Cycle thermal efficiency

This is the inverse of the closed cycle thermal efficiency, when and W are expressed in the same units. 

Two objectives are immediately clear. If the top temperature can be raised and the bottom temperature lowered, then the ratio t= (Tjnin/Tjnax) decreased and, as with a Carnot cycle, thermal efficiency will be increased (for given /a,). The limit on top temperature is likely to be metallurgical while that on the bottom temperature is of the surrounding atmosphere. 

In a Rankine power plant, the steam temperature and pressure at the turbine inlet are 1000°F and 2000 psia. The temperature of the condensing steam in the condenser is maintained at 60° F. The power generated by the turbine is 30,000 hp. Assuming all processes to be ideal, determine (1) the pump power required (hp), (2) the mass flow rate, (3) the heat transfer added in the boiler (Btu/hr), (4) the heat transfer removed from the condenser (Btu/hr), and (5) the cycle thermal efficiency (%). 

Steam is generated in the boiler of a steam power plant operating on an ideal Rankine cycle at 10 MPa and 500° C at a steady rate of 80 kg/sec. The steam expands in the turbine to a pressure of 7.5 kPa. Determine (1) the quality of the steam at the turbine exit, (2) rate of heat rejection in the condenser, (3) the power delivered by the turbine, and (4) the cycle thermal efficiency (%). 

The pressure and temperature at the start of compression in an air Diesel cycle are 101 kPa and 300 K. The compression ratio is 15, and the amount of heat addition is 2000kJ/kg of air. Determine (a) the maximum cycle pressure and maximum temperature of the cycle, and (b) the cycle thermal efficiency. 

Try to modify his design (use pi, pig, p and pg as design parameters only) to get a better cycle thermal efficiency than his /cycie= 55.16%. 

Determine the pressure and temperature of each state, power required by the top-cycle compressor, power produced by the top-cycle turbines, thermal efficiency of the combined cycle, thermal efficiency of the top cycle, thermal efficiency of the bottom cycle, power input to the combined cycle, power output by the combined cycle, power net output of the combined cycle, rate of heat added to the combined cycle, rate of heat removed from the combined cycle, power input to the top cycle, power output by the top cycle, power net output of the top cycle, rate of heat added to the top cycle, rate of heat removed from the top cycle, power input to the bottom cycle, power output by the bottom cycle, power net output of the bottom cycle, rate of heat added to the bottom cycle, and rate of heat removed from the bottom cycle. 

Determine the pressure and temperature of each state, power required by the top-cycle compressor, power produced by the top-cycle turbines, thermal efficiency of the combined cycle, thermal efficiency of the top cycle, thermal efficiency of the bottom cycle, power input to... 

Determine the mass flow rate of the freon cycle, thermal efficiency of the combined cycle, power input to the combined cycle, power output by the combined cycle, power net output of the combined cycle, rate of heat added to the combined cycle, and rate of heat removed from the combined cycle. 

The energy requirements of the three sections (using the modified Neumann model for the iodine section) are gathered in Table 1. Using a heat to electricity conversion factor of 50%, they correspond to a cycle thermal efficiency of 39.3%. 

Most condensers used in steam power plants operate at pressures well below the atmospheric pressure (usually under 0.1 atm) to maximize cycle thermal efficiency, and operation at such low pressures raises the possibility of air (a noncondensable gas) leaking into the condensers. Experimental studies show that the presence of noncondensable gases in the vapor has a detrimental effect on condensation heat transfer. Even small amounts of a noncondensable gas in the vapor cause significant drops in heat transfer coefficient during condensation. Eor example, the presence of less than 1 percent (by mass) of air in steam can reduce the condensation heat transfer coefficient by more than half. Therefore, it is common practice to periodically vent out the noncondensable gases that accumulate in the condensers to ensure proper operation. 

