Theory questions Flashcards
- Define the pitch and the pitch ratio of a propeller. (2p)
The pitch P(x) at radius x is the distance every blade section screws itself forward in axial direction during one rotation.
The pitch ratio is defined as P(x)/D
- Define the velocities and angles relevant for describing the operation of a propeller blade section. (4p)
- Pitch angle, fi(x) - Angle of the blade
- Angle of attack, alfa - Attack of the flow measured from propeller centerline
- Advance velocity, V_A - Velocity of the incoming fluid
- Propeller velocity, V - Velocity of the propeller V=n*R
- Induced axial velocity, u_a - Inflow axial velocity
- Induced tangential velocity, u_t - Inflow tangential velocity
- Propeller rot. speed, n - Rotational speed [rpm]
- Deduce by help of a sketch how profile drag and lift contribute to thrust and torque. (2p)
T = z * int [ dL*cos(beta) - dR*sin(beta) ] Q = z* int [ dL*sin(beta) + dR*cos(beta) ]*r
- What is the benefit of adding skew to the propeller? (2p)
Adding skew will reduce vibration and voice without affecting the efficiency far too much.
- Describe the principles for an open water test. In which type of facility is it made? What is measured? How are the results presented? (3p)
The open water propulsion test is carried out with the propeller operating in a uniform inflow, either in a towing tank or in a cavitation tunnel. The propeller rotational speed is usually kept constant while the advance velocity, V_A, is varied. The thrust, T and torque, Q are measured. Depending on the characteristics of the equipment it might be necessary to vary the rotational speed as well as the advance velocity.
The advance velocity, rotational speed and diameter is then used for definition of the advance coefficient, J_A.
J_A = V_A / (n*D)
Furthermore, the thrust and torque coefficients K_T and K_Q are defined as:
K_T = T / (rho*n^2*D^4) K_Q = Q / (rho*n^2*D^5)
Power delivered is then found as:
P_D = 2pin*Q
And finally the open water efficiency eta_0
eta_0 = JK_T / (2pi*K_Q)
- Derive by applying momentum theorem an expression for the open water efficiency of a propeller. Neglect the rotation of the propeller race as well as viscous effects. (6p)
i) Momentum theorem force
ii) Momentum theorem volume flow
iii) Insert ii into i and solve for T
iv) Continuity equation yields A0
v) Insert iv into iii, express T
vi) Apply Bernoulli upstream
vii) Apply Bernoulli downstream
viii) Put vi into vii and solve for delta_p
ix) Use T=delta_p*A0 and viii to find an expression similar to the one in v
x) Solve u_A0
xi) Delivered power PD is obtained from increase of kinetic energy
xii) Finally insert xi and v into efficiency formula to solve the open water efficiency
- Describe the losses occurring for an open water propeller and their dependency on propeller diameter and rate of revolution. (3p)
AXL
- Axial losses due to the induced velocities u_Ainf left in the propeller jet far downstream.
ROTL
- Rotational losses caused by the rotation of the propeller jet
FRL
- Frictional losses due to viscosity
FBNL
- Finite number of blades
- Explain why you may gain propeller efficiency by choosing a larger propeller diameter. (3p)
The question is falsely asked. You cannot gain propeller efficiency by increasing the diameter, however you can increase the propulsive efficiency by increasing the diameter. Since a larger propeller does not need to push the fluid as fast as a small one to reach the desired thrust and velocity is proportional to resistance. Therefore, the propeller is less effective but the propulsive system is more efficient.
- Describe the principles for a self-propulsion test. What is measured? How are the results used? (3p)
The purpose of the self propulsion test is to determine the required power, PD and rotational speed, n of the propeller to reach a specific ship velocity.
The tests are done after scaling the Froude number. Due to that, the Reynold number will be far too low resulting in a too high viscous resistance. To avoid this, the propeller is unloaded with a towing force R_A.
The test is carried out as follows:
i) The model is towed to required speed
ii) The towing force is applied and the model is released. The propeller rotational speed is adjusted until equilibrium.
T = R-R_A or T=deltaR
iii) When equilibrium is established, thrust T, torque Q, rotational speed n and model speed V_M are recovered.
iv) The results from the self propulsion test are then used to determine the propulsive factors
- Thrust deduction factor, t
- Effective mean wake fraction, w_f
- Relative rotative efficiency, eta_R
- Total or propulsive efficiency, eta_D
- Derive by applying momentum theorem the towing force for a submerged body. (4p)
i) Momentum theorem, solve for R
ii) Mass conservation, solve for Q_0
iii) Insert i into ii and solve for R
- Explain why it is beneficial to have the propeller operating in the wake. You may exemplify by referring to momentum theory, but a complete derivation with all details is not necessary. (4p)
Due to viscous forces, a boundary layer will occur on the hull and increase the resistance. If the propeller is placed in the low velocity region, the momentum loss will decrease and thereby the resistance on the hull will also decrease.
- Why is towing a less effective way to move a ship than by a propeller? (3p)
Due to the wake region behind the ship. The propeller will increase the velocity behind the hull compensating for the boundary layer caused by the hull
- Define the nominal wake fraction (according to Taylor) and show by applying the Bernouilli equation how it can be measured. (3p)
Definition of wake fraction according to Taylor:
w_N = (V_S - V_A(r,fi) ) / V_S = 1 - V_A(r,fi) / V_S
where V_A is the local velocity without presence of the propeller and (r,fi) are the polar coordinates.
The nominal wake is usually divided into three parts:
w_N = w_f + w_d + w_w
w_f = Frictional wake (Velocity loss) w_d = Displacement wake (Pressure disturbances) w_w = Wave wake (Waves around stern)
From Bernoulli we receive:
p1(r,fi) + 0.5rhoV_A(r,fi) = P1(r,fi)
p1 = static pressure V_A = velocity in propeller plane P1 = Total pressure
When using a Prandtl-tube the nominal wake is directly obtained as:
w_N = 1- sqrt ( (P1-p1) / (0.5rhoV_S^2) )
V_S = inflow velocity
- Define the effective wake fraction and how it is determined. What is the difference in comparison with the nominal wake? (3p)
i) Determine KT from sel propulsion test
KT = T / rhon^2D^4
ii) Enter the open water characteristics with this KT-value and read the J_TM-value
iii) With J_TM, calculate effective mean advance velocity V_AT as:
V_AT = J_TMDn
iv) Find the effective wake as:
w_TM = 1 - V_AT / V_S = 1 - (J_TMnD) / V_S
The effective wake is taken from model tests whilst the nominal wake depends on full ship tests.
- Describe the character of the flow in a ship wake. Indicate how the nominal wake fraction is usually decomposed into three components, and briefly describe each component. (3p)
The wake fraction is often divided into three parts:
i) w_f, Frictional wake
Due to viscous forces a velocity loss will occur in the propeller plane
ii) w_d, Displacement wake
Due to that the hull displaces water there will be a pressure difference along the hull.
iii) w_w, Wave wake
Caused by the influence from the flow in the ship generated waves around the stern.
