Temperature ratio

Note that under choked conditions, the exit velocity is V = V = c = V/cKTVM not V/cKT(/M, . Sonic velocity must be evaluated at the exit temperature. For air, with k = 1.4, the critical pressure ratio p /vo is 0.5285 and the critical temperature ratio T /Tq = 0.8333. Thus, for air discharging from 300 K, the temperature drops by 50 K (90 R). This large temperature decrease results from the conversion of internal energy into kinetic energy and is reversible. As the discharged jet decelerates in the external stagant gas, it recovers its initial enthalpy. 

Liner holes. Liner area to casing area and liner hold area to casing area are important to the performance of combustors. For example, the pressure loss coefficient has a minimum value in the range of 0.6 of the liner area/ casing area ratio with a temperature ratio of 4 1. 

Next, the temperature ratio relationship in Equation 2.65 will be used. This relationship is the result of combining Equations 2.6 and 2.57 as well as a half dozen algebraic steps ... 

For more exact work, the temperature ratios of fj and f, related to the mode of heating can be used. These relate to 100% convective, such as forced warm air to a high-temperature radiant system, which gives 90% radiant and 10% convective. 

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... 

The important point here is that the efficiency is a function of the temperature ratio 6 as well as the pressure ratio r (and d, whereas it is a function of pressure ratio only for the reversible cycle, [CHT]r. 

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... 

As mentioned before, the thermal efficiency for the irreversible plant [CHT]i is a function of the temperature ratio 6= T T (as opposed to that of the reversible simple cycle [CHT]r, for which tj is a function of x only, and pressure ratio r, as illustrated in Fig. 3.3). Fig. 3.9 illustrates this difference, showing the irreversible thermal efficiency Tj(a , 6) which is strongly 0-dependent. 

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

Fig. 3.13 shows the overall efficiency for the [CBTJic, plant plotted against the i.sentropic temperature ratio for various maximum temperatures Tj (and 6= Ty/Ti, with T, = 27°C (3(X) K)). The following assumptions are also made polytropic efficiency, rjp = 0.9 for compressor and turbine pressure loss fraction in combustion 0.03 fuel (methane) and air supplied at 1 bar, 27°C (3(X) K). 

Fig. 3.13. Overall efficiency of CBT)ig cycle as a function of pressure ratio r with (and temperature ratio 6) as...

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. ... 

Fig. 4.10. Calculation of efficiency of. -iimple CBT plant—single-step cooled [CBT n ] as a function of iseniropic temperature ratio with maximum temperature (7 ) as a parameter.

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... 

The assumptions made by the various authors (viz. polytropic efficiencies, combustion pressure loss and temperature ratio, etc.) are all roughly similar to those used in the calculations of uncooled dry cycles. Some modest amounts of turbine cooling were allowed in certain cases [9] but the effect of these on the efficiency should not be large at max 250°C (see later for discussion of more detailed parametric calculations by some of these authors). 

Guirao and Bach (1979) used the flux-corrected transport method (a finite-difference method) to calculate blast from fuel-air explosions (see also Chapter 4). Three of their calculations were of a volumetric explosion, that is, an explosion in which the unbumed fuel-air mixture is instantaneously transformed into combustion gases. By this route, they obtained spheres whose pressure ratios (identical with temperature ratios) were 8.3 to 17.2, and whose ratios of specific heats were 1.136 to 1.26. Their calculations of shock overpressure compare well with those of Baker et al. (1975). In addition, they calculated the work done by the expanding contact surface between combustion products and their surroundings. They found that only 27% to 37% of the combustion energy was translated into work. 

Note Because the solution temperature of data for Figure 9-82D is 75-81 °F, it is assumed ambient, and no correction is made. If the operating temperature were higher or lower, then a temperatinre correction multiplier should be used above, with the absolute temperatures ratio being raised to the 6.0 power. 

In the present study, the pyrolysis of a waste polystyrene plastic (PSP) has beat investigated in a swirling fluidized-bed reactor to develop an effective reactor. Effects of the reaction time, temperature, ratio of the swirling gas and the gas velocity on the yields of an oil and a styrene monomer have been discussed. 

The relaxation of gaseous methane, ethane and propane is by the spin-rotation mechanism and each pure component can be correlated with density and temperature [15]. However, the relaxation rate is also a function of the collision cross section of each component and this must be taken into account for mixtures [16]. This is in contrast to the liquid hydrocarbons and their mixtures that relax by dipole-dipole interactions and thus correlate with the viscosity/temperature ratio. 

The correction factor is a function of the shell and tube fluid temperatures, and the number of tube and shell passes. It is normally correlated as a function of two dimensionless temperature ratios ... 

A Charles s law states that the volume/temperature ratio is constant (temperature in kelvins). 

Equation (9.103) can give an estimate for the flame thickness that is similar to that of the premixed flame by using Equation (9.100) and an estimate of 3 for the temperature ratio ... 

The two-zone model gives the result in terms of the neutral plane height (//rl) and the layer height (Hs) for a doorway vent of area A0 and height //,. The ambient to room temperature ratio is designated as 0 = T0/T ... 

Density. 1.0749iao. This is an actual density of benzoic acid taken at 130 °C. There is no temperature ratio as there is for the specific gravity (1.265918/4). 

The great disadvantage is the large uncertainty in the temperature ratio T0/T necessary to obtain p /p0. Other disadvantages are the facts that (1) the method can only be used for fast flames to avoid the convective effect of hot gases and (2) the method cannot work with dry mixtures. 

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