Reversible adiabatic flow

To solve a particular problem, we must also specify the process. For example, reversible adiabatic flow through a nozzle yields the following familiar expressions relating the properties at some point in the flow to the Mach number and the stagnation properties, i.e., the properties where the velocity is zero ... 

For a reversible, adiabatic flow, neither the reservoir conditions nor the critical conditions change from point to point in the systehn. Thus, a measurement or calculation of them for any point in the flow gives the values for the entire flow. However, in flow with friction (Sec. 8.4) or flow with heating or cooling (not treated in this text) or for normal shock waves (Sec. 8.5), the reservoir and critical conditions change from point to point in the flow. For such flows we must be conceptually prepared to use the apparatus shown in Fig. 8.7 at many points in the flow, and we must not assume that the values we find (or calculate) at one point would be the same as those at another. 

Total Pressure is the pressure that would occur if the fluid were brought to rest in a reversible adiabatic process. Many texts and engineers use the words total and stagnation to describe the flow characteristics interchangeably. To be accurate, the stagnation pressure is the pressure that would occur if the fluid were brought to rest adia-baticaUy or diabatically. 

Total pre.ssure is the pressure of the gas brought to rest in a reversible adiabatic manner. It can be measured by a pitot tube placed in the flow... 

Response time constant 403 Rkster. S. 6-13,655 Return bends, heat exchanger 505 Reversed flow 668 Reversibility, isothermal flow 143 Reversible adiabatic, isentropic flow 148... 

Annular flow reactors, such as that illustrated in Figure 3.2, are sometimes used for reversible, adiabatic, solid-catalyzed reactions where pressure near the end of the reactor must be minimized to achieve a favorable equilibrium. Ethylbenzene dehydrogenation fits this situation. Repeat Problem 3.7 but substitute an annular reactor for the tube. The inside (inlet) radius of the annulus is 0.1m and the outside (outlet) radius is 1.1m. 

Fig. 13. Comparison of simulated and experimental temperature profiles in a 2-m, near-adiabatic, packed-bed S02 reactor using a Chinese S101 catalyst and operating under periodic reversal of flow direction with r = 180 min, SV = 477 h"1, and inlet S02 = 3.89 vol% and T = 25°C. (Figure adapted from Wu et at., 1996, with permission of the authors.)...

Putting k = y gives an approximate equation for adiabatic flow. The result is only approximate because it implies an isentropic change, ie a reversible adiabatic change, but this is not the case owing to friction. A rigorous solution for adiabatic flow is given in Section 6.5. 

Equation 6.19 is the basic equation relating the pressure drop to the flow rate. The difficulty that arises in the case of adiabatic flow is that the equation of state is unknown. The relationship, PVy = constant, is valid for a reversible adiabatic change but flow with friction is irreversible. Thus a difficulty arises in determining the integral in equation 6.19 an alternative method of finding an expression for dPIV is sought. 

Accordirrg to the secorrd law, the irreversibilities due to fluid frictiorr m adiabatic flow cause arr errtropy irrcrease hr the fluid hr the directiorr of flow, hr the lirrrit as the flow approaches reversibility, this irrcrease approaches zero, hr gerreral, therr. 

The processes tlrat occur as tire working fluid flows around the cycle of Fig. 8.1 are represented by lines on tire TS diagram of Fig. 8.2. The sequence of lines shown coirfomrs to a Carnot cycle. Step 1 - 2 is tire vaporization process taking place in the boiler, wherein saturated liquid water absorbs heat at tire constant temperahire Th, and produces saturated vapor. Step 2 3 is a reversible, adiabatic expansion of saturated vapor into the two-phase... 

These inviscid flows are said to be reversible adiabatic or isentropic. ... 

A very important special case of the polytropic flow equation (5.25) is that describing a reversible, adiabatic expansion, where no heat is exchanged with the surroundings, i.e. an isentropic expansion. In this case, the ratio of specific heats, y, is substituted for n in the mass-flow equation ... 

Now consider a steam turbine as shown by the methods in Chap. 8, the reversible, adiabatic expansion of steam through a nozzle from about lOOpsia to atmospheric pressure produces a flow with a velocity of about 3000 ft/s. Thus, the blade desirable to use a... 

Figure 13.12 The principle of USO temperature and conversion profiles in an adiabatic catalytic reactor before the first reversal of flow direction (redrawn from Matros et al., 1984).

Phase changes under isothermal conditions and those in flowing fluids show a fundamental difference. In the first case the latent heat of evaporation has to be transferred between the system and the environment. Many flow processes, however, are adiabatic and some of them are almost reversible. In such adiabatic flows the latent heat must be provided from the internal energy of the fluid. The ratio of internal energy and latent heat which depends mostly on the molar specific heat of the substance characterizes the extent of phase change attainable in adiabatic processes. Obviously, adiabatic phase changes can take place much faster than isothermal phase changes. 

The maximum flow is obtained for the reversible adiabatic, that is, isentropic state change. However, for the calculation of this process, the speed of sound has to be evaluated at the conditions in the cross-flow area (index 1) of the valve. For this purpose, an iterative procedure is necessary. The necessary steps are as follows ... 

Figure 21.2 Schematic diagram showing the flow from a supersonic nozzle into a low-pressure region. Inside the isentropic core, the flux is a reversible adiabatic expansion. Adapted from Hudson,SoffoceSc7C/7ce, 1998, with permission of John Wiley Sons Ltd...

Any reversible process can be carried out in reverse. Thus, by reversing the reversible nonadiabatic process, it is possible to change the state from B to A by a reversible process with a net flow of heat out of the system and with Aq either negative or zero in each element of the reverse path. In contrast, the absence of an adiabatic path from B to A means that it is impossible to carry out the change A B by a reversible adiabatic process. 

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