airfoil_simulation/sourcePanelMethod.py at main · camerondix/airfoil_simulation · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
from panelGeometry import Point, Panel
import math
import csv
import matplotlib
import numpy as np


# Methods


def computeLambdas(panels: list, freestreamVelocity: float) -> list:
    for index, panel in enumerate(panels):
        if panel.startPoint.x - panels[index - 1].endPoint.x > 0.00000001:
            raise Exception("Panels must form a closed path.")
        if panel.startPoint.y - panels[index - 1].endPoint.y > 0.00000001:
            raise Exception("Panels must form a closed path.")
    matrixA = []
    matrixB = []
    for paneli in panels:
        lambdas = []
        for panelj in panels:
            if paneli == panelj:
                lambdas.append(1 / 2)
            else:
                a = -(paneli.controlPoint.x - panelj.startPoint.x) * math.cos(
                    panelj.phi
                ) - (paneli.controlPoint.y - panelj.startPoint.y) * math.sin(panelj.phi)
                b = (paneli.controlPoint.x - panelj.startPoint.x) ** 2 + (
                    paneli.controlPoint.y - panelj.startPoint.y
                ) ** 2
                c = math.sin(paneli.phi - panelj.phi)
                d = (paneli.controlPoint.y - panelj.startPoint.y) * math.cos(
                    paneli.phi
                ) - (paneli.controlPoint.x - panelj.startPoint.x) * math.sin(paneli.phi)
                Sj = math.sqrt(
                    (panelj.endPoint.x - panelj.startPoint.x) ** 2
                    + (panelj.endPoint.y - panelj.startPoint.y) ** 2
                )
                e = (paneli.controlPoint.x - panelj.startPoint.x) * math.sin(
                    panelj.phi
                ) - (paneli.controlPoint.y - panelj.startPoint.y) * math.cos(panelj.phi)
                integral = (c / 2) * math.log((Sj ** 2 + 2 * a * Sj + b) / b) + (
                    (d - a * c) / e
                ) * (math.atan((Sj + a) / e) - math.atan(a / e))
                lambdas.append(integral / (2 * math.pi))
        matrixA.append(lambdas)
        matrixB.append(-freestreamVelocity * math.cos(paneli.beta))
    lambdas = np.linalg.solve(matrixA, matrixB)
    return lambdas


def computeGammas(panels: list, freestreamVelocity: float) -> list:
    for index, panel in enumerate(panels):
        if panel.startPoint.x - panels[index - 1].endPoint.x > 0.00000001:
            raise Exception("Panels must form a closed path.")
        if panel.startPoint.y - panels[index - 1].endPoint.y > 0.00000001:
            raise Exception("Panels must form a closed path.")
    matrixA = []
    matrixB = []
    for paneli in panels:
        gamas = []
        for panelj in panels:
            if paneli == panelj:
                gamas.append(1)
            else:
                a = -(paneli.controlPoint.x - panelj.startPoint.x) * math.cos(
                    panelj.phi
                ) - (paneli.controlPoint.y - panelj.startPoint.y) * math.sin(panelj.phi)
                b = (paneli.controlPoint.x - panelj.startPoint.x) ** 2 + (
                    paneli.controlPoint.y - panelj.startPoint.y
                ) ** 2
                c = math.sin(paneli.phi - panelj.phi)
                d = (paneli.controlPoint.y - panelj.startPoint.y) * math.cos(
                    paneli.phi
                ) - (paneli.controlPoint.x - panelj.startPoint.x) * math.sin(paneli.phi)
                Sj = math.sqrt(
                    (panelj.endPoint.x - panelj.startPoint.x) ** 2
                    + (panelj.endPoint.y - panelj.startPoint.y) ** 2
                )
                e = (paneli.controlPoint.x - panelj.startPoint.x) * math.sin(
                    panelj.phi
                ) - (paneli.controlPoint.y - panelj.startPoint.y) * math.cos(panelj.phi)
                integral = (c / 2) * math.log((Sj ** 2 + 2 * a * Sj + b) / b) + (
                    (d - a * c) / e
                ) * (math.atan((Sj + a) / e) - math.atan(a / e))
                gamas.append(integral / (2 * math.pi))
        matrixA.append(gamas)
        matrixB.append(freestreamVelocity * math.cos(paneli.beta))
    kuttaCond = list(np.zeros(len(gamas)))
    kuttaCond[0] = 1
    kuttaCond[-1] = 1
    matrixA[-1] = kuttaCond
    matrixB[-1] = 0
    gamas = np.linalg.solve(matrixA, matrixB)
    return gamas


def computeCpsFromLambdas(
    panels: list, lambdas: list, freestreamVelocity: float
) -> tuple:
    accuracy = 0
    cps = []
    for paneli in panels:
        vi = 0
        for panelj, lamj in zip(panels, lambdas):
            if paneli == panelj:
                vi += freestreamVelocity * math.sin(paneli.beta)
                accuracy += lamj * panelj.length
            else:
                a = -(paneli.controlPoint.x - panelj.startPoint.x) * math.cos(
                    panelj.phi
                ) - (paneli.controlPoint.y - panelj.startPoint.y) * math.sin(panelj.phi)
                b = (paneli.controlPoint.x - panelj.startPoint.x) ** 2 + (
                    paneli.controlPoint.y - panelj.startPoint.y
                ) ** 2
                c = math.sin(paneli.phi - panelj.phi)
                d = (paneli.controlPoint.y - panelj.startPoint.y) * math.cos(
                    paneli.phi
                ) - (paneli.controlPoint.x - panelj.startPoint.x) * math.sin(paneli.phi)
                Sj = math.sqrt(
                    (panelj.endPoint.x - panelj.startPoint.x) ** 2
                    + (panelj.endPoint.y - panelj.startPoint.y) ** 2
                )
                e = (paneli.controlPoint.x - panelj.startPoint.x) * math.sin(
                    panelj.phi
                ) - (paneli.controlPoint.y - panelj.startPoint.y) * math.cos(panelj.phi)
                integral = ((d - a * c) / (2 * e)) * math.log(
                    (Sj ** 2 + 2 * a * Sj + b) / b
                ) - c * (math.atan((Sj + a) / e) - math.atan(a / e))
                vi += (lamj / (2 * math.pi)) * integral
        cps.append(1 - (vi / freestreamVelocity) ** 2)
    print(f"Accuracy: {accuracy}")
    return cps, accuracy


def computeCpsFromGammas(panels: list, gammas: list, freestreamVelocity: float) -> list:
    cps = []
    for panelj, gamj in zip(panels, gammas):
        dx = panelj.startPoint.x - panelj.endPoint.x
        dy = panelj.startPoint.y - panelj.endPoint.y
        cps.append(1 - (gamj / freestreamVelocity) ** 2)
    return cps