[FDS-SMV Developer Blog] Hydrodynamics and Turbulence

[rmcdermo]

Following the announcement of the v6 beta release, we thought it might be helpful expand a little bit on some of the topics in the release notes.  Our aim here is to explain why certain changes were necessary or why certain choices were made in a way that might provide more insight than can be gleaned from just reading the formal documentation (though reading the guides is still highly encouraged!).

The focus in this article will be hydrodynamics and turbulence.  Hydrodynamics is the foundation of any CFD code, especially a reacting flow code like FDS.  Chemical species cannot react until they have mixed, and (in a diffusion flame) they cannot mix until they have been transported.  The velocity field, therefore, plays a critical role in fire dynamics.  In a model like FDS, other things being equal, the model for the turbulent viscosity determines the behavior of the velocity field and hence to a large extent the dynamics of the fire.

In v5, the turbulent viscosity was modeled by constant coefficient Smagorinsky (1963) (csmag), which has the drawback being overly dissipative (have you ever seen a 10-foot fire look like a candle flame?).  Thus, finer grid resolution was required to achieve accurate results.  But even highly resolved flames did not look qualitatively correct.  The reason: csmag is not convergent.  That is, the modeled term does not go away (as it should) when the grid is refined to the level of a DNS.

The original candidate to replace csmag was the dynamic Smagorinsky model (dsmag).  While this model added about 20% to the cost of computing the velocity field, in theory this cost could be recovered by achieving more accurate results (statistically) with coarser grid resolution.  So, dsmag was implemented and run through a battery of verification and validation tests with more or less satisfactory results.  On the plus side, we were getting very realistic-looking flames at moderate grid resolution.  But on the minus side, if the resolution was too coarse (often inevitable in engineering calculations), the flames were erratic---instead of a 10-foot flame looking like a candle, dsmag might produce an unstable ball of fire.

The solution to this dilemma came in the form of Deardorff’s model (1972), with a twist.  In the model Deardorff originally proposed, he solved a transport equation for the subgrid kinetic energy (sgs ke).  This strategy is expensive, but it allows for the inclusion of complex subgrid physics, like unresolved buoyancy production.  To avoid this cost, we employ a simple algebraic model for the sgs ke based on the scale similarity model of Bardina (1986).  The result is a model that is cheap and performs reasonably well at both coarse and fine resolution.  As an added benefit, the framework is now in place to utilize a transported sgs ke, a topic that might be worth explorating as FDS gets pushed to model large-scale outdoor flows in both wildfire and wind engineering applications.

While the new turbulence model is certainly significant, the change that really defines v6 is the new scalar transport scheme.  The ripple effects of this modification were not fully appreciated until a couple of years after the initial implementation.  What follows is the “saga of removing spurious temperature wiggles.”

Take FDS 5 and simulate a simple fire plume with open boundaries and 20 C ambient air temperature.  Now look closely at the temperature field near the corner of the burner.  You will see unphysical excursions of the local temperature to well below ambient, near 0 C.  Clearly this is undesirable.  What is not as obvious is that there are also unphysical excursions well above ambient, within the fire.  Of course, 1020 C versus 1000 C is not as dramatic a problem.

So why does this happen?  The root cause is central differencing in the solution of the density equation.  Purely centered schemes are notorious for generating dispersion errors---wiggles.  To combat this problem, v5 uses a boundedness correction which tries to prevent the scalar fields (density and species concentration) from going above or below defined limits.  With mass fractions the limits are easy to set (0 and 1).  With density there is only one hard limit (0).

In v6, we have decided to try another approach: total variation diminishing (TVD) scalar transport.  This is a fancy way of saying “we use just the right amount of upwinding.”  Pure upwind schemes are too dissipative (translation: inaccurate).  But TVD schemes are specially designed to track scalar discontinuities with minimal dispersion error and minimal dissipation.  This effectively solved the temperature wiggles problem.

Several TVD schemes are implemented in v6.  The default for LES is Superbee (Roe, 1986), so chosen because this scheme does the best job preserving the scalar variance in highly turbulent flows with coarse grid resolution.  The default scheme for DNS is Charm (Zhou, 1996) because the gradient steepening used in Superbee forces a stair step pattern at high resolution, while Charm is convergent.   A few other schemes (including Godunov and central differencing) are included for completeness; more details can be found in the Tech Guide.

