Aviation Engines Part 3

The phenomena of the brilliant light and its accompanying heat at the moment of explosion have been witnessed in the experiments of Dugald Clerk in England, the illumination lasting throughout the stroke; but in regard to time in a four-cycle engine, the incandescent state exists only one-quarter of the running time. Thus the time interval, together with the non-conductibility of the gases, makes the phenomena of a high-temperature combustion within the comparatively cool walls of a cylinder a practical possibility.

THE ISOTHERMAL LAW

The natural laws, long since promulgated by Boyle, Gay Lussac, and others, on the subject of the expansion and compression of gases by force and by heat, and their variable pressures and temperatures when confined, are conceded to be practically true and applicable to all gases, whether single, mixed, or combined.

The law formulated by Boyle only relates to the compression and expansion of gases without a change of temperature, and is stated in these words:

_If the temperature of a gas be kept constant, its pressure or elastic force will vary inversely as the volume it occupies._

It is expressed in the formula P V = C, or pressure volume = constant. Hence, C/P = V and C/V = P.

Thus the curve formed by increments of pressure during the expansion or compression of a given volume of gas without change of temperature is designated as the isothermal curve in which the volume multiplied by the pressure is a constant value in expansion, and inversely the pressure divided by the volume is a constant value in compressing a gas.

But as compression and expansion of gases require force for their accomplishment mechanically, or by the application or abstraction of heat chemically, or by convection, a second condition becomes involved, which was formulated into a law of thermodynamics by Gay Lussac under the following conditions: A given volume of gas under a free piston expands by heat and contracts by the loss of heat, its volume causing a proportional movement of a free piston equal to 1/273 part of the cylinder volume for each degree Centigrade difference in temperature, or 1/492 part of its volume for each degree Fahrenheit. With a fixed piston (constant volume), the pressure is increased or decreased by an increase or decrease of heat in the same proportion of 1/273 part of its pressure for each degree Centigrade, or 1/492 part of its pressure for each degree Fahrenheit change in temperature. This is the natural sequence of the law of mechanical equivalent, which is a necessary deduction from the principle that nothing in nature can be lost or wasted, for all the heat that is imparted to or abstracted from a gaseous body must be accounted for, either as heat or its equivalent transformed into some other form of energy. In the case of a piston moving in a cylinder by the expansive force of heat in a gaseous body, all the heat expended in expansion of the gas is turned into work; the balance must be accounted for in absorption by the cylinder or radiation.

THE ADIABATIC LAW

This theory is equally applicable to the cooling of gases by abstraction of heat or by cooling due to expansion by the motion of a piston. The denominators of these heat fractions of expansion or contraction represent the absolute zero of cold below the freezing-point of water, and read -273 C. or -492.66 = -460.66 F. below zero; and these are the starting-points of reference in computing the heat expansion in gas-engines. According to Boyle's law, called the first law of gases, there are but two characteristics of a gas and their variations to be considered, _viz_., volume and pressure: while by the law of Gay Lussac, called the second law of gases, a third is added, consisting of the value of the absolute temperature, counting from absolute zero to the temperatures at which the operations take place. This is the _Adiabatic_ law.

The ratio of the variation of the three conditions--volume, pressure, and heat--from the absolute zero temperature has a certain rate, in which the volume multiplied by the pressure and the product divided by the absolute temperature equals the ratio of expansion for each degree.

If a volume of air is contained in a cylinder having a piston and fitted with an indicator, the piston, if moved to and fro slowly, will alternately compress and expand the air, and the indicator pencil will trace a line or lines upon the card, which lines register the change of pressure and volume occurring in the cylinder. If the piston is perfectly free from leakage, and it be supposed that the temperature of the air is kept quite constant, then the line so traced is called an _Isothermal line_, and the pressure at any point when multiplied by the volume is a constant, according to Boyle's law,

_pv_ = a constant.

If, however, the piston is moved very rapidly, the air will not remain at constant temperature, but the temperature will increase because work has been done upon the air, and the heat has no time to escape by conduction. If no heat whatever is lost by any cause, the line will be traced over and over again by the indicator pencil, the cooling by expansion doing work precisely equalling the heating by compression.

This is the line of no transmission of heat, therefore known as _Adiabatic_.

[Ill.u.s.tration: Fig. 11.--Diagram Isothermal and Adiabatic Lines.]

