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 x 1 Equillibrium at x 0 Compressibility modulus k~10 10 kg/m*s 2 typical maximum x 1 /x o = 1.2 corresponds to ΔV/V= 1/3 P theory = 3x x10 5 atm Reality: <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, t m If time of applied force that creates movement is less than t m, no plastic deformation will occur t >> t m is fluidity –t m 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: 373K L~2x10 6 m 2 /s 2 with = 20K shows = 1atm

Homogeneous Nucleation Surface tension, S, is intermolecular force that holds molecules together Pressure depression: tension Random thermal motion creates a void at P=P v –Propagation of the void Vapor bubbles form: Inside a bubble: if only vapor, P B =P V P<P B to maintain equilibrium R increases as P drops, eventual burst at R c

Homogeneous Nucleation Three relations critical to homogeneous nucleation: –1. R c & critical tension –2. Work on the bubble volume: –3. Gibbs number: probability of nucleation κ = Boltzmann Constant

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 -C p reaches cavitation number, fluid will vaporize Incipient cavitation number in a flow occurs at the lowest C p C p = f (Re) in viscous fluids: σ i = f (Re)

Experimental Effects Phenomenon that affect inception cavitation number: –Contamination will increase σ i –Residence time can reduce σ i –Existence of a tensile strength can reduce σ i –Steady viscous effects can cause σ i to be a function of Re –Turbulence effects can increase σ i

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