# Case Studies

Often the inlet device (air supply) in a ventilated room is geometrically complicated. To resolve the flow around such a device would require a very fine grid. Instead of trying to resolve the complex flow near the inlet device, one can choose to use the “box method”25’29 or the “prescribed velocity method.”30’31 Both methods are based on the observation that downstream of the inlet, the flow behaves like a wall jet. Thus it is important that the bound —

FIGURE 11.9 Example of a multiblock grid. At the interface two cells of one block meet one cell of an adjacent block. B

FIGURE 11.10 Inlet region. The flow enters through the inlet with velocity Uin

Ary A (see Fig. 11.10) is located sufficiently far downstream that the wall jet is fully developed, but not too far downstream, because the box should be small compared to the room size.

Consider an inlet region as in Fig. 11.10. In the box method all depen­dent variables are prescribed along surfaces A and B. The variables are not solved for inside the box. Along surface A, the mean flow quantities such as the streamwise velocity component U and the temperature are set from wall jet data. The turbulent kinetic energy K is also taken from wall jet data, and together with a prescribed turbulent length scale the dissipation e can be found. Along boundary B zero gradient ДФ/ду is prescribed. Spe­cial care must be taken to conserve mass and energy in the box. For more details, see ref. 29.

In refs. 32 and 33 a separate computation was carried out for the inlet re­gion (inlet box). The results from this computation were then used for pre­scribing all variables at all faces of the inlet box when computing the flow in the rest of the room.

The other method is the prescribed velocity (PV) method. In this method only the streamwise velocity component U and the temperature profile are prescribed inside the volume Ab. The remaining variables ( V, W, k, and E) Are solved for as usual in the whole room, including the Ab volume. The tem­perature level has to be readjusted after each iteration to ensure conservation of energy.

In Fig. 11.11 the predicted U velocity is compared with and without use of the PV method.

11.2.5.2 Displacement Ventilation

Because displacement ventilation flow systems have become increas­ingly popular and are replacing the traditional mixing ventilation systems, it is of great interest to carry out numerical investigation of the flow. In mixing ventilation, fresh air is supplied at high velocity (momentum), in­ducing an overall recirculation in the room, which gives an efficient mixing. In this way the polluted air is diluted in an efficient way. In displacement  Xp/H FIGURE1M. I Comparison of the predicted U velocity with and without use of the PV method,31

Ventilation, however, the object is to keep the fresh and polluted air sepa­rated. A schematic diagram of a room ventilated by displacement is shown in Fig. 11.12

In displacement ventilation systems air is supplied to the room at low ve­locity, with a volume flow rate vin near the floor, and is extracted near the ceil­ing. The temperature of the supplied air is slightly lower than that of the room. Air is heated by the objects in the room, e. g., computer terminals and photocopying machines, and it rises due to buoyancy. [FIGURE 11.12 Ventilation by displacement. (Ђ> I99S Munksgaard International Publishers Ltd., Copenhagen. Denmark.)

When designing a displacement ventilation system, it is important to accu­rately predict the flow over heat sources. The rising flow above a heat source re­sembles a plume. The flow in the plume rises up to the ceiling. The volume flow rate in plumes for a given vertical distance from the heat source y is V/p|umf(y), and increases with Y due to entrainment. At the ceiling the flow spreads out laterally. Below the ceiling the exit is located through which air is extracted at a rate of V^. The remainder of the flow, Vplumc(H) — Vin (H is the height of the room) flows downward. The stratification front >’fton( is located where Vm =

One of the first simulations of displacement ventilation was presented in refs. 34 and 35. The predictions were compared with water-model experi­ments, and hence radiation was not taken into account. In ventilated rooms radiation should be taken into account.16 In ref. 36 plumes related to displace­ment ventilation were numerically studied.

