Room Ventilation and Its Influence on the Performance of Fume

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Ind. Eng. Chem. Res. 1997, 36, 458-466

Room Ventilation and Its Influence on the Performance of Fume Cupboards: A Parametric Numerical Study Jordan A. Denev,† Franz Durst,* and Bernhard Mohr LSTM, Friedrich Alexander University Erlangen-Nuernberg, Erlangen, D-91058 Germany

The three-dimensional turbulent flow in a typical chemical laboratory containing two fume cupboards and furniture is investigated numerically in order to obtain detailed information needed for the improved design of ventilating systems for such rooms. The flow inside the two fume cupboards is simulated simultaneously with the room flow, and its dependence on the flow structure in the room is shown. The flow inside the cupboards and in the vicinity of their sash openings has been found to be essentially three-dimensional. Several room parameters are varied, and a quantitative evaluation of their influence on the flow, the comfort characteristics, and the ventilation efficiency is given. Additional ceiling-mounted openings, which extract room air outside the fume cupboards, can affect the capture efficiency of the cupboards, as well as the quality of the air in the room. It has been found also that small changes in the position of the radial inlet ceiling-mounted diffuser can influence the air quality of the room and at the same time the draught risk. These effects are shown for a given room arrangement. To accommodate the complex geometry, the elliptical nature of the mathematical problem, and the use of a turbulence model, a multigrid acceleration method with 245 000 control volumes is used, allowing CPU times on a workstation to become acceptable. 1. Introduction The interaction of the flow in open-fronted containment facilities with the flow in the surrounding room is often pointed out as an important factor for the reliable performance of such devices and hence has been the subject of considerable investigation and discussion (Bunse and Gra¨ff, 1985; Gra¨ff and Stahl, 1986; Durst and Pereira, 1991; see also Standards BS 7258, 1998, ANSI/ASHRAE 110-1985 R, and SEFA-1/1992). The influence of sitting and room ventilation on the performance of fume cupboards will for the first time be part of the new European CEN Standard for fume cupboards, currently in preparation. O ¨ zdemir et al. (1993) have investigated experimentally the flow in a fume cupboard and its dependence on the room flow, showing that a modest draught from a poorly designed ventilation system can cause greater nonuniformity for the inflowing velocity distribution of the facility. They simulated the draught by means of a fan remote from the cupboard and observed up to 2 times higher concentration rates in its sash opening compared with the case without a draught. Even for the case without a draught the velocity in the sash opening showed an uneven and asymmetrical distribution. Khezzar and Whitelaw (1993) made a numerical investigation of the flow inside a fume cupboard in accordance with the above experiments. As a boundary condition in the sash plane they used the experimental values for the inflowing velocity, with the assumption of unidirectional inflow. They attributed some discrepancies in the calculated values of the concentration of species to this unidirectional assumption and so undertook an evaluation of the influence of the boundary conditions. By extending the computational mesh some * Author to whom correspondence is addressed. Telephone: (++)9131-85-95-01. Fax: (++)9131-85-95-03. Email: [email protected]. † Present address: Department of Hydroaerodynamics, Technical University of Sofia, Kliment Ochridski Str. 8, Sofia 1000, Bulgaria. S0888-5885(96)00218-7 CCC: $14.00

distance upstream of the inlet plane, they obtained a clearly different flow in the vicinity of the sash handle, a flow which was actually directed downward and not unidirectionally inward in the sash opening. A downward translation of the main spanwise vortex at the upper frontal part of the fume cupboard and a related leakage tendency near the sash handle were also important consequences of the changed boundary conditions. However, in contrast to this study, a similar but two-dimensional numerical study by Hu et al. (1993) on the influence of the position of the inflowing boundary on the flow inside fume cupboards did not reveal changes in the direction of the inflowing stream in the sash plane. The present study, concerning a typical chemical laboratory, is based on the numerical simulation in three dimensions of the flow in a whole room, including the flow inside two fume cupboards. Such calculations give the possibility of investigating the influence of the room flow on the flow structure at the front plane and inside the containment facilities. In order to provide detailed information on this influence, different room parameters such as the positions of the supply outlets and the extract openings and the size of the sash opening of the cupboards, as well as the furniture arrangement, are varied. Special attention is given to the flow parameters in and around the sash openings because they precondition the overall performance of the fume cupboards and also they are also of interest by imposing boundary conditions for numerical studies. The simulation revealed a decrease in the capture efficiency of the facilities due to negative inflowing velocity for a 0.90 m sash opening. After analyzing the complex flow structure in the vicinity of the fume cupboard, the reason for this negative velocity is found to lie in the arrangement of the furniture, causing strong momentum flows outside the fume cupboards. The ventilation efficiency, which is crucial for rooms with possible exposure to contamination, is used for a comparative evaluation of the different competitive cases studied. As a measure of the ventilation ef© 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 459

