Principle of Calculation

Principle of CalculationThere are currently two approaches to the design of damper-type air heat cur­tains: cinematic and dynamic.

Principle of Calculation

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A. M

Principle of Calculation

In the cinematic method the airflow in the aperture is understood to be the re­sult of interaction of the air curtain jet and the incident flow’. Some of the cine­matic methods that were developed1-6 did not apply the laws of conservation of the impulse and mechanical energy. These methods did not correspond satisfacto­rily to test results and were not developed further. In these cases the determination of the jet trajectory does not take into account the effect of the enclosures and the interaction of the jets, and the division of airflows between the room and the outer atmosphere is performed with an arbitrary geometrical construction. The above-mentioned facts lead to divergence of design results and existing test results as to both the release speed and the initial temperature of the air curtain.7,8

The dynamic method sees airflow as a result of the effect of differential pressure on the jet in the gate aperture. Dynamic methods do consider the law of conservation of the impulse in the isolated circuit. According to the type of isolation of the circuit, dynamic methods are divided into methods that deter­mine the trajectory of the jet9-14 and methods that determine the integral flow rate of air through the aperture.7,8’ 15>16 This method, due to consideration of the aperture and surrounding enclosures in the design circuit and application of the law of conservation of mechanical energy, achieved for the design of the air release speed a dependence that corresponds well to test results.7; 8 Figures 7.90-7.92 illustrate examples of isolated circuit design.

In the following we apply the dynamic method of air curtain design (see Fig. 7.92). The basic dependency is illustrated for a one-sided air curtain that is supplied at angle a and developed on the plane surface XOY. Since the jet of the air curtain is bent by the effect of differential pressure from outside (Pout) and inside (Pin) the building, the jet of the air curtain flows to the oppo­site side of the aperture and splits into two parts. After the division, one part of the jet flows along the outer surface of the enclosure and the other one en­ters the room at an angle fi to the plane surface of the aperture. We isolate the

АP i (H-h0)gAp

подпись: аp i (h-h0)gap

FIGURE 7.91 Schematic of air curtains for process equipment: nonisothermal processes.

подпись: 
figure 7.91 schematic of air curtains for process equipment: nonisothermal processes.

Jaa-

подпись: jaa-Circuit ABVGDKMN. Surfaces AB, AN, and BV are led at a distance from the gate where the speed of air flowing to the jet is near zero and the quantity of air impulse coming in through the surface NABV may be disregarded.

The equation of momentum of the isolated circuit in projection at the Y-axis is

(7.213)

подпись: (7.213)/ 0sina +Jh sin(i = A PAQ + (Pin-Ny)(AAB-A0),


Principle of Calculation

FIGURE 7.92 Theoretical model of air curtains.

Where

(7.214)

подпись: (7.214)AP = P0Ut-Pm(Pa)

J0, Jfy are impulses of airflows supplied by the air curtain that flow into and out of the room (N)

Aab, A0 are the areas of the surface AB and the gate aperture (m2)

Ny is the average value of reactive pressure in the scope of plane surfaces VG and MN (Pa)

We derive the concept of the dynamic efficiency of the air curtain, E, which is equivalent to the ratio between aerostatic pressure forces affect­ing the gate aperture and the doubled initial impulse of the air curtain jets:

.215)

подпись: .215)E = APA0/2./c

The factor E shows the efficiency of utilization of the initial impulse of the curtain jets. Using this form to represent factor E allows us to estimate the ef­ficiency of the curtain in fractions of the unit.

The dependence for factor E results from the joint solution of the Eqs. (7.213 ) and (7.215) as follows:

.216)

подпись: .216)E = 0.5(sina + Rv),

The quantity Ry is a function of geometrical parameters and is determined ex­perimentally. Similar dependencies for the factor E have been obtained for all patterns of the air curtains introduced above.

