Understanding the Relationship between Turbulence, Drag, and the Reynolds Number

[ArielGenesis]

Just to the point

How to calculate Re number? in example for calculating Re number at diffrent points in a boat.

How turbulence affect drag? I know simply turbulence will increase the drag but, to what extent; or simply, the formula connecting both. Comparing the drag between turbulence and laminar flow.

Sorry as I am not sure if this is the correct place for this topic. I just looks and it says aerospace, so some one here, I assume, must be familiar with fluid dynamic.

thank you.

 

[Astronuc]

This is the right forum - fluid mechanics and drag are appropriate subjects in mechanical and aerospace engineering, but here one perhaps needs an expert in marine engineering.

Drag in water/liquid is discussed here.
https://www.physicsforums.com/showthread.php?t=76108

Re and Fr (Froude) numbers are important, but likely the shape of the boat is quite important (i.e. how streamlined it is), and the drag would be determined experimentally, or numerically with a code like Fluent.

http://www.fluent.com/about/news/newsletters/00v9i2/a2.htm

 

[Clausius2]

Just to the point

How to calculate Re number?

That's a nice question. And it hasn't got a simple answer. Engineers usually confuse Re and don't divise the true meaning of that number. This number measures the flow instability, and it is a relative measure of the importance of advection in the flow field. For building up a Re you need a characteristic scale for velocity and length. In a turbulent flow, it is usual to take the characteristic rms of the fluctuation velocity as a scale of velocity, and the length of the largest eddies as the characteristic length.

How turbulence affect drag? I know simply turbulence will increase the drag but, to what extent; or simply, the formula connecting both. Comparing the drag between turbulence and laminar flow.

Turbulence makes skin drag to be less than in the laminar case if you have a free flow over a solid surface. On the other hand, the drag in a closed channel flow (head loss) increases in turbulent regime. This has to do with the nature of the turbulent boundary layer.

 

[FredGarvin]

Engineers usually confuse Re and don't divise the true meaning of that number. This number measures the flow instability, and it is a relative measure of the importance of advection in the flow field.

I have never heard of it in those terms. It works best for me to think of it the way it was taught to me in that it's the ratio of inertial forces to viscous. The higher the Re, the more dominant the more inertial effects dominate the situation. Hmm...I'm going to have to work out the new reasoning in my mind...

 

[Clausius2]

I have never heard of it in those terms. It works best for me to think of it the way it was taught to me in that it's the ratio of inertial forces to viscous. The higher the Re, the more dominant the more inertial effects dominate the situation. Hmm...I'm going to have to work out the new reasoning in my mind...

Well, both of us are right here. I'm basically saying the same than you . Re# is a mathematical artifact. Lot of students use to wonder how to define a Re# when given some problem, but I think I should define it depending on what do I want to work out. Sometimes there is only one characteristic length scale in the problem, sometimes you have three. In particular, in turbulent flow you know that there is a wide range of scales (that's the difficulty of that regime). Classical turbulence experiments (see Brown&Roshko) have the same way of defining the Re#. An engineer working for the design of a wing may have lot of choices for defining a Re#. But, what does it account for? I mean, the engineer is going to say: this flow is turbulent! and no more. If he wants to calculate a given correlation for instance for heat convection, he will choose (blindly) the length scale given by his handbook.

I work with fluid mechanics in science, and for me the Re# is an important measure of the flow in terms that it defines the unstable behavior of the flow, as well as gives me an scalement between the viscous length and the convective length. The Re# is just the non dimensional parameter written in front of the viscous term, and it gives a lot of troubles when it is large, because the momentum equation becomes numerically highly unstable and the advection predominates in the flow. Also, the Re# can be used as a very famous perturbation parameter when dealing with low Re flow.

Complex flows deal with several scales, and therefore severals Re can be defined. A turbulent flow over a wing has lot of scales, ranging from the chord to the Kolmogorov microscale. Each calculation should get a well defined Re, because each Re should serve for each desired purpose.

