Polytropic specific work

Combining equations (17.78) and (17.80), the polytropic specific work emeiges as ... 

In fact, an experimental determination of the exponent, m, making use of equation (17.83) (or an equivalent) will introduce a small error due to the implicit inclusion of an imperfect model of compressibility effects. To compensate for this, manufacturers sometimes introduce an additional factor, /, into the equation for polytropic specific work, although in most cases... 

The power absorbed by the compressor section is given by equation (17.68). We may use equation (17.80) to express the power in terms of polytropic specific work/ polytropic head and polytropic efficiency ... 

Fig. 3.16 showed carpet plots of efficiency and specific work for several dry cycles, including the recuperative [CBTX] cycle, the intercooled [CICBTX] cycle, the reheated [CBTBTX] cycle and the intercooled reheated [CICBTBTX] cycle. These are replotted in Fig. 6.17. The ratio of maximum to minimum temperature is 5 1 (i.e. T nx 1500 K) the polytropic efficiencies are 0.90 (compressor), 0.88 (turbine) the recuperator effectiveness is 0.75. The fuel assumed was methane and real gas effects were included, but no allowance was made for turbine cooling.

The fact that the isentropic efficiency varies with pressure ratio for a constant value of polytropic efficiency has led some to regard the polytropic efficiency as a preferable foundation on which to base their analysis of the compressor section. Instead of taking the isentropic specific work as our ideal against which to measure the actual specific work, it is possible to devise a new ideal measure, the poly tropic specific work, —Wp, defined so that its ratio to the actual specific work is the polytropic efficiency, r/p-. 

In reality, most compressor conditions are neither purely isothermal nor purely isentropic but somewhere in between. This can be accounted for in calculating the compression work by using the isentropic equation [Eq. (8-21)], but replacing the specific heat ratio k by a polytropic constant, y, where 1 < y < k. The value of y is a function of the compressor design as well as the properties of the gas. 

PCp compressor power for a polytropic compression PE electric motor power Pf fan power Pp pump power PT turbine power R gas constant s entropy T absolute temperature v average velocity or specific volume V gas volumetric flow rate W work... 

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