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Rarefied Gas Dynamics


Rarefied Gas Dynamics

Fundamentals for Research and Practice
1. Aufl.

von: Felix Sharipov

111,99 €

Verlag: Wiley-VCH
Format: PDF
Veröffentl.: 16.11.2015
ISBN/EAN: 9783527685073
Sprache: englisch
Anzahl Seiten: 328

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Beschreibungen

<p>Aimed at both researchers and professionals who deal with this topic in their routine work, this introduction provides a coherent and rigorous access to the field including relevant methods for practical applications. No preceding knowledge of gas dynamics is assumed.</p>
<p>Preface XIII</p> <p>List of Symbols XV</p> <p>List of Acronyms XXI</p> <p><b>1 Molecular Description 1</b></p> <p>1.1 Mechanics of Continuous Media and Its Restriction 1</p> <p>1.2 Macroscopic State Variables 2</p> <p>1.3 Dilute Gas 3</p> <p>1.4 Intermolecular Potential 4</p> <p>1.4.1 Definition of Potential 4</p> <p>1.4.2 Hard Sphere Potential 4</p> <p>1.4.3 Lennard-Jones Potential 5</p> <p>1.4.4 Ab initio Potential 5</p> <p>1.5 Deflection Angle 7</p> <p>1.6 Differential Cross Section 8</p> <p>1.7 Total Cross Section 9</p> <p>1.8 Equivalent Free Path 10</p> <p>1.9 Rarefaction Parameter and Knudsen Number 10</p> <p><b>2 Velocity Distribution Function 13</b></p> <p>2.1 Definition of Distribution Function 13</p> <p>2.2 Moments of Distribution Function 15</p> <p>2.3 Entropy and Its Flow Vector 18</p> <p>2.4 Global Maxwellian 18</p> <p>2.5 Local Maxwellian 20</p> <p><b>3 Boltzmann Equation 23</b></p> <p>3.1 Assumptions to Derive the Boltzmann Equation 23</p> <p>3.2 General Form of the Boltzmann Equation 23</p> <p>3.3 Conservation Laws 25</p> <p>3.4 Entropy Production due to Intermolecular Collisions 27</p> <p>3.5 Intermolecular Collisions Frequency 27</p> <p><b>4 Gas–Surface Interaction 31</b></p> <p>4.1 General form of Boundary Condition for Impermeable Surface 31</p> <p>4.2 Diffuse–Specular Kernel 33</p> <p>4.3 Cercignani–Lampis Kernel 34</p> <p>4.4 Accommodation Coefficients 34</p> <p>4.5 General form of Boundary Condition for Permeable Surface 37</p> <p>4.6 Entropy Production due to Gas–Surface Interaction 38</p> <p><b>5 Linear Theory 43</b></p> <p>5.1 Small Perturbation of Equilibrium 43</p> <p>5.2 Linearization Near Global Maxwellian 43</p> <p>5.3 Linearization Near Local Maxwellian 46</p> <p>5.4 Properties of the Linearized Collision Operator 47</p> <p>5.5 Linearization of Boundary Condition 48</p> <p>5.5.1 Impermeable Surface Being at Rest 48</p> <p>5.5.2 Impermeable Moving Surface 49</p> <p>5.5.3 Permeable Surface 50</p> <p>5.5.4 Linearization Near Reference Maxwellian 50</p> <p>5.5.5 Properties of Scattering Operator 50</p> <p>5.5.6 Diffuse Scattering 51</p> <p>5.6 Series Expansion 51</p> <p>5.7 Reciprocal Relations 53</p> <p>5.7.1 General Definitions 53</p> <p>5.7.2 Kinetic Coefficients 54</p> <p><b>6 Transport Coefficients 57</b></p> <p>6.1 Constitutive Equations 57</p> <p>6.2 Viscosity 58</p> <p>6.3 Thermal Conductivity 59</p> <p>6.4 Numerical Results 61</p> <p>6.4.1 Hard Sphere Potential 61</p> <p>6.4.2 Lennard-Jones