add notes on pumps, turbines

uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbines.md

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+---
+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