 

[ArielGenesis]

Astronuc: What i was actually thinking was if i could measure how aerodynamic the boat is by finding the reynold number and CFD is too complicated. But thanks, nice links.

Clausius2: So is Re# basically impractical in experiment?

i am in an experiment consisting of flowing a current through an obstacle. How could I measure the Re#.

 

[Astronuc]

The Re number is used "empirically". It is a matter of difining the appropriate 'characteristic' dimension (length or diamter).

It works well in many applications related to flow of liquid or gas in a pipe - up to certain conditions, and it probably works alright for flow around blunt objects.

We use is in convective heat transfer correlations, e.g. Dittus-Boelter.

In turbulence modeling, the situation is a little more complicated as Clausius indicates.

In addition to the Froude number, I have used the Strouhal number for flow instability.

The Froude number gives the ratio of inertial forces to gravitational forces, and is used by ship designers to determine the size and speed of models for tank testing, when wave-making behaviour is the primary interest and frictional forces may be neglected. When frictional forces are of primary interest, the Reynolds number is the appropriate scaling factor.

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

The ship pushes water up (or makes waves) as well as experiencing friction in the water, so one has to look at both effects.

This might be useful - http://www.aeromech.usyd.edu.au/aero/fprops/dimension/node5.html

and this is interesting
http://hypertextbook.com/physics/matter/turbulence/

I can't find anything better at present.

 

[Clausius2]

Clausius2: So is Re# basically impractical in experiment?

I have never said that. As a matter of fact Re# is very important when dealing with dynamical similarity and numerical experiments. But a Re# of 1.000.000 is going to say you nothing, in part because almost any bulk property of the flow depends on it at such high regimes.

About your experiment, choose as a characteristic scale of velocity the free stream velocity, and as a characteristic length the width of the obstacle. That'll give you an upper limit of the Re#, even though small scales effects are based on lower Re#.

 

[RainmanAero]

Hi Folks,

I have never said that. As a matter of fact Re# is very important when dealing with dynamical similarity and numerical experiments.

Exactly, and I think this is precisely what ArielGenesis needs for the experiement he describes.

But a Re# of 1.000.000 is going to say you nothing, in part because almost any bulk property of the flow depends on it at such high regimes.

Well, in dynamic similarity using wind tunnels, we characterize both skin friction drag and pressure drag (subsonically) as a function of both RE and Mach, so it does tell us a lot about the body aerodynamically if we test it over a range of Re and M. And in this case there is a very "special" Re which we call Re-crit... the Re where flow transitions from laminar to turbulent. Of course this has a large impact on how much pressure drag is generated because turbulent flow will separate from the body further down the streamline. But turbulent flow gives higher skin friction drag. Hence why aerodynamic body design is such a touchy art when trying to minimize drag for any flight condition!

About your experiment, choose as a characteristic scale of velocity the free stream velocity, and as a characteristic length the width of the obstacle. That'll give you an upper limit of the Re#, even though small scales effects are based on lower Re#.

I kind of agree, but by using the constant obstacle width, and varying the freestream velocities (again, he said he was doing an experiment) one can test the object over a range of Re (since water is incompressible, no need to worry about Mach). At any given angle of attack, over the range of Re, you can take drag data and then non-dimensionalize it to Cd (divide by dynamic pressure and characteristic area). By plotting the Cd against Re you can find the Re for minimum Cd. Thus, your minimum drag operating condition for that angle of attack.

Rainman

 

[Clausius2]

Well rainman,

Seems you are digging in a ground of concrete.

Well, in dynamic similarity using wind tunnels, we characterize both skin friction drag and pressure drag (subsonically) as a function of both RE and Mach, so it does tell us a lot about the body aerodynamically if we test it over a range of Re and M. And in this case there is a very "special" Re which we call Re-crit... the Re where flow transitions from laminar to turbulent. Of course this has a large impact on how much pressure drag is generated because turbulent flow will separate from the body further down the streamline.

