Introduction

Introduction#

Flow360 solves the governing equations in non-dimensional form. Every variable is divided by a reference value before entering the solver:

(1)#\[\text{non-dimensional variable} = \frac{\text{dimensional variable}}{\text{reference value}}\]

The table below lists the reference quantities used throughout Flow360 and how to access them via the Python API. Here, project is the cloud asset containing the case, and params is the SimulationParams object (for a completed case: case.params). See the Python API guide for details.

Reference quantities#

Symbol

Definition

SI unit

Python API access

\(L_{gridUnit}\)

Physical length per mesh unit (e.g. if the mesh is in feet, \(L_{gridUnit} = 0.3048\;\text{m}\))

m

 
project.length_unit

\(C_\infty\)

Speed of sound (freestream)

m/s

 
case.params.operating_condition \
.thermal_state.speed_of_sound

\(\rho_\infty\)

Density (freestream)

kg/m³

 
case.params.operating_condition \
.thermal_state.density

\(\mu_\infty\)

Dynamic viscosity (freestream)

N·s/m²

 
case.params.operating_condition \
.thermal_state.dynamic_viscosity

\(p_\infty\)

Static pressure (freestream)

Pa

 
case.params.operating_condition \
.thermal_state.pressure

\(T_\infty\)

Temperature (freestream)

K

 
case.params.operating_condition \
.thermal_state.temperature

\(U_\text{ref}\)

Reference velocity (used for force and moment coefficients)

m/s

 
case.params.reference_velocity

\(A_\text{ref}\)

Reference area

m²

 
case.params.reference_geometry \
.area

\(L_\text{ref}\)

Moment length (can be a 3-component vector)

m

 
case.params.reference_geometry \
.moment_length

Reference Velocity Scaling#

\(U_\text{scale}\) is the velocity used to non-dimensionalize most solver variables (velocity fields, heat flux, volumetric heat sources, angular speeds):

if operating_condition.type_name == "LiquidOperatingCondition":
    U_scale = operating_condition.reference_velocity
else:  # AerospaceCondition
    U_scale = operating_condition.thermal_state.speed_of_sound

Important

\(U_\text{scale}\) and \(U_\text{ref}\) are not the same quantity. \(U_\text{scale}\) non-dimensionalizes solver fields (velocity, pressure, heat flux, …). \(U_\text{ref}\) non-dimensionalizes force and moment coefficients (\(C_L\), \(C_D\), \(C_F\), \(C_M\)). Mixing them up produces incorrect conversions.

Grid Unit Length#

\(L_{gridUnit}\) scales all length-related quantities. The mesh can use any unit; L_{gridUnit} for common mesh units lists common values.

\(L_{gridUnit}\) for common mesh units#

Mesh unit

\(L_{gridUnit}\)

metres [m]

1.0 m

millimetres [mm]

0.001 m

feet [ft]

0.3048 m

inches [in]

0.0254 m

unit chords [c = 1.0]

value of c_ref in metres

The following pages explain how these reference quantities apply to:

  • Inputs — non-dimensionalizing user-supplied values (angular speed, heat flux, …)

  • Outputs — converting solver fields back to physical units

  • Force & moment coefficients — converting \(C_L\), \(C_D\), \(C_M\), and raw BET/AD/PM forces to Newtons and Newton-meters

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