Real gas effects

In practical open circuit gas turbine plants with combustion, real gas effects are present (in particular the changes in specific heats, and their ratio, with temperature), together with combustion and duct pressure losses. We now develop some modifications of the a/s analyses and their graphical presentations for such open gas turbine plants, with and without heat exchangers, as an introduction to more complex computational approaches. 

The Hawthorne and Davis analysis is first generalised for the [CBT]i open circuit plant, with fuel addition for combustion,/ per unit air flow, changing the working fluid from air in the compressor to gas products in the turbine, as indicated in Fig. 3.11. Real gas effects are present in this open gas turbine plant specific heats and their ratio are functions off and T, and allowance is also made for pressure losses. 

A series of calculations for open circuit gas turbines, with realistic a.s.sumptions for various parameters, have been made using a code developed by Young [7], using real gas tables. These illustrate how the analysis developed in this chapter provides an understanding of, and guidance to, the performance of the real practical plants. The subscript G here indicates that the real gas effects have been included. 

The [CBT]ig efficiency is replotted in Fig. 3.14, against (Tt,ITx) with pressure ratio as a parameter. There is an indication in Fig. 3.14 that there may be a limiting maximum temperature for the highest thermal efficiency, and this was observed earlier by Horlock et al. [8] and Guha [9]. It is argued by the latter and by Wilcock et al. [10] that this is a real gas effect not apparent in the a/s calculations such as those shown in Fig. 3.9. This point will be dealt with later in Chapter 4 while discussing the turbine cooling effects. 

The discussion of the performance of gas turbine plants given in this chapter has developed through four steps reversible a/s cycle analysis irreversible a/s cycle analysis open circuit gas turbine plant analysis with approximations to real gas effects and open circuit gas turbine plant computations with real gas properties. The important conclusions are as follows ... 

There are several papers in the literature which give details of cycle calculations, and include details of how the cooling flow quantity may be estimated and used. Here we describe one such approach used by the author and his colleagues. Initially, we summarise how i/rcan be obtained (fuller details are given in Appendix A). We then illustrate how this information is used in calculations, once again using a computer code in which real gas effects are included. 

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.

Calculation of the equilibrium composition of a mixture, allowing for real gas effects... 

For high gas pressures, ideal gas law predictions can become inaccurate and real gas effects have to be taken into account. More details on high-pressure effects can be found in Ohe [34]. 

Real gas effects in steady Laval nozzle flows of fluids undergoing adiabatic phase changes lead to discontinuous choking and in case of large-heat-capacity fluids to multiple shocks including expansion shocks. 

The steady two-dimensional diabatic flow is described by the equations for mass, momentum and energy in conservation form (Schnerr and Dohrmann [7], Dohrmann [8]). Real gas effects are not yet included and inviscid fluids are assumed. Here the classical nucleation theory of Volmer [9] is used which gives a good qualitative representation of the behavior of condensing in the supersaturated state (Wegener [iO]). Oswatitsch [11] introduced this theory into the calculation of flow processes, a summary of all basic relationships for compressible flows with heat addition is given by Zierep [12]. To compute the nucleation rate J per unit time and volume, we take... 

The specific heat capacity of an ideal gas is the basic quantity for the enthalpy calculation, as it is independent from molecular interactions. It is also possible to define a real gas heat capacity, but for process calculations it is more convenient to account for the real gas effects with the enthalpy description of the equation of state used (see Section 6.2). In process calculations, the specific heat capacity of ideal gases mainly determines the duty of gas heat exchangers, and it has an influence on the heat transfer coefficient as well. 

Also for the simplified reaction kinetics, figure 3 illustrates the influence of the vapor-phase dimerization of acetic acid. In Aspen Plus, this effect is included by specifying the Hayden OGonnell option in the vapor-liquid-equilibrium. However, this includes real gas effects as well, which are not included in the compared GAMS model. So, this different data basis is mainly responsible for the small deviations in the results. Neglecting the acetic acid dimerization, the reboiler loads for both calculations are Q = 1597 kW. Comparing this to the results displayed in figure 3 for the same simulations, the enthalpy effect of the dimerization becomes apparent. 

At higher pressures it may be necessary to take real gas effects of the sorptive medium into account. A simple way to do this is, to replace the... 

The exponential function in this expression mirrors the influence of the other components (k i) on the adsorption of component (i). The series expansions (7.55, 7.59) can be derived from equivalent virial expansions of the thermal equation of state (EOS) of the single- or multicomponent adsorbate by standard thermodynamic methods. Details are given in [7.2, 7.3]. Real gas effects of the sorptive gas mixture can be taken into account by replacing the partial pressures (pi, i = 1...N) in (7.60) by the (mixture) fugacities (fi = fi (pi... pN, T)) of the system [7.17]. 

Figure 15.6 Sizing coefficient versus reduced inlet stagnation pressure calculated according to EN-ISO 4126-7 and a nozzle flow model including real gas effects for ethylene at inlet stagnation temperatures of 300 and 443 K.

Calculation of Flow Coefficient Accounting for Real Gas Effects... 

Sizing coefficient for gases including real gas effects Sizing coefficient for gases according to EN-ISO 4126-7 Specific enthalpy (J/kg)... 

Johnson, R.C. (1964) Calculations of real gas effects in flow through critical flow nozzles./. Basic Eng., 86, 519-526. Baurfeind, K. and Friedel, L. (2003) Berechnung der dissipationsbehafteten kritischen Diisenstromimg realer Gase. Forsch. Ingenieunves., 67, in-iys. 

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