Thermodynamics

Chapter 17COMPRESSIBLE FLOWFor the most part, we have limited our consideration sofar to flows for which density variations and thus compressibilityeffects are negligible. In this chapter we liftthis limitation and consider flows that involve significantchanges in density. Such flows are called compressible flows,and they are frequently encountered in devices that involvethe flow of gases at very high velocities. Compressible flowcombines fluid dynamics and thermodynamics in that bothare necessary to the development of the required theoreticalbackground. In this chapter, we develop the general relationsassociated with one-dimensional compressible flows for anideal gas with constant specific heats.We start this chapter by introducing the concepts of stagnationstate, speed of sound, and Mach number for compressibleflows. The relationships between the static andstagnation fluid properties are developed for isentropic flows ofideal gases, and they are expressed as functions of specificheatratios and the Mach number. The effects of areachanges for one-dimensional isentropic subsonic and supersonicflows are discussed. These effects are illustrated byconsidering the isentropic flow through converging andconverging–diverging nozzles. The concept of shock wavesand the variation of flow properties across normal and obliqueshocks are discussed. Finally, we consider the effects of heattransfer on compressible flows and examine steam nozzles.ObjectivesThe objectives of Chapter 17 are to:• Develop the general relations for compressible flowsencountered when gases flow at high speeds.• Introduce the concepts of stagnation state, speed of sound,and Mach number for a compressible fluid.• Develop the relationships between the static and stagnationfluid properties for isentropic flows of ideal gases.• Derive the relationships between the static and stagnationfluid properties as functions of specific-heat ratios andMach number.• Derive the effects of area changes for one-dimensionalisentropic subsonic and supersonic flows.• Solve problems of isentropic flow through converging andconverging–diverging nozzles.• Discuss the shock wave and the variation of flow propertiesacross the shock wave.• Develop the concept of duct flow with heat transfer andnegligible friction known as Rayleigh flow.• Examine the operation of steam nozzles commonly used insteam turbines.| 823