based on chord length

S Pitch of blade, m

s Pitch/spacing between rods, m

S.S Suction surface of the blade

SWG Standard wire gauge

Turb. intensity = 2 2 2( ' ' ' ) / 3 /u v w U

U Mean inlet velocity, m/s

u, v, w Velocity components, m/s

u’, v’, w’ Fluctuating components of the velocity, m/s

x, y, z Cartesian coordinates

λ Velocity gradient, 1/s, =∂U/∂z

λ h/U Shear parameter

ωe End wall loss

σ Solidity of rods

INTRODUCTION

The secondary flow in a blade row is defined as any flow, which

is not in the direction of the reference (primary or stream wise) flow.

Hawthorne (1951) proposed that secondary flows are generated due

to the turning of the vorticity vector generated as a result of the

boundary layer approaching a row of blades. The strength of the

secondary flows is a function of the blade turning angle and the

incoming vorticity (Squire and Winter, 1951). In an actual

compressor, the spanwise gradient in velocity may be caused by

endwall boundary layers or by the presence of an upstream blade

row. Since the early work of Hawthorne (1951), extensive

publications are available on details of secondary flows. In a

modern day compressor with higher blade loading on low aspect

ratio blades, the effects of secondary flows are significant. This

obviously leads to a major loss in the performance and hence an

attempt to further enhance the efficiency encourages studying the

behaviour of flow in a cascade under shear flow at the inlet.

Various devices like rods, screens, perforated plates, honeycomb

etc. were used in the past, by researchers to generate an

approximate homogeneous, turbulent and nearly uniform shear

flow to study the turbulent structures that would help in developing

flow models. Most of the earlier methods to generate shear profile

were rather crude. Owen and Zienkiewicz (1957) developed a

mathematical approach to produce a desired velocity profile using a

grid of rods. The rate of shear and velocity profile suffers no

appreciable decay downstream of the grid from x/h = 1.2 ~ 4.2,

excluding the boundary layer region. The turbulence intensities are

maintained uniform by the constant mean shear downstream. The

shear flow generated did not accompany any large-scale secondary

flow. Based on Owen’s design, Livesey (1964) used a shear

parameter as high as 0.8 and obtained a symmetrically high shear

flow, which deviated from uniformity. In the near wall region,

reduced velocity can be obtained by changing the local solidity

International Journal of Gas Turbine, Propulsion and Power Systems October 2014, Volume 6, Number 2

Copyright © 2014 Gas Turbine Society of Japan

Manuscript Received on August 6, 2013 Review Completed on April 21, 2014

17

between the rods. Any profile decay, in the far downstream, was

attributed to the encroaching boundary layers and a change in the

sign of the shear flow at symmetry. The selection of suitable

resistance grading ensures a constant total pressure downstream of

the grid that eventually leads to a constant vorticity. Some

modification to the theoretical resistance grading of the rods is

necessary to achieve a non-decaying velocity profile(Livesey,

1964).

Lloyd (1966) compared the shear flow profile from the grid of

rods and flat plates and found that the former generated a less

accurate profile. The theory to generate shear profile with flat plate

fails for plates with a turbulence generator, in which case, a trial and

error method has to be adopted. Flat plates with turbulence

generators provide flexibility of varying turbulence and velocity

independently. With variation of velocity and turbulence intensities

with height, it is difficult to achieve a proper exchange of

momentum between the neighboring layers. The non-uniform flow

through the wire gauzes, in different configurations, has been

mathematically analysed by Elder (1959) and Davis (1962). Any

deviation of the measured velocity profile from the computed

profile, using Elder’s method, is attributed to higher order terms in

linearisation (1973). Tavoularis and Karnik (1989) demonstrated

shear flow with fair uniformity along the span, using strips of

selected wire gauzes based on an empirical approach. The

generated shear flow has a self-preserving structure with

unidirectional mean velocity downstream of the screens, Hergt

(2005). Higher shear rates with low turbulence intensities can be

generated by using the multiple screens in parallel (1959). Similar

shear profile is possible by honeycombs using the method

developed by Kotansky (1966).

The inflow disturbance (steady or unsteady) is one of the vital

parameter which affects the aerodynamic performance of an axial

flow compressor. Huges and Walker (2001) studied the transition

phenomena due to the variation of inflow disturbance periodicity in

an axial compressor. The inlet disturbance was produced by inlet

guide vane clocking. The study indicates that the length of the

unstable laminar flow regions and the transitional flow extends up

to 20% chord each. A similar investigation was carried out by

Hilgenfeld and Pfitzner (2004) with cylindrical bars moving

parallel to compressor cascade. The periodic variation of inlet

velocity caused a variation of 2 degrees in the incidence angle. This

induced the periodic variation of the blade loading. Large velocity

fluctuations inside the boundary layer reduced the time-mean

momentum thickness significantly compared to the steady ones.

