Determining Incomplete Combustion in Oil Engines by Exhaust Gas Analysis
Abstract Generated abstract
This paper develops a method for estimating incomplete combustion and associated heat losses in oil engines from exhaust gas analysis and fuel elemental composition. It derives material balance relations that account for carbon remaining as soot, carbon oxidized only to carbon monoxide, and possible incomplete sulfur combustion, then examines practical simplifications to reduce the required measurements. Numerical examples and Diesel engine tests on heavy liquid fuel indicate that sulfur incompleteness can usually be neglected, but that ignoring carbon monoxide gives appreciable errors in estimating combustion incompleteness and heat loss. The study recommends quantitative determination of carbon monoxide, for example by catalytic oxidation to carbon dioxide, and provides simplified formulas suitable for practical use.
Full Text
On Determining Incomplete Combustion in Oil Engines by Exhaust Gas Analysis
Yu. N. Sokolov
Associate Professor, Candidate of Technical Sciences
The calculation of the excess-air coefficient and of the incompleteness of fuel combustion on the basis of comparing the data of its elemental composition and the volumetric analysis of the products of combustion (in the absence of direct measurement of their quantity) requires, as is known, the drawing up of a material balance for some one of the elements entering into the composition of the fuel and of the air. In doing so it is necessary to proceed from a priori assumptions concerning the presence, in the exhaust gases, of products of incomplete combustion of the individual elements entering into the composition of the fuel.
A common one of such assumptions is to take into account the presence, in the products of combustion, of carbon monoxide CO as the result of incomplete combustion of the carbon of the fuel. Direct determination of the volumetric content of CO in the products of combustion is not required in this case, since it can be calculated by the well-known formula:
\[ \mathrm{CO}=\frac{21-\beta \mathrm{CO}_2-(\mathrm{CO}_2+\mathrm{O}_2)}{0.605+\beta}, \]
where
\[ \beta=\frac{3\cdot 0.79\left(h-\frac{o}{8}\right)}{c} \]
is the so-called fuel characteristic, and \(h\), \(o\), and \(c\) are the weight fractions of hydrogen, oxygen, and carbon in its elemental composition1. By generally accepted methods, the excess-air coefficient, as well as the fraction of incompletely burned carbon, can readily be established here.
For a number of years this assumption was considered generally accepted also for internal-combustion engines; subsequently, however, attention was drawn to the circumstance that, when liquid fuels are burned in the engine cylinder, incomplete combustion is expressed chiefly not by the formation of carbon monoxide, but by the liberation of free carbon in the form of soot or coke-like deposit. In accordance with this, Professor E. K. Mazing [1] in 1923 published a theory making it possible to establish the excess-air coefficient and the incompleteness of combustion of the fuel carbon, assuming that the latter is determined only by the formation of soot; moreover, calculations by Prof. Mazing’s formulas gave significant deviations from the results established on the basis of the assumption of incomplete combustion to carbon monoxide. The absence of CO in the exhaust gases, adopted in the theory of incomplete combustion with the forma-
soot formation, was supported by the fact that it is not possible in most cases to detect carbon monoxide in the products of combustion of an engine by ordinary methods (the Orsat apparatus). This circumstance made it possible, until recently, to regard incomplete combustion with soot formation as generally accepted in the theory of internal-combustion engines.
Ten years later, Dr.-Ing. Ackermann [2] arrived at the same conclusions; he gives a “combustion triangle,” which makes it possible to determine graphically the incompleteness of combustion due to soot formation.
The authors of the theory of incomplete combustion due to soot formation themselves already acknowledged the possibility that, in the engine exhaust gases, there may be present (along with soot and carbon deposit) carbon monoxide and other products of incomplete oxidation of the combustible constituents of the fuel.
In the literature there are also a number of more definite indications of the presence, in engine exhaust gases, of products of incomplete oxidation. Thus, Eng. Wenzel [3], in his experiments on the combustion of motor fuels in a bomb, under conditions close to the true conditions of their combustion in an engine cylinder, found appreciable quantities of CO in the products of combustion in cases where \(\alpha < 1.2\). There are also indications of the presence in engine exhaust gases of hydrogen (\(\mathrm{H}_2\)), and of heavy and light hydrocarbons.
In Prof. Masing’s book The Thermal Process of Internal-Combustion Engines (1937), there are already concrete examples of calculating the incompleteness of combustion with simultaneous formation of both soot and carbon monoxide (though only for a gas engine), and a formula is also given that makes it possible to establish the excess-air coefficient while taking into account soot formation and the presence of carbon monoxide, derived by Associate Professor S. E. Lebedev. The latter also carried out further work in the field of applying exhaust-gas analysis in engine tests.
The brief survey given here shows that the presence in engine exhaust gases not only of soot, but also of carbon monoxide and other products of incomplete oxidation, must at present be regarded as generally recognized. The practical necessity of taking this circumstance into account when determining the excess-air coefficient and calculating the incompleteness of combustion (given the obvious release of the main mass of unburned carbon in the form of soot or carbon deposit), however, remains unjustified, and the method of such accounting itself is insufficiently developed.
In this connection, the author set himself the task of establishing general relations that make it possible (on the basis of comparing data from volumetric analysis of the exhaust gases of an oil engine and the elemental composition of the fuel burned in it) to determine the excess-air coefficient and the heat loss due to incomplete combustion, considering that the latter is determined not only by soot formation, but also by incomplete oxidation of carbon, as well as by possible incomplete combustion of the sulfur present in the fuel; to analyze the possibility of simplifying these relations by means of certain assumptions and to establish working formulas suitable for practical use; and, finally, to verify their applicability experimentally. The present work is devoted to the solution of this problem.
We did not, however, consider it necessary to introduce an allowance for the possible presence of hydrogen in the exhaust gases, since the considerable rate of its oxidation reaction permits one to assume that its content will be still smaller than that of CO, while the determination of \(\mathrm{H}_2\) in the technical analysis of combustion products is associated with difficulties; this, together with a considerable complication of the calculation formulas, would make such an allowance practically of little use. As for hydrocarbons, in a number of experiments carried out by the author with an oil engine, precise chemical investigations succeeded in detecting them only in the form of barely perceptible traces, which, together with
considerations indicated with respect to hydrogen made it inexpedient to take these products of incomplete combustion into account as well. We believe that simultaneous accounting, in the combustion products, for elemental carbon and its oxide (CO) already in itself represents a certain step forward in comparison with the methods used until recently. It is to this question that, naturally, we have devoted the greatest attention.
