Abstract
Three practices of treating outflow boundary condition were adopted in computations for convective heat transfer of a two-dimensional jet impinging in a rectangular cavity. The three practices were local mass conservation method, local one-way method and fully developed assumption. The numerical solutions of the three methods were compared with test data obtained via, naphthalene sublimation technique. It was found that the fully developed assumption was inappropriate, and the local one-way method could provide reasonably good results for the cavity bottom, while for the lateral wall the results with this method qualitatively differed from the test data. The solution with the local mass conservation method was the best. It thus suggested that for a problem expected with a strong recirculating flow at the exit of the computation domain, the local mass conservation method be adopted to treat the outflow boundary condition.
Zusammenfassung
Es werden drei verschiedene Methoden herangezogen, um die Erfüllung der Ausflußbedingung bei der Berechnung des konvektiven Wärmeübergangs von einem zweidimensionalen Fluidstrahl an die Wände eines rechteckigen Hohlraumes zu erzwingen. Diese seien kurz bezeichnet als: (1) lokales Massenerhaltungsprinzip, (2) Einkomponentenprinzip, (3) Vollausbildung des Strömungsprofils.
Unter Verwendung dieser drei Prinzipien ermittelte numerische Lösungen wurden mit experimentell (Naphtalin-Sublimationsmethode) gefundenen Ergebnissen verglichen. Es zeigte sich, daß Methode (3) ungeeignet ist, Methode (2) gute Ergebnisse für den Hohlraumboden liefert, aber an den Seitenwänden qualitativ von den Versuchsdaten abweicht und daß Methode (1) die beste Übereinstimmung bewirkt. Bei Problemen, welche starke Rezirkulationsströmungen am Austritt des zur Berechnung vorgegebenen Kontrollraumes erwarten lassen, sollte daher dieser Methode der Vorzug gegeben werden.
Similar content being viewed by others
Abbreviations
- a :
-
long-side length of cavity bottom surface
- a P, N, E, W, S :
-
coefficients in discretization equation
- b :
-
constant term in discretization equation
- B :
-
width of slot jet nozzle
- B W :
-
thickness of jet nozzle wall
- c :
-
height of cavity lateral wall
- C p :
-
specific heat capacity
- D :
-
mass diffusion coefficient
- H :
-
distance from jet exit to cavity bottom surface
- H B :
-
height of lateral wall
- k :
-
thermal conductivity
- K :
-
mass transfer coefficient
- L :
-
grid number inx-direction
- M :
-
grid number iny-direction
- N u :
-
Nusselt number
- p :
-
pressure
- R(x, y):
-
source term
- Re :
-
Reynolds number
- Sc :
-
Schmidt number
- Sh :
-
Sherwood number
- T :
-
temperature
- u,v :
-
velocity components inx-, andy-directions
- V :
-
average velocity
- W B :
-
cavity width
- x, y :
-
Cartesian coordinates
- α :
-
heat transfer coefficient
- α u ,α v ,α p :
-
relaxation factors foru, v, andp, respectively
- Γ :
-
nominal diffusion coefficient
- ΔA :
-
area of surface element
- ΔM :
-
corrected mass loss of naphthalene during data run
- μ :
-
dynamic viscosity
- ν :
-
kinematic viscosity
- τ :
-
time duration
- Φ :
-
general variable
- i:
-
local
- j:
-
jet exit
- n:
-
naphthalene
- w:
-
wall
- ⋆:
-
previous iteration
References
Patankar, S. V. Numerical Heat Transfer and Fluid Flow. Hemisphere, Washington, D.C., 1980
Chan, Y. L.;Tien, C. L. A Numerical Study of Two-Dimensional Natural Convection in Square Open Cavity. Numer. Heat Transfer 8 (1985) 65–80
Chan, Y. L.;Tien, C. L. A Numerical Study of Two-Dimensional Natural Convection in Shallow Open Cavity. Inter. J. Heat Mass Transfer 28 (1985) 603–612
Shyy, W. Numerical Outflow Boundary Condition for Navier-Stokes Flow Calculations by a Line Iterative Method. AIAA J. 23 (1985) 1847–1848
Shyy W. Effects of Open Boundary on Incompressible Navier-Stokes Computation: Numerical Experiments. Numer. Heat Transfer 12 (1987) 157–178
Papanastasiou, T. C.;Malamataris, N.;Ellwood, K. A New Outflow Boundary Condition. Inter. J. Numer. Methods in Fluids 14 (1992) 587–608
Johanson, B.;Christer, V. Boundary Conditions for Open Boundaries for the Incompressible Navier-Stokes Equation. J. Computations Physics 105 (1993) 233–251
Gresho, P. H. A Simple Question To Simple Users. Numer. Heat Transfer (A) 20 (1991) 123
Sogin, H. H. Sublimation from Disks to Air Stream Normal to Their Surfaces. ASME Trans. 80 (1958) 61–71
Chyu, M. K. Influence of Roughness Element on Local Mass Transfer from Flat Plate. Ph.D. Thesis, University of Minnesota, Minneapolis Minnesota, 1986
Li, P. W. Experimental and Numerical Investigations on Heat/Mass Transfer of Jet Impingement in Rectangular Cavities. Thesis, Department of Power Machinery Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, China, 1991
Li, P. W.;Tao, W. Q. Numerical and Experimental Investigations on Heat/Mass Transfer of Slot Jet Impingement in a Rectangular Cavity. Inter. J. Heat and Fluid Flow 14 (1993) 246–253
Author information
Authors and Affiliations
Additional information
This work was supported by the National Natural Science Foundation of China and the Special Research Foundation for Doctorate Financed by the National Educational Commettee of China.
Rights and permissions
About this article
Cite this article
Li, P.W., Tao, W.Q. Effects of outflow boundary condition on convective heat transfer with strong recirculating flow. Warme - Und Stoffubertragung 29, 463–470 (1994). https://doi.org/10.1007/BF01539498
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01539498