The computation of turbulent natural convection flows - Turbulence ...

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425 penetration was concerned, the time-averaged predictions were again close to those of the steady RANS computations and the differences between the time-averaged and steady computations were notably smaller than for the cor- responding lower Rayleigh number comparisons. This suggested that in the higher Rayleigh number case, though present, the large scale flow oscillations within the penetration were not as influential. This conclusion, however, was only partially confirmed by the comparisons between the time-averaged and steady flow predictions of the axial flow field. In terms of the distribution of the axial velocity, the time-averaged and steady flow predictions were in close agreement over the entire length of the penetration. When it came to the level of the axial velocity on the other hand, the steady RANS predictions returned a stronger axial flow within the penetration than the time-averaged unsteady RANS. So for at least one important parameter the use of unsteady RANS does make a difference. As in the lower Rayleigh number case for the unsteady RANS, both the modelled and the total turbulent kinetic energy were included. In contrast to what was observed at the lower Ra level, there was little difference between the modelled and total levels of the time-averaged predictions. This means that the resolved turbulence, due to large-scale oscillations, was less significant at this higher Rayleigh number, as a result of which, use of unsteady RANS had only a small effect on the predicted turbulence field. 9.2 Suggested Future Work In the 60 ◦ stable and unstable cases, introduction of an RSM not only did not improve the predictions compared with the EVM’s results, but also produced more inconsistencies in comparison with the experimental data. The RSMs tested over-predicted turbulence level near the ends of the cavity where impingements occur. Further studies could, therefore be carried out to improve the RSM. It could be investigated how the process of redistribution of turbulent stresses could be improved near the impingement regions. RSM predictions for the 60 ◦ stable and unstable cases might be improved compared with the EVM after obtaining more accurate prediction of turbulent stresses near the impingement regions.
Conclusions and Future Works 426 In the 60 ◦ stable and unstable cases, implementation of more elaborate al- gebraic equation than the GGDH for the calculation of turbulent heat fluxes, in the RSM framework, produced predictive improvements near the two ends of the cavity. Within such a modelling framework one needs to solve extra transport equations for θ 2 and εθ. The comparisons of θ 2 results with the experimental data showed that θ 2 was considerably over-predicted in the near-wall regions, especially near the impingement regions. Further study could therefore be carried out on the modification of the transport equations of θ 2 and εθ to over-come the problem. The flow field may be simulated more accurate by obtaining more accurate θ 2 and εθ data, especially near the impingement regions. Three near-wall treatments were used in the present study. They were the LRN, SWF and AWF. The AWF was developed more recently than the other mentioned near-wall treatments in the University of Manchester and also called UMIST-A. Another near-wall treatment was developed at the same time in the University of Manchester which is called UMIST-N. Their concepts are similar, with the main difference being that UMIST-A solves the near-wall flow by analytical integration of the equations while UMIST-N solves it by numerical integration. A study could be carried out to test whether or not UMIST-N can produce any predictive advantage in simulation of buoyancy- driven flows compared with the UMIST-A wall treatment. The horizontal penetration case was simulated in the present work by em- ploying the EVM-AWF. Inside the lower half of the penetration there is ther- mally unstable stratification. In the 15 ◦ unstable rectangular cavity test case, use of an RSM produced predictive improvements compared with the EVM results. It might, therefore, be useful to employ an RSM in the horizontal penetration case in order to assess how it predicts the flow structure and unsteadi- ness in the horizontal penetration case. The cavities which were studied in the present research have the high longi- tudinal aspect ratio of 28.7. Baïri et. al.[1] experimentally investigated natural
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The computation of turbulent natura
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3.2 Mean Flow Equations and their s
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7.2.6 FFT analysis . . . . . . . .
