ON THE ISSUE OF AIR DRYING IN THE AUTOMATIC BRAKE SYSTEM

I. V. Gebler and S. S. Maksimova

It is known that the moisture of brake air often entails improper operation of the brakes, mainly in winter, when air from the main reservoir may enter the cold main line at a higher temperature, having been heated in the main reservoir as a result of compression during pump operation and with a high moisture content relative to atmospheric air—as a result of compression by a factor of 8–9. In the colder main line and brake devices, the air may prove to be supersaturated with respect to moisture content, and as a result excess moisture precipitates in the form of snow and ice, which leads to freezing of the brakes.

In order to get an idea of the amount of moisture that can precipitate, let us take an example. Let the temperature of the outside air be \(-10^\circ\), at a relative humidity of \(75\%\). In the table of saturation of water vapor (Hütte et al.) we find that the absolute humidity of air at \(-10^\circ\) is \(2.51\ \mathrm{g/m^3}\). Consequently, at \(75\%\) saturation the moisture content will be:

\[ 2.31 \cdot 0.75 = 1.73\ \mathrm{g/m^3}. \]

If the air in the main reservoir has an absolute pressure \(= 9\) ata, then for each cubic meter of compressed air there are \(1.73 \times 9 = 15.57\ \mathrm{g}\) of moisture. Such a moisture content corresponds to an absolute humidity of approximately about \(+18^\circ\). Thus, moisture will not condense in the main reservoir if the temperature in it is not less than \(+18^\circ\), and if braking occurs under such conditions, air with the indicated moisture content will enter the main line. If, however, the temperature in the main reservoir is below \(+18^\circ\), then part of the moisture will condense, while the air will have \(100\%\) saturation corresponding to the given temperature, since it will be in contact with water. Consequently, the amount of moisture entering the main line during braking will depend on the temperature in the main reservoir.

Suppose that in the main reservoir the air has a temperature of \(+10^\circ\), which corresponds to an absolute humidity of \(9.39\ \mathrm{g/m^3}\). If the temperature of the main line is taken as equal to the temperature of the outside air, i.e. in this case \(= -10^\circ\), and the pressure \(= 5\) ata, then the relative humidity of the air in the main line will be:

\[ \frac{5 \cdot 9.39\left(1 + \frac{10}{273}\right)} {9 \cdot 2.31 \cdot \left(1 - \frac{10}{273}\right)} = 2.42 \text{ or } 242\%. \]

This corresponds to an absolute amount of moisture \(= 5.59 \, g/m^3\). Consequently, per \(1 \, m^3\) of main-line air, the following will condense: \(5.59 - 2.31 = 3.28 \, g\) of water.

One cubic meter of air from the main reservoir at a pressure of 9 ata and \(T = +10^\circ\) will yield main-line air \((p = 5 \text{ ata}, T = -10^\circ)\):

\[ \frac{ 9 \cdot \left(1 - \frac{10}{273}\right) }{ 5 \cdot \left(1 + \frac{1}{273}\right) } = 1.67 \, m^3. \]

On the other hand, \(1\) cubic meter of atmospheric air \((p = 1, T = -10^\circ)\) will yield

\[ \text{air in the state in the main reservoir:} \quad \frac{ 1 + \frac{10}{273} }{ 9 \cdot \left(1 - \frac{10}{273}\right) } = 0.12 \, m^3. \]

Hence, per \(1\) cubic meter of atmospheric air under the given conditions, the following will condense:

\[ 3.28 \times 1.67 \times 0.12 = 0.66 \, g. \]

Taking the consumption of atmospheric air as \(40 \, m^3/\text{hour}\), we find that, under the conditions of the example taken, the main line will condense: \(0.66 \times 40 = 26.4 \, g\) of water per hour. When the temperature in the main reservoir is lowered, the moisture content of the air located in it, and consequently of the air entering the main line, decreases accordingly. Therefore, efforts are made to lower the temperature in the main reservoir.

Engineer Korvatsky believes that this temperature should not exceed the temperature of the outside air by more than \(3\)—\(4^\circ\), which corresponds to a relative humidity of the air in the main line of no more than \(85\%\), in the extreme case by \(5^\circ\) \(^{1)}\), and to achieve this he proposes lengthening the discharge pipe between the pump and the main reservoir to \(10\)—\(15 \, m\) (“cooling loop”).

