Methods to optimise the grid resolution - FSMF.UK · 2018-06-02 · Methods to optimise the grid resolution London Fire Brigade's Headquarters, Union Street, UK Fire and Smoke Modelling

Methods to optimise

the grid resolution

London Fire Brigade's Headquarters, Union Street, UK

Fire and Smoke Modelling Forum, 3rd November 2017

1

Giordana Gai

Francesco Saverio Ciani

Sapienza University of Rome, Italy

[email protected]

Guidi&Partners s.r.l., Italy

[email protected]

Outline

- Motivation, objective GG

- Methods GG

- Case studies FSC

- Conclusions FSC



2

Giordana Gai

- MsC Structural Engineering

Sapienza University of Rome

- Ph.D. Candidate

Sapienza University of Rome

- Collaboration with the Italian Fire Brigades

(Corpo Nazionale dei Vigili del Fuoco)

- Fire Practitioner

- IFireSS 2017, Interflam 2016, IF CRASC ‘15



3

Motivation

FDS LES (Large Eddy Simulation)

Navier-Stokes equations Filtered equations (Δ(x) = h(x) )

…FDS equations depend on h(x)

We choose the grid size h(x) considering:

• Theoretical background (correctness)

• Pragmatism (feasibility, time)


Motivation

4

Filter Grid size

Objective of the presentation

Review the methods currently used

D*/δx

Y+

MTR

Check them with examples

Add other global quantities for convergence check


5

Objective

Methods

Grid resolution = f ( characteristic fire diameter )

𝑄 = total heat release rate of the fire

D*/δx = 4-16 (FDS Validation Guide)


6

(A priori)

𝐷∗ = 𝑄

ρ∞𝑐∞𝑇∞ 𝑔

2/5

Coarse Fine

Methods

Methods


NUREG 1824, 2007


7

(A priori)

Methods

Methods


Computational cost


8

D*/δx Resolution δx (cm) T (hours)

4 Coarse 134 Tcoarse

8 Medium 68 16·Tcoarse

16 Fine 34 16·(16·Tcoarse)

Premises Civil

Fire size (MW) 5

D* (m) 5.4

Factor 16 = 23 · 2

CFL

δx

(A priori)

Methods

Methods

Near wall grid resolution = f ( Y+ )

FDS. LES with near-wall modeling with wall functions

(Smooth walls, Werner-Wengle wall model)

(Rough walls, Log law)

Wall models needs grid resolution near the wall to fall within a

range of y+, non dimensional distance from the wall expressed in

viscous units.

General guidelines: Y+ in the range 30-1000


9

(A posteriori)

Methods

Methods

Grid resolution = f ( measure of turbulence resolution )

Ksgs is the modeled energy (subgrid)

KLES is the calculated energy (LES)

MTR < 0.2

(Pope, 2004)London Fire Brigade's Headquarters, Union Street, UK

10

(A posteriori)

0 (all solved)

1 (all modeled)

𝑀𝑇𝑅 =𝐾𝑠𝑔𝑠

𝐾𝑠𝑔𝑠 + 𝐾𝐿𝐸𝑆

Methods

Methods


1. Does «MTR<0.2» imply reliable results?

ASET predictions based on temperature, radiative heat flux gas,

visibility and FED

2. Are we able to guarantee «MTR<0.2» in the domain?

Near fire field, Far fire field

Ceiling, Human height


11

(A posteriori)

Methods

Methods


Pope, 2004:

As currently practised, LES is incomplete because the turbulence resolution length scale Δ(x) is specified subjectively in a flow-

dependent manner.

It can be made complete through adaptive LES.

The variation of Δ(x,t) is controlled (by grid adaption) so that a

measure M(x,t) of turbulence resolution (e.g. the fraction of the

turbulent kinetic energy in the resolved motions) is everywhere below a specified tolerance εm.


12

(A posteriori)

Methods

Case study. Fire compartment (20mx10mx3m)


50 cm

25 cm

10 cm

2 MW 4 MW

Heat release rate of the burnerG

rid

sp

acin

gsiz

e

13

Case study 1. Fire compartment


Grid size: 50 cm

Y+ max: 879

Grid size: 25 cm

Y+ max: 400

Grid size : 10 cm

Y+ max: 195

14



2 MW, z = 1 m

2 MW, z = 2 m

0.2

0.2

0.2

0.2

Y direction X direction

Y direction X direction

MTR

MTR


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 100 200 300 400 500 600


0

100

200

300

400

500

600

0 100 200 300 400 500 600

0

50

100

150

200

250

300

0 100 200 300 400 500 600

0.0

5.0

10.0

15.0

20.0

0 100 200 300 400 500 600

50 cm25 cm10 cm

2 MW, Temperature (z=1m) 4 MW, Temperature (z=1m)

2 MW, Rad.heat flux gas (z=1m) 4 MW, Rad.heat flux gas (z=1m)



17

Francesco Saverio Ciani

- Fire Practitioner at Guidi & Partners s.r.l.

