Advantages of flywheels
They are very efficient
They last a long time without degrading
The recharge time is short
They can react and discharge quickly
They are environmentally friendly (don’t rely on chemicals to store energy)
Disadvantages of flywheels
They are much larger and heavier than other methods
The pose a safety risk as the wheel could break apart at high speeds
Energy can be lost through friction
If used in moving objects they can oppose changes in directions which can cause problems for vehicles
Increasing the energy stored in a flywheel
Increase the mass - the moment of inertia and hence the stored kinetic energy is directly proportional to mass
Increase the angular speed
Make it spoked - compared to a solid wheel, a spoked wheel of the same mass stores about twice as much energy
Reducing friction in flywheels
Flywheels lose energy to friction and air resistance
Lubrication
Levitate it with superconducting magnets - no contact with bearings
Operate them in vacuums or inside sealed cylinders to reduce drag from air resistance
Uses of flywheels - potters wheels
Controlled by a pedal so hard to apply a constant force
A flywheel is used to keep the speed of the wheel constant
Uses of flywheels - regenerative braking
In regular vehicles, applying the brakes causes the wheels to slow down, generating lots of heat
However, in some vehicles when the brakes are used a flywheel is engaged - charging it up
When the vehicles is ready to accelerate the flywheel can be used to turn the vehicle’s wheels
Uses of flywheels - wind turbines
Flywheels can be used to store excess power on windy days or during off-peak and give power on days without wind
Uses of flywheel - power grids
When lots of electricity is used in an area, the electricity grid can’t meet the demand
Flywheels can be used to provide the extra energy needed whilst backup power stations are started up
Uses of flywheels - riveting machines
An electric motor charges up a flywheel, which then rapidly transfers a burst of power as the machine presses down on the river
Useful as it stops rapid changes in power going through the motor - which could cause a stall
Also a less powerful motor can be used
Flywheels smoothing torque and angular velocity
In systems where the force supplied can vary a flywheel can be used to keep the angular velocity of rotating components constant
They deliver stored energy smoothly to the rest of the system
They can also smooth out force exertion by a system
Conservation of angular momentum
The angular momentum of a system remains constant unless external torque acts on the system
Isothermal changes
Changes that occur at a constant temperature so the internal energy of the gas doesn’t change
So the work done on or by a system is equal to the heat energy supplied
Q = W
Must take place very slowly in order for no energy to be transferred to dU
Adiabatic processes
No heat is lost or gained by the system so Q = 0 and dU = -W
So if work is done by the system W will be positive so internal energy will decrease
A change in temperature occurs as the internal energy only depends on temperature
Must take place fast enough that no energy is able to be transferred to the surroundings
Work done and constant pressure
For processes where the pressure doesn’t change W = p dV
For expansion the change in volume and the work done are positive
For compression the change in volume and the work done are negative
Work done and constant volume
No work is done W = 0 so Q = dU
So by transferring heat energy to he system you only increase its internal energy
P-V curves - isothermal
Smooth curve
area under the curve is work done
Curves are called isotherms
Position of isotherm depends on the temperature
Higher the temperature the further from the origin the isotherm will be
Adiabatic p-V diagrams
Similar to isotherms but they have a steeper gradient
More work is done to compress gas adiabatically rather than isothermally
Less work is done to expand has adiabatically rather than isothermally
Four stroke engine stages: induction
Piston starts at the top of the cylinder and moves down increasing the volume of gas above it
This sucks in a mixture of fuel and air through the open inlet valve
The pressure of the gas in the cylinder remains constant - just below atmospheric pressure
Four-stroke engine stages: compression
The inlet valve is closed
The piston moves back up the cylinder and does work on the gas, increasing the pressure
Just before the piston is at the end of this stroke, the spark plug creates a spark which ignites the air-fuel mixture
The temperature and pressure suddenly increase at an almost constant volume
Four-stroke engine stages: expansion
The hot air-fuel mixture expands and does work on the piston, moving it downwards
The work done by the gas as it expands is more than the work done to compress the gas, as it is now at a higher temperature. There is a net output of work
Just before the piston is at the bottom of the stroke, the exhaust valve opens and the pressure reduces
Four-stroke engine stages: exhaust
Piston moves up the cylinder and the burnt gas leaves through the exhaust valve
The pressure remains almost constant just above atmospheric pressure
Four-stroke Diesel engines
Undergo the same four strokes as petrol engines
But during the induction stroke only air is pulled into the cylinder, not an air-fuel mixture
Compression stroke - air is compressed to a high enough temperature that it ignites diesel fuel sprayed into the cylinder
For the indicator diagram there isn’t a sharp peak at the start of the expansion stroke - diesel burns it doesn’t explode
