Hi all, can you tell me what different between "fully developed laminar flow" and fully developed turbulent flow"?
A vague question. There are entire books written on each of those two types. To say something, the laminar flow is a flow where the fluid particles make a stable and smooth trajectories. Laminar flows can be stable or unstable flows. On the contrary, a turbulent flow is a flow where the fluid particles make instable and non smooth trajectories. The turbulent flow has a chaotic behavior built-in caused by the inertial instability.
Perhaps take a quick peek here: https://www.physicsforums.com/showthread.php?t=92823 It could be that the OP was looking for something simple like a fully developed flow means a non changing velocity profile. The laminar profile is parabolic and the turbulent is essentially rectangular(ish). http://www.tpub.com/content/doe/h1012v3/img/h1012v3_40_1.jpg
Thank you guys, Let consider the channels formed by S-shaped fins, as shown in the link. - A supercritical CO2 as working fluid flows inside these channels with Re ~ 10000. Do you think a fully developed turbulent flow exist? - A water as working fluid flows inside these with Re ~ 1000. Do you think it is the Fully developed laminar flow?
The character of turbulent or laminar regime DOES NOT depend on the substance, but on the scaling parameter Re--->>> we don't care what is going on with the fluid. With that I mean that your pipe configuration should have a tested critical Re for reaching the turbulent regime, that Re is universal, and I bet it is lower than the critical Re for a single pipe (which is around 2000, isn't it Fred?). EDIT: well, the transition to turbulence >may< depend on another scaling parameters, not only on the Reynolds, but also on the Richardson number as in the case of a buoyant flow, or on the Rosby number as in the case of a rotating system (The Earth). These three mechanisms (viscosity, buoyancy, and coriolis forces) are the main generators of uncontrolled vorticity eventually leading to turbulence.
Thank you Clausius2, But how about fully developed flow? Can it exist in such flow channel configuration?
Let's talk about fully developed flow. A fully developed velocity profile is such that its derivative respect to the streamwise coordinate is zero. In turbulent flow it is said that a profile is fully developed when its statistics does not depend on the streamwise coordinate. I mean, the mean velocity profile does not depend on the streamwise coordinate, is the same in every section. Looking at your thing, I saw a periodic configuration, with sudden expansions and bifurcations. Well, just after the hidrodynamic entrance length, which is the length spend by the fluid for acquiring the fully developed profile, you can assume you have a fully developed profile. For calculating your an estimation of the hydrodynamic entrance length you can use [tex]L_e\sim R\cdot Re_R[/tex] where R is the radious of your small fin interstice, and Re_R is the reynolds based on the radius. Imagine that [tex]L[/tex] is the length of each one of those small tubes formes by the fins and which are periodic in the space. If [tex]L<<L_e[/tex] then the flow is never fully developed there. If [tex]L>>L_e[/tex] which would happen in your case only if [tex]R<<L/Re[/tex], then you have the chance of getting a fully developed flow after the hydrodynamic length. Does it makes sense now?.
fully developed turbulent flow over plate Is it possible to have a “fully developed turbulent flow” over plate? I am interested is incompressible subsonic flow and I know that the fully developed turbulent flow, i.e., constant velocity profile can happen inside pipes or channels or between two parallel plates. Does the boundary layer of turbulent flow over plate reach a constant value? If so how are boundary layer displacement and boundary layer displacement thickness obtained? Thanks
Yes. Only variable here is the Reynolds' number. Incompressible flow means rho=const, which is a good approximation for Mach<0.3~0.4. If incompressibility is waived as a simplification, you may have subsonic, etc. Note that the supersonic/subsonic is generally defined locally, or for areas of flow. No. it continues to develop in the direction of the flow. They are both defined locally, and if x is the coordinate in the direction of the flow, they're function of x. Cheers
You responded that it is possible to have a “fully developed turbulent flow over a single plate” and the only variable here is the Reynolds' number. I am interested in FULLY DEVELOPED, which means its velocity profile does not depend on the streamwise coordinate. I would like to know if it really happens over a single plate and if I can assume that its statistics does not depend on the streamwise coordinate Thanks
No fully developed external flow The boundary layer thickness generally grows in the direction of the flow, and the flat plate is no exception. Thus, the velocity profile in the boundary layer will change streamwise; it is just this chage is much smaller than in the direction normal to the plate (within the boundary layer). "Fully developed" flow is pipe/duct/channel flow terminology, and doesn't really apply to external flows. Nevertheless (and especially for flat plate), boundary layer thickness (dispalcement thickness, etc) can be thought as a function of Re_x=U*x/niu, where x is the streamwise distance to the leading edge. Within the boundary layer, you can assume that variation of turbulent stresses in streamwise direction is much smaller than that in the normal direction, i.e. d[ui'*uj']/dx << d[ui'*uj']>/dym, but it is inaccurate to say that they don't change at all. Cheers. // Rope