In displacement ventilation, there are regions with very low turbulence, and the flow can even be laminar. Hence it is important to use a turbulence model which can handle these regions. The K-f model gives rise to large nu­merical problems in regions of low turbulence. The reason is that as K goes to zero, the destruction term in the E equation goes to infinity. The E equation is

. Mflde

The destruction term (the last term on the right-hand side) includes Ezlk, and this causes problems as K—>0 even if E also goes to zero; they must both go to zero at the correct rate to avoid problems, and this is often not the case.

No such problems appear in the K-to model. The model was proposed by Wilcox — ’- and is gaining in popularity; modifications have been pre­sented.11,13,37 The (o equation is

 /
 А}»1’:“’’ — 57,
 Du> Dx.
 V CT‘-V
 + F(c«>lP k~c, i>2pk(D), If K goes to zero in region of low turbulence, the turbulent diffusion term sim­ply goes to zero. The other terms remain, giving a nontrivial (i. e., neither zero nor infinity) value of M. Note that the production term in the w equation does not include K since

 RDJJj dUj Dx, dx.
 At/,- Dx ‘
 DilJ
 DUt dU, dxj dx/ V ‘ 1
 Dx (al * In ref. 38 the Ј-0) model was used to predict low-Reynolds-number, recirculat­ing flow.

11.2.5.3 Ventilation Parameters

One of the commonly used ventilation parameters is ventilation effective­ness, and it shows how certain regions in the room are influenced by contami­nant sources introduced into the room. Three definitions of ventilation effectiveness are often used, namely, the ventilation effectiveness in the occu­pied zone e^., the local ventilation index eF, and the mean ventilation effec­tiveness (e).39’40 They are defined as

C

Ol

C0(

 (11.9) Зoi

Cp

EP =

R

/ _ Wut

{ } (C) ’

Where Cx, Cp, {C) and Cout denote the mean concentration in the occupied zone, concentration at a given point P, the mean concentration in the room, and the concentration at the outlet, respectively. To numerically simulate these parameters, the velocity field is first computed. Then a contaminant source is introduced at a cell (or cells) of a region to be studied, and the transport equation for contaminant C is solved. The transport equation for C is

 ( U- ! DC Dxj
 + S

 P>

 Аya/c> = А (11.10) Where SP is the contaminant source per unit volume in the chosen cell(s). Note that the magnitude of SP does not affect the parameters in Eq. (11.9) since Eq. (11.10) is linear. The turbulent Prandtl number is usually set to a constant value 0.7 < (Tc ^0.9. The boundary conditions for C are: C = 0 at inlet(s), zero normal gradient at walls (i. e., DC/dn = 0 ), and zero streamwise gradient at outlet(s).

The concept of local age and local purging flow rate was introduced in refs. 39 and 41. These parameters were first studied in connection with CFD in refs. 32 and 42. Local age at a point is understood to mean the time that  | FIGURE 11.14 The purging flow rate. The configuration is divided into six regions (Reprinted from Building and Environment, vol. 32, S.-H. Peng and L. Davidson. “Towards the Determination of Regional Purging Flow Rate." pp. 513-525, ©1997, with permission from Elsevier Science.)

The Regional Local Purging Flow Rate

First the velocity field is computed for the room; the configuration is shown in Fig. 11.14. The regional purging flow rate is computed for regions 1-6.43 The computed values are tabulated in Table 11.3. As can be expected, Up is highest in the region near the inlet, and it is low in the region near the workbench. It should be pointed out that Up is dependent not only on the flow conditions, but also on the size of the region. The fact that Up is smallest for region 1 is that most of the supplied air is extracted via the other outlet (8).

11.2.5.4 Large Eddy Simulation (LES)

When using LES, the time-dependent three-dimensional momentum and continuity are solved for. A subgrid turbulence model is used to model the turbu­lent scales that are smaller than the cells. Instead of the traditional time averaging, the equations for using LES are Filtered in space, and U, is a function of space And Time.

