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Effects of outflow boundary condition on convective heat transfer with strong recirculating flow

Einfluß der Ausflußbedingung auf den konvektiven Wärmeübergang bei starker Rezirkulationsströmung

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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.

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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

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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.

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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

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  • DOI: https://doi.org/10.1007/BF01539498

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