Chapter 6: Stationary Combustion Systems

Chapter 6: Stationary Combustion Systems

Figure 6-1. Schematic of components of coal-fired electric plant, with conversion of coal to electricity via boiler, turbine, and generator

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Brief Thermodynamic Review Carnot Limit: The difference between the high and low process temperatures over the high process temperature. Notice that the Carnot efficiency decreases as the process limits move upward on the absolute temperature scale. This is that annoying temperature is an absolute thing. Thermal Efficiency: The difference between the work output and the work input required over the heat input. Notice that getting more work out of the same heat input (combined cycles) is a good thing.

Brief Thermodynamic Review Enthalpy - Quantity of Energy Units of energy per unit mass kj/kg or BTU/lb. Implies that systems with higher Enthalpy contain more energy per unit mass. Entrophy Quality of Energy Units of energy per units of mass-temperature kj/kg K or BTU/lb R Low values imply a more ordered system In thermodynamics high values of Entrophy in working fluids mean higher temperatures and pressures and more ability to do work.

Figure 6-2. Schematic of Simple Rankine device

Figure 6-3. Temperature-entropy diagram for the ideal Rankine cycle ω out ω in q in

Example 6-1, p 176, metric units An ideal Rankine cycle with isentropic compression and expansion operates between a maximum pressure of 4 Mpa at the turbine entry and 100 kpa in the condenser. a) Calculate the thermal efficiency of this cycle. ω in = work done by pump ω out = work done by expanding steam q in = heat provided by boiler ω in q in ω out Time for thermodynamic tables

Saturated Water Pressure Table

Saturated Water Pressure Table, Page 2

Example 6-1, p 176, metric units From Saturated Water Pressure Table or from online calculator

All we need is h 4 Use entropy values of liquid and saturated steam at 100 C to use with s 4 to derive a quality factor Use this quality factor and the known enthalpies to derive h 4.

Solution Degrees Kelvin

Figure 6-4. Components in Brayton cycle

Figure 6-5. Temperature-entropy diagram for the ideal Brayton cycle

Example 6-4, p 181, metric units A Brayton gas cycle with isentropic compression and expansion operates with 295 K air entering the compressor at 95 kpa and with a compression ratio of 6:1. The compressed air is heated to 1100 K before the combustion products are expanded in the turbine. Calculate the thermal efficiency of this cycle.

Ideal Gas Properties of Air

Figure 6-5. Temperature-entropy diagram for the ideal Brayton cycle Example 6-4 1100K h 3 = 1160.07 kj/kg P r3 =167.1 295K h 1 = 295.17 kj/kg P r1 =1.3068

Ideal Gas Properties of Air

Figure 6-5. Temperature-entropy diagram for the ideal Brayton cycle Example 6-4 1100K h 3 = 1160.07 kj/kg P r3 =167.1 P r2 = 6(1.3068) = 7.841~7.824 h 2 ~ 492.7 kj/kg 295K h 1 = 295.17 kj/kg P r1 =1.3068

Ideal Gas Properties of Air

Interpolating to find h 4 The pressure associated with h 4 falls between table values. The percentage difference in the pressures can be applied to the respective enthalpies to extrapolate h 4.

Figure 6-5. Temperature-entropy diagram for the ideal Brayton cycle Example 6-4 1100K h 3 = 1160.07 kj/kg P r3 =167.1 P r2 = 6(1.3068) = 7.841~7.824 h 2 ~ 492.7 kj/kg P r4 = 167.1/6 = 27.85 h 4 = 706.5 kj/kg by interpolation 295K h 1 = 295.17 kj/kg P r1 =1.3068

Example 6-4, p 181, metric units A Brayton gas cycle with isentropic compression and expansion operates with 295K air entering the compressor at 95 kpa and with a compression ratio of 6:1. The compressed air is heated to 1100 K before the combustion products are expanded in the turbine. Calculate the thermal efficiency of this cycle.

Figure 6-7. Schematic of combined cycle system components

Figure 6-8. Combined cycle Temperature-entropy diagram Example 6-8 calculates efficiency of 58% but would be less due to losses

Table 6-1. Thermal efficiency at design operating conditions for a selection of combined cycle power plants

Other Ways to Drive up Efficiency Super critical operation High pressures and temperatures High component costs Cogeneration Savage wasted heat Site and need specific

Figure 6-11. Comparison of cost breakdown for conventional and supercritical plants

Figure 6-9. Schematic of components of cogeneration system

Table 6-2. Summary of cost and savings for example Microturbine cogen project Supply 500 homes with electricity while generating more than 23,250 of hot water. Pp 198-200

Figure 6-14. Schematic of Cornell combined heat and power project with gas turbine, steam turbine, and district heating system for campus buildings Source: Cornell University Utilities & Energy Management. Reprinted with permission.

Figure 6-15. Load duration curve for a fictitious utility market Peaking plants Minimum capital costs High variable costs Low duty cycle Oil or gas likely Load-following plants Lower capital costs Higher variable costs Easy to vary output Gas likely Baseline plants Highest cost Most efficient Low variable costs High duty cycle Coal likely With minimum 6 GW of demand for all 8760 h of the year, and a maximum demand of 18 GW of demand in the highest- demand hour of the year

Summary, Chapter 6 What goes here? Rankine Cycle Coal and Water Less efficient Thermal eff. And Carnot Limit Brayton Cycle Gas and Air More efficient Thermal eff and Carnot limit Combined Cycle Cogeneration Supercritical