This was attributed as a potential cause for loss reduction effects.

Brandt et. al. (2002) demonstrated by the numerical study that

thicker inflow boundary layer shifts the roll-up point of the tip

leakage vortex upstream towards the leading edge. The thicker

boundary layer at the inlet adversely affects the stall mass flow

similar to higher tip clearance. Choi et.al (2008) found the adverse

effects of inlet boundary layer thickness on the rotating stall in an

axial flow compressor. The study reveals that the size of the hub

corner stall is proportional to the inlet boundary layer thickness at

higher blade loading. It is also a major contributor to the first

disturbance which triggers the rotating stall. The performance

drops sharply in the presence of thicker boundary layers at higher

flow coefficient. Zaki et. al. (2010) has well documented the

mechanism of boundary layer breakdown to turbulence on the

blade surface under the influence of turbulence intensity as a source

of inlet disturbance. The numerical investigation by Varpe and

Pradeep (2013) show that the shear flows reduces the tip leakage

losses considerably in terms of kinetic energy associated with it. It

also limits the majority of the blade loading towards the blade

midspan irrespective of the tip clearance. The inlet shear flow

induces substantial endwall effects for the tip leakage to influence

which deleteriously affects the total pressure loss in the wake. Lee

et. al. (2014) investigated, through numerical study, the effects of

idealized local shear flows on the two dimensional airfoil and

proposed a lift correction model. The study indicates that the high

shear rate in a flow causes substantial changes in the lift coefficient

and is proportionate to the reference velocity at the inlet.

The secondary flows interact with the corner vortices and the

wall boundary layers leading to complicated loss sources. It also

influences the outlet angle of the flow (Hawthorne, 1956), which

may produce off- design conditions for the downstream row of

blades. Secondary flows are influenced by the inlet vorticity and the

camber angle of the blade. In an actual multistage axial flow

compressor, the spanwise gradient in velocity may be caused by the

growing endwall boundary layers or by the presence of an upstream

blade row. Therefore, with the aim to study only the effect of shear

flow on an axial flow compressor cascade, the camber angle chosen

was relatively low. The secondary flow in this cascade

configuration can be amplified by a simulated shear flow at the inlet

of the cascade. Since the camber of a typical turbine blade is quite

high compared to the blade of an axial flow compressor, the

secondary flows are stronger. Hence, most of the literature related

to the secondary flow is on turbine cascades. The inflow

disturbance, as found in published literature, was preferably in

pitchwise direction only. Therefore, this paper explores the flow

physics of a low-speed axial flow compressor cascade in the

presence of a shear flow (spanwise variation).

SHEAR FLOW GENERATOR-DESIGN For the selected geometry of compressor blades for the

cascade, the camber angle was relatively low. Therefore, secondary

flow can be studied only by inducing it with an inlet vorticity. A

method of generating maximum shear with negligible decay

downstream has to be adopted. Amongst the various available

alternatives of designing a shear flow generator, it is important to

evaluate each, for suitability to a particular application. It is

difficult to find screens with varying porosity as desired for shear

flow generation. Specific shaped screen with constant porosity or

multiple screens with different gauges are cumbersome and

difficult to work with. Other options like honey comb and

perforated plates would render heavy drag that may subsequently

lead to considerable loss. This would also correspond to effective

resistance to flow and could cause rapid rates of decay of the

Fig. 1 Arrangement of rods in a planar grid with coordinate system

2 1 1 11 (1)02 1 2

1 0 0

1 2, - / , 1.1/ 1 , /0 1 2 02

yhKU K a h

where K P P U a K U y

velocity profile. Therefore, rods become an obvious

choice as they offer simplicity. Design details provided by

Owen and Zienkiewicz (1957) are limited only to weak

shear flows. Non-uniformity of the grid-generated

turbulent field limits the maximum solidity to about 0.4 ~

0.5 and the maximum shear parameter (λ h/U) to 0.45.

The restriction on the maximum solidity limits the

attainable maximum mean shear and, consequently, the

usefulness of a grid-produced flow of more intensely

JGPP Vol.6, No. 2

18

sheared flow.

To have stronger secondary flows in a cascade, the

near wall velocities should be as small as possible. With

higher mean velocity and large height of the test section,

one has to use aggressive values of shear parameter with workable size of the rods. Initially, using

the Eqn. (1), attempts were made to design a wire grid of SWG 9

(3.175 mm) and 20 (0.914 mm). An initial tension (pull) was

required to maintain the wires parallel to each other. However, this

was not successful as these wires were susceptible to yielding under

initial tension. Therefore, rods of 5 mm diameter were chosen.

After initial trial and error attempts, shear parameter as large as 1.2

and a grid resistance (K0) around 7 across the grid was achieved.

