some gas properties

Project.toml

@@ -3,6 +3,10 @@ uuid = "77d2bf28-a3e9-4b9c-9fcf-b85f74cc8a50"
 authors = ["Alex Fleming <[email protected]> and contributors"]
 version = "1.0.0-DEV"
 
+[deps]
+PhysicalConstants = "5ad8b20f-a522-5ce9-bfc9-ddf1d5bda6ab"
+Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
 [compat]
 julia = "1.6"
 

src/ShockwaveProperties.jl

@@ -1,5 +1,6 @@
 module ShockwaveProperties
 
-# Write your package code here.
+include("cpg.jl")
+include("normal_shocks.jl")
 
 end

src/billig.jl

@@ -0,0 +1,3 @@
+module BilligShock
+
+end

src/cpg.jl

@@ -0,0 +1,56 @@
+using Unitful
+
+const _units_cvcp = u"J/kg/K"
+const _units_ℳ = u"kg/mol"
+const _units_ρ = u"kg/m^3"
+const _dimension_ρ = Unitful.dimension(_units_ρ)
+
+"""
+Provides the properties of a calorically perfect gas (or mixture of gases). 
+"""
+struct CaloricallyPerfectGas{T}
+    c_p::Quantity{T,Unitful.dimension(_units_cvcp),typeof(_units_cvcp)}
+    c_v::Quantity{T,Unitful.dimension(_units_cvcp),typeof(_units_cvcp)}
+    ℳ::Quantity{T,Unitful.dimension(_units_ℳ),typeof(_units_ℳ)}
+
+    γ::T
+    R::Quantity{T,Unitful.dimension(_units_cvcp),typeof(_units_cvcp)}
+end
+
+function CaloricallyPerfectGas(c_p::T, c_v::T, ℳ::T) where {T}
+    return CaloricallyPerfectGas{T}(
+        Quantity(c_p, _units_cvcp),
+        Quantity(c_v, _units_cvcp),
+        Quantity(ℳ, _units_ℳ),
+        c_p / c_v,
+        Quantity(c_p - c_v, _units_cvcp)
+    )
+end
+
+const DRY_AIR = CaloricallyPerfectGas(1.0049, 0.7178, 0.0289647)
+
+enthalpy(gas::CaloricallyPerfectGas, T::Real) = gas.c_p * Quantity(T, u"K")
+enthalpy(gas::CaloricallyPerfectGas, T::Quantity{T1,Unitful.𝚯,Units}) where {T1,Units} = gas.c_p * T
+
+int_energy(gas::CaloricallyPerfectGas, T::Real) = gas.c_v * Quantity(T, u"K")
+int_energy(gas::CaloricallyPerfectGas, T::Quantity{T1,Unitful.𝚯,Units}) where {T1,Units} = gas.c_v * T
+
+function speed_of_sound(gas::CaloricallyPerfectGas, T::Real)
+    return sqrt(gas.γ * gas.R * Quantity(T, u"K"))
+end
+
+function speed_of_sound(gas::CaloricallyPerfectGas, T::Quantity{T1,Unitful.𝚯,Units}) where {T1,Units}
+    return sqrt(gas.γ * gas.R * T)
+end
+
+function pressure(gas::CaloricallyPerfectGas, ρ::Real, T::Real)
+    # calculate ρe then 
+    # calculate p from calorically perfect gas relations
+    return (gas.γ - 1) * Quantity(ρ, _units_ρ) * int_energy(gas, T)
+end
+
+function pressure(gas::CaloricallyPerfectGas,
+    ρ::Quanity{U,_dimension_ρ,Units1},
+    T::Quantity{U,Unitful.𝚯,Units2}) where {U,Units1,Units2}
+    return (gas.γ-1) * ρ * T
+end

src/normal_shocks.jl

@@ -0,0 +1,71 @@
+"""
+**Equation 4.8** from Anderson&Anderson
+
+Computes the density change across a shock wave where free stream mach number is ``M``
+and the outward (away from body) normal is ``n̂``
+"""
+function shock_density_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
+    Mn2 = (M * n̂[1])^2
+    return ((gas.γ + 1) * Mn2) / ((gas.γ - 1) * Mn2 + 2)
+end
+
+"""
+**Equation 4.9** from Anderson&Anderson
+
+Computes the pressure ratio across a shock wave where the free stream mach number is ``M``
+and the outward (away from body) normal is ``n̂``.
+"""
+function shock_pressure_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
+    Mn2 = (M * n̂[1])^2
+    return 1 + (2 * gas.γ) / (gas.γ + 1) * (Mn2 - 1)
+end
+
+"""
+**Equation 4.10** from Anderson&Anderson
+
+Computes the normal Mach number ratio across a shock wave where the free stream mach number is ``M``
+and the outward (away from body) normal is ``n̂``.
+"""
+function shock_normal_mach_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
+    MnL2 = (M * n̂[1])^2
+    Mn2sqr = (MnL2 + (2 / (gas.γ - 1))) / (2 * gas.γ / (gas.γ - 1) * MnL2 - 1)
+    Mn2 = sqrt(Mn2sqr)
+    return Mn2
+end
+
+
+"""
+Computes the normal velocity ratio across a shock wave where the free stream mach number is ``M``
+and the outward (away from body) normal is ``n̂``.
+
+Derived from speed of sound proportional to the square root of temperature.
+
+Useful for computing momentum ratio.
+"""
+function shock_normal_velocity_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
+    return sqrt(1 / shock_temperature_ratio(M, n̂; gas=gas)) * shock_normal_mach_ratio(M, n̂; gas=gas)
+end
+
+"""
+Computes the tangential mach number ratio across a shock wave, where the free stream mach number is ``M``
+and the outward (away from body) normal is ``n̂``.
+
+Derived from speed of sound proportional to the square root of temperature.
+"""
+function shock_tangent_mach_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
+    return sqrt(shock_temperature_ratio(M, n̂; gas=gas))
+end
+
+"""
+**Equation 4.11** from Anderson&Anderson
+
+Computes the temperature across a shock wave where the free stream mach number is ``M``
+and the outward (away from body) normal is ``n̂``.
+"""
+function shock_temperature_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
+    return shock_pressure_ratio(M, n̂; gas=gas) / shock_density_ratio(M, n̂; gas=gas)
+end
+
+"""
+Computes the 
+"""