From 8358109e0185fc804129d9157891e92f7e76bc3a Mon Sep 17 00:00:00 2001
From: Elias Aoubala <2432537A@student.gla.ac.uk>
Date: Wed, 24 Jan 2024 22:38:08 +0000
Subject: [PATCH 1/2] Initial push for supersonic profiling

---
 src/turborocket/meanline/lossmodels.py        | 150 ++++++++++++
 .../__pycache__/circular.cpython-311.pyc      | Bin 0 -> 4189 bytes
 .../__pycache__/transition.cpython-311.pyc    | Bin 0 -> 7073 bytes
 .../profiling/Supersonic/circular.py          | 127 ++++++++++
 .../profiling/Supersonic/transition.py        | 225 ++++++++++++++++++
 .../profiling/supersonic_profile.py           |   7 +
 .../__pycache__/solver.cpython-311.pyc        | Bin 0 -> 2457 bytes
 src/turborocket/solvers/solver.py             |  62 +++++
 ...test_circular.cpython-311-pytest-7.4.4.pyc | Bin 0 -> 13462 bytes
 ...st_transition.cpython-311-pytest-7.4.4.pyc | Bin 0 -> 24189 bytes
 tests/profiling/supersonic/test_circular.py   |  46 ++++
 tests/profiling/supersonic/test_transition.py |  69 ++++++
 .../test_solver.cpython-311-pytest-7.4.4.pyc  | Bin 0 -> 3098 bytes
 tests/solvers/test_solver.py                  |  11 +
 14 files changed, 697 insertions(+)
 create mode 100644 src/turborocket/meanline/lossmodels.py
 create mode 100644 src/turborocket/profiling/Supersonic/__pycache__/circular.cpython-311.pyc
 create mode 100644 src/turborocket/profiling/Supersonic/__pycache__/transition.cpython-311.pyc
 create mode 100644 src/turborocket/profiling/Supersonic/circular.py
 create mode 100644 src/turborocket/profiling/Supersonic/transition.py
 create mode 100644 src/turborocket/profiling/supersonic_profile.py
 create mode 100644 src/turborocket/solvers/__pycache__/solver.cpython-311.pyc
 create mode 100644 src/turborocket/solvers/solver.py
 create mode 100644 tests/profiling/supersonic/__pycache__/test_circular.cpython-311-pytest-7.4.4.pyc
 create mode 100644 tests/profiling/supersonic/__pycache__/test_transition.cpython-311-pytest-7.4.4.pyc
 create mode 100644 tests/profiling/supersonic/test_circular.py
 create mode 100644 tests/profiling/supersonic/test_transition.py
 create mode 100644 tests/solvers/__pycache__/test_solver.cpython-311-pytest-7.4.4.pyc
 create mode 100644 tests/solvers/test_solver.py

diff --git a/src/turborocket/meanline/lossmodels.py b/src/turborocket/meanline/lossmodels.py
new file mode 100644
index 0000000..379575a
--- /dev/null
+++ b/src/turborocket/meanline/lossmodels.py
@@ -0,0 +1,150 @@
+"""
+
+This file contains a series of loss-model utilities functions for mean-line design of turbines
+
+Each Loss model is encapsulated into an object with a series of functions calculating loss contributions.
