Hydrodynamic Cavitation Technological Equipment

Nomenclature

Unless otherwise stated, quantities are expressed in SI units. Subscripts identify the relevant station, phase, component, or energy boundary.

Symbol	Definition	SI unit or status
A	Flow cross sectional area	m²
Ao	Total orifice open area	m²
Ap	Pipe cross sectional area	m²
At	Venturi throat area	m²
C0	Initial concentration	Application dependent
Cn, Ct	Concentration after n passes or treatment time t	Application dependent
Cd	Discharge coefficient	Dimensionless
cp	Specific heat capacity	J kg⁻¹ K⁻¹
D	Pipe, rotor, or characteristic diameter	m
Dh	Hydraulic diameter	m
D10, D50, D90	10th percentile, median, and 90th percentile of a size distribution	m or μm
d32	Sauter mean droplet diameter	m or μm
do	Orifice diameter	m
dt	Throat diameter	m
Eel	Electrical input energy	J or kWh
Eh	Hydraulic energy across cavitation device	J
Ein	Selected input energy for yield calculation	J or kWh
Eu	Euler number	Dimensionless
f	Frequency	s⁻¹
fs	Vortex shedding frequency	s⁻¹
g	Gravitational acceleration	m s⁻²
$h_L$	Irreversible head loss	m
kpass	Apparent first order per pass coefficient	pass⁻¹
L	Length or characteristic length	m
mb	Processed batch mass	kg
ṁ	Mass flow rate	kg s⁻¹
n	Rotational frequency or number of passes, as defined	s⁻¹ or dimensionless
Nh	Number of holes	Dimensionless
Np	Nominal number of passes	Dimensionless
p	Static pressure	Pa
$p_B$	Pressure inside a cavity	Pa
pref	Reference pressure used in cavitation number	Pa
pv	Vapor pressure at liquid temperature	Pa
Pact	Active or reference volume for power density	m³
Pel	Measured electrical input power	W
Ph	Hydraulic power across cavitation device	W
Pshaft	Pump or rotor shaft power	W
Q	Volumetric flow rate	m³ s⁻¹
R	Cavity radius or rotor radius, as defined	m
Re	Reynolds number	Dimensionless
ReΩ	Rotational Reynolds number	Dimensionless
SEC	Specific energy consumption	J kg⁻¹ or kWh t⁻¹
St	Strouhal number	Dimensionless
t, tp	Time and processing time	s
U, v	Characteristic or mean velocity	m s⁻¹
utip	Rotor tip speed	m s⁻¹
V	Volume	m³
Vactive	Defined active device volume	m³
Vb	Total recirculating batch and loop volume	m³
We	Weber number	Dimensionless
YC	Concentration change yield per input energy	Application dependent
z	Elevation	m
a, b, c, d	Empirical coefficients in the vortex device Euler number correlation	Dimensionless
CP	Rotating device power coefficient	Dimensionless
Erecovered	Recovered useful thermal or mechanical energy credited to the process	J or kWh
Eu*	Scaled Euler number, Eu/50 in the cited vortex correlation	Dimensionless
fp	Nominal rotor element passage frequency	s⁻¹
Ne	Number of cavitation generating elements encountered per revolution	Dimensionless
Nexp	Nominal number of cyclic exposures in the active region	Dimensionless
Nparallel	Number of parallel cavitation units or trains	Dimensionless
$p_{dyn}$	Jet dynamic pressure	Pa
Ploss	Mechanical, electrical, and environmental power loss within the declared boundary	W
Q̇rem	Rate of heat removed by a cooler or heat exchanger	W
Q̇ret	Rate of heat retained in the processed stream	W
Re*	Scaled Reynolds number, Re/1000 in the cited vortex correlation	Dimensionless
SECnet	Net specific electrical energy after an explicitly stated recovered energy credit	J kg⁻¹ or kWh t⁻¹
T	Measured shaft torque	N m
tres	Mean residence time in the active cavitation region	s
urel	Relative velocity across a rotor stator clearance	m s⁻¹
VT	Vortex device throat velocity	m s⁻¹
Vθ, max	Maximum tangential velocity in a vortex chamber	m s⁻¹
An	Total nozzle area in a high pressure interaction cell	m²
APM	Auxiliary Processing Module	abbreviation
Bp	Backpressure ratio	dimensionless
Cv	Jet velocity coefficient	dimensionless
CIP	Clean in place	abbreviation
EC	Pion BEE Emulsifying Cell	abbreviation
eh	Hydraulic energy per unit mass	J kg−1
GMP	Good manufacturing practice	abbreviation
HPH	High pressure homogenization	abbreviation
IXC	Microfluidics Interaction Chamber	abbreviation
Lc	Distance from nozzle to principal recovery or impact region	m
pb	Controlled downstream backpressure	Pa
Pj	Jet kinetic power scale	W
tc	Mean cavity transport time to recovery region	s
vj	Characteristic jet velocity	m s−1

Greek Letters

Symbol	Letter name	Meaning
α	Alpha	Phase volume fraction or geometric angle when explicitly defined
β	Beta	Diameter ratio do/D or throat ratio
γ	Gamma	Surface or interfacial tension
Δ	Delta	Difference or change, such as pressure drop Δp
ε	Epsilon	Turbulent or cavitation induced energy dissipation rate
η	Eta	Efficiency; subscripts identify hydraulic, motor, drive, or process efficiency
λ	Lambda	Scale ratio for length, flow, or pressure
μ	Mu	Dynamic viscosity
ν	Nu	Kinematic viscosity when used
ρ	Rho	Density
σ	Sigma	Cavitation number
φA	Phi	Total open area fraction
ω	Omega	Angular velocity
π	Pi	Circular constant
δ	Delta, lowercase	Rotor stator gap or mechanical clearance
γ̇	Gamma dot	Shear rate; subscript identifies the local gap or region
θ	Theta	Tangential direction, tangential velocity component, or stated geometric angle