P-V Diagrams: Definition and Applications - Assignment Example

PV DIAGRAMS By Student’s name Course code and name Professor’s name University name City, State Date of submission Introduction The concept of PV diagrams drawn from the ideal gas laws has increasingly become utilised visual aid for creating an understanding on the working of engines. The parameters of ideal gas law which are usually expressed in the form of with presenting the pressure gas, is the allowable volume of gas within the reaction chamber, is the gas’ absolute temperature and lastly is the gas’ universal constant are used in order to come up with an acceptable way of analysing engine performance in accordance to the amount of strokes that are required to complete a single cycle (Anon., 2007). PV diagrams have been incorporated to as a way of analysing four stroke engines in which four cycles are involved prior to production of power. The working mechanism of a four stroke engine involves the suction stroke also known as induction, the compression stroke, working stroke and the exhaustion stroke. In order to understand how PV diagrams work, it is important for one to establish the use of some of these key processes mentioned above. To begin with, the suction stroke begins when the piston is at the top dead centre after which it is revolved to the bottom dead centre (0-180˚) either by momentum or electric motor when starting. This is represented by S-1 of the PV diagrams (also shown in the example in figure 1 below). Suction stroke ends when the crank completes half revolution while piston is at the bottom dead centre and gives way to the compression stroke during which inlet and exhaust valves remain closed. Compression which is always considered as an adiabatic process in which there is reduction in volume involves a massive temperature change and a slight spark ignites the entire mixture (the ignition concept). This is followed by the working or expansion stroke during which the piston moves from top dead centre to the bottom dead centre (360-540˚). Due to the adiabatic burning of gases, the volume increases and pressure decreases – this leads to opening of the exhaustion valve. The exhaustion stroke involves the piston turning from the bottom dead centre to the top dead centre in order to complete the four strokes that are usually seen in the PV diagrams (Murthy, 2010). Figure 1: Presentation of a petrol engine PV diagram. The aim of this study is to learn on how to come up with PV diagrams and out an analysis of the same. The specific example given in the task was fine-tuned to give the best results in terms of power output for both petrol and diesel engines. In order to come up with an acceptable engine for the petrol task, the compression ratio is set to 7:1 contrary to that of the diesel engine which was set at 11:1. Procedure of Plotting PV Diagrams The first step was to reproduce the spreadsheet that was given for the four stroke diesel engine in one complete cycle. This would then be improved through enhanced labelling and layout in order to make it presentable and clear. The first step was to convert the listed angles for the four strokes into radians by using the following formula; Angle in radians = Angle in degrees x (i) Drawing of PV diagrams was carried out by deriving formulae used in Microsoft Excel spreadsheet. The power output to be achieved had to be matched to that in the assignment spreadsheet in order to allow for the correct analysis. The derivation of these equation was done by visiting the Wikipedia webpage as directed by the assignment instructions. These derivations were also learned from the videos tutorials to the best of understanding. Figure 2: A presentation of crank geometry (UoB Task4 - PV (iv), 2013). The equation for piston position was derived from the triangle relation in equation (ii) as indicated workout below. The triangle relation represents the relation between the crank pin, piston pin and crank center as shown in figure 2 above. (ii) (iii) Where - Crank angle in radians - Connecting rod length - Crank radius (crank throw) - Piston position The volume swept which is also indicated within the Microsoft Excel sheet was found using the formula shown below. It was understood that volume swept is the volume through which the piston is expected to sweep through during a stroke. The formula for calculation is shown in (iv) below. Where is represents the length swept by the piston. was calculated by use of the following equation. Where = Compression ratio. = Piston diameter. = Length of stroke. = Length of the connecting rod. = Position of the piston (Denoted as Top Piston in the Excel spreadsheet) = Radius of crank throw. = Volume swept. Combining the above variables, the equation for calculating the swept volume becomes; (iv) In order to calculate the amount of work done dW, the fundamental trapezoidal rule is applied. Just as shown in the tutorial video in which the area of a closed loop (circle) was calculated through some known points, the Excel spread deployed the equation below. (v) All the common variables deployed in this assignment were given in the screenshot shown in the figure below. Figure 3: Variables to be deployed in the excel sheet. Entering the above formulae into the Microsoft Excel sheet gives the following results which are a replica of those identified in figure 3 above. Figure 4: PV diagram for diesel engine prior to tuning. Figure 5: Injection profile for diesel engine prior to tuning. The second step in this assignment was to tune the diesel engine by changing the heat release profile to in a bid to increase the power output to the achievable extremes. This could only be achieved by maintaining the amount of fuel to be injected at 0.9 units. The maximum pressure in the combustion chamber was also set at a 20 bar limit as per the instructions in order to avoid the engine from blowing up. The maximum achievable mechanical power from the attained heat release profile was 1.843 units. The graphs obtained from the tuning process are as shown in figure 6 and 7 for the injection profile and PV diagram respectively. Figure 6: PV diagram for diesel engine after tuning. Figure 7: Injection profile for diesel engine after tuning. The third step involved conversion of the diesel engine’s PV diagram into a petrol engine’s PV diagram in order to assist in the comparison between these two engines. This was done by lowering the CR from 11:1 to 7:1 since petrol engines are known to have a low compression ratio. The pressure was also maintained at the same level as that of the diesel engine (20 bar) being studied. The amount of fuel was kept at a 0.9 unit constant while tuning the heat release profile. It was noted that a single release of fuel was required to produce a maximum of 1.594 power units. In comparison to diesel engines, where the injection profile had to be spread from 360˚ to 380˚ the petrol engine only allowed for single injection at 360˚. This observation was significant since the amount of pressure achieved during the heat release was noticed to be at a maximum of 17.4757 bars which is considerably low as compared to diesel engine which could attain 20 bars from a mere 0.45 units of fuel. The reduction in compression ratio can be said to be the major determinant of power produced by internal combustion engines. The graphs in figures 8 and 9 below show exactly what was achieved in the tuning process. Figure 7: Injection profile for petrol engine after tuning. Figure 7: Injection profile for petrol engine after tuning. Conclusion The use of PV diagrams in the analysis of combustion in petrol and diesel engines is an important approach. This study was key in differentiating the compression ratios between petrol engines through plotting of PV diagrams and their heat release profiles. Engine tuning was also learned in the process with the heat release profile being on top of the learning agenda. It was discovered that the compression ratio of an engine matters a lot since it is the main determinant of power produced. To this effect the diesel engines were discovered to produce more power as compared to the petrol engines due to compression ratio differences. List of References Anon., 2007. Understanding PV diagrams. [Online] Available at: http://www.physics.umd.edu/courses/Phys260/ji/HW5.pdf [Accessed 27 May 2014]. Murthy, S. T., 2010. Textbook of Elements of Mechanical Engineering. 1 ed. New Delhi: I. K. International Pvt Ltd.. UoB Task4 - PV (iv). 2013. [Film] Directed by Jerome Leary . 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