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

More documents

Recommendations

Info

Abstract This thesis assesses the performance of the UMIST-N subgrid near-wall treatment when applied to periodic flow. The thesis also assesses the use of the k-ω turbulence model with the subgrid approach. Based on this work, the approach appears to be applicable to time-variant flow. Further research is required to improve the implementation of the k-ω model. UMIST-N solves simplified transport equations near a solid boundary at a lower computational cost than that of a low-Reynolds-number treatment. In applying the method to periodic channel flow, none of the approaches considered performed in an exemplary manner, but the subgrid exhibited no apparent failing when compared to the low-Reynolds-number results. It did offer an improvement upon the logarithmic law of the wall. This work highlights a numerical difficulty in applying the subgrid solution as a boundary layer to the main grid when the k-ω model is used. This has manifest itself in the results as an enhanced propensity toward a discontinuity in calculated profiles at the subgrid / main grid interface under certain flow conditions. A range of steady channel flow data has been compiled and presented in this thesis. Empirical correlations are offered which identify general tendencies in the data and may provide a useful tool for researchers engaged in the computation of flows. iii
Contents 1 Introduction & Literature Survey 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Turbulence Models . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Wall Functions & the Subgrid Approach . . . . . . . . . . . . 7 1.4 Relevance to Large Eddy Simulation . . . . . . . . . . . . . . 11 1.5 Periodic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Study Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.7 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Turbulence Models 17 2.1 Reynolds Averaging . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 The k-ε Model . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1 The Low-Reynolds-Number k-ε Model . . . . . . . . . 22 2.2.2 Yap Correction . . . . . . . . . . . . . . . . . . . . . . 24 2.3 The k-ω Model . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4 The Logarithmic Law of the Wall . . . . . . . . . . . . . . . . 26 3 Channel Flow 31 3.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.1 The k-ε Model . . . . . . . . . . . . . . . . . . . . . . 33 iv
Page 1 and 2: The UMIST-N Near-Wall Treatment App
Page 3: Acknowledgements I would like to th
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 and 58:
CHAPTER 3. CHANNEL FLOW 47 y + is p
Page 59 and 60:
CHAPTER 4. NUMERICAL IMPLEMENTATION
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
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
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
Page 127 and 128:
FIGURES 117 〈U〉 (Uτ ) ss k (U
Page 129 and 130:
Page 131 and 132:
FIGURES 121 〈U〉 (Uτ ) ss 〈U
Page 133 and 134:
FIGURES 123 k (U 2 τ ) ss k (U 2
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
FIGURES 129 ( ∂〈P 〉 ∂x ) (
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
show all

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

Create successful ePaper yourself

Delete template?

Save as template?