PushPull Ventilation of Open Surface Tanks
For large open surface tanks where access for machinery or operators is required above the tank, the options for local ventilation are limited. An overhead canopy would block access, and an exhaust hood placed at the side of the tank is prohibitively expensive for tanks greater than about 0.6 m across.14 In these cases, pushpull ventilation offers an appropriate mechanism for reducing the overall flow rate required, compared with side exhaust, by up to 50%, while still maintaining clear overhead access.
Pushpull ventilation systems for open surface tanks consist of two components: the push flow is generated by a jet or series of jets that are blown across the surface of the tank towards an exhaust hood along one side of the tank, which pulls and removes the fluid from the jet containing the contaminant. This is shown schematically in Fig. 10.69.
10.4.3.3 Different Forms and Boundaries Relative to Other Types
This section deals mainly with side pushpull ventilation. Center pushpull ventilation is also sometimes used, where two jets of air are blown from a central pipe towards two parallel exhaust hoods at opposite ends of the tank. Much of what we say about side pushpull systems is equally valid to center pushpull.
10.4.3.4 Specific Issues Background
During the 1980s, the United Stares’ National Institute for Occupational Safety and Health (NIOSH) published a series of papers giving the results of exper
Imental work on both side and center pushpull systems. Huebener and Hughes15
Examined side pushpull in the laboratory. They used a tank of fixed width, 1.2 m, and variable length, 1.2—1.8 m, with the pushpull system along the shorter sides. The paper suggests minimum inlet and outlet flow rates for different tank sizes and shows velocity profiles for one configuration of the system, and these data are used
For comparison with the results to be presented later. Klein16 published the results of further work by NIOSH, which used the laboratory data of Huebener and
Hughes15 in an industrial situation. He showed that Huebener’s data were valid in practical situations, even with significant obstructions in the path of the jet.
A number of workers at Pennsyl vania State University examined the Pushpull system and found good agreement between their numerical and experimental work. The computational algorithm SIMPLER was used to solve the flow in the twodimensional pushpull system and it was concluded that for a tank 1.8 m long, the push jet must have an initial velocity of 3.8 m s~’, that the exhaust flow rate per unit width should be 0.495 m2 s_1, and that the ratio of the pull to push flow rates, Q0/<j(, must be between 8.8 and 17.8.
More recently, in the middle 1990s, the UK’s Health and Safety Executive (HSE) also reviewed the pushpull system. Hollis and Fletcher17 offer A Comprehensive literature review on pushpull ventilation and note that the main conclusions of previous work on pushpull ventilation of tanks are that the control is primarily supplied by the inlet jet, forming a wall jet along the surface of the tank, and that the main purpose of the exhaust hood is to remove the air and contaminant contained within the push jet.
Flynn et al.18 applied a finite element based numerical model to solve the problem of a pushpull flow with crossdrafts and demonstrate that the results show’ good agreement with experimental data. They note, however, that the numerical method is time consuming and therefore computationally expensive.
IЫ.5 
The ACGIH14 gives recommendations for the design of a pushpull system, apparently based largely on the work of NIOSH in the 1980s: the nozzle should be between 3.2 mm and 6.4 mm and that the socalled momentum factor of the jet, the product of its velocity and flow rate per unit width, should be between 0.39 and 0.59 m’ s2. The outlet flow rate may then be calculated using the formula
(10.91
Where QO is the exhaust flow rate per unit width of tank, L is the tank length, B, is the jet nozzle height, and SF is some safety factor, recommended to be between 1 and 2.
Flow Patterns Induced by a PushPull System
In examining the fluid flow associated with the system, it is advantageous to treat the system as a twodimensional problem, i. e., to neglect the edge effects. The system can then be represented by Fig. 10.70, where the width is of arbitrary size (usually larger than the length), since all calculations are done per unit width of the tank. Various studies, for example Hollis and Fletcher17 And Huebener and Hughes,15 have suggested that it is the flow induced by the jet that is critical to the system, and others, for example Ege and Silverman,19 Have noted that the offset jet deflects towards the tank surface and acts as a
F V
FIGURE 10.70 Simplified model of a wall jet combined with an exhaust flow.
Wall jet thereafter. An obvious extension of these findings is to assume first that the flow is dominated by the effect of the push jet, and second that the jet can be treated as a wall jet rather than the offset jet, which it really is. We shall see later that the parameters of the wall jet need to be different from those of the actual offset jet, but that these can be reasonably predicted.
Turbulent wall jets have been extensively studied, and perhaps the most straightforward representation is given by a combination of the work of Verhoff20 and Launder and Rodi21 who together show that the fluid flow in a wall jet can be represented by
= U(n) (10.92)
UM
& = Ј+_§ (10.931
<T
U(v) = BlVderk(B2T}) (10.94)
And
Where U is the horizontal component of the velocity, B is the jet width, defined to be the perpendicular distance from the surface of the tank to the point where the ve
Lodty is half the local maximum, Um, and the velocity is decreasing with increasing
Distance; J, is the initial kinematic momentum of the jet per unit width of tank; P Is
The fluid velocity; X is the horizontal distance from the jet nozzle; and the similarity variable 17 is given by 17 = Y/b, where Y is the perpendicular distance from the tank surface. The constants, Bx, B2y cr, tft E, C and D, take the following values:
B, = 1.48 C = 1/2 (p = 3.98
Bt = 0.68 D = 1/7 Cr = 13.7 (10.96)
‘ e = 10 Bi
Collectively, for the sake of brevity, we refer to Eqs. (10.92) to (10.96) As The “original Verhoff formulae.” A numerical analysis of the wall jet in the pushpull situation suggests that the Verhoff formulae fit the numerical Data More closely if the following constants are taken:
Bj = 1.28 c = 0.509 (p = 3.86 B, = 0.61 D = 1/13 U = 9.68 (10.97)
‘ E = 0
With these values of the constants, we refer to the wall jet formulae as the “modified Verhoff formulae.”
The assumptions that the exhaust flow has a negligible effect and that the offset jet can be treated as an equivalent wall jet were tested by Robinson and Ingham22 and found to be reasonable over the majority of the surface of the tank, except close to the jet nozzle and exhaust hood. Far from the surface of the tank, the exhaust flow has a more noticeable effect.
We have thus introduced two main simplifications: first that the offset jet can be modeled as a simple wall jet, and second that the exhaust flow has a negligible effect. To demonstrate that these assumptions are reasonable,^Fig. 10.71 shows the normalized horizontal component of the fluid velocity, U, as a function of the similarity variable 17 for numerical results for both the wall jet and offset jet, and the original and modified Verhoff formulae, and the experimental results of Huebener and Hughes.15 It shows reasonable agreement between all the different methods. A comparison of the other significant variables, such as the width of the jet and the local maximum velocity as A Function of distance from the jet nozzle, also show good agreement.
Having established that these assumptions are reasonable, we need to consider the relationship between the parameters of the actual offset jet and the equivalent wall jet that will produce the same (or very similar) flow far downstream of the nozzle. It can be shown that the ratio of the initial kinematic momentum per unit length of nozzle of the wall jet to the offset jet, /,•//,• , and the ratio of the two nozzle heights, B/bj, depend on the ratio D/b,, where^D is the offset distance between the jet nozzle and the surface of the tank, and Bt is the nozzle height of the offset jet. The relationship, which because of the assumptions made in the analysis is not valid at small values of D/b,, is shown in Fig. 10.72.
We thus have a means of describing, albeit approximately, the fluid flow induced by the system in terms of the Verhoff formulae and a graphic relationship between the offset jet parameters and the equivalent wall jet parameters. We now wish to be able to calculate the movement of the contaminant in the system
Normalized horizontal component of the fluid velocity FIGURE 10.71 The ratio of the horizontal component of the fluid velocity to its local maximum U/ um, as a function of 17, atx = 0.75 m for the experimental results, the numerical results obtained using the commercial package for the offset and equivalent wall jet models, and the original and modified Verhoff empirical formulae. 
And to do this we assume that the diffusion coefficient 1 can be approximated by r = , where is the effective turbulent dynamic viscosity and Sc is the
Schmidt number, which is usually taken to be 0.7. We have, empirically, a description of the fluid flow, which is a similarity expression. We have determined a selfsimilar form for the effective turbulent viscosity, namely,
Ve = ^4xnh{r)), (10.98)
(f~
Where (f>* = and the function H is given by



