add notes on pumps, turbines

uni/mmme/2047_thermodynamics_and_fluid_dynamics/pumps.md

@@ -1,8 +1,8 @@
 ---
 author: Akbar Rahman
 date: \today
-title: MMME2047 // Turbomachinery
+title: MMME2047 // Turbomachinery // Pumps
-tags: [ turbomachinery ]
+tags: [ turbomachinery, pumps ]
 uuid: 11f0f745-2364-4594-8e47-127a4af39417
 lecture_slides: [ ./lecture_slides/T5 - Turbomachinery - with solutions.pdf ]
 lecture_notes: [ ./lecture_notes/turbomachinery lecture notes(H Power).pdf ]
@@ -122,3 +122,80 @@ It is important that the inlet pressure is as high as possible.
 To do this, one can reduce frictional losses (e.g. shorter smoother pipes) or install the pump lower down
 (even below the reservoir) (slides p. 36).
 
+# Dimensionless Pump Performance
+
+Output variables for a pump's performance are pump head $H$ and brake horsepower $P$.
+Input variables are discharge $Q$, impeller diameter $D$, and shaft speed $n$.
+
+The dimensional relationships that we need are
+
+$$gH = f_1(Q, D, n, \rho, \mu, \epsilon)$$
+
+$$P = f_2(Q, D, n, \rho, \mu, \epsilon)$$
+
+Pi-theorem allows the following coefficients to be derived:
+
+\begin{align}
+\Pi_1 &= C_H = \frac{gH}{n^2D^2} &\text{Head coefficient}
+\Pi_2 &= C_P = \frac{P}{\rho n^3D^5}&\text{Power coefficient}
+\Pi_3 &= C_Q = \frac{Q}{nD^3}&\text{Capacity coefficient}
+\Pi_4 &= \text{Re} = \frac{\rho nD^2}{\mu}&\text{Reynolds Number}
+\Pi_5 &= = \frac{\epsilon}{D}&\text{Roughness Parameter}
+\end{align}
+
+Therefore it can be expressed that:
+
+\begin{align*}
+C_H &= g_1(C_Q, \text{Re}, \frac{\epsilon}{D}
+C_P &= g_2(C_Q, \text{Re}, \frac{\epsilon}{D}
+\end{align*}
+
+However for pumps it is assumed that Reynolds number and roughness parameter are constant
+for a set of similar pumps:
+
+![Pump Performance Coefficients vs $C_Q$](./images/dimensionless_pump_performance.png)
+
+Similar pumps are those which have the same design, other than the dimensions.
+Therefore it can be written that:
+
+\begin{align*}
+C_H &\approx g_3(C_Q)
+C_P &\approx g_4(C_Q)
+\end{align*}
+
+Pump efficiency is already dimensionless but can be related to the other dimensionless
+groups:
+
+$$\eta = \frac{C_HC_Q}{C_P} \approx \eta(C_Q)$$
+
+A nondimensional NPSH can also be defined:
+
+$$C_{HS} = \frac{g\cdot\text{NPSH}}{n^2D^2} \approx C_{HS}(C_Q)$$
+
+However, larger impellers for similar pump designs can lead to higher efficiencies, higher Reynolds
+number, lower friction head, and lower leakage low.
+
+# Mixed and Axial Flow Pumps
+
+Centrifugal pumps are high-head, low discharge machines, and therefore not suitable when high flow
+rates are required.
+
+For high flow rates, mixed-flow and axial-flow pumps are preferred.
+The flow passes through the impeller with an axial flow component and less centrifugal component.
+
+![Types of Pumps, showing how axial pumps differ from centrifugal pumps. ](./images/pump_types.png)
+
+## Specific Speed
+
+Specific speed is a nondimensional shaft speed which is obtained by eliminating the diameter
+between $C_Q$ and $C_H$:
+
+$$N'_S = \frac{C_Q^{\frac12}}{C_H^{\frac34}}$$
+
+There is also 'lazy' dimensional version which may be used by manufacturers:
+
+$$N'_S = \frac{N_S}{2734}$$
+
+where $N_S$ is the 'lazy' dimensional version, $N'_S$ is the dimensionless version.
+
+![Chart of Specific Speeds and Efficiency of Pump Types](./images/specific_speed.png)

uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbines.md

@@ -0,0 +1,79 @@
+---
+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