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
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
|
{
"metadata": {
"name": "",
"signature": "sha256:c40ddac3b7701237847f45087b69fa1d6ec2c89a5cfffd6cb1ce1ff8fa694b86"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter4-Axial-flow Turbines:Two-dimensional Theory"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg101"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the\n",
"\n",
"##given data\n",
"phi = 0.4;\n",
"epsilon = 28.6;##in deg\n",
"\n",
"##calculations\n",
"alpha2 = (180./math.pi)*math.atan(1./phi);##in deg\n",
"zeta = 0.04*(1+ 1.5*(alpha2/100.)**2);\n",
"eta = 1 + (phi**2)*(zeta*((1./math.cos(math.pi*alpha2/180.))**2) +0.5);\n",
"\n",
"##results\n",
"print'%s %.2f %s'%('The efficiency = ',1/eta,'');\n",
"print('This value appears to be the same as the peak value of efficiency curve.\\n');\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The efficiency = 0.86 \n",
"This value appears to be the same as the peak value of efficiency curve.\n",
"\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg105"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the\n",
"\n",
"##given data\n",
"alpha2 = 70.;##in deg\n",
"p01 = 311.;##in kPa\n",
"T01 = 850.;##in degC\n",
"p3 = 100.;##in kPa\n",
"eff_tot_stat = 0.87;\n",
"U = 500.;##in m/s\n",
"Cp = 1.148;##in kJ/(kgC)\n",
"gamma = 1.33;\n",
"\n",
"##Calculations\n",
"delW = eff_tot_stat*Cp*(T01+273.15)*(1.-(p3/p01)**((gamma-1.)/gamma));##specific work\n",
"cy2 = delW*1000./U;##in m/s\n",
"c2 = cy2/math.sin(math.pi*alpha2/180.);##in m/s\n",
"T2 = (T01+273.15) - 0.5*(c2**2)/(Cp*1000.);##Nozzle exit temperature in K\n",
"M2 = c2/math.sqrt(gamma*287.*T2);##Nozzle exit mach number\n",
"cx = c2*math.cos(math.pi*alpha2/180.);##axial velocity in m/s\n",
"eff_tot_tot = 1./((1./eff_tot_stat)-((cx**2)/(2.*1000.*delW)));##Total to total efficiency\n",
"R = 1. - 0.5*(cx/U)*math.tan(math.pi*alpha2/180.);##stage reaction\n",
"\n",
"##results\n",
"print'%s %.2f %s'%('(i) The specific work done =',delW,' kJ/kg.\\n');\n",
"print'%s %.2f %s'%('(ii) The Mach number leaving the nozzle = ',M2,'');\n",
"print'%s %.2f %s'%('(iii) The axial velocity = .\\n',cx,'m/s');\n",
"print'%s %.2f %s'%('(iv) The total-to-total efficiency = .\\n',eff_tot_tot,'');\n",
"print'%s %.2f %s'%('(v) The stage reaction = .\\n',R,'');\n",
"\n",
"\n",
"##there are small errors in the answers given in the book\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) The specific work done = 275.24 kJ/kg.\n",
"\n",
"(ii) The Mach number leaving the nozzle = 0.96 \n",
"(iii) The axial velocity = .\n",
" 200.36 m/s\n",
"(iv) The total-to-total efficiency = .\n",
" 0.93 \n",
"(v) The stage reaction = .\n",
" 0.45 \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg106"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the\n",
"\n",
"##given data\n",
"H_b = 5.0;##average bladeaspect ratio for the stage\n",
"t_c = 0.2;##max. blade thickness to chord ratio\n",
"Re = 1*10**5;##average Reynolds number\n",
"cx = 200.;##in m/s\n",
"cy2 = 552.;##in m/s\n",
"U = 500.;##in m/s\n",
"c2 = 588.;##in m/s\n",
"delW = 276.;##in kJ\n",
"c3 = 200.;##in m/s\n",
"Cp = 1.148;##in kJ/(kgC)\n",
"T2 = 973.;##in K\n",
"T01 = 1123.;##in K\n",
"alpha1 = 0.;##in deg\n",
"alpha2 = 70.;##in deg\n",
"\n",
"##calculations\n",
"eps = alpha1 + alpha2;##in deg\n",
"zetaN = 0.04*(1. + 1.5*(eps/100.)**2);\n",
"zetaN1 = (1.+zetaN)*(0.993 + 0.021/H_b) - 1;\n",
"beta2 = (180./math.pi)*math.atan((cy2-U)/cx);\n",
"beta3 = (180./math.pi)*math.atan(U/cx);\n",
"epsR = beta2 + beta3;\n",
"zetaR = 0.04*(1. + 1.5*(epsR/100.)**2);\n",
"zetaR1 = (1.+zetaR)*(0.975 + 0.075/H_b) - 1;\n",
"w3_U = math.sqrt(1.+(cx/U)**2);\n",
"eff_ts = 1./(1. + (zetaR1*w3_U + zetaN1*((c2/U)**2) + (cx/U)**2)/(2.*cy2/U));\n",