Derivation of General Relations
Let us first consider the most general case, assuming that the incompleteness of carbon combustion is expressed both in the formation of soot and (partly) in the formation of carbon monoxide, CO, while the sulfur present in the fuel also burns only partially.
The weight composition of the fuel
\[ c+s+h+o+n=1\ \text{kg} \]
must, of course, be known; we shall assume that, of all the carbon \((c)\) in the fuel, a certain fraction
\(x_1c\)—burns, forming carbon monoxide CO, and
\(x_2c\)—remains in the form of amorphous carbon, forming soot. In this case
\(x=x_1+x_2\) will express the total fraction of incompletely burned carbon, and
\((1-x)c\)—that part of the fuel carbon which burns completely, forming \(\mathrm{CO_2}\).
In exactly the same way we assume that the sulfur contained in the fuel in the amount
\(ys\)—does not burn, being deposited in the form of elemental sulfur,
and \((1-y)s\)—burns completely, forming \(\mathrm{SO_2}\).
Under these conditions, in the combustion products of one kilogram of fuel we shall have:
\[ \mathrm{CO_2}\;-\;\frac{1}{12}(1-x)c\ \text{moles} \]
\[ \mathrm{CO}\;-\;\frac{1}{12}x_1c\quad ” \]
\[ \mathrm{C}\;-\;\frac{1}{12}x_2c\quad ” \]
\[ \mathrm{SO_2}\;-\;\frac{1}{32}(1-y)s\quad ” \]
\[ \mathrm{S}\;-\;\frac{1}{32}ys\quad ” \]
\[ \mathrm{H_2O}\;-\;\frac{1}{2}h\quad ” \]
\[ \mathrm{N_2}\;-\;\frac{1}{28}n+0.79\alpha L_0\quad ” \]
\[ \mathrm{O_2}\;-\;0.21\alpha L_0+\frac{o}{32} \]
\[ -\left\{ \frac{1}{12}(1-x)c+\frac{1}{24}x_1c+\frac{1}{32}(1-y)s+\frac{1}{4}h \right\}\ \text{moles}, \]
where
\[ L_0=\frac{1}{0.21}\left[\frac{c}{12}+\frac{s}{32}+\frac{n}{4}-\frac{o}{32}\right] =\frac{c}{0.21\cdot 12}\cdot \sigma \ \text{moles/kg} \tag{1} \]
—is the theoretical amount of air, calculated from the conditions of complete combustion,
\[ \alpha=\frac{\text{actual amount of air}}{\text{theoretical amount of air for complete combustion}} \]
—is the coefficient of excess air for complete combustion, and
\[ \sigma=1+\frac{3}{c}\left(h+\frac{s-o}{8}\right) \tag{2} \]
—is the so-called German fuel characteristic.
The quantity of dry gases obtained in the combustion of one kg of fuel must be
\[ M_{\mathrm{sg}}=\frac{1}{28}n+\frac{100}{21}\cdot\frac{1}{12}c\alpha\sigma+\frac{o}{32} +\frac{1}{24}x_1c-\frac{1}{4}h' =\frac{1}{12}A \ \frac{\text{moles}}{\text{kg}}, \tag{3} \]
where, for simplification, the conventional quantity
\[ A=0.429n+0.375\,o+4.76c\alpha\sigma+0.5x_1c-3h. \tag{4} \]
has been introduced.
If we now express the relative volume fractions of carbon dioxide, carbon monoxide, sulfurous anhydride, oxygen, and nitrogen in the dry combustion products in percent and denote them respectively by \(\mathrm{CO}_2\), \(\mathrm{CO}\), \(\mathrm{SO}_2\), \(\mathrm{O}_2\), and \(\mathrm{N}_2\), it is easy to obtain the following five equations:
\[ \frac{A}{100}\mathrm{CO}_2=(1-x)c \tag{5} \]
\[ \frac{A}{100}\mathrm{CO}=x_1c \tag{6} \]
\[ \frac{A}{100}\mathrm{SO}_2=0.375(1-y)s \tag{7} \]
\[ \frac{A}{100}\mathrm{O}_2=c\alpha\sigma+0.375\,o-(1-x+0.5x_1)c-0.375(1-y)s-3h. \tag{8} \]
\[ \frac{A}{100}\mathrm{N}_2=0.429n+3.76c\alpha\sigma. \tag{9} \]
Given data from the volumetric analysis of the products of combustion and the elemental composition of the fuel, the unknowns in these equations will be \(\alpha\) and the quantities determining the incompleteness of combustion of the individual constituent parts of the fuel, \(x_1\), \(x\), and \(y\).
In equations (6) and (9) we have only two unknowns, \(x_1\) and \(\alpha^1\). Solving them as a system, we obtain:
\[ \alpha= \frac{(100-0.5\mathrm{CO}-\mathrm{N}_2)0.429n+\mathrm{N}_2(3h-0.375\,o)} {\left[4.76\mathrm{N}_2-3.76(100-0.5\mathrm{CO})\right]c\sigma} \tag{10} \]
and
\[ x_1=\frac{\mathrm{CO}}{c}\cdot \frac{0.429n+0.375\,o+4.76c\alpha\sigma-3h} {100-0.5\mathrm{CO}} \tag{11} \]
\(^1\) It should not be forgotten that the quantity \(A\) includes the unknowns \(\alpha\) and \(x_1\).
From equation (5) the total incompleteness of combustion is also readily determined:
\[ x=1-\frac{A}{100}\cdot\frac{\mathrm{CO}_2}{c}, \tag{12} \]
and the incompleteness of combustion due to soot formation will be
\[ x_2=x-x_1. \tag{13} \]
Finally, the incompleteness of sulfur combustion \((y)\) can most simply be determined from equation (7), from the content of \(\mathrm{SO}_2\) in the exhaust gases:
\[ y=1-\frac{1}{0.375}\cdot\frac{A}{100}\cdot\frac{\mathrm{SO}_2}{s}. \tag{14} \]
From the relative characteristics of incompleteness of combustion \(x_1\), \(x_2\), and \(y\), the heat losses per kg of fuel consumed can readily be calculated:
\[ \left. \begin{array}{ll} \text{from incomplete combustion of carbon} & \left\{ \begin{array}{ll} \text{to CO} & q_{co}=5700\,x_1 c\ \text{kcal/kg} \\ \text{to soot} & q_c=8140\,x_2 c\quad ” \end{array} \right. \end{array} \right\} \tag{15,16} \]
\[ \text{From incomplete combustion of sulfur}\qquad q_s=2452\,ys\quad ” \tag{17} \]
\[ \text{and the total loss}\qquad q=q_{co}+q_c+q_s\ \text{kcal/kg} \tag{18} \]
The quantities \(c\) and \(s\), as well as \(x_1\), \(x_2\), and \(y\), must here be taken as fractions of unity, and not as percentages.
