Billig Formulae.

src/billig.jl

@@ -72,7 +72,7 @@ The shock wave parametrization developed by *Billig* parametrizes the shock wave
 """
 function shock_tangent(α, M_inf, R_b)
     n = shock_normal(α, M_inf, R_b)
-    return [n[2], 1]
+    return [n[2], -n[1]]
 end
 
 end # module

src/normal_shocks.jl

@@ -56,6 +56,10 @@ function shock_tangent_mach_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
     return sqrt(shock_temperature_ratio(M, n̂; gas=gas))
 end
 
+@inline function shock_normal_momentum_ratio(M, n̂; gas::CaloricallyPerfectGas=DRY_AIR)
+    return shock_density_ratio(M, n̂; gas=gas) * shock_normal_velocity_ratio(M, n̂; gas=gas)
+end
+
 """
 **Equation 4.11** from Anderson&Anderson
 
@@ -73,6 +77,7 @@ The outward (away from body) normal is ``n̂``.
 function conserved_state_behind(state_L::ConservedState, n̂, t̂; gas::CaloricallyPerfectGas=DRY_AIR)
     @assert t̂ ⋅ n̂ == 0. "tangent and normal vectors should be normal."
     M_L = state_L.ρv / (state_L.ρ * speed_of_sound(gas, state_L))
-    mach_t_ratio = shock_tangent_mach_ratio(M_L, n̂; gas=gas)
-    M_R_n = (M_L⋅n̂) * shock_normal_mach_ratio(M_L, n̂; gas=gas)
+    ρv_n_L = (state_L.ρv ⋅ n̂) * shock_normal_momentum_ratio(M_L, n̂; gas=gas)
+    ρv_t_L = (state_L.ρv ⋅ n̂) * shock_density_ratio(M_L, n̂; gas=gas)
+
 end

test/runtests.jl

@@ -2,12 +2,12 @@ using LinearAlgebra
 using ShockwaveProperties
 using Test
 
-@testset "ShockwaveProperties.jl" begin
+@testset verbose=true "ShockwaveProperties.jl" begin
     @testset "BilligShockParametrization" begin
         using .BilligShockParametrization
         @testset "Shockwave Normals" begin
             y = -10:0.1:10
-            for R_b ∈ 1.0:0.25:4.0, M ∈ 1.5:0.5:5.0
+            for R_b ∈ 1.0:0.5:4.0, M ∈ 2.0:1.0:5.0
                 vals = mapreduce(hcat, y) do α
                     shock_normal(α, M, R_b) ⋅ shock_tangent(α, M, R_b)
                 end