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Cavitation and Bubble Dynamics

Ch.1 Cavitation and Boiling

Cavitation and Bubble Dynamics

• Solids v. Liquids

• Tensile Strength of fluids

• Boiling v. Cavitation

• Homogeneous Nucleation

• Heterogeneous Nucleation

• Cavitation Inception

• Experimental effects

Solids v. Liquids

• Similar densities for most substances• Similar density behaviors• Similar specific heat, behavior• Solids do have fluidity: creep• Fluidity in liquids dominates elasticity• Gasses show difference in all these categories

Tensile Strength of Fluids

• Molecular theory:

Maximum at x1 Equillibrium at x0

Compressibility modulus k~1010 kg/m*s2

typical maximum x1/xo= 1.2 corresponds to ΔV/V= 1/3

Ptheory= 3x104 - 3x105 atmReality: <200 atm in experiments

• Solids can handle ~100 times less than theory– Due to imperfections (cracks, fractures)

Tensile Strength of Fluids

• Characteristic time for a molecule to move positions in a substance, tm

• If time of applied force that creates movement is less than tm, no plastic deformation will occur

• t >> tm is fluidity– tm large in solids, small in liquids

• Consider movement of a void or “hole” in a substance

Boiling v. Cavitation

• Boiling: vaporization at constant pressure – Superheat of liquid:

• Cavitation: vaporization at constant temperature– Tensile strength of liquid:

• Easy to change bulk pressure, difficult to change bulk temperature

Boiling v. Cavitation

• Related by Clausius-Clapeyron:

L=latent heat of vaporization

Ex: Water @ 373K L~2x106m2/s2 with = 20K shows = 1atm

1 1saturation v L

dp L

dT T

c cv

TT p

L

L v

Homogeneous Nucleation

• Surface tension, S, is intermolecular force that holds molecules together

• Pressure depression: tension• Random thermal motion creates a void at P=Pv

– Propagation of the void

• Vapor bubbles form:

• Inside a bubble: if only vapor, PB =PV

• P<PB to maintain equilibrium• R increases as P drops, eventual burst at Rc

2B

Sp p

R

Homogeneous Nucleation

• Three relations critical to homogeneous nucleation:– 1. Rc & critical tension

– 2. Work on the bubble volume:

– 3. Gibbs number: probability of nucleation

κ = Boltzmann Constant

2c

c

Sp

R

24

3c cW R S

cB

WG

T

Heterogeneous Nucleation

• Void or defect acts as a site of seeding for vapor growth• Contaminants or imperfections in solid boundary• Void of radius R~10-5 m sufficient for growth with a

depression of only 1/10 atm in water• Quantifying the nature and number of impurities is difficult• Differentiating between solids and dissolved gasses hard• Boiling starts at hottest part of fluid, cavitation can start

anywhere in the liquid

Cavitation Inception

• Coefficient of pressure at a point in free flow:

• Cavitation number of the flow:

• When -Cp reaches cavitation number, fluid will vaporize• Incipient cavitation number in a flow occurs at the lowest Cp

• Cp = f(Re) in viscous fluids: σi = f(Re)

2

( )( )

12

iP i

L

p x pC x

U

2

( )12

v

L

p p T

U

mini PC

Experimental Effects

• Phenomenon that affect inception cavitation number:– Contamination will increase σi

– Residence time can reduce σi

– Existence of a tensile strength can reduce σi

– Steady viscous effects can cause σi to be a function of Re

– Turbulence effects can increase σi

Experimental Effects

Scaling of experiments can become difficult

• Residence time for bubble growth• Reynolds Number• Ratio of nuclei size to chord length• Surface roughness• Nuclei number and character across different liquids