The reactor could be designed, built and operated as a boiling water reactor (BWR), a pressurized water reactor (PWR) or a direct-flow system with superheated steam at the core outlet. The latter offers the potential for having a steam cycle thermal efficiency of about 43%, which could decrease the capital costs per kW(e) by nearly one-third. The present short description is based on the data for a BWR version of the AFPR. 

Because a 95% effective recuperator is sized here, the pressure ratio across the compressor that results in the optimum cycle efficiency is 1.65. Using this pressure ratio with the appropriate cycle parameters results in a cycle thermal efficiency of 28.2% with a HeXe40 mass flow of 6.28 kg/s. Thus, for the proposed core thermal power of 500 kW, 150 kW of shaft power is available. With a generator efficiency of 95%, the electrical power resulting from this design is projected to be 141 kW. 

This component allows the core to add a lesser amoimt of heat to the flow at a higher temperature and thus increase overall thermal efficiency. The recuperator parameter of interest is the efiectiveness, which is a measure of the actual heat transferred to the maximiun possible heat that could be transferred. A low value of effectiveness will decrease cycle thermal efficiency but have a small physical size. A high value of effectiveness will increase cycle efficiency at the expense of a larger physical size. An appropriate value balancing the cycle efficiency and the physical size is 95%. 

One parameter of choice is the recuperator effectiveness. Effectiveness is defined as the actual heat transferred divided by the maximal possible heat transferred with an infinite area heat exchanger. As might be expected, the higher the effectiveness, the higher the resultant cycle thermal efficiency. The disadvantage of a higher effectiveness is that the heat transfer area and volume, as well as pressure drop, increase as the effectiveness increases. Because recuperators with a high effectiveness of 95% are currently reasonably achievable in hardware, this parameter will be used in this study. 

The remaining parameter is the compressor ratio P. The pressure ratio is a design parameter for the compressor component so it can be varied for optimum overall cycle thermal efficiency. 

The expression for cycle thermal efficiency can now be calculated by varying the pressure ratio. Other curves representing the thermal efficiency as a function of pressure ratio for different recuperator effectiveness were also calculated. The results are shown in Fig. 4.45. 

From inspection of Fig. 4.45, the optimum cycle thermal efficiency is 28.2%, occurring at a pressure ratio of 1.65 for a recuperator effectiveness of 95%. It is clear from Fig. 4.45 that the higher the effectiveness, the higher the cycle thermal efficiency. Also, note that the maximal efficiency occurs at a lower pressure ratio as the effectiveness increases. The cycle heat balance showing the temperatures throughout the cycle are shown in Fig. 4.46. 

From inspection of Fig. 4.50, the thermal conductance (solid line) increases as the number of fins increases but at the cost of an increasing pressure drop (dotted line). As stated previously, a low parasitic pressure drop will increase overall cycle thermal efficiency. A pressure drop of 1% was budgeted arbitrarily for the core heat transfer surface, which results in a thermal conductance of 11.3 kW/K for a fin count of 420 (fin spacing of 6 mm) as shown on Fig. 4.50. Thus for a core power level of 500 kW, the metal temperature at the fin root would be 44 K higher than the working fluid. If a lower pressure drop is considered to potentially improve the overall cycle thermal efficiency, the core temperatures would increase to accommodate the lower thermal conductance of the heat removal finned aimulus. 

A range of operating parameters (e g., pressure and temperature) will need to be established early in the design, taking into consideration measurement uncertainty, minimum slider movement, minimum Brayton speed increment, operating bands, slider (or drum) sensitivity, component performance decrement over life, overall cycle thermal efficiency, and transients during normal operations and recoverable casualties. 

An ideal diatomic gas in an amount of v = 1 mole is under a pressure = 250 kPa and occupies volume Vj = 10 L. The gas is heated to Tj = 400 K and further isothennicaUy expanded to initial pressure. After that, the gas returns to its initial state by isobaric compression. Define the cycle thermal efficiency e. 

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