In an air standard Diesel cycle, the compression ratio is 15 , and at the beginning of isentropi

In an air standard Diesel cycle, the compression ratio is 15...

Key Concepts

Air Standard Diesel Cycle

This is a simplified thermodynamic model that represents the idealized operation of a Diesel engine. It assumes that the working fluid (air) behaves as an ideal gas and that the processes involved (compression, heat addition, expansion, and heat rejection) follow idealized paths such as isentropic or constant pressure. This cycle is used to analyze engine performance parameters like efficiency and mean effective pressure.

Isentropic Process

An isentropic process is one that occurs without any change in entropy, meaning it is both reversible and adiabatic. In the context of engine cycles, the compression and expansion phases are often assumed to be isentropic, simplifying the analysis by using relationships between pressure, volume, and temperature governed by the adiabatic law.

Compression Ratio

The compression ratio is defined as the ratio of the maximum volume to the minimum volume in the engine cylinder during a cycle. It is a key parameter in determining the efficiency and performance of an engine, as higher compression ratios typically lead to higher thermal efficiencies in ideal cycles.

Cut-off Ratio

The cut-off ratio in a Diesel cycle is the ratio of the volume at the end of the constant pressure heat addition process to the volume at the beginning of this process. It represents the amount of fuel added during the cycle and directly affects the engine’s work output and thermal efficiency.

Constant Pressure Process

In the Diesel cycle, the heat addition occurs at constant pressure. This process is characterized by a linear relationship between the volume and temperature of the gas under constant pressure conditions, which contrasts with the isochoric (constant volume) process in other cycles like the Otto cycle.

Specific Heats

Specific heats (cp and cv) are properties of the working fluid that indicate the amount of heat required to raise the temperature of a unit mass of the substance by one degree at constant pressure and constant volume, respectively. They play a crucial role in determining the temperature changes during heat addition or rejection in a thermodynamic cycle.

Heat Addition Process

The heat addition process in the Diesel cycle occurs at constant pressure and increases the temperature of the working fluid. The amount of heat added can be determined using the specific heat at constant pressure and the temperature change, and it directly influences the work output of the engine.

Cycle Efficiency

Cycle efficiency is a measure of how effectively a thermodynamic cycle converts the heat supplied into work. In the Diesel cycle, the efficiency depends on factors such as the compression ratio, the cut-off ratio, and the specific heat ratio of the air. It is an important parameter in assessing engine performance.

Mean Effective Pressure

Mean effective pressure is an indicator of the engine’s ability to do work and is defined as the constant pressure which, if acted on the piston during the power stroke, would produce the same net work as the actual cycle. It provides a useful way to compare the performance of different engine sizes and designs.

Transcript

00:01 Looking at power plants, for this standard business cycle, we want to look at the cutoff ratio, the amount of cutoff ratio, the heat addition, okay, and constant pressure, thermal efficiency as well as the main effective pressure.

00:23 So if you have this as a temperature, entropy diagram.

00:38 Okay, that's entropy in units.

00:41 I will have this.

00:44 So this is point one to two constant as entropy compression process, 2 to 3, constant pressure heat addition, 3 to 4 to 4 ,000 constant volume heat rejection.

01:03 So that we have the pilb diagram.

01:07 Let's say this is in bar.

01:10 Okay, volume that says in cubic meter.

01:17 And then we'll have this, okay.

01:24 So if we have this as point one, point two, point three, and point four, all right? so on the, at t1, 201, so to solve the problem, we'll just apply the governing equation is for a standard data cycle, to determine those parameters right so at this is 300 kelvin so if we check it from our table or better still can get the internal energy a point one applying a cv temperature temperature which we already know which we give out of course c3 is 0 .718 per kilogram per kelvin okay see if big is supposed to 0 .718.

02:25 Okay, 718, kilo per kilogram per kelvin, okay? in kilojou per kilogram per kelvin, all right? all right, so if we plug it in here, solve that we are going to have around 15 .4 kilojo per kilogram, all right? so that so vrr at point two okay okay so that's that about that we can get uh vrr point one from there too okay so let's do that and go to the error point so using uh this information can get the r a point there one to be 600 and using the table 621 table for air .2 okay so we cannot come and determine for uh consider the isentropic ascentropic compression process okay process one to two you can have b arrow 2 equal to 3 arrow over arrow which is equal to 621 .2 over the 15 15 is arrow compression ratio so if we do that we have this okay so we can just use the same value now to just interpolate and we can get t at 0 .2 as 837 .15 .15 kelvin and u at point two equal to 627 .9 kelvin, sorry, kilojou per kilogram, 627 .5, 9 kilo kilo, okay? so we can apply the, what you call the id gas equation.

05:30 So just trying make p2 the solid for the formula straight ahead.

05:41 Over t1.

05:51 So if you plug in values in there, to all the values, you have arrived at this to be 141 .86 bar.

06:01 Okay? all right.

06:03 So that's that about that.

06:05 Then having gotten that, we can also apply the ideal gas equation as well, considering process two, two, three.

06:14 And of course, we know that that is a constant treasure process.

06:19 So if you come to this, the volume at 3 over the volume at 3, volume at 2 over volume at 10xia at 3, we're at 10 % at 3...