- Temporary Research Fellow

Alma Mater Studiorum, University of Bologna

- M.Eng Building Engineering

Alma Mater Studiorum, University of Bologna

- IFireSS 2017



Case Studies

Pearson correlation coefficient (r)

-1 10-0.25-0.75 0.750.25

strong strongintermediate intermediateweak weak

no relation

Directindirect


Case Studies

0

100

200

300

400

500

600

700

800

900

1000

0 100 200 300 400 500 600 700 800 900 1000

Tem

pe

ratu

re _

me

sh 2

5 c

m [

°C]

Temperature _ mesh 50 cm [°C]

4 MW _ z = 2m

y_6m__z_2m x_11.5m__z_2m y_8m__z_2m x_11.5m__z_2m

r Pearsoncoefficient

r2 Coefficient of determination

Factory Building Case Study: Description


A simplified version of areal factory building

Factory Building Case Study



MAIN BURNER CHARACTERISTICS

Italian Fire Prevention Code

(2015)

• RHRMAX= 50 MW• Fire Growth Rate= 75 s

(ultra-fast)• Soot Yield= 0.18 kg/kg

The Burner



Three Grid resolution were tested

0

50

100

150

100 cm 50 cm 25 cm

PC hours

ho

urs

The devices were placed in60 different positions in themodel.

Factory Building Case Study : y+ @ boundaries


Cell dim: 50 cm

Y+max: 1300

Cell dim: 25 cm

Y+max: 750

Cell dim: 100 cm

Y+max: 3000

Y+ @ boundaries

Factory Building Case Study : MTR


Leve

l : 1

,5 m

Leve

l : 4

,5 m

Leve

l : 7

,5 m

Leve

l : 1

,5 m

Leve

l : 4

,5 m



Leve

l : 7

,5 m



Leve

l : 1

,5 m

Leve

l : 4

,5 m

Leve

l : 7

,5 m

Dev

cso

n t

he

Y p

lan

e



Leve

l : 1

,5 m

Leve

l : 4

,5 m

Leve

l : 7

,5 m

Dev

cso

n t

he

X p

lan

e



Leve

l : 1

,5 m

Leve

l : 4

,5 m

Leve

l : 7

,5 m

Dev

cso

n t

he

X p

lan

e



Leve

l : 1

,5 m

Leve

l : 4

,5 m

Leve

l : 7

,5 m

Far

Fiel

d

0.2

0.2

0.2

Grid Sensitivity AnalysisCase Studies Results: Grid Sensitivity Analysis


240 different devices were placed inthe model:• 60 Temperature devcs;• 60 Rad. Heat Flux Gas devcs;• 60 Visibility devcs;• 60 FED devcs.

0

0.2

0.4

0.6

0 200 400 600 800

Radiative Heat Flux Gas100 cmRad_X99.5_Y1_Z4.5

50 cmRad_X99.25_Y1_Z4.75

25 cmRad_X99.125_Y1_Z4.625

We need to filter thisdata!!!!

240 Gridsensitivity

assessments

The FilterCase Studies Results: The filter


100 cm 50 cm 25 cm

Find the Pearson’scoefficient

Find the Pearson’scoefficient

50 cm

Find the meanerror

Find the meanerror

100 cm 25 cm

PC1<PC2

Yes

Convergent

NoPC2>0.75

Yes

NotConvergent

NoEM1>EM2

(EM1) (EM2)(PC1) (PC2)

NoNot

Convergent

Yes

Convergent (EM1)(EM1)

Results : Percentage of ConvergenceCase Studies Results: Grid Sensitivity Analysis


88%

88%

72%

82%

0% 20% 40% 60% 80% 100%

FED

Visibility

Radiative Heat Flux Gas

Temperature

FED Visibility Radiative Heat Flux Gas

Temperature

Conclusions -Factory Building Case Study-

• The Y+ assessment points out that the 100 cm grid spacing

should be avoided in the near-wall field

• The MTR assessment points out that the grid should be

refined in the upper layer volume and in the fire-plume zone

• The pearson correlation coefficient could be a good

parameter in order to assess if the solutions don’t have

appreciable differences

• The grid Sensitivity study of the Factory Building model

shows that a 50 cm grid spacing could be used.

Conclusions


Future Developments

• The «convergence filter» should be improved in order to

evaluate if the grid spacing is on the safe side considering

the objective of our PBD approach

• Considerations on the computational cost might be added

to the filter

• This filter should be tested in a lot of different case studies

in order to find if there are limits for the use of the

correlation Pearson coefficents

Conclusions


Documents

Methods to optimise the grid resolution - FSMF.UK · 2018-06-02 · Methods to optimise the grid resolution London Fire Brigade's Headquarters, Union Street, UK Fire and Smoke Modelling