l AIVC 11621 pERGAMON Building and Environment 34 ( 1999) 245-251 Mixing characteristics in a ventilated room with non-isothermal ceiling air supply H. Xue*, C. Shu Department of Mechanical and Production E11ginel!ring, National Cnieersit_r of Singapore, JO Kent Ridge Crescent, Singapore 119260 Received 16 September 1997; accepted in revised form 17 April 1998 Abstract A two-dimensional turbulence k-e model is used to predict distribution of air velocity, temperature and turbulence kinetic energy in an air-conditioned room using ceiling air supply. Mixing characteristics of the airflow are analyzed under different air supply velocities and temperatures. A modified Archimedes number is correluted with the p�1rnmeter ·characterizing heat transfer, ventilation system, and turbulence kinetic energy of room air flow. Significant correlations have been hown. fl is found that the linear ceiling air supply air-conditioning system with a high level return air provides excell nl mi i g a wide range of Archimedes air x n across numbers. The results are useful for air-conditioning design and thermal comfort study. 1998 Elsevier Science Ltd. All rights •· reserved. Nomenclature V volumetric flow rate A cross section area W length of room Ar modified Archimedes number (=Gr/ Re2 5) x, y Cartesian coordinates B width of room y+ dimensionless distance from wall ( = uy/v) C1,, C1, C2, C3 turbulent constants Dh hydraulic diameter of room Greek symbols turbulence dissipation rate g gravitational acceleration e ), thermal conductivity G0 buoyancy production term molecular viscosity Gk shear production term J.l gD�!},,To/T'" J.l, eddy viscosity Gr Grashof number = turbulent dynamic viscosity ( 2 ) v, ,. turbulent Prandtl number aT H height of room turbulent Schmidt number k turbulent kinetic energy ab a., 1 exchange coefficient k" average turbulent kinetic energy Nu local Nusselt number Subscripts Nu average Nusselt number e at air exhaust duct p pressure eff effective Pr Prandtl number I at left wall DhUr r at right wall Re Reynolds number = - ( v-) 0 at air supply inlet T temperature Tm mean room temperature Tw wall temperature 1. Introduction U, equivalent room velocity Understanding the indoor air distribution charac­ u, mean velocity components v teristics is essential to the design of a ventilation system friction velocity Ur and the control of room thermal and air quality conditions. Ceiling air supply is one of the most widely *Corresponding author. Tel.: 0065 874 6479; fax: 0065 779 1459: used ventilation and air conditioning methods in the e-mail: mpexueh(;, nus.edu.sg region. This method requires that the supply air and S0360-1323/99 $-see front matter {' 1998 Elsevier Science Ltd. All rights reserved Pll: S0360-l 323(98)00015-8 246 H. Xue. C. Sh11/Bui/di11g and £11riro11111e111 34 ( 1999) 245-251 room air are mixed well by the interactions of the supply Air Supply . Ad1abat1c. Wall jet momentum and buoyancy. The supply air is func­ sic � Air ExhaL tioned to dilute the concentration of contaminants in the lssssssss11 s11ssssssssss1sssssssS\$)SS<<sss� room. Because the non-isothermal air is supplied at high level, the concentration levels above the occupied zone E are generally lower than those existing within the zone, I.{) which results in an overall relative ventilation efficiency C\I II Tw=30°C T w= 30°C of less than one. In addition, stagnant zones of high :::c concentration levels and short circulating of supply air to the extract points can cause a sharp drop in the ven­ y Adiabatic Wall tilation efficiency.To a void these occurrences, it is impor­ x tant to carry out an accurate prediction on the air mixing o��=s:l:sss.'il='<5'm:n:� characteristics during design stage. W=3.5m The prediction of air movement in rooms by com­ Fig. I. Schematics of simulated room. putational fluid dynamic (CFO) method started in the 1970s [l]. With rapid increase of computer power, the topic has attracted more and more attention [2, 3, 4]. ASHRAE technical meeting now regularly includes tech­ nical sessions on CFO developments and application to to simplify the numerical simulation by using a t\1 room air motion studies. However, .numerical studies on dimensional mathematical model. Assuming that L air mixing characteristics of ceiling air supply con­ fluid is incompressible and that the Boussinesq appro figurationare few to date. In addition, the available over­ mation is valid, and employing the eddy viscos concept, which assumes that the turbulent stresses whelming majority of contributions are from the United � States and Europe. While these areas certainly cover a proportional to the mean velocity gradients, the tin broad range in the climatic spectrum, the research of averaged continuity, momentum and energy equatio room air distribution under the equatorial climate is are written as grossly underpresented in the literature. C Ct' The present study simulates the air motion in an air­ -+-LI = 0 conditioned room with ceiling air supply. The main pur­ ex oy pose is to investigate the effects of important parameters cu cu cP c cu such as Archimedes number on air velocity and tem­ pL1-;;-+pe-;;- = --::;--+2-;;- 1 -;;- cx ey ex ex · ex ) perature distribution. ventilation efficiency, heat transfer ( 11.. 