Is Reynold's number really matter?

In summary, Reynolds number is an important factor in understanding drag on objects in air flow. It can be used to compare different geometries and fluid characteristics. Different size objects, temperature, and speed conditions in a wind tunnel can give different Re values.
  • #1
Donny
16
0
Can I neglect it when talking about drag force or making a wind tunnel test? Why is it so important?

Thank you for replying.
 
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  • #2
Reynolds number is not something you can "neglect", that is a complete misconception.

Reynolds number arises when the Navier-Stokes flow equation is brought to dimensionless form and it is, roughly speaking a measure of inertial effect compared to viscous effects.

Reynolds number tells you what kind of flow you are dealing with, and thus, which *other* things you might neglect: If Re << 1 you have what is known as a viscous or laminar flow, and the convective terms in the NSeq may be dropped - nice thing!. If on the other hand you have Re >> 1 you have a inertial or convective flow, and things get a whole lot more nasty.

Reynolds number is quite important in calculation of drag, as the drag force in laminar flow scales as [tex] \sim v^{\phantom} [/tex] while in inertial flow it scales as [tex] \sim v^2[/tex] and only Reynolds number can give you an idea of which to use in you particular case
 
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  • #3
Interesting facts, I never know about that before.

You said that drag calculation was affected by Reynold's number, but how to get the right Reynold's number value when we are talking about wind tunnel and there is an object in it.

Is it true that different size of an object, temperature and speed condition in wind tunnel will give different Re?
 
  • #4
It's basically air speed times wing chord distance:

Wiki link:

http://en.wikipedia.org/wiki/Reynolds_number

A lot of small, slow speed, wind tunnel smoke stream tests can give a false, overly laminar, impression of air flow across a wing, because the Reynolds number is too small.
 
  • #5
The Reynolds number can be defined several ways, one way is Re = [itex]\frac{2\rho Q}{\pi \mu L}[/itex] where [tex]\rho[/tex] is the fluid density (which can depend on temperature), [tex]\mu[/tex] the viscosity (which also depends on temperature), Q the volumetric flux of fluid (which will depend on velocity) and L a length scale.

The Reynolds number, like any dimensionless group, is used for several types of analysis. First, one can compare different geometries and fluid characteristics in a rational manner. Second, the relative importance of one phenomena with respect to another (viscosity vs. inertia, velocity vs. diffusivity, surface tension vs. gravity, etc...) can be related rationally and this gives insight as to what is the most important characteristic governing a system.

As an extreme example, ship designers can use flow chambers containing liquid helium as the fluid- the viscosity is near zero, so incredibly large Reynolds numbers can be simulated, corresponding to large ocean-going vessels. This allows the use of small-scale models that physically fit in the lab.
 
  • #6
Andy hit the nail on the head. Reynolds effects have to be taken into account. If you don't you would have to test full scale models all the time at the conditions they are intended. Similitude is very important for your data to mean anything in the real world.

http://www.centennialofflight.gov/essay/Dictionary/Reynolds_no/DI114.htm [Broken]
http://quest.arc.nasa.gov/aero/teachers/windtunnels.html
 
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  • #7
When working on a prototype or a small model can I assume in all condition the Reynold's number are the same? For example, same speed, same temperature, etc will result the same Re.
 
  • #8
Defintely not. Look at the definition of the Reynolds number I wrote above- if the size of the object changes, the velocity must also change, holding the other parameters constant.

The Reynolds number is a *combination* of parameters.
 
  • #9
oke thank you for your explanation.

And also whoever replied to this thread. I'll figure it now. ;)
 

1. What is Reynold's number and how is it related to fluid dynamics?

Reynold's number is a dimensionless number used in fluid dynamics to characterize the ratio of inertial forces to viscous forces in a fluid flow. It is important in determining the type of flow, whether it is laminar or turbulent.

2. How is Reynold's number calculated?

Reynold's number is calculated by multiplying the fluid velocity, the characteristic length of the flow, and the fluid density, and then dividing by the fluid viscosity. The formula is Re = (ρ * V * L) / μ, where ρ is the density, V is the velocity, L is the characteristic length, and μ is the viscosity.

3. Can Reynold's number affect the behavior of a fluid flow?

Yes, Reynold's number can affect the behavior of a fluid flow. When Reynold's number is low, the flow is usually laminar and the fluid flows in smooth and orderly layers. However, when Reynold's number is high, the flow becomes turbulent and the fluid experiences chaotic and irregular motion.

4. Is Reynold's number only important in fluid dynamics?

No, Reynold's number is also important in other fields such as heat transfer, mass transfer, and chemical reactions. In these cases, it is used to determine the type of flow and to predict the behavior of the system.

5. How does Reynold's number influence the design of objects such as airplanes and ships?

Reynold's number plays a crucial role in the design of objects that are moving through a fluid, such as airplanes and ships. It helps engineers determine the appropriate size and shape of the object to minimize drag and maximize efficiency based on the type of flow that the object will experience.

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