In refs. 51 and 52 LES of flow in a ventilated room (height H, length L, width W) is presented. The configuration data are

L/H = 3, W/H = 1, B/H = 0.056, T/H = 0.16, Re

 TABLE 11.3 The Purging Flow Rate for the Six Regions Defined in Fie. 11.14*3 We have used H=3m, Uin = 0.455 m/s. The inlet (height H) is located at the left-side wall adjacent to the ceiling, and a wall jet is formed below the ceiling. The exit is located at the right-side wall near the floor (height T).

With LES we get much more information than with traditional time — averaged turbulence models, since we are resolving most of the turbulence. In Fig. 11.15 the computed U velocity is shown as a function of time in two cells; one cell is located in the wall jet (Fig. WAS a), and the other cell is in the middle of the room (Fig. 11.156). It is found the instantaneous fluctuations are very large. For example, in the region of the wall jet below the ceiling where the time-averaged velocity (u)/U0 is typically 0.5, the instantaneous velocity fluctuations are between 0.2 and 0.9. In the middle of the room, which is a low-velocity region, the variation of Ii is much slower, i. e., the frequency is lower.

The probability density function of Ii is shown for four points in Fig. 11.16, two points in the wall jet and two points in the boundary layer close to the floor. For the points in the wall jet (Fig. 11.16a) the probability function shows a preferred value of It showing that the flow has a well-defined mean velocity and that the velocity is fluctuating around this mean value. Close to the floor near the separation at X/H = 1 (Fig. 11.16ft) it is hard to find any — preferred value of U, which shows that the flow is irregular and unstable with no well-defined mean velocity and large turbulent intensity. From Figs. 11.15 and 11.16 we can see that LES gives us information about the nature of the turbulent fluctuations that can be important for thermal comfort. This type of information is not available from traditional CFD using ^-e models.

11.2.5.5 Combination with Outdoor Environment

In many applications there is some sort of airflow interaction between in­doors and outdoors through some small openings (small compared with the whole interface area between inside and outside space).

There are two feasible ways of handling this problem: one is to include some of the outdoor space in the CFD computation domain; the other is to cal­culate the quantities through the interfaces of concern by other methods. Such methods include the use of analytical formulas, e. g., for temperature-difference — driven flow through an opening, or the use of a multizone program. The latter method is illustrated in the following example.53

The geometric situation is shown in Fig. 11.17 (see color insert). The fig­ures show a large industrial parcel-distribution hall, where the parcels are col­lected from the main office and sorted in the rest of the hall for the fine distribution in the region. All the transport is done by trucks which are docked at over 140 doors around the building. When a truck is docked for loading or unloading, some spacings between the open door and the truck re­main open. These openings lead to drafts inside the hall, particularly in the neighborhood of this door. As most of the time a large number of trucks are docked around the whole hall, there may be a large net draft through the hall, depending on the wind situation. The building is much exposed to the wind, so in this case obviously the wind-induced draft through all these openings strongly affects the comfort situation for the workers in the hall.

In this case the net draft through the hall was calculated for the whole year using the multizone program COMIS. All the scheduled loading and unloading Time (s)

(B) YlH = 0.50

FIGURE I 1. 15 Time history of 0 at cwo chosen cells. Z/H = 0.5, XlH = I.51 (a) y/H = 0.92

 14 -0.8 -0.6 -0.4 -0.2 0 0.2 UlUm
 16 (.B) Y/H = 0.24

FIGURE 11.16 Probability density function of u. Solid line: x/H = 1.0; dotted line: x/H = 2.0.52

Processes and the whole wind situation of the design reference year meteoro­logical data for the location of the building have been taken into account (see Fig. 11.18, color insert). For this calculation, the hall has been divided into about 12 zones: 8 at a lower level in the occupants’ zone and 4 at a higher level.

An extreme situation (strong wind, low outside temperature, high number of docked trucks with open connections between inside and outside) has been chosen to investigate the influence on the indoor working situation. Figure 11.19 (see color insert) shows the mass flows through the openings on all sides of the building, which have been calculated using the multizone program and are fed as input to the CFD calculation in this case.

