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

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CHAPTER 1. INTRODUCTION & LITERATURE SURVEY 16 of the wall is introduced. Chapter 3 contains a detailed discussion of channel flow. The governing equations associated with the various turbulence models are adapted to channel flow. The chapter also presents various experimental and DNS channel flow results arising from other studies. Correlations are presented to identify trends in the data that may be useful for the design and testing of CFD codes. Alternative nondimensionalisation schemes are also investigated. Chapter 4 contains a discussion of the numerical implementation of the turbulence models. This includes a discussion of the Finite Volume method and the particular grid arrangements used in this work. Boundary conditions are also discussed, including the implementation of the logarithmic law of the wall. Since the novelty of UMIST-N is essentially in its numerical treatment of the boundary layer problem, the approach is detailed in this chapter. Chapter 5 presents an analysis of the results computed for the various config- urations considered. This includes steady channel flow, periodic flow results compared to data with the same driving pressure gradient, and periodic flow results compared to data with the same bulk flow rate. Chapter 6 offers conclusions and suggestions for future work.
Chapter 2 Turbulence Models The Reynolds Averaged Navier Stokes equations are obtained for continuity, conservation of momentum, and generic transport. The assumptions of the EVM are employed where appropriate. Then, specific transport equations are introduced for the turbulence parameters tracked by the k-ε and k-ω models. The logarithmic law of the wall is introduced. 2.1 Reynolds Averaging Consider a flow field containing an incompressible fluid with constant proper- ties: density (ρ), dynamic viscosity (µ), and kinematic viscosity (ν = µ ). In ρ Cartesian coordinates, the flow field extends in three orthogonal directions, x, y, and z. The flow field may vary in time, t. A pressure field, P (x, y, z, t) and a velocity field, U (x, y, z, t) = (U, V, W ) T are associated with the flow. This flow field is governed by continuity and the conservation of momentum. 17
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 and 10: 5.32 k vs y + snapshots through tim
Page 11 and 12: Chapter 1 Introduction & Literature
Page 13 and 14: CHAPTER 1. INTRODUCTION & LITERATUR
Page 25: CHAPTER 1. INTRODUCTION & LITERATUR
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 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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