ESL Results
Once a working simulation had been constructed, work could begin on exploring the effects of different model alterations on the output of the engine.
The areas to be investigated are as followed:
1. Varying input temperature
2. Different operating gases
3. Varying regenerative efficiencies
The areas to be investigated are as followed:
1. Varying input temperature
2. Different operating gases
3. Varying regenerative efficiencies
Varying Temperature Input
P-V Plots with Varying Hot Cap Temperature
In the ESL file the temperature to which the hot cap was heated could be easily altered. We experimented with various temperatures which we believed would be achievable from the heat source we were wishing to use for the testing of our optimized Stirling engine. The temperature range we looked at was 500K, 550K, 600K, 650K and 700K. Whilst it would have been possible to achieve a greater temperature we decided to stay well below the melting point of the aluminium hot cap. This large safety factor is necessary to prevent the possibility of a catastrophic meltdown of the engine.
The P-V plots for each of these input temperatures are displayed in the adjacent figure.
It can be see from the graph that as the temperature rises, the pressure in the system increases at all points on the cycle, which is to be expected. What is notable, however, is that the maximum pressure rises at a greater rate than the minimum pressure. The work done by the engine is calculated by the area enclosed by the curve. Due to the maximum pressure increasing exponentially with input temperature, the work done by the engine will be larger when a higher temperature is used.
The conclusion reached from this simulation is that the engine will produce the most power when as high a temperature as possible is used. In reality this will be restricted by the melting point of the aluminium hot cap, but we will heat the engine as close as is deemed safe to this temperature.
The P-V plots for each of these input temperatures are displayed in the adjacent figure.
It can be see from the graph that as the temperature rises, the pressure in the system increases at all points on the cycle, which is to be expected. What is notable, however, is that the maximum pressure rises at a greater rate than the minimum pressure. The work done by the engine is calculated by the area enclosed by the curve. Due to the maximum pressure increasing exponentially with input temperature, the work done by the engine will be larger when a higher temperature is used.
The conclusion reached from this simulation is that the engine will produce the most power when as high a temperature as possible is used. In reality this will be restricted by the melting point of the aluminium hot cap, but we will heat the engine as close as is deemed safe to this temperature.
Comparison of different working gases
By changing the working gas in the Stirling Engine cycle, it is possible to alter the power output of the engine. Using a gas with a lower viscosity than air allows the piston and displacer to oscillate faster thus increasing power output per unit volume. Another property that should be considered when selecting an appropriate working gas is the relative heat capacity. A smaller heat capacity in relation a constant heat input, will lead to a larger temperature change and so larger pressure change. The final physical property of the working gas which is significant in the selection process is the density. A working gas with a low density will be more likely to diffuse through the body of the engine creating a loss in temperature and pressure. Other practical considerations have to be taken into account such as the cost of use and flammability of the gas was it to escape.
For our project we have considered the use of three different working gases. All three are used in Stirling Engine design for different desirable properties.
AIR - Ease of setup and operation
HYDROGEN - Lowest viscosity and highest thermal conductivity
HELIUM – Low viscosity and high thermal conductivity, inflammable
For basic Stirling Engine design air is often used, as power output per unit volume is sacrificed for a cheaper more sustainable option. More advanced designs that require a higher power output tend to use helium as the working gas, as cost and ease of setup is less of an issue.
Attempting to analyse different working gases through the dynamic model proved problematic. It was found that both Helium and Hydrogen would not allow for a cyclic operation of the engine. Both gases would allow the engine to run a few erratic cycles before reaching a state of equilibrium where the engine would stop.
To cycle correctly it is important for the working piston and displacer to run out of phase at approximately 90˚. When air is used as the working gas, it doubles as a damper for the system, allowing any irregularities to be absorbed. The low viscosity of both helium and hydrogen could therefore be attributed to the engine stall, with irregularities in the system causing a ‘jerky’ angular motion as opposed to the smooth linear cycle which is required. To adapt our engine for use with a different working gas it would be necessary to incorporate a more effective damping system. This could be in the form of a larger gas pocket behind the moving pistons by altering dimensions of the design. Although this would be a fairly simple alteration to the design it would also increase the dead air space thus reducing effeciency. Alternatively a more physical damper such as a soft rubber stopper could be added behind the displacer.
For our project we have considered the use of three different working gases. All three are used in Stirling Engine design for different desirable properties.
AIR - Ease of setup and operation
HYDROGEN - Lowest viscosity and highest thermal conductivity
HELIUM – Low viscosity and high thermal conductivity, inflammable
For basic Stirling Engine design air is often used, as power output per unit volume is sacrificed for a cheaper more sustainable option. More advanced designs that require a higher power output tend to use helium as the working gas, as cost and ease of setup is less of an issue.
