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

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CHAPTER 1. INTRODUCTION & LITERATURE SURVEY 14 riodic flow. Ahmadi-Befrui et al. [2] published mean velocity readings at various locations within a cylinder through a piston stroke. Tabaczynski [78] has investigated reciprocating flow in engines. Also, the Society of Automo- tive Engineers has published an extensive collection of results. One very notable DNS study of periodic flow is that of Kawamura & Homma [29], which investigates channel flow at a low Reynolds number driven by a periodic pressure gradient. The periodic flow results presented in this thesis are compared against the DNS results of Kawamura & Homma. Various researcher have investigated the use of turbulence models in predicting periodic flow. Cotton & Ismael [12] applied the standard k-ε model to periodic pipe flow. Cotton et al. [13] and Addad [1] have investigated the use of Reynolds Stress Transport models in predicting periodic flow. Watkins [86] produced an early investigation into the use of CFD in internal combustion engines, and various other studies have followed [60, 35]. Naitoh & Kuwahara [45] applied LES to engine flow. The relevance of wall-functions to periodic flow has received less attention. The UMIST-N subgrid wall function has not been applied to periodic flow prior to this work. Standard wall functions are generally applied to internal combustion engine studies. 1.6 Study Objectives The primary objective of this study is to assess the applicability of the UMIST-N subgrid near-wall treatment to a periodic flow problem, relative to
CHAPTER 1. INTRODUCTION & LITERATURE SURVEY 15 other popular approaches. The secondary objective is to experiment with the use of the k-ω model in the subgrid solution scheme. This work represents the first application of the UMIST-N approach to time-variant flow and the first use of a k-ω model within the subgrid calculation. These objectives are met through the analysis of the logarithmic law of the wall, the standard low-Reynolds number k-ε treatment, a k-ε subgrid treatment, and a k-ω subgrid treatment in steady channel flow and in periodically variable channel flow. The results of this study are compared against the detailed DNS data of Kim et al. [30] in the case of steady flow and Kawamura & Homma [29] in the case of periodic channel flow. A tertiary objective that arose over the course of the project was to inves- tigate the study of channel flow in general, so as to provide some input to other CFD efforts that make use of channel flow data. This objective is met through a detailed background discussion of channel flow, a compilation of some useful experimental and DNS results concerning channel flow, and the revision and presentation of a set of analytical profiles to characterise the ex- pected behaviours of flow parameters in a channel as a function of Reynolds number. 1.7 Thesis Outline The various turbulence models employed in this work are discussed in Chap- ter 2. This includes a more detailed discussion of the RANS approach and a presentation of the k-ε and k-ω models. The differences between the high- and low-Reynolds-number k-ε models are highlighted. The logarithmic law
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 23: 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
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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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