Air Movement Near Sinks
7.6.3.1 Theoretical Considerations
Airflow near the hood can be described using the incompressible, irrota — tional flow (i. e., potential flow) model. The potential flow theory is based on
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TABLE 7.21 Ranges of Capture (Control) Velocity
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Note: In each category above, a range of capture velocities is shown. The proper choice of value depends on several factors: |
Lower end of range:
•Room air currents favorable to capture
•Contaminants of low toxicity or of nuisance value only
•Intermittent, low production
•Large hood; large air mass in motion
Upper end of range:
• Distributing room air currents •Contaminants ot high toxicity
•High production, heavy use •Small hood; local control only
Several assumptions.3 For instance, the fluid is assumed frictionless. Another assumption is that the flow is steady. That means there are no changes in velocity at a given point with respect to time.
The total pressure ptot in the area upstream of the hood remains constant and can be described with the following equation:
Ptot = Pst + Pd = constant (7.208)
Where
Pst is the static pressure, Pa, at any point of the flow
Pci = pv2 /2 is the dynamic pressure, Pa, at any point of the flow
P = air density, kg/m3
V = air velocity, m/s
G = gravitational acceleration, 9.8 m/s2
At some distance from the hood, the total pressure in the airflow pKt is equal to the ambient air pressure, e. g., pmt = 0. Thus,
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The above discussion does not apply to the wakes, with a vortex air movement (Fig. 7.82).
Numerical simulation of hood performance is complex, and results depend on hood design, flow restriction by surrounding surfaces, source strength, and other boundary conditions. Thus, most currently used methods of hood design are based on experimental studies and analytical models. According to these models, the exhaust airflow rate is calculated based on the desired capture velocity at a particular location in front of the hood. It is easier
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FIGURE 7.82 Airflow in the hood vicinity. |
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To understand the design process for the sink with vanishingly small dimensions—a point or a linear source of suction.
7.6.3.2 Air Movement Near a Point Sink
The point sink can approximate airflow near a hood with round or square/rectangular shape. The point sink will draw air equally from all directions (Fig. 7.83). The radial velocity vr (m/s) at a distance r (m) from the sink can he calculated as a volume rate of exhaust airflow q (mVs) divided by the surface area of an imaginary sphere of radius r:
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(7.210)
CHAPTER 7 PRINCIPLES OF AIR AND CONTAMINANT MOVEMENT INSIDE AND AROUND BUILDINGS TABLE 7.22 Values of a (rad) for Some Typical Point Sink Locations
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Type of airflow restriction |
A, rad |
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U^restricted airflow |
4tt’ |
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Sink within the infinite surface |
2tt |
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Sink in the vertex of the dihedral angle with the right angle i 90’’)of deflection |
P |
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Sink in the vertex of the trihedral angle with the right angle (90’’)of deflection in all directions |
Ii/2 |
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Sink in the vertex of the dihedral angle with the angle <t>, rad, |
2<t> |
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Sink in the vertex of the cone with an angle of deflection cb, rad |
2-rrfl — c |
Os <t> /2) |
Restriction of the airflow by surfaces decreases the area through which the air flows toward the sink, which results in increased radial velocity. For cases with a restricted airflow created by the sink, Eq. (7.210) can be modified to
Vr = -2L (7.211)
A r-
Where a is in radians. Values for some typical airflow restrictions are listed in Table 7.22.
Equations for the inflow velocity (vr) and the corresponding capture distance (rc) are listed in Table 7.23 for the most common point sink locations,
7.6.3.3 Air Movement Near a Linear Sink
A linear sink will create a two-dimensional airflow. The radial velocity vr (m/s) at a distance r (m) from the sink is calculated as a volume rate of g(mVs) per meter of linear sink length divided by the surface area of an imaginary cylinder of radius r:
V. = (7.212)
1 it r ‘
The effect of restricting surfaces on the flow created by the linear sink will be similar to that described for the point source. The equations for the inflow velocity (vr) and the corresponding capture distance (rc) for some typical situations are listed in Table 7.24.
