a numerical investigation of loss coefficient variation in

A NUMERICAL INVESTIGATION OF LOSS COEFFICIENT VARIATION IN VARIOUS INCIDENCE ANGLES IN TANDEM BLADES CASCADE

Arash Soltani Dehkhaqani Amirkabir University of Technology

(Tehran Polytechnic) Tehran, Iran

Masoud Boroomand Amirkabir University of Technology


Hamze Eshraghi Amirkabir University of Technology


ABSTRACT There is a severe tendency to reduce weight and increase

power of gas turbine. Such a requirement is fulfilled by higher pressure ratio of compressor stages. Employing tandem blades in multi-stage axial flow compressors is a promising methodology to control separation on suction sides of blades and simultaneously implement higher turning angle to achieve higher pressure ratio. The present study takes into account the high flow deflection capabilities of the tandem blades consisting of NACA-65 airfoil with fixed percent pitch and axial overlap at various flow incidence angles. In this regard, a two-dimensional cascade model of tandem blades is constructed in a numerical environment. The inlet flow angle is varied in a wide range and overall loss coefficient and deviation angles are computed. Moreover, the flow phenomena between the blades and performance of both forward and afterward blades are investigated. At the end, the aerodynamic flow coefficient of tandem blades are also computed with equivalent single blades to evaluate the performance of such blades in both design and off-design domain of operations. The results show that tandem blades are quite capable of providing higher deflection with lower loss in a wide range of operation and the base profile can be successfully used in design of axial flow compressor. In comparison to equivalent single blades, tandem blades have less dissipation because the momentum exerted on suction side of tandem blades confines the size of separation zone near trailing edges of blades.

INTRODUCTION The history of tandem blades can be traced back to approximately six decades ago. Tandem cascade configuration varies from conventional cascade and be divided into two parts, forward and afterward airfoil. These two airfoils are placed in an axial direction with a small distance from each other in a row. The idea of this type of blades in turbomachinery is obtained from flap concept. Flaps are employed to transfer momentum from pressure side to suction side. Therefore, wings with flap arrangement can be operated in high deflection range without losing lift coefficient. Forming a new boundary layer over the afterward blade is the most basic concept of using tandem blades that allows the flow to reach high deflection without separation. Due to the reduced cross-section area of the flow between two blades, velocity increases and afterward blade suction side boundary layer thickness decreases. According to mentioned basis, values of losses resulting from flow separation and growth of boundary layer are decreased.

Bammert et al (1980) [1] designed and tested a four-stage compressor which consisted of a conventional rotor for the first stage and tandem configuration rotor for the others. The airfoils used in this type of compressor are NACA-65 and total pressure ratio on design point was obtained approximately 2.51with efficiency of 84. Saha et al (1996) [2] experimentally investigated low mach-number flow field in cascade and three various configurations (two tandems and one conventional type) performances are compared with each other. Conventional airfoils were CDA43 type and tandem airfoils compounded of CDA21-21 and CDA32-21. Canon and Willinger (2005) [3] numerically explored steady-state

Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014

November 14-20, 2014, Montreal, Quebec, Canada

IMECE2014-39881

1 Copyright © 2014 by ASME

incompressible flow in cascade. FLUENT 6.1 was used for analysis and k-ε turbulence model was selected. The first and second airfoils in referred investigation consisted of NACA651210 and NACA652110 respectively and structured mesh was generated for 16 different states by GAMBIT. Qiushi et al (2008) [4] explored stator inflow properties with tandem layout by using two-dimensional numerical analysis. In conducted research airfoil’s stagger and flow inlet angle were constant and optimized tandem configuration to achieve the minimal loss coefficient was acquired by changing axial overlap and percent pitch parameters. McGlumphy et al (2009) [5] investigated two-dimensional numerical analysis within tandem cascade by employing ADPAC code. NACA65 was used for airfoils and axial overlap and percent pitch changes impact on the cascade performance has been studied.

NOMENCLATURE M Mach number P Static Pressure (Pa) Re Reynolds number W Velocity (m/s) 11 Inlet of Forward airfoil 22 Outlet of Afterward airfoil O Stagnation Point FA Forward Airfoil AA Afterward Airfoil

effK Effective Conductivity

J Diffusion Flux T Temperature

hS Generated Heat

1X Vertical Distance between Forward Airfoil Trailing Edge and Afterward Airfoil Leading Edge

2X Vertical Distance between Forward Airfoil Leading Edge and Afterward Airfoil Trailing Edge

t Minimum Horizontal Distance between Airfoils S Maximum Horizontal Distance between Airfoils AO Axial Overlap PP Percent Pitch