Taking the temperature difference between the air in the main reservoir and the outside air on average as \(5^\circ\), for the preceding example we shall have: the air temperature in the main reservoir is \(-10^\circ + 4^\circ = -6^\circ\); the absolute humidity of the air at this temperature, according to the tables, is \(3.13 \, g/m^3\). Analogously to the preceding, we find that the relative humidity of the air in the main line will be:

\[ \frac{ 5 \cdot 3.13 \cdot \left(1 - \frac{6}{273}\right) }{ 9 \cdot 2.31 \cdot \left(1 - \frac{10}{273}\right) } = 0.76 \text{ or } 76\% \]

and, consequently, there will be no condensation.

If the goal is the absence of condensation in the main line at higher air temperatures in the main reservoir, bearing in mind that the cooling effect of the lengthened pipe will be insufficient, for example during forced operation of the compressor, which may occur in individual cases, then the question may be raised of dehydrating the brake air by other methods.

\(^{1)}\) Vagonnoe khozyaistvo, 1935, Nos. 8—9.

The methods most commonly used for drying air are, generally speaking, the following: compression with simultaneous cooling, washing the air with hygroscopic liquids, and absorption of moisture from the air by solid absorbents. The first of these methods is obviously unacceptable, since in the process of preparing the air it would be necessary to use intensive cooling in order to have the air at any moment dehydrated to the proper degree; under the conditions of a brake installation this is inconvenient because of the complication of the apparatus. The second method, using liquid absorbents (solutions of calcium chloride, glycerin), which is sometimes used for drying air and gases in stationary installations, is also completely unsuitable. In this case constancy of the external temperature and regeneration of the absorbents are necessary; the latter is a rather complex and cumbersome operation and requires special installations.

The only method that can be considered possible for the present purpose is the use of solid desiccants. Such substances absorb moisture either as a result of the formation of hydrates, or by adsorption, possessing the ability to lower the elasticity of water vapor when in contact with a moist gas. Among such solid moisture absorbents, first of all, is calcium chloride (\(\mathrm{CaCl_2}\)), which is widely used in laboratories for drying gases. The technical product is very readily available, being a waste product of soda production and accumulating in large quantities at soda plants operating by the ammonia process.

Anhydrous calcium chloride (\(\mathrm{CaCl_2}\)) and its dihydrate \((\mathrm{CaCl_2 \cdot 2H_2O})\) absorb moisture well, converting into the hexahydrate \((\mathrm{CaCl_2 \cdot 6H_2O})\). In this process more water is absorbed than is required for the formation of the crystalline hydrate \(\mathrm{CaCl_2 \cdot 6H_2O}\), since the latter also possesses hygroscopicity and deliquesces upon further absorption of moisture. As a result a semi-liquid mass is formed which, at elevated temperature, becomes quite fluid, since the hexahydrate melts at \(30^\circ\). In connection with these properties, difficulties may be expected in regenerating calcium chloride that has absorbed moisture directly in the brake installation by means of superheated steam, in view of the thinning of the mass and the clogging by it of the air-outlet openings of the drying filter, with a simultaneous increase in the resistance to the passage of steam. Moreover, dehydration of calcium chloride during regeneration should apparently proceed only as far as the formation of the dihydrate, at heating not above \(200^\circ\), since at a higher temperature the formation of anhydrous \(\mathrm{CaCl_2}\) is accompanied by its partial decomposition with the formation of hydrochloric acid according to the equation:

\[ \mathrm{CaCl_2 + H_2O = CaO + 2HCl.} \]

Small quantities of hydrogen chloride, when air is subsequently admitted, may enter the brake main, which is obviously completely inadmissible in view of the strong corrosive action of hydrogen chloride on metals. Maintaining a definite temperature regime during regeneration under the conditions of a brake installation would probably be difficult.