+
+Loss-Models currently implemented:
+
+    - craigcox: Loss Model by Craig and Cox
+    - kackerOkapuu: Loss Model by Kacker and Okapuu (1982)
+    - Aungier: Loss Modely by Aungier    
+
+"""
+
+import numpy as np
+
+class Aungier:
+    """
+    
+    The Aungier Loss Model
+
+    Variables:
+        Y_p:    Profile Loss parameters
+        K_mod:  Experience factor (derived from the kackerOkapuu method)
+        K_inc:  Off-design incidence factor
+        K_m:    Mach Number Factor
+        K_p:    Compressibility Factor
+        K_RE:   Reynolds Number Factor
+
+        Y_p1:   Profile Loss coefficient for nozzle blades (beta_1 = 0)
+        Y_p2:   Profile Loss coefficent for rotor blades (beta_1 = alpha_2)
+
+        Y_s:    Secondary Flow Losses for low aspect ratio
+
+    """
+
+    def __init__():
+        # Intialising core parameters of the loss model
+        return
+
+    def Y(self):
+        """
+        Total Pressure Loss Coefficient (Y)
+
+        This function solves for the profile loss coefficient of the turbine stage, characterising the increase in total pressure of the turbine exit stage
+
+        Y = (P_t1 - P_t2) / (P_t2 - P_2)
+
+        Variables:
+            Y_p:    The Profile Loss Coefficient
+            Y_s:    The Secondary Flow loss coefficient
+            Y_tcl:  The blade clearnace loss coefficient
+            Y_te:   The trailing edge loss coefficient
+            Y_ex:   The supersonic expansion loss coefficient
+            Y_sh:   The shock loss coefficient
+            T_lw:   The lashing wire loss coefficient (rotors)
+        """
+
+        return Y_p + Y_s + Y_tcl + T_te + Y_ex + Y_sh + Y_lw
+
+    def delta_h_par(self):
+        """
+        Parasitic Losses (delta_h_par)
+
+        The parasitic losses accounts for waster work due to losses in disk friction, shear forces and partial admission.
+
+        These are reflected in an increase in total enthalph of the discharge flow
+        relative to the value produced when the flow passes through the blade row.
+
+        In contrast to the pressure loss coefficient, these losses do not affect total pressure, but do influence stage efficiency.
+
+        Variables:
+            delta_h_adm:    Partial admission losses (rotors)
+            delta_h_df:     Disk friction work (diaphragm-disk rotors)
+            delta_h_seal:   Leakage bypass loss (shourded rotors and rotor balance holes)
+            delta_h_gap:    Clearnace gap windage loss (shrouded blades and nozzles of diaphragm-disk rotors)
+            delta_h_q:      moisture work loss (rotors)
+        """
+
+        return delta_h_adm + delta_h_df + delta_h_seal + delta_h_gap + delta_h_q
+
+    def yp(self):
+        """
+        The Profile Loss Coefficient (Y_p)
+
+        This pressure loss coefficient characterises the profile losses of the turbine stage
+
+        Variables:
+            K_mod:  kackerOkapuu Experience factor
+            K_inc:  Correction for off-design incidence effects
+            K_m:    Correction for Mach Number effects
+            K_p:    correction for Compressibility effects
+            K_re:   correction for Reynolds Number effects
+            Y_p1:   profile loss coefficient for nozzle blades (beta_1 = 90)
