T-s- Diagram

For thermodynamic analysis, the T-s-diagram with temperature Tversus entropy s as axes and lines of constant pressure, density, and enthalpy has proven very helpful. Changes of states and heat or work released or absorbed can be illustrated clearly using the T-s-diagram. 

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FIG, 2-13 Temperahire-entropy diagram for nitrogen. Seotion of T-S diagram for nitrogen by E. S. Burnett, 1950. (Repainted from U.S. Bur Minos Rop. Invest. 4729.)... 

Although the T-s diagram is veiy useful for thermodynamic analysis, the pressure enthalpy diagram is used much more in refrigeration practice due to the fact that both evaporation and condensation are isobaric processes so that heat exchanged is equal to enthalpy difference A( = Ah. For the ideal, isentropic compression, the work could be also presented as enthalpy difference AW = Ah. The vapor compression cycle (Ranldne) is presented in Fig. H-73 in p-h coordinates. 

Figure 2-9. T-S diagram of the actual open simple cycle.

We next consider the application of the exergy flux equation to a closed cycle plant based on the Joule-Brayton (JB) cycle (see Fig. 1.4), but with irreversible compression and expansion processes—an irreversible Joule-Brayton (IJB) cycle. The T,.s diagram is as shown in Fig. 2.6. 

We use the original Joule-Bray ton cycle as a standard—an internally reversible closed gas turbine cycle 1,2,3,4 (see the T, s diagram of Fig. 3.1), with a maximum temperature 3 = Tb and a pressure ratio r. The minimum temperature is taken as 7, the ambient temperature, so that 7, = 7. ... 

Fig.. 1.1. T.s diagram for reversible closed simple cycle, (CHTJr.

A reversible recuperative a/s cycle, with the maximum possible heat transfer from the exhaust gas, qj = Cp(74 — 7y), is illustrated in the T,s diagram of Fig. 3.2, where 7y = 72. This heat is transferred to the compressor delivery air, raising its temperature to 7x = 74, before entering the heater. The net specific work output is the same as that... 

If reheat is introduced between a high pressure turbine and a low pressure turbine then examination of the T,s diagram (Fig. 3.4a) shows that the complete cycle is now made up... 

Fig. 3.4. T. s diagram for reheating added lo reversible simple and recuperative cycles.

Fig. 3.5. T. s diagram for inlercooling added to reversible simple and recuperalive cycles.

Fig. 3.6. T,s diagram for ultimate reversible gas turbine cycle [CICIC- BTBT- X r.

A closed cycle [CHT]i, with state points 1,2,3,4, is shown in the T,s diagram of Fig. 3.7. The specific compressor work input is given by... 

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

For the closed recuperative cycle [CHTXJi, with states 1,2,X,3,4, Y as in the T,s diagram of Fig. 3.10, the net specific work is unchanged but the heat supplied has to be reassessed as heat qj is transferred from the turbine exhaust to the compressor delivery air. Using the heat exchanger effectiveness, e = (Tx — — Ti) the heat supplied... 

A reversible cycle with turbine expansion split into two steps (high pressure, HP, and low pressure, LP) is illustrated in the T, s diagram of Fig. 4.3. The mass flow through the heater is still unity and the temperature rises from T2 to Tt, = Tq hence the heat supplied (3b is unchanged, as is the overall isentropic temperature ratio (x). But cooling air of mass flow i//H is used at entry to the first HP turbine (of isentropic temperature ratio. xh) and additional cooling of mass flow is introduced subsequently into the LP turbine (of isentropic temperature ratio Xl)- The total cooling flow is then i/( = i/ h + >h.-... 

Consider again the simplest case of compressor delivery air (mass flow i/>, at T ), mixed at constant pressure with unit mass flow of combustion products (at Tf) to give mass flow (1 + i/>) at Ts (see the T, s diagram of Fig. 4.5). The compression and expansion processes are now irreversible. 

