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

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Chapter 4 Numerical Implementation This work uses a code derived from PASSABLE. 1 Prior to this work, the code was modified for periodic flow by Addad [1]. A finite volume method is used to discretise the equations governing the flow. More information on the numerical implementation of CFD can be found in books. [83],[20] 4.1 The Mesh As discussed in Chapter 3, the flow field is a one-dimensional expanse with a wall at y = 0 and symmetry at y = δ. This is modelled as a channel ’slice’ of finite thickness. The slice is divided into finite volumes, called ‘cells’. The slice is one cell thick in x and is divided in y according to the degree of numerical accuracy required. This is shown schematically in Figure 4.1. The actual grid used for low-Reynolds-number solutions within this work 1 PArabolic Solution Scheme Applied to Boundary Layer Equations 48
CHAPTER 4. NUMERICAL IMPLEMENTATION 49 contains 98 cells. Each cell is 5% larger than its wall-facing neighbour. This geometrical feature is referred to as an expansion factor of 1.05. † d y U P symmetry nodes vertexes wall Figure 4.1: The low-Reynolds-number grid Within each cell is a ‘node’, where parameters associated with the cell are tracked. Cell boundaries, called ‘vertexes’, are centred between nodes. Ex- ceptions exist at y = 0 and y = δ. At y = δ, a half-cell exists, with the final node placed at the symmetry plane. At y = 0, a node is placed at the wall with no associated cell. This represents a new modification to the PASSABLE code, allowing easier implementation of wall function boundary conditions. Previously, the code employed a similar mesh style at y = 0 to the mesh at y = δ. Table 4.1 shows the notation used in this thesis to refer to discretised values. Values at vertexes are not stored in the code, but may be calculated via linear interpolation from adjacent nodal values.
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The UMIST-N Near-Wall Treatment App
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Acknowledgements I would like to th
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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 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: CHAPTER 3. CHANNEL FLOW 47 y + is p
Page 61 and 62: CHAPTER 4. NUMERICAL IMPLEMENTATION
Page 77 and 78: CHAPTER 5. RESULTS 67 Table 5.1: Co
Page 79 and 80: CHAPTER 5. RESULTS 69 The solution
Page 81 and 82: CHAPTER 5. RESULTS 71 match the DNS
Page 83 and 84: CHAPTER 5. RESULTS 73 Integrating w
Page 85 and 86: CHAPTER 5. RESULTS 75 Figures 5.11,
Page 87 and 88: CHAPTER 5. RESULTS 77 gradient of k
Page 89 and 90: CHAPTER 5. RESULTS 79 The log law o
Page 91 and 92: CHAPTER 5. RESULTS 81 maxima). This
Page 93 and 94: Chapter 6 Conclusions & Suggestions
Page 95 and 96: CHAPTER 6. CONCLUSIONS & SUGGESTION
Page 97 and 98: Bibliography [1] Addad, Y., Applica
Page 99 and 100: BIBLIOGRAPHY 89 [14] Craft, T. J.,
Page 101 and 102: BIBLIOGRAPHY 91 [30] Kim J., Moin P
Page 103 and 104: BIBLIOGRAPHY 93 [47] Niederschulte,
Page 105 and 106: BIBLIOGRAPHY 95 [64] Rotta, J. C.,
Page 107 and 108: BIBLIOGRAPHY 97 [82] Tu, S. W. & Ra
Page 109 and 110:
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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