Turbines isentropic efficiency

The turbine isentropic efficiency tjt measures the ratio of the actual to ideal work obtained ... 

From the study of uncooled cycles in Chapter 3, we next move to consider irreversible cycles with compressor and turbine isentropic efficiencies, tjc and r/p, respectively. 

Steam enters a turbine of a Rankine power plant at 5 MPa and 400°C, and exhausts to the condenser at lOkPa. The turbine produces a power output of 20 MW. Given a turbine isentropic efficiency of 90% and a pump isentropic efficiency of 100% ... 

For large steam turbines, isentropic efficiency can be between 50 and 70% while efficiency for small turbines is much lower with a wide variation depending on speed, horse power (hp), and pressure conditions. Efficiency varies with turbine loading, which can be described by an efficiency curve. This curve can be used to determine actual steam rates based on specific turbine loading. 

Two parameters, namely, theoretical steam rate and turbine isentropic efficiency, can be used to determine actual steam rate required by the steam turbine to make a certain amount of power. The theoretical steam rate is described by ideal expansion. The assumption behind ideal expansion is that there is no thermal and hydraulic losses in the expansion process resulting in zero change in entropy (5) (see Figure 15.5). Thus, the theoretical steam rate is the minimum required for making a certain amount of power. In reality, losses occur in steam expansion and isentropic efficiency describes the irreversible losses in the real expansion causing deviation from the ideal expansion ... 

The sensitivity of reactor outlet temperature to overall plant performance was examined for a temperature range of 1100K to 1200K. Turbine isentropic efficiency is assumed to be constant over the range of temperatures evaluated. The results of the reactor outlet temperature sensitivity study are shown in Figure 6-7. 

Exampie A.3.1 The pressures for three steam mains have been set to the conditions given in Table A.l. Medium- and low-pressure steam are generated by expanding high-pressure steam through a steam turbine with an isentropic efficiency of 80 percent. The cost of fuel is 4.00 GJ and the cost of electricity is 0.07 h. Boiler feedwater is available at 100°C with a heat capacity... 

From this relationship, it is obvious that polytropic efficiency is the limiting value of the isentropic efficiency as the pressure increase approaches zero, and the value of the polytropic efficiency is higher than the corresponding adiabatic efficiency. Figure 3-6 shows the relationship between adiabatic and polytropic efficiency as the pressure ratio across the compressor increases. Figure 3-7 shows the relationship across the turbine. 

The polytropic efficiency in a turbine can be related to the isentropic efficiency and obtained by combining the previous two equations... 

Thus there are three modifications to the a/s efficiency analysis, involving (i) the specific heats ( and n ), (ii) the fuel-air ratio / and the increased turbine mass flow (I +/), and (iii) the pressure loss term S. The second of these is small for most gas turbines which have large air-fuel ratios and / is of the order of l/IOO. The third, which can be significant, can also be allowed for a modification of the a/s turbine efficiency, as given in Hawthorne and Davis [I]. (However, this is not very convenient as the isentropic efficiency tjt then varies with r and jc, leading to substantial modifications of the Hawthome-Davis chart.)... 

By introducing isentropic efficiencies of the turbine ni and compressor the turbine work output is given as ... 

Generally, the efficiency of steam turbines decreases with decreasing load. The overall turbine efficiency can be represented by two components the isentropic efficiency and the mechanical efficiency. The mechanical efficiency reflects the efficiency with which the energy that is extracted from steam is transformed into useful power and accounts for mechanical frictional losses, heat losses, and so on. The mechanical efficiency is high (typically 0.95 to 0.99)6. However, the mechanical efficiency does not reflect the efficiency with which energy is extracted from steam. This is characterized by the isentropic efficiency introduced in Figure 2.1 and Equation 2.3, defined as ... 

In addition to the mechanical efficiency being much higher than the isentropic efficiency, in most cases the mechanical efficiency does not change significantly with load. By contrast, the isentropic efficiency does change significantly with load. The overall steam turbine efficiency can be defined as ... 

Figure 23.10a illustrates the relationship between turbine efficiency and mass flow through the turbine. Because hMECH his, the major contribution to the nonlinear trend of the overall efficiency with part-load is from the isentropic efficiency his A turbine model needs to capture this behavior. It should also be noted that there will be an efficiency associated with an electricity generating set coupled to the steam turbine (typically 95 to 98%). 

A steam turbine operates with inlet steam conditions of 40 barg and 420°C and can be assumed to operate with an isentropic efficiency of 80% and a mechanical efficiency of 95%. Calculate the power production for a steam flowrate of 10 kg s-1 and the heat available per kg in the exhaust steam (i.e. superheat plus latent heat) for outlet conditions of ... 

A proposal is made to use a geothermal supply of hot water at 1 MPa and 170°C to operate a steam turbine as shown in Fig. 2.24a. The high-pressure water is throttled into a flash evaporator chamber, which forms liquid and vapor at a lower pressure of 400 kPa. The liquid is discarded while the saturated vapor feeds the turbine and exits at lOkPa. Cooling water is available at 15°C. The turbine has an isentropic efficiency of 88%. Find the turbine power per unit geothermal hot-water mass flow rate. Find the optimized flash pressure that will give the most turbine power per unit geothermal hot-water mass flow rate. 

The third step is to model the components of the conceptual plant. For example, a steam turbine may be modeled as an adiabatic process with 85% isentropic efficiency. 

Steam is fed to a turbine at 614.7 psia and 825°F and is discharged at 64.7 psia. (a) Find the theoretical steam rate, lb/kWh, by using the steam tables, (b) If the isentropic efficiency is 70%, find the outlet temperature, (c) Find the theoretical steam rate if the behavior is ideal, with Cp Cv = 1.33. 

First, it is instructive to examine the performance of a recuperated system that has only one compressor (i.e., remove the IC and C2 from Figure 8.2) and compare this to a simple cycle GT (i.e., also remove the recuperator from the diagram). Consider an isentropic compressor efficiency of 85%, isentropic turbine expander efficiency of 90%, recuperator effectiveness of 88% and no pressure losses. A fixed turbine inlet temperature of 1200 K will be assumed for various pressure ratios. This value is based on an assumed 1000 K SOFC inlet temperature, and a 200 K temperature rise from the SOFC inlet to the turbine inlet. The 200 K temperature increase from the cathode inlet to the turbine inlet is reasonable to assume given a cathode temperature difference across the cell of 150 K, and another 50 K temperature increase from anode exhaust combustion. Thus, 1200 K will be used as a base case for the turbine inlet temperature, and for sensitivity, values of 1100 and 1300 K will also be analyzed. 

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