+            Y_p2:   profile loss coefficients for impulse blades (alpha_2 = beta_1) 
+        
+        Returns:
+            _type_: _description_
+        """
+
+        prt = (y_p1 + ((beta_1/alpha_2)**2 ) * (y_p2 - y_p1))*((5*t/c)**(beta_1/alpha_2)) - delta_y_te
+
+        y_p = k_mod * k_inc * k_m * k_p * k_re * prt;
+
+        return y_p
+    
+    def F_ar(self):
+
+        if h_c < 2:
+            f_ar = 0.5 * (2*c/h)**(0.7)
+        else:
+            f_ar = (c/h)
+        
+        return f_ar
+
+    def Y_s(self):
+        y_bar_s = 0.0334 * F_ar * (C_l / (s_c))**2 * (np.cos(alpha_2)/np.cos(beta_1))*(np.cos(alpha_2)**2/np.cos(alpha_m)***3)
+
+        y_s = k_s*k_re*(y_bar_s**2 / (1 + 7.5*y_bar_s))**(1/2)
+
+        return y_s
+    
+    def Y_sh(self):
+
+        y_bar_sh = 0.8*x_1**2 + x_2**2
+
+        y_sh = (y_bar_sh**2 / (1 + y_bar_sh**2))**(1/2)
+
+        return y_sh
+    
+    def Y_ex(self):
+        
+        y_ex = ((M2 - 1)/M2)**2;
+
+        return y_ex
+    
+    def Y_te(self):
+
+        y_te = ((t_2/s) * np.sin(beta_g) - t_2)**2
+
+        return y_te
+
+    def Y_tcl(self):
+        
+        if TIP_TYPE = "shrouded":
+            B = 0.37
+        else:
+            B = 0.47
+
+        Y_tcl = B*(c/h)*(t_cl / c)**(0.78) * (C_l/(s/c))**2 * (np.cos(alpha_2)**2 /np.cos(alpha_m)**3)
\ No newline at end of file
diff --git a/src/turborocket/profiling/Supersonic/__pycache__/circular.cpython-311.pyc b/src/turborocket/profiling/Supersonic/__pycache__/circular.cpython-311.pyc
new file mode 100644
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diff --git a/src/turborocket/profiling/Supersonic/__pycache__/transition.cpython-311.pyc b/src/turborocket/profiling/Supersonic/__pycache__/transition.cpython-311.pyc
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diff --git a/src/turborocket/profiling/Supersonic/circular.py b/src/turborocket/profiling/Supersonic/circular.py
new file mode 100644
index 0000000..9b479eb
--- /dev/null
+++ b/src/turborocket/profiling/Supersonic/circular.py
@@ -0,0 +1,127 @@
+"""
+Circular.py
+
+This source file encapsulates all the functions required for sizing the circular sections of the tubrine blade, following the free vortex assumption.
+
+The following equations follows the method for supersonic turbine design presented in NASA TN D-4421.
+
+Free vortex flow is assumed for the blade flow.
+
+# noqa: E501
+"""
+
+import numpy as np
+
+
+def M_star(gamma, M):
+    """
+    Critical Velocity Ratio
+
+    This function computes the critical velocity ratio of the flow as a function of Mach number and specific heat ratio.
+
+    Variables:
+        gamma:  Specific Heat Ratio
+        M:      Mach Number
+
+    # noqa: E501
+    """
+
+    crit_vel_rat = (
+        (((gamma + 1) / 2) * M**2) / (1 + ((gamma - 1) / 2) * M**2)
+    ) ** (1 / 2)
+
+    return crit_vel_rat
+
+
+def prandtl_meyer(gamma, crit_vel_rat):
+    """
+    Prandtl Meyer Angle (v)
+
+    This function computes the Prandtl-Meyer angle v based on the mach number of a flow.
+
+    # noqa: E501
+    """
+
+    v = np.pi / 4 * (((gamma + 1) / (gamma - 1)) ** (1 / 2) - 1) + (1 / 2) * (
+        (((gamma + 1) / (gamma - 1)) ** (1 / 2))
+        * np.arcsin((gamma - 1) * crit_vel_rat**2 - gamma)
+        + np.arcsin((gamma + 1) / crit_vel_rat**2 - gamma)