Substances that absorb moisture under adsorption conditions should prove more convenient. One of the best hydrophilic (water-absorbing) sorbents at present is “silica gel.” This is the name given to a product consisting of dehydrated silicic-acid gel (colloidal silicic acid), prepared by treating a sodium silicate solution with hydrochloric acid and subsequently drying the resulting...

gel¹). Silica gel is a solid product, in outward appearance resembling quartz, but having a considerably lower specific gravity owing to the presence of a large number of capillary pores of ultramicroscopic size. This porosity constitutes the specific feature of silica gel, giving rise to an enormous surface area, as a result of which such surface phenomena occur as the absorption of water vapor or other volatile substances (benzene, acetone, etc.), and also of gases. The hardness of silica gel is 5 (on the Mohs scale), its bulk density about 0.6.

The absorptive capacity of silica gel is very great. It can absorb water up to 50% and more relative to its own weight; moreover, absorption can proceed at low concentrations of water vapor in the air. A very important circumstance is that silica gel which has absorbed moisture can easily be regenerated; this is accomplished by blowing the moist silica gel with hot air or superheated steam at a temperature of 250–350°, after which it again acquires the ability to absorb water with its former energy. For this reason silica gel is used in technology for drying, at times, very large quantities of air and certain technical gases. Thus, for example, there are installations for drying, by means of silica gel, the air supplied to blast furnaces², as well as coke-oven or illuminating gas³.

From the fundamental point of view, the use of silica gel for removing moisture from air in brake installations is entirely possible, thanks to its high adsorption properties with respect to water and the ease of regeneration; the latter is especially important in the present case. Furthermore, the possibility of working with silica gel at low temperatures is also of great significance. Taking into account the properties of silica gel, one may assume that the additional installation would not be complicated and that operation would be simple.

In this connection, the author of the present article raised the question of drying brake air with the aid of silica gel. Not being a specialist in the field of railway brakes, in October 1936 the author delivered a report at the Tomsk Transport Institute, at the Department of Cars, in the presence of specialists. The report set forth the theoretical side of the question, as well as the results of preliminary experiments carried out by the author in his laboratory at the TII. During discussion of the report, favorable judgments were expressed as to the substance of the proposal made, which aroused considerable interest and a desire to carry out a more detailed investigation of the question, first in the laboratory, then on the brake installation at the Transport Institute, and subsequently on a steam locomotive.

The research work was organized and carried out in the laboratory of the Tomsk Railway. Its results are presented below.

Bearing in mind that the properties of silica gel are, generally speaking, known, in the present investigation it was necessary to test silica gel for drying air as applied to the operation of automatic brakes, namely at various temperatures and air humidities, at a specified volumetric velocity corresponding to the output of an air pump or to discharge into the main line for braking, with respect to the required amount of sorbent for the brake installation and the conditions of its rege-

of regeneration, the operating time of the sorbent in the first cycle, and, finally, the place of installation of the dehydrating filter in the brake line. Under laboratory conditions the experiments were carried out on a small scale, under conditions analogous to those obtaining in brake installations. Air was taken in liters, silica gel in grams. The silica gel used in the experiments was always ground so as to pass through a sieve with openings of 1 mm; moreover, from the product ground to this degree, fines and dust were removed by screening through a sieve with 400 openings/cm². The bulk (apparent) density of silica gel in this granulometric composition was about 0.60 g/cm³. Its true specific gravity was equal to 1.02.

After grinding, the silica gel was activated by heating at 400° for two hours and, in this state, was used for the experiments. The experiments were carried out as follows. The silica gel was placed in a U-shaped tube through which air was passed; from the increase in weight of the tube the amount of absorbed moisture was determined, which was calculated relative to the weight of the silica gel and to the air, whose humidity was known.

The effect of absorption of moisture from air by silica gel depends on a number of factors. It increases with decreasing temperature and with increasing concentration of water vapor in the air. It also increases with an increase in the surface of the sorbent, in other words, with a decrease in the size of its grains.

Furthermore, the linear velocity of the air in the contact apparatus is of great importance with respect to the effect of moisture absorption, since it determines the time of contact between the moisture-yielding air and the moisture-absorbing sorbent, for the same height of the layer of the latter. On the other hand, this layer height is a factor that also affects the contact time. The latter is one of the conditions determining the absorption effect and therefore depends on the linear velocity of the air in the contact apparatus and on the height of the sorbent layer.