The expressions obtained, (10)—(18), make it possible to establish the excess-air coefficient, the relative characteristics of incompleteness of combustion, and the corresponding heat losses if the chemical composition of the fuel is known and a complete analysis of the exhaust gases has been carried out, with determination of \(\mathrm{RO}_2=\mathrm{CO}_2+\mathrm{SO}_2\), \(\mathrm{O}_2\), \(\mathrm{CO}\), and \(\mathrm{SO}_2\). These expressions, however, are complicated and inconvenient for practical application. In addition, carrying out a complete analysis of the exhaust gases is also very difficult and not always feasible under practical conditions.
Naturally, there arises a desire to simplify the relations derived and to reduce the number of quantities determined by gas analysis, introducing certain assumptions that simplify the final results. Such simplifications, however, must be analyzed from the point of view of determining the admissibility of the error obtained on their account.
Possible Assumptions and Simplifications
Let us first analyze the possibility of neglecting the incompleteness of sulfur combustion, i.e., of assuming \(y=0\), which is obviously quite possible because of the insignificant sulfur content in ordinary grades of liquid fuels.
Adding equations (5) and (7) with \(y=0\), we obtain
\[ \frac{A}{100}\left(\mathrm{CO}_2+\mathrm{SO}_2\right)=\frac{A}{100}\mathrm{RO}_2=(1-x)c+0.375\,s, \]
whence
\[ x=1-0.375\,\frac{s}{c}-\frac{A}{100}\cdot\frac{\mathrm{RO}_2}{c}, \tag{19} \]
where \(\alpha\) and \(x_1\), required for computing the quantity \(A\) from equation (4), are determined, as before, from expressions (10) and (11).
Thus, for a complete determination of incomplete combustion in this case, it is necessary to establish, by analysis of the exhaust gases, only their percentage content of
\[ \mathrm{RO}_2-\mathrm{CO}_2+\mathrm{SO}_2,\qquad \mathrm{O}_2 \ \text{and}\ \mathrm{CO}. \]
To determine the possible magnitude of the error arising from neglecting incomplete combustion of sulfur, let us take a fuel with the maximum possible sulfur content:
\[ \begin{array}{ll} c=85.4\%, & n=0.4\%,\\ h=12.2\%, & o=0.0\%,\\ s=2.0\%, & \\ & 100.0\%. \end{array} \]
and assume that it burns at a moderate excess-air coefficient \(\alpha=1.5\) and at maximum values of the incompleteness of carbon combustion:
\[ \begin{array}{rl} \text{into soot} & x_2=0.30,\\ \text{into CO} & x_1=0.05,\\ \text{and of sulfur—} & y=0.5. \end{array} \]
Calculating, by the complete formulas, the volumetric content of the components of the combustion products corresponding to these conditions and taking them as the result of exhaust-gas analysis, we establish, under the assumption \(y=0\),
\[ \alpha=1.50,\quad x_1=0.05,\quad x'=0.345,\quad x'_2=0.295. \]
The errors due to the assumption \(y=0\) are therefore:
\[ \Delta_{\alpha}^{y=0}=0;\quad \Delta_{x_1}^{y=0}=0;\quad \Delta_x^{y=0}=\frac{x'-x}{x}\,100=-1.43\% \]
and
\[ \Delta_{x_2}^{y=0}=\frac{x'_2-x_2}{x_2}\,100=-1.67\%. \]
The heat loss due to incomplete combustion corresponding to the adopted values \(x_1, x_2\), and \(y\) should be \(q=2353\ \text{kcal/kg}\); while, calculated under the assumption \(y=0\), it will be only \(q'=2293\ \text{kcal/kg}\). The error in the heat loss due to the assumption \(y=0\) will therefore be
\[ \Delta_q^{y=0}=\frac{q'-q}{q}\,100=-2.55\%. \]
The obtained error values are at the limit of admissibility (for ordinary accuracy of measurements and calculations). It should, however, be borne in mind that the example considered provides for the maximum possible (scarcely likely to be encountered in practice) sulfur content and up to 50% incomplete combustion of it.
In order to ascertain the concrete values of incomplete combustion that may occur, we carried out a series of tests on a Diesel compressor engine (the “CO” series)\(^1\), covering a very wide range of operating conditions, from the standpoint of the possible degree of incomplete combustion. Incomplete combustion in each of these tests was calculated by the complete formulas and with the presence of various simplifications.
\(^1\) For a description of these tests and their general results, see below.
Table I
Comparison of the results of calculating incomplete combustion by different formulas, taking \(y=0\) for the experiments of the CO series
| Quantity | Subquantity | Designation | Dimension | CO-40 | CO-45 | CO-50 | CO-58 | CO-min | CO-max |
|---|---|---|---|---|---|---|---|---|---|
| Coefficient of excess air | — | \(\alpha\) | — | 1,310 | 1,590 | 1,663 | 1,854 | 2,635 | 1,665 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; with oxygen of incomplete combustion | in CO | \(X_1\) | % % | 3,3 | 1,6 | 2,1 | 1,8 | 0,0 | 4,9 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; with oxygen of incomplete combustion | in soot | \(X_2\) | % % | 24,5 | 17,3 | 13,2 | 9,2 | 19,3 | 12,6 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; with oxygen of incomplete combustion | total | \(X\) | % % | 27,8 | 18,9 | 15,3 | 11,0 | 19,3 | 17,5 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; with oxygen of incomplete combustion | sulfur | \(y\) | % % | 52,9 | 52,1 | 29,6 | \((-35?)\) | \((-15?)\) | 9,3 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; heat loss from incomplete combustion | in CO | \(q_{co}\) | kcal/kg | 164 | 82 | 102 | 90 | — | 242 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; heat loss from incomplete combustion | in soot | \(q_c\) | kcal/kg | 1735 | 1225 | 934 | 651 | 1367 | 892 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; heat loss from incomplete combustion | sulfur | \(q_s\) | kcal/kg | 3 | 3 | 2 | — | — | 1 |
| Taking incomplete combustion to be composed of \(CO_2\) and \(SO_2\) in the exhaust gases; heat loss from incomplete combustion | total | \(q\) | kcal/kg | 1902 | 1310 | 1038 | 741 | 1367 | 1135 |