+    )
+
+    return v
+
+
+def arc_angles_upper(beta_o, beta_i, v_i, v_o, v_u):
+    """
+    Upper Circular Arc Angles Alpha
+
+    This function computes the circular arc angles based on the inlet and outlet angles,
+    coupled with their prantl-meyer angles
+
+    Variables:
+        alpha_l_i:  Lower Arc Inlet Angle
+        alpha_l_o:  Lower Arc Outlet Angle
+        alpha_u_i:  Upper Arc Inlet Angle
+        alpha_u_o:  Upper Arc Outlet Angle
+        beta_i:     Inlet relative flow angle
+        beta_o:     Exit relative
+
+    # noqa: E501
+    """
+
+    alpha_u_i = beta_i - (v_u - v_i)
+
+    alpha_u_o = beta_o + (v_u - v_o)
+
+    return [alpha_u_i, alpha_u_o]
+
+
+def arc_angles_lower(beta_o, beta_i, v_i, v_o, v_l):
+    """
+    Lower Circular Arc Angles Alpha
+
+    This function computes the arc angles based on the inlet and outlet angles, coupled with their prantl-meyer angles
+
+    Variables:
+        alpha_l_i:  Lower Arc Inlet Angle
+        alpha_l_o:  Lower Arc Outlet Angle
+        alpha_u_i:  Upper Arc Inlet Angle
+        alpha_u_o:  Upper Arc Outlet Angle
+        beta_i:     Inlet relative flow angle
+        beta_o:     Exit relative
+
+    # noqa: E501
+    """
+
+    alpha_l_i = beta_i - (v_i - v_l)
+
+    alpha_l_o = beta_o + (v_o - v_l)
+
+    return [alpha_l_i, alpha_l_o]
+
+
+def beta_o(M_i, M_o, gamma, beta_i):
+    """ """
+
+    exit_o = -np.arccos(
+        (
+            (M_i / M_o)
+            * ((1 + (gamma - 1) / 2 * M_o**2) / (1 + (gamma - 1) / 2 * M_i**2))
+            ** ((gamma + 1) / (2 * (gamma - 1)))
+        )
+        * np.cos(beta_i)
+    )
+
+    return exit_o
+
+
+def A_rat(beta_i, beta_o):
+    """
+    The Area Ratio (A_i / A_o)
+
+    This equation computes the area ratio of the supersonic turbine blade, assuming that the spacings are equal on the inlet and exit sides of the turbine (Axial turbine)
+
+    # noqa: E501
+    """
+
+    return np.cos(beta_i) / np.cos(beta_o)
diff --git a/src/turborocket/profiling/Supersonic/transition.py b/src/turborocket/profiling/Supersonic/transition.py
new file mode 100644
index 0000000..255b8ea
--- /dev/null
+++ b/src/turborocket/profiling/Supersonic/transition.py
@@ -0,0 +1,225 @@
+"""
+transition.py
+
+This source file encapsulates all the functions required for sizing the transition arc sections of the turbine blade, utilising the method of characteristics.
+
+The following equations follows the method for supersonic turbine design presented in NASA TN D-4421.
+
+
+
+# noqa: E501
+
+"""
+
+from src.turborocket.solvers.solver import adjoint
+
+import numpy as np
+
+
+def func_R_star(R_star, gamma):
+    """
+    Function of R* ( f(R*) )
+
+    This equation describes the generalised function of the non-dimentionalised radius
+    defining the expansion line angle.
+
+    Variables:
+        gamma:  Specific Heat Ratio
+        R_star: Non-dimentionalised Radius
+
+    """
+
+    f_r_star = ((gamma + 1) / (gamma - 1)) ** (1 / 2) * np.arcsin(
+        (gamma - 1) / R_star**2 - gamma
+    ) + np.arcsin((gamma + 1) * R_star**2 - gamma)
+
+    return f_r_star
+
+
+def func_R_star_k(gamma, v_i, dv, k):
+    f_r_star_k = (
+        2 * v_i
+        - np.pi / 2 * (((gamma + 1) / (gamma - 1)) ** (1 / 2) - 1)
