內(nèi)容空氣動力學(xué)chapter

1、Chapter 7 Compressible Flow: Some Preliminary Aspects 可壓縮流動基礎(chǔ)Department of Fluid Mechanics, School of Aeronautics, Northwestern Polytechnical University, Xian, China主講人：宋文萍E-mail: 2014.10.15High-Speed Aerodynamics CourseLecture #4(1)第七章路線圖 完全氣體 內(nèi)能和焓 熱力學(xué)第一定律 熵及熱力學(xué)第二定律 等熵關(guān)系式熱力學(xué)復(fù)習(xí)壓縮性定義無粘可壓縮流動的控制方程總參數(shù)定義

2、有激波可壓縮流動的定性了解2022/8/33回到本節(jié)的開頭，我們考慮流體微團(tuán)通過一個給定點，對應(yīng)的當(dāng)?shù)貕簭?qiáng)、溫度、密度、馬赫數(shù)、速度分別為 Once again, imagine that you grab hold of the fluid element and slow it down to zero velocity, but this time, let us slow it down both adiabatically and reversibly. That is, let us slow the fluid element down to zero velocity isen

3、tropically. 總壓&總密度Total Pressure & Total Density 總壓與總密度定義Definition of Total Pressure & Total Density 定義：當(dāng)流體微元被等熵地減速至靜止時對應(yīng)的壓強(qiáng)和密度被定義為其總壓 p0 和總密度 。 Definition: When the fluid element is brought to rest isentropically, the resulting pressure and density are defined as the total pressure p0 and total de

4、nsityAs before, keep in mind that we do not have to actually bring the flow to rest in real life in order to talk about total pressure and total density; rather, they are defined quantities that would exist at a point in a flow if (in our imagination) the fluid element passing through that point wer

5、e brought to rest isentropically. Therefore, at a given point in a flow, where the static pressure and static density are p and , respectively, we can also assign a value of total pressure p0 , and total density 0 defined as above.注意：總壓和總密度只是定義量，是假想將流體速度等熵地降為零來定義的，而并不是真的這樣做。 對于流場中任意一點，我們都可以定義總壓和總密度；

6、 總壓和總密度的概念適用于任意等熵流或非等熵流。非絕熱流與絕熱流的比較非絕熱流:沿流線總焓（總溫）是變化的絕熱流：沿流線總焓（總溫）不變非等熵流:沿流線總壓和總密度是變化的；等熵流：沿流線總壓和總密度不變。非等熵流與等熵流的比較因為等熵過程是絕熱的，因此對于等熵流，總溫不變。Since an isentropic process is also adiabatic, total temperature remains unchanged.總壓的物理意義：流體微元作有用功的能力問題：為什么等熵流沿流線總壓和總密度不變？：The total pressure and total density a

7、re constants along a streamline in an isentropic flow. Why? 2022/8/310舉例：高超聲速乘波體繞流的總溫云圖2022/8/311舉例：高超聲速乘波體繞流的總壓云圖推論T*的定義: 假想把具有當(dāng)?shù)仂o溫T的流體微元絕熱地由亞音速加速到音速,或絕熱地由超音速減速到音速, 流體微元對應(yīng)的溫度, 被定義為T*。T*同樣是對于一給定點的定義量。Total temperature T0 and total enthalpy h0 are defined as the properties that would exist if the flo

8、w is slowed to zero velocity adiabatically.Total pressure p0 and total density 0 are defined as the properties that would exist if the flow is slowed to zero velocity isentropically.If the general flow field is adiabatic, h0 is constant throughout the flow.If the general flow field is isentropic, p0

9、 and 0 are constant throughout the flow. Summary2022/8/314Example 7.3(第5版7.6） 氣流中一點處的壓強(qiáng)、溫度和速度分別為1atm, 320K,1000m/s。計算這一點的總溫和總壓。2022/8/3157.6 Some Aspects of Supersonic Flow: Shock Waves超音速流的一些特征：激波61頁圖1.43（5版66頁圖1.,4 ）An essential ingredient of a supersonic flow is the calculation of the shape and s

10、trength of shock waves. This is the main thrust of chaps. 8 and 9. 超音速流動研究的一個重要內(nèi)容就是計算激波的形狀和強(qiáng)度。這是第8章和第9章的主題。2022/8/316A shock wave is an extremely thin region, typically on the order of 10-5 cm, across which the flow properties can change drastically.激波是一個極其薄的區(qū)域，厚度大約只有10-5cm的量級，通過激波流動特性發(fā)生劇烈變化。激波是一個大振

11、幅壓縮波。什么是激波：對激波的初步認(rèn)識2022/8/317圖7.52022/8/3187.7 Summary(小結(jié)）1、熱力學(xué)關(guān)系式：狀態(tài)方程： 對于量熱完全氣體：2022/8/319熱力學(xué)第一定律的各種表達(dá)形式：熵的定義：熱力學(xué)第二定律：或?qū)τ诮^熱過程：可逆過程：2022/8/320量熱完全氣體的熵增計算公式： （7.25) (7.26)等熵流動的等熵關(guān)系式： (7.32)2022/8/3212、壓縮性壓縮性的一般定義： （7.33）對于等溫過程： (7.34)對于等熵過程： (7.35)2022/8/3223、無粘、可壓縮流的控制方程：連續(xù)方程：動量方程：（7.39）（7.40）(7.41

12、)(7.41a)(7.41b)(7.41c)2022/8/323能量方程：（7.43)(7.44)對于定常、絕熱、無粘流，（7.44)和(7.43)可以寫成：（7.53),(7.55)完全氣體狀態(tài)方程：量熱完全氣體內(nèi)能：（7.1)(7.6a)2022/8/3244、總溫、總焓、總壓、總密度的定義及概念：“總溫” T0 和“總焓” h0定義為把流體微元（在我們的想象中）絕熱地減速為靜止時流體微元所對應(yīng)的溫度和焓值。類似地，“總壓” p0和“總密度” 0定義為把流體微元（在我們的想象中）等熵地減速為靜止時流體微元所對應(yīng)的壓強(qiáng)和密度。在均勻自由來流的絕熱流場中，總焓h0在全流場中為常數(shù)，相反，在非絕熱流場中， h0隨流場點的不同而不同。類似地，在等熵流場中，總壓和總密度在整個流場