Let us suppose (Fig. 1) that we have a contact apparatus consisting of a cylinder with diameter \(d\) m; between the planes AB and CD is the sorbent, whose layer height is \(h\) m. The inlet and outlet of the air are indicated by arrows. The volumetric velocity of the air is \(Q\) m³/sec. If we call the free cross-sectional area inside the contact layer \(\omega\), then the linear velocity of the air inside this layer will be:

Fig. 1.

\[ v=\frac{Q}{\omega}\ \text{m/sec.}, \]

and the contact time \(\tau\) is determined from the expression

\[ \tau=\frac{h}{v}=\frac{\omega h}{Q}. \tag{1} \]

If we double the layer height, then we shall have:

\[ \tau_{1}=\frac{2\omega h}{Q}=3\tau. \]

With a twofold increase in the free cross-sectional area we have:

\[ v_{1}=\frac{Q}{2\omega}\quad \text{and}\quad \tau=\frac{h}{v_{1}}=\frac{2\omega h}{Q}=2\tau. \]

Thus, in order to increase the contact time, one may increase either the height of the sorbent layer or the free cross-sectional area. But since increasing the height of the layer increases the hydraulic resistance of the apparatus, it is more expedient to increase the cross-sectional area. The latter, however, is of significance only at low pressures in the system, on the order of \(1/10\)—\(1/5\) atm.

The free cross-sectional area inside the sorbent layer is determined from the expression:

\[ \omega = \frac{G}{h}\cdot\left(\frac{1}{i}-\frac{1}{d}\right), \tag{2} \]

where \(G\) is the weight of the sorbent (kg);
\(h\) is the layer height (m);
\(i\) is the bulk density \((\mathrm{kg}/\mathrm{m}^{3})\);
\(d\) is the true specific weight.

The absorption effect depends, in addition to the contact time, also on the nature of the air motion as a function of velocity (jetting, eddying), and does not vary in proportion to the free cross-sectional area. The same may be said of the height of the sorbent layer, which is related to the decrease in the concentration of water vapor as the layer is traversed.

Initially, experiments were carried out with air saturated at the given temperature; for this purpose the air was fed to the dryer from a water gasometer at a volumetric rate of about 50 l/hour. This rate was chosen approximately in accordance with the fact that the hourly air consumption in brakes is (according to the Brake Handbook) about 40 m³, and was increased to the indicated figure on the laboratory scale.

Experiment 1.

Cross-sectional area of the tube with silica gel in the clear . . . 0.61 cm²
Free cross-sectional area . . . 0.26 cm²
Height of the silica-gel layer . . . 13.30 cm.
Weight of silica gel . . . 4.7 g.
Volumetric air velocity . . . 51 l/hour.
Linear air velocity in the tube . . . \(V\)—0.54 m/sec.
Contact time . . . \(\tau\)—0.246 sec.
Air temperature 13°C.

Table 1.

Experiment 2.

Cross-sectional area of the tube with silica gel in the clear . . . 1.35 cm².
Free cross-sectional area . . . 0.54 cm².
Height of the silica-gel layer . . . 13.7 cm.
Weight of silica gel . . . 10 g.

Volumetric air velocity . . . . . . . . . . . . . . . . . . . 51 l/hour.
Linear velocity of the air in the tube . . . . . . . . . . \(v = 0.26\) m/sec.
Contact time . . . . . . . . . . . . . . . . . . . . . \(\tau = 0.527\) sec.
Air temperature \(t \sim 8^\circ\).

Table II

Experiment 3.

Cross-sectional area of the tube with silica gel, clear opening . . . . . . . . . . . . . . . . . . . . 0.61 cm².
Free cross-sectional area . . . . . . . . . . . . . . . . . . . . 0.26 cm².
Height of the silica-gel layer . . . . . . . . . . . . . . . . . 26.6 cm.
Weight of silica gel . . . . . . . . . . . . . . . . . . . . 9.4 g.
Volumetric air velocity . . . . . . . . . . . . . . . . . . . . 51 l/hour.
Linear velocity of the air in the tube . . . . . . . . . . . . . . \(0.54\) m/sec.
Contact time \(\tau = 0.492\) sec.
Air temperature \(t \sim 18^\circ\).