Sure, Re is important when dealing with transitional flow, but once it is turbulent, it losses importance. Still it is important: it gives us the turbulent energy spectrum, the disparity of scales, the energy cascade, and also variables of engineering interest such as skin friction, which at very high Re has little dependence on Re.

[

I kind of agree, but by using the constant obstacle width, and varying the freestream velocities (again, he said he was doing an experiment) one can test the object over a range of Re (since water is incompressible, no need to worry about Mach). At any given angle of attack, over the range of Re, you can take drag data and then non-dimensionalize it to Cd (divide by dynamic pressure and characteristic area). By plotting the Cd against Re you can find the Re for minimum Cd. Thus, your minimum drag operating condition for that angle of attack.

He has an obstacle. Angle of attack here is pointless (it's a ridge at the bottom right?). You may know from your knowledge in classical hydrodynamics of channel flows that in lab conditions (say U=10 m/s, L=10cm, water) the Re is high enough for neglecting its effect in the main flow variables. It turns out that the Froude number is the fundamental parameter of this problem, which is going to give directly the drag over the obstacle depending on the nature of the flow (critical-subcritical).

 

[RainmanAero]

Hi Clausius,

Well rainman,
Seems you are digging in a ground of concrete.

Huh? Sorry, I am not sure I understand what this refers to.

Sure, Re is important when dealing with transitional flow, but once it is turbulent, it losses importance.

Yes, I do agree. But it was my impression from the OP from ArielGenesis that he was interested in transition:

Comparing the drag between turbulence and laminar flow.

He has an obstacle. Angle of attack here is pointless (it's a ridge at the bottom right?).

Well, again I am reading the OP and I would disagree that AoA is pointless:

How to calculate Re number? in example for calculating Re number at diffrent points in a boat.

How turbulence affect drag? I know simply turbulence will increase the drag but, to what extent; or simply, the formula connecting both

Now maybe as an airplane guy I overtly focus on the aero/hydrodynamic connection here. But to me, a boat in an open water channel can and will have an AoA WRT the freestream flow, especially if it is making a lateral maneuver. So again, in my mind, it is relevant to his question.

In fact, if I read the last bit of his question quoted above correctly, what he is really asking about is the classic aerodynamic tradeoff between skin friction drag and pressure drag. And just based on my experience, when this is the area you are trying to analyze both transition AND AoA become important. Note in the quote above how he assumes turbulent flow increases drag, but when looking at total drag and the SF vs. PD tradeoff this is not necessarily true. If PD is the dominant drag term (for instance at a non-zero AoA), then transition to turbulent flow can actually cause total drag to reduce by delaying streamline separation from the body.

I don't mean to be annoying or argumentative with you Clausius. I just thought what he was asking about was how transition (diff between LAM and TURB) affected drag. If I am wrong in any of this, please let me know where.

Thanks,
Rainman

 

[ArielGenesis]

Astronuc: I followed up your links and found out that they are too technical. Thx however, I might ask someone to explain them.

Clausius2: I might have misunderstood. Using width of the obstacle as the characteristic length is what i really need, thx. I was thinking about using the width of boundary layer. My experiment happens to include turbulence. Shall I exclude Re#?

Rainman: I am varying the angle of attack and they do create diffrent flows (laminar and turbulent). How to calculate Cd by the way. I could use the drag equation but i don't know the drag.

First of all, I got confused. Do turbulence increase drag? I had always think that aerodynamic objects expirienced less drag because they induced less turbulence.

From the explenations since the begining, I might graph Cd againts AoA for my experiment.

I had done anexperiment and took some photographs and I upload them to www.geocities.com/arian_m3/fluid.html Sorry, i found troubles in converting them into smaller images. Hopefuly they will explain what I am doing. Hint: the water flowing from the left to the right.

