p density of fluid, kg/m3 [Greek letter rho] V mean velocity of fluid, m ...

Real_Fluid_Flowhttp://www.centennialofflight.gov/essay/Theories_of_Flight/Real_Flui...1 of 3 1/1/2011 8:33 AMReal Fluid FlowThere are two different types of real fluid flow: laminar and turbulent. Inlaminar flow, the fluid moves in layers called laminas. Laminar flow need not bein a straight line. For laminar flow, the flow follows the curved surface of theairfoil smoothly, in layers. The closer the fluid layers are to the airfoil surface,the slower they move. Moreover, the fluid layers slide over one another withoutfluid being exchanged between the layers.Laminar andturbulent flow.Dependence of flowon Reynoldsnumber.In turbulent flow, secondary random motions are superimposed on the principalflow and there is an exchange of fluid from one adjacent sector to another.More importantly, there is an exchange of momentum such that slow movingfluid particles speed up and fast moving particles give up their momentum tothe slower moving particles and slow down themselves.Another example of a common occurrence of laminar and turbulent flow is thewater faucet. Opened slightly, at low speeds the water flows out in a clearcolumn—an instance of laminar flow. But open the faucet fully and the waterspeeds out in a cloudy turbulent column. In a mountain brook, the water mayslide over smooth rocks in laminas. In the Colorado River after the snow hasmelted, the flow churns downstream in confused, turbulent rapids. It will beseen that the flow over airfoil surfaces may assume both a laminar andturbulent characteristic depending upon a number of factors.In some cases, turbulent flow will appear "naturally" in a laminar flow as insmoke rising in the air. In other cases, by causing a disturbance, a laminar flowcan be changed to a turbulent flow. The question arises as to how one can tellwhether a flow is to be laminar or turbulent. In 1883, Osborne Reynoldsintroduced a dimensionless parameter that gave a quantitative indication of thelaminar to turbulent transition.In an experiment, Reynolds demonstrated that, under certain circumstances,the flow in a tube changes from laminar to turbulent over a given region of thetube. He used a large water tank that had a long tube outlet with a stopcock atthe end of the tube to control the flow speed. The tube went smoothly into thetank. A thin filament of colored fluid was injected into the flow at the mouth.Surface roughnessand flow field. Allcases have thesame Reynoldsnumber.When the speed of the water flowing through the tube was low, the filament ofcolored fluid maintained its identity for the entire length of the tube. However,when the flow speed was high, the filament broke up into the turbulent flowthat existed through the cross section.Reynolds defined a dimensionless parameter, which has since been known as theReynolds number, to give a quantitative description of the flow. In equationform, the Reynolds number R iswherepVdensity of fluid, kg/m 3 [Greek letter rho]mean velocity of fluid, m/sec

Real_Fluid_Flowhttp://www.centennialofflight.gov/essay/Theories_of_Flight/Real_Flui...2 of 3 1/1/2011 8:33 AMd characteristic length, mµ coefficient of viscosity, kg/m-secFor this setup, Reynolds found, by using water, that below R = 2,100, the flow inthe pipe was laminar as evidenced by the distinct colored filament. This valuewas true regardless of the varying combinations of values of p, V, d, or µ. Atransition between laminar and turbulent flow occurred for Reynolds numbersbetween 2,100 and 40,000 depending upon how smooth the tube junction wasand how carefully the flow entered the tube. Above R = 40,000, the flow wasalways turbulent, as evidenced by the colored fluid filament breaking upquickly. The fact that the transition Reynolds number (between 2,100 and40,000) was variable indicates the effect that induced turbulence has on theflow.The numerical values given for the transition are for this particular experimentsince the characteristic length chosen, d, is the diameter of the pipe. For anairfoil, d would be the distance between the leading and trailing edge called thechord length. Additionally, water was used in the Reynolds experiment whereasair flows about an airfoil. Thus, the transition number between laminar andturbulent flow would be far different for the case of an airfoil. Typically, airfoilsoperate at Reynolds numbers of several million. The general trend, however, isevident. For a particular body, low Reynolds number flows are laminar and highReynolds number flows are mostly turbulent.The Reynolds number may be viewed another way:The viscous forces arise because of the internal friction of the fluid. The inertiaforces represent the fluid's natural resistance to acceleration. In a low Reynoldsnumber flow, the inertia forces are negligible compared with the viscous forces,whereas in a high Reynolds number flow, the viscous forces are small relative tothe inertia forces. An example of a low Reynolds number flow (called Stoke'sflow) is a small steel ball dropped into a container of heavy silicon oil. The ballfalls slowly through the liquid; viscous forces are large. Dust particles settlingthrough the air are another case of a low Reynolds number flow. These flows arelaminar. In a high Reynolds number flow, such as typically experienced in theflight of aircraft, both laminar and turbulent flows are present.Surface roughness also affects a body immersed in a flow field. Surfaceroughness causes the flow near the body to go from laminar to turbulent. As thesurface roughness increases, the first occurrence of turbulent flow will moveagainst the direction of the flow along the airfoil. The Reynolds number andsurface roughness are not independent of each other and both contribute to thedetermination of the laminar to turbulent transition. A very low Reynoldsnumber flow will be laminar even on a rough surface and a very high Reynoldsnumber flow will be turbulent even though the surface of a body is highlypolished.Another important factor in the transition from laminar to turbulent flow is thepressure gradient in the flow field. If the static pressure increases withdownstream distance, disturbances in a laminar flow will be amplified andturbulent flow will result. If the static pressure decreases as distance in thedirection of the airflow increases, disturbances in a laminar flow will damp out(or decrease) and the flow will tend to remain laminar. Over an airfoil, thestatic pressure decreases up to the point of maximum thickness. A laminar flow

Real_Fluid_Flowhttp://www.centennialofflight.gov/essay/Theories_of_Flight/Real_Flui...3 of 3 1/1/2011 8:33 AMwill be encouraged in this region. Beyond the point of maximum thickness (orshoulder of the airfoil), the static pressure increases. The laminar flow now ishindered and may go turbulent before reaching the trailing edge.—Adapted from Talay, Theodore A. Introduction to the Aerodynamics ofFlight. SP-367, Scientific and Technical Information Office, NationalAeronautics and Space Administration, Washington, D.C. 1975. Available athttp://history.nasa.gov/SP-367/cover367.htmFor Further Reading:Anderson, Jr., John D. A History of Aerodynamics. Cambridge, England:Cambridge University Press, 1997.Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag,1991.EducationalOrganizationInternationalTechnology EducationAssociationNational Council ofTeachers ofMathematicsNational ScienceEducation StandardsNational ScienceEducation StandardsStandard Designation(where applicableStandard 2N/AContent Standard AContent Standard BContent of StandardStudents will develop anunderstanding of the coreconcepts of technology.Instructional programsfrom pre-kindergartenthrough grade 12 shouldenable all students tounderstand numbers,ways of representingnumbers, relationshipsamong numbers, andnumber systems.As a result of activities ingrades 9-12, all studentsshould developunderstandings aboutscientific inquiry.As a result of activities ingrades 9-12, all studentsshould develop anunderstanding of motionsand forces.Home | About Us | Calendar | Wright Brothers History | History of Flight | Sights & Sounds | Licensed Products | Education | Links | Sitemap