Where E and tj0 are known constants, and e is some small value. As a check that this is a reasonable choice for the effective viscosity, we used this in the boundarylayer approximation to the NavierStokes equation to find the velocity profile and compared the result with the empirical formulae, We determined that, except at large tj, the predicted flow patterns are graphically indistinguishable from the modified Verhoff formulae, and are a good fit to the numerical results.
Movement Of the Contaminant
The full concentration equation for the contaminant may be simplified in the same manner as the NavierStokes equations to derive a boundarylayer approximation for the concentration, namely,
ЈdC Pdy 
. A dy 
/ _
(10.100)
Dx ay
Where C is the mass fraction of the contamiriant.^Writing our formula for the horizontal component of the fluid velocity as U = f'{tj) and using, as described in the previous section, T/p = (1 /Sc)(<j>*c/cr~)xnb(Tj), we can reduce Eq. (10.100) to the ordinary differential equation
(10.101) 
B c
Where prime denotes differentiation with respect to 77. The natural boundary conditions are to let the concentration be unity on the tank surface and zero far from the tank surface, i. e., C(0) = 1 and C —> 0 as tj —> .
The ordinary differential equations for F and C now form a fifthorder system which can be solved using a standard NAG library routine. The results are shown in Fig. 10.73. This figure also shows the numerical results for concentration obtained using a full numerical approach, and there is reasonable agreement between the two.
The results above are for a neutrally buoyant contaminant. In practical situations, the contaminant is often buoyant in air, and so we need to consider the effects of this. To include it, we extend a theory from aerosol science, as given by De Marcus and Thomas,23 and assume that the governing equation becomes
8 dy dy pdy ‘ 
)dЗ = i. frdз’ 