| Taking complete combustion to be composed of \(RO_2 = CO_2 + SO_2\) | relative incomplete combustion; oxygen of incomplete combustion | in CO | \(X'_1\) | % % | 3,30 | 1,65 | 2,06 | 1,82 | 0,00 |
| Taking complete combustion to be composed of \(RO_2 = CO_2 + SO_2\) | relative incomplete combustion; oxygen of incomplete combustion | in soot | \(X'_2\) | % % | 24,50 | 17,20 | 13,19 | 9,04 | 19,10 |
| Taking complete combustion to be composed of \(RO_2 = CO_2 + SO_2\) | relative incomplete combustion; oxygen of incomplete combustion | total | \(X'\) | % % | 27,80 | 18,85 | 15,25 | 10,86 | 19,10 |
| Taking complete combustion to be composed of \(RO_2 = CO_2 + SO_2\) | heat loss from incomplete combustion | in CO | \(q'_{co}\) | kcal/kg | 164 | 82 | 102 | 90 | — |
| Taking complete combustion to be composed of \(RO_2 = CO_2 + SO_2\) | heat loss from incomplete combustion | in soot | \(q'_c\) | kcal/kg | 1735 | 1218 | 934 | 641 | 1353 |
| Taking complete combustion to be composed of \(RO_2 = CO_2 + SO_2\) | heat loss from incomplete combustion | total | \(q'\) | kcal/kg | 1899 | 1300 | 1036 | 731 | 1353 |
| Error in heat loss when assuming \(y=0\) | — | \(\dfrac{q'-q}{q}\) | % % | \(-0,16\) | \(-0,75\) | \(-0,19\) | \(-1,35\) | \(-1,02\) | \(-0,35\) |
Table II
Magnitude of errors from assuming \(CO=0\) for the experiments of the CO series
| Quantity | Subquantity | Designation | Dimension | CO-40 | CO-45 | CO-50 | CO-58 | CO-min | CO-max |
|---|---|---|---|---|---|---|---|---|---|
| Coefficient of excess air | taking \(y=0\) | \(\alpha'\) | — | 1,310 | 1,590 | 1,663 | 1,854 | 2,635 | 1,665 |
| Coefficient of excess air | taking \(y=0\) and \(X_1=0\) | \(\alpha''\) | — | 1,240 | 1,546 | 1,607 | 1,798 | 2,635 | 1,537 |
| Coefficient of excess air | error | \(\Delta_{\alpha}^{CO=0}\) | % % | \(-5,3\) | \(-2,8\) | \(-3,4\) | \(-3,0\) | 0,0 | \(-7,7\) |
| Relative incomplete combustion; total | taking \(y=0\) | \(X'\) | % % | 27,80 | 18,85 | 15,25 | 10,86 | 19,10 | 17,44 |
| Relative incomplete combustion; total | taking \(y=0\) and \(X_1=0\) | \(X''\) | % % | 32,11 | 21,35 | 18,45 | 13,89 | 19,10 | 24,33 |
| Relative incomplete combustion; total | error | \(\Delta_{X}^{CO=0}\) | % % | +15,5 | +13,3 | +21,0 | +27,9 | 0,0 | +89,5 |
| Relative incomplete combustion; in soot | taking \(y=0\) | \(X'_2\) | % % | 24,50 | 17,20 | 13,19 | 9,04 | 19,10 | 12,55 |
| Relative incomplete combustion; in soot | taking \(y=0\) and \(X_1=0\) | \(X''_2\) | % % | 32,11 | 21,35 | 18,45 | 13,89 | 19,10 | 24,33 |
| Relative incomplete combustion; in soot | error | \(\Delta_{X_2}^{CO=0}\) | % % | 31,1 | 24,1 | 39,9 | 53,7 | 0,0 | 93,8 |
| Heat loss from incomplete combustion | taking \(y=0\) | \(q'\) | kcal/kg | 1899 | 1300 | 1036 | 731 | 1353 | 1131 |
| Heat loss from incomplete combustion | taking \(y=0\) and \(X_1=0\) | \(q''\) | kcal/kg | 2274 | 1512 | 1307 | 984 | 1353 | 1723 |
| Heat loss from incomplete combustion | error | \(\Delta_{q}^{CO=0}\) | % % | +19,8 | +16,2 | +26,2 | +34,6 | 0,0 | +52,3 |
| CO content in exhaust gases | — | \(CO\) | % % | 0,39 | 0,16 | 0,19 | 0,15 | traces | 0,45 |
Table 1 gives the results of such calculations for each of the experiments mentioned. As is evident from consideration of this table, the incompleteness of carbon combustion due to soot formation reaches almost 25%, and due to the formation of CO—up to 5%.
As for the incompleteness of sulfur combustion, in some experiments negative (?) values were obtained for it. This can evidently be explained only by inaccuracies in the determination of SO₂ in the exhaust gases, quite possible owing to absorption of SO₂ by water condensing in the sampling tubes and its subsequent release again as the temperature rises (at the moment the portion of gas being analyzed is passed through them). In any case, the values of SO₂ obtained in the experiments should be regarded as more likely exaggerated than understated. At the same time, the maximum incompleteness of sulfur combustion (experiment CO—40) was found to be 52.9%; however, the error in the heat loss resulting from neglecting it, when using fuel with a normal sulfur content (0.25%), is in the same experiment only 0.16%. The maximum value of this error (experiment CO—48), with an obviously overestimated determination of SO₂ \((y < 0)\), does not exceed 1.35%.
Thus, consideration of material based on direct experiment leads to the conclusion that the errors in heat loss which may result from neglecting the incompleteness of sulfur combustion are quite permissible; consequently, this simplification may safely be used in practice, especially since the errors in the values of \(x_1\), \(x_2\), and \(x\) are almost entirely imperceptible.
The advisability of such an assumption is dictated not so much by the desire to simplify the calculation formulas as by the wish to avoid the necessity of determining the SO₂ content in the exhaust gases, which in practice proves to be very important, since this determination is one of the most difficult and least reliable.
The matter is quite different when analyzing the possibility of disregarding the content of carbon monoxide CO in the exhaust gases. The error that may arise from this neglect can already reach a very considerable value.
Nevertheless, the assumption that CO is absent from the exhaust gases so greatly simplifies their analysis (it remains only to determine \(RO_2 = CO_2 + SO_2\) and \(O_2\), while nitrogen can be calculated by difference \(N_2 = 100 - (RO_2 + O_2)\)) and the treatment of the experimental results, that analyzing the influence of this error and establishing the extent to which it may be allowed becomes absolutely necessary.