Table III

The results of all three experiments for the figures in the next-to-last column are presented in Fig. 2. As can be seen, the amount of moisture absorbed in all cases decreases with each hour. In other words, the adsorption capacity of the silica gel falls as it becomes moistened, although this moistening, amounting to a maximum of 7.8% of the weight of the sorbent, is far from the limiting value. The experiments were carried out at approximately the same temperature and concentration of water vapor in the air; what changed was the contact time: in the second experiment it was increased by roughly a factor of two by a corresponding increase in the free cross-sectional area while maintaining the same layer height; in the third experiment the same increase in time

Fig. 2.

contact time was achieved by the opposite method—the height of the layer was doubled, while the free cross-sectional area was left the same as in the first experiment. The total amount of moisture absorbed over all the hours, per 1 l of air, is:

\[ \begin{aligned} \text{I experiment: }&25\ \text{mg/l}.\\ \text{II experiment: }&34.9\ \text{ ”}\\ \text{III experiment: }&35.1\ \text{ ”} \end{aligned} \]

Thus, increasing the contact time twofold gives practically identical figures in both cases, and the total amount of absorbed moisture increases by a round 40%. But the absorption process proceeds somewhat differently: namely, in the third experiment, with the greater layer height, in the hours following the first, more moisture is absorbed; this occurs because the portions of the sorbent layer more distant along the course of the air initially take up less moisture, which is adsorbed to a greater extent in the portions located closer to the air inlet.

Thus, if absorption is carried out for one hour, it is much more advantageous to increase the cross-sectional area of the adsorption vessel; if the first operating cycle (before regeneration) is carried out for 4 hours, then, with respect to the absorption effect, in order to increase it, it is evidently more advantageous to increase the height of the layer, since in this case absorption is greater in the last hour.

The results of the experiments carried out under the specified conditions provide a basis for calculating the dimensions of the adsorption dryer and the quantity of sorbent for the brake installation (see below).

Subsequently, a numerous series of experiments was conducted at various temperatures and concentrations of moisture in the air, but always under the conditions of experiment 2, i.e., with a free cross-sectional area in the tube of \(0.54\ \text{cm}^2\), a layer height of \(13.7\ \text{cm}\), a contact time of \(+0.5\ \text{m/sec}\), and an amount of silica gel of 10 g. In cases where air of arbitrary humidity (room, outside) was used, the latter was determined by the dew point with an Alluard ether hygrometer. The hygrometer readings in individual cases were compared with the data from analytical determination of moisture in the air by absorbing it in tubes with \(H_2SO_4\) or \(P_2O_5\).

An experiment on moisture absorption at a temperature of \(+45^\circ\) and full saturation \((65.14\ \text{mg/l})\) gave the following results for the 1st hour.

Table IV

The degree of absorption, therefore, in this case is considerably greater than at \(T +18^\circ\), which is due to the higher concentration of water vapor. However, the percentage of moisture removed is too small. To increase it, it would be necessary to use a considerably larger quantity of sorbent. Therefore, at such a high temperature, the use of silica gel is evidently not advantageous, and the absorption experiments in the following hours were of no interest.

At a temperature between \(+6.5\) and \(+7.5^\circ\) and full saturation, the following results were obtained:

Table V.

In comparison with the absorption effect at \(+18^\circ\) (Table III), we see that in the 1st hour the degree of absorption is lower because of the lower concentration of moisture in the air, but in the subsequent hours it is relatively much greater and, consequently, the process proceeds more favorably.

The degree of absorption at identical temperatures but different concentrations is characterized, in comparison with the results of experiment 2, by the following data from an absorption experiment at an air temperature of \(+18^\circ\) with a relative humidity of 36.58% (5.6 mg/l).

Table VI.

That is, the absorption effect is somewhat lower because of the lower concentration of water vapor.

