Urgent PV Diagrams - Assignment Example

PV DIAGRAMS By Student’s name Course code and name Professor’s name University name City, State Date of submission Introduction and theory Most of the conventional four stroke diesel and petrol engines are usually driven through internal combustion. Internal combustion in four stroke engines means that fuel oxygen mixture undergoes a four cycle process within the cylinder in order to produce required automotive power. These engines have been found to have superior traits over external combustion engines which were used prior to its invention due to some of the advantages which include; high efficiency, mechanical simplicity, low weight to power ratio, low initial cost, easy start and reduced installation space (Rajput, 2007). Understanding the thermodynamic action of four-stroke engines requires the analysis of each process involved. In way of explaining, a stroke is made up of a single thermodynamic that travels the piston along the full length of the cylinder. These strokes normally involve commonly known automotive cycles such as intake, compression, power and exhaustion. During the intake cycle, the piston starts moving right from the dead end and descends to the bottom of the cylinder thereby increasing the volume of the cylinder forcing fuel air mixture in. In the compression process, both exhaust and intake valves remain closed while the piston returns compressing the fuel-air mixture forcing it into the cylinder head. The third cycle also known as the power cycle sees the compressed air fuel mixture ignited by compression (diesel engines) or a spark plug (petrol engines). The ignited mixture degenerates into heat resulting to a massive pressure change which forces the piston to move back to the bottom dead centre. The last cycle i.e. exhaustion cycle is characterised by the return of the return of the piston back to the dead centre; an action that sees the expulsion of spent air fuel mixture (Blair, 1999). This process is guided by the first two laws of thermodynamics which are focused on conservation of energy within a system and limits of efficiency respectively. Carrying out a simple thermodynamic analysis on four stroke engines exhibit the aspect of adding energy in form of heat and utilising that energy to undertake work on the other. This can be simply carried out by analysing the principle parameters that are involved in this process such as pressure, temperature and volume. However the widely used parameters for this analysis are pressure and volume which have also emerged as visualisation tools for the same. The pressure volume diagrams involve ideal gas laws in which all the three variables are analysed by tracking the engine cycle. The pressure volume diagram presents work done by an engine with temperatures that are evaluated using the ideal gas laws (HyperPhysics, 2000). This study is motivated by the major cycles and respective principle variables involved through pressure volume (PV) diagrams visualisation. PV diagrams have been used in the analysis of thermodynamic processes especially engines for a long time. A four stroke engine usually utilises heat energy to carry out work and eventually exhaust whatever cannot be utilised during a given cycle. Figure 1: An example of a PV diagram as utilised in the tutorial. Procedure of Drawing PV Diagrams Step 1 of the assignment requirements stated clearly that the spreadsheet shown in figure 1 below had to be reproduced through derivation of formulae involved. The results would produce a PV diagram and an injection profile for a four stroke diesel engine that would further be adjusted to aid in completion of task number 2 and 3. In order to carry out the initial steps, it was suggested within the guidelines that the crankshaft geometry would be very important in attaining some of the most important parameter that was required for the drafting of PV diagrams. In order to carry out this analysis, the derivations are based on crankshaft velocity which is also related to the RPM that the engine makes. (1) To establish the top angular position of the crank as required by the first preparatory step, the triangle relation is applied. In the triangle relation the crank pin, crank centre and piston pin form triangle NOP as shown in figure 2 below. This relationship exhibits that the rod length is obtained by equation 2 shown below; Figure 2: Crank geometry. (2) Where = rod length. = crank radius. = piston pin position. = crank angle. To calculate the position of the crank, equation (3) derived by rearranging the triangle relation was utilised. This formula was keyed into Microsoft Excel sheet to calculate for the values in the top piston position. (3) The variables for the above equation were given as follows: = 0.05m = varies with piston top position. = 0.1m Calculating the volume that was swept by the piston requires equation below to be utilised. (4) The variables in equation (4) are represented as follows; = Volume swept. = Length of stroke. = Compression ratio. = Length of the connecting rod. = Radius of crank throw. Top piston = Position of the piston. = Piston diameter. The values of these variables are indicated in figure 3 below. Figure 3: Experimental values and expected PV diagram. Calculating dW which is estimated to be the power dissipated or work done at each piston position, a simple procedure that is exhibited in the provided tutorials is utilised. In the given example, some points around the enclosure are assumed to be known thus applying Microsoft Excel in establishing the area occupied using the trapezoidal rule is possible. The trapezoidal rule is applied in coming up with values for dW as shall be observed in the results section below. Results and Discussion Following the instructions to carry out the first exercise of coming up with the exact graphs as the ones obtained in the example was successful thereby resulting to the graphs shown below for the injection profile and the PV. Figure 4: PV diagram. Figure 5: Injection profile. On tuning the engine by altering the heat release or injection profile, the maximum amount of mechanical power output was increased to 1.861. This was achieved even as the total amount of fuel was maintained at the nominal amount of 0.9units. The maximum pressure was also maintained at 20 bar to avoid the engine from blowing up. Below are the graphs that were obtained for this exercise. Figure 6: PV diagram for tuned diesel engine. Figure 7: Fuel injection profile for a tuned diesel engine. Further modification of the existing engine PV diagram into petrol engine was carried out by changing the compression ratio to 9:1. The maximum power achieved at this point was 1.619 units prior to carrying out the tuning process. The limit of maximum pressure was maintained at 20 bar as per the initial engine and the same fuel amount. The engine was tuned to alter the heat release profile in order to change the shape of the PV diagram. The spark explosion was produced utilising a single shot thereby increasing the power to a maximum of 1.766 units. The following graphs were obtained for this modification. Figure 8: PV diagram for a tuned petrol engine of CR 9:1. Figure 9: Injection profile of a tuned petrol engine. Conclusion The results obtained from the PV diagrams above successfully portray the engine modelling exercises that are used in petrol and engine design. It is established that the lower the compression ratio, the lower the maximum engine power obtainable unless other forces set in. This can be boosted compression through turbo charging and many other modifications that have come up for engines. However, changing the injection profile is also realized to have a very powerful impact on the engine in terms of power dissipated. List of References Blair, G. P., 1999. Design and Simulation of Four-stroke Engines. London: Society of Automotive Engineers. HyperPhysics, 2000. PV Diagrams. [Online] Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heaeng.html [Accessed 26 May 2014]. Rajput, R. K., 2007. A Text Book of Automobile Engineering. 1 ed. Masachussets: Laxmi Publications Ltd. Read More