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List of Figures 2.1 Comparison of e
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6.15 Temperature and stream lines w
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6.45 Temperature fluctuations withi
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7.9 rms velocity fluctuations compa
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7.43 Temperature contours within x-
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7.82 Mean velocity distributions re
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7.119Time-averaged rms velocity flu
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8.23 Contour plots of V, W andk at
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8.49 Contour plots of V, W andk at
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For the inclined tall cavities, in
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Declaration No portion of the work
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Acknowledgements I would like to ex
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Nomenclature Acronyms AWF Analytica
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λ Thermal conductivity µ Molecula
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cl Equilibrium length scale constan
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yd Thickness of the dissipative lay
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Chapter 1 Introduction In this rese
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41 need fine numerical resolution n
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43 nonlinear discretization methods
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45 the only way to achieve computat
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47 elaborate expressions for modell
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Chapter 2 Literature Review In this
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51 local Nusselt number occurs in t
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53 Cavities and Enclosures Kirkpatr
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55 boundary conditions which avoid
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57 of cold wall. They showed that t
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59 their predictions and their expe
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61 and the fluid near the vertical
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63 term in the ε equation performe
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65 space and time. Then the full al
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67 with heated vertical walls. They
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69 horizontal axis. This tall cavit
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71 • Large eddy simulation (LES):
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73 ρuiuj = 2 3 ρkδij ∂Ui −
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75 3.3.3 Low-Reynolds Number k-ε m
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77 diffusivity model is rather simp
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79 ∂(ρεθ) ∂t + ∂(ρUjεθ)
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81 stresses can be derived from the
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83 One option is to derive and solv
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85 εθ = 2α ∂θ Basic Different
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87 c1 c2 c3 c1w c2w 1.8 0.6 0.5 0.5
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89 are defined as: A = 1− 9 8 (A2
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91 2/3εδij. At moderate Reynolds
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93 Figure 4.1 - A low-Reynolds-numb
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95 energy over the near-wall contro
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97 wall heat flux can be obtained f
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99 values. • The convection terms
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101 is: Θ1 = Prυ µυ + Prυbµ
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103 where Θwall = Θn − Prυ + P
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105 C = µ2 υ ρ 2 υ kP ∂(ρUU
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107 +A1y ∗ + by∗2 2 + bµy ∗
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109 where B2 = y ∗ C1 υ 2 y∗
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111 where ∂U2 ∂y∗ = C2y∗ +A
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113 and the other option is to calc
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115 explained. It might be noted th
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117 near-wall treatments available
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119 N n W w P e E s S Figure 5.2 -
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121 φw = φW + φP −φW 2 − φ
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123 The schemes are SIMPLE (“Semi
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125 Pe = P ∗ +P ′ ′ 1 +P 2 (5
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127 Update P ′ from equation 5.26
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129 5.6 Time-dependent computations
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131 For the thermal boundary condit
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133 gx = g cos(Ψ) (5.42) gy = −g
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135 stable and unstable inclined ta
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137 variations. In these calculatio
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139 Rayleigh number Ra = βg∆ΘL3
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141 V/V 0 0.2 0 -0.2 Y=0.95 EXP 0 0
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143 U/V 0 0.2 0 -0.2 0 0.2 0.4 0.6
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145 Temperature contours Stream lin
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153 diagrams show that the LRN k-ε
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155 2 k/V0 V/V 0 0.08 0.06 0.04 0.0
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157 2 k/V0 2 k/V0 0.03 0.02 0.01 LR
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159 Figure 6.26 - Mean velocity vec
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161 6.4.2 k-ε predictions In Figur
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163 In Figure 6.29, the Nusselt num
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165 moves down from the top of the
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167 v rms /V 0 v rms /V 0 v rms /V
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169 T T T T 1 0.8 0.6 0.4 0.2 Y=0.9
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171 2 uv/V0 2 uv/V0 2 uv/V0 2 uv/V0
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173 Nu 20 15 10 5 Cold Wall 0 0 0.2
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175 T T T T 1 0.8 0.6 0.4 Y=0.95 0.