The expansion of a gas 1/273 of its volume for every degree Centigrade, added to its temperature, is equal to the decimal .00366, the coefficient of expansion for Centigrade units. To any given volume of a gas, its expansion may be computed by multiplying the coefficient by the number of degrees, and by reversing the process the degree of acquired heat may be obtained approximately. These methods are not strictly in conformity with the absolute mathematical formula, because there is a small increase in the increment of expansion of a dry gas, and there is also a slight difference in the increment of expansion due to moisture in the atmosphere and to the vapor of water formed by the union of the hydrogen and oxygen in the combustion chamber of explosive engines.

TEMPERATURE COMPUTATIONS

The ratio of expansion on the Fahrenheit scale is derived from the absolute temperature below the freezing-point of water (32) to correspond with the Centigrade scale; therefore 1/492.66 = .0020297, the ratio of expansion from 32 for each degree rise in temperature on the Fahrenheit scale. As an example, if the temperature of any volume of air or gas at constant volume is raised, say from 60 to 2000 F., the increase in temperature will be 1940. The ratio will be 1/520.66 = .0019206. Then by the formula:

Ratio acquired temp. initial pressure = the gauge pressure; and .0019206 1940 14.7 = 54.77 lbs.

By another formula, a convenient ratio is obtained by (absolute pressure)/(absolute temp.) or 14.7/520.66 = .028233; then, using the difference of temperature as before, .028233 1940 = 54.77 lbs.

pressure.

By another formula, leaving out a small increment due to specific heat at high temperatures:

Atmospheric pressure absolute temp. + acquired temp.

I. -------------------------------------------------------- = Absolute temp. + initial temp.

absolute pressure due to the acquired temperature, from which the atmospheric pressure is deducted for the gauge pressure. Using the foregoing example, we have (14.7 460.66 + 2000)/(460.66 + 60) = 69.47 - 14.7 = 54.77, the gauge pressure, 460.66 being the absolute temperature for zero Fahrenheit.

For obtaining the volume of expansion of a gas from a given increment of heat, we have the approximate formula:

Volume absolute temp. + acquired temp.

II. ------------------------------------------ = Absolute temp. + initial temp.

heated volume. In applying this formula to the foregoing example, the figures become:

460.66 + 2000 I. ----------------- = 4.72604 volumes.

460.66 + 60

From this last term the gauge pressure may be obtained as follows:

III. 4.72604 14.7 = 69.47 lbs. absolute - 14.7 lbs. atmospheric pressure = 54.77 lbs. gauge pressure; which is the theoretical pressure due to heating air in a confined s.p.a.ce, or at constant volume from 60 to 2000 F.

By inversion of the heat formula for absolute pressure we have the formula for the acquired heat, derived from combustion at constant volume from atmospheric pressure to gauge pressure plus atmospheric pressure as derived from Example I., by which the expression

absolute pressure absolute temp. + initial temp.

---------------------------------------------------- initial absolute pressure

= absolute temperature + temperature of combustion, from which the acquired temperature is obtained by subtracting the absolute temperature.

Then, for example, (69.47 460.66 + 60)/14.7 = 2460.66, and 2460.66 - 460.66 = 2000, the theoretical heat of combustion. The dropping of terminal decimals makes a small decimal difference in the result in the different formulas.

HEAT AND ITS WORK

By Joule's law of the mechanical equivalent of heat, whenever heat is imparted to an elastic body, as air or gas, energy is generated and mechanical work produced by the expansion of the air or gas. When the heat is imparted by combustion within a cylinder containing a movable piston, the mechanical work becomes an amount measurable by the observed pressure and movement of the piston. The heat generated by the explosive elements and the expansion of the non-combining elements of nitrogen and water vapor that may have been injected into the cylinder as moisture in the air, and the water vapor formed by the union of the oxygen of the air with the hydrogen of the gas, all add to the energy of the work from their expansion by the heat of internal combustion. As against this, the absorption of heat by the walls of the cylinder, the piston, and cylinder-head or clearance walls, becomes a modifying condition in the force imparted to the moving piston.

It is found that when any explosive mixture of air and gas or hydrocarbon vapor is fired, the pressure falls far short of the pressure computed from the theoretical effect of the heat produced, and from gauging the expansion of the contents of a cylinder. It is now well known that in practice the high efficiency which is promised by theoretical calculation is never realized; but it must always be remembered that the heat of combustion is the real agent, and that the gases and vapors are but the medium for the conversion of inert elements of power into the activity of energy by their chemical union. The theory of combustion has been the leading stimulus to large expectations with inventors and constructors of explosive motors; its entanglement with the modifying elements in practice has delayed the best development in construction, and as yet no really positive design of best form or action seems to have been accomplished, although great progress has been made during the past decade in the development of speed, reliability, economy, and power output of the individual units of this comparatively new power.

