Nomenclature

General conventions for variable names:

• Symbol or numeric subscripts are not separated by underscores: Vx, Alpha1.

• Accents and descriptive subscripts are separated by underscores: Vt2_rel, mdot_stall.

• Stagnation quantities are denoted by a subscript letter oh: Po, ho_rel.

• Depending on context, concatenation of symbols is either: a product, such as rhoVx; or a stack along the first array dimension, like xrt.

The yaw angle, Alpha or \(\alpha\), is defined as the angle between the flow direction and the meridional direction:

\[\alpha = \arctan\left(\frac{V_\theta}{V_m}\right)\]

where \(V_\theta\) is the tangential and \(V_m\) the meridional components of flow velocity. In the rotating frame, the relative yaw angle, Alpha_rel or \(\alpha^\mathrm{rel}\), is defined as:

\[\alpha^\mathrm{rel} = \arctan\left(\frac{V_\theta^\mathrm{rel}}{V_m}\right)\]

The pitch angle, Beta, is defined as the angle between the meridional flow direction and the axial direction:

\[\beta = \arctan\left(\frac{V_r}{V_x}\right)\]

where \(V_r\) is the radial velocity component. Throughout the code, angles have units of degrees.

Symbol	Quantity	Units
a	Acoustic Speed	m/s
cp	Specific heat capacity at constant pressure	J/kg/K
cv	Specific heat capacity at constant volume	J/kg/K
gamma	Ratio of specific heats
h	Specific enthalpy	J/kg
mu	Dynamic viscosity	kg/m/s
P	Pressure	Pa
Pr	Prandtl number
rgas	Specific gas constant	J/kg/K
rho	Mass density	kg/m^3
s	Specific entropy	J/kg/K
T	Temperature	K
u	Specific internal energy	J/kg
x	Axial coordinate	m
r	Radial coordinate	m
t	Tangential coordinate	rad
m	Meridional coordinate	m
Omega	Shaft angular velocity	rad/s
y	Cartesian vertical coordinate	m
z	Cartesian horizontal coordinate	m
spf	Span fraction coordinate
V	Velocity	m/s
mdot	Mass flow rate	kg/s
Alpha	Yaw angle	deg
Beta	Pitch angle	deg
U	Blade speed	m/s
e	Specific total energy	J/kg
I	Rothalpy	J/kg
Ma	Mach number
A	Area	m^2
zeta	Surface distance coordinate	m