modelPelton

Information

Pelton Turbine Model

Mechanistic Pelton turbine model based on the Euler turbine equation and impulse turbine principles.

Figure: Key concepts of the Pelton turbine.

Shaft Power

The shaft power \(\dot{W}_s\) produced in the Pelton turbine is:

$$ \dot{W}_s=\dot{m}v_R\left[\delta(u_\delta)\cdot v_1-v_R\right]\left(1-k\cos\beta\right) $$

where:

• \(\dot{m}\) is the mass flow rate through the turbine
• \(v_R = \omega R\) is the reference velocity (\(R\) = radius of rotor where flow hits the bucket, \(\omega\) = angular velocity constrained by grid frequency)
• \(v_1=\frac{\dot{V}}{A_1}\) is water velocity at position "1" (end of nozzle), with \(\dot{V}\) = volumetric flow rate and \(A_1\) = cross-sectional area
• \(\beta\) is the reflection angle (typically \(\beta= 165^{\circ}\))
• \(k<1\) is a friction factor (typically \(k\in[0.8, 0.9]\))
• \(\delta(u_\delta)\) represents deflector mechanism to reduce velocity and avoid over-speed

Total Work and Friction Losses

Total work rate removed through the turbine:

$$ {\dot{W}_t} = {\dot{W}_s+\dot{W}_{ft}} $$

Friction losses:

$$ \dot{W}_{ft}=K\left(1-k\cos\beta\right)\dot{m}v_R^2 $$

with friction coefficient \(K=0.25\).

Nozzle Pressure Drop

Pressure drop across the nozzle (positions "0" and "1"):

$$ \Delta p_n=\frac{1}{2}\rho\dot{V}\left[\dot{V}\left(\frac{1}{A_1^2(Y)}-\frac{1}{A_0^2}\right)+k_f\right] $$

where \(A_0\) is cross-sectional area at nozzle beginning, \(A_1(Y)\) is area at nozzle end (function of needle position Y), and \(k_f\) is the nozzle friction loss coefficient.

Connectors

• TurbineContacts for connection to waterway and electro-mechanical units
• RealInput connector for angular velocity (typically from generator)

Parameters

User specifies: turbine runner radius, nozzle input diameter, runner bucket angle, friction factors and coefficients, deflector mechanism coefficient.

Note: This model has not been tested.

More info in: Resources/Documents/Turbines_model.pdf

Parameters

Connectors

Components