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Hydrodynamic Cavitation for Wastewater Processing
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Nomenclature
The following symbols are used in this article. Unless otherwise stated, quantities are expressed in SI units. Symbols retained from cited sources may follow the convention of the original source; the corresponding equation and surrounding definitions govern their interpretation.
| Symbol | Definition | SI unit or status |
|---|---|---|
| Ac | Flow area at the constriction or designated cavitating section | m² |
| C | Contaminant concentration | mol m⁻³, mg L⁻¹, or specified |
| C₀ | Initial contaminant concentration | same as C |
| Ct | Contaminant concentration at time t | same as C |
| CW | Disinfectant concentration in the Chick Watson model | mass volume⁻¹ |
| D | Characteristic hydraulic length or diameter | m |
| Da | Damköhler type reaction to hydraulic time ratio | dimensionless |
| DDCOD | Degree of sludge disintegration based on soluble COD | % |
| EEO | Electrical energy per order of contaminant reduction | kWh m⁻³ order⁻¹ |
| Ein | Energy input to the treatment system | J or kWh |
| Es | Specific electrical energy input | J m⁻³ or kWh m⁻³ |
| g | Gravitational acceleration | m s⁻² |
| hL | Specific irreversible hydraulic loss | J kg⁻¹ |
| k | Empirical inactivation or reaction constant | specified by model |
| kobs | Observed pseudo first order rate constant | s⁻¹ or min⁻¹ |
| kreaction | Characteristic reaction rate constant used in Da | s⁻¹ |
| LRV | Logarithmic reduction value | dimensionless |
| N₀ | Initial viable organism concentration | CFU or organisms per volume |
| Nt | Viable organism concentration after treatment time t | CFU or organisms per volume |
| Npass | Nominal number of treatment loop turnovers | dimensionless |
| p | Static pressure | Pa |
| p₂ | Recovered downstream reference pressure | Pa |
| pB | Pressure inside a cavity | Pa |
| p∞ | Far field liquid pressure | Pa |
| Pel | Estimated electrical pump power | W |
| Ph | Hydraulic power transferred to the liquid | W |
| pv | Liquid vapor pressure | Pa |
| Q | Volumetric flow rate | m³ s⁻¹ |
| R | Instantaneous bubble radius | m |
| Rmax | Maximum bubble radius before collapse | m |
| Re | Reynolds number | dimensionless |
| SCOD₀ | Initial soluble chemical oxygen demand | mg L⁻¹ |
| SCODt | Soluble chemical oxygen demand after treatment | mg L⁻¹ |
| SCODmax | Reference maximum soluble COD | mg L⁻¹ |
| t | Treatment time | s or min |
| tc | Idealized Rayleigh collapse time | s |
| V | Treated or recirculating liquid volume | m³ |
| v | Mean fluid velocity | m s⁻¹ |
| vc | Velocity in the constriction or designated cavitating region | m s⁻¹ |
| We | Weber number | dimensionless |
| Ycav | Cavitational yield | mass energy⁻¹ |
| YCH₄, c | Control methane yield | mL CH₄ g⁻¹ VS or specified |
| YCH₄, t | Methane yield after pretreatment | mL CH₄ g⁻¹ VS or specified |
| z | Elevation | m |
| cp | Specific heat capacity | J kg⁻¹ K⁻¹ |
| Dr | Rotor diameter | m |
| Eavoided | Avoided process or disposal energy credited in the net balance | J or kWh |
| Ebiogas | Recoverable energy associated with additional biogas | J or kWh |
| Ecooling | Cooling energy demand | J or kWh |
| Echem | Energy or equivalent energy assigned to chemical consumption | J or kWh |
| EHC | Electrical energy used by the HC process | J or kWh |
| Enet | Net energy benefit | J or kWh |
| m | Mass of treated liquid | kg |
| N | Rotational speed | s⁻¹ or rpm |
| Ploss | Heat loss or rejected thermal power | W |
| Po | Power number | dimensionless |
| Pshaft | Measured shaft power | W |
| S | Kinetic synergy index | dimensionless |
| u tip | Rotor tip speed | m s⁻¹ |