## [CFD] Calculating Initial Conditions for Turbulence

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Vyssion
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Joined: Sun Jun 10, 2012 1:40 pm

### [CFD] Calculating Initial Conditions for Turbulence

Hi all,

I posted this within the CFD main thread stickied up the top of this sub-forum, but figured that I would put it here in its own thread so that the information wouldnt be lost within the pages of it. As always, any questions, please do feel free to post here or DM me

I will go over all the "major" variables that people may or may wish to calculate here - there are ways to skip to the ones you want, but this way will give you all that you need, I hope.

One equation for turbulent kinetic energy (k), in J/kg, is:

$k=\frac{\overline{u'_i u'_i}}{2}$

This basically reads as "k" being equal to the time average of the velocity fluctuations in one direction squared, all divided by 2. So a rough way to calculate this would be to take your domain's inlet velocity, multiply it by your turbulence intensity (i.e. 5% = 0.05 ), and then square it. From there, you divide by 2, but since we only looked into one direction, a crude way of approximating this throughout the domain is to multiply that final result by 3; one for each axis, since there will be fluctuations in velocity in all directions.

Alternatively, you can split them out into each separate axis if you have a vector with a non-zero second or third component. If that is the case, do the same thing but use this equation below:

${\displaystyle k={\frac {1}{2}}\left(\,{\overline {(u')^{2}}}+{\overline {(v')^{2}}}+{\overline {(w')^{2}}}\,\right)}$

For Omega, its a little more involved... Assuming you know the air Pressure [Pa] and Temperature [K}, then you can use the ideal gas law equation to calculate your air density:

$\rho = \frac{p}{R_{\rm specific} T}$

From there, we need to use Sutherland's Law for calculating the fluid dynamic viscosity of air as it relates to temperature:

${\displaystyle \mu =\mu _{0}{\frac {T_{0}+C}{T+C}}\left({\frac {T}{T_{0}}}\right)^{\frac {3}{2}}.}$

which can be written as:

${\displaystyle \mu =\lambda {\frac {T^{\frac {3}{2}}}{T+C}}}$ , where ${\displaystyle \lambda ={\frac {\mu _{0}\left(T_{0}+C\right)}{T_{0}^{\frac {3}{2}}}}}$

Taking "$\lambda$" as being equal to 0.000001458 and "C" as being equal to 110.4 (these are commonly used values of dynamic viscosity of air at a specific temperature within CFD literature), you can then calculate back through to get your actual at your given temperature in [ Pa . s ].

Next we need to calculate the turbulent length scale [m] of the flow, which can be done crudely (yes, I am aware that the k-$\epsilon$ model has it's own definition of the length scale utilizing the relationship between k, epsilon and $C_\mu$) by:

$l = 0.038 \; d_h$

Note that $d_h$ is the hydraulic diameter and so depending on your shape of domain, there will be a different equation for calculating the equivalent circular section. For a rectangular domain, use this equation:

${\displaystyle D_{\text{H}}={\frac {4ab}{2(a+b)}}={\frac {2ab}{a+b}}}$

Next, we can calculate Epsilon [J / kg . s ] by using the k-$\epsilon$ specific coefficient $C_\mu$ = 0.09 along with the turbulent length scale we just worked out and the turbulent kinetic energy (k) from before:

$\epsilon = C_\mu \, \frac{k^\frac{3}{2}}{l}$

Next we need to calculate something called nuTilda which is our turbulent viscosity [ m^2 /s ]. We can do that by

${ \mu }_{ t }={ C }_{ \mu }\frac { { k }^{ 2 } }{ \varepsilon }$

Finally, for Omega [J / kg . s ]

$\omega = \frac{\rho \, k}{\mu} \, (\frac{\mu_t}{\mu})^{-1}$

Where "k" is the turbulent energy, $\rho$ is the density, $\mu$ is the molecular dynamic viscosity and $\frac{\mu_t}{\mu}$ is the eddy viscosity ratio.

Hope this helps!!
"And here you will stay, Gandalf the Grey, and rest from journeys. For I am Saruman the Wise, Saruman the Ring-maker, Saruman of Many Colours!"

#aerosaruman

"No Bubble, no BoP, no Avenging Crusader.... HERE COMES THE INCARNATION"!!"

