The UMIST-N Near-Wall Treatment Applied to Periodic Channel Flow

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List of Tables 2.1 Constants in the standard k-ε model [33] . . . . . . . . . . . . 22 2.2 Constants in the Wilcox 1988 k-ω model [89] . . . . . . . . . . 26 2.3 Log-law constants [83] . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Near-wall flow regimes adapted from [53] . . . . . . . . . . . . 28 3.1 Qualitative behaviour of terms in Equation 3.41 . . . . . . . . 41 3.2 Qualitative behaviour of terms in Equation 3.42 . . . . . . . . 42 4.1 The notation for discretised values . . . . . . . . . . . . . . . 50 4.2 Under-relaxation factors used in the main grid . . . . . . . . . 65 4.3 Under-relaxation factors used in the subgrid . . . . . . . . . . 65 5.1 Configurations of turbulence models . . . . . . . . . . . . . . . 67 ix
Chapter 1 Introduction & Literature Survey 1.1 Background Computational Fluid Dynamics (CFD) is a field of study that seeks to simu- late and predict fluid flow using computers. CFD may occasionally be used to investigate the physical behaviour of flow, but the usual goal is to provide an input to engineering analysis and design. Following from this goal, the thrust of most CFD development is to continually reduce the extent of the tradeoff between the predictive accuracy and the computational affordability of CFD. The field of CFD has developed quickly in recent decades because of the rapid advance and increasing accessibility of computer technology. Having first made CFD possible, then practical as an engineering tool, this ongoing advancement increasingly drives a trend toward more complex cal- culations. Recognising this, researchers in CFD tend to direct their efforts toward enhancing the predictive accuracy per unit cost of CFD treatments 1
Page 1 and 2: The UMIST-N Near-Wall Treatment App
Page 3 and 4: Acknowledgements I would like to th
Page 5 and 6: Contents 1 Introduction & Literatur
Page 7 and 8: List of Figures 2.1 The log-law com
Page 9: 5.32 k vs y + snapshots through tim
Page 13 and 14: CHAPTER 1. INTRODUCTION & LITERATUR
Page 27 and 28: Chapter 2 Turbulence Models The Rey
Page 29 and 30: CHAPTER 2. TURBULENCE MODELS 19 The
Page 31 and 32: CHAPTER 2. TURBULENCE MODELS 21 2.2
Page 33 and 34: CHAPTER 2. TURBULENCE MODELS 23 way
Page 35 and 36: CHAPTER 2. TURBULENCE MODELS 25 y i
Page 37 and 38: CHAPTER 2. TURBULENCE MODELS 27 The
Page 39 and 40: CHAPTER 2. TURBULENCE MODELS 29 In
Page 41 and 42: Chapter 3 Channel Flow Channel flow
Page 43 and 44: CHAPTER 3. CHANNEL FLOW 33 of x and
Page 45 and 46: CHAPTER 3. CHANNEL FLOW 35 varies o
Page 47 and 48: CHAPTER 3. CHANNEL FLOW 37 u 2 +
Page 49 and 50: CHAPTER 3. CHANNEL FLOW 39 3.4.1 Em
Page 51 and 52: CHAPTER 3. CHANNEL FLOW 41 profile
Page 53 and 54: CHAPTER 3. CHANNEL FLOW 43 Figure 3
Page 55 and 56: CHAPTER 3. CHANNEL FLOW 45 The prof
Page 57 and 58: CHAPTER 3. CHANNEL FLOW 47 y + is p
Page 59 and 60: CHAPTER 4. NUMERICAL IMPLEMENTATION
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CHAPTER 4. NUMERICAL IMPLEMENTATION
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CHAPTER 5. RESULTS 67 Table 5.1: Co
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CHAPTER 5. RESULTS 69 The solution
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CHAPTER 5. RESULTS 71 match the DNS
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CHAPTER 5. RESULTS 73 Integrating w
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CHAPTER 5. RESULTS 75 Figures 5.11,
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CHAPTER 5. RESULTS 77 gradient of k
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CHAPTER 5. RESULTS 79 The log law o
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CHAPTER 5. RESULTS 81 maxima). This
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Chapter 6 Conclusions & Suggestions
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CHAPTER 6. CONCLUSIONS & SUGGESTION
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Bibliography [1] Addad, Y., Applica
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BIBLIOGRAPHY 89 [14] Craft, T. J.,
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BIBLIOGRAPHY 91 [30] Kim J., Moin P
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BIBLIOGRAPHY 93 [47] Niederschulte,
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BIBLIOGRAPHY 95 [64] Rotta, J. C.,
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BIBLIOGRAPHY 97 [82] Tu, S. W. & Ra
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Figures 99
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FIGURES 101 − 〈uv〉 + 1.0 0.9
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FIGURES 103 k + 5 4 3 2 1 0 10 0 +
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FIGURES 105 1.4 〈vv〉 + 1.2 1.0
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FIGURES 107 y ∗ y ∗ 600 500 400
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FIGURES 109 y ∗ v2 y ∗ v2 600 5
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FIGURES 111 〈U〉 + 〈U〉 + 20
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FIGURES 113 〈U〉 + 〈U〉 + 20
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FIGURES 115 U U ss U U ss 3.0 3.0 2
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FIGURES 117 〈U〉 (Uτ ) ss k (U
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FIGURES 121 〈U〉 (Uτ ) ss 〈U
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FIGURES 123 k (U 2 τ ) ss k (U 2
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FIGURES 129 ( ∂〈P 〉 ∂x ) (
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The UMIST-N Near-Wall Treatment Applied to Periodic Channel Flow

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