The document summarizes numerical simulations of mixed convection airflow under a dome-shaped roof. It describes the numerical methods used, including the finite volume method and turbulence modeling. Validation cases are presented and simulations are shown for natural convection in a tall cavity, mixed convection in a square cavity, and mixed convection airflow under domes with varying parameters like the Grashof and Reynolds numbers.

1. Numerical Simulation of Mixed
Convection Airflow Under
a Dome-Shaped Roof
By: Masih Khoshab
Supervisor: Dr. A.A. Dehghan

2. Domed Roofs

3. One of the typical underground cold water storage with
domed roof equipped with wind catchers (Baadgir)
Domed Roofs & underground cold water storage

4. One of the typical underground cold water storage with
domed roof equipped with wind catchers (Baadgir)
Domed Roofs & underground cold water storage

5. • Finite-Volume Method
• Staggered Grid
• SIMPLER Algorithm
• Scheme ADI (Implicit Line-by-Line)
• Turbulence Modeling (LRN K-ω model of Wilcox)
Solution Procedure

6. Validation and Verification
Concentric Isothermal Spheres
Natural convection in tall cavity
Mixed convection in square cavity

7. Buoyancy-Induced Flow
Between Two Concentric Isothermal
Spheres

8. Problem Definition
Physical Model and Coordinates System

9. 5
107.392Ra 
2.17R*

5
10261.2Ra 
*
R =1.78O
i
r
r

Numerical & Experimental Results

10. *
R 2, Pr=0.72 6
Ra 1 10 5 10   
Effects of Rayleigh Number

11. Effects of Rayleigh Number
*
R 1.5, Pr=0.73 6
Ra 1 10 1 10   

12. *
R 1.2, Pr=0.73 6
Ra 1 10 1 10   
Effects of Rayleigh Number

13. Variation of Nusselt Number with Rayleigh Number

14. Natural convection in tall cavity
Mixed convection in square cavity

15. Natural convection in tall cavity
From Peng and Davidson, J. Heat Fluid Flow 20, 172–184 (1999)

16. Streamlines and
Isothermal Contours
Streamline (right) and
Isothermal Contours (left)

17. Peng and Davidson, J. Heat Fluid Flow 20, 172–184 (1999).
Cheesewright et al., HTD 60, ASME, pp. 75–81, (1986).
Profiles at Midsection and Nu Number

18. Mixed convection in square cavity

19. Mixed convection in square cavity
From Peng and Davidson, J. Heat Fluid Flow 20, 172–184 (1999)
Blay et al., HTD 213, ASME (1992)

20. Velocity Profile at Midsection

21. Temperature Profile at Midsection

22. Turbulence Kinetic Energy Profile at Midsection

23. Dome-Shaped Roof

24. Spherical Coordinates

25. Effects of Grashof Number
6 10
Gr=1 10 1 10  
4
Re=1 10
Streamline (right) and
Isothermal Contours (left)

26. Effects of Reynolds Number
3 4
Re=5 10 5 10   6
Gr=1 10
Streamline (right) and Isothermal Contours (left)

27. Modifications and Accomplishments
• I extended the solver for Micropolar fluid and
Nanofluid flows.
• Yuri Feldman and Tim Colonius,
International Journal of Heat and Mass Transfer 64, 514–525, (2013).
• Two MSc. Student.