For Clausius2, using phytagoras, I could convert AoA to width of the obstacle. That is what I am thinking.

 

[Clausius2]

Jokay, it seeems I misunderstood the set up of the experiment. I thought it was a ridge at the bottom of a tunnel. Ariel, base your Reynolds in the length of your obstacle (which at the end of the day seems to be a flat plate inmersed in a water stream with different AoA). The Re based on the boudary layer thickness will be always less than that Re. The skin drag coefficient seems to me to be dependent on Re. Read again the words of Rainman who I think explained very well what happens with pressure drag and skin drag in turbulent flow vs laminar flow.

 

[ArielGenesis]

In summary according to what I had comprehend.

Re= velocity length density / viscosity
I could measure the velocity, the length, the density and I assume that viscosity is constant. This could result in a constant Re neglecting the AoA. However, my experiment had proven that turbulence (high Re) appears in high AoA. If I use the width of obstacle:

cos Aoa = width / length
Re = velocity*density*length (cos AoA) / viscosity
Cd = velocity*density*length*(cos AoA) / (viscosity*dynamic pressure*characteristic area)

I can graph Cd againts AoA, but what is dynamic pressure and characteristic area? From Re somehow I could measure the Skin Drag according to Clausius2. And According to http://en.wikipedia.org/wiki/Pressure_drag , Pressure drag is affected by the AoA.

 

[RainmanAero]

Hi Ariel,

Ahhh... now that I see the photos, yes, I can see you are doing the classic "flat plate in a constant speed flow" experiment! I should be able to help you quite a bit, as I teach these concepts to freshman ARO engineering students!

Rainman: I am varying the angle of attack and they do create diffrent flows (laminar and turbulent). How to calculate Cd by the way. I could use the drag equation but i don't know the drag.

Without a drag balance to measure overall drag on the plate when immersed in the flow, it may get very technical to estimate drag, but I will try to lead you through some parts of it that are fairly standard. First of all, let's start with the definition of CD as we will need to refer to it for answers to other questions you asked:

CD = Drag/(q*Sref)
q = dynamic pressure (see answers to your next post for this)
Sref = characteristic (reference) area. For drag on a flat plate we would typically use the "wetted" area of the plate... IOW, Sref=2*length*width.

First of all, I got confused. Do turbulence increase drag? I had always think that aerodynamic objects expirienced less drag because they induced less turbulence.

Now let us look at the components of total drag (subsonic, incompressible) to answer your question and help you understand:

CD = CDsf + CDp
CDsf = drag coefficient due to skin friction.
CDp = pressure drag coefficient due to pressure difference front-to-back & flow separation from the body (at high AoA).

For LAMINAR flow:
CDsf is LESS than it would be for turbulent flow.
CDp is GREATER than it would be for turbulent flow sinc the flow will separate sooner along the body.

For TURBULENT flow:
CDsf is GREATER than it would be for laminar flow because more air molecules are crossing streamlines and making contact with the surface of the plate (higher friction forces).
CDp is LESS than it would be for laminar flow, because the "random mixing" action of turbulent flow allows the flow to remain attached to the body for a longer length down the body before it eventually separates.

From the explenations since the begining, I might graph Cd againts AoA for my experiment.

The way us "professionals" would do this would be to plot Cd (y axis) against Re (x-axis), and THEN you create a "family of curves" that are all at different values of AoA. This will show you that Cd is smallest at zero AoA, and it will also show you how drag diverges with AoA increase as well as showing the drag effect of Re.

Now let me move on to your next reply...
Rainman

 

[RainmanAero]

Hi again Ariel,

In summary according to what I had comprehend.
However, my experiment had proven that turbulence (high Re) appears in high AoA.

