Adiabatic expansion flow

To calculate the heat duty it must be remembered that the pressure drop through the choke is instantaneous. That is, no heat is absorbed or lost, but there is a temperature change. This is an adiabatic expansion of the gas w ith no change in enthalpy. Flow through the coils is a constant pressure process, except for the small amount of pressure drop due to friction. Thus, the change in enthalpy of the gas is equal to the heat absorbed. 

Figure 4-14 The expansion factor Kg for adiabatic pipe flow for y = 1.4. From AICHE/CCPS, Guidelines for Consequence Analysis of Chemical Releases (New York American Institute of Chemical Engineers, 1999).

Orifice Discharge for Gas Flow The analytic solution for discharge through an orifice of an ideal gas is derived by invoking the equation of state for adiabatic expansion of an ideal gas ... 

The air-intake used to induce air from the flight-altitude atmosphere plays an important role in determining the overall efficiency of ducted rockets. The air pressure built up by the shock wave determines the pressure in the ramburner. The temperature of the compressed air is also increased by the heating effect of the shock wave. The fuel-rich gaseous products formed in the gas generator burn with the pressurized and shock-wave heated air in the ramburner. The nozzle attached to the rear-end of the ramburner increases the flow velocity of the combustion products through an adiabatic expansion process. This adiabatic expansion process is equivalent to the expansion process of a rocket nozzle described in Section 1.2. 

Air, at a pressure of 10 MN/m2 and a temperature of 290 K, flows from a reservoir through a mild steel pipe of 10 mm diameter and 30 m long into a second reservoir at a pressure P2. Plot the mass rate of flow of the air as a function of the pressure P2. Neglect any effects attributable to differences in level and assume an adiabatic expansion of the air. ji = 0.018 rnN s/m2, y = 1.36. 

The reaction occurs in an adiabatic stirred flow reactor with feed flow rate F, transient compositions cA, and cB and reaction rate JT, and total mass of reacting mixtures M. For small perturbations around the stationary state(s), the following expansions are used ... 

Equation (26-137) is recognized as the expression for all-gas flow by adiabatic expansion across an orifice or nozzle. The factor k is the expansion coefficient for the adiabatic flow equation of state ... 

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... 

Adiabatic expansion may be carried out as a butch process in a cloud chamber or as a steady-flow process in the diverging section of the nozzle of a steam turbine or supersonic wind tunnel. If the process is carried out reversibly (this is often a good approximation), the conditions along the path for an ideal gas are related by the expression... 

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 ... 

Since the flow through the valve is governed by the area of the throat, it is reasonable to surmise that equation (7.3) will produce its best results when the specific volume term refers to the throat. The incompressible nature of liquids means that the inlet specific volume and the throat specific volume will be identical, so that the surmise is answered by equation (7.3) in its present form for liquids. However, we must make a change to cater for gases. Assuming a perfectly adiabatic expansion through the valve as far as the throat, the specific volume of the gas at the throat, v, will be given by... 

When sonic flow occurs in the throat as the result of an adiabatic expansion of a perfect gas, the mass velocity at the throat is given (from equation (14.57)) by ... 

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... 

Throttling and adiabatic expansion of gas in turbo-expanders occur as a result of gas flow in pipes and channels of variable cross-section. To determine the temperature, pressure, and degree of supersaturation of a mixture in these devices it is necessary to carry out appropriate gas-dynamic calculations. An approach to performing such calculations, based on ref. [5], is outlined below. 

It has been pointed out that appreciable systematic errors might occur in some cases when the pressure-drop method of flow calibration is used, on account of adiabatic expansion which leads to a slight decrease in temperature in the gas storage bulbs. 

The laser spectroscopic techniques provide much more detailed information about the state-dependent velocity distribution than measurements with mechanical velocity selectors. Note that in Fig. 4.13 not only Up(Na2) > t p(Na) but the velocity distribution of the Na2 molecules differs for different vibration-rotation levels (v, J). This is due to the fact that molecules are being formed by stabilizing collisions during the adiabatic expansion. Molecules in lower states have suffered more collisions with atoms of the cold bath. Their distribution n(v) becomes narrower and their most probable velocity Vp more closely approaches the flow velocity u. 

---