0.2









Concentration of contaminant, C
FIGURE 10.73 Concentration of contaminant, C, as a function of 7), for the full numerical results and the semianalytical similarity solution when H(r)) is given by Eq. (10.99), when j/p = 0.54 m3 s~2, b, = 0.01 m, L = 2m, and SF = 1.5.
In aerosol theory, Vg is the velocity of free fall of a particle, and by extension in the current work Vg is an empirical velocity related to the buoyancy of the contaminant in air. We further assume that the overall fluid flow pattern is unaffected by the minor quantity of he buoyant contaminant.
Now when we substitute U = f'(i7) into our equation, and introduce a change of variable Ј = Ijd to reflect the need to capture the very rapid changes of variables close to the tank surface, the concentration equation (10.102) becomes
DC 13З DV dx 
« Aз 
2R 


Where
I — 1 
З‘hh’, 




A Sc R,
= cdxf ’
And the prime now indicates differentiation with respect to subject to
Boundary conditions C{x, 0) =1, F(x, 0) = F'(x, 0) = 0 and C—>0 as ^ . These equations can be discretized using a semiimplicit Crank
Nicolson method and solved numerically.
We are thus able to find the concentration predicted by this model at any position over the tank surface. Figure 10.74 shows contours of concentration both for the original and modified Verhoff conditions for the operating parameters
MJ 
B, = 0.02 m Jj/p = 1 






It is worth commenting here on the more obvious effects of varying the parameters of the system. As we would expect, if we increase the momentum of the initial jet, the movement of the contaminant away from the surface of the tank is restricted. Conversely, if we increase the buoyancy of the contaminant, by increasing Vg, the contaminant moves further from the surface of the tank.
F 0.4.3.S Design Equations and/or Parameters
We consider here two possible criteria for deciding on safe operating parameters for the inlet parameters, before turning our attention to the exhaust requirements.
Capture Velocity Criterion
The ACGIH14 gives guidelines for the minimum capture velocity, V^p, which must be induced to move a contaminant toward an exhaust. The recommended value depends on the industrial process and the local conditions, and Table 10.12 shows the recommendations for typical opensurfacetank processes.
From the ACGIH recommendations, we can say that the system is operating safely if a fluid velocity greater than or equal to the capture velocity is induced across the whole of the tank surface, and the exhaust flow rate is sufficient to capture all the fluid in the jet. Since the maximum velocity at any
Vertical distance above rhe tank surface, y im) 
FIGURE 10.74 Contours of concentration derived from the semianalytical method, in the original and modified Verhoff cases, when the operating parameters are given by Eq. (10.105). 
Horizontal distance from the jet nozzel, X (m) 
Distance from the tank surface is given by Um = ■/p)x~c, where C is ap
Proximately onehalf, we know that the lowest value of Um will be at X — L, and therefore we require J/p S: (Vap/<l>)2L~c. Comparison with those experimental studies that provide enough information to calculate the initial momentum broadly supports this hypothesis; see for example Robinson and
TABLE 10.12 Recommended Capture Velocities for Different Operating Conditions, Based on Table 3.1 (ACGIH14)

