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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition 16 CHAPTER Thermodynamics of High-Speed Gas Flow

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition (fig.16-1) Steady Flow of a Liquid through an Adiabatic Duct 16-1

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Three States of a Fluid on an h-s Diagram 16-2 (Fig.16-3) The actual state, actual stagnation state, and isentropic stagnation state of a fluid on an h-s diagram

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Completely Arresting the Flow of an Ideal Gas can Raise its Temperature 16-3 (Fig.16-5) The temperature of an ideal gas flowing at a velocity V rises by V 2 /(2C P ) when it is brought to a complete stop STOP

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Propagation of a Small Pressure Wave Along a Duct 16-4

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Control Volume Moving With the Small Pressure Wave Along a Duct (Fig. 16-8) 16-5

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The Velocity of Sound Changes With Temperature (Fig. 16-9) 16-6

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The Mach Number Can Vary With Different Temperatures Even With Equivalent Velocities (Fig ) 16-7

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Throat: The Smallest Flow Area of a Nozzle 16-8

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Supersonic Velocities Cannot be Obtained by Attaching a Converging Section 16-9 We cannot obtain supersonic velocities by attaching a a converging section to a converging nozzle. Doing so will only move the sonic cross section farther downstream

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Variation of Flow Properties in Subsonic and Supersonic Nozzles and Diffusers (Fig ) 16-10

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Effect of Back Pressure on the Pressure Distribution Along a Converging Nozzle (Fig ) 16-11

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Effect of Back Pressure of a Converging Nozzle on Mass Flow Rate and Exit Pressure (Fig ) The effect of back pressure P b on the mass flow rate m and the exist pressure P e of a converging nozzle

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Variation of the Mass Flow Rate Through a Nozzle with Inlet Stagnation Properties (Fig ) 16-13

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The Effect of Back Pressure on the Flow Through a Converging-Diverging Nozzle (Fig.16-26) 16-14

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The h-s Diagram for Flow Across a Normal Shock (Fig ) 16-15

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Entropy Change Across the Normal Shock (Fig ) 16-16

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Isentropic and Actual (Irreversible) Flow in a Nozzle (Fig ) Isentropic and actual flow in a nozzle between the same inlet state and the exit pressure

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Schematic and h-s Diagram for the Definition of the Diffuser Efficiency (Fig ) 16-18

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The h-s Diagram for the Isentropic Expansion of Steam in a Nozzle (Fig ) 16-19

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Schematic and h-s Diagram for Example (Fig.16-38) 16-20

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary In this chapter the thermodynamic aspects of high-speed fluid flow are examined. For high- speed flows, it is convenient to combine the enthalpy and the kinetic energy of the fluid into a single term called stagnation (or total) enthalpy h 0, defined as (kJ/kg) The properties of a fluid at the stagnation state are called stagnation properties and are indicated by the subscript zero

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The stagnation temperature of an ideal gas with constant specific heats is which represents the temperature an ideal gas will attain when it is brought to rest adiabatically. Chapter Summary 16-22

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The (isentropic) stagnation properties of an ideal gas are related to the static properties of the fluid by 16-23

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary When stagnation enthalpies are used, the conservation of energy equation for a single- stream, steady-flow device can be expressed as where h 01 and h 02 are the stagnation enthalpies at states 1 and 2, respectively

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The velocity at which an infinitesimally small pressure wave travels through a medium is the velocity of sound (or the sonic velocity). It is expressed as 16-25

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary For an ideal gas the velocity of sound becomes 16-26

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The Mach number is the ratio of the actual velocity of the fluid to the velocity of sound at the same state: 16-27

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The flow is called sonic when M = 1, subsonic when M 1, hypersonic when M >> 1, and transonic when M 1. = ~ 16-28

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The nozzles whose flow area decreases in the flow direction are called converging nozzles. Nozzles whose flow area first decreases and then increases are called converging-diverging nozzles. The location of the smallest flow area of a nozzle is called the throat

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The highest velocity to which a fluid can be accelerated in a convergent nozzle is the sonic velocity. Accelerating a fluid to supersonic velocities is only possible in converging-diverging nozzles. In all supersonic converging-diverging nozzles, the flow velocity at the throat is the velocity of sound

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The ratios of the stagnation to static properties for ideal gases with con-stant specific heats can be expressed in terms of the Mach number as 16-31

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary When M = 1, the resulting static-to-stagnation property ratios for the temperature, pressure, and density are called critical ratios and are denoted by the superscript asterisk: 16-32

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The pressure outside the exit plane of a nozzle is called the back pressure. For all back pressures lower than P*, the pressure at the exit plane of the converging nozzle is equal to P*, the Mach number at the exit plane is unity, and the mass flow rate is the maximum (or choked) flow rate

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary Under steady-flow conditions, the mass flow rate through the nozzle is constant and can be expressed as 16-34

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The variation of flow area A through the nozzle relative to the throat area A* for the same mass flow rate and stagnation properties of a particular ideal gas is 16-35

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The parameter M* is defined as the ratio of the local velocity to the velocity of sound at the throat (M = 1): It can also be expressed as 16-36

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary In some range of back pressure, the fluid that achieved a sonic velocity at the throat of a converging-diverging nozzle and is accelerating to supersonic velocities in the diverging section experiences a normal shock, which causes a sudden rise in pressure and temperature and a sudden drop in velocity to subsonic levels. Flow through the shock is highly irreversible, and thus it cannot be approximated as isentropic

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The properties of an ideal gas with constant specific heats before (subscript x) and after (subscript y) a shock are related by 16-38

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary The entropy change across the shock is obtained by applying the entropy-change equation for an ideal gas across the shock: 16-39

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The deviation of actual nozzles from isentropic ones is expressed in terms of the nozzle efficiency N, nozzle velocity coefficient C V, and the coefficient of discharge C D, which are defined as where h 01 is the stagnation enthalpy of the fluid at the nozzle inlet, h 2 is the actual enthalpy at the nozzle exit, and h 2s is the exit enthalpy under isentropic conditions for the same exit pressure. Actual kinetic energy at nozzle exit Kinetic energy at nozzle exit for isentropic flow from the same inlet state to the same exit pressure Actual velocity at nozzle exit Velocity at nozzle exit for isentropic flow from the same inlet state to the same exit pressure Actual mass flow rate through nozzle Mass flow rate through nozzle for isentropic flow from the same inlet state to the same exit pressure = = = = = Chapter Summary 16-40

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition The performance of a diffuser is expressed in terms of the diffuser efficiency D the pressure recovery factor F P, and the pressure rise coefficient C PR. They are defined as Chapter Summary Actual stagnation pressure at diffuser exit Isentropic stagnation pressure Actual pressure rise Isentropic pressure rise = = = = FpFp C pr 16-41

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary Steam often deviates considerably from ideal-gas behavior, and no simple property relations are available for it. Thus it is often necessary to use steam tables instead of ideal-gas relations. The critical-pressure ratio of steam is often taken to be 0.546, which corresponds to a specific heat ratio of k = 1.3 for superheated steam

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WCB/McGraw-Hill © The McGraw-Hill Companies, Inc.,1998 Thermodynamics Çengel Boles Third Edition Chapter Summary At high velocities, steam does not start condensing when it encounters the saturation line, and it exists as a supersaturated substance. Supersaturation states are nonequilibrium (or metastable) states, and care should be exercised in dealing with them

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