Question

What are the air-standard assumptions and the cold air-standard assumptions in analysing engine cycles? How an actual combustion process is being simplified in ideal engine cycles?

Answer 1

1)

###The Air-Standard Assumptions

1. The working fluid is air and it behaves as an ideal gas
2. The cycle is modeled as a closed cyclewith the air cooled in the chiller heat exchanger and recirculated to the compressor.
3. The combustion chamber is replaced by combustion heat exchanger
4. All processes are internally reversible

The Air-Standard Assumptions

• The first analysis of most gas power cycles begins with the air-standard assumptions.
• First, we assume that the working fluid is air and that at all points within the system, it behaves as an ideal gas.
• Next we approximate the open cycle as a closed cycle. We must add heat exchanger #2 in order to cool the turbine effluent and complete the cycle.
• The presence of fuel and combustion products like carbon dioxide and water in the working fluid can greatly complicate the analysis of the cycle.
• So, to avoid these complications in our basic analysis, we will model the internal combustion cycle as an external combustion cycle.
• These assumptions simplify the analysis of the Brayton and other gas power cycles and maintain the essential characteristics of the cycles.
• The processes that make up the resulting Air-Standard Brayton Cycle are listed here.
• Notice that the turbine and compressor are still considered to be isentropic, but that the two heat exchangers are isobaric processes and NOT isothermal processes.
• Now, we are ready to begin to analyze the air-standard Brayton Cycle.

Process 1-2:

Combustion HEX

Heat is tranferred to the working fluid at constant pressurefrom the external heat source, usually the exhaust gases from a combustion reaction.

Process 2-3:

Turbine

Hot gases expand isentropically to produce shaft work, some of which is used to drive the compressor.

Process 3-4:

Chiller HEX

Heat is rejected to the low temperature reservoir or sink atconstant pressure.

Process 4-1:

Compressor

Cool air is compressed isentropically.

###Cold Air-Standard Assumptions

The heat capacities of air are constant and have the values determined at 25°C.

• Here is a quick review of the air-standard assumptions that we used in the analysis of the air standard Brayton Cycle.
• We will use all of the same assumptions in our analysis of the air-standard refrigeration cycle.
• All except #3. There isn’t a combustion reactor in a refrigerator ! Not in mine, anyway !
• Instead of a combustion reactor, we have an ordinary hot reservoir.
• In most cases, the hot reservoir is the surroundings. You just can’t beat the cost … free !
• The cold air-standard assumption just makes all the calculations more simple.
• We assume that the heat capacities of air are constant and always have the value at 25oC.
• This certainly makes integrating the Gibbs equations easier !
• The cycle that we are going to analyze based on these assumptions is made of 4 steps.
• Step 1-2: Isobaric heating by absorbing heat from the cold reservoir
• Step 2-3: Isentropic compression from the low pressure of HEX #2 to the high pressure of HEX #1.
• Step 3-4: Isobaric cooling by rejecting heat to the hot reservoir.
• Step 4-1: Isentropic expansion in the turbine from the high pressure of HEX #1 down to the low pressure of HEX #2.
• The process moves counterclockwise around the cycle like all refrigeration cycles.
• The cycle shown here is an ideal cycle.

2) actual combustion process is being simplified in ideal engine cycles

The Otto cycle is a set of processes used by spark ignition internal combustion engines (2-stroke or 4-stroke cycles). These engines a) ingest a mixture of fuel and air, b) compress it, c) cause it to react, thus effectively adding heat through converting chemical energy into thermal energy, d) expand the combustion products, and then e) eject the combustion products and replace them with a new charge of fuel and air. The different processes are shown in Figure 3.8:

1. Intake stroke, gasoline vapor and air drawn into engine ( ).
2. Compression stroke, , increase ( ).
3. Combustion (spark), short time, essentially constant volume ( ). Model: heat absorbed from a series of reservoirs at temperatures to .
4. Power stroke: expansion ( ).
5. Valve exhaust: valve opens, gas escapes.
6. ( ) Model: rejection of heat to series of reservoirs at temperatures T₄TO T₁
7. Exhaust stroke, piston pushes remaining combustion products out of chamber ( ).

We model the processes as all acting on a fixed mass of air contained in a piston-cylinder arrangement, as shown in Figure 3.10.

Figure 3.8: The ideal Otto cycle

Figure 3.9: Sketch of an actual Otto cycle

Figure 3.10: Piston and valves in a four-stroke internal combustion engine

The actual cycle does not have the sharp transitions between the different processes that the ideal cycle has, and might be as sketched in Figure 3.9.