The analysis of gasoline injector flow using LES-VOF

Zoran Pavlović1

Wilfried Edelbauer2

Branislav Basara2

AVL List GmbH (Headquarters)

Public

The analysis of gasoline injector flow using

LES-VOF approach: Spray G case Large-Eddy Simulation for Internal Combustion Engines Rueil-Malmaison, France, 11-12 December 2018

1Advanced Simulation Technologies, AVL-AST, Maribor, Slovenia2Advanced Simulation Technologies, AVL List GmbH, Graz, Austria

contact: [email protected]

Zoran Pavlović, Wilfried Edelbauer, Branislav Basara | | 08 December 2018 | 2Public

CONTENT

▪ Introduction

▪ Mathematical model

▪ LES-CSM

▪ Multiphase VOF+EE (cavitation)

▪ Simulation setup & Results

▪ Spray G (GDI)

▪ Conclusions / Further steps


INTRODUCTION

▪ (Fuel) Jet primary breakup –

important/decisive role in overall

spray development (consecutively,

mixture preparation, combustion,

emissions…).

▪ But, still not fully understood.

▪ Diagrams based on non-

dimensional numbers can give just

rough idea about breakup regime.

Main contributing effects:▪ Turbulence▪ Cavitation▪ Aerodynamic forces▪ Capillary forces

Ohnesorge Hobbie & Eggers

𝑍 = 𝑂ℎ𝜇𝑙𝜇𝑔

𝑊𝑒𝑔


INTRODUCTION

MEASUREMNTS – probed region optically

dense; sophisticated measurement techniques

SIMULATIONS – heavy requirements of CPU

power (high spatial/time resolution)

Wu, 1992 Paciaroni, 2005

Reddemann, 2014

Menard, 2007

Herrmann, 2008 Shinjo, 2010

AVL, 2014

Duke, 2017


MATHEMATICAL MODEL - LESCSM

Large Eddy Simulation (LES) Coherent Structure Model (CSM):

𝜕ത𝑢𝑖𝜕𝑡

+𝜕(ത𝑢𝑖 ത𝑢𝑗)

𝜕𝑥𝑗= −

1

𝜌

𝜕 ҧ𝑝

𝜕𝑥𝑖+

𝜕

𝜕𝑥𝑗𝜈𝜕ത𝑢𝑖𝜕𝑥𝑗

− 𝜏𝑖𝑗

𝜏𝑖𝑗 −𝛿𝑖𝑗

3𝜏𝑘𝑘 = −2𝜈𝑠𝑔𝑠𝑆𝑖𝑗 𝜈𝑠𝑔𝑠 = 𝐶𝐶𝑆𝑀Δ

2 𝑆 𝑆 = 2𝑆𝑖𝑗𝑆𝑖𝑗

coherent structure function (plays the role of wall damping)

energy-decay suppression function(accounts for the suppression of the dissipation with the increase of an angular velocity)

𝐶𝐶𝑆𝑀 = 𝐶1 𝐹𝐶𝑆3/2𝐹Ω

Cs values – Pipe flow▪ no need for separate wall damping function,

▪ can be also applied to laminar flow,

▪ no need to solve additional transport equations,

▪ robust

Ref: Kobayashi, Physics of Fluids, 2005


MATHEMATICAL MODEL – VOL + EE (cavitation)

Volume of Fluid (VOF) used to resolve/track liquid-air interface.

𝜕𝛼𝑘𝜕𝑡

+𝜕

𝜕𝑥𝑗𝛼𝑘𝑈𝑘,𝑗 = 𝑆𝛼 ,

𝜌𝑚 =𝛼𝑙𝜌𝑙 + 𝛼𝑎𝜌𝑎𝛼𝑙 + 𝛼𝑎

Compressive Interface Capturing Scheme for Arbitrary Meshes (CISCSM) combines two differencing schemes in order to achieve bounded, monotonic solution with sharp interface:

𝛼𝑓 = 𝛾𝑓 𝛼𝑓𝐶𝐵𝐶 + 1 − 𝛾𝑓 𝛼𝑓𝑈𝑄 , 𝛾𝑓 = min 1, cos𝜃𝑓𝐶𝜃

.

