4.2 Diesel and Dual Cycle Analysis

Diesel and Dual cycles are key players in the world of gas power cycles. They're like the tough cousins of the Otto cycle, packing more punch with higher compression ratios and unique heat addition processes.

These cycles power engines that are workhorses in heavy-duty applications. Understanding their principles and performance characteristics is crucial for grasping how they fit into the broader family of gas power cycles.

Diesel and Dual cycle principles

Thermodynamic cycles

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• The Diesel cycle is a thermodynamic cycle that describes the operation of a compression-ignition engine
  • The fuel is ignited by the high temperature achieved through compression (air-standard cycle)
• The Dual cycle, also known as the mixed cycle, combines the characteristics of both the Otto and Diesel cycles
  • The heat addition process is divided into two parts: constant volume heat addition followed by constant pressure heat addition
  • The Dual cycle has a higher compression ratio than the Otto cycle but lower than the Diesel cycle

Processes in Diesel and Dual cycles

• The Diesel cycle consists of four processes:
  1. Isentropic compression
  2. Constant pressure heat addition
  3. Isentropic expansion
  4. Constant volume heat rejection
• The working fluid in Diesel and Dual cycles is typically air
  • The air is compressed to a high pressure and temperature before the fuel is injected (near the end of the compression stroke)

Diesel vs Otto cycles

Comparison of thermodynamic cycles

• The Otto cycle is a thermodynamic cycle that describes the operation of a spark-ignition engine
  • The fuel-air mixture is ignited by a spark plug (gasoline engines)
• The Otto cycle consists of four processes:
  1. Isentropic compression
  2. Constant volume heat addition
  3. Isentropic expansion
  4. Constant volume heat rejection
• The Diesel cycle differs from the Otto cycle in the heat addition process
  • Constant pressure heat addition in the Diesel cycle
  • Constant volume heat addition in the Otto cycle

Engine characteristics

• Diesel and Dual cycle engines typically have higher compression ratios compared to Otto cycle engines
  • Higher compression ratios lead to higher thermal efficiencies (improved fuel economy)
• The fuel injection in Diesel and Dual cycle engines occurs near the end of the compression stroke
  • In Otto cycle engines, the fuel-air mixture is present during the entire compression stroke (pre-mixed combustion)
• Diesel and Dual cycle engines are more robust and durable due to their higher compression ratios and combustion characteristics
  • Suitable for heavy-duty applications (trucks, generators, marine propulsion)

Performance of Diesel and Dual cycles

Key performance parameters

• Thermal efficiency measures the fraction of heat input converted into useful work output
  • Influenced by factors such as compression ratio, cut-off ratio, and specific heat ratio of the working fluid
• Mean effective pressure (MEP) represents the average pressure acting on the piston during the power stroke
  • Indicator of an engine's ability to produce torque (work output per unit displacement)
• Brake specific fuel consumption (BSFC) measures the fuel efficiency of an engine
  • Expresses the amount of fuel consumed per unit of power output (g/kWh or lb/hp-hr)

Additional performance considerations

• Volumetric efficiency quantifies the effectiveness of an engine's air induction system
  • Compares the actual amount of air drawn into the cylinder to the theoretical maximum (affected by intake system design and operating conditions)
• Emissions, such as nitrogen oxides (NOx) and particulate matter (PM), are important considerations in assessing the environmental impact of Diesel and Dual cycle engines
  • Emissions regulations drive the development of advanced combustion strategies and aftertreatment systems (exhaust gas recirculation, selective catalytic reduction, diesel particulate filters)

Efficiency and power of Diesel and Dual cycles

Calculating thermal efficiency

• The thermal efficiency of a Diesel cycle can be calculated using the following parameters:
  • Compression ratio ($r_c$)
  • Cut-off ratio ($r_c$)
  • Specific heat ratio of the working fluid ($\gamma$)
• For a Dual cycle, the thermal efficiency depends on:
  • Compression ratio ($r_c$)
  • Ratio of constant volume to constant pressure heat addition ($\rho$)
  • Specific heat ratio ($\gamma$)
• The thermal efficiency equations for Diesel and Dual cycles are derived from the application of the first law of thermodynamics to the respective processes

Determining power output

• Power output can be determined by multiplying the work output per cycle by the number of cycles per unit time (engine speed) and the number of cylinders
  • $Power = W_{cycle} \times N \times n$, where $W_{cycle}$ is the work output per cycle, $N$ is the engine speed, and $n$ is the number of cylinders
• The work output per cycle is calculated by integrating the pressure-volume diagram for the respective thermodynamic cycle (Diesel or Dual)
  • $W_{cycle} = \oint P \, dV$, where $P$ is the pressure and $V$ is the volume
• Brake horsepower (BHP) represents the actual power output available at the engine's crankshaft
  • Considers frictional losses and auxiliary component power consumption (alternator, water pump, etc.)
• Indicated horsepower (IHP) is the theoretical power output of an engine
  • Calculated from the pressure-volume diagram without accounting for losses (represents the work done by the gas on the piston)