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Numerical modelling of film cooling with and without mist injection

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Abstract

Two-phase CFD calculations, using a Lagrangian model and commercial code Fluent 6.2.16, were employed to calculate the gas and droplet flows and film cooling effectiveness with and without mist on a flat plate. Two different three dimensional geometries are generated and the effects of the geometrical shape, size of droplets, mist concentration in the coolant flow and temperature of mainstream flow for different blowing ratios are studied. A cylindrical and laterally diffused hole with a streamwise angle of 30° and spanwise angle of 0° are used. The diameter of film cooling (d) hole, and the hole length to diameter ratio (L/d) for both of geometries are 10 mm and 4, respectively. Also the blowing ratio ranges from 1.0 to 2.0, and the mainstream Reynolds number based on the mainstream velocity and hole diameter (Re d) is 6,219. The results are shown for different droplets diameters (1–10 μm), concentrations (1–5%) and mainstream temperatures (350–500 K). The centreline effectiveness and distribution of effectiveness on the surface of cooling wall are presented.

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Abbreviations

A :

area (m)

C :

concentration (kg m−3)

C D :

drag coeffieint

c p :

specific heat (J kg−1 K−1)

D :

mass diffusion coefficient (m2 s−1)

d :

diameter (m)

F :

force (N)

g :

gravity acceleration

k :

turbulence kinetic energy (m2 s−2)

k c :

mass transfer coefficient (m s−1)

h :

convective heat transfer coefficient (W m−2 K−1)

h fg :

latent heat (J kg−1)

M :

blowing ratio (ρ c u c/ρ ∞ u ∞ )

m :

mass (kg)

Nu :

Nusselt number (hd/k)

P :

pressure (N m−2)

Pr :

Prandtl number (ν/α)

R :

Reynolds stress tensor

Re :

Reynolds number (ρul/μ)

S :

source term

Sc :

Schmidt number (ν/D)

Sh :

Sherwood number (kcd/D)

T :

temperature (K)

t :

time (s)

t p :

particle relaxation time

α:

thermal diffusivity (m2 s−1)

ε:

turbulence dissipation rate (m2 s−3)

η:

adiabatic film cooling effectiveness ((Taw-T∞)/(Tc- T∞))

λ:

heat conductivity (Wm−1 K−1)

μ:

dynamic viscosity (kgm−1 s−1)

ν:

kinematic viscosity (m2/s)

ρ:

density (kg m−3)

τ:

stress tensor (kg m−1 s−2)

aw:

adiabatic wall

c:

coolant or jet flow

op:

operating condition

p:

particle or droplet

t:

turbulent

sat:

saturate

∞:

values far away from droplets

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, No.15, Pardis St., Mola Sadra St., Vanak Sq., Tehran, Iran

    Homayoon Kanani, Mehrzad Shams & Reza Ebrahimi

Authors
  1. Homayoon Kanani
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  2. Mehrzad Shams
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  3. Reza Ebrahimi
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Correspondence to Homayoon Kanani.

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Kanani, H., Shams, M. & Ebrahimi, R. Numerical modelling of film cooling with and without mist injection. Heat Mass Transfer 45, 727–741 (2009). https://doi.org/10.1007/s00231-008-0465-6

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  • DOI: https://doi.org/10.1007/s00231-008-0465-6

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