Figure 11.20 (see color insert) shows the resulting temperatures in the hall. Along the longer sides and the right of the hall, the lowest air tempera­tures are found. Air velocities higher than 0.5 m/s are found in this case at many locations inside. Finally, the working comfort was calculated, also tak­ing into account the effect of radiant heating systems above the working area,

IS .2.5.6 Simplification of Real Situation

The simplification of the real situation is a very important topic. Simplifi­cation is necessary due to limited resources, but the important flow features still should be captured.

No fixed rules can be given; it is up to the experience of the engineer to judge the necessary steps. Good advice, however, is to define a model with only the flow feature of concern, to test several levels of simplification on this model, and to decide from these numerical experiments the level of simplifica­tion for the full model under investigation.

The examples in this subsection illustrate some possible problems and so­lutions.

• Shapes of inside objects which are only partly permeable to airflow (sometimes referred to as porous objects), such as inlet grills, vents, etc.

• Sometimes a large number of small objects are grouped together and modeled as a large, semiporous object. However, this can give wrong answers in some cases, as the flow through a homogeneously semiporous object is different from the flow around a number of discrete objects.

• Volumetric sources

• Heat or contaminant sources can also be assigned to parts of the fluid volume to account for very small real sources or a distribution of a large number of small sources. Care must be taken, however, to make sure that this representation of distributed sources correctly describes the real situation.

Example I: Farm with Animals

Figure 11.21 shows a farm with animals moving around.54 Due to the symmetry of geometry and ventilation, only half of the scene is modeled and calculated. The pigs are simulated either as discrete objects (Fig. 11.21 A) or as distributed semiporous objects (Fig. 11.21ft).

For the first case, Figure 11.22 shows the airflow field above the floor in a plane through the objects. It obviously is very different from the solution ob­tained with homogeneously distributed semiporous objects, which shows more or less an average velocity all over the plane.

Which model is preferred depends on the final information needed. If the interest is in the magnitude of air velocity that is to be found, the discrete modeling method is certainly better.

Example 2: Textile Machine Hall

Figure 11.23 shows a textile machine hall with a large number of spinning machines. The interest is focused on the distribution of particles generated in the upper part of the machines (large rolls in Fig. 11.11 A), Which should be prevented by the ventilation system from propagating to Real building

 Model

 FIGURE 11.21
 Groups of objects that are too complex to model (a) can be modeled as volumes
 With certain characteristics (b).  FIGURE 11.22 Calculated airflow field in a plane through discrete objects.  The lower parts of the machines, where the particles would lead to thread damage.

Due to the symmetry of geometry and ventilation, only a small part of the hall is modeled and calculated, i. e., a section about 6mm width, 2 m in depth, and extending over the full height (Fig. 11.24b).

The machines are very complicated, so they are simplified to a level which maintains the main features observed. In this case, the hall already existed, and the ventilation system needed to be improved. In the lower part of the machines are rotating wheels and axes which lead to a net flow across the floor in one direction through all the machines. Such a flow was generated by adding moving walls in the lower part of the machine model (Fig. 11.24), and the size of the velocity was adjusted to fit the measured speed in the real hall. Periodic boundary conditions are attached to the walls to the left and right in Fig. 11.24.

Figure 11.25 shows the flow with the redesigned ventilation system around the machines. In the lower part, the parallel flow along the floor due to the rotating parts is clearly visible. Figure 11.26 illustrates the effectiveness of the ventilation system by tracking massless particles. This method was used here as the particles are considered very small. Particles generated in the upper part of the machines are prevented from reaching the lower parts of the ma­chines.

11.2.5.7 Partide Tracking

Particle tracking can often be very helpful. Sometimes the particle distri­bution is directly asked for; in other cases, it is an attractive way of illustrating the effectiveness of the ventilation system. For massless particles, only a postprocessing of the result field is needed, where so-called streaklines that follow the given vector field are calculated. If rhe particles have a certain mass, additional equations have to be solved.

Example 2 in the previous subsection shows the use of massless parti­cles. FIGURE 11.26 Streak lines showing path of massless particles.