A spark-ignition engine has a compression ratio of 10, an...

A spark-ignition engine has a compression ratio of 10, an isentropic compression efficiency of 85 percent, and an isentropic expansion efficiency of 95 percent. At the beginning of the compression, the air in the cylinder is at 13 psia and $60^{\circ} \mathrm{F}$. The maximum gas temperature is found to be $2300^{\circ} \mathrm{F}$ by measurement. Determine the heat supplied per unit mass, the thermal efficiency, and the mean effective pressure of this engine when modeled with the Otto cycle. Use constant specific heats at room temperature.

Key Concepts

Mean Effective Pressure (MEP)

Mean effective pressure is a useful parameter that represents an average pressure acting on the piston during the power stroke, which is equivalent to the net work output per cycle divided by the engine displacement. It provides a single value indicator of an engine’s ability to do work, making it a convenient measure for comparing different engine designs or operating conditions.

Thermal Efficiency

Thermal efficiency in the context of the Otto cycle measures the fraction of the heat supplied that is converted into useful work. It is primarily a function of the compression ratio and the specific heat ratio of the working fluid. By understanding thermal efficiency, engineers can gauge the performance of an engine and optimize design parameters to enhance fuel economy and power output.

Assumption of Constant Specific Heats

Assuming constant specific heats simplifies the thermodynamic analysis of the cycle by treating the specific heats at constant pressure and constant volume as constants. This assumption, typically valid at room temperature, allows for analytical solutions in cycle analysis but may introduce some inaccuracies when temperature variations are significant during the engine cycle.

Compression Ratio

The compression ratio is defined as the ratio of the total cylinder volume when the piston is at the bottom dead center to the clearance volume when it is at the top dead center. It is a critical parameter in the Otto cycle, as higher compression ratios tend to increase thermal efficiency by achieving a higher temperature rise during combustion. However, practical limits exist due to material and knocking limitations in real engines.

Otto Cycle

The Otto cycle is an idealized thermodynamic cycle that models the internal combustion process in spark-ignition engines. It consists of two adiabatic (isentropic) processes and two constant-volume processes, representing the compression, heat addition, expansion, and heat rejection stages. This cycle forms the basis for evaluating engine performance parameters such as efficiency and work output under ideal operating conditions.

Isentropic Process and Efficiency

An isentropic process is a reversible adiabatic process where entropy remains constant. In real engine processes, deviations from the ideal isentropic behavior occur, which are quantified by isentropic efficiency. This efficiency compares the actual performance with the ideal isentropic process, for both compression and expansion. Accounting for these efficiency losses is essential for a more accurate analysis of engine performance.

Transcript

00:01 Our question is, a spark ignition engine has a compression ratio of 10, a centropic compression efficiency of 85 % and isotropic expansion efficiency of 95%.

00:11 At the beginning of the compression, the air is cylinder as at 13 and 560 fahrenheit, the gas, maximum temperatures found to be with 3 ,300 fahrenheit, memory, determine heat supplied per unit mass, thermal efficiency, and mean effective pressure of this engine when modeled with the auto -savile.

00:28 Use constant specific heats at room temperature.

00:33 So solve this question, an auto cycle with isentropic compression and expansion process is considered.

00:46 Here the figure is like this.

00:50 B and u is considered.

01:13 In thermal efficiency, we have to find the heat addition and the mean effective facial auto be determined.

01:19 As the properties of air are given at room temperature is given as 0 .3.

01:27 704 is 8 cube value by iguyen dot r.

01:45 Cp is given as 0 .240 british thermal unit.

01:55 Cv is 0 .171, british thermal unit by ivenan and k is equals to 1 .4.

02:13 We will begin by determining the temperatures of the cycle states, using the process equations and component efficiencies, the ideal temperature at the end of now we will write the ideal temperature at end of compression.

02:42 Is then, t2s is equal to t1 v1 over v2, k minus 1 is equal to t1r k minus 1 which is equals to 520 r into 10, 1 .4 minus 1 which is equal to 1 3 .06 hour.

03:13 With the isentropic expression, compression efficiency, the actual temperature at the end of compression is with isotropic compression efficiency.

03:41 The actual temperature at end of compression is, eta is equals to t2 s minus t 1 over t 2 minus t 1 which is equal to t 2 minus t 1 which is equals to t 2 minus t 1 plus t 2 s minus t 1 over eta is equals to 520 putting the values over here plus 13 06 minus 520 divided by 0 .85...

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