7.6.3.4 Air Movement Near Sinks with Finite Dimensions
Realistic exhausts used to capture contaminants are complex, varying in their geometry and size. In many cases, the airflow rate ensuring a desired capture velocity at a particular location can be obtained only from empirical studies. Air velocities in front of the hood suction opening depend on the exhaust airflow rate, the geometry of the hood, and the surfaces comprising the suction zone. Studies have established the principle of similarity of velocity contours (expressed as a percentage of the hood face velocity) for zones with similar geometry.4
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Where Vg is the average velocity calculated based on the total duct width. The velocity distribution in the suction area of an unrestricted round duct is similar, with an “effective suction diameter” De = 0.81 D and a maximum velocity Vm = 1.11/0.
The size of these wakes and the velocity uniformity level depend on the hood design and the airflow pattern in close proximity to the hood face.
Figure 7.84 shows the approximate relation between the wake size and the angle of cone deflection for the typical hood.5 Wake size increases (“effective suction area” decreases) with an increase in the angle of the hood deflection. Thus, it can be recommended that the value for hood deflection angle not exceed tt/4.
Extensive review of equations for centerline velocities in flows in the vicinity of realistic hoods resulting from experimental and theoretical studies was performed by Braconnier.6 This review shows certain inconsistencies in equations available from the technical literature due to effects of parameters related to opening (shape, length-to-width ratio, presence of a flange) and the opening location (in an open space or limited by surfaces). The summary of equations from this review complemented by information from Posokhin5 is presented in Tables 7.25 and 7.26.
Comparison of the relative velocity change in the airflow created by a hood with a finite face area and by a point source is graphically illustrated in Fig. 7.85. At a distance greater than X/R = 1, the velocities induced by a realistic hood and by a point source are practically equal. This means that in some cases airflow in front of realistic hoods can be described using the simplified point source equations.
TABLE 7.25 Inflow Velocity for Some Other Common Locations of a Linear Sink
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Inflow velocity, v |
Schematic of airflow restriction
Q
2rnX1 + h1-hjx1 + k1
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Sink set forth from the infinite surface |
Sink with flanges
‘AU ^CD—^y2
— 6 X-h V[]X~ TTX2 + 2 Xh
6 X
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Sink within the infinite surface with an airflow obstruction from one side |
1T X2 + /;2
Q (h + Y) Y(2h+Y)
, Y < 0
Ir Jьо^+h^UX-aџ + h2-] — (X — a)2 — h2
Q a-X___________
J(az + b1)(X-a)1 + h2 — (z — X2) + /;2
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<Vn = |
X-a
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Dral angle a-rr (rad) |
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Q Q |
,.1/a, -1/a
I cosTra J
F * ■ f I cos it a I
(icontinues)
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Inflow velocity, v |
Schematic of airflow restriction
; = Q smfe(TTY) T h
1 Mj HCOsh(TTh) — cosh(TTџ)’ W
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L’n a = — |
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2//uK:r(fxj «*•(->) _2___________ sin/j(TTX) H2(?X) + C°s2(п^) J2 sin(TTџ)__ |
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2 H |
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IH |
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Cos 2(jY |
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SinMirX) |
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0 0.4 0.8 1.2 1.6 X FIGURE 7.85 Centerline velocity, V, and decay in the flow created by exhausts with finite dimensions and point sinks. /, round free-standing pipe; 2, round opening in a infinite surface; 3, unrestricted point sink, V = q/irr2; 4 point sink in an infinite surface, V = 2q/ttr2. |
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Us Log» —X |
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{= |
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I x b |
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2xjx1 + a" + bl |
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— = 1 — — atan |
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Ab |
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-1.3 |
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= 0.2 (x/jA) |
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X atp |
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AF = (x/JВ)(a/b)^F |
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Posokbin5 |
Slot in the pipe wall
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Posted in INDUSTRIAL VENTILATION DESIGN GUIDEBOOK