At temperatures below \(0^\circ\), the experiments were carried out with outside air. For this purpose the tube with silica gel was placed outside the window and, by means of a rubber tube passing through an opening in the frame, was connected to a gasometer located indoors and filled with water. Water was let out of the gasometer, and the air was drawn at the proper rate through the absorption tube. These experiments showed that at low temperatures the amount of moisture removed, in relation to that present in the air, is greatest, and in the first two hours of passing air through the absorbent about 100% of the moisture is removed, as can be seen from the following examples:

Table VII.

This circumstance is favorable, bearing in mind that dehydration of brake air is especially necessary at low temperatures.

Regeneration of moisture-containing silica gel may be carried out by blowing it through with heated air or with superheated steam. For a brake installation, of course, superheated steam should be considered; therefore the corresponding experiments were conducted only with superheated steam.

Blowing wet silica gel with steam was carried out after the absorption experiments, in the same tube. The steam obtained in the steam generator was passed through a copper coil heated by a burner, and then entered the tube at ordinary pressure.

The experiments showed that at a steam temperature of \(150^\circ\), about \(0.5\text{--}0.6\%\) moisture remains in the silica gel, i.e., regeneration proves incomplete. At a steam temperature of \(250^\circ\), the moisture is removed completely when blowing is continued for 20 minutes. Steam at a temperature of \(200\text{--}300^\circ\) gave the same effect in 15 minutes. The amount of steam is approximately about 2 g per 1 g of silica gel (dry).

In view of the imperfect setting and the absence of certain precise instruments in the laboratory of the Tomsk Railway, which was not adapted for physico-chemical work, the experiments were not carried out under such conditions as would have been desirable; therefore the figures obtained cannot claim great accuracy. Nevertheless, they are sufficient for a preliminary judgment on the advisability of using silica gel for drying brake air and for the corresponding approximate calculations, to which we now turn.

III.

In the brake line there are two points where installation of an adsorber may be assumed possible: 1) in the suction line before the compressor, immediately after the dust filter, and 2) in the line between the main reservoir and the driver’s valve (immediately after the main reservoir). In the delivery line between the compressor and the main reservoir, the possibility of installation obviously falls away, since the air here contains all the heat of compression and has a temperature, generally speaking, above \(100^\circ\).

When installing an adsorber at the first of the indicated points, it should be borne in mind that the humidity of the brake air depends only on the state of the air in the main reservoir, where a reduction in the volume of the air, an increase in moisture concentration, and precipitation of its excess in the form of condensate take place. In this connection, removal of moisture from the outside air forced into the main reservoir must be carried out to such an extent that, in the main reservoir, a humidity is established at which condensation in the line would not occur, which is connected with the temperature in the main reservoir.

How great the degree of drying of the atmospheric air must be is seen from the following approximate calculation.

Let the temperature of the atmospheric air be \(t_2 = 20^\circ\), with a relative humidity of 70%, so that \(W_0 = 0.73 \text{ g}/\text{m}^3\); the temperature of the air in the main reservoir \(T_1 = 0^\circ\). The pressures in the main reservoir \((p_1)\) and in the line \((p_2)\) are respectively equal to 9 and 5 ata. From the condition of preventing condensation in the line, for the moisture content of the air in the main reservoir \(W_1\), we have:

\[ W_1 < \frac{0.85 \cdot 9 \cdot 1.05 \cdot \left(1 - \frac{20}{273}\right)}{5} > 1.48 \text{ g}/\text{m}^3; \]

The saturation of air at \(0^\circ\) is \(4.89\ \mathrm{g/m^3}\); consequently, \(4.89 - 1.48 = 3.41\ \mathrm{g}\) of water must be removed per \(1\ \mathrm{m^3}\) of air in the main reservoir. \(1\ \mathrm{cu.\ m}\) of outside air gives air in the state in the main reservoir:

\[ \frac{1}{9 \cdot \left(1-\frac{20}{273}\right)} = 0.12\ \mathrm{m^3}. \]

Thus, \(1\ \mathrm{m^3}\) of air in the main reservoir is obtained from \(8.3\ \mathrm{m^3}\) of outside air. Consequently, per \(1\ \mathrm{m^3}\) of outside air it is necessary to remove moisture:

\[ \frac{3.41}{8.3} = 0.41 \]

or \(57\%\) of the moisture contained in the air.

