Irreversible simple cycle

The analysis of Hawthorne and Davis [1] for irreversible a/s cycles is developed using the criteria of component irreversibility, firstly for the simple cycle and subsequently for the recuperative cycle. In the main analyses, the isentropic efficiencies are used for the turbomachinery components. Following certain significant relationships, alternative expressions, involving polytropic efficiency and. tc and jcj, are given, without a detailed derivation, in equations with p added to the number. 

Fig. 3.7. T.s diagram for irreversible elosed simple cycle [CHTJi.

As mentioned before, the thermal efficiency for the irreversible plant [CHT]i is a function of the temperature ratio 6= T T (as opposed to that of the reversible simple cycle [CHT]r, for which tj is a function of x only, and pressure ratio r, as illustrated in Fig. 3.3). Fig. 3.9 illustrates this difference, showing the irreversible thermal efficiency Tj(a , 6) which is strongly 0-dependent. 

The nomenclature introduced by Hawthorne and Davis [4] is adopted and gas turbine cycles are referred to as follows CHT, CBT, CHTX, CBTX, where C denotes compressor H, air heater B, burner (combustion) T, turbine X, heat exchanger. R and I indicate reversible and irreversible. The subscripts U and C refer to uncooled and cooled turbines in a cycle, and subscripts 1,2, M indicate the number of cooling steps (one, two or multi-step cooling). Thus, for example, [CHT] C2 indicates an irreversible cooled simple cycle with two steps of turbine cooling. The subscript T is also used to indicate that the cooling air has been throttled from the compressor delivery pres.sure. 

During the last century, the concept of the limiting step was revised several times. First simple idea of a "narrow place" (a least conductive step) could be applied without adaptation only to a simple cycle of irreversible steps that are of the first order (see Chapter 16 of the book Johnston (1966) or the paper of Boyd (1978)). When researchers try to apply this idea in more general situations they meet various difficulties such as ... 

There exist several estimates for relaxation time in chemical reactions (developed, e.g. by Cheresiz and Yablonskii, 1983), but even for the simplest cycle with limitation the main property of relaxation time is not widely known. For a simple irreversible catalytic cycle with limiting step the stationary rate is controlled by the smallest constant, but the relaxation time is determined by the second in order constant. Hence, if in the stationary rate experiments for that cycle we mostly extract the smallest constant, in relaxation experiments another, the second in order constant will be observed. 

The arguments of this section are developed sequentially, starting with internally reversible cycles and then considering irreversibilities. Here we concentrate on the gas turbine with simple closed or open cycle (CHT, CBT). 

The half-wave potentials of (FTF4)Co2-mediated O2 reduction at pH 0-3 shifts by — 60 mV/pH [Durand et ah, 1983], which indicates that the turnover-determining part of the catalytic cycle contains a reversible electron transfer (ET) and a protonation, or two reversible ETs and two protonation steps. In contrast, if an irreversible ET step were present, the pH gradient would be 60/( + a) mV/pH, where n is the number of electrons transferred in redox equilibria prior to the irreversible ET and a is the transfer coefficient of the irreversible ET. The —60 mV/pH slope is identical to that manifested by simple Ee porphyrins (see Section 18.4.1). The turnover rate of ORR catalysis by (ETE4)Co2 was reported to be proportional to the bulk O2 concentration [Collman et ah, 1994], suggesting that the catalyst is not saturated with O2. 

First, there must be a large number of reacting substances. Even for linear reaction mechanisms, there does not exist a simple "rule of adding characteristic times for the steps forming a reaction mechanism. For example, let us consider a linear irreversible cycle Aj -+ A2 A - Ax in which... 

It is the aim of this paper to present a comparison of thermal and chemical recuperation options 1n a thermodynamic framework. The paper will begin by identifying the major irreversibilities in a simple gas-turbine cycle with liquid methanol fuel continue with a comparison of thermodynamic losses and overall efficiencies among various options utilizing thermal and/or... 

As the reduced matrix 8.45 shows, steps following the irreversible second one in the cycle do affect the rate. This is another example for the fact that the rules for noncatalytic simple pathways do not apply unless the free catalyst is the macs. A more general set of rules will be given in the next section. 

A general formula for single catalytic cycles with arbitrary number of members and arbitrary distribution of catalyst material has been derived by Christiansen. Unfortunately, the denominator of his rate equation for a cycle with k members contains k2 additive terms. Such a profusion makes it imperative to reduce complexity. If warranted, this can be done with the concept of relative abundance of catalyst-containing species or the approximations of a rate-controlling step, quasi-equilibrium steps, or irreversible steps, or combinations of these (the Bodenstein approximation of quasi-stationary states is already implicit in Christiansen s mathematics). In some fortunate instances, the rate equation reduces to a simple power law. 

Hervagault, J.F. S. Cemu. 1987. Bistability and irreversible transitions in a simple substrate cycle. J. Theor. Biol. 127 439-49. 

---