1、Transport PhenomenaDepartment of Chemical EngineeringTianjin University Jingtao Wang, Ph.D Content in the Previous Classes Equation of continuity The equation of motionChapter 4: Velocity distributions with more than one independent variableSection 4.4: Flow near solid surfaces by boundary-layer the

2、ory Outline The materials covered in todays class: Chapter 5: Velocity distributions in turbulent flow Section 5.1: Comparisons of laminar and turbulent flows Transport PhenomenaFormer president of Peking University, an academician of Chinese Academy of Sciences. He has great contributions to the st

3、udy of turbulent flows.Zhou Peiyuan (周培源) Transport PhenomenaLaminar flow: orderly Turbulent flow: chaotic (Posing all sorts of difficulties) Transport PhenomenaThe differential equations describing laminar flow are well understood. For a number of simple systems, the velocity distribution and vario

4、us derived quantities can be obtained in a straightforward fashion. The limiting factor in applying the equations of change is the mathematical complexity (Several velocity components are functions of several variables.) With the rapid development of computational fluid dynamics (CFD), such problems

5、 are gradually yielding to numerical solution.In the previous chapters: laminar flow only Transport PhenomenaQuestion:Whether or not the equations of change given in the previous Chapters are capable of describing the violently fluctuating motions in turbulent flow? In this chapter: turbulent flowAn

6、swer:Since the sizes of the turbulent eddies are several orders of magnitude larger than the mean free path of the molecules of the fluid, the equations of change are applicable. Transport PhenomenaIn this chapter we shall concern primarily with methods that enable us to define the time-smoothed vel

7、ocity profiles. Numerical solutions of these equations are obtainable and can be used for studying the details of the turbulence structure. However, we are not interested in having such detailed information, due to the required computational effort. Transport PhenomenaSection 5.1:Comparisons of lami

8、nar and turbulent flows Transport Phenomena Laminar flowsIn laminar flow, fluid layers move smoothly over one another in the direction of flow. Transport PhenomenaTurbulent flowIn turbulent flow, the flow pattern is complex and time-dependent, with considerable motion perpendicular to the principal

9、flow direction. Transport PhenomenaTurbulent flows Transport PhenomenaThe drawings of Water passing Obstacles and falling (c. 1508 - 1509) is done by Leonardo da Vinci. Transport PhenomenaLaminar flows in Chemical Engineering Seven aqueous streams, each colored with a different dye, converge in a mi

10、crochannel and proceed in parallel laminar flow, without turbulent mixing. Using laminar flows of reagents is the basis of a technique for fabricating microstructures inside capillaries. Transport PhenomenaLaminar flows in Chemical Engineering Schematic of diverse microfluidic devices for emulsifica

11、tion Laminar flows in Chemical Engineering Transport PhenomenaLaminar flows in Chemical Engineering Transport PhenomenaTurbulent flows in Chemical Engineering Most flows encountered in conventional chemical engineering are turbulent and not laminar! Transport Phenomena(a) Laminar pipe flow yields a

12、parabolic velocity profile .(b) Turbulent pipe flow yields a velocity profile that is much flatter across the core of the flow. Simple comparison between laminar flow and turbulent flow Transport PhenomenaBefore discussing any theoretical ideas about turbulence, it is important to summarize the diff

13、erences between laminar and turbulent flows in two simple systems: (a) the flow in pipes of circular and (b) flow along a flat plate. (a)(b) Transport Phenomena(a) Circular Tubes For the steady, fully developed, laminar flow in a circular tube of radius R we know that the velocity distribution and t

14、he average velocity are given by andand that the pressure drop and mass flow rate w are linearly related: Transport PhenomenaFor turbulent flow, the velocity is fluctuating with time at each point in the tube. The time-smoothed velocity (which is defined in the next section) will have a ponent repre

15、sented by , and its shape and average value will be given very roughly by andThe mass rate of flow and the pressure drop are no longer proportional but are related approximately by Transport PhenomenaLaminar flowTurbulent flowFig. 5.1-1. Qualitative comparison of laminar and turbulent velocity profi

16、les. Transport PhenomenaLaminar flowTurbulent flowThe stronger dependence of pressure drop on mass flow rate for turbulent flow results from the fact that more energy has to be supplied to maintain the violent eddy motion in the fluid. Transport PhenomenaThis type of instrument is not sensitive to r

17、apid velocity fluctuations, but measures the velocity averaged over several seconds.We can measure a “time-smoothed velocity” at each point with a Pitot tube (皮托管). It is a pressure measurement instrument used to measure fluid flow velocity. The pitot tube was invented by the French engineer Henri P

18、itot in the early 1700s. Henri Pitot(1695-1771) Transport Phenomena (b) Flat Plate For the laminar flow around a flat plate, wetted on both sides, the solution of the boundary layer equations gave the drag force expression. in which is the Reynolds number for a plate of length L; the plate width is

19、W, and the approach velocity of the fluid is v. Transport Phenomena For turbulent flow, the dependence of drag force on the physical properties is quite different: Thus the force is proportional to the 3/2-power of the approach velocity for laminar flow, but to the 9/5-power for turbulent flow. The

20、stronger dependence on the approach velocity reflects the extra energy needed to maintain the irregular eddy motions in the fluid. Transport PhenomenaThe laminar-turbulent transition in circular pipes normally occurs at a critical Reynolds number of roughly 2100.Re =UL/ = UL/The transition from lami

21、nar flow to turbulent flow can be demonstrated by the simple experiment originally performed by Reynolds. laminar-turbulent transition Transport PhenomenaOne sets up a long transparent tube equipped with a device for injecting a small amount of dye into the stream along the tube axis. Transport Phen

22、omena At low velocities the streak of dye extended in a straight line along the tube.2. If the water in the tank was not at rest, the streak would shift about the tube.3. As the velocity increased, at some point in the tube, the color band would all at once mix up with the surrounding waters. Actually, this mixed fluid looked like a bunch of eddies.laminar-turbulent transition Transport PhenomenaAt low velocities, fluids flow in a streamlined pattern called laminar motion.At high velocities, fluids flow in a