From a3ca4a70d41f42986412253725cc9b276226f6cf Mon Sep 17 00:00:00 2001
From: Ilan Upfal <103550915+iupfal@users.noreply.github.com>
Date: Tue, 8 Apr 2025 20:35:50 -0400
Subject: [PATCH] fix initial wake velocities

---
 MITRotor/BEMSolver.py              | 16 ++-----
 MITRotor/Momentum.py               | 42 +++++++++++++---
 examples/MITRotor_quickstart.ipynb | 77 ++++++++----------------------
 examples/example_01_basic_BEM.py   |  4 +-
 4 files changed, 63 insertions(+), 76 deletions(-)

diff --git a/MITRotor/BEMSolver.py b/MITRotor/BEMSolver.py
index b5b5722..42817a7 100644
--- a/MITRotor/BEMSolver.py
+++ b/MITRotor/BEMSolver.py
@@ -41,10 +41,8 @@ class BEMSolution:
     geom: BEMGeometry = field(repr=False)
     converged: bool
     niter: int
-
-    def __post_init__(self):
-        sol = Heck()(self.Ctprime(), self.yaw)
-        self._u4, self._v4 = sol.u4, sol.v4
+    u4: float
+    v4: float
 
     def a(self, grid: Literal["sector", "annulus", "rotor"] = "rotor"):
         return average(self.geom, self.aero_props.an, grid)
@@ -99,12 +97,6 @@ def Ctau_uncorr(self, grid: Literal["sector ", "annulus", "rotor"] = "rotor"):
 
     def F(self, grid: Literal["sector", "annulus", "rotor"] = "rotor"):
         return average(self.geom, self.aero_props.F, grid)
-
-    def u4(self):
-        return self._u4
-
-    def v4(self):
-        return self._v4
     
     def Cp(self, grid: Literal["sector", "annulus", "rotor"] = "rotor"):
         dCp = (
@@ -218,5 +210,7 @@ def post_process(self, result: FixedPointIterationResult, pitch, tsr, yaw, U=Non
         an, aprime = result.x
         aero_props = self.aerodynamic_model(an, aprime, pitch, tsr, yaw, self.rotor, self.geometry, U, wdir)
         aero_props.F = self.tiploss_model(aero_props, pitch, tsr, yaw, self.rotor, self.geometry)
+        avg_Ct = average(self.geometry, aero_props.C_x)
+        u4,v4 = self.momentum_model.compute_initial_wake_velocities(avg_Ct, yaw)
 
-        return BEMSolution(pitch, tsr, yaw, aero_props, self.geometry, result.converged, result.niter)
+        return BEMSolution(pitch, tsr, yaw, aero_props, self.geometry, result.converged, result.niter, u4, v4)
diff --git a/MITRotor/Momentum.py b/MITRotor/Momentum.py
index 9252427..63edbe8 100644
--- a/MITRotor/Momentum.py
+++ b/MITRotor/Momentum.py
@@ -21,10 +21,6 @@
 
 
 class MomentumModel(ABC):
-    @abstractmethod
-    def compute_induction(self, Cx: ArrayLike, yaw: float) -> ArrayLike:
-        ...
-
     @abstractmethod
     def __call__(
         self,
@@ -36,6 +32,16 @@ def __call__(
         geom: "BEMGeometry",
     ) -> ArrayLike:
         ...
+
+    @abstractmethod
+    def compute_induction(self, Cx: ArrayLike, yaw: float) -> ArrayLike:
+        ...
+
+    @abstractmethod
+    def compute_initial_wake_velocities(self, Ct: float, yaw: float) -> ArrayLike:
+        ...
+
+
     
     def _func_rotor(
         self,
@@ -109,9 +115,13 @@ class ConstantInduction(MomentumModel):
     def __init__(self, a = 1/3):
         self.a = a
 
-    def _func(self, aero_props, pitch, tsr, yaw, rotor, geom) -> ArrayLike:
+    def compute_induction(self, Cx, yaw) -> ArrayLike:
         return self.a * np.ones_like(yaw)
-
+    
+    def compute_initial_wake_velocities(self, Ct: float, yaw: float) -> ArrayLike:
+        u4 = 1 - 2 * self.a
+        v4 = - (1/4) * Ct * np.sin(yaw)
+        return u4, v4
 
 
 class ClassicalMomentum(MomentumModel):
@@ -128,6 +138,11 @@ def __init__(self, averaging: Literal["sector", "annulus", "rotor"] = "rotor"):
 
     def compute_induction(self, Cx, yaw):
         return 0.5 * (1 - np.sqrt(1 - Cx))
+    
+    def compute_initial_wake_velocities(self, Ct: float, yaw: float) -> ArrayLike:
+        u4 = np.sqrt(1 - Ct)
+        v4 = - (1/4) * Ct * np.sin(yaw)
+        return u4, v4
 
 
 