If we assume that the temperature of the air in the main reservoir is \(= +10^\circ\), then we shall have:

\[ W_1 < \frac{0.85 \cdot 9 \cdot 1.05 \cdot \left(1-\frac{20}{273}\right)} {5 \cdot \left(1+\frac{10}{273}\right)} = 1.43\ \mathrm{g/m^3}. \]

Per \(1\ \mathrm{m^3}\) of outside air it will be necessary to remove \(9.55\ \mathrm{g}\) of moisture, or about \(77\%\) of the moisture contained in the air, which can probably be achieved even at such low concentrations, in view of experiments at low temperature, as well as literature indications of the possibility of reducing the moisture content of air by means of silica gel to a dew point of \(-46^\circ\)¹. Final judgments about this can be obtained only from experiments on a brake installation.

When installing the adsorber at the second point, one may be guided by the following considerations. In the main reservoir we always have saturated air at one temperature or another, depending on which the amount of moisture in the air is determined. We saw above that this temperature should differ from the air temperature in the main line (which is taken as equal to the outside-air temperature) by no more than \(3\text{–}4^\circ\); if, however, the air temperature in the main reservoir is higher, then condensation of water will take place in the main line. By removing excess moisture from the air of the main reservoir, one can have a relative humidity of the air in the main line of no more than \(85\%\), as is required, at higher temperatures.

For the relative humidity of the air in the main line we have:

\[ G_m = \frac{p_2 \cdot W_1 \cdot (1+\alpha t_1)} {l_1 \cdot W_2 \cdot (1-\alpha t_2)} < 0.85, \]

where the notation is the same as on p. 23. Let \(p_1 = 9\) ata, \(p_2 = 5\) ata and \(t_2 = -10^\circ\). Let us find the greatest temperature of the air in the main reservoir at which there will be no condensation in the main line, taking into account the absorption of moisture by silica gel. Let this absorption proceed according to the figures of Table III, and let the first working cycle (i.e., the passage of moist air through the dryer) continue for 4 hours. From the preceding expression, substituting the values, we have:

\[ W(1+\alpha t_1) = \frac{0.85 \cdot 9 \cdot 2.31 \cdot \left(1-\frac{10}{273}\right)} {5} \]

or

\[ W_1(1+\alpha t_1)=3.59. \]

Neglecting the factor \((1+\alpha t_1)\), in view of its small value, we have:

\[ W_1=3.59\ \text{g}/\text{m}^3. \]

Taking the smallest amount of moisture removed for the 4th hour: \(6.3\ \text{g}/\text{m}^3\), we find that the moisture content in the air of the main reservoir must be no more than

\[ W^\circ=3.59+6.3=9.89\ \text{g}/\text{m}^3, \]

which corresponds to a temperature above \(+10^\circ\). Thus, in the present case condensation will be absent when the temperature difference of the air in the main reservoir and in the main line is

\[ 10-(-10)=20^\circ. \]

If we limit ourselves to a 3-hour operating period in the first cycle, then we shall have:

\[ W_0=3.59+7.2=10.79\ \text{g}/\text{m}^3, \]

which corresponds to a temperature of about \(+12^\circ\), and the corresponding difference is \(22^\circ\).

For an outside temperature equal, for example, to \(-20^\circ\), by the same method we find:

\[ \begin{array}{lll} \text{with 4 hours of operation:} & W_0=7.79; & t_1=+7^\circ;\\ \text{`` 3 `` ``} & W_0=7.89; & t_1=+8.5^\circ. \end{array} \]

To determine the required dimensions of the adsorber, we adopt the following conditions on the basis of laboratory experimental data:

\[ \begin{array}{ll} \text{contact time } \tau: & 0.5\ \text{sec.}\\ \text{height of the sorbent layer:} & 0.3\ \text{m.} \end{array} \]

1. When the adsorber is installed at the first point. The capacity of the tandem pump is \(1.46\ \text{m}^3/\text{min}\). The air velocity inside the sorbent layer (from Eq. 1) will be:

\[ V=\frac{h}{\tau}=\frac{0.3}{0.5}=0.6\ \text{m}/\text{sec}. \]

