Whittle Laboratory Film Cooling Database

This repository contains a database of flat plate film cooling effectiveness measurements, and associated documentation.

Reading material

• Bogard and Thole (2006): review paper with good background information, but second half (VII. Airfoils and Endwalls; VIII. CFD Predictions) not so relevant for us.
• Taylor et al. (2019): paper from the Whittle Lab applying machine learning to compressor measurements.
• Fischer et al. (2020): scaling of film cooling experiments with different coolant gases.
• Ornano and Povey (2020): a comprehensive study on the choice of non-dimensional groups to characterise film cooling. A bit dense but some useful insights.
• scikit-learn documentation: one choice of machine learning library. We are most interested in Gaussian processes but could try other methods as well. Lots of tutorial/examples available elsewhere.
• Bayesian ensemble neural networks
  • Pearce et al. (2018): Theoretical background to the method.
  • Sengupta et al. (2021): Application with code on his GitHub.
• Correlations for film effectiveness with implementations in correlations.py
  • Baldauf et al.: cylindrical cooling holes.
  • Colban et al. (2011): shaped cooling holes only.

Geometry definitions

The largest cross-section that is fully enclosed by the hole, labelled $A_*$, over the metering section area $A_\mathrm{c}=\pi D^2 / 4$, defines the area ratio. In terms of diffusion lengths and angles,

$$\mathit{AR} = \frac{A_*}{A_\mathrm{c}} = 1 + \frac{4}{\pi} \left[ \left( 2 \frac{L_\phi^*}{D} \tan \phi + 1 \right) \left(\frac{L_\psi^*}{D} \tan \psi + 1 \right) - 1 \right]\,,\label{eqn:AR}\\$$$$

with,

$$\frac{L_\phi^*}{D} = \frac{L_\phi}{D} - \frac{1}{2\tan\alpha}\,,\quad \frac{L_\psi^*}{D} = \frac{L_\psi}{D} - \frac{1}{2\tan\alpha}\,. \nonumber$$

The width of the hole breakout at the hole axis defines the coverage width, $W$, which normalised by the hole pitch gives a coverage ratio $W/P$. The coverage ratio only depends on the lateral expansion parameters and the pitch-to-diameter ratio,

$$\frac{W}{P} = \frac{1}{P/D}\left(1 + 2\frac{L_\phi}{D}\tan \phi\right)\,. \label{eqn:W_P}$$

See util.py for an implementation of these formulae.

File format

There is one JSON file per published figure.

The root JSON object has keys:

• geometry
• dimensional
• flow
• metadata
• distributions each of which has nested fields given below.

Geometry

JSON field	Symbol	Units	Description
is_single_hole	-	-	True if a single hole, False if periodic row
alpha	$\alpha$	deg	Hole inclination angle
beta	$\beta$	deg	Hole compound angle
phi	$\phi$	deg	Hole lateral diffusion half angle
psi	$\psi$	deg	Hole forward diffusion full angle
Lphi_D	$L_\phi/D$	-	Hole lateral diffusion length
Lpsi_D	$L_\psi/D$	-	Hole forward diffusion length
is_x_origin_trailing_edge	-	-	True if $x=0$ at hole trailing edge, False if $x=0$ at hole center

Dimensional

JSON field	Symbol	Units	Description
Vinf	$V_\infty$	m/s	Main-stream velocity
Tc	$T_\mathrm{c}$	K	Coolant temperature
Tinf	$T_\infty$	K	Main-stream temperature
D	$D$	m	Hole diameter

Flow

JSON field	Symbol	Units	Description
DR	$\mathit{DR}$	-	Density ratio
BR	$\mathit{BR}$	-	Blowing ratio
Tu	$\mathit{Tu}$	%	Main-stream turbulence intensity
del_D	$\delta/D$	-	Boundary layer displacement thickness
Lam_D	$\Lambda/D$	-	Main-stream turbulence integral length scale
H	$H$	-	Boundary layer shape factor
Reinf	$\mathit{Re}_\infty$	-	Main-stream Reynolds number
Mainf	$\mathit{Ma}_\infty$	-	Main-stream Mach number
coolant	-	-	String for coolant gas, e.g. CO2
mainstream	-	-	String for main-stream gas, e.g. Air

Metadata

JSON field	Symbol	Units	Description
doi	-	-	URL for digital object identifier of publication
ref	-	-	Short key for publication author and year, e.g. Smith2000
fig	-	-	Figure reference within the publication, e.g. Fig8a
comment	-	-	Human-readable comment on this database entry
uncertainty_eff_abs	$\delta \varepsilon$	-	Typical measurement uncertainty in film effectiveness

Distributions

JSON field	Symbol	Units	Description
x_D	$x/D$	-	List of streamwise coordinates for measurement locations
eff	$\varepsilon$	-	List of effectiveness values at the measurement locations

Notes on calculating non-dimensionals

• There is one JSON file per published figure.
• If field takes a list of values, then the file contains data for multiple lines on the same axes (or a list of lists for distributions).
• Only one of $T_\mathrm{c}$ and $T_\infty$ are given, depending on what is specified in the description of experimental apparatus in the publication.
• Either $V_\infty$ for incompressible experiments, or $Ma_\infty$ for compressible flows is specified.
• Assume $p_\infty \approx p_\mathrm{c}$ for density calculation.
• We can get gas properties using the CoolProp library like this:

from CoolProp import CoolProp
T = 300.
P = 1e5
fluid_name = "Air"
# Constant
Mair = CoolProp.PropsSI("molar_mass", fluid_name)
# Function of temperature and pressure
cpair = CoolProp.PropsSI("Cp0mass", "T", T, "P", P, fluid_name)
cvair = CoolProp.PropsSI("Cv0mass", "T", T, "P", P, fluid_name)
muair = CoolProp.PropsSI("viscosity", "T", T, "P", P, fluid_name)