These modifications were completed by the summer of 2009 (yes, you are reading that right).  It seemed at this point that we were very close to a v6 release.  Then… the wheels came off the bus.  In what we thought would be a routine pass through the verification suite, we hit a snag: our energy budget cases were off, by about 10%.  In addition, several of the validation cases now showed low upper layer temperatures---yep, by about 10%.

Hmmm.  A lot of head scratching ensued---two years, in fact, until Jason Floyd finally developed a test case that pinpointed the problem.  Imagine a T-mixer in which equal mass fluxes of a hot gas with a low cp (heat capcity) and a cold gas with a high cp mix and exit together.  The critical aspect of this case is that the flow paths are one cell thick and we artificially set the diffusivity and conductivity to zero.  Thus, any mixing is purely numerical.  What we found was that the outlet stream temperature was mass weighted instead of enthalpy weighted---there was no accounting for the variation in cp.  The pieces of the puzzle finally started to come together because another relatively recent development (actually in v5) was the inclusion of variable temperature specific heats.

The aftermath of this discovery was a torturous dissection of the energy equation (see appendix of the Tech Guide) illustrating that basic assumptions of the low-Mach number approximation can hide the effects of the numerical mixing from TVD transport schemes.  The bright side of the story is that through this analysis we were able to derive corrections for numerical mixing that force FDS to satisfy the discrete, conservative form of the sensible enthalpy equation, ultimately solving the temperature issues.

The benefit of the delayed release is that many other parts of the code were improved in the mean time.  So stay tuned for our next installment.

--
Posted By rmcdermo to FDS-SMV Developer Blog at 11/05/2012 05:19:00 PM

[Daniel_eval_firegas]

Great job to all of you FDS Developers!
You will get closer and closer to reality. This issue of temperature drops near hot surfaces in FDS5 was very strange for me, so that I almost would say that the the results are only true for open boundaries and in the upper hot temperature layers. Now you have fixed it and my discovery with FDS6 can continue. I'm so exited to validate your work and to post it.
Greetings
Daniel

[Mahfuz Sarwar]

Hi Randy!

You have nicely explained various LES schemes.

In FDS 6 Tech guide there is another turbulent viscosity model included called Vreman’s model. But here you haven’t mentioned about the Vreman’s model. We would like to know more about it.

In addition, I would like to know is there any validation case where all four turbulent viscosity models were applied. And which one gives the best prediction?

Regards

Mahfuz

[Randy McDermott]

I think I explain Vreman's mode in the Tech Guide and you can find the reference there.  Here is a link to the nightly builds of the Tech Guide:

https://docs.google.com/folder/d/0B_wB1pJL2bFQaDJaOFNnUDR4LXM/edit?docId=0B_wB1pJL2bFQUEVMX3hGQlNWVDQ

All the available turbulence models are compared for decaying isotropic turbulence and for decay of the centerline velocity in a turbulent jet.  See the verification guide:

https://docs.google.com/folder/d/0B_wB1pJL2bFQaDJaOFNnUDR4LXM/edit?docId=0B_wB1pJL2bFQVDdfY3ZkZnh0Rms

The choice to make Deardorff the default for v6 was made after exploring all the models on many different V&V cases.  This comparison considered both cost of the model and performance across a range of grid spacings.  What you find is that for very high resolution, aside from constant coefficient Smagorinsky, all the models converge.  But for very coarse resolution of fire dynamics, Deardorff performed much better than either dynamic Smagorinsky or Vreman---these models exhibit wildly oscillatory unphysical behavior if the grid is not sufficiently resolved.  In practice it is very difficult to find the sweet spot for resolution.  We therefore need a model that is forgiving and can return sensible results across a broad range of resolution.

[Khalid Moinuddin]

Hi Randy,

Is the beta version of WFDS6 out yet? If yes, does it have these four LES models ?

Kind regards,

Khalid

---

From: fds...@googlegroups.com [fds...@googlegroups.com] on behalf of Randy McDermott [randy.m...@gmail.com]
Sent: Thursday, 21 March 2013 12:00 AM
To: fds...@googlegroups.com
Subject: [fds-smv] Re: [FDS-SMV Developer Blog] Hydrodynamics and Turbulence

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[Kevin]

Is there a WFDS5? I don't see it on the Downloads page.