The distribution of the solidity up to the mid-span was then adjusted

to have a nearly uniform shear flow with lower velocity near the

endwall as shown in Fig. 2. The applied distribution of rods to the

experiments aided in achieving a strong shear flow unlike the

earlier published work that was limited to weak shear flow due to

non-uniformity of the grid generated turbulent field.

Fig 2 Grid solidity distribution, based on the analysis of Owen and

Zienkiewicz (1957)

EXPERIMENTAL SET-UP The experimental investigations were carried out in a low

speed, open circuit, cascade wind tunnel, shown in Fig. 3. A 55 kW

centrifugal blower to provide uniform flow at the inlet of test

section powers the facility. The test section is a rectangular duct of

cross section 690 mm x 150 mm to accommodate eight NACA65

(10)08 blades. The cascade arrangement along with the grid of rods

in the test section is shown in Fig. 4. The cascade parameters are

summarized in Table 1. The cascade was operated at a Reynolds

number of 2.1x105, based on the blade chord. A minor variation in

the inlet mean velocity of the approximate 0.5% was found at mid

span along the pitch-wise direction.

Fig. 3 Schematic diagram of open circuit cascade wind tunnel

TABLE 1. Specification of the cascade.

Chord length (C) 115 mm

Stagger ( ) 300

Solidity (C/s) 1.51

Aspect ratio (H/C) 1.3

Blade inlet angle ('β1

) 460

Blade outlet angle ('β2

) 7.50

Reynolds number 2.1x105

Fig. 4 Plan-view of the wind tunnel test section with shear

generator upstream of a cascade.

INSTRUMENTATION To acquire detailed information of the static pressure

distribution, a large number of pressure ports were provided on the

blade surface. Sixteen pressure taps of 2 mm diameter running

along the span, were embedded on the two blades forming the

central flow passage. On each surface of interest, 12 rows of ports

were internally connected to the pressure taps. The first row of

ports was 6 mm away from endwall, while the others were spaced 5

mm apart and the last row was located at the mid-span. The markers

in the Cp contour plots, discussed later in section 5.2.1, indicate

these measuring locations. This arrangement had a total of 192 taps

on the pressure surface and the suction surface. The static pressures

of each row, by masking remaining rows, were picked up by a 16

channel pressure transducer (from M/s Scanivalve Corp, USA).

The raw data was acquired and processed using the DSALINK©

software provided along with scanivalve. The total pressure

distribution and velocity vectors in the wake was measured using a

7 hole conical probe (from M/s Aeroprobe Inc, USA) placed at 24%

of the chord length behind the trailing edge of the cascade blades.

The diameter of the probe head was 3.2mm. At the inlet, located

one chord ahead of the leading edge of the cascade, the 7-hole

probe picked up velocity and static pressure. The estimated

uncertainty of the pressure measurements on the blade surface was

about 1% in static pressure coefficient values.

The endwall loss is obtained by subtracting the total pressure

loss at a location from that at the mid span. The pitch averaged

outlet flow angle at the midspan is taken as the reference outlet flow

angle for determining the secondary flow vectors. The secondary

flow vectors are non- dimensionalised with the inlet mean velocity.

COMPUTATIONAL STUDY To get a better insight of the effect of the inlet shear flow

(generated by the array of rods) on the cascade, a detailed

numerical analysis using ANSYS Fluent© was carried out. The

experimentally measured velocity profile was prescribed at the inlet

of the domain.

JGPP Vol.6, No. 2

19

Fig. 5 Plan-view of the multi-block structured mesh with the ‘O’

grid around the airfoil

x/C

Cp

0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

ExperimentCFD

(a) z/H= 50 %, mid-span

x/C

Cp

0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

ExperimentCFD

(b) z/H=4%, near endwall

Fig. 6 Cp on blade surface with experiment and CFD at i = 00

A multi-block structured mesh with ‘O’ grid attached to the

airfoil was generated using the grid generator, GAMBIT© and is

shown in the Fig. 5. A grid insensitivity analysis was carried out to

234

56 6

7 78

9

x/C

y/S

0 0.2 0.4 0.6 0.8 100.20.40.60.8

11.21.41.6

P.S

S.S

a) Experiment

34

56 67

77

8

8

9

9

x/C

y/S

0 0.2 0.4 0.6 0.8 100.20.40.60.8

11.21.41.6 b) CFD

P.S

S.S

LevelCp0:

1-0.43

2-0.34

3-0.25

4-0.17

5-0.08

60.01

70.10

80.18

90.27

100.36Cp

Fig. 7 Contours of Cp on endwall between the experiment and CFD

at i = 00

study the effect of different grid sizes on the cascade performance.

Based on this study, a mesh size of about 2.4 million was finalized.