𝐶𝜃 ቊ= 0≫ 1

- compressive and gradient-sharpening differencing scheme (HYPER-C)

- more diffusive Ultimate Quickest scheme

Surface tension represented by Continuum Surface Force method (Brackbill et al.):

Ԧ𝐹 = න

𝑉

𝜎𝜅𝛻𝛼 𝑑𝑉 = 𝜎𝜅𝑃(𝛻𝛼)𝑃𝑉𝑃

a - volume fraction of tracked phase𝜇𝑚 =𝛼𝑙𝜇𝑙 + 𝛼𝑎𝜇𝑎𝛼𝑙 + 𝛼𝑎

𝑆𝛼 ቊ= 0= − ΤΓ𝑙𝑣 𝜌𝑘

- for air

- for liquid (due to cavitation)

𝜅𝑃 = − 𝛻 ∙ 𝑛 = − 𝛻 ∙𝛻𝛼

𝛻𝛼𝑃



Continuity equation (Euler-Euler):

𝜕𝛼𝑘𝜌𝑘𝜕𝑡

+𝜕

𝜕𝑥𝑗𝛼𝑘𝜌𝑘𝑈𝑘,𝑗 =

𝑙=1,𝑙≠𝑘

𝑛𝑝ℎ

𝛤𝑘𝑙

Momentum conservation (Euler-Euler):

𝜕𝛼𝑘𝜌𝑘𝑈𝑘,𝑖𝜕𝑡

+𝜕

𝜕𝑥𝑗𝛼𝑘𝜌𝑘𝑈𝑘,𝑗𝑈𝑘,𝑖 = −𝛼𝑘

𝜕𝑝

𝜕𝑥𝑖+

𝜕

𝜕𝑥𝑗𝛼𝑘 𝜏𝑘,𝑖𝑗 + 𝜏𝑘,𝑖𝑗

𝑡 +

𝑙=1,𝑙≠𝑘

𝑛𝑝ℎ

M𝑘𝑙,𝑖 +

𝑙=1,𝑙≠𝑘

𝑛𝑝ℎ

𝑈𝑘𝑙,𝑖Γ𝑘𝑙

Mass interfacial exchange from linearized Rayleigh-Plesset equation:

Γ𝑙𝑣,𝑐𝑎𝑣 = 𝐶𝑐𝑎𝑣𝜌𝑑𝑁′′′ 𝛼𝑑 4𝜋𝑅2

2 𝑝∞−𝑝𝑠𝑎𝑡

3𝜌𝑐Γ𝑣𝑙,𝑐𝑜𝑛𝑑 = −

1

𝐶𝑐𝑜𝑛𝑑𝜌𝑑𝑁

′′′ 𝛼𝑑 4𝜋𝑅22 𝑝∞−𝑝𝑠𝑎𝑡

3𝜌𝑐

Momentum interfacial exchange:

𝑀𝑘𝑙,𝑖 = 𝐶𝐷1

8𝜌𝑘𝐴

′′′ 𝐔𝑟 𝑈𝑟,𝑖 = −𝑀𝑙𝑘,𝑖

▪ Cavitation model based on simplified Rayleigh-Plesset equation applied on vapor cloud.

▪ Interfacial momentum exchange due to drag force

Mass transfer Momentum exchange



Validated on simple configurations*:

*W. Edelbauer, Computers and Fluids 144 (2017) 19–33*W. Edelbauer et al., Int. J. Comp. Mech. And Exp. Meas., Vol. 6, No. 2, 2018


MATHEMATICAL MODEL – Evaluation of ligaments/droplets

Determine principal axes of inertia and measures the lengths 𝑙𝑥, 𝑙𝑦, and 𝑙𝑧

▪ Evaluation can be performed at defined times/frequency.

▪ Can be applied in the whole domain or only in defined selection (e.g. chamber).

▪ Ligaments/droplets touching the boundaries are additionally marked.