Assumptions for theoretical models for engine cycles
Same gas is taken continuously around the cycle - pure air with adiabatic constant = 1.4
Pressure and temperature changes can be instantaneous
Heat source is external
The engine is frictionless
First law of thermodynamics
Q = dU + W
Q is energy transferred by heating either to (+) or from (-) the system
dU is the change in internal energy
W is the work done to (-) or by (+) the system
Differences between theoretical and real engine diagrams
Rounded corners - inlet and exhaust valves take time to open and close
Heating doesn’t take place at a constant volume - pressure and temperature increase isn’t instantaneous
Theoretical model doesn’t include small amount of negative work it assumes the same air cycles around continuously
Area inside the loop is slightly less due to friction
Fuel is never completely burnt - so you can’t get maximum energy out and pressures are higher in theoretical model
Engines have an internal heat source, not an external one - temperature rise isn’t as large in the theoretical model due to the assumption of an external heat source
Heat is lost - not adiabatic, heat is lost to metal surroundings
Engine efficiency - mechanical efficiency
= brake power/indicated power
Engine efficiency - thermal efficiency
Thermal efficiency = indicated power/input power
Overall engine efficiency
Overall efficiency = brake power/input power
Second law of thermodynamics applied to engines
Heat engines must operate between a heat source and a heat sink (a region which absorbs heat from the engine)
1) Heat energy transferred from the heat source to the engine is Qh
2) Some of this energy is converted into useful work, W
3) But some of this energy (Qc) must be transferred to a heat sink, which has a lower temperature (Tc) than the heat source
4) This means engines can never be 100% efficient
CHP plants
Engines are very inefficient - lots of heat is is transferred to the surroundings
Combined heat and power plants (CHP) try to limit energy waste by using it for other purposes - e.g. Heating houses and businesses nearby
Markinch Biomass CHP plant in Scotland - excess heat is used to create steam to dry paper in the paper mill
Reversed heat engines
Operate between hot and cold reservoirs
Direction of energy transfer - heat energy is taken from the cold reservoir and transferred to the hot reservoir
For reversed heat engines sources and sinks are instead called hot and cold spaces
To transfer heat from a colder space to a hotter space work must be done
Refrigerators
Aims to extract as much heat energy from the cold space as possible for each joule of work done
The cold space is inside the refrigerator whilst the hot space is the room the refrigerator is in
Refrigerators keep enclosed spaces cool that can then be used to store perishable food to keep it fresh for longer
Heat pumps
Aims to pump as much heat as possible into the hot space per joule of work done
Cold space is usually outdoors and the and the hot space is the inside of the house
Used to heat rooms and water in homes
Coefficient of performance
A measure of how well the work done is converted into heat transfer
Similar to efficiency but can be above 1
E.g. Heat pump with coefficient of performance of 4 transfers 4J for every 1J of work done
Uses of flywheels
Potters wheel Regenerative braking Power grids Wind turbines Riveting machines Smoothing torque, energy delivery and angular velocity
Friction power
Net Torque
Indicated power - output power
Applied torque - frictional torque
Function of the crankshaft
Converts the up and down motion of the piston into rotational motion
What would happen to an engine if it didn’t operate between a heat source and a heat sink?
The engine will reach the same temperature as the heat source and so no more heat energy will flow
This is why the second law of thermodynamics and its application to heat engines so important
Flywheels in crankshaft
Flywheel maintains angular momentum, helping to take the crankshaft over dead centres
There is a variation in engine torque due to changes in engine pressure, the flywheel is used to smooth out these changes
The greater the flywheels moment of inertia, the less fluctuations there are in angular velocity over one cycle
Flywheel stores energy when the gas expands, doing work on the piston and uses this energy to compress the gas
How do you know if the overall change of internal energy of a cycle is zero?
The cycle will return to the same initial temperature
Change in internal energy is only dependent on temperature
Unit for angular momentum
kg m^2 s^-1
Law of conservation of angular momentum
Angular momentum of a system remains constant unless acted on by an external torque
Flywheel design features to store maximum kinetic energy
Put more mass at a greater radius (e.g. make it spoked) - increases moment of inertia, use a thin axle
Use high density materials - larger mass for a given size
Low friction bearings and smooth outer surface
Rotational speed limited due to the tensile strength of the material - due to the centripetal force acting on the material
Needs to be perfectly balanced to avoid any adverse gyroscopic effects
How does a heat pump obey the second law of thermodynamics and the law of conservation of energy?
Obeys 2nd law of thermodynamics as it operates between hot and cold spaces and work is done to move energy against the temperature gradient.
Obeys law of conservation of energy as although it delivers more energy than is supplied to it this is because the additional energy is the energy transferred from the hot space.