+        - 2 * (k - 1) * dv
+    )
+
+    return f_r_star_k
+
+
+def R_star(gamma, v_i, dv, k, guess):
+    # We use the ajoint equation
+
+    target = func_R_star_k(gamma, v_i, dv, k)
+
+    r_star = adjoint(func_R_star, guess, -0.01, 50, 0.1, target, params=[gamma])
+
+    return r_star
+
+
+def phi_k(v_i, v_l, k, dv):
+    phi_k_i = v_i - v_l - (k - 1) * dv
+
+    return phi_k_i
+
+
+def vortex_coords(R_star_k, phi_k):
+    x_star = -R_star_k * np.sin(phi_k)
+    y_star = R_star_k * np.cos(phi_k)
+
+    return [x_star, y_star]
+
+
+def mue_k(gamma, R_star_k):
+    mach_angle = -np.arcsin(
+        (((gamma + 1) / 2) * R_star_k**2 - ((gamma - 1) / 2)) ** (1 / 2)
+    )
+
+    return mach_angle
+
+
+def mach_slope(phi_k_1, phi_k_2, mue_k_1, mue_k_2):
+    # This function computes the gradient of the mach line
+
+    m_k = np.tan(((phi_k_1 + phi_k_2) / 2) + ((mue_k_1 + mue_k_2) / 2))
+
+    return m_k
+
+
+def wall_slope(phi_k_1):
+    # This function computes the slope the wall at a given segment
+
+    m_bar_k = np.tan(phi_k_1)
+
+    return m_bar_k
+
+
+def wall_coords(x_star_l_k_1, y_star_l_k_1, y_star_k, x_star_k, m_bar_k, m_k):
+    x_star_l_k = (
+        (y_star_l_k_1 - m_bar_k * x_star_l_k_1) - (y_star_k - m_k * x_star_k)
+    ) / (m_k - m_bar_k)
+    y_star_l_k = (
+        m_k * (y_star_l_k_1 - m_bar_k * x_star_l_k_1)
+        - m_bar_k * (y_star_k - m_k * x_star_k)
+    ) / (m_k - m_bar_k)
+
+    return [x_star_l_k, y_star_l_k]
+
+
+def transform_coord(x_star_l_k, y_star_l_k, alpha_l_i):
+    # This function does the co-ordinate transformation for the transition co-ords
+
+    x_star_l_k_t = x_star_l_k * np.cos(alpha_l_i) - y_star_l_k * np.sin(alpha_l_i)
+
+    y_star_l_k_t = x_star_l_k * np.sin(alpha_l_i) + y_star_l_k * np.cos(alpha_l_i)
+
+    return [x_star_l_k_t, y_star_l_k_t]
+
+
+def moc(k_max, v_i, v_l, gamma, alpha_l_i):
+    # This function encapsulates the overall method of characteristics procedure for solving
+    # for the shape of the transition arcs
+
+    # First we need to define the k_max value, this needs to be an integer,
+    # so what we do is we can invert this
+
+    delta_v = (v_i - v_l) / k_max
+
+    # We setup our history arrays accordingly
+    phi_hist = []
+    r_star_hist = []
+    xk_hist = []
+    yk_hist = []
+    mue_hist = []
+    mk_hist = []
+    m_bar_k_hist = []
+    xlk_hist = []
+    ylk_hist = []
+    xlkt_hist = []
+    ylkt_hist = []
+
+    # We can now do the intial look to get the intial values of the loop.
+    phi = phi_k(v_i, v_l, k_max + 1, delta_v)
+
+    phi_hist.append(phi)
+
+    # We now must solver R* using the adjoint method
+    r_star = R_star(gamma, v_i, delta_v, k_max + 1, 1)
+
+    r_star_hist.append(r_star)
+
+    # We can now compute the co-ordinates of the expansion line
+    [xk, yk] = vortex_coords(r_star, phi)
+
+    xk_hist.append(xk)
+    yk_hist.append(yk)
+
+    # We need to now compute the mach angle
+    mue = mue_k(gamma, r_star)
+
+    mue_hist.append(mue)
+
+    # Gradients need to be 0 at the intial point which is vertical
+    mk_hist.append(0)
+    m_bar_k_hist.append(0)
+
+    # Wall co-ordinates are the same as the intial co-ordinates
+    xlk_hist.append(xk)
+    ylk_hist.append(yk)
+
+    # Finally, we do a co-ordinate transformation
+