Under the assumption \(CO = 0\), if the incompleteness of sulfur combustion is also neglected, we return to the theory of incomplete combustion with soot formation, given by Prof. Masing and subsequently by Dr. Ackerman. Proceeding, however, in the present case as well from the relations established above, we shall have:
\[ \alpha = \frac{(100 - N_2)\,0.429\,n + N_2(3h - 0.375\,o)} {[4.76\,N_2 - 376]\,c\sigma}; \tag{20} \]
\[ A = 0.429\,n + 0.375\,o + 4.76\,c\alpha - 3h, \tag{21} \]
\[ x = x_2 = 1 - \frac{A}{100}\,\frac{CO_2}{c}. \tag{12} \]
Since the Orsat apparatus gives, as is usually assumed, not \(CO_2\), but \(RO_2 = CO_2 + SO_2\), it is more convenient to use the expression
\[ x = x_2 = 1 - 0.375\,\frac{s}{c} - \frac{A}{100}\cdot\frac{RO_2}{c}, \tag{19} \]
all the more so since the term \(0.375 \dfrac{S}{C}\) depends only on the composition of the fuel and can be calculated in advance for an entire series of tests.
To check the practical possibility of the assumption under consideration \((\mathrm{CO}=0;\ x_1=0)\), let us determine the magnitude of the error that may occur for the cases:
\[ \begin{aligned} \mathrm{I})\quad &x=0.35, & x_1&=0.05, & x_2&=0.30, & \alpha&=1.5,\\ \mathrm{II})\quad &x=0.10, & x_1&=0.005, & x_2&=0.095, & \alpha&=2.0, \end{aligned} \]
where the first of them corresponds to the maximum values of the characteristics of incomplete combustion, and the second to the most commonly encountered ones.
Taking the same fuel composition as in the preceding example (when determining the error from the assumption \(y=0\)), and using an analogous procedure (calculating from the complete formulas the exhaust-gas composition corresponding to the adopted values of incomplete combustion, and determining from it, under the assumption \(\mathrm{CO}=0\), the characteristics of incomplete combustion anew), we obtain the following magnitudes of the errors possible from neglecting the formation of CO.
| Quantity | Case | \(\alpha\) | \(x\) | \(x_1\) | \(x_2\) | \(q\), kcal/kg |
|---|---|---|---|---|---|---|
| Adopted values | case I | 1.500 | 0.350 | 0.050 | 0.300 | 2355 |
| Adopted values | case II | 2.000 | 0.100 | 0.005 | 0.095 | 710 |
| Values from the calculation at \(x_1=0\) | case I | 1.470 | 0.366 | 0.000 | 0.366 | 2545 |
| Values from the calculation at \(x_1=0\) | case II | 1.979 | 0.110 | 0.000 | 0.110 | 765 |
| Error in % | case I | −2.00 | +4.67 | −100.00 | +22.0 | +8.07 |
| Error in % | case II | −1.05 | +10.00 | −100.00 | +15.8 | +7.74 |
As we see, the values of the excess-air coefficient \(\alpha\), when the presence of CO in the exhaust gases is not taken into account, are obtained as underestimated, while the characteristics of incomplete combustion are overestimated. The relative magnitude of the error obtained from this assumption is comparatively small in calculating \(\alpha\). In calculating incomplete combustion, however, this error far exceeds the limits usually permissible, reaching \(x_2\)—22% and even, in the heat loss from incomplete combustion—8%1, while both cases considered are entirely possible.
Turning to the material directly obtained from experiment in the same series of tests as that referred to when considering the influence of neglecting the incomplete combustion of sulfur, we establish the magnitudes of the errors from neglecting the presence of CO in the exhaust gases, given in Table II. These errors are still greater than those obtained in the examples considered above, and in some cases they are even more than 50%. It is characteristic that the relative magnitude of the error becomes quite appreciable not only at high CO contents in the exhaust gases, but even at low ones, if the total incomplete combustion is then small (test CO—58).
The material considered shows with complete obviousness that one should not neglect the presence of CO in the engine exhaust gases (that is, assume that all incomplete combustion is due only to the formation of soot), since in this case it is easy to obtain—
to make an extremely large error in the final results of the estimate of the incompleteness of combustion.
In the general relations established above, it was assumed that complete data on the elemental composition of the fuel were available, and that its oxygen and nitrogen contents had to be known separately. In most cases, when analyzing a liquid fuel, one is limited only to the direct determination in it of carbon, hydrogen, and sulfur; the remainder, which usually amounts to only fractions of a percent, is taken as the sum of oxygen and nitrogen without subsequently separating them. Naturally, in determining the incompleteness of combustion, there arises a desire to get rid of the need to have separate values of \(o\) and \(n\), while at the same time introducing certain simplifications into the structure of the formulas themselves established above.
Since the nitrogen and oxygen contents in the ordinary grades of liquid fuels are very small, the difference in the final results of the calculation of the quantities of interest to us will evidently be small if we take the entire sum \(o+n\) as only \(o\), or only as \(n\).
The fuel considered in the preceding examples, with \(n=0.4\%\) and \(o=0.0\%\), should be regarded as limiting with respect to nitrogen content. Let us see what the difference will be in the quantities determined for the composition of the combustion products \(RO_2=6.68\%\), \(O_2=10.59\%\), \(CO=0.51\%\), and \(N_2=82.22\%\), corresponding to the maximum values of \(x_1\) and \(x_2\) for the two limiting cases of the fuel composition with respect to oxygen and nitrogen:
\[ \begin{aligned} \text{I)}\quad & c=85.4\%,\qquad h=12.2\%,\qquad s=2.0\%,\qquad o=0.4\%,\qquad n=0.0\%,\\ \text{II)}\quad & c=85.4\%,\qquad h=12.2\%,\qquad s=2.0\%,\qquad o=0.0\%,\qquad n=0.4\%. \end{aligned} \]
Carrying out the corresponding calculations by the formulas valid for \(y=0\), but \(CO\ne O\), we obtain the following results:
| I case \(n=0.0\) \(o=0.4\) |
II case \(n=0.4\) \(o=0.0\) |
Difference \(\dfrac{\mathrm{I}-\mathrm{II}}{\mathrm{I}}\cdot 100\%\) |
|
|---|---|---|---|
| 1) German fuel characteristic \(\sigma\) | 1.436 | 1.437 | 0.07% |
| 2) Excess-air coefficient \(\alpha\) | 1.497 | 1.503 | 0.40% |
| 3) Quantity \(A\) | 835 | 842 | 0.83% |
| 4) Relative incompleteness of combustion in CO, \(x_1\) | 0.0496 | 0.0500 | 0.80% |
| 5) Relative incompleteness of combustion in soot, \(x_2\) | 0.296 | 0.300 | 1.33% |
The discrepancies obtained, even for these limiting cases, are evidently quite admissible.
