---
author: Akbar Rahman
date: \today
title: MMME2047 // Turbomachinery // Turbines
tags: [ turbomachinery, turbines ]
uuid: 1690fa4a-086a-4c2e-b52e-8a6fe7ddb62c
lecture_slides: [ ./lecture_slides/T5 - Turbomachinery - with solutions.pdf ]
lecture_notes: [ ./lecture_notes/turbomachinery lecture notes(H Power).pdf ]
exercise_sheets: [ ./exercise_sheets/Turbomachinery-problems.pdf]
---

Turbines extract energy from a fluid, taking it from a higher head to a lower head state.

There are two types of turbines:

- reaction turbine --- essentially the inverse of a centrifugal pump (lecture slides p. 55-56)
- impulse turbine --- high pressure of the flow is converted into a high speed jet (lecture slides p. 57)

# Dimensionless Turbine Performance

The dimensionless groups are the same as in pumps:

\begin{align}
C_H &= \frac{gH}{n^2D^2} &\text{Head coefficient} \\
C_P &= \frac{P}{\rho n^3D^5}&\text{Power coefficient} \\
C_Q &= \frac{Q}{nD^3}&\text{Capacity coefficient} \\
\end{align}

However, in a turbine the efficiency is written as:

$$\eta = \frac{P}{P_w} = \frac{P}{\rho QgH}$$

Additionally, similarly to how pumps performances can be approximated as a function of only $C_Q$,
the performance of a pump can be approximated to a function of $C_P$:

\begin{align*}
C_H &\approx g_3(C_P)
C_Q &\approx g_4(C_P)
\end{align*}

![Performance curve for a Francis radial turbine](./images/francis_turbine_performance_curve.png)

The maximum efficiency point for turbines is called normal power.

## Power Specific Speed

Equivalent to specific speeds for pumps.

$$N'_{SP} = \frac{C_P^{\frac12}}{C_H^{\frac54}}$$

![Pump efficiency curves for different types of pumps.](./images/pump_efficiency_curves.png)

# Wind Turbines

There are two types of turbines: 

- horizontal axis wind turbine (hawt)
- vertical axis wind turbine (vawt)

The lecture slides (p. 65-70) detail the wind turbine theory, but this will not be assessed.

## Horizontal Axis Wind Turbine (HAWT)

![Picture of a HAWT](./images/hawt.png)

They come with a couple advantages:

- more efficient than VAWT
- taller than VAWT therefore more efficient

## Vertical Axis Wind Turbine (VAWT)

![Picture of a VAWT](./images/vawt.png)

- smaller than HAWT, therefore cheaper
- gearbox and generator can be put at ground level
- easier to build and maintain
- quieter
- can be used in places where wind changes frequently