+    [xlkt, ylkt] = transform_coord(xk, yk, alpha_l_i)
+
+    xlkt_hist.append(xlkt)
+    ylkt_hist.append(ylkt)
+
+    # Having established the delta_v, we can then loop through k values
+
+    for k in np.linspace(k_max, 1, num=k_max):
+        # We evaluate our phi angle
+        phi = phi_k(v_i, v_l, k, delta_v)
+
+        phi_hist.append(phi)
+
+        # We now must solver R* using the adjoint method
+        r_star = R_star(gamma, v_i, delta_v, k, 1)
+
+        r_star_hist.append(r_star)
+
+        # We can now compute the co-ordinates of the expansion line
+        [xk, yk] = vortex_coords(r_star, phi)
+
+        xk_hist.append(xk)
+        yk_hist.append(yk)
+
+        # We need to now compute the mach angle
+        mue = mue_k(gamma, r_star)
+
+        mue_hist.append(mue)
+
+        # We must thus compute the slope of the mach line, based on the average of the current point and previous (k+1)
+        m_k = mach_slope(phi_hist[k_max - k], phi, mue_hist[k_max - k], mue)
+
+        mk_hist.append(m_k)
+
+        # We can now compute the wall segment slope
+        m_bar_k = wall_slope(phi_hist[k_max - k])
+
+        m_bar_k_hist.append(m_bar_k)
+
+        # Wall Co-ordinates
+        [xlk, ylk] = wall_coords(xlk_hist, ylk_hist, yk_hist, xk_hist, m_bar_k, m_k)
+
+        xlk_hist.append(xlk)
+        ylk_hist.append(ylk)
+
+        # Finally, we do a co-ordinate transformation
+
+        [xlkt, ylkt] = transform_coord(xlk, ylk, alpha_l_i)
+
+        xlkt_hist.append(xlkt)
+        ylkt_hist.append(ylkt)
+
+    # Finally, we return the transformed co-ordinates
+
+    return [xlkt_hist, ylkt_hist]
diff --git a/src/turborocket/profiling/supersonic_profile.py b/src/turborocket/profiling/supersonic_profile.py
new file mode 100644
index 0000000..e912984
--- /dev/null
+++ b/src/turborocket/profiling/supersonic_profile.py
@@ -0,0 +1,7 @@
+# This file encapsulates the main function for computing the supersonic profile
+
+
+def supersonic_profile(beta_I, beta_o, M_i, M_o):
+    
+    # The first process required for the design of the supersonic blade profile is the definition of the upper and lower circular arcs.
+
diff --git a/src/turborocket/solvers/__pycache__/solver.cpython-311.pyc b/src/turborocket/solvers/__pycache__/solver.cpython-311.pyc
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diff --git a/src/turborocket/solvers/solver.py b/src/turborocket/solvers/solver.py
new file mode 100644
index 0000000..85304e4
--- /dev/null
+++ b/src/turborocket/solvers/solver.py
@@ -0,0 +1,62 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def adjoint(func, x_guess, dx, n, relax, target, params=[], RECORD_HIST=False):
+    # We first evaluate the error as a function of x
+
+    x_hist = []
+    guess_hist = []
+    error_hist = []
+    error_grad_hist = []
+    dx_hist = []
+
+    # We first evaluate the error of the guess
+    guess = func(x_guess, *params)
+
+    error = guess - target
+
+    guess_hist.append(guess)
+    error_hist.append(error)
+    x_hist.append(x_guess)
+    error_grad_hist.append(0)
+
+    for k in np.linspace(1, n, num=n, dtype=int):
+        # We now timestep in the x space
+        guess = func(x_hist[k - 1] + dx, *params)
+
+        error = guess - target
+
+        guess_hist.append(guess)