PlatinumZealot
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### Re: [CFD] Calculating Initial Conditions for Turbulence

Hmm. Great topic.

So I know what level to ask questions. What are your experience and qualifications in the field if you don't mind?

I have often ignored these turbulence parameters in CFD, but that' mostly because I have no clue what to put there.
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Vyssion
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Joined: Sun Jun 10, 2012 1:40 pm

### Re: [CFD] Calculating Initial Conditions for Turbulence

PlatinumZealot wrote:
Mon Aug 06, 2018 5:40 pm
Hmm. Great topic.

So I know what level to ask questions. What are your experience and qualifications in the field if you don't mind?

I have often ignored these turbulence parameters in CFD, but that' mostly because I have no clue what to put there.
I did two Bachelors in Engineering and a Masters of Race Car Aerodynamics which has been followed up by quite a lot of aero-design and CFD in a couple of different industries... Let's just say, feel free to ask whatever you'd like, however you'd like.
"And here you will stay, Gandalf the Grey, and rest from journeys. For I am Saruman the Wise, Saruman the Ring-maker, Saruman of Many Colours!"

#aerosaruman

"No Bubble, no BoP, no Avenging Crusader.... HERE COMES THE INCARNATION"!!"

Zynerji
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### Re: [CFD] Calculating Initial Conditions for Turbulence

Vyssion wrote:
Mon Aug 06, 2018 9:58 pm
Let's just say, feel free to ask whatever you'd like, however you'd like.

How possible would it be to add a re-laminating grid in front of the front wing to clean turbulent flow before it reaches the wing surface. What negative effect?

Vyssion
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### Re: [CFD] Calculating Initial Conditions for Turbulence

Zynerji wrote:
Tue Aug 07, 2018 2:44 am
Vyssion wrote:
Mon Aug 06, 2018 9:58 pm
Let's just say, feel free to ask whatever you'd like, however you'd like.

How possible would it be to add a re-laminating grid in front of the front wing to clean turbulent flow before it reaches the wing surface. What negative effect?
I suppose I should have stated "CFD" questions No matter, here goes:

You're assumption that the the loss of downforce is from the "turbulence" coming off the car in front which isn't strictly true... I think jjn9128 made a post on this a while ago in his PhD thesis thread, but boardly speaking, the main contributor to downforce loss is the reduction in dynamic pressure that the wing sees whilst in the wake region of the car upstream. This has the effect of reducing the total surface pressure on the downstream car's aerodynamic surfaces.

As the upstream car moves, it sort of pulls and shears at the air around it and in it's path and leaves a sort of "suction wake" region behind it. The air in that region now has a non-zero velocity in the same direction as the car is travelling and so the relative velocity between it and the downstream car is now reduced: you can use that reduction to calculate a dynamic pressure loss. Which in turn will have some effect on the Y250 vortex, front wing endplate + upper flap vortices, bargeboards, etc.

Now this makes up like 90+% of the loss of downforce that the downstream car will experience, however, there is an effect from the local upwash and non-uniformities (i.e. turbulence) which does have a small effect, so you would only be affecting a small number of %-points with attempting to "re-laminate", as you say, the flow.

Having turbulence screens in front of the wing, similar to wind tunnels, may increase or decrease the intensity levels depending on their design - however, they will mostly serve to make the velocity profile more uniform and improve the turbulence dispersion over the cross section. These "intensities" or fluctuations will have an associated length scale to them, and it is this variable which will be what controls the "turbulent buffetting" that you could expect. Only thing is, is that the front wing in F1 is deliberately tripped into a turbulent boundary layer which is more able to withstand the strong adverse pressure gradients present on its aggressive geometry. Because of this, your turbulent length scale will kinda have only a small effect.

Mesh screens are used in wind tunnels to try and make the airflow more uniform, and so I can see where the idea comes from... However, those screens with their meshes and honeycomb sections, are sometimes hundreds of millimeters thick (or more!!) and there are various stages of them within the "flow conditioning block" of the tunnel.
"And here you will stay, Gandalf the Grey, and rest from journeys. For I am Saruman the Wise, Saruman the Ring-maker, Saruman of Many Colours!"