"T3 = T01 - (delW*1000. + 0.5*c3**2.)/(Cp*1000.);\n",
"eff_ts1 = 1/(1. + (zetaR1*(w3_U)**2 + (T3/T2)*zetaN1*((c2/U)**2.) + (cx/U)**2.)/(2.*cy2/U));\n",
"\n",
"##Results\n",
"print'%s %.2f %s'%('The total-to static efficiency = ',eff_ts,'');\n",
"print('\\n The result is very close to the value assumed in first example.')\n",
"print'%s %.2f %s'%('\\n The total-to-static efficiency after including the temperature ratio in the equation = ',eff_ts1,'');\n",
"\n",
"##there are small errors in the answers given in the book\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total-to static efficiency = 0.87 \n",
"\n",
" The result is very close to the value assumed in first example.\n",
"\n",
" The total-to-static efficiency after including the temperature ratio in the equation = 0.87 \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg119"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the\n",
"\n",
"##given data\n",
"T02 = 1200.;##in K\n",
"p01 = 4.0;##in bar\n",
"dt = 0.75;##tip diameter in m\n",
"hb = 0.12;##blade height in m\n",
"v = 10500.;##shaft speed in rev/min\n",
"R = 0.5;##degree of reaction at mean radius\n",
"phi = 0.7;##flow coefficient\n",
"psi = 2.5;##stage loading coefficient\n",
"eff_noz = 0.96;##Nozzle efficiency\n",
"Cp = 1160.;##in kJ/(kgC)\n",
"gamma = 1.33;\n",
"Rg = 287.8;##specific gas constant\n",
"A2 = 0.2375;##in m^2\n",
"K = 2/3.;##stress taper factor\n",
"rho = 8000.;##in kg/m^3\n",
"\n",
"##calculations\n",
"beta3 = (180./math.pi)*math.atan((0.5*psi + R)/phi);\n",
"beta2 = (180./math.pi)*math.atan((0.5*psi - R)/phi);\n",
"alpha2 = beta3;\n",
"alpha3 = beta2;\n",
"rm = (dt-hb)/2.;\n",
"Um = (v/30.)*math.pi*rm;\n",
"cx = phi*Um;\n",
"c2 = cx/(math.cos(alpha2*math.pi/180.));\n",
"T2 = T02 - 0.5*(c2**2)/Cp;\n",
"p2 = p01*((1-((1.-(T2/T02))/eff_noz))**(gamma/(gamma-1.)));\n",
"mdot = ((p2*10**5)/(Rg*T2))*A2*cx;\n",
"Ut = (v/30.)*math.pi*0.5*dt; \n",
"sig_rho = K*0.5*(Ut**2)*(1-((dt-2.*hb)/dt)**2);\n",
"sig1 = rho*sig_rho;\n",
"Tb = T2 + 0.85*((cx/math.cos(beta2*math.pi/180.))**2.)/(2.*Cp);\n",
"\n",
"##Results\n",
"print'%s %.2f %s %.2f %s'%('(i)The relative and absolute angles for the flow: \\n beta3 = ',beta3,' deg' and 'beta2 = ',beta2,' deg.');\n",
"print'%s %.2f %s %.2f %s'%(' alpha2 = ',alpha2,' deg' and 'alpha3 = ',alpha3,'deg.');\n",
"print'%s %.2f %s'%('\\n (ii) The velocity at nozzle exit = ',c2,' m/s');\n",
"print'%s %.2f %s %.2f %s %.2f %s '%('\\n (iii)The static temperature and pressure at nozzle exit assuming a nozzle efficiency of ',eff_noz,''and ': \\n T2 = ',T2,'K'and '\\n p2 =',p2,' bar');\n",
"print'%s %.2f %s' %('\\n and mass flow = ',mdot,'kg/s');\n",
"print'%s %.2f %s %.2f %s '%('\\n (iv)The rotor blade root stress assuming the blade is tapered with a stress taper factor K of 2/3 and \\n the blade material density is ',rho,' kg/m2'and ' =',sig1/(10**6),' MPa');\n",
"print'%s %.2f %s'%('\\n (v) The approximate average mean blade temperature is Tb = ',Tb,' K');\n",
"\n",
"\n",
"\n",
"#\n",
"\n",
"##there are very small errors in the answers given in textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i)The relative and absolute angles for the flow: \n",
" beta3 = 68.20 beta2 = 46.97 deg.\n",
" alpha2 = 68.20 alpha3 = 46.97 deg.\n",
"\n",
" (ii) The velocity at nozzle exit = 652.82 m/s\n",
"\n",
" (iii)The static temperature and pressure at nozzle exit assuming a nozzle efficiency of 0.96 1016.30 \n",
" p2 = 1.99 bar \n",
"\n",
" and mass flow = 39.10 kg/s\n",
"\n",
" (iv)The rotor blade root stress assuming the blade is tapered with a stress taper factor K of 2/3 and \n",
" the blade material density is 8000.00 = 243.74 MPa \n",
"\n",
" (v) The approximate average mean blade temperature is Tb = 1062.56 K\n"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}
|
