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Local convective heat transfer for laminar and turbulent flow in a rotor-stator system

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Abstract

The aim of this work is to show a better comprehension of the flow structure and thermal transfer in a rotor-stator system with a central opening in the stator and without an airflow imposed. The experimental technique uses infrared thermography to measure the surface temperatures of the rotor and the numerical solution of the steady-state heat equation to determine the local heat transfer coefficients. Analysis of the flow structure between the rotor and the stator is conducted by PIV. Tests are carried out for rotational Reynolds numbers ranging from 5.87×104 to 1.4×106 and for gap ratios ranging from 0.01 to 0.17. Analysis of the experimental results has determined the influence of the rotational Reynolds number, the gap ratio and system’s geometry on the flow structure, and the convective exchanges in the gap between the rotor and the stator. Some correlations expressing the local Nusselt number as a function of the rotational Reynolds number and the gap ratio are proposed.

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Abbreviations

c :

constant

C m :

=2 M / ρω 2 R 25, moment coefficient for one side of the rotor

C w :

= Q m / μr, mass flow rate coefficient

G :

= s / R 2, gap ratio

h :

local heat transfer coefficient (W.m-2.K-1)

J :

radiosity (W.m-2)

K 0 :

Kapinos parameter

m :

constant

M :

moment on one side of the rotor

n :

constant

Nu :

= hr / λ a , local Nusselt number on the rotor

\( \overline{{Nu}} \) :

mean Nusselt number on the rotor

Nu ∞ :

local Nusselt number on the free disc

\( {\overline{{Nu}} } \) ∞ :

mean Nusselt number on the free disc

Q m :

mass flow rate (kg.s-1)

r :

radial coordinate on the rotor (m)

R 1 :

inner radius of the study zone (m)

R 2 :

outer radius of the study zone (m)

r *:

=( r − R 1)/( R 2− R 1) dimensionless radius

Re :

= ωR 2 2/ν, peripheral rotational Reynolds number

Re * :

= ωr 2/ν, local Reynolds number

Re s :

= ωs 2/ν a , Reynolds number relative to gap between rotor and stator

s :

rotor/stator spacing (m)

T :

temperature (K)

U r :

radial velocity component (m.s-1)

U θ :

tangential velocity component (m.s-1)

x :

= r/R 2 , dimensionless radius

ε :

emissivity

λ :

thermal conductivity (W.m-1.K-1)

μ :

dynamic viscosity (Kg.m-1.s-1)

ν :

kinematic viscosity (m2.s-1)

ρ :

density (kg.m-3)

σ :

Stefan-Boltzmann’s constant (W.m-2.K-4)

φ :

heat flux (W.m-2)

ω :

rotational speed (rad.s-1)

a :

air

cd :

conductive

cv :

convective

lim :

limit

ray :

radiation

r :

rotor

s :

stator

∞ :

value far from the boundary layer

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Authors and Affiliations

  1. Laboratoire de Mécanique et Energétique, Université de Valenciennes et du Hainaut Cambrésis, 59313, Le Mont Houy, Valenciennes Cedex 9, France

    Rachid Boutarfa & Souad Harmand

Authors
  1. Rachid Boutarfa
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  2. Souad Harmand
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Correspondence to Rachid Boutarfa.

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Boutarfa, R., Harmand, S. Local convective heat transfer for laminar and turbulent flow in a rotor-stator system. Exp Fluids 38, 209–221 (2005). https://doi.org/10.1007/s00348-004-0900-5

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  • DOI: https://doi.org/10.1007/s00348-004-0900-5

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