Uncertainty Quantification in Heat and Fluid Flows Around Staggered Pin-Fin Arrays Based on Hybrid RANS/LES Model

다국어 초록 (Multilingual Abstract)

In the present work, the three dimensional heat and fluid flows around staggered pin-fin arrays are predicted using two Hybrid RANS/LES, Improved Delayed Detached Eddy Simulation(IDDES) and Stress Blended Eddy Simulation (SBES) and one transitional Unsteady Reynolds Averaged Navier-Stokes (URANS) model, k- SSTLM. The periodic segment geometry with total 8 pins is considered with the channel height of 2D and the distance of 2.5D between each pin. The corresponding Reynolds number based on the pin diameter and the maximum velocity between pins is 10,000. Two Hybrid RANS/LES results show superior prediction in mean velocity profiles around pins, pressure distributions on the pin wall and Nusselt number distributions. However, transitional model, k- SSTLM show large discrepancy except in the front part where the flow is not fully developed. The two Hybrid RANS/LES models resolve the vortical structures well Specially, SBES model is able to capture the three dimensional vortical structures after the pin. The effect of the blending function switching between RANS and LES mode of two Hybrid RANS/LES model is investigated.

The Uncertainty Quantification Forward problem is conducted with non-intrusive polynomial chaos expansion. The input variable is set as inlet velocity. it is assumed as a uniform distribution or normal distribution. Its mean μ is 3.45m/s and standard deviation σ is ±0.1 μ. The quantity of interest is the average Nusselt number and the local Nusselt number. The results show that probability density function of output is strongly affected by probability distribution of input.

목차 (Table of Contents)

• Chapter 1. Introduction 6
• Chapter 2. Numerical Method 9
• 2.1 Governing Equation 9
• 2.2 Turbulence Models 11
• 2.2.1 k-ω SSTLM 11
• 2.2.2 Improved Delayed Detached Eddy Simulation (IDDES) 12
• 2.2.3 Stress Blended Eddy Simulation (SBES) 14
• 2.3 Discretization scheme and Coupling algorithm 15
• 2.3.1 Upwind scheme 15
• 2.3.2 Implicit discretization 16
• Chapter 3. Theorical Background for Uncertainty Quantification 19
• 3.1 The Definition of Uncertainty Quantification 19
• 3.2 Polynomial Chaos Expansion 19
• 3.3 Sampling Method 21
• Chapter 4. Deterministic Simulations for Staggered Pin-Fin Arrays 22
• 4.1 Geometry 22
• 4.2 Grid 22
• 4.3 Boundary Conditions 23
• 4.4 Results 24
• 4.4.1 Grid Test 24
• 4.4.2 Velocity Profile 25
• 4.4.3 Pressure Coefficient Around The Cylinder 28
• 4.4.4 Nusselt Number Distribution Around The Cylinder 29
• 4.4.5 Pin Nusselt Number Distribution 30
• 4.4.6 Local Nusselt Number Distribution 31
• 4.4.7 Average Nusselt Number 34
• 4.4.8 Nusselt Number Contour 34
• 4.4.9 Q-Criterion 37
• 4.4.10 Turbulence Structure 37
• 4.4.11 Blending Function 40
• Chapter 5. Uncertainty Quantification for Staggered Pin-Fin Arrays 42
• 5.1 gPCE results . 42
• Chapter 6. Conclusion 44
• 6.1 Conclusions 44
• 6.2 Future works 45
• REFERENCES 46