FAC Forward Airfoil Chord

AAC Afterward Airfoil Chord

OVC Effective Chord

11 Forward Airfoil Inlet Angle

12 Forward Airfoil Outlet Angle

21 Afterward Airfoil Inlet Angle

22 Afterward Airfoil Outlet Angle

FA Flow Deflection in Forward Airfoil

AA Flow Deflection in Afterward Airfoil Loss Coefficient

D Cascade Efficiency

pC Pressure Coefficient

GOVERNING EQUATIONS The present numerical analysis based on steady-state, tow-

dimensional, compressible and turbulent governing equation. Inlet flow mach-number in cascade inlet boundary is roughly 0.4. According to the critical much number for incompressible flow which is considered 0.3, compressible flow equations should be applied. Second order discretization used for equations and all equations are solved in pressure base method. Pressure based analysis takes advantages of pressure and velocity coupling to solve the equations. This method reduces number of iterations and therefore this strategy is used to simulate flow in the designed cascade.

Mass, momentum and energy conservation in general form for numerical analysis are expressed bellow respectively [6].

)1( mSv

t

).(

On the right side of the equation, mS is the amount of

added mass.

)2( Fgpvvvt

).().()(

Where is stress tensor, g and F are defined as gravity

force and external force respectively. In two dimensional problems, such as compressor blades cascade, solving two equation in X and Y directions is enough for momentum conservation.

Due to the fact that energy parameter is a scalar, like mass, energy equation is expressed as an equation.

)3(

)(.()( PEvEt

heffjjeff SvJhTK )).(.( Finally, the equation of state which is given bellow

completes system of equations.

)4( RTP So we have six equations and six unknown variables that

can be solved in terms of the mathematical solution.

TANDEM BLADES CONFIGURATION Tandem and conventional blades are very similar in terms

of geometry and aerodynamic parameters except two parameters which are defined for tandem blades that demonstrate relative position of two blades to each other.

These two parameters are called axial overlap and percent pitch. Tandem blades cascade and airfoils arrangement and notations of the terms are shown in Fig. 1.


As noted above, tandem blades have distinctive geometric parameters and notations. In order to introduce these terms, the following equations are presented.

(5)21 XXAO

(6)StPP Each of these variables is shown in Fig. 1.

Fig. 1: Schematic layout of tandem cascade

Solidity is one of the effective parameters on the cascade

performance which is defined for tandem cascade according to following equation.

)7( effeffeff SC

Each terms of solidity equation are defined in following

equations.

)8( )1()( AOCCC AAFAeff

)9( SAOSeff )5.01( Flow deflection in tandem airfoils is defined as follows for

forward and afterward airfoil respectively.

)10( 1211 FA

)11( 2221 AA

Total deflection is calculated by the following equation.

)12( AAFA

According to the recent researches on tandem airfoils configuration and the optimal distance between two airfoils, presented geometry parameters in Tab. 1 has been decided at design point [3],[9].

Value Parameter

5 AO (chord %) 85 PP (chord %)

0.0571)(mCeff

1.16 eff Tab. 1: Geometry parameters of tandem cascade

The conventional airfoil geometry parameters are the same

as tandem airfoil. Single airfoil chord and solidity are exactly equal to tandem airfoil effective chord and solidity. Also the base profile of two designs is the same.

NUMERICAL ANALYSIS OF CASCADE As mentioned before, the present numerical analysis is

based on steady-state, tow-dimensional, compressible and turbulent governing equation. Kω-SST turbulence model was selected according to the [7] in which this model was used to verify for Naca65-(12A2I8b)10 conventional airfoil. Simulation was performed for the cascade with two different Mach numbers and the results of numerical solution were compared to the experimental results of [7]. The Reynolds numbers of this research and our investigation are similar. Due to this fact, we would apply mentioned numerical solution on our research. The main purpose of numerical solution of present paper is to investigate the effect of incidence angle, in off design condition, on amount of loss coefficient. Second purpose is to investigate flow pattern in tandem blades in comparison to the conventional blade with same deflection. Finally the value of aerodynamic coefficient of tandem blades will be compared to the typical ones. Later, initial equations are presented to explain the theory of loss coefficient calculations:

(13) 1111

2211

PP

PP

O

OO

At the Equation (13) numerator and denominator represents total pressure changes through cascade and equivalent dynamic pressure, respectively [8].

In 2-D cascade for compressor blades, the efficiency is defined as same as for diffuser. It is noteworthy that compressibility parameter has been taken into account.

(14) )()( 22221111

1122

PPPP

PP

ooD

Pressure coefficient is another parameter to investigate

cascade performance and presents as;


Cp

the seco

perforefer

equa

D

rate

confcommthis perce

domto thmeshcan bvaliddiffereferthan mesh

and grid this, optimmeshshowshowand cells

C

casca

11

11

11PP

PP

O

At the abovestatic pressurnd term repreLift-drag ratiormance. Thirence [8]. The diffusion

ation (16).

