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
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
|
{
"metadata": {
"name": "",
"signature": "sha256:58be2ba5e7552ab96c774dd3b25145aaa3c2ce840367ab463ac8e75c36ccb849"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter5-Axial-flow Compressors and Fans"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg156"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the\n",
"\n",
"##given data\n",
"T01 = 293.;##in K\n",
"pi = 5.;##pressure ratio\n",
"R = 0.5;##stage reaction\n",
"Um = 275.;##in m/s\n",
"phi = 0.5;##flow coefficient\n",
"psi = 0.3;##stage loading factor\n",
"eff_stage = 0.888;##stage efficiency\n",
"Cp = 1005.;##J/(kgC)\n",
"gamma = 1.4;\n",
"\n",
"##Calculations\n",
"beta1 = (180./math.pi)*math.atan((R + 0.5*psi)/phi);\n",
"beta2 = (180./math.pi)*math.atan((R - 0.5*psi)/phi);\n",
"alpha2 = beta1;\n",
"alpha1 = beta2;\n",
"delT0 = psi*(Um**2)/Cp;\n",
"N = (T01/delT0)*((pi**((gamma-1.)/(eff_stage*gamma))) - 1.);\n",
"N = math.ceil(N);\n",
"eff_ov = ((pi**((gamma-1.)/gamma)) - 1.)/((pi**((gamma-1.)/(eff_stage*gamma))) - 1.);\n",
"print'%s %.2f %s %.2f %s'%('The flow angles are: beta1 = alpha2 = ',beta1,' deg' and 'beta2 = alpha1 = ',math.ceil(beta2),' deg.');\n",
"print'%s %.2f %s '%('\\n The number of stages required = ',N,'');\n",
"print'%s %.2f %s'%('\\n The overall efficiency = ',eff_ov*100,' percentage');\n",
"\n",
"##there is a small error in the answer given in textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The flow angles are: beta1 = alpha2 = 52.43 beta2 = alpha1 = 35.00 deg.\n",
"\n",
" The number of stages required = 9.00 \n",
"\n",
" The overall efficiency = 86.06 percentage\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg160"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the\n",
"\n",
"##given data\n",
"R = 0.5;##stage reaction\n",
"s_c = 0.9;##space-chord ratio\n",
"beta1_ = 44.5;##in deg\n",
"beta2_ = -0.5;##in deg\n",
"h_c = 2.0;##height-chord ratio\n",
"lamda = 0.86;##work done factor\n",
"i = 0.4;##mean radius relative incidence\n",
"rho = 3.5;##density in kg/m^3\n",
"Um = 242.;##in m/s\n",
"eps_max = 37.5;##in deg\n",
"eps = 37.5;##in deg\n",
"delp0 = 0.032;##the profile total pressure loss coefficient\n",
"##Calculations\n",
"theta = beta1_ - beta2_;\n",
"deltaN = (0.229*theta*(s_c**0.5))/(1 - (theta*(s_c**0.5)/500.));\n",
"beta2N = deltaN + beta2_;\n",
"eps_ = 0.8*eps_max;\n",
"i_ = beta2N + eps_ - beta1_;\n",
"i = 0.4*eps_ + i_;\n",
"beta1 = beta1_ + i;\n",
"beta2 = beta1 - eps;\n",
"alpha2 = beta1;\n",
"alpha1 = beta2;\n",
"phi = 1/(math.tan(alpha1*math.pi/180.) + math.tan(beta1*math.pi/180.));\n",
"psi = lamda*phi*(math.tan(alpha2*math.pi/180.) - math.tan(alpha1*math.pi/180.));\n",
"betam = (180./math.pi)*math.atan(0.5*(math.tan(beta1*math.pi/180.) + math.tan(beta2*math.pi/180.)));\n",
"CL = 2*s_c*math.cos(betam*math.pi/180.)*(math.tan(beta1*math.pi/180.) - math.tan(beta2*math.pi/180.));\n",
"CDp = s_c*(delp0)*((math.cos(betam*math.pi/180.))**3)/((math.cos(beta1*math.pi/180.))**2);\n",
"CDa = 0.02*s_c/h_c;\n",
"CDx = 0.018*CL**2;\n",
"CD = CDp + CDa + CDx;\n",
"eff_tt = 1. - (CD*phi**2)/(psi*s_c*((math.cos(betam*math.pi/180.))**3));\n",
"delp = eff_tt*psi*rho*Um**2;\n",
"\n",
"##Results\n",
"print'%s %.2f %s %.2f %s'%('(i)The nominal deflection= ',eps_,' deg'and '.\\n the nominal incidence = ',i_,' deg.');\n",
"print'%s %.2f %s %.2f %s '%('\\n (ii)The inlet flow angle, beta1 = alpha2 = ',beta1,' deg'and '\\n outlet flow angle beta2 = alpha1 = ',beta2,' deg.');\n",
"print'%s %.2f %s %.2f %s '%('\\n (iii)The flow coefficient = ',phi,''and '\\nThe stage loading factor = ',psi,'');\n",
"print'%s %.2f %s'%('\\n (iv) The rotor lift coefficient = ',CL,'');\n",
"print'%s %.2f %s '%('\\n (v) The overall drag coefficient of each row = ',CD,'');\n",
"print'%s %.2f %s %.2f %s'%('\\n (vi) The total-to-total stage efficiency = ',eff_tt,''and '\\n The pressure rise across the stage =',delp/1000,' kPa');\n",
"\n",
"\n",
"##there are small errors in the answers given in textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i)The nominal deflection= 30.00 .\n",
" the nominal incidence = -4.31 deg.\n",
"\n",
" (ii)The inlet flow angle, beta1 = alpha2 = 52.19 \n",
" outlet flow angle beta2 = alpha1 = 14.69 deg. \n",
"\n",
" (iii)The flow coefficient = 0.64 0.57 \n",
"\n",
" (iv) The rotor lift coefficient = 1.46 \n",
"\n",
" (v) The overall drag coefficient of each row = 0.09 \n",
"\n",
" (vi) The total-to-total stage efficiency = 0.86 100.34 kPa\n"
]
}
],
"prompt_number": 2
}
],
"metadata": {}
}
]
}
|
