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

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CHAPTER 1. INTRODUCTION & LITERATURE SURVEY 2 that are ever more complex. The type of flow considered in this thesis is incompressible and Newtonian. On scales that are several orders of magnitude larger than the molecular scale, the flow is governed by the Navier-Stokes equations. These equations model a flow field as a continuum. CFD codes discretise the flow domain to allow variables to be represented numerically. The most common type of discretisation is the Finite Volume method, which is applied in this work. The governing equations of fluid flow identify a large degree of interconnectedness between the various properties of a flow field. Because of this, most CFD codes use an iterative approach. This involves traversing the flow field and everywhere calculating flow parameters based on local information. The solution converges as this process is repeated with updated local information. In general, a flow field is a complex system with mechanisms for internal feedback. Because of this, a flow field can exhibit chaotic behaviour. This means that, although fluid flow is deterministic, it may appear to include randomness because of its extreme physical complexity. A flow is classed as turbulent when it behaves chaotically. This is a subjective definition, and there does exist ‘transitional flow’ where the appropriateness of classing the flow as turbulent is unclear. However, most flows of relevance to engineering applications are clearly turbulent, and most CFD work is aimed at predicting the behaviour of turbulent flow. Most commonly, this is accomplished by the adoption of a turbulence model that makes use of certain assumptions to approximate flow behaviour using more tractable equations. This precludes the possibility of predicting every feature of the flow, but the parameters providing the greatest engineering relevance may be estimated at a greatly reduced computational cost.
CHAPTER 1. INTRODUCTION & LITERATURE SURVEY 3 One approach to turbulence modelling is the Reynolds Averaged Navier- Stokes (RANS) type. RANS models use time- or ensemble-averaged Navier- Stokes equations to calculate the mean values of flow parameters. 1 The fluctuating components of these parameters are modelled, rather than being fully resolved. Conceptually, this amounts to solving a flow as though it were laminar, but with the addition of modelled turbulence superimposed over the bulk flow behaviour. This modelled turbulence affects the bulk flow according to the details of the model. The most popular RANS models are the Eddy-Viscosity Models (EVMs). EVMs model the affect of turbulence on bulk flow via the concept of turbulent viscosity. Local turbulence is presumed to manifest itself as an increase in the effective viscosity of the fluid. The physical justification for this concept is that turbulence entails greater interaction between fluid particles. This leads to a greater exchange of energy between adjacent parcels of fluid. In terms of the momentum equations, this interaction produces an effect that is analogous to increased viscosity. The EVM may be extended by the incorporation of non-linear terms [77, 14] This is the non-linear type of EVM. An alternative to EVMs is presented by the Reynolds Stress Transport models [69, 15]. Here, the products and squares of root-mean-square velocity fluctuations (Reynolds stresses) are cal- culated as being convected and diffused through the flow field according to their own transport equations. This thesis deals with the application of linear EVM RANS. 1 Ensemble averaging is associated with periodic flow problems, and time averaging is associated with steady problems.
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: Chapter 1 Introduction & Literature
Page 15 and 16: 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: 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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