1 and turbulent mixing. As a preliminary step, the effluence of room partitions, furnishings as well as internal heat source are not considered so that the basic mixing charac­ teristics of air can be examined carefully. �c /c - �p pu + p = + � 11 +2 ex cy c.i· ex (11 .. �cex) ;cy (11e··11 �v)oy 2. Mathematical model c cu p T - + -;;- p,.11· -;;- + g /3( T;) ex ( ey ) During the last two decades, a number of numerical models have been compiled for the prediction of room cT cT a a air motion. Besides the k-e model, engineers in this field p -;-- + pr = r + r LI -:::-ey -;;- ( ..11 -::.--t8cy -;;-cy · a8L'}' have begun applying more sophisticated models, such 1.,x ex ( ,.11 -;-- as algebraic and Reynolds stress models. Using ad-hoc where the pressure term in the momentum equations modifications on the standard k-e model to improve the actually a pseudo-pressure. 11,.11 is combined laminar a1 computed results is also a common practice. However, a turbulent stresses and C11 is effectiveexchange coefficie1 recent study by Chen [5, 6] showed that, in simulating air They are given by flow in rooms, the standard k-e model gives stable and good results across all the cases. The standard k-e model is therefore used for the present study. fl fl, With reference to Fig. steady, turbulent flow and f,./l:T=-+- I, Pr heat transfer are considered within a rectangular room O", that is supplied with cooled air from a linear ceiling slot. where Pr and are the laminar and turbulent Pram O", The room has an exhaust outlet at the up-right wall. numbers respectively. The eddy viscosity is obtained I The linear ceiling air supply configuration enables us the Prandtl-Kolmogorov relation. H. Xue, C. Shu1Building and E11ciro11111e11134 ( 1999) 245-251 247 kl The wall functions are valid for forced convection flow (7) .IS! JI=' pC,,-e with small pressure gradients and for y+ > 10.8. Since the friction velocity can be expressed as (1, being empirically determined coefficient. The turbulent kinetic energy and dissipation transport = u = 3 equations for buoyant flows can be written as follows. , '>/'t h-J.. '>/(Tu! (1 ) flM'(� ll) " l'--;: . ck ck c ck P11-.:;- +pr--;;-- = C·1n-;;­ where y is the distance between the wall and first grid ex cy --;;--C.\' ( · · ) ex point, the constraint fory+ requires a corresponding local Reynolds number Jul_v/v to be larger than 117. For the (8) near wall grid points where JuJy/v � 117, laminar flow calculation will be carried out locally. At the inlet, all dependent variables are prescribed. A ce ce c cs c ce Pu-.:;- +pr--;;-- = r 11.c--;;-- + r,.11:.:-.:;- uniform vertical velocity and temperature are assumed. 0.\' cy --;;--( .. ) --;;--.cy ( cy ) ex · ox The values of k and are empirically given as e ko = 0.02r6 and c,,k,\ 5/0.05. 80 = At the outlet, a five-grid-long(0.5 m) extension is added into the exhaust duct to facilitate boundary condition IQ­ specifications that do not compromise local flow field .he where accuracy. Zero-gradient conditions are prescribed at the Xl­ end of the extension for all dependent variables. ity The partial differential equations governing turbulent ire mixed convection are reduced to systems of simultaneous 1e­ equations by a control-volume based, finite-difference ·ns Gk = 2 + 2 - + + -.:;- (I 0) [ (au)2--;;-- (ar)2 (au-.:;-C)' C.\'cr)2] procedure where the velocity control volumes are stag­ ex oy gered with respect to the main control volumes. The ( 1 I) resulting algebraic equations are solved iteratively using a I) line-by-line TOMA solution procedure and the SIMPLE algorithm described by Patankar [8]. Steady-state solu­ In the above equations, G8 represents an exchange tions are obtained using underrelaxation techniques. between the turbulent kinetic energy and the potential To decide whether a solution is converged, the ratio of energy. The constant controls the effect of buoyancy C3 the residual mass source to the maximum mass fluxacross on the equation. Rodi [7] suggested that flux Richardson F. a control surface is set to be less than 0 1 % . A general 2) number can be defined as . convergence is then usually satisfiedafter 6000 iterations. The computations are performed on 42 27 grids. The x ( 12) solution procedure has been validated against the bench­ mark results of de Yahl Davis (9] for laminar natural for horizontal shear layers and Rr = 0 for vertical shear convection in an enclosure with aspect ratio of I, with layers.