Diesel Cycle

Figure 9-3 represents the air-standard Diesel cycle (also known as the compression-ignition cycle) in both P-V and T-s ordinates. The ideal Diesel cycle consists of an isentropic compression of the air after it has been inducted into the cylinder (A-B), followed by the injection of fuel and combustion at constant pressure (B-C), then an isentropic expansion from which work is extracted (C-D), and a reversible constant-volume rejection of heat (D-A).

Note that this is a mathematical description of the ideal constant-volume air cycle in which the properties of air are assumed to be consistent throughout the cycle. The Otto cycle, however, calls for the compression of an air-fuel mixture. Ideal thermal efficiency can therefore be expressed as a function of the compression ratio.

Compression ratio (rc) expresses the relationship of the maximum volume of an engine cylinder (VT) (with the piston at the bottom of its stroke) to the minimum, or clearance, volume (V c), of the cylinder (with the piston at the top of its stroke):

Fig. 9-3 The Air-Standard Diesel Cycle.

In the ideal Diesel cycle, the heat added along the constant-pressure path from B to C is:

The heat rejected along the constant-volume path from D to A is:

Qout = mcv (TD-Ta) Thus, the net work of the cycle is:

and the thermal efficiency of the cycle is:

Qou qin

where k is the ratio of specific heat at constant volume and at constant pressure. Assuming k to be constant, ideal cycle thermal efficiency for the Otto cycle is solely dependent on the compression ratio. For example, with k held constant at a value of 1.4, a compression ratio of 11:1 would yield the following ideal thermal efficiency:

Whereas in the ideal Otto Cycle thermal efficiency is a function of compression ratio, the same is not true for the Diesel cycle. In the Otto cycle, the isentropic compression and expansion ratios are equal. As shown in Figure 9-3, in the Diesel cycle, the isentropic compression ratio is greater than the isentropic expansion ratio. The compression and expansion ratios are expressed as:

th r c and compression ratio rc =

expansion ratio re =

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