StuDocu is not sponsored or endorsed by any college or universityFinals crash part 4Fluid Mechanics II(Concordia University)StuDocu is not sponsored or endorsed by any college or universityFinals crash part 4Fluid Mechanics II(Concordia University)Downloaded by wadgdgfdg asemd ([email protected])lOMoARcPSD|8295821
MECH 361: FLUID MECHANICS IIFINAL CRASH PART 4: Compressible Flow. ConceptualProblems.Downloaded by wadgdgfdg asemd ([email protected])lOMoARcPSD|8295821
Le Cartier 3410 Peel, Suite B2, Montreal QC, H3A 1H32Introduction to Compressible FlowCompressible flow mainly deals with gas dynamics. More specifically, it compares the velocity of a flowwith respect to the speed of sound.In general, disturbances will produce pressure waves. After some time t, the pressure wave will travel atthe speed of sound. When these pressure waves coincide, a Mach line will be produced. At higher Machnumbers, the Mach lines would create an angle with the line of action, thus creating a cone.The speed of sound is defined as:± = ²³´µNote that:³ =±¶±·The Mach number is defined as:¸ =¹±The angle at which the Mach line makes with the line of action is found by:º = »¼½¾¿À1¸ÁDepending on the Mach number, the flow can be defined as:±M < 1, subsonicM < 1M = 1M > 1Mach lineMach lineMach angleDownloaded by wadgdgfdg asemd ([email protected])lOMoARcPSD|8295821
Le Cartier 3410 Peel, Suite B2, Montreal QC, H3A 1H33±M = 1, transonic±V > c, supersonic±M > 5, hypersonicReference State: Local Isentropic Stagnation PropertiesRecall that stagnation properties are found when the velocity of the fluid is zero. When the fluid isbrought to rest isentropically, this state becomes a reference state, which is very useful in gas dynamics.The properties of a fluid in terms of Mach number can be found by:ÂÃÂ= Ä1 +Å − 12¸ÆÇÈȾ¿µÃµ= 1 +Å − 12¸ÆÉÃÉ= Ä1 +Å − 12¸ÆǿȾ¿Note that the fluid at both states have the same stagnation pressure, just as long as there is noshockwave.Critical ConditionsWhen a fluid reaches M = 1, the properties here are called critical conditions, where:ÂÃÂ∗= ÄÅ + 12ÇÈȾ¿µÃµ∗=Å + 12ÉÃÉ∗= ÄÅ + 12ǿȾ¿These stagnation and critical properties are used as reference points. These values have been tabulated.Downloaded by wadgdgfdg asemd ([email protected])lOMoARcPSD|8295821
Le Cartier 3410 Peel, Suite B2, Montreal QC, H3A 1H34Isentropic Flow Through a Varying Area ChannelFrom basic fluid mechanics, recall the functions of nozzles and diffusers. It so happens that when M > 1,traditional nozzles reduce the velocity of a supersonic flow, whereas a traditional diffuser wouldincrease the velocity of the flow.Converging Nozzles and Converging-Diverging NozzlesSince flow velocity is increased, there will be a point where the velocity will reach M = 1, depending onthe exit pressure. If M = 1 is reached within the nozzle, a shockwave will form within the device, thuscausing it to be choked. A shockwave is a point of discontinuity within the flow, where it goes fromsupersonic to subsonic flow, and thus flow properties would change.
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