Simulation of Cryogenics Cavitation Sean Kelly and Corin Segal University of Florida Orlando January 2010

Overview Experimental Setup Theoretical Description Results High and low cavitation numbers Discussion Comparisons to water Comparison to CFD

Motivation Cavitation is known to cause large volume changes and high pressures that can damage equipment Large performance losses in rocket engine turbopumps

Test Facility NACA 0015 hydrofoil High speed camera Chord Length: 50.8 mm Span: 100 mm Angle of Attack: ± 10 ° Nine Pressure Transducers Seven on suction side Two on pressure side High speed camera 500 images per second 10μs exposure time Closed loop watertunnel Filled with a degased working fluid Operation at 5-10m/s and 25-70° C Pmax = 5 atm Optical and laser sheet access

Working Fluid Fluoroketone Exhibits a large ΔT* at reasonable temperatures When heated ΔT* comparable to cryogenics High density ratio Liquid at STP Boiling Point 48 °C at 1 atm Primarily a function of density ratio Water shows a low T* even at high temperatures

The Cavitation Process Turbopumps High liquid-vapor density ratio

Critical Cavitation Number σi Ratio of phase change pressure drop to kinetic energy per unit volume Describes the potential of the fluid to cavitate Lower cavitation number indicates more intense cavitation Critical Cavitation Number σi Indicates cavitation is present on the hydrofoil –Cp is equal to vapor pressure Bubbles begin to form on the line of peak –Cp

Additional Parameters of Interest Strouhal Number f = frequency of oscillation of formation and collapse of bubbles Reynolds Number 780,000 - 2,110,000 Flow is fully developed, turbulent σ/2α Used to normalize cavitation number against α Mode I transition: Water: 8.5 Fluoroketone: 17 Mode II transition: Water: 7.7 Fluoroketone: 14

Mode I: Incipient Cavitation Cavitation Modes Mode I: Incipient Cavitation σ = σi Mode II: Cloud Cavitation σ < σi Mode III: Supercavitation σ << σi Images from Arndt, 1981

Test Conditions II I Correlation of Strouhal Number versus σ/2α in previous studies Indication of the values at which different cavitation modes occur

Experimental Conditions Angle of attack 0, 2, 5, 7.5 ° Tests showing effect of independent temperature and velocity changes Tests at the same cavitation number

0 AOA U∞ = 5.9 m/s

0 AOA U∞ = 5.9 m/s, T = 50 C

High Cavitation Number σ =2.11, U∞ = 5.9 m/s T = 25°C, α = 2° Top View Side View Incipient (Mode I) cavitation at a small angle of attack Bubbles form at line of peak Cp and propagate downstream No cavity is formed Streaks of bubbles are thin and close to body

High Cavitation Number Cp along the chord length σ = 1.5 and 2.8 are incipient cavitation Upward trend indicates no cavity σ = 1 is cloud cavitation Note nose of hydrofoil sees lower pressure due to vapor cavity Note the change in curve between σ = 1 and 1.5

Low Cavitation Number σ = 0.7, U∞ = 7.16 m/s T = 40°C, α = 7.5° Top View Side View Blue vertical lines indicate leading and trailing egdes Supercavitation shows a cavity over the entire span and chord Separation of bubble from main cavity 3-D and turbulent nature Some very fine structures and bubbles

Low Cavitation Number Cp along chord length σ = 0.7 and 0 both supercavitation Nose of profile has been engulfed in the cavity Cp at x/c = o nearly zero Oscillation of cloud front farther down chord cause average Cp drop below Pv

Comparison of all Cavitation Numbers Comparison of Cp for all modes of cavitation Cloud cavitation tends to stay above –Cp = 1 Cavity is compressed by freestream and collapses before covering entire hydrofoil Higher cavitation numbers can have –Cp < 1 Cp at nose can indicate cavitation mode

Cavitation Video σ =1.00, U∞ = 5.9 m/s, T=40 °C, α =7.5 Top View Cloud cavitation Bubbles leaving cloud and collapsing downstream Cloud surges from line of peak –Cp to ~15% of chord

Still image series 1 2 3 4 5 6 Frames 1-5 show 1 cycle of bubble growth and separation from the main cloud, over 0.01 s Series of images at σ = 1, T=40 °C Δt = 0.002 s

Comparison to Computation CFD code showing pressure Shows similar behavior as experimental data Bubble growth, separation, and collapse Re-entrant jet Cavity covers entire hydrofoil and is periodic Second cloud forms at trailing edge Even in supercavitation, parts of the hydrofoil surface see pressures higher than Pv Including the two-phase cavity and more accurate prediction of thermal effect are necessary σ=0.33, U∞ =10.43 m/s, T= 40 °C, α= 7.5° Courtesy University of Michigan Aerospace Engineering CFD Group

Comparisons to tests in water Top View Top View Fluoroketone at σ =2.11, T = 25 °C Water at σ =1.25, T = 25 ° C Comparison of cavitation in water to that in fluoroketone Notice incipient cavitation at much higher σ in fluoroketone Bubble size in water is much larger Less noticeable streaks in water Cavity in cloud and supercavitation in water has discreet phase boundaries, in fluoroketone it is a 2-phase, frothy mixture

Conclusions Different modes of cavitation and how they are identified Parameters used to describe cavitating flows and how we relate values to transition between modes Justification for use of a thermosensitive fluid Reasons to study cavitation and the negative effects it can have on equipment Observed what incipient cavitation looks like and how it transitions to cloud cavitation Behavior of pressure on Cp curves of all modes How bubbles formed and separated from cavity them moved downstream to collapse Experimental and computational results align and further motivation to study and predict cavitation Main differences between tests in water and fluoroketone are bubble size, different critical cavitation numbers

NASA Constellation project Acknowledgements NASA Constellation project Combustion and Propulsion Laboratory at University of Florida