The lower end of the range applies when (a) rhe room air currents are minimal or favorable to capture, (b) the contaminant is of low toxicity or nuisance value only, (c) the tank is used only intermittently, and (d) there is a large exhaust hood, i. e., there is a large air mass in motion. 
The upper end of range applies when (a) the room air currents are significant or unfavorable to capture, (b) the contaminant is of high toxicity, (c) the tank is in heavy use, and (d) there is a small exhaust hood, i. e., small amounts of air are in motion.
Ingham.24 This gives the required minimum value for the momentum of the equivalent wall jet; we must also recall the relationship shown in Fig. 10.72 to determine the required momentum of the offset jet in the pushpull system.
The biggest drawback to this approach is that the only inclusion of the con
Taminant buoyancy is in the choice of the appropriate value for Vcap and this is necessarily subjective. We therefore consider another alternative criterion.
For this safety criterion, we consider the fact that as the velocity decreases with increasing distance from the surface of the tank, it will reach some critical velocity, Vcrit, at which the induced movement of air will be insufficient to overcome the effects of crossdrafts or the buoyancy velocity Vg. At this point, we must ensure that the concentration is at, or below, some critical allowable concentration, Ccnr The values of the critical concentration and velocity will depend on particular circumstances, but it is worth noting that Vcrit must be at least equal to Vg in order to overcome the effects of buoyancy, and the appropriate value will depend on the crossdrafts, which typically vary between 0.05 m s^1 to 0.5 m s l. For the sake of providing examples, we have chosen Vcrit to be the maximum of the buoyancy velocity and the typical crossdraft velocity. For the critical concentration we have chosen two values, C = 0.05 and C = 0.10. The actual value used by a designer would depend on the toxicity of the contaminant in question.
From Fig. 10.72 we can see that the ratio of the momentum of the equivalent wall jet to that of the offset jet is typically about 0.46 and we have taken this value in the sample results presented here.
Figures 10.75 and 10.76 show the initial kinematic momentum required to meet this criterion as a function of the buoyancy velocity and the length of the tank, for different values of the allowable concentration Ccrit and critical velocity As we would expect, the required momentum increases both as the length of the tank increases and as the buoyancy of the contaminant increases.
Other Parameters
So far, since we have been treating the flow as being dominated by the jet, we have ignored the effects of the exhaust flow. Of course, the exhaust flow will increase the overall movement of the air, to a small extent far from the exhaust hood but quite significantly close to the hood. We shall discount these positive effects, and consider only the fact that the exhaust hood should remove all the fluid contained within the jet. This can be expressed as
(10.10′ 
Q o = SFtfy(L),
Where Q0 is the volume flow per unit width of tank at the exhaust hood; SF is a safety factor greater than unity, the precise value of which is left to the discretion of the designer; and Qj(L) is the flow rate in the jet at X = L. This may be calculated by integrating the formula for the fluid velocity (Eq. (10.92)), which yields
(10.108)
Integrating this equation numerically and substituting the values of the con
Length of tank, L (m) FIGURE 10.75 Required initial kinematic momentum, F/p, As a function of the length of the tank, L, And the buoyancy velocity, vs, when the critical contour criterion is applied with the critical concentration, Ccrrt, equal to 5% and the crossdrafts equal to 0.05 m s_1. 
Flow rate as a function of the length of the tank, the initial jet momentum, the jet nozzle height, and the safety factor:
L + 106, JL 
0.316 
<7o = 


0.491 
0.443 L 
According to the modified Verhoff fomulae.
(10.109)
Thus the outlet flow rate can be determined once the dimensions of the tank and the inlet jet momentum have been determined.
The above considerations give us a technique for estimating the required jet momentum and outlet flow rates. Other important parameters are the heights of the inlet and outlet apertures. The choice of these parameters will not, in general, have a significant effect on Thй Overall fluid flow pattern and the resulting distribution of the contaminant, and these should be chosen to optimize the performance of the inlet and exhaust pumps.
: i i i i i i i i i i i i i i i i 0 5 10 Length of tank (m) M FIGURE 10.76 Required initial kinematic momentum, F/p, as a function of the length of the tank, L, And the buoyancy velocity, Vg, when the critical contour criterion is applied with the critical concentration, Ccllt, equal to 10% and the crossdrafts equal to 0.5 m s’1. 
Even with modern CFD commercial software packages, achieving accurate results for a full numerical model for the pushpull system is time consuming because of the very fine grid required close to the jet nozzle and close to the surface of the tank. With the techniques described in this section, it is possible to produce at least first estimates of the required parameters for a given pushpull system. It is then recommended that a designer would conduct full numerical testing of the system at the suggested operating parameters and make final adjustments according to those results. Finally, when the system is installed, it is important to allow for some adjustment of the operating parameters following in situ testing of the ventilation system.
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