Étude numérique et expérimentale du phénomène de la transition en convection mixte dans le cas d'un tube vertical pour un nombre de reynolds inférieur à 2000
Combined forced and free convection (mixed convection) heat transfer for upward airflow through a vertical tube at relatively low Reynolds numbers was studied numerically and experimentally. The research focused on the axial and radial evolutions of hydrodynamic and thermal parameters of the flow field at Re < 2000, particularly on flow field transitions at such low Reynolds numbers. Therefore, a formulation based on Launder and Sharma Low Re [kappa]-[epsilon] turbulent model was proposed. Its main advantage is that it can predict laminar as well as turbulent flow fields. The elliptical form of the governing equations was also used in order to predict developing flow field parameters. The ability of the formulation and numerical procedure to predict the flow field characteristics was shown by comparison with experimental results. The calculated results were compared with experimental measurements that were found in the literature for very low Reynolds number (Re = 380) and high Reynolds number (Re = 5000). They were also compared with our experimental results at relatively low Reynolds number (Re = 1588). The calculated results for Re = 430, 1000 and 1500 established two critical Grashof numbers for which transitions occur (these transitions did not appear for Re = 430). At the first one (Gr [approximate] 9 × 10[superscript 6] for Re = 1000 and Gr [approximate] 2 × 10[superscript 6] for Re = 1500), the flow regime changes from laminar to turbulent. At the second critical point (Gr [approximate] 5 × 10[superscript]7 for Re = 1000 and Gr [approximate] 9 × 10[superscript 7] for Re = 1500), the flow regime comes back to laminar because of the accelerating effect of heating. Two flow reversal patterns were predicted and discussed. The first one includes the centerline while the second one occurs between the tube axis and the wall. In spite of the analytical solution by Hallman (1956), which confirms the existence of the second one, it had not been predicted numerically before. An experimental apparatus was designed and built to study the flow field transitions and their structure. FFT spectra of the temperature fluctuations and the velocity fluctuations indicator determined the critical Grashof numbers for which the flow field changes from laminar to turbulent. These critical Grashof numbers are 3.78 × 10[superscript 6] , 1.09 × 10[superscript 6], and 3.81 × 10[superscript 5] corresponding to Re [approximate] 1000, Re [approximate] 1300 and Re [approximate] 1600. The most important thermal fluctuations oscillate with f = 0.45Hz and its multiples while the velocity fluctuations oscillate with f = 1.8Hz (which is also a multiple of f = 0.45Hz) and its multiples.
- Génie – Thèses