UNIVERSITY OF WISCONSIN - ENGINE RESEARCH CENTER As of June 5, 2012

Large Eddy Simulation of Diesel Sprays

Chi-Wei Tsang, Prof. Christopher Rutland Funding Sponsor – Caterpillar

Motivation OpenFOAM has great potential in internal combustion engines research

Objective Test and improve the turbulence and spray models in OpenFOAM

Dynamic structure model validation

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0 50 100 150 200 250 300

uiu

j/uτ

^2

y+

model <uu>

model <vv>

model <ww>

DNS <uu>

DNS <vv>

DNS <ww>

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<U

>/U

ba

r

y/delta

modelDNS

- Model shows good agreement with DNS results near the wall in principal direction (uu) - Away from the wall, the model performs well too

x

y

z

- Test case: channel flow - Domain size: 4 x 2 x 2 (m) - Total cells: 120000

Add spray source term for sub-grid

kinetic energy equation in OpenFOAM

𝜕𝝆 𝒌𝒔𝒈𝒔

𝜕𝒕+ 𝝏𝝆 < 𝒖𝒋 > 𝒌𝒔𝒈𝒔

𝝏𝒙𝒋=

𝝏

𝝏𝒙𝒋𝝁𝑻

𝝏𝒌𝒔𝒈𝒔

𝝏𝒙𝒋+ 𝐏 − 𝜺𝒔𝒈𝒔 + 𝑾 𝒔,𝒔𝒈𝒔

In OpenFOAM, none of the turbulence models have a spray source

term as circled. Without this source term spray penetration is

over–predicted in LES simulation [1], so it is necessary to

implement it in the code. The model for the source term is

𝑾 𝒔,𝒔𝒈𝒔 = − 𝑭𝒋,𝒅𝒅

𝒖𝒋𝒔𝒈𝒔 𝑽𝒄𝒆𝒍𝒍 =

= − 𝟑

𝟖

𝑪𝑫𝑽𝒄𝒆𝒍𝒍

𝒎𝒅𝝆 𝑽𝒓𝒆𝒍𝒓𝒅𝝆𝒍

< 𝒖𝒋 > +𝒖𝒑,𝒋′ − 𝒖𝒅,𝒋 𝟐 < 𝒖𝒋 > −𝟑 ≪ 𝒖𝒋 ≫+<<< 𝒖𝒋 >>>

𝒅

Sandia Engine Combustion Network (ECN)

spray–H non reacting case

fuel type N - heptane

injector type Single – hole, 100 μm diameter

ambient air 0 % O2

ambient pressure 4.33 MPa

ambient temperature 1000 K

initial fuel temperature 373 K

KH – RT breakup model constants

B0 0.61

B1 (KH time constant) 30

Cτ (RT time constant) 1

CRT 0.1

Cb (RT breakup length) 1.9

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liq

uid

pe

ne

tra

tio

n [

mm

]

Time [μs]

simulation

experiment

480 μs 640 μs 960 μs 1120 μs

- Liquid length is sensitive to B1, but vapor boundary is not - The upper row of plots below is vapor boundaries obtained from LES simulation; bottom row is Rayleigh scattering images from ECN - At early times, vapor penetrations are over–predicted, but later vapor shapes are well-captured

References [1] Bharadwaj, N., “Large Eddy Simulation Turbulence Modeling of Spray Flows”, Ph.D. Thesis, UW – Madison, 2010. [2] Amsden, A. A, Orourke, P. J., Butler, T. D., “KIVA – 2: A computer program for chemically reactive flows with sprays”, Los Alamos National Labs, 1989

Future work - Study fuel properties ,e.g., density, viscosity and surface tension

effects on spray breakup and evaporation models in OpenFOAM

𝑮 𝒖𝒑′ =

𝟏

𝝈 𝟐𝝅𝒆𝒙𝒑 −

𝒖𝒑′𝟐

𝟐𝝈𝟐

where Fj,d is the drag force on the parcels and is modeled assuming

a linear drag law [2]; Cd is the drop drag coefficient; is gas density; is droplet density; rd is droplet radius; Vrel is magnitude velocity between droplet and gas.

The droplet dispersion velocity is induced by turbulence. It is

chosen randomly from Gaussian distribution [2]

l

', jpu

where variance . k is sub – grid kinetic energy for LES

simulation and turbulent kinetic energy for RANS. Currently we

update the dispersion velocity in every time step to ensure that

there are sufficient turbulence effects on spray droplets.

3

22 k