()1(11

22

W

W

The terms reand deflectionComputationa

figurations anmercial softwarticle were Nent pitch fromUnstructured

main and highlyhe airfoil surfh density neabe observed cdity of bounderent values arences for K

one is attrihes this paramAfter determithe thickness independency4 grids with

mum mesh whes with variaws the variatiwn, the differ59304 cells w

s will be used

Cell Number (*1000) 38-47 47-59 59-77

Tab

Fig.2 demonade.

e equation, firre of any arbsents cascade io is anotheris value has

n factor or diff

2(

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22,11,

W

WW

eff

epresented in n rate of flow,al grid for nd conventio

ware Gambit NACA65-(10)

m each other. mesh was

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y on the accudifferent cell

was chosen. Taations of perfion of paramrence betweenwas less thanfor future wor

DiffusioVariati

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b. 2: Results o

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rst term of nubitrary point inlet static pr

r criterion tobeen calcul

fusivity is pres

)

equation (16) respectively every one o

onal blades 2.3.16. Airfo)10 with fixed

generated ructured meshucing boundancreases and y+ parameter

mesh. This pathe turbulenc

nce model theis parameter. e value less thah type and boyer, it is necesuracy of the l numbers werab. 1 shows thformance par

meters betweenn two meshesn 2% and therks.

on Factor ion (%) 101 605 509

of independenc

ptimum mesh

umerator repreon the blade

ressure. o analyze calated accordin

sented accord

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for computah was createdary layer mesvelocity variis used to stud

arameter may ce model. In e value one o

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rameters. Eachn two meshes with 47665e mesh with 4

Loss CoefficVariation (%

3.621.950.51

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h used for ta

(15)

esents e and

ascade ng to

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(16)

fusion

blades ed in ere in ap and

ational d close h, the ations dy the

have most

or less mented

mesh stigate fulfill

ed and ers of h row es. As 5 cells 47665

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andem

wth

b

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Fig. 2 As shown

with respect tohe selected m

Fig. 3

The gene

boundary cond

Fig. 4: C

During th

from -10 to +angle. Tab. 3 sandem cascad

2: Computatio

n before, the vo turbulence m

mesh which is u

3: y+ diagram con

erated mesh fditions was as

Computationa

he analysis, th+10 in order shows the flowde.

onal Grid used

value of y+ shmodel. Fig. 3 used for tande

of the selectednfiguration.

for convention the same as t

al Grid used focascade

he incidence anto compute

w conditions

d for tandem b

hould be less displays y+ di

em configurati

d mesh for tan

nal airfoil (Ftandem config

or conventiona

ngle varied 20the optimumand flow defl

blades

than one iagram of ion.

ndem

Fig.4) and guration.

al blade

0 degrees m incident flection of


Value Parameter 310447 Re

0.44 M

30.52 FA 33 AA

Tab. 3: Flow conditions and flow deflection of tandem cascade

RESULTS As described before, results were obtained in different

range of incidence angles. Fig.5 demonstrates static pressure coefficient of tandem structure along the forward and afterward airfoils at design point.

Fig. 5: Static pressure coefficient of tandem structure

According to the shown diagram, acceleration on suction

side of forward blade continues approximately up to 25% of effective chord from trailing edge. Accordingly, deceleration will be remarkable to trailing edge of forward blade. Pressure distribution on the pressure side is roughly equal and flow separation could happen.

According to the Fig. 5, flow behavior on the suction side of afterward blade is as same as for forward blade and acceleration continues up to 75% of effective chord from leading edge of afterward blade.

Diagram of loss coefficient and flow deflection in terms of flow incidence angle for tandem blades and equivalent conventional blade are shown in Fig. 6.

Fig. 6: Tandem and conventional blade cascade

characteristics

According to the graph, the minimum loss coefficient in tandem blades and typical blade occurs in -3 and -9 respectively. Increasing in incidence angle causes loss coefficient rising quickly. The loss coefficient and its growth rate increase by increasing incidence angle. This coefficient growth rate suddenly increases in tandem configuration after +5 and in conventional airfoil after 0 degree.

In Tab.4 loss coefficient, total deflection and diffusion

factor are presented for different scenarios.

DF Blade Type and Incidence Angle

0.343 16.57 0.0270 Conventional Blade, -9 0.49 23.13 0.0297 Tandem Blade, -3

0.535 19.694 0.1785 Conventional Blade, +5 0.671 29.925 0.0585 Tandem Blade, +5

Tab. 4: Tandem blades and conventional blade performance

As can be seen, total deflection value for minimum loss

coefficient for tandem blades has increased almost 40%, while loss coefficient only 10% has risen in comparison with single blade.

