From e759f79a8c798284acf3aeb030c83a55aa053cdc Mon Sep 17 00:00:00 2001
From: Alexander Fleming <alexander.fleming@rwth-aachen.de>
Date: Tue, 2 Jan 2024 08:20:48 +0100
Subject: [PATCH] Billig Formulae.

---
 src/billig.jl        | 2 +-
 src/normal_shocks.jl | 9 +++++++--
 test/runtests.jl     | 4 ++--
 3 files changed, 10 insertions(+), 5 deletions(-)

diff --git a/src/billig.jl b/src/billig.jl
index b42f546..23c2b55 100644
--- a/src/billig.jl
+++ b/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
\ No newline at end of file
diff --git a/src/normal_shocks.jl b/src/normal_shocks.jl
index 7d3a2d5..ea51413 100644
--- a/src/normal_shocks.jl
+++ b/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
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 255593a..42c2b1e 100644
--- a/test/runtests.jl
+++ b/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