Figure 1. Laboratory room with two fume cupboards and four tables.

ficiency, the “local mean age” of the air is chosen. It is known (Nielsen, 1992) that, in addition to the positioning of the supply outlet, the positioning of the extract opening also has a decisive influence on the ventilation efficiency. Based on the local mean age, a quantitative evaluation of this influence is represented and a rule for establishing the appropriate positioning of these openings at the design stage is conducted. The high flow rates prescribed by the standard for such laboratory rooms necessitate the estimation and comparison of the rates at which the comfort requirements for the different cases are satisfied. Results on this aspect are also presented. 2. Room Arrangement and the Flow Cases Studied A typical chemical laboratory room with dimensions 5.80 × 3.5 × 2.80 m is simulated. The equipment consists of two fume cupboards, each with outside dimensions 1.50 × 0.90 × 2.80 m and four tables of 1.50 × 0.90 m and 0.9 m height above the floor. With regard to the door of the room, the symmetry plane passing through the equipment and the supply outlet at 2.25 m does not align with the symmetry plane of the room itself, which is at 2.90 m. The room arrangement and the Cartesian coordinate system associated with it is represented in Figure 1. It can be seen that the fume cupboards separate the plan view of the room into two parts: the left-hand side where x < 1.50 m and the right-hand side, for which x > 3.0 m. A minimum flow rate of 1380 m3/h (prescribed by the German standard DIN 1946 according to the above room dimensions) is assumed. All of the air is sucked through the top of the two fume cupboards. The outlet openings

of the fume cupboards have dimensions 0.12 × 1.23 m, which results in a mean velocity of 1.3 m/s, which is set as a boundary condition for these openings. The radial air supply outlet has a diameter of 0.6 m, and the boundary condition for the normal velocity component in it is 1.4 m/s. The sizes of the sash openings studied are set at 0.10, 0.30, and 0.90 m as required by the German standard DIN 12 924, Part 1. This results in mean inflowing velocities in the sash openings of 1.39, 0.46, and 0.15 m/s, respectively. The geometry of the fume cupboards is assumed to be simple, without auxiliary apertures such as baffles, sash handles, and sills, which can strongly influence the flow structure. We chose this arrangement not only for reasons of simplicity for the grid generation state but also for the ability to establish clearly the effect of the influence of the room on the flow inside the fume cupboards. For the sake of simplicity, the different flow cases studied are abbreviated as follows: (1) DIFFOP. The sizes of the sash openings of the two fume cupboards are set to 0.30 and 0.90 m, respectively. This is the main reference case and all other cases are variations of it and are compared with it. (2) MIDINL. For this case the supply outlet of the room was set in the middle of the ceiling at x ) 2.90 m and y ) 1.75 m. (3) THEXTR. A third extract opening, in addition to the two inside the fume cupboards, is placed on the ceiling at x ) 5.6 m and y ) 1.75 m in order to establish its influence on the local mean age of the air in the room. Its dimensions are 20 × 30 cm, and the flow rate

460 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 Table 1. Characteristic Geometrical Parameters for the Four Flow Cases Studied

flow case

coordinates of the ceiling-mounted supply outlet

no. of extract openings

no. of tables in the room

DIFFOP MIDINL THEXTR TWOTBL

x ) 2.25, y ) 1.75 x ) 2.90, y ) 1.75 x ) 2.25, y ) 1.75 x ) 2.25, y ) 1.75

2 2 3 2

4 4 4 2

through it is 20% of the total room flowrate (by which amount the flowrate through the fume cupboards is reduced). (4) TWOTBL. The two tables on the right-hand side are removed in order to study their influence on the overall room flow pattern and on the flow inside the fume cupboards. The characteristic geometrical parameters for the four flow cases studied are summarized in Table 1. 3. Mathematical Model for the Mean Velocity Field and the Turbulence Quantities The system of equations solved is based on the timeaveraged Navier-Stokes equations, closed by the standard version of the k- turbulence model:

