University of Notre Dame Particle Dynamics Laboratory

Michael P. Davis and Patrick F. Dunn

Department of Aerospace and Mechanical Engineering

Particle Dynamics Laboratory

B032 Hessert Laboratory

University of Notre Dame

Notre Dame, IN 46556 USA

mdavis7@nd.edu

University of Notre DameAME - Graduate Student Conference

October 19, 2006

SPONSOR: Honeywell International, Incorporated

Jet Fuel Cavitation in a Converging-Diverging Nozzle

University of Notre Dame Particle Dynamics Laboratory

Brennan (1995).

Cavitation - “the process of rupturing a liquid by decrease in pressure at roughly constant liquid temperature”

FLUENT simulation

Cavitation Fundamentals

University of Notre Dame Particle Dynamics Laboratory

Motivation - Honeywell Fuel Pump• Honeywell product line includes valves, flow controllers, and fuel pumps

• Common to all devices is high flow rates through very small orifices, resulting in cavitation

• Presence of bubbles causes damage to components, vibrations, and a loss of pump efficiency

pitting damage caused by cavitation

University of Notre Dame Particle Dynamics Laboratory

sphericalbubbles slug-like

gas voidsbubbly shock

microbubble nucleioriginating from microparticles or walls

liquid

solid

gas pockets

xflow

Void Fraction = f(x)Pressure = f(x)

Void Fraction = Gas Volume/Total Volume

Problem Description

University of Notre Dame Particle Dynamics Laboratory

€

R˙ ̇ R +3

2˙ R 2 =

1

ρPv + PGo

Ro

R

⎛

⎝ ⎜

⎞

⎠ ⎟3γ

− P∞(t) −2σ

R− 4μ

˙ R

R

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

bubble interface,surface tension

far field,

bubble inertia bubble contents far fieldpressurein liquid

surfacetension

viscous effects

€

P∞(t)

ρ

μ- fluid density

- fluid viscosity

Vapor+

GasR(t)

Bubble Dynamics - Raleigh Plesset Equation

University of Notre Dame Particle Dynamics Laboratory

Raleigh-Plesset in a C-D Nozzle

€

∂∂t

1−α( )A[ ] +∂

∂x1−α( )uA[ ] = 0

∂u

∂t+ u

∂u

∂x= −

1

2 1−α( )

∂Cp

∂x

RD2R

Dt 2+

3

2

DR

Dt

⎛

⎝ ⎜

⎞

⎠ ⎟2

= −Ca

21− R−3γ( ) +

4

Re

1

R

DR

Dt+

2

WeR−1 − R−3γ

( ) +Cp

2

⎛

⎝ ⎜

⎞

⎠ ⎟

(continuity)

(momentum)

(bubble dynamics)

€

α(x) =4 /3πηR3(x)

1+ 4 /3πηR3(x)

Ca =P∞ − Pv

1/2ρU∞2

We =ρU∞

2Ro

σ

Re =ρU∞Ro

μ

Cp =P(x) − Pv

1/2ρU∞2

(void fraction)

(viscosity)

(pressure forcing)

(surface tension)

(liquid tension)

University of Notre Dame Particle Dynamics Laboratory

Transducers measure P

Experimental Apparatus

University of Notre Dame Particle Dynamics Laboratory

University of Notre Dame Particle Dynamics Laboratory

flow

JP-8

H2O

University of Notre Dame Particle Dynamics Laboratory

Void Fraction by Laser Light Scattering

• Initialize counter and increment each time voltage drops below threshold• Compute running average as a function of time and look for convergence• Need a way to calibrate output signal

Flow direction

Vout = f(α

Runningaverage

Test section

CavitationBubbles

Photo-diodearray

HeNelaser

University of Notre Dame Particle Dynamics Laboratory

flow

University of Notre Dame Particle Dynamics Laboratory

flow

University of Notre Dame Particle Dynamics Laboratory

flow

JP-8

H2O

University of Notre Dame Particle Dynamics Laboratory

• The experimentally determined JP-8 mass flux under choked conditions can be used to identify the maximum volumetric flow rates achievable for a given minimum flow cross-sectional area assuming similar, fully choked flow conditions.

Maximum Flow Rate Estimate

University of Notre Dame Particle Dynamics Laboratory

• Reliably predict cavitation in internal flows involving hydrocarbon fuels.

• Obtain experimental void fraction and pressure profiles for model comparison.

• Parallel experimental and computational approach is focused on model development.

• Development of passive and active cavitation control strategies.

Goals of Research - Summary