Compressible flows adiabatic flow

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

FIG, 6"22 Adiabatic compressible flow in a pipe with a well-rounded entrance. 

Compressible fluid flow occurs between the two extremes of isothermal and adiabatic conditions. For adiabatic flow the temperature decreases (normally) for decreases in pressure, and the condition is represented by p V (k) = constant. Adiabatic flow is often assumed in short and well-insulated pipe, supporting the assumption that no heat is transferred to or from the pipe contents, except for the small heat generated by fricdon during flow. Isothermal pVa = constant temperature, and is the mechanism usually (not always) assumed for most process piping design. This is in reality close to actual conditions for many process and utility service applications. 

Lawlb. C. . Trans. Am. Inst. Chem. Eng. 39 (1948) 385. Isothermal and adiabatic flow of compressible fluids. 

Figure 9-2 provides a convenient way of solving compressible adiabatic flow problems for piping systems. Some iteration is normally required, because the value of K( depends on the Reynolds number, which cannot be determined until G is found. An example of the procedure for solving a typical problem follows. 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

In this example we describe the calculation of the minimum work for ideal compressible adiabatic flow using two different optimization techniques, (a) analytical, and (b) numerical. Most real flows lie somewhere between adiabatic and isothermal flow. For adiabatic flow, the case examined here, you cannot establish a priori the relationship between pressure and density of the gas because the temperature is unknown as a function of pressure or density, hence the relation between pressure and... 

The differential energy balances of Eqs. (6.10) and (6.15) with the friction term of Eq. (6.18) can be integrated for compressible fluid flow under certain restrictions. Three cases of particular importance are of isentropic or isothermal or adiabatic flows. Equations will be developed for them for ideal gases, and the procedure for nonidcal gases also will be indicated. 

Adiabatic flow of a perfect gas without friction. An ideal frictionless process is represented where a gas is compressed, the area indicating the flow work, which is equal to the change in kinetic energy if no mechanical work in a machine is involved. Thus ... 

As a result of heating through dissipation of kinetic energy, local temperature and therefore local density changes can exist in adiabatic flows. A flow, in which the density of a volume element of the material changes in the course of its motion is known as compressible. In the following we will discuss of heat transfer phenomena in these compressible flows. We will restrict ourselves to steady flows. 

Fig. 3.53 Temperature profiles in compressible flow of ideal gases. Adiabatic wall...

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