This mesh was refined near the wall to capture the viscous effects

adequately. The y+ corresponding to this case was about 2.0. The

steady-state flow solution was achieved using κ-ω SST turbulence

model. To yield better accuracy by reducing numerical diffusion, a

third order MUSCL discretization was employed. SIMPLEX

method is used for pressure velocity coupling. For convergence of

the scaled residuals to 10-6 for all the equations, approximately

4000 iterations were required.

VALIDATION OF THE CFD WITH EXPERIMENTAL DATA

Comparisons of CFD and experiment with uniform flow at the

inlet, in terms of static pressure coefficients on the blade surface

and the endwall were carried out. The static pressure coefficients of

the blade surface at the mid-span and close to the endwall are as

shown in Fig. 6. At the mid-span, the CFD results agree closely

with the pressure distribution from the experiments. It obviously

indicates that numerical modeling with the prescribed boundary

conditions is reliable. Near the endwall, CFD model’s prediction of

the pressure distribution on the blade surface is poor. This may be

due to CFD model’s limitation to account for three-dimensional

separations induced by secondary flow and boundary layers of the

blade and the endwall. The other possible explanation for this

discrepancy could be the fabrication errors that might have altered

the flow conditions close to blade surface in the experiments.

The close agreement of Cp on the endwall between CFD and

experiment is shown in Fig. 7. As the ports on the endwall were

away from blade surface, influence of corner vortex is partly

captured.

RESULTS AND DISCUSSION

Shear Profile Generation The solidity distribution obtained from the shear flow theory,

generated a nearly stable velocity profile, but with considerable

velocity near the walls. To achieve maximum shear from the

available flow energy at the inlet, the velocity near the wall should

be as minimum as possible. Therefore, the spaces between the rods

were adjusted by reducing the gap between the endwall and the first

rod, and then fitting a smooth second order trend line. The resulting

velocity profiles generated downstream of the shear generator at

different axial locations, for i=±60, are shown in Fig. 8. The

measurement locations are with respect to the coordinates system

shown in Fig. 1. The velocity components u, v and w are along the

‘x’, ‘y’, and ‘z’ directions respectively. To check any variations in

the velocity profile along ‘y’ direction, the measurement was done

at y/s=±0.277 so that nearly a two-dimensional flow is generated in

an ‘x-z’ plane. As the flow proceeds downstream of the shear

generator, the peak axial velocity is reduced by the shear stress

produced from the resistance grading of the shear generator. The

turbulence produced by the small-scale shear between the

consecutive jets and wakes of the rods, increases the interaction

between the near wall flow region and the free stream flow. This

increases the mean velocity in the region near the endwall, as can be

seen in Fig. 8a. The overall effect is the reduction of the shear rate

in the downstream regions. Grid generated turbulence decays

downstream under the influence of the shear stresses. Thus, the

velocity field has a nature of self-preserving development of a

turbulent flow. The rate of profile decay is a function of the rod size.

Smaller the size of the rods, the more stable is the velocity profile.

However, fabrication of such a shear generator is very difficult.

There is, therefore, a compromise has to be made between the grid

size and the profile stability.

Among the lateral components, ‘z’ velocity variation along the

span of the grid is higher as seen in Fig. 8(c). This is because the

fluid under shear, on account of its reduced velocity in the

x-direction, readily acquires a motion in the z-direction in response

to the pressure gradient than the faster-moving fluid in the main

stream. Once a lateral flow is well established in the boundary

JGPP Vol.6, No. 2

20

layers, a compensating flow must appear in the main stream in

order to preserve continuity, which would occur under stable flow

z/Z

u/U

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6 x/h = 2.67x/h = 4.67, y/s = +0.277x/h = 4.67, y/s = - 0.277x/h = 7.88

( h)/U = 1.219

(a)

z/Z

v/U

0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1 x/h = 2.67x/h = 4.67, y/s = +0.277x/h = 4.67, y/s = - 0.277x/h = 7.88

(b)

z/Z

w/U

0 0.2 0.4 0.6 0.8 1-0.05

0

0.05

0.1

0.15

0.2

0.25x/h = 2.67x/h = 4.67, y/s = +0.277x/h = 4.67, y/s = - 0.277x/h = 7.88

(c)

Fig. 8 Span-wise variation of velocity components for ±60,

downstream of the plane of rods

conditions. In general, the velocity profile decays very slowly in the

interested region (with respect to the cascade test section)

downstream of the grid. Figure 8 shows that the magnitude of the

shear parameter (λh/U=1.219) obtained through experimentation is

close to the designed value. This indicates that a stable and strong

shear flows can be generated using a planar grid of rods.

Effect of Shear Flow on the Cascade Cascade performance parameters like blade loading, wake loss

etc. are greatly influenced by the incidence angle, as the apparent

camber or the flow turning angle changes with incidence.

