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Calculation of a three-dimensional turbulent cascade flow

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Abstract

A three-dimensional steady incompressible viscous flow through a plane cascade of turbine blades has been analyzed through a numerical method based on the Navier-Stokes equation. Particular attention is paid to the prediction of secondary flows occurring due to the endwall boundary layer and the blade geometry. A standard k-ε model is used for the modelling of Reynolds stress and boundary-fitted coordinates are adopted to represent the complex blade geometry accurately. Two differencing schemes are applied to the convective terms to investigate the effect of numerical diffusion. Experimental data obtained for the flows through the Langston cascade are selected for code validation. Computed results for the velocity vectors and static pressure distributions are in good agreement with presious measurements and provide validity of this numerical method. Three-dimensional viscous flow phenomena and the distribution of total pressure loss caused by secondary flows are also reasonably well predicted.

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Abbreviations

A w :

area of the control volume surface

a :

coefficient of the discretized equation

B :

product of the transformation matrix

b :

transformation matrix

C x :

axial chord of the airfoil

C p :

pressure coefficient \( = (p - p_1 )/\tfrac{1}{2}\rho _1 q_1^2\)

C pt :

total pressure loss coefficient \( = (p_n - p_t )/\tfrac{1}{2}\rho _1 q_1^2\)

\(\overline C _{pt}\) :

mass-averaged total pressure loss coefficient

C ε1, C ε2, C μ :

coefficients of the standard k-ε model

E :

constant used in the law of the wall

\(\vec e_x , \vec e_y , \vec e_z\) :

unit vectors in the Cartesian coordinate system

F :

mass flux through the control volume surface

f :

linear interpolation constant

G :

production term in the turbulent kinetic energy, or the contravariant velocity

J :

Jacobian

k :

turbulent kinetic energy

L :

characteristic length

l + :

nondimensionalized vertical distance from the wall

p :

pressure

p t :

total pressure

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, Seoul National University, 151-742, Seoul, Korea

    J. Y. Yoo

  2. Department of Mechanical Design and Production Engineering, Kunsan National University, 573-360, Kunsan, Cholla-bukdo, Korea

    J. W. Yun

Authors
  1. J. Y. Yoo
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  2. J. W. Yun
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Additional information

Communicated by S. N. Atluri, 4 September 1993

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Yoo, J.Y., Yun, J.W. Calculation of a three-dimensional turbulent cascade flow. Computational Mechanics 14, 101–115 (1994). https://doi.org/10.1007/BF00350278

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