Potential 61</p> <p>6.4.3 Ab Initio Potential 62</p> <p><b>7 Model Equations 65</b></p> <p>7.1 BGK Equation 65</p> <p>7.2 S-Model 67</p> <p>7.3 Ellipsoidal Model 69</p> <p>7.4 Dimensionless Form of Model Equations 70</p> <p><b>8 Direct Simulation Monte Carlo Method 73</b></p> <p>8.1 Main Ideas 73</p> <p>8.2 Generation of Specific Distribution Function 74</p> <p>8.3 Simulation of Gas–Surface Interaction 75</p> <p>8.3.1 Kernel Decomposition 75</p> <p>8.3.2 Diffuse Scattering 75</p> <p>8.3.3 Cercignani–Lampis Scattering 76</p> <p>8.4 Intermolecular Interaction 77</p> <p>8.5 Calculation of Post-Collision Velocities 78</p> <p>8.6 Calculation of Macroscopic Quantities 80</p> <p>8.7 Statistical Scatter 81</p> <p><b>9 Discrete Velocity Method 83</b></p> <p>9.1 Main Ideas 83</p> <p>9.2 Velocity Discretization 85</p> <p>9.2.1 Onefold Integral 85</p> <p>9.2.2 Twofold Integral 86</p> <p>9.3 Iterative Procedure 87</p> <p>9.4 Finite Difference Schemes 88</p> <p>9.4.1 Main Principles 88</p> <p>9.4.2 One-Dimensional Planar Flows 89</p> <p>9.4.3 Two-Dimensional Planar Flows 90</p> <p>9.4.4 One-Dimensional Axisymmetric Flows 93</p> <p>9.4.5 Full Kinetic Equation 96</p> <p><b>10 Velocity Slip and Temperature Jump Phenomena 97</b></p> <p>10.1 General Remarks 97</p> <p>10.2 Viscous Velocity Slip 98</p> <p>10.2.1 Definition and Input Equation 98</p> <p>10.2.2 Velocity and Heat Flow Profiles 100</p> <p>10.2.3 Numerical and Experimental Data 101</p> <p>10.3 Thermal Velocity Slip 104</p> <p>10.3.1 Definition and Input Equation 104</p> <p>10.3.2 Velocity and Heat Flow Profiles 106</p> <p>10.3.3 Numerical and Experimental Data 107</p> <p>10.4 Reciprocal Relation 108</p> <p>10.5 Temperature Jump 110</p> <p>10.5.1 Definition and Input Equation 110</p> <p>10.5.2 Temperature Profile 112</p> <p>10.5.3 Numerical Data 112</p> <p><b>11 One-Dimensional Planar Flows 115</b></p> <p>11.1 Planar Couette Flow 115</p> <p>11.1.1 Definitions 115</p> <p>11.1.2 Free-Molecular Regime 116</p> <p>11.1.3 Velocity Slip Regime 117</p> <p>11.1.4 Kinetic Equation 117</p> <p>11.1.5 Numerical Scheme 119</p> <p>11.1.6 Numerical Results 120</p> <p>11.2 Planar Heat Transfer 121</p> <p>11.2.1 Definitions 121</p> <p>11.2.2 Free-Molecular Regime 122</p> <p>11.2.3 Temperature Jump Regime 123</p> <p>11.2.4 Kinetic Equation 124</p> <p>11.2.5 Numerical Scheme 126</p> <p>11.2.6 Numerical Results 127</p> <p>11.3 Planar Poiseuille andThermal Creep Flows 128</p> <p>11.3.1 Definitions 128</p> <p>11.3.2 Slip Solution 130</p> <p>11.3.3 Kinetic Equation 131</p> <p>11.3.4 Reciprocal Relation 133</p> <p>11.3.5 Numerical Scheme 133</p> <p>11.3.6 Splitting Scheme 134</p> <p>11.3.7 Free-Molecular Limit 137</p> <p>11.3.8 Numerical Results 137</p> <p><b>12 One-Dimensional Axisymmetrical Flows 145</b></p> <p>12.1 Cylindrical Couette Flow 145</p> <p>12.1.1 Definitions 145</p> <p>12.1.2 Slip Flow Regime 146</p> <p>12.1.3 Kinetic Equation 147</p> <p>12.1.4 Free-Molecular Regime 148</p> <p>12.1.5 Numerical Scheme 149</p> <p>12.1.6 Splitting Scheme 150</p> <p>12.1.7 Results 152</p> <p>12.2 Heat Transfer between Two Cylinders 153</p> <p>12.2.1 