Let us note further that in the expressions
\[ A=0.429\,n+0.375\,o+4.76\,c\,\alpha+0.5\,x_1c-3h \]
\[ \text{and}\quad A-0.5\,x_1c=0.429\,n+0.375\,o+4.76\,c\,\alpha-3h \]
the quantity \(0.429\,n\), when \(n=0.15\) in the experiments of the CO series, amounts to only about \(0.009\%\) of the entire quantity \(A\), or \(A-0.5x_1c\), even for cases with the minimum values of these quantities. The error will evidently be of the same order if one even takes \(0.429\,n\simeq 0\).
Moreover, in the formula for determining \(\alpha\),
\[ \alpha= \frac{(100-0.5\,CO-N_2)\,0.429\,n+N_2(3h-0.375\,o)} {[4.76\,N_2-3.76\,(100-0.5\,CO)]\,c\sigma} \]
the first term of the numerator in the worst case for the experiments of the CO series (CO—min) amounts to only
\[ \frac{1{,}229}{2958}\cdot 100 = 0{,}04\% \]
of the entire numerator.
All that has been noted permits the conclusion that in all practically possible cases it is entirely permissible:
a) to take the sum \(o+n\) in the elementary composition of the fuel as \(o\), i.e., to put \(n=0\);
b) to simplify the formulas themselves as well, by discarding the 1st term of the numerator in the expression for \(\alpha\), and, in the expressions for \(A\) and \(A-0{,}5x_1c\), to combine the terms containing \(o\) and \(n\) by a common coefficient
\[ \frac{0{,}429+0{,}375}{2} \simeq 0{,}4, \]
without thereby risking any appreciable errors in the final results.
The above analysis of possible assumptions thus establishes that the principal relations obtained above may be simplified:
1) by neglecting the incomplete combustion of sulfur;
2) by neglecting the nitrogen in the fuel, or by combining the terms containing \(o\) and \(n\) with a common coefficient.
At the same time, simplification of the calculation formulas by neglecting the presence of CO in the exhaust gases is in no case permissible.
Calculation formulas and their application
Implementing the simplifications admitted on the basis of the analysis carried out, we bring the principal formulas for determining the excess-air coefficient and the characteristics of incomplete combustion to the form:
\[ \alpha = \frac{N_2(3h-0{,}375\,o)} {\left[4{,}76\cdot N_2-3{,}76(100-0{,}5CO)\right]c\sigma}; \tag{22} \]
\[ x_1= \frac{CO}{c}\, \frac{4{,}76c\alpha\sigma-\left[3h-0{,}4(o+n)\right]} {100-0{,}5CO}; \tag{23} \]
\[ A=4{,}76c\alpha\sigma-\left[3h-0{,}4(o+n)\right]+0{,}5x_1c, \tag{24} \]
where, as before:
\[ x=1+0{,}375\,\frac{s}{c}-\frac{A}{100}\,\frac{RO_2}{c}, \tag{19} \]
\[ x_2=x-x_1, \tag{13} \]
and
\[ \sigma=1+\frac{3}{c}\left(h+\frac{s-o}{8}\right). \tag{2} \]
These formulas may also be regarded as calculation formulas; however, their external form is rather complicated.
It would have been possible, by introducing still some additional assumptions, to exclude from the expression for \(\alpha\) (22) the constituent parts of the fuel, expressing everything only through the fuel characteristic \(\sigma\) or \(b=1-\sigma\). We consider, however, that this is inadvisable and believe that the convenience of practical
the use of the calculation formulas will be ensured to a greater extent if, in addition to \(\sigma\), some further coefficients are introduced:
\[ a=\frac{3h-0.375\,o}{c\sigma}; \tag{25} \]
\[ b=4.76c; \tag{26} \]
\[ d=3h-0.4(o+n) \tag{27} \]
and
\[ e=1+0.375\,\frac{s}{c}, \tag{28} \]
which depend only on the composition of the fuel and, consequently, can be calculated in advance for an entire series of experiments carried out with fuel of one and the same composition.
The calculation formulas will now take the form:
\[ \alpha=\frac{a\cdot N_2}{4.76N_2-3.76(100-0.5CO)}=f(N_2,CO); \tag{29} \]
\[ x_1=\frac{CO}{c}\cdot\frac{b\alpha-d}{100-0.5CO}=\varphi(\alpha,CO); \tag{30} \]
\[ A=b\alpha-d+0.5x_1c=\psi(\alpha,x_1); \tag{31} \]
\[ x=e-\frac{A}{100}-\frac{RO_2}{c}=\Phi(A,RO_2), \tag{32} \]
and calculations by these formulas, with the numerical values of the coefficients \(a\), \(b\), \(d\), and \(e\) established in advance, no longer present substantial difficulties.
From the exhaust-gas analysis data, the volumetric content in them of \(RO_2\), \(O_2\), and \(CO\) must be known (\(N_2\) is calculated by difference). The first two determinations are carried out with the aid of the ordinary Orsat apparatus, while for determining the volumetric content of \(CO\) some more sensitive method must be applied, since here one has to deal with tenths and hundredths of a percent.
In the mass processing of the results of a whole series of experiments carried out on the given fuel, it is advisable to nomograph the relations established above. Such a nomogram is given in Fig. 1. It makes it possible, from known values of \(N_2\), \(CO\), and \(RO_2\), to determine by successive readings the quantities of interest to us, \(\alpha\), \(x_1\), \(A\), and \(x\), after which the incomplete combustion into soot \(x_2\) is calculated from the difference \(x-x_1\), while the quantity \(A\) can be used in determining the volume of dry gases, since the number of their moles per 1 kg of fuel consumed, according to what was indicated above, will be \(M_{\mathrm{dry}}=\frac{A}{12}\ \frac{\text{moles}}{\mathrm{kg}}\), if the values of \(c\), \(h\), \(o\), and \(n\) are substituted in the calculation as fractions of unity, or \(M_{\mathrm{dry}}=\frac{1}{12}\cdot\frac{A}{100}\ \frac{\text{moles}}{\mathrm{kg}}\), if these quantities, as is usually accepted, are expressed in percent.
The construction of the nomogram is carried out according to expressions (29), (30), and (32), and its use becomes clear upon considering the dotted straight lines drawn on it, corresponding to two cases, of which in the first the \(CO\) content was \(0.45\%\), while in the second carbon monoxide was absent.
Nomogram
for determining incomplete combustion by exhaust-gas analysis
Figure 1
Experimental Verification of the Established Relations
In order to verify the results of applying the relations established above under practical conditions of testing oil engines, and also to establish possible values of the volumetric content of the ordinarily undetermined constituents of combustion products \((\mathrm{CO}, \mathrm{SO}_2)\) used in the examples considered above, the author carried out a series of experiments on a small (15 hp) Diesel compressor engine in the internal-combustion-engine laboratory of the Tomsk Polytechnic Institute.