As mentioned earlier, diffusion factor is one of the investigated parameter for compressor cascade. Diffusion factor value for tandem structure is about 43% higher than equivalent one at minimum loss coefficient level.

Due to the calculated loss coefficient value, tandem blade lift-drag coefficient was predicted higher than single blade. Also numerical analysis upheld the claim and determined that this parameter in identical condition is far more for tandem blades. Fig.7 illustrates lift-drag ratio for various incidence angles for two structures.


Fig. 7: Lift-drag ratio for tandem and conventional blade

As can be seen, this ratio is maximized in 0 degree for

tandem blades and -6 degree for single blade. Diffusion factor values in these degrees are 0.559 for tandem and 0.405 for single blade. Analysis of this term shows that diffusion factor of tandem blades is far more than single blade at maximum lift-drag ratio.

Fig. 8 compares efficiency of tandem structure and single equivalent airfoil.

Fig. 8: Efficiency of tandem structure and single equivalent

airfoil According to the diagram, it is determined that efficiency

of tandem configuration is almost constant in a wide range of incidence angles (-4 to +4) and does not change substantially, while it drops sharply after incidence angle -1 for single blade.

Fig. 9 illustrates mach contour of two configurations on design point.

Fig. 9: Mach contour for tandem structure and single blade

on design point

Flow between two tandem blades prevents separation on suction side of afterward blade and causes uniform flow over second blade. Maximum Mach number for single blade and tandem blade is 0.64 and 0.581 respectively that occurs on the forward blade. By airfoil modification maximum Mach number would be declined and consequently inlet velocity can be increased. On account of stagnation point moving upward on the afterward blade, pressure side would be affected.

CONCLUSION A through CFD research has been conducted to investigate

the performance characteristics of the particular tandem cascade. The results indicate that tandem blades have an incredible ability to provide high loading with lower loss in comparison with equivalent single blade in wide range of operation. Due to momentum transfer to suction side of the afterward blade, separation zone at trailing edge of afterward airfoil will be minimized, and as a result of this phenomena loss coefficient will be lowered.

Tandem blades in comparison with equivalent single blade have higher lift-drag ratio and the difference percentage of this term in two mentioned configuration depends heavily on incidence angle.

Efficiency of tandem blades on off-design performance is preferable to the single blade in same condition. Due to the fact that this parameter is almost constant in a wide range of incidence angles, there is no concern to change incidence angel.

Increasing the loss coefficient in tandem blades is consistent with the increase in incidence angle. However in conventional blades, this rise is severe.

REFERENCES [1] Bammert, K. and H. Beelte (1980). “Investigations of an

Axial Flow Compressor with Tandem Cascades.” Journal


of Engineering for Gas Turbines and Power 102(4): 971-977.

[2] Saha, U. K. and B. Roy (1996). “Development of a New Tandem Cascade for Axial Flow Fan/Compressor Application.” International Journal of Turbo and Jet Engines. 13: 91.

[3] Canon, G. and Willinger, R. “Numerical Investigation of Flow Interference Effects in Tandem Compressor Cascades.” Proc. of the 17th International Symposium of Air Breathing Engines (2005). Paper No. 2005-1053.

[4] Qiushi, L., W. Hong, et al. (2010). “Application of Tandem Cascade to Design of Fan Stator with Supersonic Inflow.” Chinese Journal of Aeronautics 23(1): 9-14.

[5] McGlumphy, J., W.-F. Ng, et al. (2009). “Numerical Investigation of Tandem Airfoils for Subsonic Axial-Flow Compressor Blades.” Journal of Turbomachinery 131(2): 021018-021018.

[6] Anderson, J. D. (1995). Computational Fluid Dynamics: The Basics With Applications, McGraw-Hill Education.

[7] Dunavant, J. C., Emery, J. C., Walsh, H. C. and Westphal, W. R., 1955. “High-speed cascade tests of the NACA 65-(12A10)-10 and NACA 65-(12A2I8b)10 compressor blade sections”. Research Memorandum RM-L55I08, NACA, Washington, DC.

[8] Dixon, S. L. (2005). Fluid Mechanics and Thermodynamics of Turbomachinery, Elsevier Science.

[9] McGlumphy, J. (2008). “Numerical Investigation of Subsonic Axial Flow Tandem Airfoils for a Core Compressor Rotor”. PhD Thesis, Virginia Polytechnic Institute and State University

[10] Lieblein, S., (1965), “Aerodynamic Design of Axial-Flow Compressors”, NASA Report No. SP-36.


a numerical investigation of loss coefficient variation in

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