Definitions 153</p> <p>12.2.2 Temperature Jump Solution 154</p> <p>12.2.3 Kinetic Equation 155</p> <p>12.2.4 Free-Molecular Regime 156</p> <p>12.2.5 Numerical Scheme 157</p> <p>12.2.6 Splitting Scheme 158</p> <p>12.2.7 Numerical Results 159</p> <p>12.3 Cylindrical Poiseuille andThermal Creep Flows 161</p> <p>12.3.1 Definitions 161</p> <p>12.3.2 Slip Solution 163</p> <p>12.3.3 Kinetic Equation 163</p> <p>12.3.4 Reciprocal Relation 165</p> <p>12.3.5 Free-Molecular Regime 165</p> <p>12.3.6 Numerical Scheme 166</p> <p>12.3.7 Results 168</p> <p><b>13 Two-Dimensional Planar Flows 173</b></p> <p>13.1 Flows Through a Long Rectangular Channel 173</p> <p>13.1.1 Definitions 173</p> <p>13.1.2 Slip Solution 174</p> <p>13.1.3 Kinetic Equation 175</p> <p>13.1.4 Free-Molecular Regime 177</p> <p>13.1.5 Numerical Scheme 177</p> <p>13.1.6 Numerical Results 178</p> <p>13.2 Flows Through Slits and Short Channels 180</p> <p>13.2.1 Formulation of the Problem 180</p> <p>13.2.2 Free-Molecular Regime 181</p> <p>13.2.3 Small Pressure and Temperature Drops 183</p> <p>13.2.3.1 Definitions 183</p> <p>13.2.3.2 Kinetic Equation 184</p> <p>13.2.3.3 Hydrodynamic Solution 186</p> <p>13.2.3.4 Numerical Results 186</p> <p>13.2.4 Arbitrary Pressure Drop 189</p> <p>13.2.4.1 Definition 189</p> <p>13.2.4.2 Kinetic Equation 189</p> <p>13.2.4.3 Numerical Results 190</p> <p>13.3 End Correction for Channel 194</p> <p>13.3.1 Definitions 194</p> <p>13.3.2 Kinetic Equation 196</p> <p>13.3.3 Numerical Results 197</p> <p><b>14 Two-Dimensional Axisymmetrical Flows 201</b></p> <p>14.1 Flows Through Orifices and Short Tubes 201</p> <p>14.1.1 Formulation of the Problem 201</p> <p>14.1.2 Free-Molecular Flow 202</p> <p>14.1.3 Small Pressure Drop 203</p> <p>14.1.3.1 Definitions 203</p> <p>14.1.3.2 Kinetic Equations 204</p> <p>14.1.3.3 Hydrodynamic Solution 205</p> <p>14.1.3.4 Numerical Results 205</p> <p>14.1.4 Arbitrary Pressure Drop 206</p> <p>14.2 End Correction for Tube 210</p> <p>14.2.1 Definitions 210</p> <p>14.2.2 Numerical Results 212</p> <p>14.3 Transient Flow Through a Tube 213</p> <p><b>15 Flows Through Long Pipes Under Arbitrary Pressure and Temperature Drops 219</b></p> <p>15.1 Stationary Flows 219</p> <p>15.1.1 Main Equations 219</p> <p>15.1.2 Isothermal Flows 221</p> <p>15.1.3 Nonisothermal Flows 223</p> <p>15.2 Pipes with Variable Cross Section 224</p> <p>15.3 Transient Flows 226</p> <p>15.3.1 Main Equations 226</p> <p>15.3.2 Approaching to Equilibrium 227</p> <p><b>16 Acoustics in Rarefied Gases 231</b></p> <p>16.1 General Remarks 231</p> <p>16.1.1 Description ofWaves in Continuous Medium 231</p> <p>16.1.2 Complex Perturbation Function 232</p> <p>16.1.3 One-Dimensional Flows 233</p> <p>16.2 Oscillatory Couette Flow 234</p> <p>16.2.1 Definitions 234</p> <p>16.2.2 Slip Regime 235</p> <p>16.2.3 Kinetic Equation 237</p> <p>16.2.4 Free-Molecular Regime 238</p> <p>16.2.5 Numerical Scheme 239</p> <p>16.2.6 Numerical Results 241</p> <p>16.3 LongitudinalWaves 242</p> <p>16.3.1 Definitions 242</p> <p>16.3.2 Hydrodynamic Regime 244</p> <p>16.3.3 Kinetic Equation 246</p> <p>16.3.4 Reciprocal Relation 