Investigation of the Performance analysis
of a Four-stroke diesel engine with varying
compression rates.
Thermodynamics-I
Submitted by:
Haad Raza
24-ME-28
Awais Khalid
24-ME-08
Umair Khalid
24-ME-12
Khuzaifa khan
24-ME-184
Usman Naeem
24-ME-16
Section-D
Submitted to:
Engr. Muhammad Sumair
Department of Mechanical Engineering University of Engineering & Technology
Taxila, Pakistan.
1
Table of Content
Title ................................................................................................................................... 3
1
Objectives ................................................................................................................. 3
2
Introduction ............................................................................................................... 3
2.1
Derivation ........................................................................................................... 7
2.2
............................................................................................................................ 8
2
Tables of figure
Figure 1: Schematic of Internal-Combustion diesel engine........................................................... 7
Figure 2: P-V diagram of diesel cycle ...................................................................................... 8
Figure 3: TS diagram of Diesel cycleОшибка! Закладка не определена.
……………………………………………………… 9
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List of Tables
Table 1: Effect of change in inlet vane angle on power at the outlet of the pump, power
available at the impeller, manometric, mechanical, and overall efficiencies. ..... Ошибка!
Закладка не определена.
ii
Title
Performance analysis of a Four-stroke diesel engine with varying compression rates
1. Objectives
In this report we will discuss the efficiency and working of a diesel cycle, in a 4-stroke
compression engine, and the objectives are as follow,

To analyze the effect of compression ratio on maximum temperature and pressure
during the cycle.

To determine the effect of compression ratio on net Work output.

To investigate the influence of compression ratio on thermal efficiency.