One of the most serious difficulties in the practical development of pressure, due to the theoretical computations of the pressure value of the full heat, is probably caused by imparting the heat of the fresh charge to the balance of the previous charge that has been cooled by expansion from the maximum pressure to near the atmospheric pressure of the exhaust. The r.e.t.a.r.dation in the velocity of combustion of perfectly mixed elements is now well known from experimental trials with measured quant.i.ties; but the princ.i.p.al difficulty in applying these conditions to the practical work of an explosive engine where a necessity for a large clearance s.p.a.ce cannot be obviated, is in the inability to obtain a maximum effect from the imperfect mixture and the mingling of the products of the last explosion with the new mixture, which produces a clouded condition that makes the ignition of the ma.s.s irregular or chattering, as observed in the expansion lines of indicator cards; but this must not be confounded with the reaction of the spring in the indicator.

Stratification of the mixture has been claimed as taking place in the clearance chamber of the cylinder; but this is not a satisfactory explanation in view of the vortical effect of the violent injection of the air and gas or vapor mixture. It certainly cannot become a perfect mixture in the time of a stroke of a high-speed motor of the two-cycle cla.s.s. In a four-cycle engine, making 1,500 revolutions per minute, the injection and compression in any one cylinder take place in one twenty-fifth of a second--formerly considered far too short a time for a perfect infusion of the elements of combustion but now very easily taken care of despite the extremely high speed of numerous aviation and automobile power-plants.

TABLE I.--EXPLOSION AT CONSTANT VOLUME IN A CLOSED CHAMBER.

=====+================================+======+=======+========+====== Dia- Temp. Time Ob- Com- gram of of served puted Curve Mixture Injected. Injec- Explo- Gauge Temp.

Fig. tion sion Pressure Fahr.

8. Fahr. Second. Pounds -----+--------------------------------+------+-------+--------+------ _a_ 1 volume gas to 14 volumes air. 64 0.45 40. 1,483 _b_ 1 " " " 13 " " 51 0.31 51.5 1,859 _c_ 1 " " " 12 " " 51 0.24 60. 2,195 _d_ 1 " " " 11 " " 51 0.17 61. 2,228 _e_ 1 " " " 9 " " 62 0.08 78. 2,835 _f_ 1 " " " 7 " " 62 0.06 87. 3,151 _g_ 1 " " " 6 " " 51 0.04 90. 3,257 _h_ 1 " " " 5 " " 51 0.055 91. 3,293 _i_ 1 " " " 4 " " 66 0.16 80. 2,871 -----+--------------------------------+------+-------+--------+------

In an examination of the times of explosion and the corresponding pressures in both tables, it will be seen that a mixture of 1 part gas to 6 parts air is the most effective and will give the highest mean pressure in a gas-engine. There is a limit to the relative proportions of illuminating gas and air mixture that is explosive, somewhat variable, depending upon the proportion of hydrogen in the gas. With ordinary coal-gas, 1 of gas to 15 parts of air; and on the lower end of the scale, 1 volume of gas to 2 parts air, are non-explosive. With gasoline vapor the explosive effect ceases at 1 to 16, and a saturated mixture of equal volumes of vapor and air will not explode, while the most intense explosive effect is from a mixture of 1 part vapor to 9 parts air. In the use of gasoline and air mixtures from a carburetor, the best effect is from 1 part saturated air to 8 parts free air.

TABLE II.--PROPERTIES AND EXPLOSIVE TEMPERATURE OF A MIXTURE OF ONE PART OF ILLUMINATING GAS OF 660 THERMAL UNITS PER CUBIC FOOT WITH VARIOUS PROPORTIONS OF AIR WITHOUT MIXTURE OF CHARGE WITH THE PRODUCTS OF A PREVIOUS EXPLOSION.

[A] Proportion, Air to Gas by Volumes.

[B] Pounds in One Cubic Foot of Mixture.

[C] Specific Heat. Heat Units Required to Raise 1 Lb. 1 Deg.

Fahrenheit. Constant Pressure.

[D] Specific Heat. Heat Units Required to Raise 1 Lb. 1 Deg.