249</p> <p>16.3.5 High-Frequency Regime 250</p> <p>16.3.6 Numerical Results 252</p> <p><b>A Constants and Mathematical Expressions 257</b></p> <p>A.1 Physical Constants 257</p> <p>A.2 Vectors and Tensors 257</p> <p>A.3 Nabla Operator 259</p> <p>A.4 Kronecker Delta and Dirac Delta Function 259</p> <p>A.5 Some Integrals 260</p> <p>A.6 Taylor Series 260</p> <p>A.7 Some Functions 260</p> <p>A.8 Gauss–Ostrogradsky’sTheorem 262</p> <p>A.9 Complex Numbers 262</p> <p><b>B Files and Listings 263</b></p> <p>B.1 Files with Nodes andWeights of Gauss Quadrature 263</p> <p>B.1.1 Weighting Function (9.16) 263</p> <p>B.1.1.1 File cw4.dat, Nc = 4 263</p> <p>B.1.1.2 File cw6.dat, Nc = 6 263</p> <p>B.1.1.3 File cw8.dat, Nc = 8 263</p> <p>B.1.2 Weighting Function (9.22) 264</p> <p>B.1.2.1 File cpw4.dat, Nc = 4 264</p> <p>B.1.2.2 File cpw6.dat, Nc = 6 264</p> <p>B.1.2.3 File cpw8.dat, Nc = 8 264</p> <p>B.2 Files for Planar Couette Flow 264</p> <p>B.2.1 Listing of Program “couette_planar.for” 264</p> <p>B.2.2 Output File with Results “Res_couette_planar.dat” 266</p> <p>B.3 Files for Planar Heat Transfer 266</p> <p>B.3.1 Listing of Program “heat_planar.for” 266</p> <p>B.3.2 Output File with Results “Res_heat_planar.dat” 268</p> <p>B.4 Files for Planar Poiseuille and Creep Flows 268</p> <p>B.4.1 Listing of Program “poiseuille_creep_planar.for” 268</p> <p>B.4.2 Output File “Res_pois_cr_pl.dat” with Results 272</p> <p>B.5 Files for Cylindrical Couette Flows 272</p> <p>B.5.1 Listing of Program “couette_axisym.for” 272</p> <p>B.5.2 Output File “Res_couet_axi.dat” with Results 275</p> <p>B.6 Files for Cylindrical Heat Transfer 276</p> <p>B.6.1 Listing of Program “heat_axisym.for” 276</p> <p>B.6.2 Output File “Res_heat_axi.dat” with Results 280</p> <p>B.7 Files for Axi-Symmetric Poiseuille and Creep Flows 280</p> <p>B.7.1 Listing of Program “poiseuille_creep_axisym.for” 280</p> <p>B.7.2 Output File “Res_pois_cr_axi.dat” with Results 284</p> <p>B.8 Files for Poiseuille and Creep FlowsThrough Channel 284</p> <p>B.8.1 Listing of Program “poiseuille_creep_chan.for” 284</p> <p>B.8.2 Output File “Res_pois_cr_ch.dat” with Results 287</p> <p>B.9 Files for Oscillating Couette Flow 287</p> <p>B.9.1 Listing of Program “couette_osc.for” 287</p> <p>B.9.2 Output File “Res_couette_osc.dat” with Results 290</p> <p>References 291</p> <p>Index 303</p>
Professsor Felix Sharipov graduated from the Moscow University of Physics and Technology, Faculty of Aerophysics and Space Research, and the Ural State Technical University. Since 1988 he is active in rarefied gas dynamics, since 1992 at the Federal University of Parana in Brazil. His research interests are numerical methods of rarefied gas dynamics applied to microfluidics, vacuum technology and aerothermodynamics. His group develops both probabilistic and deterministic approaches. Prof. Sharipov was organizer of numerous vacuum gas dynamics meetings, and published over a hundred journal articles, conference papers, and book chapters. He is a member of editorial board of international journal ?Vacuum?

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