∂Ui )0 ∂xi FUj

(

)]

∂Ui ∂Ui ∂Uj ∂P ∂ )+ (µ + µt) + ∂xj ∂xi ∂xj ∂xj ∂xi

FUj

FUj

[

(1)

[( ) ] [( ) ] ( ) ( )

∂ ∂k ) Pk - F + ∂xj ∂xj

∂ ∂  2 ) C1Pk - FC2 + ∂xj k k ∂xj

Pk ) 2µtSijSij;

Sij )

µ+

µ+

1 ∂Ui ∂Uj + ; 2 ∂xj ∂xi

Fuiuj ) -µt

µt ∂k σk ∂xj

∂Ui ∂Uj + ∂xj ∂xi

µt ∂ σ ∂xj

(2)

(3)

momentum sources of these control volumes, the following expression is used (equation for the velocity component in the x direction):

Sm ) F × velox × velox × Arx

where Arx is the area of the control volume in planes normal to the x axis and velox is a linear function of the distance from the center of the diffusor. A similar expression follows also for the velocity component along the y axis. In the present study, in order to obtain the desired velocity field distribution arising from the diffuser, different linear functions were used for the fine grid control volumes along planes of constant height. It is now clear that this leads to discrepancies between the two numerical grids used: the same accuracy of modeling the diffuser flow cannot be achieved for the coarser grid, as the number of control volumes there is 8 times lower. 4. Local Mean Age: Nature and Mathematical Description The local mean age parameter at point P, τP (also called “residence time” by Sandberg, 1981), represents the average time needed for the molecules to pass from the intake device to that point. By using the so-called “step-down” experimental method for estimation of the local mean age, the whole room is filled initially with an equal concentration C0 of tracer gas. Then the HVAC (heating, ventilating, and air-conditioning) system is started, and fresh air is supplied to the room. The concentration at the point of interest P is recorded as a function of time, CP ) CP(t). Following Davidson and Olsson (1987), the local mean age is given by

(4)

k2 (5) µt ) FCµ  (6)

The model constants are Cµ ) 0.09, σk ) 1, σ ) 1.3, C1 ) 1.44, and C2 ) 1.92. The boundary conditions applied to the surfaces of the tables, fume cupboards, and room walls make use of the wall functions approach (Launder and Spalding, 1974). No use was made of symmetry-type boundary conditions owing to the different sash openings of the fume cupboards and the intended further investigations, including supply outlets with swirling jets. In order to reduce considerably the number of control volumes on the structured numerical grid, the flow in the vicinity of the circular ceiling diffuser was approximated using artificial momentum sources for the velocity components tangential to the supply opening. The benefit of this method lies in a correct setting of both the mass flow rate and the momentum in the area of the supply outlet with complex geometry, which appears to be difficult in other cases (see Hekkinen and Piira, 1994). The momentum sources Sm are added to the source terms in the linearized equations which belong to the control volumes just below the inlet opening, thus forcing the jet toward the wall. For the

(7)

τP )

∫0∞CP(θ) dθ

1 C0

(8)

from which its estimation from the measurements is obvious. Parts of the room, where the concentration falls rapidly after the start of the HVAC system, appear to be areas of low local mean age; i.e., they are well“ventilated”. This quantity is directly related to the quality of the ventilation system, as actually one of the definitions of the ventilation efficiency (see Sandberg, 1983) is the reciprocal of the local mean age. In the calculations, the local mean age distribution τ is obtained by an equation additional to the system of equations (1)-(6) governing a passive scalar quantity (which does not affect the velocity field):

FUj

∂ ∂τ m ˘ + ∂xj τ ∂xj

[( ) ] µ+

µt ∂τ στ ∂xj

(9)

where στ is a turbulent Schmidt number, given a value of 0.9 in this study. Sandberg (1981) proved theoretically that, in order to obtain the local mean age distribution from the above equation, the source term m ˘ τ should be set equal to unity at every point in the room. Under this condition the stationary problem described by this equation becomes equal to the nonstationary problem used for the experimental estimation of the local mean age distribution. For the passive scalar equation, from which the local mean age is obtained, zero-gradient boundary conditions

Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 461

Figure 2. Numerical grid at the ceiling of the room using general nonorthogonal coordinates.