To compute the mean effective pressure for varying compression ratios.
2. Introduction
Compression ignition (CI) engines, commonly known as Diesel engines, are a cornerstone of
modern mechanical engineering and industrial technology. Their high thermal efficiency and
robust performance make them an essential choice for heavy-duty applications, ranging from
transportation to power generation. The Diesel cycle, which governs the operation of these
engines, provides a theoretical framework for analyzing their performance under varying
conditions. By studying the parameters of the Diesel cycle, engineers can optimize engine
performance, improve fuel efficiency, and reduce emissions.
The Diesel cycle is a thermodynamic cycle widely used in compression-ignition engines. It
consists of four main processes isentropic compression, constant-pressure heat addition, isentropic
expansion, and constant-volume heat rejection. This study aims to evaluate the performance of the
Diesel cycle by varying the compression ratio, a key parameter affecting engine efficiency and
output. The performance is assessed using the following parameters maximum temperature and
pressure, net Work output, thermal efficiency, and mean effective pressure.
In a Diesel engine, the working principle is based on compressing air to a high temperature,
followed by the injection of fuel into the compressed air. The heat generated by compression is
sufficient to ignite the fuel, eliminating the need for spark plugs. This process allows Diesel
engines to achieve high compression ratios, leading to superior fuel economy and Thermal
efficiency compared to spark ignition engines. However, the performance of a Diesel engine is
influenced by several factors, with the compression ratio being one of the most critical design
parameters.
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The compression ratio (CR), defined as the ratio of the cylinder’s maximum volume to its
clearance volume, plays a pivotal role in determining the engine’s overall efficiency and power
output. A higher compression ratio typically increases the thermal efficiency of the engine, as
dictated by the thermodynamic principles of the Diesel cycle. However, increasing the
compression ratio also results in higher peak pressures and temperatures within the cylinder, which
can impose significant stresses on engine components. Therefore, optimizing the compression
ratio is a key challenge in Diesel engine design.
The Diesel cycle itself consists of four key thermodynamic processes:
1. Isentropic Compression: The air is compressed adiabatically, raising its pressure and
temperature without heat transfer to or from the surroundings.
2. Constant Pressure Heat Addition: Fuel is introduced and burned at constant pressure,
leading to a significant increase in the temperature of the working fluid.
3. Isentropic Expansion: The high-pressure gases expand adiabatically, performing work on the
piston as they push it downward.
4. Constant Volume Heat Rejection: Heat is expelled at constant volume, completing the cycle
and returning the system to its initial state.
Under idealized conditions, the Diesel cycle is often analyzed using cold air standard assumptions,
where air is treated as an ideal gas with constant specific heats. These assumptions provide a
simplified yet effective approach to studying the cycle’s performance.
This particular problem focuses on a four-stroke CI engine operating on an ideal Diesel cycle with
a cutoff ratio of 2. The cutoff ratio (rc), which is the ratio of the cylinder volume at the end of the
combustion process to the volume at the start of combustion, determines the extent of heat addition
during the cycle. Maintaining a constant cutoff ratio while varying the compression ratio allows
for an in-depth analysis of how the compression ratio alone impacts engine performance.
At the beginning of the compression process in this study, the air is at ambient conditions of 95
kPa pressure and 27°C temperature. These starting conditions provide a realistic baseline for
evaluating the thermodynamic behavior of the cycle. As the compression ratio increases, the
pressure and temperature at the end of compression also increase, leading to changes in the overall
cycle performance.
Understanding the relationship between compression ratio and Diesel cycle performance
is critical for several reasons. First, the maximum pressure and temperature achieved during the
cycle directly influence the material and structural requirements of the engine. Components such
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as the cylinder head, piston, and valves must withstand these conditions without failure. Second,
the net Work output of the cycle, which represents the useful energy extracted from the system, is
a key indicator of the engine’s power capabilities. Third, the thermal efficiency of the cycle reflects
how effectively the engine converts fuel energy into mechanical work, a crucial factor in
determining fuel consumption and environmental impact. Lastly, the mean effective pressure
(MEP) provides a measure of the engine’s ability to produce power relative to its displacement,
aiding in the design of compact and efficient engines.
In the context of engineering design, the study of the Diesel cycle’s performance is not just a
theoretical exercise but a practical necessity. With global emphasis on energy efficiency and
sustainability, optimizing Diesel engines to achieve higher performance while reducing emissions
is more important than ever. By investigating the effects of varying the compression ratio, this
analysis contributes to the ongoing efforts to develop advanced engine technologies that meet the
demands of modern applications.
Figure 1: Schematic of Internal-Combustion diesel engine.
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Figure 2: P-V diagram of diesel cycle.
A Temperature-Entropy (TS) diagram illustrating the processes of the Diesel cycle.
Figure 3: TS diagram of Diesel cycle.
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2.1.
Derivation
Key equations used to analyze the Diesel cycle
a) Isentropic compression process
𝑉
𝑉2
𝑇2 = 𝑇1 ( 1 )𝛾 …………………….…………………….... (1)
b) Pressure volume relation
𝑃2 𝑉2 𝛾 = 𝑃1 𝑉1 𝛾 ………………………………………….. (2)
c) Temperature pressure relation
𝛾−1
𝑇2
𝑃
= (𝑃2 ) 𝛾 …………………………………...………..…. (3)
𝑇1
1
Where 𝑃1 𝑉1is the initial pressure and volume at the starts of compression and
𝑃2 , 𝑉2 is the final pressure and volume at the end of compression and
𝐶
( 𝛾 = 𝐶𝑃 ) which is the ratio of specific heat capacity of gas at constant pressure and volume of
𝑉
the gas inside the combustion chamber or cylinder, known.
In the analysis of a Diesel cycle, two important parameters are: compression ratio (𝑟0 )and
the cut-off ratio ( 𝑟𝑐 ). The cut-off ratio is defined as the ratio of the volume at the end of
constant-pressure energy addition process to the volume at the beginning of the energy addition
process.
𝑉
𝑟𝑐 = 𝑉3 ………………………………………… (1)
2
And
𝑉
𝑟𝑐 = 𝑉1 …………………………………………. (2)
2
Energy added
𝑄1 = 𝑚𝑐𝑃 (𝑇3 − 𝑇2 ).............................................. (3)
Energy rejected
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𝑄2 = 𝑚𝑐𝑃 (𝑇4 − 𝑇1 ) …………………………… (4)
Thermal efficiency “𝜂” of diesel cycle is as
𝜂=
𝑄1 −𝑄2
𝑄1
𝑇 −𝑇
= 1 − 𝛾(𝑇4 −𝑇1 )
3
2
Or,
𝜂 = 1−
𝑇
𝑇1
𝑇
𝛾( 3 −1)𝑇2
𝑇2
( 4 −1)𝑇1
………..…………………… (5)
1-2 is Isentropic: so
𝑇1
𝑉
2
1
𝛾
1 𝛾−1
= (𝑉2 ) = (𝑟 )
𝑇
0
………………………… (6)
4-1 is Constant volume: so
𝑇4
𝑃
𝑃
𝑃
1
1
3
1
= 𝑃4 = 𝑃4 × 𝑃3……….……………………... (7)
𝑇
But 𝑃2 = 𝑃3 Hence (7) becomes
𝑇4
𝑇1
𝑃
𝑃
3
1
= 𝑃4 × 𝑃2 …………….……………………... (8)
Since 1−2 and 3−4 are isentropic processes so
𝑃𝑉 𝛾 = 𝐶
And,
𝑃2
𝑉
1
1
𝛾
= (𝑉1 ) and
𝑃
𝛾
𝑃4
𝑉
3
4
= (𝑉3 ) ...................(11)
𝑃
Hence (8) becomes,
𝑇4
𝑉
1
4
𝛾
𝑉
𝛾
= (𝑉3 ) (𝑉1 ) = (𝑟𝐶 )𝛾
𝑇
𝑇4
𝑇3
1
2
1
Substituting value of 𝑇 and 𝑇 in (5) we get
((𝑟 )𝛾 −1)
𝐶
𝜂 = 1 − 𝛾(𝑟 )𝛾−1
…………………………(12)
(𝑟 −1)
0
𝐶
8
Also to be noted
𝑇3
𝑇2
=
𝑃3 𝑉3
𝑃2 𝑉3
=
𝑉3
𝑉2
= 𝑟𝑐
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