Turbomachinery Performance Coefficients Flashcards
Reminders of the formulae for various of the above (16 cards)
What is the annulus area?
The area of an engine air can flow through, found by Ax = π(r_casing^2-r_hub^2) = 2πr_meanh, where h is blade height
What is the effective flow area
A = Ax * cos(α)
What is represented by α?
Local flow angle, either relative or absolute depending on subscript
What is represented by Ψ?
Ψ represents stage loading coefficient, which is Δh/(U^2), proportional to work transfer/blade kinetic energy (since h refers to enthalpy change across stage)
What is represented by φ?
φ is the flow coefficient, and is found by Vx/U
What does Vx represent?
Axial velocity of flow (often assumed constant)
What does U represent?
Blade velocity, often approximated as uniform along short blades and constant across turbine stages
What does Λ represent?
Λ represents “reaction”, a measure of enthalpy increase across rotor, h_rotor compared to the increase overall for a rotor-stator pair, h_stage
Λ = h_rotor/h_stage
What does “s” represent?
”s” represents the “pitch” or spacing of the blades
What is Euler’s work equation?
h_02 - h_01 = U_2V_θ2 - U_1V_θ1
What does σ represent?
σ represents the slip factor, the discrepancy in flow angle off the back of a component from the ideal angle - σ = V_θactual/V_θideal
What is rothalpy?
Rothalpy is the quantity shown to be constant along a streamline in the Euler work equation: R = h_0 - UV_θ = h_0rel - 0.5U^2
What is the pressure rise coefficient?
ΔP_0 / (ρ* Ω^3 * D^5)
What is the power coefficient?
m[dot] * w_x / (ρ* Ω^3 * D^5)
What is the stagnation pressure loss coefficient?
Y_p = [loss of relative stag pressure due to irreversibility]/[reference isentropic dynamic pressure]
What is the simple radial equilibrium equation for isentropic flow?
An equation showing the distribution of enthalpy along a rotor blade: dh0/dr = Vx*dVx/dr + Vθ/r * d(rVθ)/dr