Consequently, the flow physics gets affected. It was therefore

decided to evaluate the overall performance of the cascade, in the

incidence angle range of ± 60.

Static Pressure Distribution On Blade Surface The span-wise distribution and the contours of surface static

pressure on the blade at different incidences are shown in Fig. 9.

The left column shows the Cp distribution on the pressure surface

and right column shows on the suction surface. The shear-imposed

flow with boundary layer interaction renders minor variation of Cp

on the pressure surface at small incidences. However, on the

suction surface, the zones of low-pressure regions from the leading

edge to the trailing edge can be observed. With shear flow, the

dynamic pressure varies along the span. Since drag is a function of

the square of velocity, the span wise fluid layers towards the

midspan will experience relatively larger flow resistance from the

blade surface compared to those away from the midspan. Therefore,

any reduction in the dynamic pressure would correspond to a

proportional rise in the static pressure for the available total

pressure. This does not happen with uniform flow as the velocity is

almost constant along the span and the span wise static pressure

remains nearly invariant. In addition, the secondary flow that

prevails near the wall region carries fluid layers partly away from

the pressure surface towards the suction surface, (which is

discussed in the subsequent section), contributes to the drop in

static pressure on the pressure surface. Further, the total pressure is

one of the factors that influence the blade loading. It increases away

from the endwall in a shear flow. Therefore, the Cp on the blade

surface is higher for the locations away from the endwall. Since the

flow is sensitive to the curvature of the surface, the static pressure

rises on the concave surface. On the other hand, the static pressure

reduces on the suction surface. In the NACA65 (10)08 blade with

a=1, the pressure surface is relatively flat and in the operating range

of incidence, adverse pressure gradient on the suction surface

becomes severe. Near the pressure surface, the flow moves slowly

downstream from the stagnation point and then it is carried by the

accelerating flow from the leading edge of the suction surface and

the passage and later decelerates due to diffusion. As a result, the

pressure surface shows higher Cp towards the leading edge and

trailing edge of the blade. Near the leading edge, on the suction

surface, the contours are relatively denser than the rest of the

surface indicating rapid acceleration and subsequent gradual

deceleration of the flow. On the contrary, static pressure decreases,

rapidly and then gradually rises owing to diffusion in the later part

of the flow passage. Local dynamic pressure is influenced by the

curvature of the blade surface negotiated by the fluid stream and the

drag, which in turn gets affected by the incidence. As the incidence

increases, the static pressure, which is proportional to the local

dynamic pressure, rises on the pressure surface and reduces on the

suction rises along the span. The slope of the Cp contours depends

on the incidence and the shear rate of the flow at inlet. From the Fig.

9, it is observed that the slope of the contours on the suction surface

increases with the increase in the incidence, and increases on

pressure surface. This effect may be due to the local resultant

dynamic pressure influenced by the factors mentioned earlier.

7

x/C

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5L.E P.S T.E

6

67

x/C

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5L.E S.S T.E

i= - 60

8

8

x/C

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5L.E P.S T.E

4

5 6

6

7

7

x/C

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5L.E S.S T.E

i= 00

8

8

8

8

9

x/C

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5L.E P.S T.E

2

345

6

6

7

7

x/C

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5L.E S.S T.E

i= 60

x/C

z/H

0 0.2 0.4 0.6 0.8 100.10.20.30.40.5

LevelCp:

1-1.9

2-1.6

3-1.3

4-1.0

5-0.7

6-0.3

7-0.0

80.3

90.6

100.9

Fig. 9 Distributions of the static pressure coefficient on the blade

JGPP Vol.6, No. 2

21

surface for inlet shear flow, at different incidence angle

Surface Static Pressure - Endwall The pressure coefficients on the end wall at different

incidences are shown in Fig. 10. The region of flow acceleration

and deceleration shrinks and shift towards the leading edge with

increase in the incidence. This is also indicated by the Cp contours

on the suction surface. With increased incidences, the pitch wise

pressure gradient rises and encourages secondary flow near the

endwall. This leads to the separation point shifting towards the

leading edge. Static pressure ratio between the outlet and the inlet

on the suction surface side rises considerably compared to the

pressure surface side. This indicates that the pressure surface being

nearly flat, has relatively less contribution towards the rise in static

pressure.

The magnitude of the secondary flow depends on the balance

between the forces due to the pitch wise pressure gradient and the

inertia of the flow. As the incidence increases, the flow has to

negotiate a longer path owing to the apparent increase in the turning

angle by utilizing its energy. Therefore, the pitch wise pressure

gradient rises adequately relative to the inertia of the flow that leads

to stronger secondary flows. With increase in the incidence, in the

corner region formed by the endwall and the blade suction surface,

the static pressure contours retreat. This indicates the influence of

corner stall formed by the interaction of secondary flows and the

boundary layers of the blade and the endwall. The corner vortex

thus formed, siphons out the energy from the passage flow and

dissipates it. Therefore, the secondary flow not only forms a flow

blockage, but also contributes to loss mechanisms.