+        error_hist.append(error)
+        x_hist.append(x_hist[k - 1] + dx)
+        dx_hist.append(dx)
+        # Now we computed the gradient
+
+        error_grad = (error_hist[k] - error_hist[k - 1]) / (x_hist[k] - x_hist[k - 1])
+
+        error_grad_hist.append(error_grad)
+        if abs(error) < 1e-5:
+            break
+
+        # based on this gradient, we can thus find the new x-step based on this gradient # noqa: E501
+
+        dx = -(1 / error_grad) * error_hist[k] * relax
+
+    if RECORD_HIST is True:
+        plt.plot(x_hist, error_hist)
+
+        plt.show()
+
+        print("Guess History")
+        print(guess_hist)
+        print("Error History")
+        print(error_hist)
+        print("x History")
+        print(x_hist)
+        print("Error Grad History")
+        print(error_grad_hist)
+        print("Dx hist")
+        print(dx_hist)
+
+    return x_hist[k]
diff --git a/tests/profiling/supersonic/__pycache__/test_circular.cpython-311-pytest-7.4.4.pyc b/tests/profiling/supersonic/__pycache__/test_circular.cpython-311-pytest-7.4.4.pyc
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diff --git a/tests/profiling/supersonic/test_circular.py b/tests/profiling/supersonic/test_circular.py
new file mode 100644
index 0000000..21c7325
--- /dev/null
+++ b/tests/profiling/supersonic/test_circular.py
@@ -0,0 +1,46 @@
+from src.turborocket.profiling.Supersonic.circular import (
+    M_star,
+    prandtl_meyer,
+    arc_angles_lower,
+    arc_angles_upper,
+    beta_o,
+    A_rat,
+)
+
+import numpy as np
+
+
+def test_M_star():
+    assert np.isclose(M_star(1.4, 2), 1.63299316, rtol=1e-3)
+
+
+def test_prandtl_meyer():
+    assert np.isclose(prandtl_meyer(1.4, 1.63), 0.457243, rtol=1e-3)
+
+
+def test_arc_angles_lower():
+    alpha_l_i, alpha_l_o = arc_angles_lower(
+        -np.pi / 3, np.pi / 3, np.pi / 3, -np.pi / 3, np.pi / 2
+    )
+
+    assert np.isclose(alpha_l_i, 1.570796327, rtol=1e-3)
+
+    assert np.isclose(alpha_l_o, -3.665191429, rtol=1e-3)
+
+
+def test_arc_angles_upper():
+    alpha_u_i, alpha_u_o = arc_angles_upper(
+        -np.pi / 3, np.pi / 3, np.pi / 3, -np.pi / 3, np.pi / 2
+    )
+
+    assert np.isclose(alpha_u_i, 0.5235987759, rtol=1e-3)
+
+    assert np.isclose(alpha_u_o, 1.570796327, rtol=1e-3)
+
+
+def test_beta_o():
+    assert np.isclose(beta_o(2, 1.5, 1.4, np.pi / 4), -1.055440078, rtol=1e-3)
+
+
+def test_A_rat():
+    assert np.isclose(A_rat(np.pi / 4, -np.pi / 4), 1, rtol=1e-3)
diff --git a/tests/profiling/supersonic/test_transition.py b/tests/profiling/supersonic/test_transition.py
new file mode 100644
index 0000000..eecfc72
--- /dev/null
+++ b/tests/profiling/supersonic/test_transition.py
@@ -0,0 +1,69 @@
+from src.turborocket.profiling.Supersonic.transition import (
+    func_R_star,
+    func_R_star_k,
+    R_star,
+    phi_k,
+    vortex_coords,
+    mue_k,
+    mach_slope,
+    wall_slope,
+    wall_coords,
+    transform_coord,
+    moc,
+)
+
+import numpy as np
+
+
+def test_func_R_star():
+    assert np.isclose(func_R_star(0.9967412602371031, 1.4), -2.276853164, rtol=1e-3)
+
+
+def test_func_R_star_k():
+    assert np.isclose(func_R_star_k(1.4, np.pi, 2, 3), -3.993667857, rtol=1e-3)
+
+
+def test_R_star():
+    assert np.isclose(R_star(1.4, np.pi, 1.5708, 3, 1), 1, rtol=1e-3)