#aerosaruman

"No Bubble, no BoP, no Avenging Crusader.... HERE COMES THE INCARNATION"!!"

Zynerji
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Joined: Wed Jan 27, 2016 3:14 pm

### Re: [CFD] Calculating Initial Conditions for Turbulence

Thank you! I appreciate your time to explain, and not only does it now make sense to me, it opens another question!

Dipesh1995
Dipesh1995
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### Re: [CFD] Calculating Initial Conditions for Turbulence

Vyssion wrote:
Tue Aug 07, 2018 10:21 am
Zynerji wrote:
Tue Aug 07, 2018 2:44 am
Vyssion wrote:
Mon Aug 06, 2018 9:58 pm
Let's just say, feel free to ask whatever you'd like, however you'd like.

How possible would it be to add a re-laminating grid in front of the front wing to clean turbulent flow before it reaches the wing surface. What negative effect?
Only thing is, is that the front wing in F1 is deliberately tripped into a turbulent boundary layer which is more able to withstand the strong adverse pressure gradients present on its aggressive geometry.
Isn’t there a “catch” with that that aerodynamicists have to be careful of because a turbulent boundary layer has greater thickness compared to its laminar boundary layer counterpart. Thicker boundary layers tend to be more prone flow separation in adverse pressure gradients so for a “fixed” transition case i.e flow being deliberately tripped at a certain location, wouldn’t a too premature transition to a turbulent boundary layer introduce a bit of trailing-edge flow separation on an aerofoil with this separation being able to move further upstream depending on AoA?

I don’t know if it’s strictly correct to say this but I like to think of introducing a turbulent boundary layer in a flow separation context as a sort of “temporary power boost”. If it’s deployed too early (premature tripping of the flow) then the boundary layer will run out of momentum before the end of the surface (underside of an aerofoil) thus trailing edge flow separation will be present. If it’s deployed too late then complete laminar flow separation with no flow reattachment will occur and if it’s deployed just right then transition will take place at the right location such that no flow separation occurs at all apart from the laminar separation bubble which is the typical free-transition mechanism.

jjn9128
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### Re: [CFD] Calculating Initial Conditions for Turbulence

Dipesh1995 wrote:
Tue Aug 07, 2018 2:17 pm
wouldn’t a too premature transition to a turbulent boundary layer introduce a bit of trailing-edge flow separation on an aerofoil with this separation being able to move further upstream depending on AoA?
A trailing edge separation is a normal part of the lift--incidence curve of a wing. In fact even after the trailing edge begins to separate the wing will continue to produce more lift/downforce, just at a slower rate. This is the curve bit of the slope after the straight line. The peak force will be produced with a fairly large portion from the trailing edge of the wing separated.

Wing angle on an F1 car is fixed so this isn't so much an issue - where it may an issue on the front wing is the changing ground clearance. But the same mechanisms are in place as wing height is reduced, the force enhancement has no separation, the force plateau and peak downforce has moderate to fairly extreme trailing edge separation. Where this is undesirable for a front wing is the thickness of the wake - which affects the rest of the car. So, without wishing to seem overly obvious, you design the wing to have no (or only moderate) trailing edge separation at all foreseeable car attitudes and Reynolds numbers.
#aerogandalf
"There is one big friend. It is downforce. And once you have this it’s a big mate and it’s helping a lot." Robert Kubica

Vyssion
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Joined: Sun Jun 10, 2012 1:40 pm

### Re: [CFD] Calculating Initial Conditions for Turbulence

EDIT - Seems jjn beat me to the trailing edge separation as I was typing
Dipesh1995 wrote:
Tue Aug 07, 2018 2:17 pm
Vyssion wrote:
Tue Aug 07, 2018 10:21 am
Only thing is, is that the front wing in F1 is deliberately tripped into a turbulent boundary layer which is more able to withstand the strong adverse pressure gradients present on its aggressive geometry.
Isn’t there a “catch” with that that aerodynamicists have to be careful of because a turbulent boundary layer has greater thickness compared to its laminar boundary layer counterpart. Thicker boundary layers tend to be more prone flow separation in adverse pressure gradients so for a “fixed” transition case i.e flow being deliberately tripped at a certain location, wouldn’t a too premature transition to a turbulent boundary layer introduce a bit of trailing-edge flow separation on an aerofoil with this separation being able to move further upstream depending on AoA?

