Particle velocity and Stokes number assumptions

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mkrupcale
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Particle velocity and Stokes number assumptions

Post by mkrupcale »

I have a few questions about some of the basic assumptions of the Langevin model used by HYSPLIT:
  1. The (virtual or Lagrangian) particle velocity is given by the sum of the mean fluid velocity (from the meteorological data) and the turbulent fluid velocity component (determined using the [discretized] turbulent fluid velocity Langevin equation). This assumes then that the (virtual or Lagrangian) particle velocity is given by the carrier fluid (i.e. air) velocity, yes? This is to say that there is no difference between particle velocity and instantaneous / total fluid velocity at the particle position.
  2. If this is the case, does this implicitly require that the Stokes number of the physical particles represented by the virtual or Lagrangian particles be very small so that particles respond sufficiently rapidly to the carrier fluid flow velocity so as to have equal velocity? If not, why not?
  3. If that is correct, then what is an approximate upper bound on the particle response time and the particle diameter for a typical solid particle density (e.g. 2500 kg/m^3) which could be modeled with the HYSPLIT Langevin model?
alicec
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Re: Particle velocity and Stokes number assumptions

Post by alicec »

For inertial particles, the main effect is due to gravitational settling.
HYSPLIT includes two gravitational settling schemes for inertial particles.
See here for more details.
viewtopic.php?f=28&t=2211&p=6406&hilit= ... ling#p6406

The other effects are generally small. Reference below may be helpful. They suggest decreasing velocity autocorrelation time
scale for heavier particles as well. But as estimation of this time scale at any particular moment / place in the atmosphere has
a high uncertainty, this is not done in HYSPLIT automatically. You can adjust the autocorrelation times in the Namelist parameters.
https://www.ready.noaa.gov/hysplitusersguide/S625.htm


Trajectory models for heavy particles in atmospheric turbulence: Comparison with observations
By: Wilson, JD
JOURNAL OF APPLIED METEOROLOGY Volume: ‏ 39 Issue: ‏ 11 Pages: ‏ 1894-1912 Published: ‏ NOV 2000
alicec
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Joined: February 8th, 2016, 12:56 pm
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Re: Particle velocity and Stokes number assumptions

Post by alicec »

You may also be interested in this reference

Forecasting volcanic ash deposition using HYSPLIT
Tony Hurst & Cory Davis
Journal of Applied Volcanology volume 6, Article number: 5 (2017)

https://appliedvolc.biomedcentral.com/a ... 017-0056-7
mkrupcale
Posts: 5
Joined: December 19th, 2016, 5:05 pm
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Re: Particle velocity and Stokes number assumptions

Post by mkrupcale »

alicec wrote:
June 17th, 2021, 2:59 pm
For inertial particles, the main effect is due to gravitational settling.
Yes, I understand that inertial particles have gravitational settling, but that is not really my question. My question has to do with where the single-phase flow Langevin model used by HYSPLIT breaks down.

To give you a better idea of what I mean, see e.g. Minier [1] sections I, II.A (e.g. Eqs. 5), and III. In particular, the single-phase flow Langevin model corresponds to the zero particle inertia limit, whereas the two-phase flow Langevin model should be consistent with the Equilibrium Eulerian approach (criteria P-6). Both of these models thus place limits on the Stokes number, particle response time, and particle diameter.
alicec wrote:
June 17th, 2021, 2:59 pm
Trajectory models for heavy particles in atmospheric turbulence: Comparison with observations
By: Wilson, JD
JOURNAL OF APPLIED METEOROLOGY Volume: ‏ 39 Issue: ‏ 11 Pages: ‏ 1894-1912 Published: ‏ NOV 2000
This suggests that they are able to use the single-phase ("first-order") Lagrangian stochastic model Eqs. 4-7a for particles sized up to 100 µm (for which the response time is much less than the Lagrangian time scale) when accounting for the gravitational settling velocity differential. Near the ground boundary, however, they say that the two-phase ("inertial particle") Langevin model Eq. 8 is required. They conclude though that given other uncertainties, it may be acceptable to use the single-phase model alone, but I am interested in understanding exactly how accurately the single-phase Langevin model used by HYSPLIT reflects the underlying physics.
alicec wrote:
June 17th, 2021, 3:27 pm
You may also be interested in this reference

Forecasting volcanic ash deposition using HYSPLIT
Tony Hurst & Cory Davis
Journal of Applied Volcanology volume 6, Article number: 5 (2017)

https://appliedvolc.biomedcentral.com/a ... 017-0056-7
Quickly looking through that reference, they limit their simulation to particles less than 100 µm, although their reasoning has more to do with the long residence times of such particles and the ability to calculate the terminal velocity by Stokes' law. So this too does not really answer my question.

[1] https://aip.scitation.org/doi/full/10.1063/1.4901315
alicec
Posts: 411
Joined: February 8th, 2016, 12:56 pm
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Re: Particle velocity and Stokes number assumptions

Post by alicec »

tvf_curves.png
HYSPLIT uses equations for passive tracers - non-inertial particles. It only uses Langevin equations for a single phase flow.
For inertial particles, a gravitational settling velocity is added but that is the only correction made.

I think what you are asking is when using equations for a two phase flow would produce significantly different results than using those for the single phase flow. I don't have an exact answer. Here is some background.

HYSPLIT is generally used to model particles less than 20 um. One exception is for volcanic eruptions when the goal is to obtain ash deposition patterns in the vicinity of the volcano as in the Davis/Hurst study (they were looking at particles larger than 100um with the Ganser equation for fall velocity). For aviation forecasting, the focus is still on smaller sizes. Consequently most of HYSPLIT development has focused on that size range.

HYSPLIT minimum time step is currently one minute. For particles much larger than 100 um (with density 2500 kg/m3), settling velocity is getting upwards of 30 meters in a minute and for 200 um particles it is upwards of 100 meters in a minute (see graph. note that velocity is in ft/min on the graph). So the jump in vertical position at each time step becomes fairly large for really large particles and they deposit very fast.

There are uncertainties involved in calculating the velocity autocorrelation time, ratio of vertical to horizontal turbulence, and the turbulent velocity variance. There are also relatively large uncertainties in NWP wind fields which are generally used to drive HYSPLIT. These will generally contribute more to errors in the results than using the single phase flow equations.

So for instance in the case of the Davis/Hurst study on the ash deposition, there are many reasons the results are not going to be quite right. The uncertainty in wind field and uncertainty in source term (initial spatial distribution of mass and size distribution of the particles) are the biggest contributors. The model time step with the large fall velocities is probably another limitation.
Turbulence parameterizations are probably second order corrections and use of the single phase flow equations probably more like 3rd order. The volcanology field is generally used to dealing with large uncertainties and finds the results useful despite them.

There are some efforts to adapt HYSPLIT for use at higher spatial and temporal resolutions. This involves things like reducing model time step and coupling HYPSLIT to LES model. For some of these future applications, if they involve heavy particles, it may be necessary to look at this question in more detail but this is beyond the scope of a simple forum post.
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