On Mar 20, 8:34 pm, Khalid Moinuddin <Khalid.Moinud...@vu.edu.au>
wrote:

> Hi Randy,
>
> Is the beta version of WFDS6 out yet? If yes, does it have these four LES models ?
>
> Kind regards,
>
> Khalid
> ________________________________

> From: fds...@googlegroups.com [fds...@googlegroups.com] on behalf of Randy McDermott [randy.mcderm...@gmail.com]

> Sent: Thursday, 21 March 2013 12:00 AM
> To: fds...@googlegroups.com
> Subject: [fds-smv] Re: [FDS-SMV Developer Blog] Hydrodynamics and Turbulence
>
> I think I explain Vreman's mode in the Tech Guide and you can find the reference there.  Here is a link to the nightly builds of the Tech Guide:
>

> https://docs.google.com/folder/d/0B_wB1pJL2bFQaDJaOFNnUDR4LXM/edit?do...

>
> All the available turbulence models are compared for decaying isotropic turbulence and for decay of the centerline velocity in a turbulent jet.  See the verification guide:
>

> https://docs.google.com/folder/d/0B_wB1pJL2bFQaDJaOFNnUDR4LXM/edit?do...

>
> The choice to make Deardorff the default for v6 was made after exploring all the models on many different V&V cases.  This comparison considered both cost of the model and performance across a range of grid spacings.  What you find is that for very high resolution, aside from constant coefficient Smagorinsky, all the models converge.  But for very coarse resolution of fire dynamics, Deardorff performed much better than either dynamic Smagorinsky or Vreman---these models exhibit wildly oscillatory unphysical behavior if the grid is not sufficiently resolved.  In practice it is very difficult to find the sweet spot for resolution.  We therefore need a model that is forgiving and can return sensible results across a broad range of resolution.
>
> On Wednesday, March 20, 2013 1:38:50 AM UTC-4, Mahfuz Sarwar wrote:
>
> Hi Randy!
> You have nicely explained various LES schemes.
>
> In FDS 6 Tech guide there is another turbulent viscosity model included called Vreman’s model. But here you haven’t mentioned about the Vreman’s model. We would like to know more about it.
>
> In addition, I would like to know is there any validation case where all four turbulent viscosity models were applied. And which one gives the best prediction?
>
> Regards
> Mahfuz
>
> On Tuesday, November 6, 2012 9:19:15 AM UTC+11, Randy McDermott wrote:
>

> Following the announcement of the v6 beta release, we thought it might be helpful expand a little bit on some of the topics in the release notes<http://code.google.com/p/fds-smv/wiki/FDS_Release_Notes>.  Our aim here is to explain why certain changes were necessary or why certain choices were made in a way that might provide more insight than can be gleaned from just reading the formal documentation (though reading the guides is still highly encouraged!).

>
> --
> You received this message because you are subscribed to the Google Groups "FDS and Smokeview Discussions" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to fds-smv+u...@googlegroups.com.
> To post to this group, send email to fds...@googlegroups.com.
> To view this discussion on the web visithttps://groups.google.com/d/msg/fds-smv/-/x0P-BtuYDIsJ.

> For more options, visithttps://groups.google.com/groups/opt_out.

[Ruddy]

Version 6 of WFDS is at SVN 9977. Shortly after this SVN, FDS was modified significantly, especially in how particles are used to handle vegetation. We are still in the process of testing how well the current beta version of FDS6 handles vegetation. FDS6 SVN 9977 does have the four LES models and uses Deardorff by default. However, Randy and others know better if modifications of FDS subsequent to SVN9977 are required to fully explore these sub-grid turbulence models.

So, as we continue to test the beta version of FDS6 our working version of WFDS6 is SVN 9977 which has undergone fairly significant testing. It can be obtained through https://sites.google.com/site/wuifiresfiremodels/

[Khalid Moinuddin]

Thanks, Ruddy. We will look at the WFDS6 (SVN 9977) testing and if we have any question, we will get back to you.

Kind regards,

Khalid

---

From: fds...@googlegroups.com [fds...@googlegroups.com] on behalf of Ruddy [rudd...@gmail.com]
Sent: Friday, 22 March 2013 2:16 AM
To: fds...@googlegroups.com
Subject: Re: [fds-smv] Re: [FDS-SMV Developer Blog] Hydrodynamics and Turbulence

To view this discussion on the web visit https://groups.google.com/d/msg/fds-smv/-/jb-UroJSdKAJ.

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