Effect of increasing heat addition to choked

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Effect of Increasing Heat Additionto Choked Supersonic Flowthermally chokedthermally chokedincreasing heat addition: δq2*> δq1*po, ToMin2< Min1< 1δq2*Mexit= 1Mindecreasesmass flow decreasesexit conditions still sonicincreasing heat addition: δq2*> δq1*Mthroat=1po, ToMin2< 1Mexit= 1δq2*shock forms in nozzlemass flow constantexit conditions still sonicincreasing heat addition further: δq3*> δq2*Mthroat<1po, ToMin3< 1Mexit= 1δq3*shock forced to throatmass flow decreases with furtherincrease in δqexit conditions still sonicshock
Compressible Fluids Notes11912.Oblique Shock WavesThis chapter begins our discussion of two-dimensional, steady supersonic flow.In this chapter, we will examine shock waves that result when supersonic flowencounters a compressive corner(i.e., a corner that turns intothe flow). Theabrupt change in flow direction results in a shock wave, but the shock wavecan now be at an angle with respect to the flow rather than normal; such ashock wave is termed an oblique shock. In the next chapter, we will examinethe flow over an expansive corner(i.e., a corner that turns awayfrom theflow).Oblique shock waves are encountered in external supersonic flow (the flowover wings and fuselages) and in internal flows where the area change is notgradual (i.e., supersonic inlet/diffusers). Oblique shocks also appear whenconverging/diverging nozzles exhaust into a chamber in which the backpressure does not exactly match the exit pressure (overexpanded andunderexpanded nozzles). These applications are treated in Chapter 14.12.1Oblique Shocks Derived from Normal ShocksTo begin our study of oblique shock waves, we will return to the normal shockwave of Chapter 7. Consider a steady shock wave:Recall that we can make any shock wave steady by transforming into itsreference frame. Now, consider if we transform into a reference frame movingperpendicular to the normal shock (i.e., moving up or down along the shock).We can do this by adding a velocity VT(tangential) to the picture above:We will denote the original velocities normal to the wave as VxNand VyN, andthe resultant velocities as Vxand Vy. If we simply rotate the above picture inthe clockwise direction, we obtain:We can interpret this picture as a steady, supersonic flow approaching from theleft at velocity Vx, and then being deflected upward at an angle δ, the deflectionangleor wedge angle. The angle between the resulting shock and theincoming flow is σ, the shock angle.*xypxρxTxshock at restVxpyρyTyVycontrol volume*Suggested mnemonic devise: sigma” for shock, “delta” for deflection.xyshock at restVyNVxNVTVxVyxyVyNVxNVTVxVyδσ
Compressible Fluids Notes120The goal is to now develop a set of relations for oblique shock waves that areanalogous to the normal shock relations developed in Section 7. Our shockrelations will now have to include the geometric parameters σand δ.12.2Oblique Shock Relations

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