@@ -167,6 +182,12 @@ def compute_induction(self, Cx: ArrayLike, yaw: float) -> ArrayLike:
                 a[mask] = (Cx[mask] - Ctc) / slope + self.ac
 
         return a
+    
+    def compute_initial_wake_velocities(self, Ct: float, yaw: float) -> ArrayLike:
+        a = self.compute_induction(Ct, yaw)
+        u4 = 1 - Ct /(2  * (1 - a))
+        v4 = - (1/4) * Ct * np.sin(yaw)
+        return u4, v4
 
 
 class UnifiedMomentum(MomentumModel):
@@ -192,6 +213,10 @@ def __init__(self, averaging: Literal["sector", "annulus", "rotor"] = "rotor", b
     def compute_induction(self, Cx: ArrayLike, yaw: float) -> ArrayLike:
         sol = self.model_Ct(Cx, yaw)
         return sol.an
+    
+    def compute_initial_wake_velocities(self, Ct: float, yaw: float) -> ArrayLike:
+        sol = self.model_Ct(Ct, yaw)
+        return sol.u4[0], sol.v4[0]
 
 
 class MadsenMomentum(MomentumModel):
@@ -222,3 +247,8 @@ def compute_induction(self, Cx: ArrayLike, yaw: float) -> ArrayLike:
 
         an = Ct**3 * 0.0883 + Ct**2 * 0.0586 + Ct * 0.2460
         return an
+
+    def compute_initial_wake_velocities(self, Ct: float, yaw: float) -> ArrayLike:
+        u4 = np.sqrt(1 - Ct)
+        v4 = - (1/4) * Ct * np.sin(yaw)
+        return u4, v4
diff --git a/examples/MITRotor_quickstart.ipynb b/examples/MITRotor_quickstart.ipynb
index 76e89ab..7f53cd5 100644
--- a/examples/MITRotor_quickstart.ipynb
+++ b/examples/MITRotor_quickstart.ipynb
@@ -20,7 +20,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -63,7 +63,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -94,11 +94,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
-    "rotor_geometry = mr.BEMGeometry(Nr = 100, Ntheta = 30)"
+    "rotor_geometry = mr.BEMGeometry(Nr = 20, Ntheta = 30)"
    ]
   },
   {
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -159,7 +159,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -182,7 +182,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -205,7 +205,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -224,7 +224,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -234,7 +234,7 @@
     "    tiploss_model = prandtl_tip_loss,\n",
     "    momentum_model = unified_momentum_model,\n",
     "    tangential_induction_model = tangential_induction_model,\n",
-    "    aerodynamic_model = default_aerodynamic_model\n",
+    "    aerodynamic_model = kragh_aerodynamic_model\n",
     ")"
    ]
   },
@@ -254,25 +254,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "BEM solution converged in 29 iterations.\n",
-      "Control setpoints: sol.pitch=0.00, sol.tsr=7.00, sol.yaw=0.35\n",
-      "Power coefficient: 0.42\n",
-      "Thrust coefficient: 0.63\n",
-      "Local thrust coefficient: 1.12\n",
-      "Axial induction: 0.20\n",
-      "Rotor-effective windspeed: 1.00\n",
-      "Far-wake streamwise velocity: 0.60\n",
-      "Far-wake lateral velocity: -0.05\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "pitch, tsr, yaw = np.deg2rad(0), 7.0, np.deg2rad(20.0)\n",
     "sol = bem_model(pitch, tsr, yaw)\n",
@@ -289,8 +273,8 @@
     "print(f\"Local thrust coefficient: {sol.Ctprime():2.2f}\")\n",
     "print(f\"Axial induction: {sol.a():2.2f}\")\n",
     "print(f\"Rotor-effective windspeed: {sol.U():2.2f}\")\n",
-    "print(f\"Far-wake streamwise velocity: {sol.u4():2.2f}\")\n",
-    "print(f\"Far-wake lateral velocity: {sol.v4():2.2f}\")\n"
+    "print(f\"Far-wake streamwise velocity: {sol.u4:2.2f}\")\n",
+    "print(f\"Far-wake lateral velocity: {sol.v4:2.2f}\")\n"
    ]
   },
   {
@@ -302,30 +286,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0.0, 1.0)"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 3 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "fig, axes = plt.subplots(3, 1, sharex=True)\n",
     "axes[0].plot(sol.geom.mu, sol.Cp(grid=\"annulus\"), label=\"$C_P$\")\n",
@@ -361,7 +324,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.6"
+   "version": "3.9.13"
   }
  },
  "nbformat": 4,
diff --git a/examples/example_01_basic_BEM.py b/examples/example_01_basic_BEM.py
index 87940cd..0d0168c 100644
--- a/examples/example_01_basic_BEM.py
+++ b/examples/example_01_basic_BEM.py
@@ -23,5 +23,5 @@
     print(f"Local thrust coefficient: {sol.Ctprime():2.2f}")
     print(f"Axial induction: {sol.a():2.2f}")
     print(f"Rotor-effective windspeed: {sol.U():2.2f}")
-    print(f"Far-wake streamwise velocity: {sol.u4():2.2f}")
-    print(f"Far-wake lateral velocity: {sol.v4():2.2f}")
+    print(f"Far-wake streamwise velocity: {sol.u4:2.2f}")
+    print(f"Far-wake lateral velocity: {sol.v4:2.2f}")