Numerical Simulation of Performance of an Axial Turbine ... · wkh remhfwlyh lw zdv frqvwuxfwhg d...

LIST OF SYMBOLS

H: Total enthalpyS: Scalar measure of the deformation tensorT: TemperatureT2: Temperature at exit of staged: Distance from the wallfv1, fv2, fw: Empirical functions in the turbulence modelkK: Constant in the turbulence modelp: Pressurest: Timeu: Velocity component in a Cartesian systemx: Cartesian coordinateg,r,S�˜

: Density

ij: Shear stress tensor

i, j, k

in, out : Inlet and exit conditions0

INTRODUCTION

In the past, the experimental method was the single tool

-ance of computational techniques in the last 40 years, another

-

at the design point is around ±2%, if one takes into account uncertainty in the numerical methods, models, geometry,

Numerical Simulation of Performance of an Axial Turbine First StageVinícius Guimarães Monteiro1,*, Edson Luiz Zaparoli1, Cláudia Regina de Andrade1, Rosiane Cristina de Lima2

1

2

Abstract: T is work s pr s nt d t rst st g p rfor n t d sign nd off d sign op r ting points of n xi tur in , wit two st g s using nu ri si u tion xp ri nt t ods of pr di ting t p rfor n of xi tur in is ost nd ti onsu ing o p r d to t o put tion uid d n i s ppro T r for , o put tion t ni u s w r dopt d to d t r in t st g p rfor n T is stud n d t rst st g p rfor n of n

xi ow tur in , using o put tion too for si u ting t st d st t two t r di nsion vis ous ow o put tion uid d n i s softw r w s us d to so v t r ns u tions wit t sp rt r s tur u n od T o put tion uid d n i s r su ts w r o p r d wit t os o t in d fro t n in oss od

od T o p risons v n ondu t d to provid pr t st p rfor n for t tur in rst st g

Keywords: xi Tur in s, s Tur in s, o put tion uid n i s, u ri Si u tion, rfor n

175J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 2, pp. 175-184, Apr.-Jun., 2012

Computational techniques are less costly and time-consuming if compared to the experimental approach to predict the

Dorney (2003) conducted a pretest performance for a

was to quantify the performance of the turbine at off- design

-tions were performed using a three-dimensional unsteady

uses a combination of the one-dimensional equations of

and they were used to help determining the locations of the

-

design and off-design performances of the 3D computational results are consistent with the mean line analysis used in the

-

losses than predicted by the mean line loss correlations and

the 3D computational results yield good agreement with the -

performance must be done at the beginning of an engine

satisfy all the operation requirements (design and off-design

Despite of 2D CFD approach limitations, it is important to

compared with the mean line loss model code ones, which

hub to tip of stator blade and rotor blade in the region near

parameters calculated by the 3D CFD simulations was made against mean line loss model code results generated by the

COMPUTATIONAL METHODOLOGY

Conservation equations

t

+ = 0x

ujj

(2)

uit xj

xjijxi

u

p

i uj

ui uj

Ht xj

u

p

Hj

uiui i j i jt

u Hj

xj

Tx

kj

t

176 J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 2, pp. 175-184, Apr.-Jun., 2012

TURBULENCE MODEL

blades (Pecnik t

-

of the Spalart-Allmaras turbulence model are expressed by

t = vt , = v fv1vt �˜

v +Uj = cb1 v - cw1 fwj

�˜ 2�˜�˜�˜

�˜ �˜

�˜

�˜

v

vk

�˜

dv

+ (v + v) +k

1 k k

cb2 v v

b1 b2 v1 = 2 3

k ² cw1 =cb1 +

(1 + cb2), cw2 = 0,3, cw3 = 2, k = 0,41

fv1 = fv 2 = 1 - fw = gX 3

X 3+ c3v1

1 + c6w3

g6 + c6w3

X

1 + X fv1

16

X = g = r + cw2 (r6 - r),

Sk 2d

2r =v�˜ v�˜�˜

,v

S = S + S = 2 ij ijk 2d 2

fv2 ,v�˜ �˜ (10)