Before eonsidering the effects of water injection in an EGT type plant, it is worthwhile to refer to the earlier studies on the performanee of some dry recuperative cycles. Fig. 6.6 shows the T..s diagram of a [CBT i X r cyele, with a heat exchanger effectiveness of unity. It is implied that the surface area for heat transfer is very large, so that the outlet temperature on the cold side is the same as the inlet temperature on the hot side. However, due to the higher specific heat of the hot gas, its outlet temperature is higher than the inlet temperature of the cold air. 

We describe a parametric point calculation of the efficiency of a simple CCGT plant, firstly with no feed heating. It is supposed that the main parameters of the gas turbine upper plant (pressure ratio, maximum temperature, and component efficiencies) have been specified and its performance (t)o)h determined (Fig. 7.3 shows the T,s diagram for the two plants and the various state points). 

This is essentially the approach adopted by Ruffi [9] in a comprehensive set of calculations, but he assumed that the economiser entry water temperature 7b is raised above the condenser temperature by feed heating, which was specified for all his calculations. The T,s diagram is shown in Fig. 7.6 the feed pump work terms are neglected so that h.j, = hy and h. = /ib. 

Figure 12-36(1), part la illustrates the state variation of the two-stage intercooled compressor on the T-S diagram (reproduced from Skrotzki by permission) ... 

Plots of the properties of various substances as well as tables and charts are extremely useful in solving engineering thermodynamic problems. Two-dimensional representations of processes on P-V, T-S, or H-S diagrams are especially useful in analyzing cyclical processes. The use of the P-V diagram was illustrated earlier. A typical T-S diagram for a Rankine vapor power cycle is depicted in Figure 2-36. 

Figure 2-36. (a) Schematic diagram of system, (b) T-S diagram of process. 

Because temperature (T) and salinity (S) are the main factors controlling density, oceanographers use T-S diagrams to describe the features of the different water masses. The average temperature and salinity of the world ocean and various parts of the ocean are given in Fig. 10-3 and Table 10-3. The North Atlantic contains the warmest and saltiest water of the major oceans. The Southern Ocean (the region around Antarctica) is the coldest and the North Pacific has the lowest average salinity. 

Conventional T-S diagrams for specific locations in the individual oceans are shown in Fig. 10-4. The inflections in the curves reflect the inputs of water from different sources. The linear regions represent mixing intervals between these core sources. For example, in the Atlantic Ocean the curves reflect input from Antarctic Bottom Water (AABW), North Atlantic Deep Water (NADW), Antarctic Intermediate Water (AIW), Mediterranean Water (MW), and Warm Surface Water (WSW). 

Fig. 10-3 Simulated three-dimensional T-S diagram of the water masses of the world ocean. Apparent elevation is proportional to volume. Elevation of highest peak corresponds to 26.0 x 10 km per bivariate class 0.1°C X 0.01%o. (Reproduced with permission from L. V. Worthington, The water masses of the world ocean some results of a fine-scale census. In B. A. Warren and C. Wunsch (1981). Evaluation of Physical Oceanography," MIT Press, Cambridge, MA.)...

Further insight can be gained from the idealized T - S diagram for the cycle. Figure 9-14. The compression of the air and fuel streams is represented here as a single adiabatic reversible (constant S) process in which the temperature of the gases rises above ambient. The heating of... 

T-S diagrams based on ocean data typically exhibit curvature. Causes for this nonlinearity include (1) mixing of more than two end members (Figure 4.18e), (2) temporal variations in environmental conditions during fiarmation of the end members, and (3)... 

T-S diagrams for the western and eastern basins of the South Atlantic, (a) and (b) represent two locales in the western basin of the South Atlantic on the same line of longitude but different by 20° of latitude, (c) and (d) are in the eastern basin of the South Atlantic, again about the same 20° of latitude apart from one another but on the same longitude. The small numbers on each graph line represent depths in meters. The horizontal portion of each diagram indicates mixing. 

T-S diagram The x-y graph of the temperature and salinity of water samples used to identify source water masses and types. 

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