Temperature isentropic ratio

Plots of thermal efficiency for the [CHTJr and [CHTXJr cycles against the isentropic temperature ratio x are shown in Fig. 3.3, for 6 = Ty/Tf = 4, 6.25. The efficiency of the [CHTJr cycle increases continuously with x independent of 6, but that of the [CHTXJr cycle increases with 6 for a given x. For a given 6 = Ty/T, the efficiency of the [CHTXJr cycle is equal to the Carnot efficiency at j = 1 and then decreases with x until it meets the... 

By differentiating Eq. (3.13) with respect to x and equating the differential to zero, it may be shown that the isentropic temperature ratio for maximum thermal efficiency (jCe) is given by the equation... 

The isentropic temperature ratio for maximum efficiency (x ) is again obtained by writing dp/hx = 0 after some algebra this yields... 

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.-... 

Fig. 4.10 shows more fully calculated overall efficiencies (for turbine cooling only) replotted against isentropic temperature ratio for various selected values of Tj = T,.,. This figure may be compared directly with Fig. 3.9 (the a/s calculations for the corresponding CHT cycle) and Fig. 3.13 (the real gas calculations of efficiency for the uncoooled CBT cycle). The optimum pressure ratio for maximum efficiency again increases with maximum cycle temperature T. ... 

The thermal efficiencies (ij) of these five cycles, all with perfect recuperation, are plotted in Fig. 6.7 against the isentropic temperature ratio a-, for = 0-8 and Tj/Ti = 5... 

Obtain an expression for the maximum flow for a given upstream pressure for isentropic flow through a horizontal nozzle. Show that for air (ratio of specific heats y = 1.4) the critical pressure ratio is 0,53 and calculate the maximum flow through an orifice of area 30 mm2 and coefficient of discharge 0.65 when the upstream pressure is 1.5 MN/m2 and the upstream temperature 293 K,... 

A gas well contains hydrocarbon gases with an average molecular weight of 24, which can be assumed to be an ideal gas with a specific heat ratio of 1.3. The pressure and temperature at the top of the well are 250 psig and 70°F, respectively. The gas is being produced at a slow rate, so conditions in the well can be considered to be isentropic. 

If we compare the work required to compress a given gas to a given compression ratio by isothermal and isentropic processes, we see that the isothermal work is always less than the isentropic work. That is, less energy would be required if compressors could be made to operate under isothermal conditions. However, in most cases a compressor operates under more nearly adiabatic conditions (isentropic, if frictionless) because of the relatively short residence time of the gas in the compressor, which allows very little time for heat generated by compression to be transferred away. The temperature rise during an isentropic compression is determined by eliminating p from Eqs. (8-17) and (8-19) ... 

An engine operates on an Otto cycle with a compression ratio of 8. At the beginning of the isentropic compression process, the volume, pressure, and temperature of the air are 0.01 m, llOkPa, and 50°C. At the end of the combustion process, the temperature is 900°C. Find (a) the temperature at the remaining two states of the Otto cycle, (b) the pressure of the gas at the end of the combustion process, (c) the heat added per unit mass to the engine in the combustion chamber, (d) the heat removed per unit mass from the engine to the environment, (e) the compression work per unit mass added, (f) the expansion work per unit mass done, (g) MEP, and (h) thermal cycle efficiency. 

An ideal Diesel cycle with a compression ratio of 17 and a cut-off ratio of 2 has an air temperature of 105°F and a pressure of ISpsia at the beginning of the isentropic compression process. Determine... 

An ideal Diesel cycle with a compression ratio of 17 and a cutoff ratio of 2 has a temperature of 313 K and a pressure of 100 kPa at the beginning of the isentropic compression process. Use the cold air-standard assumptions and assume that k= A. Determine (a) the temperature and pressure of the air at the end of the isentropic compression process and at the end of the combustion process, and (b) the thermal efficiency of the cycle. 

The thrustor was considered to consist of two sections 1) where the mixture is formed and 2) where combustion takes place and the pressure is generated. The principal mechanism involved in the combustion process was assumed to be successive ignition, but other mechanisms such as turbulent frontal combustion were also considered. The analysis yielded two instability criteria, expressed in terms of the Mach number in zone 1, the velocity ratio in zones 1 and 2, the isentropic exponent in zone 2, the activation energy, the temperature of the cold gas, the pressure upstream of the combustion zone, and the pressure drop due to the combustion... 

The thermodynamic state of liquids is a changing polytropic one (close to isentropic) during quick compression (see Fig.4.1-1, for C02) and the corresponding temperature rise is low for liquids and large for gases (see AB in Fig. 4.1-1). The final compression temperature limits the compression ratio per stage with gas compressors. 

The isentropic temperature in terms of compression ratio is given for ideal gases by... 

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. 

Consider an air-standard cycle for representing the turbojet power plant shown in Fig. 8.13. The temperature and pressure of the air entering the compressor are 1 bar and 30°C. The pressure ratio in the compressor is 6,5, and the temperature at the turbine inlet is l,I00°C. If expansion in the nozzle is isentropic and if the nozzle exhausts at 1 bar. what is the pressure at the nozzle inlet (turbine exhaust) and what is the velocity of the air leaving the nozzle ... 

At very high compression ratios, on the other hand, as p,/pu approaches a limiting or near-limiting value, the temperature climbs precipitously, as does the Mach number. It can be readily shown, by comparing the shock temperatures with those obtained in an adiabatic and isentropic compression T oc of comparable pressure change that there is much... 

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