cavitation-analysis

name	cavitation-analysis
description	Cavitation analysis — inception (σ), NPSH, bubble dynamics (Rayleigh-Plesset), erosion mechanisms, pump cavitation, hydrofoil cavitation, supercavitation, mitigation.
metadata	{"priority":7,"promptSignals":{"phrases":["cavitation","NPSH","cavitation erosion","pump cavitation","cavitation inception","bubble collapse"],"minScore":3}}

Cavitation Analysis — Complete Skill

Cavitation Fundamentals

Cavitation: formation of vapor cavities in liquid when local pressure drops below vapor pressure P_v

Inception condition: P_local ≤ P_v(T) [vapor pressure depends on temperature]

Water vapor pressure: T = 20°C: P_v = 2.34 kPa; T = 40°C: P_v = 7.38 kPa; T = 60°C: P_v = 19.9 kPa; T = 100°C: P_v = 101.3 kPa

Cavitation Number (σ)

Dimensionless measure of cavitation tendency: σ = (P_ref - P_v) / (½ρV²)

P_ref = reference pressure [Pa]; V = reference velocity [m/s] σ_i = cavitation inception number (flow type specific; from experiments or correlation)

Cavitation occurs when: σ ≤ σ_i Safe design: σ >> σ_i → margin from cavitation

NPSH (Pump Cavitation)

Net Positive Suction Head: NPSH_A (available) = (P_suction - P_v) / (ρg) + V_suction² / (2g)

P_suction from suction pressure, pipe losses, elevation: NPSH_A = (P_atm - P_v) / (ρg) - Z_s - h_L,suction

Z_s = suction lift [m]; h_L = suction pipe losses [m]

NPSH_R (required): from pump manufacturer; increases with Q Design requirement: NPSH_A > NPSH_R + 0.5 m safety margin (minimum 10% margin: NPSH_A > 1.1 × NPSH_R)

Sigma (σ_s) for pumps: σ_s = NPSH_R / H_total (head generated by pump) S_s = N √Q / (NPSH_R)^(3/4) [suction specific speed; S_s < 9000 for good NPSH margin]

Rayleigh-Plesset Equation (Bubble Dynamics)

ρ_L [R R̈ + (3/2) Ṙ²] = (P_B - P_∞) - 4μ Ṙ/R - 2σ/R

R = bubble radius; P_B = pressure inside bubble; P_∞ = far-field pressure σ = surface tension; μ = dynamic viscosity

Collapse velocity: Ṙ_collapse = -√(2(P_∞ - P_v) / (3ρ)) [Rayleigh collapse] Collapse time: t_c = 0.915 R_max √(ρ / (P_∞ - P_v))

Collapse pressure: P_collapse >> P_∞ (shock wave emission; up to GPa locally) Temperature: T_max inside collapsing bubble → 10,000+ K (sonoluminescence) Shock wave + microjet → damage to nearby surfaces

Cavitation Types

Sheet (Attached) Cavitation

Fixed sheet on suction side of blade/foil; σ slightly below σ_i Relatively benign if stable; erosion at reattachment

Cloud Cavitation

Periodic shedding of cavitation cloud from trailing edge of sheet Violent; high erosion potential; cloud collapse creates massive shock

Vortex Cavitation

In tip vortex or hub vortex; elongated cavities; noise Propeller tip vortex: σ_v = f(lift coefficient, tip geometry)

Hydraulic Shock (Water Hammer + Cavitation)

Valve closure → pressure wave → vapor pockets → cavitation collapse

Erosion Mechanism

Collapse of bubbles near surface → high-velocity microjet (100–500 m/s) + shockwave Repeated impact → fatigue of surface → pitting → material loss Most vulnerable materials: soft metals (Al, Cu); less vulnerable: SS, Stellite, ceramics

Erosion rate estimation: Rate ∝ (P_collapse - S_y)^2 × N_bubble_collapse Quantified by ASTM G32 (vibratory cavitation) and G134 (jet cavitation)

Hydrofoil Cavitation

Lift coefficient at inception: σ_i ≈ -C_p,min = -(P_min - P_∞)/(½ρV²) C_p,min from potential flow + viscous correction

For symmetric airfoil at angle α: σ_i ≈ 0.06 × C_L (approximation)

Cavitation breakdown: Below σ_breakdown → lift drops sharply (cavity extends past trailing edge)

Supercavitation

At very low σ (σ < 0.1): large stable cavity envelopes entire body Drag reduction (cavity is gas; skin friction negligible) Applications: supercavitating torpedoes (VA-111 Shkval: 200 knots), high-speed propellers

Mitigation Strategies

Pump: Increase NPSH_A: lower Z_s, larger suction pipe, cooler fluid Decrease NPSH_R: lower N, use inducer (pre-cavitating element upstream), larger impeller eye Double-suction impeller: halves NPSH_R

Hydrofoil/Propeller: Modify angle of attack; adjust P/D (pitch-diameter); increase σ (increase P_∞) Rounded leading edge vs. sharp: lower C_p,min, better cavitation resistance

Material selection for erosion resistance: CA-6NM stainless steel: good cavitation resistance for pump impellers Stellite 6 (Co-Cr-W): excellent resistance; hard coating 316SS: moderate; better than carbon steel; poor vs. Stellite

Output

Provide: σ (operating), σ_i (inception), NPSH_A vs. NPSH_R [m], suction specific speed S_s, P_collapse [MPa] from Rayleigh, erosion risk rating (low/moderate/high), material recommendation, mitigation options (with NPSH improvement estimate).