The initial speed of the air supplied by the air curtain is determined ac­cording to the following universal dependence, which results from the joint solution of Eqs. (7.213)-(7.216):

T’o = (APA0/2PopASE)1/2 [m/s], (7.217)

Where

P0 = the Boussinesq factor (1.05-1.1) p = density of air supplied by the air curtain [kg/m3]

As = total area of the outlet apertures of the air curtain [m2]

The value of the ratio f = A0 / As is recommended to be taken based on the following technical and economical considerations:

• For air curtains with heated indoor air, unheated indoor air, or combined air curtains with indoor air: f = 10-20

• For air curtains with unheated outdoor air, air curtains for cooled rooms, air curtains with long passages, or air curtains for process equipment: f = 20-40

The average values of factor E in the recommended range of f are shown in Table 7.27.

The mass flow of air supplied by the air curtain is

G0 = Po*V*s [kg/s]- (7.218)

The purpose of the thermal design of the air curtain is to find the depen­dence between the average initial temperature of the jets supplied by the air curtain and the average temperature of the part of damping airflow coming in through the gate aperture. The temperature distribution of the air curtain jet significantly differs from the temperature distribution of the free jet as a result of the different temperatures of the air masses joined to the air curtain jet (Figs. 7.93 and 7.94).

TABLE 7.27 Factor of Dynamic Efficiency, E

Sin a

Type of air curtain

With heated indoor air, with unheated indoor air, or combined curtains with indoor air

With unheated outdoor air or for cooled rooms

For gates with a long passage

0.1

0.1

0.15

0.2

0.15

0.2

_

0.3

0.2

0.25

0.4

0.25

0.3

0.5

0.3

0.4

0.6

0.35

O

I

3

Ц

-1.0

Principle of Calculation

Principle of Calculation

10

20

30

/

40

50

FIGURE 7.93 Heat losses of air curtains.

The distribution of excess temperature of the curtain air (in relation to the outdoor air temperature, tOM) is found from the conservation of the heat con­tent of the jet as follows:

$ = AeolNcosh^y/CX + O.5A0B(l — (tanh Y)/CX)(1 — N coslr^Y/CX),

(7.219)

Where

N = (4/vj3Cx)JTjJT0 ■ (1/cp)

= 00 “ ®out = 0in _ ®out

C is an experimental constant (C = 0.1) x = X/ba

Bn = width of the air outlet slot

Y, Mm

— о,„

O Experimental points — Theoretical equation

подпись: 
- о,„
o experimental points — theoretical equation
FIGURE 7.94 Air temperature distribution in air curtain jet.

JTjJTo — correction factor for the nonisothermal jet = average temperature of the environment (K)

9 = Xjt, = correction factor for the jet impulse Ј = factor of the local resistance of the air outlet nozzle

The formula for the determination of the necessary initial temperature of the air curtain jet results from the integration of the equation for the heat con­tent of the jet in the section XA corresponding to the inlet of the jet into the room in the scope ( — YA). The ordinate of point A is obtained from the

Law of conservation of the mass in the section XA:

Ya — CXarctanhD,

Where

D = U — (pm, xq/p0)](l/v)(‘l/JTj JT0)/(pmixq/p0)(j3Cx) (7.220)

Q — G0 /Gg is the relative mass flow of air through the curtain Gg is the mass flow of air through the aperture

Simplified formulas are applied in engineering design. For example, in the case of an air curtain with heated indoor air the necessary temperature of the supplied air may be calculated according to the following formula:

7.221)

подпись: 7.221)60 ®out (®mix ®out) w2(^in ^out)?

F

M.

M2

10

2

-0.6

15

2.5

-]

20

2.9

-1.3

30

3.5

-1.8

40

4.1

-2.2

Where

0out, Gin are design temperatures of the outdoor air and room air, respectively (°C)

0mix is the temperature of the air mixture coming through the aperture of the gate

Ni] and m2 are factors with average values as shown in Table 7.28 for total damping of the aperture (q = 1)

The temperature of air supplied by the air curtain should not exceed 70 °C in case the technological process does not require any other temperature. The thermal capacity of the air curtain is determined according to the equation

P = CpGo(eo-0H) [W], (7.222)

Where

Cp is the heat capacity of air, 1004 J/kg °C 8H is the discharge temperature of the air curtain

Parameters for combined air curtains are determined by optimized cal­culations based on minimal expenses. Usually the share of heated air in a combined air curtain is 20-40% of the total flow and its temperature is

60-70 °C.

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