Turbines worked example

A useful rule of thumb is that the turbine work in a STIC plant is increased by a factor of about (1 + 25), since the specific heat of the steam is about double that of the specific heat of the dry gas. This is in agreement with the example given above and with the earlier detailed calculations by Fraize and Kinney [3]. (Their work was based on the assumption that the mixture of air and steam in the turbine behaved as a semi-perfect gas, with specific heats being determined simply by mass averaging of the values for the two components.)... 

We can make an estimate of the efficiency of a power plant using a gas turbine (see Figure 9.10). We assume that the combustor inlet temperature of the gases is T2 = 298.15 K and turbine inlet temperature of T3 = 1423.15 K and use the data from the methane combustion example. We further assume that the turbine has a total efficiency of 0.75. We will first compute the turbine work if the expansion is isentropic to 1 bar. Consider Equation 9.9, where we set AS = 0. We can derive the following [10] ... 

WORKED EXAMPLE FOR CALCULATING THE PERFORMANCE OF A GAS TURBINE Therefore, from (2.17),... 

Appendix F Worked Example for Calculating the Performance of a Gas Turbine 551... 

Since the amount of pumping work is much smaller than the work received in the turbine (see Example 6.iq1 there is a net production of work. The efficiency of the plant is defined as the ratio of the net work produced to the amount of heat in the boiler ... 

The choice of a candidate turbine generator plant for the UNITHERM NPP depends on the plant capacity and operation mode (electricity generation or cogeneration) as requested by its users. It is planned to use standard turbine equipment, for example, manufactured by the Kaluga Turbine Works (AO KTZ) [II-6], These turbine-generators use steam of low parameters. 

The minus sign indicates that power is given out. This is a useful addition to the 100-kW electrical power output of the fuel cell, but note that it provides less than half of the power needed to drive the compressor, as calculated with the worked example of Section 9.5. Furthermore, this example is the best possible result turbine efficiencies will usually be somewhat lower than the 0.7 we obtained here. As can be seen from the chart, much of the operating region is at greatly lower efficiencies. 

The second law can also suggest appropriate corrective action. Eor example, in combustion, preheating the air or firing at high pressure in a gas turbine, as is done for an ethylene (qv) cracking furnace, improves energy efficiency by reducing the lost work of combustion (Eig. 4). 

An impulse-type turbine experiences its entire enthalphy drop in the nozzle, thus naving a very high velocity entering the rotor. The velocity entering the rotor is about twice the velocity of the wheel. The reaction type turbine divides the enthalphy drop in the nozzle and in the rotor. Thus, for example, a 50 percent reaction turbine has a velocity leaving the nozzle equal to the wheel speed and produces about V2 the work of a similar size impulse turbine at about 2-3 percentage points higher efficiency than the impulse turbine (0 percent reaction turbine). The effect on the efficiency and ratio of the wheel speed to inlet velocity is shown in Fig. 29-27 for an impiilse turbine and 50 percent reaction turbine. 

It can be seen from Fig. 7.10 that the eurve for wcv lies above that for wh. As for the gas turbine eyele the pressure ratio for maximum effieiency in the eombined plant may be obtained by drawing a tangent to the work output curve from a point on the x-axis where x= 1 +7 (.(0— 1), i.e. X = 4.6 in the example. The optimum pressure ratio for the eombined plant (r = 18) is less than that for the gas turbine alone (r = 30) although it is still greater than the pres.sure ratio which gives maximum speeific work in the higher plant (r = 11). However, the efficieney tjcp varies little with r about the optimum point. 

If all the heat absorbed were converted into work, the efficiency would be 1, or 100 percent. If none of the heat absorbed was converted into work, the efficiency would be 0. The first law of thermodynamics limits the efficiency of any heat engine to 1 but does not prevent an efficiency of 1. The efficiency of practical heat engines is always less than 1. For example, the efficiency of a large steam turbine in an electric power plant is about 0.5, which is considerably more efficient than the typical 0.35 efficiency of an auto engine. When two objects at different temperatures are m... 

The gas turbine shown in Figure 3-7 is an open-cycle type. An open-cycle type gas turbine uses the same air that passes through the combustion process to operate the compressor. This is the type most often used for stationary power unit applications. A typical example of power requirements for an open-cycle type gas turbine would be for the unit to develop a total of 3,000 hp. However, about 2,000 hp of this would be needed to operate its compressor. This would leave 1,000 hp to operate the generator (or other systems connected to the ga.s turbine). Thus, such a gas turbine power unit would be rated as a 1,000-hp unit because this is the power that can be utilized to do external work. 

An example is shown in Figure 15.14. By raising steam at high pressure (say, 60 bar-absolute and 540°C) and then expanding this through a turbine to the process steam pressure requirements of 3 bar then useful work can be done by the turbine for generation of electrical power. For this example, each kg/s of steam gives 590 kW of electrical power. 

For actual Rankine cycles, many irreversibilities are present in various components. Fluid friction causes pressure drops in the boiler and condenser. These drops in the boiler and condenser are usually small. The major irreversibilities occur within the turbine and pump. To account for these irreversibility effects, turbine efficiency and pump efficiency must be used in computing the actual work produced or consumed. The T-s diagram of the actual Rankine cycle is shown in Fig. 2.9. The effect of irreversibilities on the thermal efficiency of a Rankine cycle is illustrated in the following example. 

The last of these methods has been applied particularly to chemical reaction vessels. It is covered in detail in Chapter 17. In most cases, however, the RTDs have not been correlated with impeller characteristics or other mixing parameters. Largely this also is true of most mixing investigations, but Figure 10.3 is an uncommon example of correlation of blend time in terms of Reynolds number for the popular pitched blade turbine impeller. As expected, the blend time levels off beyond a certain mixing intensity, in this case beyond Reynolds numbers of 30,000 or so. The acid-base indicator technique was used. Other details of the test work and the scatter of the data are not revealed in the published information. Another practical solution of the problem is typified by Table 10.1 which relates blend time to power input to... 

Microturbines can take many forms. For example, researchers at Hong Kong University, working with Motorwave, Ltd., have developed a micro wind turbine. These light turbines are only 25 centimeters in diameter and may be appropriate for installation in sets of several turbines in a series. 

Students are reminded of the upper thermodynamic limit set on the efficiency of a heat engine, for example the internal combustion and gas-turbine engines. The ideal and totally unrealistic engine would operate on the so-called Carnot cycle where the working substance (e.g. the gas) is taken in at the high temperature (Th) and pressure and after doing external work is exhausted at the lower temperature (Tc) and lower pressure. The Carnot efficiency, /, is given by... 

The method used in the previous example, called the extraction method, assumes that the sole purpose of the turbine is to produce shaft power. Therefore, the shaft work is charged for the capital cost of the turbine and for the exergy extracted from the steam by the turbine to produce the work. With this rationale, the additional equation is obtained by equating the unit costs of... 

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