1. Characteristics of Turbomachines

Question 1

What is the formula for meridional velocity V(m)

Answer 1

• V(m)^2 = V(x)^2 + V(r)^2
• V(x) = axial velocity
• V(r) = radial velocity

Question 2

what is the continuity equation applied along a stream tube

Answer 2

• ρ V(m) 2pi r t = 𝑚̇ = const
• t = stream tube thickness
• r = local radius

Question 3

what is an assumption we can use for axial machines to simplify their analysis

Answer 3

• r is constant
• so V(r) = 0 meaning V(m) = V(x)

Question 4

what is the formula for the torque that the blades exert on the fluid T(f)

Answer 4

• T(f) = 𝑚̇(r(2)V(θ2) - r(1)V(θ1))

Question 5

what is the formula for the torque that the fluid exerts on the blade and why

Answer 5

• T(b) = -T(f)
• because the torque on the blade is equal and opposite to that on the fluid

Question 6

what is eulers work equation in terms of stagnation enthalpy h(0)

Answer 6

• h(0) - ΩrV(θ) = constant along a streamline
• Ω = blade/shaft speed

Question 7

what is the formula for relative stagnation enthalpy h(0,rel)

Answer 7

• h(0,rel) = h + 1/2*V(rel)^2

Question 8

what is the formula for V(θ,rel)

Answer 8

• V(θ,rel) = V(θ) - Ωr

Question 9

what is the formula for V(rel)^2

Answer 9

V(rel)^2 = V(m)^2 + V(θ,rel)^2

Question 9

what is eulers work equation in terms of relative stagnation enthalpy h(0,rel)

Answer 9

• h(0,rel) - 1/2Ω^2r^2 = constant along a streamline

Question 10

what are the 5 scenarios that eulers work equation is valid for

Answer 10

• flow along any stream tube
• steady flow
• adiabatic flow
• viscous and inviscid flow
• torque provided by the blades only

Question 11

what is eulers work equation in terms of power W(x)-dot

Answer 11

• W(x)-dot = 𝑚̇(U(2)V(θ2) - U(1)V(θ1))

Question 12

what is the formula for the local speed of sound c

Answer 12

• c = sqrt(γRT)

Question 13

what is the formula for the flow coefficient φ

Answer 13

• φ = V(m)/U

Question 14

what is the formula for the loading coefficient Ψ

Answer 14

• Ψ = dh(0)/U^2

Question 15

what is the formula for the loading coefficient Ψ if the radius is constant

Answer 15

• Ψ = dV(θ)/U

Question 16

what is the formula for the reaction Λ and what kind of enthalpies are being used

Answer 16

• Λ = dh(rotor)/dh(stage)
• these are static enthalpies

Question 17

considering the flow is usually nearly isentropic, what is an approximation for the reaction Λ

Answer 17

• Λ = dp(rotor)/dp(stage)

Question 18

what does a reaction of 50% for axial turbomachinery imply

Answer 18

• the velocity triangles are symmetrical
• and the stator and rotor blades have similar shapes

Question 19

what is the relationship between the reaction Λ across a rotor and a stator

Answer 19

Λ = dh(rotor)/dh(stage) = 1 - dh(stator)/dh(stage)

Question 20

what is the formula for the reaction Λ in terms of the flow and loading coefficients

Answer 20

• Λ =1 - [1/2*φ^2]/[Ψ(tan^2(a2) - tan^2(a1))]

Question 21

what do you need to remember about how to draw the rotors and stators for repeating axial compressors and turbines

Answer 21

• the rotor blades are always going up
• the stator blades are always going down
• the compressor has rotor then stator
• the turbine has stator then rotor