Cycle calculations

Typical elements in Groups V. VI and VII would be expected to achieve a noble gas configuration more easily by gaining electrons rather than losing them. Electron affinity is a measure of the energy change when an atom accepts an extra electron. It is difficult to measure directly and this has only been achieved in a few cases more often it is obtained from enthalpy cycle calculations (p. 74). 

Essentially, the analytical approach outlined above for the open circuit gas turbine plants is that used in modem computer codes. However, gas properties, taken from tables such as those of Keenan and Kaye [6], may be stored as data and then used directly in a cycle calculation. Enthalpy changes are then determined directly, rather than by mean specific heats over temperature ranges (and the estimation of n and n ), as outlined above. 

In this chapter, cycle calculations are made with assumed but realistic estimates of the probable turbine cooling air requirements which include some changes from the uncooled thermal efficiencies. Indeed it is suggested that for modern gas turbines there may be a limit on the combustion temperature for maximum thermal efficiency [2,3]. 

Subsequently, in Chapter 5, we shall show how the cooling quantities may be determined we give even more practical cycle calculations, with these cooling quantities (ip) being determined practically rather than specified ab initio. But for the discussions in this chapter, in which we assess how important cooling is in modifying the overall thermodynamics of gas turbine cycle analysis, it is assumed that tp is known. 

From (a) and (b), the stagnation pressure and temperature can thus be calculated at exit from the cooled row they can then be used to study the flow through the next (rotor) row. From there on a similar procedure may be followed (for a rotating row the relative (7 o)r, i and (po)k replace the absolute stagnation properties). In this way, the work output from the complete cooled turbine can be obtained for use within the cycle calculation, given the cooling quantities ip. 

The choice of these values is arbitrary. In practice, the cooling fraction will depend not only on the combustion temperature but also on the compressor delivery temperature (i.e. the pressure ratio), the allowable metal temperature and other factors, as described in Chapter 5. But with ip assumed for the first nozzle guide vane row, together with the extra total pressure loss involved (k = 0.07 in Eq. (4.48)), the rotor inlet temperature may be determined. These assumptions were used as input to the code developed by Young [11] for cycle calculations, which considers the real gas properties. 

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. 

In the cycle calculations de.scribed below [2], film cooling was as.sumed. Further, as described in Appendix A, various a.s.sumptions were made for the critical constants, as follows. The constant C in Eq. (5.13) was taken as 0.045, and within W, the cooling efficiency tJcooi as 0.7 and the film cooling effectiveness ep as 0.4. All were assumed to be constant over the range of cooling flows considered. 

At very high combustion temperatures, it is not sufficient that the first blade row alone needs to be cooled. In practice, up to half a dozen rows may be cooled in an industrial gas turbine, if the combustion temperature is high and the allowable blade metal temperature is low. The cooling fractions for each of the cooled rows must be estimated and u.sed in the cycle calculations, which now become complex. 

The cycle calculations for this multi-cooling then proceeded in a similar fashion to those for the single-.step cooling calculations of Section 5.4 (full details are given in Ref. [2]). 

To further understand the thermodynamic philosophy of the improvements on the EGT cycle we recall the cycle calculations of Chapter 3 for ordinary dry gas turbine cycles—including the simple cycle, the recuperated cycle and the intercooled and reheated cycles. 

Tgi and T -, are usually determined from and/or specified for cycle calculation so that the cooling effectiveness o implicitly becomes a requirement (subject to 7hi which again can be assumed for a level of technology ). If and C are amalgamated into a single constant K, then... 

In practice, h(g increases above hg, and (I + B) is increased as TBC is added. For the purposes of cycle calculation, fx is therefore taken as unity and... 

Experience gives values of for various geometries, but St is also a weak function of Reynolds number and so, in practice, there is relatively little variation in cooling efficiency (0.6 < < 0.8). In the cycle calculations described in Chapter 5, tJcqoi was taken as... 

Since open film cooling is now used in most gas turbines, the form of Eq. (A 13) was adopted for the cycle calculations of Chapter 5, i.e. 

Taking (r pg/rpc)(AsgM, ) = 20 as representative of modern engine practice, and 5/g = 1.5 X 10 a value of C = 0.03 is obtained. The ratio (Cpg/Cpc) should then increase with Tg (but only by about 8% over the range 1500-22()0 K). This variation was, therefore, neglected in the cycle calculations described in Chapter 5. 

In any particular cycle calculation, with the inlet gas temperature known together with the inlet coolant temperature Tcj, and with an assumed allowable metal temperature Tb), E() was determined from Eq. (A7). W" was then obtained from Eq. (A 18) and the cooling flow fraction i/ from Eq. (A16). 

I must express my appreciation to many colleagues in the Whittle Laboratory of the Engineering Department at Cambridge University. In particular I am grateful to Professor John Young who readily made available to me his computer code for real gas cycle calculations and to Professors Cumpsty and Denton for their kindness in extending to me the hospitality of the Whittle Laboratory after I retired as Vice-Chancellor of the Open University. It is a stimulating academic environment. 

Leaching can be analyzed with respect to both the catalyst (rest state) and catalyst degradation products. The above reactions involve the separation of an n-octane product solution from a 5a catalyst residue at - 30 °C, and a subsequent n-octane extraction at - 30 °C. The data in Fig. 2, together with the solvent quantities employed, predict catalyst leaching of < 0.33% per cycle (calculated from the solubility at - 20 °C). This rises to 1.0 and 3.6% if phase separations are conducted at 0 and 20 °C, respectively. 

An ideal split-shaft Brayton cycle receives air at 14.7 psia and 70° F. The upper pressure and temperature limits of the cycle are 60 psia and 1500°F, respectively. Find the temperature and pressure of all states of the cycle. Calculate the input compressor work, the output power turbine work, heat supplied in the combustion chamber, and the thermal efficiency of the cycle, based on variable specific heats. 

Table 2.12 gives the absolute enthalpies of hydration for some anions. The values are derived from thermochemical cycle calculations using the enthalpies of solution in water of various salts containing the anions and the lattice enthalpies of the solid salts. 

Hydrogen fluoride in aqueous solution is a weak acid, characterized by its pKa value of 3.2. By comparison, the other hydrogen halides are extremely strong acids in aqueous solution all three are fully dissociated in dilute solution, and their pA", values may be estimated by thermochemical cycle calculations. The thermochemical cycle shown in Figure 3.1 represents the various processes as the aqueous hydrogen halide, HX, is converted to a solution containing hydrated protons and hydrated halide ions. The enthalpy of acid dissociation of the HX(aq) compound is given by ... 

Students have already / v / employed Hess s law when performing Born-Haber cycle calculations in Chapter 6. 8.9 Hess s Law Now that we ve discussed in general terms the energy changes that occur during chemical reactions, let s look at a specific example in detail. In particular, let s look at the Haber process, the industrial method by which approximately 13 million tons of ammonia are produced each year in the United States, primarily for use as fertilizer. The reaction of hydrogen with nitrogen to make ammonia is exothermic, with AH0 = -92.2 kj. 

In order to simplify and standardize the cycle calculations, the following conditions were assumed ... 

From the product of C and ST found in the above steps of an iterative cycle, calculate an estimate of the original data matrix, D. 

Theoretical value COPa, corresponding to a Camo cycle calculates under the formula ... 

Molecule Protonation (P) or Deprotonation (D) P (So) Forster cycle calculations Fluorescence intensity measurements pK(Ti) Forster cycle calculations Ref... 

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