+
+
+def test_phi_k():
+    assert np.isclose(phi_k(np.pi / 2, np.pi / 4, 3, 1.57), -2.354601837, rtol=1e-3)
+
+
+def test_vortex_coords():
+    xk, yk = vortex_coords(0.8, np.pi / 2)
+
+    assert np.isclose(xk, -4 / 5, rtol=1e-3)
+
+    assert np.isclose(yk, 0, rtol=1e-3)
+
+
+def test_mue_k():
+    assert np.isclose(mue_k(1.4, 0.8), -0.8536095489, rtol=1e-3)
+
+
+def test_mach_slope():
+    assert np.isclose(
+        mach_slope(np.pi / 2, np.pi / 4, np.pi / 3, np.pi / 2), -0.767326988, rtol=1e-3
+    )
+
+
+def test_wall_slope():
+    assert np.isclose(wall_slope(np.pi / 4), 1, rtol=1e-3)
+
+
+def test_wall_coords():
+    xkl, ykl = wall_coords(1, 1, 0.8, 0.8, -0.76, 1)
+
+    assert np.isclose(xkl, 1, rtol=1e-3)
+
+    assert np.isclose(ykl, 1, rtol=1e-3)
+
+
+def test_transform_coord():
+    xklt, yklt = transform_coord(2, 3, np.pi / 3)
+
+    assert np.isclose(xklt, -1.598076, rtol=1e-3)
+
+    assert np.isclose(yklt, 3.232050808, rtol=1e-3)
diff --git a/tests/solvers/__pycache__/test_solver.cpython-311-pytest-7.4.4.pyc b/tests/solvers/__pycache__/test_solver.cpython-311-pytest-7.4.4.pyc
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diff --git a/tests/solvers/test_solver.py b/tests/solvers/test_solver.py
new file mode 100644
index 0000000..f87003b
--- /dev/null
+++ b/tests/solvers/test_solver.py
@@ -0,0 +1,11 @@
+from src.turborocket.solvers.solver import adjoint
+
+import pytest
+
+
+def dummy_function(x):
+    return x**2 - 4
+
+
+def test_adjoint():
+    assert adjoint(dummy_function, 4, 0.1, 100, 0.6, 0) == pytest.approx(2, 1e-3)

From 2e84e029813bac3c38e6a7ee38194171366054c9 Mon Sep 17 00:00:00 2001
From: Elias Aoubala <2432537A@student.gla.ac.uk>
Date: Wed, 24 Jan 2024 22:40:22 +0000
Subject: [PATCH 2/2] Fixed local .gitignore for caches

---
 .gitignore                                      |   1 +
 .../__pycache__/circular.cpython-311.pyc        | Bin 4189 -> 0 bytes
 .../__pycache__/transition.cpython-311.pyc      | Bin 7073 -> 0 bytes
 .../solvers/__pycache__/solver.cpython-311.pyc  | Bin 2457 -> 0 bytes
 .../test_circular.cpython-311-pytest-7.4.4.pyc  | Bin 13462 -> 0 bytes
 ...test_transition.cpython-311-pytest-7.4.4.pyc | Bin 24189 -> 0 bytes
 .../test_solver.cpython-311-pytest-7.4.4.pyc    | Bin 3098 -> 0 bytes
 7 files changed, 1 insertion(+)
 create mode 100644 .gitignore
 delete mode 100644 src/turborocket/profiling/Supersonic/__pycache__/circular.cpython-311.pyc
 delete mode 100644 src/turborocket/profiling/Supersonic/__pycache__/transition.cpython-311.pyc
 delete mode 100644 src/turborocket/solvers/__pycache__/solver.cpython-311.pyc
 delete mode 100644 tests/profiling/supersonic/__pycache__/test_circular.cpython-311-pytest-7.4.4.pyc
 delete mode 100644 tests/profiling/supersonic/__pycache__/test_transition.cpython-311-pytest-7.4.4.pyc
 delete mode 100644 tests/solvers/__pycache__/test_solver.cpython-311-pytest-7.4.4.pyc

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ed8ebf5
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+__pycache__
\ No newline at end of file
diff --git a/src/turborocket/profiling/Supersonic/__pycache__/circular.cpython-311.pyc b/src/turborocket/profiling/Supersonic/__pycache__/circular.cpython-311.pyc
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