The test series (in a number of the author’s other experiments it is designated CO) consisted of a series of experiments at the same (about 75%) engine load, with variation of the atomizing-air pressure, which usually changes the combustion conditions (and the degree of incomplete combustion) most radically. Of these experiments, only four were recognized as successful.
In addition, two experiments were carried out (min and max), corresponding to conditions providing the greatest (large excess-air coefficient) and the smallest (small) possibility of carbon monoxide formation in the combustion products.
All experiments were deliberately carried out with the engine fuel-injection system not sufficiently well adjusted.
The fuel in all experiments was one and the same motor fuel, of composition by weight:
\[ \begin{aligned} c &= 87.00\%, & n &= 0.15\%,\\ h &= 12.23\%, & o &= 0.37\%,\\ s &= 0.25\%, & & \overline{100.00\%,} \end{aligned} \]
the analysis of which was carried out with particular care.
Special attention was also paid to the analysis of the exhaust gases. The content of carbon dioxide \((\mathrm{CO}_2)\) and oxygen \((\mathrm{O}_2)\) in them was determined by the usual Orsat apparatus, but with special precautions being observed, with careful monitoring of the absorptive capacity of the reagents and with a considerable number of mutually checking analyses for each experiment.
In order to make it possible to take into account very small quantities of \(\mathrm{CO}\) and \(\mathrm{SO}_2\) in the exhaust gases and to verify (at least qualitatively) the probability of the presence of heavy hydrocarbons in them, the apparatus shown in Fig. 2 was used. The essence of the method here consisted in drawing, by aspirators, a definite portion of gases from the exhaust pipe through the entire system of instruments according to Fig. 2; here \(\mathrm{SO}_2\) was trapped in filter 1 by cotton wool moistened with hydrogen peroxide, and, after all the carbon dioxide had been absorbed in a series of Kali apparatuses (4—5), in a U-shaped tube with mercuric oxide, which served as a good catalyst for this purpose, the carbon monoxide remaining in the gases was further oxidized to \(\mathrm{CO}_2\) (at the expense of the free oxygen in the gases themselves), from the results of absorption of which \((\mathrm{CO}_2)\) in the subsequent Drechsel bottles with baryta water (11—13) the amount of carbon monoxide present in the gases was established.
The results of the gas analysis for the experiments under consideration are presented in Table III (lines 20—25), and in Fig. 3 these data are presented graphically as a function of the excess-air coefficient \(\alpha\). The position of the points in the immediate vicinity of the curves \(\mathrm{RO}_2\) and \(\mathrm{O}_2\), which are almost straight lines, indicates the satisfactory accuracy of these determinations. The CO content increases rather intensively as the excess air decreases, which is quite obvious. In one of the experiments (CO max), however, the point rose considerably higher, which may be expla-
RESULTS OF SERIES TESTS
Table III
| No. | Parameter | Symbol | Unit | 1: CO-40, 13.VI.38 | 2: CO-45, 13.VI.38 | 3: CO-50, 10.VI.38 | 4: CO-58, 10.VI.38 | 5: CO-min., 13.VI.38 | 6: CO-max., 13.VI.38 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | Test number | — | — | 24 | 70 | 40 | 40 | 20 | 40 |
| 2 | Date conducted | — | — | 13.VI.38 | 13.VI.38 | 10.VI.38 | 10.VI.38 | 13.VI.38 | 13.VI.38 |
| 3 | Duration of test | — | min | 40 | 70 | 40 | 40 | 20 | 40 |
| 4 | Barometric pressure | $H$ | mm Hg | 751 | 751 | 732 | 732 | 751 | 751 |
| 5 | Surrounding-air temperature | $t$ | °C | 18.6 | 18.6 | 18.5 | 18.5 | 18.0 | 18.0 |
| 6 | Fuel grade | — | — | solar oil | solar oil | motor oil | motor oil | solar oil | solar oil |
| 7 | Volumetric weight of fuel | $Q_t$ | kg/l | 0.8985 | 0.8985 | 0.900 | 0.900 | [[unclear]] | [[unclear]] |
| 8 | Upper calorific value | $U$ | cal/kg | 11070 | 11070 | [[unclear]] | [[unclear]] | [[unclear]] | [[unclear]] |
| 9 | Mean load | $B$ | kg | 3.070 | 3.520 | 3.220 | 3.080 | 2.295 | 3.325 |
| 10 | Mean speed | $n$ | rpm | 342 | 332 | 284 | [[unclear]] | 327 | 235 |
| 11 | Mean power | $N_e$ | hp | 229.8 | 233.9 | 233.0 | 233.0 | 226.8 | 234.3 |
| 12 | Effective power | $N_e$ | hp | 11.88 | 11.60 | 11.33 | 11.40 | 7.37 | 14.34 |
| 13 | Mean indicator pressure | $p_i$ | kg/cm² | 5.18 | 5.49 | 5.54 | 5.78 | 4.27 | 6.23 |
| 14 | Indicator power | $N_i$ | hp | 16.35 | 17.57 | 17.74 | 18.50 | 13.30 | 19.77 |
| 15 | Mechanical efficiency | $\eta_m$ | % | 40.0 | 46.0 | 50.0 | 58.2 | 64.8 | 64.9 |
| 16 | Mean pressure of mechanical losses | $p_m$ | kg/cm² | 15.0 | 21.1 | 22.5 | 23.9 | 20.6 | 22.6 |