Attempting to analyse different working gases through the dynamic model proved problematic. It was found that both Helium and Hydrogen would not allow for a cyclic operation of the engine. Both gases would allow the engine to run a few erratic cycles before reaching a state of equilibrium where the engine would stop.
To cycle correctly it is important for the working piston and displacer to run out of phase at approximately 90˚. When air is used as the working gas, it doubles as a damper for the system, allowing any irregularities to be absorbed. The low viscosity of both helium and hydrogen could therefore be attributed to the engine stall, with irregularities in the system causing a ‘jerky’ angular motion as opposed to the smooth linear cycle which is required. To adapt our engine for use with a different working gas it would be necessary to incorporate a more effective damping system. This could be in the form of a larger gas pocket behind the moving pistons by altering dimensions of the design. Although this would be a fairly simple alteration to the design it would also increase the dead air space thus reducing effeciency. Alternatively a more physical damper such as a soft rubber stopper could be added behind the displacer.
Varying Regenerator Efficiencies
Regenerator Efficiencies
Our Stirling Engine houses a regenerator which is contained within the hot-cap/cold-cap and runs along the length of the displacers working stroke. This regenerator is the only route where the working fluid can flow from the hot-cap to the cold-cap and then travelling along into the working piston. During this movement the regenerator acts as a capacitor for heat, extracting the heat between the hot-side/cold-side which increases the temperature difference. As the displacer travels back down through the stroke, the working fluid returns through the regenerator. Here a portion of the stored heat is returned into the fluid which reduces the requirement for extensive heating and retains the temperature difference between the hot and cold sides.
In order to model the dynamics of the regenerator the ESL model required alterations. An entirely new orifice sub-model was the initial idea to mimic the action of the regenerator. However by understanding the function of the current orifice model a method was discovered which could mimic the use of a regenerator. Within the current orifice model a ratio could be applied which reduced the amount of heat passing from the hot to cold side of the engine. This in turn represents the regenerator, storing heat as it flows and increasing the temperature difference.
The ratios used to analyse the regenerator are given on the right.
To shown what these ratios result in for the working fluid an example is described. Taking a 40% efficient regenerator with the hot cap temperature of 550K the resultant temperature once passing through the regenerator (i.e. cold cap temperature) would be 220K.
From these values the P-V plots can be made. The value used for the hot cap temperature was 550K through these varying regenerator trials. This allows direct comparison between the actions of varying regenerator efficiencies. The P-V plots can are shown below.
In order to model the dynamics of the regenerator the ESL model required alterations. An entirely new orifice sub-model was the initial idea to mimic the action of the regenerator. However by understanding the function of the current orifice model a method was discovered which could mimic the use of a regenerator. Within the current orifice model a ratio could be applied which reduced the amount of heat passing from the hot to cold side of the engine. This in turn represents the regenerator, storing heat as it flows and increasing the temperature difference.
The ratios used to analyse the regenerator are given on the right.
To shown what these ratios result in for the working fluid an example is described. Taking a 40% efficient regenerator with the hot cap temperature of 550K the resultant temperature once passing through the regenerator (i.e. cold cap temperature) would be 220K.
From these values the P-V plots can be made. The value used for the hot cap temperature was 550K through these varying regenerator trials. This allows direct comparison between the actions of varying regenerator efficiencies. The P-V plots can are shown below.
PV Plots for varying Regenerator Efficiencies
The variations in the plots show the results from changing the efficiency of the regenerator. This is equivalent to changing the quality of the regenerative substance. Some materials can be built into different structures which increases the ability to trap the heat as the fluid flows through. The figure above shows that even with the largest alterations to the regenerator efficiency only minor differences are expressed in the P-V plots. The expected trend for the increase in regenerator efficiency was to be similar to that seen in the above figure with varying hot cap temperatures. This is because, along with increasing the hot cap temperature, an increase of regenerator efficiency also results in a larger temperature difference between hot and cold chambers.
However an 80% efficient regenerator, i.e. a structure that only allows 20% of the hot cap heat to be transferred into the cold chamber, does not relate to a massive increase in working pressure and therefore power output. One reason for this could be inaccuracy in the regenerator model. As previously stated there was not a separate orifice model constructed which displayed the true dynamics of the regenerator. If our group had more time it would be an interesting and worthwhile venture to construct a working regenerator model within ESL. Only then could we fully trust the output results from this section of the dynamic model.
However an 80% efficient regenerator, i.e. a structure that only allows 20% of the hot cap heat to be transferred into the cold chamber, does not relate to a massive increase in working pressure and therefore power output. One reason for this could be inaccuracy in the regenerator model. As previously stated there was not a separate orifice model constructed which displayed the true dynamics of the regenerator. If our group had more time it would be an interesting and worthwhile venture to construct a working regenerator model within ESL. Only then could we fully trust the output results from this section of the dynamic model.
