FlowRef.jl

FlowRef.jl is a small library for computation of consistent reference quantities for inviscid and viscous flows. These are helpful when using non-dimensionalized/scaled flow equations.

Usage

The package defines a ReferenceFlowQuantities struct that stores all necessary reference quantities for scaling of the compressible Navier-Stokes equations. A derivation of the reference quantities in the context of multi-species multi-temperature Navier-Stokes equations can be found here. To ensure that the quantities are computed in a consistent manner, utility functions are provided that return a ReferenceFlowQuantities instance given a set of independent reference quantities that are used define all other reference values:

• p_m_rho_L(p_ref, m_ref, rho_ref, L_ref) - computes all reference quantities given a reference pressure p_ref, reference mass m_ref, reference density rho_ref, and reference L_ref
• p_T_rho_L(p_ref, T_ref, rho_ref, L_ref) - computes all reference quantities given a reference pressure p_ref, reference temperature T_ref, reference density rho_ref, and reference L_ref
• T_v_rho_L(T_ref, v_ref, rho_ref, L_ref) - computes all reference quantities given a reference temperature T_ref, reference velocity v_ref, reference density rho_ref, and reference L_ref

A dictionary may be instantiated from ReferenceFlowQuantities instance rfq by simply calling dict_rfq = Dict(rfq).

Example usage:

rfq = p_m_rho_L(101325.0, 4.65e-26, 1.1375, 1.0) # atmospheric pressure, N2 molecular mass, 1.1375 kg/m^3 density, 1 m reference length
println(rfq.T_ref)  # 300.0094102901551
println(rfq.v_ref)  # 298.4575733281417

# we can use computed quantities and check that we get our reference pressure and mass
rfq2 = T_v_rho_L(rfq.T_ref, rfq.v_ref, 1.1375, 1.0)
println(rfq2.p_ref)  # 101324.99999999999
println(rfq2.m_ref)  # 4.650000000000001e-26

Computed quantities

The ReferenceFlowQuantities struct has the following fields:

• p_ref: reference pressure
• T_ref: reference temperature
• rho_ref: reference density
• v_ref: reference velocity
• n_ref: reference number density
• m_ref: reference mass
• e_ref: reference specific energy (per unit mass)
• c_v_ref: reference specific heat
• R_specific_ref: reference specific gas constant
• t_ref: reference time
• μ_ref: reference viscosity coefficient
• λ_ref: reference thermal conductivity coefficient
• Diff_ref: reference diffusion coefficient
• Reynolds_ref: reference Reynolds number