on the walls and in the extract openings inside the fume cupboards are imposed. 5. Numerical Details and Resources Used The finite volume code FASTEST/3D, based on general curvilinear coordinates, colocated grid, the SIMPLE algorithm, and multigrid acceleration, was used. Owing to the restrictions on the complex geometry and the available computational resources (HP 9000/ 735/100 MHz workstation), a two-level multigrid technique with 76 × 62 × 52 ) 245 024 nodes on the finer grid was applied, which gave about a 3.67-fold acceleration in the CPU time. The CPU time was 26 h for one flow case by the chosen convergence criterion of 1 × 10-0.5 for the residuals for all equations, and about 138 Mbyte RAM was necessary for double-precision computations. For more details, see the FORTWIHR Report (1994). 24 × 16 × 34 ) 13 056 nodes inside each of the fume cupboards allowed the overall flow structure inside them and the influence of the room flow on this structure to be studied. The radial supply outlet at the ceiling of the room was approximated by 64 control volumes, as can be seen in Figure 2.

Figure 3. General overview of the flow patterns within the room.

6. Results and Discussion 6.1. Velocity Field and the Flow Patterns. 6.1.1. DIFFOP Case. A general overview of the flow patterns most interesting for further discussion is given in Figure 3, where some selected trajectories are plotted. Trace lines 1 and 2 originate from the ceiling-mounted diffuser and show the trajectory of the radial wall jet in the xz plane; note also the deflection of line 1 toward the sash opening of the right fume cupboard. In the plane yz the radial wall jet causes two small recirculation zones adjacent to the upper front walls of the fume cupboards, shown by means of trace lines 3 and 4. Some parts of the fluid (also approximately in the plane yz) follow the shortest way from the diffusor to the extract openings: these parts are presented by trace lines 5 and 6; the parts of the lines inside the fume cupboards, which are invisible for the viewer, are presented by dashed lines. The presence of complicated recirculation zones due to the furniture is presented by trace lines 7 and 8. Considering the inflowing velocity component in the facility with an opening of 0.90 m, a small area of negative values (up to -0.018 m/s) is discovered at medium height on the left-hand side of the sash opening (see Figure 4a). The small positive inflowing velocities existing around this area are also undesirable owing to

Figure 4. Distribution of the inflowing velocity component Uj (m/ s) in the 0.90 m sash opening. The higher values at the upper part correspond with the experiments of O ¨ zdemir et al. (1993): (a) DIFFOP case; (b) THEXTR case.

possible bursts as a consequence of turbulent pulsations. On the right-hand side of the opening, no negative velocities appear; rather, they remain at least 60% of the mean inflowing velocity. To explain these negative and small values, let us follow the flow structure in the vicinity of this facility. The supply jet trajectory passes close (the so-called Coanda effect) to the ceiling and to the side walls of the room, where it is deflected from the tables. Considerably different room flows on the two sides of the facility are established for two reasons: the first is the asymmetric position (with regard to the room) of the supply

462 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997

Figure 5. Velocity vectors close to the left outer side wall of the fume cupboards. Vertical cut of the room at distance x ) 1.44 m; DIFFOP case.

Figure 6. Horizontal plane at height z ) 1.30 m, where the negative inflowing velocities in the fume cupboard with a 0.90 m sash opening appear; case DIFFOP.

outlet and of the furniture and the second that the tables on the left-hand side are placed in the corners of the room, exactly perpendicular to the supply jet trajectory. Considering the vertical plane along the left-hand wall of the facility, it can be seen that strong momentum flow, deflected from the table and passing upward at an angle of 30°, is directed against the inflowing velocity into the cupboards (see Figure 5, also trace line 8 in Figure 3). A comparison with the corresponding velocity vectors at the other side wall of the facility shows about 2.5 times smaller values. This can be seen also in Figure 6, which represents a horizontal cut at a height of 1.30 m above the floor, where the outward velocities in the sash plane appear. As can be seen, owing to inertial effects, the side-wall flows from outside need a certain distance to be redirected toward the inside of the cupboard. Hence, suction occurs with a higher velocity in the middle of the sash opening, thus causing two strong vortices inside the fume cupboard for which the flow direction near the wall is toward the outside. As the outer flow on the left-hand side is much stronger, it causes a greater prolongation of the corresponding inner vortex, which in that case even reaches outside the sash opening, causing negative values for the inflowing velocity component (see Figure 6). Let us follow also the flow in front of this fume cupboard. By approaching the facility in planes parallel to its face, two vortices can be clearly distinguished in front of it at a distance of 0.35 m (Figure 7a). The vortices propagate through the sash opening inside the facility, interact further with the inside flow coming downward just after the sash, and disappear on the side