The free cross-sectional area is

\[ \omega=\frac{1.46}{60\cdot 0.6}=0.041\ \text{m}^2. \]

The weight quantity of sorbent (from Eq. 2)

\[ G=\frac{0.041\cdot 0.3\cdot 1000}{0.66}\simeq 19\ \text{kg}. \]

The total area of the adsorber:

\[ \frac{\pi D^2}{4}=\frac{19}{600\cdot 0.3}=0.106\ \text{m}^2. \]

Diameter of the adsorber:

\[ D=\sqrt{\frac{0.106\cdot 4}{3.14}}=0.367\ \text{m}. \]

With the “Duplex-Compound” MGZ pump having a capacity of \(3.3\ \text{m}^3/\text{min}\),

\[ \begin{array}{ll} \text{Weight quantity of sorbent} &= 41\ \text{kg}\\ \text{Diameter of the adsorber} &= 0.538\ \text{m}. \end{array} \]

1. When installed at the second point. The air velocity in the main line during braking, with a pipe diameter of \(1''\), we take as \(100\ \text{m}/\text{sec}\). The linear velocity of the air inside the sorbent layer will be (from equation 1):

\[ V=\frac{h}{\tau}=0.6\ \text{m}/\text{sec}. \]

Free cross-sectional area:

\[ \omega=\frac{100\cdot 3.14\cdot 0.0254^2}{4\cdot 0.6}=0.0844\ \text{m}^2 \]

Weight of sorbent:

\[ G=\frac{0.0844\cdot 0.3\cdot 100.0}{0.66}=58\ \text{kg}. \]

Total area of the adsorber:

\[ \frac{\pi D^2}{4}=\frac{38}{600\cdot 0.3}=0.211\ \text{m}^2 \]

Diameter of the adsorber:

\[ D=\sqrt{\frac{0.211\cdot 4}{3.14}}=0.518\ \text{m}. \]

The proposed design of the adsorber (for the 2nd case) consists of an iron cylinder with a conical part at the bottom. By means of flanges the cylinder is bolted at the upper part to the helmet. The perforated bottom, which consists of a perforated iron sheet with round holes 3 mm in diameter. The total area of the holes is \(=\frac{\omega}{2}\), in order to create a higher air velocity in the holes and the corresponding head loss needed to create this velocity, with the aim of a more uniform distribution of the air in the sorbent layer. Thus, the number of holes

\[ =\frac{0.0844}{3.14\cdot 0.003^2}\simeq 2950. \]

The lower perforated sheet has \((\varnothing=3\ \text{mm})\) 5900 holes.^1)

The granulometric composition of the silica gel corresponds to passage through a sieve with 1 mm openings, with the fines screened out on a sieve with 400 openings/cm\(^2\). In order that the grains not fall through the holes, asbestos wool is placed on the bottom and on top of the sorbent layer in a layer 10 mm thick—6, 7—a ring for removing the perforated sheets during disassembly.

The first operating cycle (for absorption) may apparently last no less than 4 hours (and perhaps longer), after which blowing with steam for 15–20 minutes should follow; then the next working cycle again, and so on.

If the silica gel may become contaminated with dust or oil, after a certain interval of time it may be necessary to activate the sorbent by heating it at a temperature of 400–500° in a special stationary installation, which should be associated with recharging the adsorber at certain intervals. How long these intervals are can be established only in practice, but they probably should be considerable, assuming slight contamination in the presence of a dust filter and with the adsorber located away from the compressor, behind the main reservoir.

In the laboratory, under the existing conditions, it was impossible to study the effect of increased pressure on the moisture-absorption effect (all experiments were carried out at atmospheric pressure).

Everything that could not be clarified in the laboratory, as well as verification of the results obtained and of the preliminary calculations, must be carried out under practical operating conditions. The present data may be regarded only as a first approximation.

^1) The adsorber and the steam line to it must, of course, be thermally insulated.

1. Zeitschr. für deutscher Ingenieure 70, 907 (1926). ↩↩

2. Zeitschr. des. Verein. deutlicher Ingenieure. 70, 8, 907 (1936). ↩

3. Gas Age-Record, 1926, 1. ↩