SIMULATION SETUP

Number of holes 8

Spray Shape circular

Bend Angle 0°

L/D ratio 1.4

Hole shape straight

Manufacturing EDM

Flow rate 15 cc/s @10 MPa

Fuel injector Delphi solenoid-activated

Nozzle type Valve-covered orifice (VCO)

Nozzle shape Step hole

Orifice diameter0.165 mm specification(0.170 mm measured)

Orifice length 0.16-0.18 mm

Step diameter 0.388 mm specification

Orifice drill angle 37° relative to nozzle axis

Full outer spray angle 80°

DELPHI GDI 8-HOLE INJECTOR – ECN Network (Spray G)


SIMULATION SETUP

DELPHI GDI 8-HOLE INJECTOR – ECN Network (Spray G)

Operation condition as in Duke et al. (Experimental Thermal and Fluid Science 88 (2017) 608–621):

Real injector geometry deviates from nominal (CAD) dimensions, however, for the present simulation those deviations are not taken into account, i.e. idealized geometry is simulated.


SIMULATION SETUP – Computational mesh

AVL FIRE®

Two variants investigated:

▪ Coarse (11 million cells)

▪ Fine (95 million cells)

Time-step automatically adjusted(CFL < 0.5)

Topology at hole outlet

Non-moving mesh/needle; variable pressure imposed at outlet (mimic needle movement):


SIMULATION RESULTS

▪ 𝑚𝑠𝑢𝑚 = 10.2𝑚𝑔

▪ Discharge coefficient 0.45-0.46

(measured: 0.48±0.02)

▪ Hole-to-hole distribution quite uniform, unlike in measurements (but, real/ideal geometry)


SIMULATION RESULTS

@0.44ms

vapor (cavitation)

vapor (cavitation)

Iso-surface of Q invariant (+ iso-surface of vapor volume fraction – bottom right)

95M

11M 11M


SIMULATION RESULTS

Iso-surface of liquid volume fraction (𝛼 = 0.5); Mid-cut – liquid volume fraction

Complex flow structure leads to strong and fast breakup.

Cavitation facilitates breakup process. Cavitation induced at sharp hole inlet, but also string cavitation (due to vortices generated in the sac and hole inlet section). Real life geometry might result in less pronounced “edge cavitation”.


SIMULATION RESULTSLiquid, vapor, air volume fraction; velocity

@0.21ms

Vapor mass negligibly small, but can fill large portion of hole.More pronounced on fine mesh.


SIMULATION RESULTS

Rapid breakup/disintegration – in line with measurement observations

95M

11M


SIMULATION RESULTS

Instabilities – Kelvin-Helmholtz?

WAVE (JET): SHEET:

Linear stability analysis

𝜔 = −2𝜈𝑙𝑘2 + 4𝜈𝑙

2𝑘4 + 𝑄𝑈2𝑘2 −𝜎𝑘3

𝜌𝑙

Λ

𝑟= 9.02

1 + 0.45𝑍0.5 1 + 0.4𝑇0.4

1 + 0.87𝑊𝑒𝑔1.67 0.6

Ω𝜌𝑙𝑟

3

𝜎

0.5

=0.34 + 0.38𝑊𝑒𝑔

1.5

1 + 𝑍 1 + 1.4𝑇0.6


SIMULATION RESULTS

Ligament analysis evaluation (<2mm from hole outlet)

Number of ligaments ≈ 340000


SIMULATION RESULTS

Starting velocity and position taken from VOF.

Aerodynamic & TAB breakup model.

Cell size: 0.25mm


SIMULATION RESULTS

Evaluated 15mm from the nozzle:SMD [micorns] = 8.80

D10 [micorns] = 2.33

DV50 [micorns] = 11.48

DV90 [micorns] = 20.36


CONCLUSIONS & FURTHER STEPS

▪ LES VOF simulation can offer additional insight into complex jet breakup process of high-pressure gasoline injector.

▪ Cavitation effect can be included, using coupled Eulerian-Eulerian and VOF approach. Additional evaluation required.

▪ Obtained results can qualitatively (also quantitatively) reproduce experimental observation.

▪ Results from LES-VOF simulation could be used as a starting point for more accurate Lagrangian spray simulations.

▪ Repeat simulation on even finer meshes (maybe focus on smaller number of holes.)

▪ Evaluate impact of certain numerical aspects of the models.

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The analysis of gasoline injector flow using LES-VOF