Figure 7. Vortex structure in front of the fume cupboard with a 0.90 m sash opening, plane y ) 2.25 m: (a) DIFFOP case; (b) DIFFOP case, results from the coarse grid computations; (c) MIDINL case.

walls of the cupboard at a distance of 0.20 m inside it. Figure 8 shows the velocity vectors and the vortices in the room plane passing through the sash opening. The velocities projected on it are of a comparable size to the inflowing velocity (shown in Figure 4a), which clearly points to the three-dimensionality of the flow. The vortex structure is supported by an increase in the turbulent kinetic energy, the maximum of which is coincident with the vortex center. It is interesting to note that the behavior of the vortices in front of the other fume cupboard, the opening of which is of size 0.30 m, is similar; the two vortices can be distinguished in the sash plane even when the calculations are made with a sash opening of 0.10 m. In order to compare the results from the two numerical grids, the velocity vectors from the coarse-grid computations in the plane y ) 2.25 m are also presented (cf. parts a and b of Figure 7). As can be seen in the figure, all recirculation zones on the coarse grid are predicted with the same destination and of equal size

Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 463

Figure 8. Vortices in the 0.90 m sash opening, plane y ) 2.58 m; DIFFOP case.

as the corresponding recirculation zones on the finer numerical grid. Despite the considerably lower number of nodes for this grid, the two vortices in front of the fume cupboard are also clearly presented. As already explained in section 3, the main differences between the solutions from the two grids appear near the diffuser outlet and are due to the limited possibilities of the coarse grid resolution to capture and model this area of the flow with the corresponding accuracy. This causes, of course, some differences, when the results are compared quantitatively: as written in the figures, the maximal velocities in the two planes are 0.351 and 0.359 m/s for the coarse and fine grids, respectively. Unfortunately, the velocities in other planes give deviations of up to 35%. However, the close overall correspondence of the flow pattern for the two grids provides good evidence that at least for the second numerical grid the results are within the accuracy necessary for engineering prediction. 6.1.2. Other Flow Cases. In the MIDINL case only one stable vortex in front of the facilities is distinguished (Figure 7c). The reason for this is the driving of the vortex by the jet deflected from the face of the fume cupboard and the asymmetrical arrangement of the air supply between the facilities. Actually, the flow outside the fume cupboards remains without any other qualitative differences. As the air supply is now further away from the left-hand side of the room, the flow deflected from the tables on the left-hand side is less strong and accordingly the negative values in the inflowing velocity are 13% lower compared with the DIFFOP case. In general, for the performance of a fume cupboard symmetry of the flow in the sash plane and inside the fume cupboard is desirable because of the stability of the inside directed flow. A comparison of DIFFOP and MIDINL cases shows that supply outlets asymmetrically placed with respect to the fume cupboards cause asymmetric velocity profiles in the face area of the fume cupboards (cf. parts a and b of Figure 9). Despite this result, the effect of a weaker deflection from the tables in the MIDINL case predominates over the advantages of symmetry. It should be noted again that, even when symmetrical, the flow remains three-dimensional. Concerning the size of the sash opening, smaller sizes provide more uniform flow parameters in this opening, approaching closely the assumption of two-dimensionality. Despite this, the three-dimensionality and asymmetry of the flow inside the facilities are not decreased by reducing the size of the sash opening. The 20% lower flowrates through the facilities in the THEXTR case make their capturing possibilities more

Figure 9. Velocity vectors at a height of z ) 1.75 m: (a) DIFFOP case; symmetrical distribution of the flow in the fume cupboards is observed; (b) asymmetrical flow in the fume cupboards for the MIDINL case.