5 5

6 6

6

7

x/C

y/S

0 0.2 0.4 0.6 0.8 100.20.40.60.8

11.21.41.6

T.EL.E

S.S

P.S

5

6 6 6

77 7

7

8

x/C

y/S

0 0.2 0.4 0.6 0.8 100.20.40.60.8

11.21.41.6

T.EL.E

S.S

P.S

i= - 60 i = 00

34

56 6

7 78

8 8

99

x/C

y/S

0 0.2 0.4 0.6 0.8 100.20.40.60.8

11.21.41.6

T.EL.E

S.S

P.S

6 8

x/C

y/S

0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.6LevelCp:

1-0.3

2-0.2

3-0.1

4-0.1

50.0

60.1

70.2

80.2

90.3

100.4

S.S

i= 60

Fig. 10 Contours of Cp on the endwall with shear flow at the inlet

4

4

5 5

56

6

6

67

7

7

78

8

8

89

9

9

910

10

1010

y/S

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5P.S S.S

4 45 5

5

6

6

6

6

7

7

7

7

7

8

8

8

8

8

9

9

9

910

10

10

y/S

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5P.S S.S

3

44

5

5

5

5

6

6

6

6

7

7

7

78

8

8

8

9

9

9

910 10

y/S

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5P.S S.S

i= - 60 i = -30 i = 00

2 23

3

4

4

4

5

5

5

5

66

6

7

7

7

7

7

8

8

8

8

89

9 9

9

y/S

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5P.S S.S

4

45 5

5

6

6

6

6

7

7

7

7

8

8

8

8

9

9

9

y/S

z/H

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5P.S S.S

8

L e v e l

w :

1-0 .6

2-0 .4

3-0 .3

4-0 .1

50 .0

60 .2

70 .3

80 .5

90 .6

1 00 .8

P .S

C :p 0 i = 30 i = 60

Fig. 11 Contours of total pressure loss coefficient at 24% chord downstream from trailing edge at different incidence angle

JGPP Vol.6, No. 2

22

z/H

0 0.4 0.80

0.1

0.2

0.3

0.4

0.5 Uf i = 0Sf i =- 6Sf i =- 3Sf i = 0Sf i = 3Sf i = 6

Midspan

Endwall

i

e

(a)

D e v ia tio n fro m m id s p a n flo w

z/H

-1 5 -1 2 -9 -6 -3 0 3 6 9

0 .1

0 .2

0 .3

0 .4

0 .5

U f, i= 0S f, i= -6S f, i= -3S f, i= 0S f, i= 3S f, i= 6

P SS S

i

(b )

Fig. 12 Mass averaged: - a) endwall loss and b) deviation from the

midspan flow, along the span

Total Pressure Loss, Endwall Loss And Flow Deviation wrt

Reference Outlet Flow Angle In The Wake

The contours of the exit total pressure loss coefficient

superimposed by the secondary vectors in the wake of the blades

for different incidences are shown in Fig. 11. With shear flow at

the inlet, it is expected that a rise in total pressure loss would occur

with increase in the incidence as in the case of uniform flow. In

contrast, the contours of the total pressure loss indicate decrease in

the loss with increase in incidence, where as secondary flow

increases, but less intensely. This behavior can be attributed to the

significant turbulence generated by the planar grid of rods that

promotes intense mixing between the layers. Consequently, the

peak loss is alleviated and redistribution of loss occurs. With

increase in the incidence, the passage vortex becomes stronger and

The span-wise variation of the endwall loss and the flow

deviation from the midspan flow is shown in Fig. 12. With a shear

flow at the inlet, it is expected that a rise in endwall loss would

i (deg.)-6 -3 0 3 60

0.1

0.2

0.3

SF

UF

Cp

0

(a)

i (deg.)

Cp

-6 -3 0 3 60

0.1

0.2

0.3

0.4

SF

UF

(b)

i (deg.)

(de

g.)

-6 -3 0 3 620

25

30

35

SF

UF

(c)

2

i (deg.)

SK

E%

-6 -3 0 3 60

0.5

1

1.5

2

2.5

3

SF

UF

(d)

Fig. 13 Overall effects in the wake, with reference to incidence,

UF- uniform flow, SF-shear flow

occur in proportion to the incidence angle as in the case of uniform

flow. In contrast, the endwall loss contours show an opposite trend,

where as secondary flow is enhanced. This behavior can be

attributed to the significant turbulence generated by the flow as it

travels through the blade passage. The net intensity of turbulence

can be considered as the resultant of the grid generated turbulence

and the turbulence generated by the instability of shear stress

between the layers of shear flow while negotiating the flow path.