Be careful here that you do not confuse FLOW SEPARATION with TURBULENCE. Flat plate boundary layer theory is well established, and it shows us that even at ZERO AoA the flow will eventually (at some distance x from the leading edge of the plate) trip from laminar to turbulent. This is where things get a bit more technical, as to find out where the transition point it you would need to measure pressures all along the length of the body and above the body. This would allow you to characterize the velocity profile of the boundary layer. Laminar and turbulent bounday layers are very distinctive, so you could then find at what point along the plate (at zero AoA) that the flow transitioned from laminar to turbulent.

If I use the width of obstacle:

cos Aoa = width / length
Re = velocity*density*length (cos AoA) / viscosity
Cd = velocity*density*length*(cos AoA) / (viscosity*dynamic pressure*characteristic area)

Why assume the above COS(AoA) relation? If your water flow is uniform (and it looked from the photo that it was) you should be able to use a protractor or angle inclinometer to measure the angle between the plate and the flow. IOW, measure the AoA rather than assuming the above is correct (which it is not). Also, you don't need the (cos AoA) in your Re equation. Just use the characteristic length of the plate. And your equation for Cd is incorrect (see above reply). The one piece I did not give you in the above reply is dynamic pressure (q) which is:

q = 0.5*density*flow velocity^2 (one-half-rho-Vee-squared)
Characteristic area = Sref (see above reply)

From Re somehow I could measure the Skin Drag according to Clausius2. And According to http://en.wikipedia.org/wiki/Pressure_drag , Pressure drag is affected by the AoA.

For flat plate flow there are some very good empirically-derived relations that could be used to estimate the overall skin friction drag coefficient. It would take me a LONG time to lead you through this, so I would rather just refer you to one of the best aerodynamics textbooks that explains this process: "Introduction to Flight" by John D. Anderson. It is a freshman-level aero engineering book, and one I use in my classes. Chapter 4 (specifically sections 4.15 thru 4.20 provides all the information you need to know for this type of experiment). It provides equations for computing the skin friction drag on both the laminar and turbulent sections of the flat plate. All you need to know is approximately what distance from the leading edge the flow transitions to turbulent. In your case, at zero AoA, you MAY be able to visually pick out this point, sort of like the point at which cigarette smoke from the tip of a cigarette changes from smooth (laminar) to turbulent (chaotic).

Pressure drag coefficient is MUCH more involved to try to predict, and this is generally why we will measure total drag in a wind tunnel over various Re and various AoA. From the data, and the above flat plate skin friction theory, we can "back out" an estimate of the pressure drag coefficient and how it varys with AoA. Here is a link that will at least explain pressure drag a bit more:

http://selair.selkirk.bc.ca/aerodynamics1/Drag/Page2.html

You may think that this has become MUCH more complex than you wanted it to be. Such is physics and engineering. But we have not even yet begun to discuss "induced drag" (or drag-due-to-lift). This is a component of drag which goes beyond SF and P drag, and is due to the 3 dimensional effects of a real wing, producing lift and reducing the wing's effective AoA.

I won't "go there" unless you want me to!
Rainman

 

[Clausius2]

Ariel, basically you've got everything in rainman's reply. Even though I don't agree with some particular words employed in his post, his reply is really good (the discussion of rainman and me now would continue face to face and having some beers in between) .

 

[RainmanAero]

Hi Clausius,

Ariel, basically you've got everything in rainman's reply. Even though I don't agree with some particular words employed in his post, his reply is really good (the discussion of rainman and me now would continue face to face and having some beers in between) .

I must say, the "sacred hop juice" has always been an effective fuel for discussions of a technical nature with many of my fellow engineers. My studies consistently show an empirical trend: The more beers two engineers share together, the more the lines get blurred on the differences between their personal analyses, and the more they conspire to define something with the utmost technical accuracy! (Some of us call it "geeking out" and see it as highly productive, as well as amusing and fun.)