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177 V/V 0 V/V 0 0.4 0.2 0 -0.2 -0.4
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179 In Figures 6.44-6.46, the rms t
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181 θ rms /ΔΘ θ rms /ΔΘ θ rm
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183 θ rms /ΔΘ θ rms /ΔΘ θ rm
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185 of the cavity. Figure 6.49 pres
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187 T T 1 0.8 0.6 0.4 0.2 Y=0.1 0 0
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189 θ rms /ΔΘ θ rms /ΔΘ 0.15
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191 Nu 20 15 10 5 Cold Wall 0 0 0.2
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193 Figure 6.58 - Stream traces and
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195 and SWF treatments is compared
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197 T T T T T 1 0.8 0.6 0.4 0.2 0 0
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199 Nu 60 40 20 LES AWF LRN SWF 0 0
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201 After validation of the STREAM
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203 V/V 0 V/V 0 0.5 0 -0.5 0.6 0.4
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205 T T 1 0.8 0.6 0.4 0.2 0 0 0.2 0
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207 v rms /V 0 v rms /V 0 0.2 0.15
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209 V/V 0 V/V 0 0.4 0.2 0 -0.2 -0.4
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211 the distance between the hot an
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213 1.5 Y 2 1 0.5 0 0 0.05 0.1 0.15
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215 7.2.4 3D time dependent simulat
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217 0.65 1.5 Y 0.5 Y 2 1 0.65 0.65
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219 0.35 0.5 0.05 0.5 0.5 0.65 0.65
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221 Y Y 2 1.5 1 0.5 0.35 0.5 0.5 0.
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223 data. The comparisons show that
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225 flow at this angle of inclinati
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227 T T T 1 0.8 0.6 0.4 0.2 T X 1 0
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229 U/V 0 U/V 0 U/V 0 0.4 0.2 0 -0.
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231 u rms /V 0 u rms /V 0 u rms /V
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233 u rms /V 0 u rms /V 0 0.15 0.1
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235 T 1 0.8 0.6 0.4 0.2 T Y=0.5 X 1
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237 U/V 0 0.4 0.2 0 -0.2 -0.4 Y=0.9
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239 u rms /V 0 0.25 0.2 0.15 0.1 0.
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241 Figure 7.34 - Time average vect
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243 Y 2 1.5 1 0.5 0.3 0.5 0.55 0.35
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245 PSD (T) PSD (T) PSD (T) 1 0.8 0
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247 PSD (T) PSD (T) PSD (T) 1 0.8 0
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249 PSD (T) PSD (T) PSD (T) 1 0.8 0
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251 the central, z=0.5, longitudina
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253 1.5 Y 2 1 0.5 Y 0 0 0.05 0.1 0.
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255 τ * =550 τ * =495 τ * =440
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257 Y 2 1.5 1 0.5 0.3 0.45 0.45 0.3
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259 not sufficiently detailed to pr
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261 T 1 0.8 0.6 0.4 0.2 T Y=0.5 X 1
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263 V/V 0 V/V 0 V/V 0 0.4 0.2 0 -0.
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265 V/V 0 V/V 0 0.4 0.2 0 -0.2 -0.4
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267 v rms /V 0 v rms /V 0 v rms /V
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269 v rms /V 0 v rms /V 0 0.25 0.2
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271 X X X 0.15 0.1 0.05 0 0 0.1 0.2
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273 1.5 Y 2 1 0.5 0 0 0.05 0.1 0.15
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275 PSD (T) PSD (T) PSD (T) 1 0.8 0
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277 PSD (T) PSD (T) PSD (T) 1 0.8 0
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279 PSD (T) PSD (T) PSD (T) 1 0.8 0
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281 cold wall temperatures are 53
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283 The reverse feature is observed
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285 normal components in Figures 7.
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287 V/V 0 V/V 0 0 -0.2 -0.4 -0.6 0
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289 v rms /V 0 v rms /V 0 0.15 0.1
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291 T T 1 0.8 0.6 0.4 0.2 Y=0.7 0 0
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293 V/V 0 0.8 0.6 0.4 0.2 0 -0.2 Y=
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295 V/V 0 V/V 0 0.6 0.4 0.2 0 -0.2
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297 v rms /V 0 v rms /V 0 0.15 EXP
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299 active sides, y-z, there are re
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301 V/V 0 V/V 0 0.2 0 -0.2 -0.4 -0.
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303 v rms /V 0 v rms /V 0 0.15 0.1
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305 T 1 0.8 0.6 0.4 0.2 Y=0.05 EXP
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307 T 1 0.8 0.6 0.4 0.2 Y=0.05 T 1
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309 V/V 0 0.8 0.6 0.4 0.2 0 -0.2 Y=
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311 v rms /V 0 0.15 0.1 0.05 EXP k-
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313 U/V 0 0.15 0.1 0.05 0 -0.05 -0.