The secondary flow is influenced by the blade loading and

becomes stronger at higher incidence angle. Therefore, later

component of turbulence is relatively more intense for higher

incidences. The flow path to be negotiated by the shear flow

increases with the incidence angle. The low energy fluid in the

near wall region can negotiate the curvature of the path more

easily as compared to the flow away from the wall due to inertia.

However while doing so it also spends energy resulting in a

relatively slow moving chunk of fluid i.e. stalling zone. This in

combination with secondary flow induces the instability of the

shear stress between the fluid layers that manifest into second

intensity of resultant turbulence promotes mixing. As the flow

proceeds downstream the mixing process energizes the fluid in the

region close to the wall. Therefore the endwall loss reduces with

the increase in incidence angle. Since the endwall effects are

stronger in a shear flow conditions, the endwall loss is

considerable compared to uniform flow.

The strength of secondary flow is indicated by the

overturning cause in the near wall regions as shown in the Fig. 12b.

It appears that the influence of secondary flow is in 20% of the

span and becomes more intense with increase in incidence. This is

obvious as the blade loading, which influences the secondary flow,

increases with the rise in the incidence angle. Since the flow is

three dimensionally complex, under the influence of shear flow,

turbulence and secondary flow, for which the deviation trend

seems random in nature near midspan and appears to be nearly

sinusoidal along the span.

Overall Effect In The Wake The effect of intense shear flow on the blade and in the wake

were detailed in previous sections it is interesting to know, in

comparison with uniform flow, the gross effects in terms of

secondary kinetic energy, coefficient of total pressure loss,

coefficient of static pressure and exit flow angle with respect to

incidence angle.

As seen from the Fig. 13(a), with the increase in the incidence

of uniform flow, the rise in total pressure loss is small compared to

inlet shear flow. This occurs due to the tendency to the flow

separation from the suction surface owning to the increase in

apparent turning angle. It is expected to have the same behavior of

Cp0 with the intense shear flow but it is observed that the trend of

Cp0 is opposite to that with the uniform flow accompanied with

large magnitudes. This attributes to the turbulence produced by the

shear flow generator and the shear effect that promotes rapid

mixing. Higher turbulence delays the flow separation on the

suction surface by initiating early transition

of the wall boundary layers. Further the flow profile decays

gradually downstream that increase the momentum in the near

wall regions. The stall region formed near the trailing edge of the

suction surface is energized and therefore the resulting effect is the

reduction of loss with increase in incidence angle.

The coefficient of static pressure, as seen in Fig.13 (b), improves

with the incidence angle, irrespective of the inflow conditions.

This occurs owning to the increased blade loading with the flow

incidence. Since losses with the shear flow are higher in

comparison to uniform flow, therefore the corresponding pressure

rise is lower.

Similarly, the exit flow angle and secondary kinetic energy,

refer Fig.13 (c)-(d), exhibit the trend of Cp. However, the exit flow

angle is a function of incidence angle and deviation angle. The

enhanced secondary flows due to shear effect lowers the

magnitude of exit flow angle and increases the secondary kinetic

energy with inlet shear flow.

Wake -Secondary Flow Structure The critical point theory is a technique used to analyze the

flow structure near the wall surfaces to know the flow separation,

attachment and other 3D flow features. In this paper, this

technique is applied to the streamlines on a plane far away from

the wall surfaces to understand the complex flow structure using

streamlines only. The combined influence of shear effect,

JGPP Vol.6, No. 2

23

turbulence intensity and incidence angle makes the secondary

flow structure complicated. Therefore, it is interesting to

understand the secondary flow structure using critical point

analysis.

Figure 14 shows the variation of the secondary flow

structure with respect to incidence angle. At incidence angle of -60,

the saddle point ‘C1’ appears at 40% of pitch close to the endwall

and it connects the separation node ‘N1’ through a separating line

‘S1’. The node ‘N1’ is close to ‘C1’ and away from the midspan

region. This indicates that the flow in the wake is three

dimensional with a stable ‘N1’node. The separation lines prevent

the streamlines of the respective side from intersecting. This also

conveys that the vortex core is closer to the endwall region. At

incidence of 0o, the point ‘C1’ slightly moves leftwards and ‘N1’

toward the midspan. This attributes to the tendency of the

secondary flow to under-turn the flow at higher incidence and

lifting up of loss core away from the endwall region. An additional

separation node ‘N2’ appears. In critical point theory, since two

similar nodes cannot connect each other and therefore an

additional point ‘C2’ connects them through a separation lines

‘S2’ and ‘S3’ respectively. Further, at incidence at +6o, only the

node ‘N1’ and point ‘C1’ exits. Now the node ‘N1’ has slightly

moved towards the right side where as ‘C1’ continues to shift

y/S

z/H

0 0.2 0.4 0.6 0.8

0.1

0.2

0.3

0.4

P.S S.S

S1

C1

N1

(a)

