diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/exercise_sheets/Turbomachinery-problems.pdf b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/exercise_sheets/Turbomachinery-problems.pdf new file mode 100644 index 0000000..cdebee5 Binary files /dev/null and b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/exercise_sheets/Turbomachinery-problems.pdf differ diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/images/cavitation.png b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/images/cavitation.png new file mode 100644 index 0000000..5f42cdf Binary files /dev/null and b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/images/cavitation.png differ diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/images/vimscrot-2023-03-13T10:07:58,750255090+00:00.png b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/images/vimscrot-2023-03-13T10:07:58,750255090+00:00.png new file mode 100644 index 0000000..2f69b29 Binary files /dev/null and b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/images/vimscrot-2023-03-13T10:07:58,750255090+00:00.png differ diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_notes/turbomachinery lecture notes(H Power).pdf b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_notes/turbomachinery lecture notes(H Power).pdf new file mode 100644 index 0000000..2604338 Binary files /dev/null and b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_notes/turbomachinery lecture notes(H Power).pdf differ diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_slides/T5 - Turbomachinery - no solutions.pdf b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_slides/T5 - Turbomachinery - no solutions.pdf new file mode 100644 index 0000000..050cb32 Binary files /dev/null and b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_slides/T5 - Turbomachinery - no solutions.pdf differ diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_slides/T5 - Turbomachinery - with solutions.pdf b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_slides/T5 - Turbomachinery - with solutions.pdf new file mode 100644 index 0000000..9932263 Binary files /dev/null and b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/lecture_slides/T5 - Turbomachinery - with solutions.pdf differ diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbomachinery.md b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbomachinery.md new file mode 100755 index 0000000..2061029 --- /dev/null +++ b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbomachinery.md @@ -0,0 +1,124 @@ +--- +author: Akbar Rahman +date: \today +title: MMME2047 // Turbomachinery +tags: [ turbomachinery ] +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 ] +exercise_sheets: [ ./exercise_sheets/Turbomachinery-problems.pdf] +--- + +Turbomachinery are rotating devices that add (pump for liquids; fan, blower, or compressor for gases at <0.02, <1 bar, and > 1 bar respectively) or extract (turbine) energy from a fluid. + +# Positive Displacement (PD) Pumps + +- PD pumps force fluid along using volume changes (e.g. bike pumps, the heart) +- All PD pumps deliver a periodic flow +- They deliver any fluid regardless of viscosity (dynamic pumps struggle with viscous fluids) +- They are self priming (will be filled automatically) +- They can operate under high pressures (300 atm) but low flow rates (25 m$^3$h$^{-1}$) +- flow rate can be only be changed by vary speed or displacement + +# Dynamics Pumps + +- add momentum to fluid by fast moving blades or vanes +- classified based on direction of flow at exit: + + - centrifugal + - axial + - mixed flow + +- fluid increases momentum while moving through open passages and extra velocity is converted to + pressure through exiting it into a diffuser section +- provide high flow rates (up to 70000 m$^3$h$^{-1}$) but usually at moderate pressure rises (a few atm) +- require priming + +# Centrifugal Pumps + +- fluid enters through eye of casing and gets caught in impeller blades +- fluid is whirled outwards until it leaves via the expanding area section, known as the diffuser or volute + +## Blades + +- backward inclined blades - most common and efficient, intermediate pressure rise, less robust +- straight blades - simplest geometry, high pressure rise, less robust +- forward inclined blades - more blades but smaller, lowest pressure rise, lowest efficiency, more robust + + +## Integral Analysis of Centrifugal Pumps + +Derivation in slides (p. 23-25). + +\begin{align} +\frac{w_s}{g} - \left(\frac{u_2-_1-q}{g}\right) = \left(\frac{p_2}{\rho g} + z_2 + \frac{v_2^2}{2g}\right) -\left(\frac{p_1}{\rho g} + z_1 + \frac{v_1^2}{2g}\right) \\ +H_s - H_f &= H = H_{T,2} - H_{T,1} \nonumber +\end{align} + +where $H_s$ is supplied head to pump, $H_f$ friction loss head, $H$ is head supplied to fluid, $H_{T,1}$ is total head at inlet, and $H_{T,2}$ is total head at outlet. + +Assuming that $z_1 \approx z_2$, $v_1 \approx v_2$ (from inlet and outlet diameters are equal) then: + +\begin{equation} +H \approx \frac{p_2-p_1}{\rho g} +\end{equation} + +and the power to the fluid (water horsepower) is: + +\begin{equation} +P_w = \rho QgH +\end{equation} + +where $Q$ is volumetric flow rate. + +Power supplied to the pump (brake horsepower), $P = \omega T$, lets us find the overall pump efficiency: + +\begin{equation} +\eta = \frac{P_w}{P} = \frac{\rho QgH}{\omega T} = \eta_h \eta_m \eta_v +\end{equation} + +where: + +- $\eta_h = 1 - \frac{H_f}{H_s}$ is hydraulic efficiency +- $\eta_m = 1- \frac{P_f}{P}$ is mechanical efficiency +- $\eta_v = \frac{Q}{Q+Q_L}$ (where $Q_L$ is loss due to leakage flow) is the volumetric efficiency + +## Performance + +![](./images/vimscrot-2023-03-13T10:07:58,750255090+00:00.png) + +# Cavitation + +Cavitation is when bubbles form in liquid by sudden pressure drop, followed by their implosion when +original pressure is restored. +The implosion generates a high pressure wave that can damage nearby solid surfaces. + +In a centrifugal pump, the fluid pressure drops at the impeller's eye, where it has the minimum +value. +If pressure falls below saturation pressure, bubbles appear. +Pressure grows as the fluid flows between the blades as the ducts are diverging. +Pressure is maximum at the trailing edge of the blades, on their front side. +This is where cavitation occurs and causes wear on the blade. + + + + + + +![](./images/cavitation.png) + +# Net Positive Suction Head (NPSH) + +The following conditions must be satisfied to prevent cavitation: + +\begin{equation} +H_i - \frac{p_v}{\rho g} > \text{NSPSH} +\end{equation} + +where $H_i = \frac{p_i}{\rho g} + \frac{v_i^2}{2g}$ is total head at inlet, $p_v$ is saturation +pressure at $T_i$. + +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). +