The tensor ij=1 i

2j

j i is the rotation tensor and d

is the distance from t

BOUNDARY CONDITIONS

t t

conditions to the absolute reference frame were applied to the

computational cost, due to the numbers of blade rows neces-

reason, it was chosen the mixing plane approach in the stage

The boundary conditions used in the inlet and outlet of 2D

Total pressure inletTotal temperature inlet 1,100 K

Static pressure outletTurbulent intensity inlet

The walls for 2D and 3D approaches are adiabatic and

+ are smaller than six for the

of the wall is applied appropriately to the turbulent boundary layer, when

Numerical Simulation of Performance of an Axial Turbine First Stage


NUMERICAL METHODS

The 2D approach was simulated by ANSYS Fluent

is coupled, implicit, with a time marching to reach the steady state condition, and taking into account the turbulence effects

The 3D approach was simulated by ANSYS CFX soft-

CFX software for the 3D simulation, because the software

the turbulence effects by Spalart-Allmaras one-equation

The algebraic multigrid was employed to accelerate the

MESH GENERATION

The mesh was constructed for two sub-domains, one for

In the 2D model, the mesh is composed by quadrilaterals elements near to the blade region, in order to capture high

-

-

Figure 1 represents the mesh of all computational domains

The mesh constructed in the 3D model is composed by

made in regions where there are high gradients normal to the

MEAN LINE LOSS MODEL CODE The mean line loss model code uses a combination of the one-dimensional equations of motion in the mean line and

t

from hub to tip in regions near the leading and trailing edges

analysis used by the manufacturer in the conceptual design of

t


The performance maps constructed by CFD simulation

The loss model is established by means of applying boundary layer theories, basic thermodynamic equations, and

-

instance, attached blade boundary layers, the loss mechanisms

the loss mechanisms are still not clearly understood and

edge loss ( Te), tip leakage loss ( Tip), end-wall boundary layer loss ( b), shock loss ( s o k p

;

p Te Tip Eb

i

shock

HH T2

PERFORMANCE MAP

performance maps were constructed, which are the most

et

t), pressure ratio (rp orr), and corrected speed ( orr

(13)Hinin out

outt

HH H

p0 inprp0 out

(14)

mcorrm T0 inT0 in

TN

0Ncorr

in

RESULTS AND DISCUSSION

The

and rotor blades in the 2D simulation, which imply that the law of

It will be presented, at the design point operation, the

of these parameters calculated by 3D CFD approach was

The mean line analysis represents a good comparison tool

can be attributed to the fact that the design data do not take



distribution along the blade span, as mentioned by Tomita and

The boundary layer effects, in the hub and tip of the blade, are

Table 2 presents a comparison of design data against 2D

Descriptions Design data

2D CFD results

Difference (%)

3D CFD results

Difference (%)

- -

Pressure ratio

The difference between CFD results and design data is mainly due to one-dimensional characteristic of the mean

Similar conclusion can be obtained when comparing 2D and 3D

-

by empirical correlations (Kacker-Okapuu loss model), which

et

Leading edge

Trailing edge

Leading edge

Trailing edge


suction side of the rotor blade, which reduces the pressure

The present study also focused on the performance maps

but 3D CFD results are in better agreement with Denton loss

et


Leading edge

Trailing edge

Leading edge

Trailing edge


ratios, which produce chocking conditions at some point in

Chocking conditions happen when the pressure ratio is

CONCLUSIONS

-

concludes that the 3D CFD results are consistent with mean line

by the CFD simulation and mean line loss model using Denton

results are in better agreement with Denton loss model when

et


-

-ison is made against mean line loss model code, is the large

ACKNOWLEDGMENTS

The authors thank e So u es e nergi (VSE) for the

REFERENCES

et

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et Secondary Flow of a Transonic Turbine Stage Using

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Numerical Simulation of Performance of an Axial Turbine ... · wkh remhfwlyh lw zdv frqvwuxfwhg d...

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