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

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Chapter 5 Results The performance of the UMIST-N near-wall subgrid treatment was tested in channel flow. The PASSABLE code was used to implement a parabolic solution method to solve this flow domain. For this work, the PASSABLE code was extended to allow high-Reynolds-number (wall function and subgrid) solutions. Also, a separate implementation of the turbulence models and a separate solver were written to be employed in solving the subgrid region near the wall (extending from y/δ = 0 to y/δ = 0.2). The models implemented in the subgrid are the standard k-ε model [33] with Yap correction [92] and the 1988 k-ω model [89]. PASSABLE supports a range of turbulence models for the solution of the main grid. The models employed in this work were the low-Reynolds-number k-ε model with Yap correction, the 1988 k-ω model, and the high-Reynolds-number k-ε model (newly added). The configurations of turbulence models used in this work are summarised descriptively in Table 5.1. 66
CHAPTER 5. RESULTS 67 Table 5.1: Configurations of turbulence models Low-Re k-ε The subgrid was not employed and the low-Reynolds- number standard k-ε model was used. k-ε with log law The subgrid was not employed and the high-Reynolds- number standard k-ε model was used with a log-law boundary condition near the wall. Subgrid k-ε The high-Reynolds-number standard k-ε model was used in the main grid with a near-wall boundary condition derived from a subgrid solution. The subgrid employed the low-Reynolds-number standard k-ε model. Subgrid k-ω The 1988 k-ω model was used in the main grid with a near-wall boundary condition derived from a subgrid solution. The subgrid also employed the 1988 k-ω model. Three test cases were implemented: steady channel flow, channel flow driven by a periodically variable pressure gradient, and channel flow constrained to exhibit a periodically variable bulk flow rate. The two periodic cases differ in that the former matches the pressure gradient fluctuation of the DNS study of Kawamura & Homma [29] while the latter matches the bulk flow variation presented in that DNS result. The steady flow case was performed at a nominal friction velocity Reynolds number of Reτ = 180. 1 The periodic flow cases were configured such that the time average flow would conform to 1 The boundary conditions on the code were configured such that 180 would be a correct value of Reτ based on a theoretical analysis. The actual Reynolds number obtained was different, as discussed below. This is what is meant by ‘nominal’ Reτ .
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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 25 and 26: 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 75: CHAPTER 4. NUMERICAL IMPLEMENTATION
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
Page 121 and 122: FIGURES 111 〈U〉 + 〈U〉 + 20
Page 123 and 124: FIGURES 113 〈U〉 + 〈U〉 + 20
Page 125 and 126: 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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