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

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CHAPTER 4. NUMERICAL IMPLEMENTATION 60 4.4.4 The Subgrid Approach The subgrid implementation employed in this work begins with the same grid used for a log-law wall function, discussed above. This is referred to as the ‘main grid’. Within the wall-adjacent cell of the main grid, the subgrid code generates a subgrid mesh, as shown schematically in Figure 4.3. Within the subgrid mesh, 50 nodes were used, with an expansion factor of 1.10. The subgrid mesh is similar to the low-Reynolds-number mesh shown in Figure 4.1, but it fills only the near-wall region corresponding to the wall- adjacent cell of the main grid. The subgrid mesh differs from the main grid mesh in the choice of node locations. While the main grid uses cell vertexes centred between nodes, the subgrid coded in this work uses nodes centred between vertexes. 7 This affects way in which linear interpolations are calculated within the code. main grid node subgrid node subgrid region Figure 4.3: The subgrid mesh, adapted from Gant [21] 7 This is due only to programmer preference.
CHAPTER 4. NUMERICAL IMPLEMENTATION 61 The subgrid values are updated within the main iteration loop of the CFD code. After 〈U〉, k, and ε or ω in the main grid have been updated in one iteration, the subgrid update function is called. This function is essentially the main iteration loop of another, embedded CFD code that performs one iteration to solve for 〈U〉, k, and ˜ε or ω in the subgrid. Before the subgrid calculations are performed, data are taken from the main grid to act as boundary conditions on the subgrid. After the subgrid is updated, subgrid- averaged values are extracted in order to act as wall function inputs to the next main grid iteration. Thus, there is a cyclic exchange of information. The data required as input to the subgrid calculation are the values of 〈U〉, k, and ε or ω at the outer extent of the subgrid (where the subgrid ends and the main grid transport equations begin). Transport equations are solved in every subgrid cell (except in the case of the k-ω model, where the very-near- wall values of ω are prescribed, as discussed above). At the wall node, zero values of 〈U〉, k, and ˜ε are set. At the node placed farthest from the wall, at the outer-most point on the subgrid, the values of 〈U〉, k, and ˜ε or ω are set as being equal to the corresponding values linearly interpolated from the two nearest main grid nodes. The boundary conditions on the main grid are more complex. 〈U〉 receives its boundary condition as in the above section on log-law wall functions, except that the wall shear stress, τw is obtained from the application of Newton’s law of viscosity at the subgrid’s near-wall cell node: ∂ 〈U〉 τw = ρν ∂y y=0 Taking s1 as the near-wall subgrid cell node and discretising ∂〈U〉 ∂y y=0 (4.28) within
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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
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List of Figures 2.1 The log-law com
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5.32 k vs y + snapshots through tim
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Chapter 1 Introduction & Literature
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CHAPTER 1. INTRODUCTION & LITERATUR
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Page 19 and 20: 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
Page 69: 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
Page 111 and 112: FIGURES 101 − 〈uv〉 + 1.0 0.9
Page 113 and 114: FIGURES 103 k + 5 4 3 2 1 0 10 0 +
Page 115 and 116: FIGURES 105 1.4 〈vv〉 + 1.2 1.0
Page 117 and 118: FIGURES 107 y ∗ y ∗ 600 500 400
Page 119 and 120: 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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