I don’t know if it’s strictly correct to say this but I like to think of introducing a turbulent boundary layer in a flow separation context as a sort of “temporary power boost”. If it’s deployed too early (premature tripping of the flow) then the boundary layer will run out of momentum before the end of the surface (underside of an aerofoil) thus trailing edge flow separation will be present. If it’s deployed too late then complete laminar flow separation with no flow reattachment will occur and if it’s deployed just right then transition will take place at the right location such that no flow separation occurs at all apart from the laminar separation bubble which is the typical free-transition mechanism.
The statement in isolation that " a thicker boundary layer is more prone to separation" is both correct and incorret depending what type of boundary layer you are referring to.

A boundary layer may be laminar or turbulent, and the underlying physics at play within each respectively is similar, but different in one key aspect: mixing.

A laminar boundary layer is one where the flow exists in "layers" which slide along adjacent to one another. This is in contrast to a turbulent boundary layer in which there is an intense agitation of the flow which creates a mixing effect.

Once again with laminar boundary layers, any exchange of mass or momentum between the layers can only occur with those that are directly adjacent to the layer receiving or donating that eddy packet at a sort of microscopic scale. Consequently, the molecular viscosity is able to predict the induced shear stress from these interactions.

A turbulent boundary layer, however, is marked by this mixing I referred to which happens across several of these "layers", and now occurs on a relatively macroscopic scale. This means that there is a much larger exchanging of mass, momentum and energy between each of these "layers", often from the edge of what we define as the boundary layer, and down to the wall surface itself. It also has a much steeper gradient of velocity at the wall and therefore a larger shear-stress. Because of this, the molecular viscosity on it's own cannot handle all of the mixing. Instead, what we calculate, is called a "Turbulence Viscosity" or an "Eddy Viscosity" which must be modelled... Hence why most RANS methods which utilize this "Eddy Viscosity" approximation will solve their equations with the assumption that the entire boundary layer is turbulent, and only by introducing additional equations into the simuilation, such as the k-omega SST intermittancy model, can you actually tell the solver that there is a portion of the boundary layer that needs to be solved as being laminar with its lower skin friction and wall shear stress, etc accordingly.

Because of all of this, a turbulent boundary layer can withstand an adverse pressure gradient for longer (or a much stronger adverse pressure gradient for a short time) than the same sized laminar boundary layer would be able to. But if this were a laminar layer without as much mixing, then yes it would most likely separate and cause problems.

As for your question about the trailing edge separation etc, let me explain that with a metaphor of tyres and slip angles. The way that you gain traction with a tyre is "loosely" (and without the desire to step on the vehicle dynamics engineers toes here) by torquing the inner axle which then in turn shears the tyre sidewall and bunches up the sidewall under the contact patch... this is where your grip comes from, but towards the rear portion of your contact patch, there is a region which has to slip back to its resting position else it would continue to wind up. This slippage is what propells you forward. There is a similar thing going on when you have a tyre and you are cornering with the corner slip angle too. I forget the exact derivation, but in most cases where you are right on the limit, you actually have more traction if your tyres are slightly slipping a little more than you would think.

It is a similar effect with this trailing edge separation. Trailing edge separation is still an inportant part of the force plateau of wings. And so you will still be getting some amount of downforce out of that slight separation. Leading edge separation is terrible and should be avoided at all costs, of course, but a little trailing edge separation can still be beneficial if done correctly.
"And here you will stay, Gandalf the Grey, and rest from journeys. For I am Saruman the Wise, Saruman the Ring-maker, Saruman of Many Colours!"

#aerosaruman

"No Bubble, no BoP, no Avenging Crusader.... HERE COMES THE INCARNATION"!!"

turbof1
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Location: MountDoom CFD Matrix

### Re: [CFD] Calculating Initial Conditions for Turbulence

Vyssion wrote:
Tue Aug 07, 2018 3:58 pm
EDIT - Seems jjn beat me to the trailing edge separation as I was typing
Ah, competition among our writers.

Love it .
#AeroFrodo

Dipesh1995
Dipesh1995
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Joined: Mon Apr 21, 2014 4:11 pm

### Re: [CFD] Calculating Initial Conditions for Turbulence

Thanks for the responses.