y/Sz/H

0 0.2 0.4 0.6 0.8

0.1

0.2

0.3

0.4

P.S S.S

S1

N1

C1

N2

S3

S2

C2

(b)

y/S

z/H

0 0.2 0.4 0.6 0.8

0.1

0.2

0.3

0.4

P.S S.S

S1

N1

C1

(c)

i = - 60 i = 00 i = 60

Fig.14 Experimentally determined stream lines of secondary flow in the wake, normal to the exit flow angle, with SF at i = -6,0 and 6 degrees

a) With uniform flow

b) With shear flow

z/H = 0.04 and 0.5 z/H = 0.1 and 0.3 z/H = 0.1 , 0.3 and 0.5

Wake view Pitchwise view

C p 0 : 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0Tu rb . in te n s ity % :

Fig.15 Path lines superimposed with turbulence intensity, as predicted by CFD, in the wake and in the pitch wise view at different span wise

location

JGPP Vol.6, No. 2

24

leftward and towards the endwall. The combined effect of higher

intensity of turbulence and downstream decay of shear flow

alleviates the net loss and the flow appears to be less complicated

compared to 0o incidence. Hence, additional critical points ‘N2’

and ‘C2’ disappear.

Passage Flow Behavior The conventional instrumentation makes it difficult to probe

into the passage of the blades and the intrusive methods would

affect the flow. Therefore, CFD was used to explore the flow

structure along the passage. Comparison of the streamlines at

different positions along the span, with uniform flow and shear

flow are shown in Fig. 15. The static pressure in the region near

the wall is proportional to the local dynamic pressure evolved

under the influence of the inlet shear rate, curvature of the blade

surface and the drag. In the case of shear flow, the fluid layers near

the endwall are dominated by the pitch wise pressure gradient and

are deflected towards the suction surface. Secondary flow

encounters the boundary layers of the blade surface and suffers

further deceleration. Consequently, the rise in static pressure is

relatively higher compared to the flow away from the endwall,

which has higher inertia and is less influenced by the pitch wise

pressure gradient. As a result, the near wall flow, marked as ‘AB’,

climbs up on the suction surface. Further it pickups up the energy

from neighboring flow by the exchange of momentum and

undergoes a twist of 90o as indicated by ‘A1B1’ in Fig. 15. On the

pressure surface, with higher energy of the flow and a minor

variation of static pressure along the span, the fluid layers away

from the endwall would respond rapidly than those closer to the

endwall. Therefore, near the pressure surface, as the flow closer to

the endwall moves away from the pressure surface, the flow from

relatively higher span moves toward the endwall region to

maintain continuity. Streamlines in the pitch wise view on to the

suction surface and pressure surface clearly indicates the

magnitude of movement towards and away from the endwall.

In spite of the low camber of the blade, shear flow at the inlet

results in a complex three-dimensional flow in the passage.

Therefore, in the secondary flow definition, one has to choose the

primary or reference flow direction and carefully resolve velocity

vectors to obtain the secondary vectors. For an airfoil, a minimum

inlet velocity results in the lowest loss due to separation on the

suction surface of the blade. With shear flow, the total pressure and

velocity varies along the span. The separation point moves

towards the trailing edge with the position away from endwall. In

the region near the endwall, the flow is dominated by the pitch

wise pressure gradient. Along the span and away from the endwall,

the dynamic head counters the pressure gradient and promotes

delay in separation on suction surface, thereby reducing the

corresponding losses.

CONCLUSIONS In this paper, the effect of a prescribed shear flow on the flow

structures in an axial flow compressor cascade. A NACA65 series

blade with a relatively low camber was used for the compressor

cascade. The shear flow was generated in the test section of. Both

numerical and experimental approaches were used to understand

the flow physics through the compressor cascade under inflow

shear. The computational results of the cascade were compared

with the available measured data. The following conclusions can

be drawn from this study:

Profile decay downstream of the shear flow generator

can be controlled by choosing low resistance wire

gauges or rods provided the wires remain parallel to

each other without yielding.

Fluid layers near the endwall are turned through 900 by

the flow passage under the influence of shear flow at the

inlet.

Majority of the blade loading occurs towards the

midspan region due to the presence of relatively higher

energy fluid.

The grid generated turbulence reduces the endwall loss

with the increase in incidence angle.

The trend of static pressure coefficient, yaw angle and

the secondary kinetic energy in the wake with respect to

the incidence angle is similar to uniform flow case but

with an offset.

Secondary flows were successfully induced in a low

cambered compressor cascade using shear flow at the

inlet. This would aid in designing and evaluating

different control mechanisms to alleviate secondary

flows and the associated losses in a low speed

applications.

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