Figure 10. Velocity profiles along three lines in the 0.90 m sash opening: solid line, DIFFOP case; dashed line, TWOTBL case.

vulnerable by the room flow. Figure 4b shows a considerable enlargement of the area of negative inflowing velocities (values up to -0.041 m/s) and hence a substantial reduction in their capturing possibilities. Figure 10 shows a comparison of Uj velocity profiles along three vertical lines in the sash opening with size 0.90 m (at the left-hand, middle-hand, and right-hand sides) for DIFFOP and TWOTBL cases. The considerable reduction in the velocity at the right-hand side for the TWOTBL case is a consequence of the increased velocities outside the cupboard on this side, caused by the removal of the tables. The lower inflowing velocity on the right-hand side requires an increase in the other

464 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997

a

a

b

b

Figure 11. Local mean age distribution in the middle plane y ) 1.75 m: (a) DIFFOP case; (b) MIDINL case.

parts of the opening and hence a reduction in the negative values at the problematic left-hand side; values of about -0.013 m/s occur. 6.2. Local Mean Age Distribution. According to its definition, the local mean age should decrease with an increase of the volume flowrate Q of the HVAC system. Hence, it is more consistent to represent the local mean age in a dimensionless form by using as a reference time the reciprocal of the air exchange rate τr ) V/Q. This form of representation is used in all figures. As the local mean age in the outlet opening is always equal to τr, (see Sandberg, 1981), the dimensionless local mean age, when averaged through the outlet opening, is unity. Since the air in the room is changed 25.8 times/h, or its average age in the extract openings is 140 s, which corresponds to the dimensionless value 1 in the figures. The local mean age in the middle plane of the room in the MIDINL case is symmetrically distributed between the left-hand and right-hand sides of the room (compare parts a and b of Figure 11) and shows 5% better results than in the DIFFOP case, when averaged throughout the occupied zone. Parts a and b of Figure 12 show the local mean age distribution for the same two flow cases at a height of 1.30 m, which represents the breathing area for a sitting person. As can be seen also in the figures, the local mean age for the MIDINL case is on average 7.5% smaller (i.e., better) than that in the DIFFOP case. This points to the sensitivity of the ventilation efficiency to the positioning of the supply outlet, as the distance between the centers of the supply outlets for the two cases was only 0.65 m (see Table 1). Even though the average velocity field is not greatly affected by the additional extract opening, the presence of the latter appears to be crucial for the efficiency of the ventilating system: on average, 11% greater values for the local mean age in the occupied zone occur for the THEXTR case than for the DIFFOP case. Although situated 3.45 m away from the supply device, the extract opening is not far downstream in terms of the radial jet trajectory, so that the extracted air has a local mean

Figure 12. Local mean age distribution at a height of 1.30 m: (a) DIFFOP case; (b) MIDINL case.

age which is far below the mean value for the room. Hence, the following rule applies: in order to improve considerably the freshness of the air in the room, the extract opening should be placed as far downstream on the jet trajectory as possible or in zones with a high local mean age. (Obviously some knowledge about the room flow patterns should be known in advance.) Such zones for the DIFFOP case are those below the tables near the fume cupboards on the right-hand side of the room (with a maximum value of 1.47) and for the MIDINL and TWOTBL cases below the tables near the side wall on the left-hand side of the room (with maximum values of 1.39 and 1.34, respectively, the latter being the lowest for all cases studied). The zones of high values for the local mean age are in agreement with the flow patternssthey are positioned in the far downstream region of the supply jet trajectory, in areas where the jet trajectory is interrupted by the furniture. The lower values observed for the TWOTBL case provide the explanation for the effect that furniture always causes additional recirculation and complication of the flow patterns, thus increasing the mean age of the air in the parts of the room in which it is positioned. The radial supply outlet drives the jet in the y direction toward the front of the fume cupboards. The jet is deflected down the front side of the fume cupboard (trace lines 5 and 6 in Figure 3) with a relatively strong impulse, as can be seen from the velocity vectors. As a consequence, part of this relatively “young” air reaches directly inside the fume cupboards and is sucked out of the room, in violation of the above-mentioned rule. However, in that case, additional considerations should be taken into accountsthis deflected flow supplies the breathing zone of a person standing in front of the fume cupboards directly with fresh air (the local mean age in that zone is 0.65-0.85), thus protecting the worker from exposure to possible contamination.

Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 465

6.3. Comfort Requirements. DIN 1946, Part 2, sets a velocity limit for the occupied zone, which depends on the temperature of the air and the surrounding walls, activity, and clothing. The activity for people in a laboratory is of type II (150 W heat flux per person). The room conditions for the simulations are isothermal, so the allowed maximum velocity level is in the range 0.22-0.31 m/s for a mean temperature in the room of 20-26 °C. According to DIN 1946, for estimating whether the comfort requirements are satisfied, the mean velocities are to be measured at heights of 0.2, 1.3, and 1.8 m above the floor; in the calculations the assessment is made only for the occupied zones between the tables, excluding the area of the wall jet very close to the lefthand wall. The maximum values of the velocities at those heights in the DIFFOP case are 0.121, 0.130, and 0.153 m/s, which are within the bounds prescribed by the standard. For the MIDINL case the corresponding values are highers0.150, 0.145, and 0.167 m/s. The higher speeds in the MIDINL case are observed in both the left-hand (due to the confinement of the radial jet from the cupboards) and the right-hand (due to the shorter jet trajectory in that case) parts of the room. 7. Conclusions The efficient multigrid method, which is able to handle complex geometries, allowed the simultaneous investigation of the three-dimensional flows both in a chemical laboratory room and in two fume cupboards positioned inside it. Thus, the interaction of the two flows, under the influence of parameters such as the arrangement of furniture and the positioning of the ventilating openings, was studied in detail. The operating safety of the fume cupboards, the ventilation efficiency in terms of the local mean age of the air, and the satisfaction of the comfort requirements for the various flow cases studied were compared. The most important issues in this study can be summarized as follows: (1) The particular arrangement of the furniture has been found to be the reason for the increased velocities in the vicinity outside the cupboards. It is shown further that this increase causes nonuniformity of the flow passing through the sash opening and that in the case of large sash openings an outward flow may even arise. (2) A reduction in the flow rate of only 20% through the fume cupboards causes much greater negative inflowing velocities in the sash opening (size 0.90 m), so that much stronger bursts of contaminants are possible. (3) All the velocity components and the turbulent kinetic energy in the vicinity of the sash opening were found to be essentially three-dimensional and nonuniformly distributed. Even by reducing the size of the sash opening, which increases the uniformity of the flow in its vicinity, the asymmetry and the three-dimensionality of the flow inside the fume cupboards do not decrease. This gives clear evidence about the restrictions which apply for numerical investigations which cover only the flow region inside the fume cupboards and assume uniform boundary conditions or twodimensional flow configurations. (4) The sensitivity of the ventilation efficiency to the positioning of the extract openings of the room and to the distribution of the flow rate through them is shown. Based on this experience, the following rule for increas-

ing the ventilation efficiency should apply: the extract openings should be placed at positions of lower values of the local mean age, i.e., far downstream of the supply jet trajectory. (5) A symmetrical disposition of the supply outlet between the two facilities (as in the DIFFOP case) has the advantages of producing nearly symmetrical flow conditions inside the fume cupboards and of lowering the draught risk in the room. When the supply opening is shifted toward the middle of the ceiling (as in the MIDINL case), the advantages found are a decrease in the negative velocities observed in the sash opening and lower values for the local mean age of the air. (6) The comparison of the symmetric and asymmetric flow conditions shows that generally positive effects can be dominated by other influences, for example, of the given furniture arrangement. In one of the studied cases a better performance of the fume cupboards was found although asymmetric inflow conditions were used. Therefore, every designed room arrangement should be investigated in connection with the expected ventilation conditions. Nomenclature C ) concentration of species, kg/m3 Cµ, C1, C2 ) constants in the turbulence model m ˘ τ ) source of species, kg/m3 P ) pressure, Pa; node P Pk ) generation rate of turbulent kinetic energy, kg/ms3 Sij ) tensor of velocity deformation, 1/s t ) time variable, s Ui ) mean velocity in the xi direction, m/s ui ) velocity fluctuation in the xi direction, m/s uiuj ) Reynolds stresses, Pa V ) room volume (fluid), m3 xi ) Cartesian coordinate in the i direction, m k ) turbulent kinetic energy, m2/s2  ) dissipation of turbulent kinetic energy, m2/s3 θ ) integration variable µ ) dynamic viscosity, kg/ms µt ) turbulent viscosity, kg/ms F ) density, kg/m3 σk, σ, στ ) turbulent Prandtl (Schmidt) number for k, , and τ, respectively τ ) local mean age of air, s Subscripts 0 ) initial value at time step zero r ) reference P ) referring to value in point P

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Received for review April 18, 1996 Revised manuscript received September 25, 1996 Accepted October 10, 1996X IE960218N

X Abstract published in Advance ACS Abstracts, December 1, 1996.