My question arised from my FYP topic which was on the effects of leading-edge debris/roughness on a multi-element wing in ground effect. A supplementary study I did was transition (T) vs no transition (NT) i.e fully turbulent using CFD.

Bit of background information:

The wing consisted of a NACA 4412 as the main element at 0 degrees AoA and a slightly cambered custom designed aerofoil as the flap at 17 degrees AoA. Total chord length was 0.273m and span was 0.5m. Chord length based Reynolds number was approximately 700,000 i.e freestream velocity of 40 m/s. Ground clearance was set to 35mm. Turbulence model was k-w SST and transition was modelled via the Gamma Re Theta model. Turbulence intensity and viscosity ratio was set to 1% and 10% respectively.

Suction-side Results:

For the T case, main element transition occurred just after the max thickness point of the aerofoil whilst flap transition occurred around 1/3 of the chord length from the leading edge. So at the trailing-edge region of both aerofoils for the T case, the boundary layer was fully turbulent.

At the trailing-edge region of the aerofoils, the boundary layer was consistently thicker for the NT case compared to the T case so much so that the trailing-edge flow separation was present only for the NT case on the flap. Downforce also reduced by approx 1.8% and drag increased by approx 1.3%.

Whilst I acknowledge that the transition model is correlation-based and does not model the actual physics of the problem, I think that similar results would also be seen experimentally regarding boundary layer thickness comparison between T and NT (not in terms of absolute thickness numbers). This leads on to my previous post, maybe I should have worded it a bit better, that trailing-edge flow separation has a greater chance of occurring (particularly at high AoA) for a fully turbulent/premature transition case compared to a free-transition case i.e unforced transition due to a thicker boundary layer regarding the former case assuming that the boundary layer for both cases at the trailing-edge region is turbulent and that transition has occurred sufficiently/considerably downstream from the leading-edge of an aerofoil or the chordwise location of the premature/fixed transition point, whichever is appropriate.

117
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### Re: [CFD] Calculating Initial Conditions for Turbulence

I have read that the teams work to cause turbulence behind their car to mess with a following car. But I have been told on boards that this is not possible because it would ruin their own down force.
In your opinion can/do the teams create extra turbulence in their wake or would doing so ruin their ability to create down force?
To achieve anything, you must be prepared to dabble on the boundary of disaster.”
Sir Stirling Moss

Vyssion
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Joined: Sun Jun 10, 2012 1:40 pm

### Re: [CFD] Calculating Initial Conditions for Turbulence

Tue Aug 07, 2018 7:24 pm
I have read that the teams work to cause turbulence behind their car to mess with a following car. But I have been told on boards that this is not possible because it would ruin their own down force.
In your opinion can/do the teams create extra turbulence in their wake or would doing so ruin their ability to create down force?
Kinda a little bit of an off-topic speculation, but if it was me in charge of aerodynamics, I would ideally want to purposefully create as much of a turbulent wake as I possibly could so that it would be incredibly difficult for cars to pass me without compromising my own performance. Some may argue that as "unethical for racing" or "potentially dangerous" but Im not here to "play fair"... I'm here to win. That being said, I doubt teams will want to spend their precious wind tunnel and CFD time per week on destroying other cars following performance vs. improving their own...
"And here you will stay, Gandalf the Grey, and rest from journeys. For I am Saruman the Wise, Saruman the Ring-maker, Saruman of Many Colours!"

#aerosaruman

"No Bubble, no BoP, no Avenging Crusader.... HERE COMES THE INCARNATION"!!"

wpsiatwin
wpsiatwin
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### Re: [CFD] Calculating Initial Conditions for Turbulence

Tue Aug 07, 2018 7:24 pm
I have read that the teams work to cause turbulence behind their car to mess with a following car. But I have been told on boards that this is not possible because it would ruin their own down force.
In your opinion can/do the teams create extra turbulence in their wake or would doing so ruin their ability to create down force?
One of my lecturers was an aerodynamicist at Toyota, marussia and I think one other team and when he did a talk about his job in F1 he was asked this and his response was basically Vyssion said, they design just to improve their cars performance but if more turbulent air behind the car is a result of that they're not unhappy.