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315 u rms /V 0 0.15 0.1 0.05 0 0 0.
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317 reproduce the measured temperat
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319 T T T 1 0.8 0.6 0.4 0.2 Y=0.9 E
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321 U/V 0 U/V 0 0.1 0.05 0 -0.05 -0
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323 u rms /V 0 u rms /V 0 0.15 0.1
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325 T 1 0.8 0.6 0.4 0.2 Y=0.05 T 1
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327 V/V 0 0.4 0.2 0 -0.2 -0.4 -0.6
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329 v rms /V 0 0.15 0.1 0.05 0 0 0.
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331 V/V 0 V/V 0 0.6 0.4 0.2 0 -0.2
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333 v rms /V 0 v rms /V 0 0.15 EXP
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335 Nu Nu X 0.15 0.1 0.05 20 15 10
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337 1.5 Y 2 1 0.5 0 0 0.1 0.2 0.3 Z
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Chapter 8 Annular horizontal penetr
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341 8.2 Grid Symmetry boundary cond
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343 Figure 8.3 - Grid in x-y plane.
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345 the diameter of the cold pipe i
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347 downward motion close to the pe
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349 Figure 8.5 - Contour plots of U
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351 Figure 8.7 - Contour plots of T
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353 Z=0.23 Z=0.46 Z=0.69 Z=0.87 Z=0
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355 Z=0.88 Z=0.92 Z=1.0 Z=0.88 Z=0.
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357 Z=0.88 Z=0.92 Z=1.0 Z=0.88 Z=0.
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359 X=0.25 X=0.5 X=0.25 X=0.5 Figur
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361 8.4 Time-dependent simulation (
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363 number, it is necessary to empl
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365 τ ∗ =240 τ ∗ =360 Figure
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367 τ ∗ =240 τ ∗ =360 Figure
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369 τ ∗ =0 τ ∗ =120 τ ∗ =2
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371 τ ∗ =0 τ ∗ =120 τ ∗ =2
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373 Z=0.69 τ ∗ =0 τ ∗ =120 τ
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Page 384 and 385: 383 Figure 8.33 - Contour plots of
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Page 388 and 389: 387 Z=0.88 Z=0.92 Z=1.0 Z=0.88 Z=0.
Page 390 and 391: 389 Z=0.88 Z=0.92 Z=1.0 Z=0.88 Z=0.
Page 392 and 393: 391 Y=0.22 (Inlet) Y=-0.11 Y=0.22 (
Page 394 and 395: 393 The contours of the instantaneo
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Page 398 and 399: 397 τ ∗ =240 τ ∗ =360 Figure
Page 400 and 401: 399 τ ∗ =240 τ ∗ =360 Figure
Page 402 and 403: 401 τ ∗ =0 τ ∗ =300 τ ∗ =6
Page 404 and 405: 403 τ ∗ =0 τ ∗ =300 τ ∗ =6
Page 406 and 407: 405 Z=0.69 τ ∗ =0 τ ∗ =120 τ
Page 408 and 409: 407 Time-averaged Steady state Figu
Page 410 and 411: 409 Time-averaged Z=0.23 Z=0.46 Z=0
Page 412 and 413: 411 8.7 Closing remarks In this cha
Page 414 and 415: Chapter 9 Conclusions and Future Wo
Page 416 and 417: 415 60 ◦ Stable Case Buoyancy-dri
Page 418 and 419: 417 using the k-ε-AWF are in close
Page 420 and 421: 419 the spanwise direction, suggest
Page 422 and 423: 421 results of the 3D numerical sim
Page 424 and 425: 423 stable and unstable configurati
Page 428 and 429: 427 convection within rectangular c
Page 430 and 431: 429 [8] D. Cooper, T. Craft, K. Est
Page 432 and 433: 431 [28] R. Boudjemadi, V. Maupu, D
Page 434 and 435: 433 [47] D. Naot, A. Shavit, and M.
Page 436 and 437: 435 [68] K. Hanjalić. Achievements
Page 438: 437 T V/V 0 v rms /V 0 1 0.8 0.6 0.
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