I wish we had a "raise the beer mug" icon on the forum, for if we did I would be hoisting it to you, friend. I'm always up for better words, and don't claim mine are in any way the best... and I would trust you to challenge me and point out where my theory, or other technical detail, may be incorrect. Take care,

RMT

 

[ArielGenesis]

These are more then helpful, thx.

I had got the big picture of my experiment as well as how all the values are related to each other, and I am looking foward for more detailed explenation in Anderson's book. Sooner or later I should manage to read through it. Yet I am still confused in three things ( be patient with me please) :

First RainmanAero said that CD = Drag / (q * Sref). Then CD = CDsf + CDp. Are both CD the same or do you meant the second CD to be the total drag and the first CD to be either CDsf or CDp?

Then, I still confused about the characteristic length. According to Clausius2, characteristic length should be the width of obstacle. In my experiment, the width of obstacle relative to the flow is length*cos AoA where length is the length of the obstacle. That's how it came into my Re # equation.

About my results, when AoA is 60 degrees or more, what I interpreted as turbulence formed. I consider them as turbulence as I they are not calm at all, nor laminar any more. However, I could hardly notice the eddies and this put me in doubt.

I also checks for "flat plate in a constant speed flow" and found out close to naught in the net. It don't really mean anything though, but I am just interested about peeking at the correct and ideal final results if this experiment had been done before.

You guys are really helpful, thanks once more.
Arian

 

[Clausius2]

Then, I still confused about the characteristic length. According to Clausius2, characteristic length should be the width of obstacle. In my experiment, the width of obstacle relative to the flow is length*cos AoA where length is the length of the obstacle. That's how it came into my Re # equation.

Forget about the width. I was confused about the geometry. I was thinking your experiment was a ridge at the bottom of a water tunnel.

 

[ArielGenesis]

I see, we all were confused at one time or the other.

 

[RainmanAero]

Hi Ariel/Arian

First RainmanAero said that CD = Drag / (q * Sref). Then CD = CDsf + CDp. Are both CD the same or do you meant the second CD to be the total drag and the first CD to be either CDsf or CDp?

Both CD's are the same, and so you can set one equation equal to the other. The aero engineer uses this, and other relations to optimize the performance of any aero-hydro-dynamic vehicle.

About my results, when AoA is 60 degrees or more, what I interpreted as turbulence formed. I consider them as turbulence as I they are not calm at all, nor laminar any more. However, I could hardly notice the eddies and this put me in doubt.

As with the practice of all the aerosciences, there are certain numbers that we all become familiar with. One number is the reasonably linear range where Lift Force is linear with Angle Of Attack. LIFT will generally increase in a linear relationship with Angle Of Attack until a specific linear range is exceeded. In the aerodynamics of our Earth atmosphere, and for typical aerodynamic wings/vehicles, we usually assume a maximum Angle Of Attack of 16 to 18 degrees. Beyond this is the "stalled" region which is terribly non-linear for even the most efficient aerodynamic shape.

I also checks for "flat plate in a constant speed flow" and found out close to naught in the net. It don't really mean anything though, but I am just interested about peeking at the correct and ideal final results if this experiment had been done before.

Again I should point out that this is a vast scientific area. I am not doing it justice with my verbal descriptions. And I must say that you are not going to be able to absorb the full meaning of these concepts in a web page or two. This is precisely why it takes an engineer FOUR AND MORE years to learn these concepts and how to apply them, and thus earn a degree.

If you are truly interested in the science behind what you are playing with, then you should work to become a scientist or engineer who specializes in this! It is really fun work, I can attest to that from a first-hand perspective!

Rainman

 

[ArielGenesis]

To be honest, I am not that interested in fluid dynamic, my interest is more towards theoretical physics. You noticed my real name, great.

I am only writing 4000 words essay so I don't think I would go to such details but I am eager for them just to have a good backgroud of what I am doing. I am having exam so I might just leave this project for about a few weeks and then when I am back, I could say how I ended like.

I have more then enough informations by now. Thx.