| 17 | Mean pressure of pump losses | $p_n$ | kg/cm² | 2.7 | 0.0 | 63.9 | 62.0 | 55.4 | 72.0 |
| 18 | Indicator efficiency | $\eta_i$ | % | 20.0 | 32.0 | 35.4 | 38.6 | 37.2 | 38.0 |
| 19 | Fuel consumption | $C$ | g/hp·h | 302.5 | 310.3 | 294.8 | 278.8 | 199.8 | 222.3 |
| 20 | Excess-air coefficient | $\alpha$ | — | 8.54 | 7.849 | 7.813 | 7.337 | 4.034 | 7.591 |
| 21 | Exhaust-gas composition: $CO_2$ | $CO_2$ | % | 0.006 | 0.005 | 0.007 | 0.021 | 0.021 | 0.009 |
| 22 | Exhaust-gas composition: $SO_2$ | $SO_2$ | % | 8.54 | 7.85 | 7.82 | 7.35 | 4.65 | 7.60 |
| 23 | Exhaust-gas composition: $O_2$ | $O_2$ | % | 0.39 | 0.56 | 0.19 | 0.16 | 0.04 | 0.15 |
| 24 | Exhaust-gas composition: $CO$ | $CO$ | % | 0.000 | 0.00 | 0.00 | 0.45 | 14.45 | 10.08 |
| 25 | Exhaust-gas composition: $N_2$ | $N_2$ | % | 82.71 | 82.14 | 81.98 | 81.63 | 80.90 | 81.87 |
| 26 | Exhaust-gas composition: total hydrogen | $H_2$ | % | 1.310 | 1.590 | 1.663 | 1.854 | 2.635 | 1.665 |
| 27 | Exhaust-gas composition: methane | $CH_4$ | % | 1.244 | 1.551 | 1.612 | 1.805 | 2.648 | 1.542 |
| 28 | Exhaust-gas composition: unsaturated hydrocarbons | $C_mH_n$ | % | 1.240 | 1.354 | 1.605 | 1.812 | 2.775 | 1.580 |
| 29 | Including: heavy gases | $C_mH_n$ | % | 0.613 | 0.750 | 0.783 | 0.880 | 1.283 | 0.788 |
| 30 | Including: light gases | $C_mH_n$ | % | 0.011 | 0.013 | 0.073 | 0.075 | 0.081 | 0.073 |
| 31 | Including: benzol hydrocarbons | $C_mH_n$ | % | 0.084 | 0.023 | 0.080 | 0.095 | 1.364 | 0.861 |
| 32 | Volumetric quantity of air according to gas analysis | $V_a$ | m³/kg fuel | 6.544; 0.000005 | 6.544; 0.0000491 | 6.544; 0.0004007 | 6.544; 0.0004867 | 6.544; 0.0004535 | 6.544; 0.0005481 |
| 33 | Volumetric quantity of exhaust gases, dry | $V_g$ | m³/kg fuel | 6.544 + 0.000251 | 6.544 + 0.000251 | 6.544 + 0.000251 | 6.544 + 0.000251 | 6.544 + 0.000251 | 6.544 + 0.000251 |
| 34 | Volumetric quantity of exhaust gases, wet | $V'_g$ | m³/kg fuel | 4.176 + 0.0003371 | 5.336 + 0.0003861 | 5.628 + 0.000404 | 6.250 + 0.0004451 | 6.278 + 0.0005781 | 6.341 + 0.0004631 |
| 35 | Air excess coefficient, according to gas analysis | $\alpha$ | — | 3.30 | 1.65 | 2.00 | 1.82 | 1.00 | 4.89 |
| 36 | Weight of air mixture | $x_1$ | — | 24.50 | 5.20 | 3.19 | 4.2 | 15.10 | 2.25 |
| 37 | Weight of gases | $x_2$ | — | 22.80 | 18.85 | 15.25 | 10.86 | 19.10 | 17.54 |
| 38 | Moisture | $y$ | — | 52.9 | 52.1 | 29.6 | −35.7 | −756.1 | 9.3 |
| 39 | According to gas analysis | $x_m$ | — | 37.7 | −29.9 | 18.0 | 13.3 | 48.6 | 23.9 |
| 40 | According to calorimeter data | $x_k$ | — | 31.7 | 20.7 | 18.4 | 13.1 | 19.1 | 23.8 |
| 41 | Noncombustible component $B$ | $B$ | kg/h | 1.247 | 0.005 | −0.425 | 0.278 | 0.438 | 0.404 |
| 42 | Mechanical efficiency | $\eta_m$ | — | 7.60 | 4.95 | 4.03 | 4.50 | 0.40 | 3.73 |
| 43 | Carbon monoxide | $CO$ | cm³ | 164 | 82 | 102 | 90 | — | 42 |
| 44 | Hydrogen | $H_2$ | cm³ | 173 | 218 | 234 | 64 | 153 | 89 |
| 45 | Methane | $CH_4$ | cm³ | 189 | 190 | 200 | 73 | 153 | 141 |
| 46 | Olefins | $C_mH_n$ | cm³ | 225 | 298 | 245 | 94 | 132 | 193 |
| 47 | Additional heat from combustion of combustible components | $\Delta Q_m$ | % | +45.5 | +44.2 | +30.3 | +30.7 | +2.52 | +68.2 |
| 48 | Incomplete-combustion loss | $\Delta Q_n$ | % | +18.2 | +13.9 | +23.0 | +28.7 | −2.6 | +49.6 |
| 49 | Heat of decomposition | $\Delta q$ | % | +18.2 | +22.9 | +25.8 | +26.8 | −0.07 | −49.1 |
| 50 | Heat supplied with fuel | $Q$ | kcal/h | 50010 | 34720 | 31760 | 30380 | 22640 | 32880 |
| 51 | Heat lost in water | $Q_e$ | % | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
| 52 | Heat equivalent to work | $Q_l$ | kcal/h | 7520 | 7330 | 7170 | 7250 | 4060 | 9050 |
| 53 | Heat carried away by exhaust gases | $Q_t$ | kcal/h | 211 | 211 | 206 | 239 | −0.6 | 276 |
| 54 | Heat not accounted for by balance | $Q_0$ | kcal/h | 9020 | 9570 | 8330 | 2250 | 370 | 3760 |
| 55 | Balance total | $Q_{\text{tot}}$ | % | 193 | 13.5 | 10.5 | 7.4 | 13.7 | 11.5 |
| 56 | Indicator heat | $Q_i$ | kcal/h | 6800 | 5880 | 5250 | 5750 | 3970 | 5450 |
| 57 | Difference: not accounted for | $\Delta Q$ | kcal/h | 43.9 | 45.9 | 46.5 | 18.8 | 17.3 | 16.6 |
| 58 | Heat equivalent to friction work | $Q_{\text{fr}}$ | kcal/h | 12520 | 12520 | 8270 | 8990 | 6280 | 11310 |
| 59 | Heat equivalent to indicated work | $Q_i$ | kcal/h | 39.6 | 36.1 | 26.0 | 29.5 | 27.8 | 34.5 |
| 60 | Heat loss to jacket water | $Q_w$ | kcal/h | 3470 | 2600 | 6740 | 6710 | 6740 | 9280 |
| 61 | Balance | $\%$ | — | 12.7 | 52.0 | 24.4 | 22.3 | 20.6 | 29.8 |
… sharply different (in the direction of worsening the combustion conditions) from the conditions of this experiment, in the presence of a significantly greater load. In the obtained values of \(SO_2\), no regularity was established. Moreover,
Apparatus used for determining CO and \(SO_2\) in exhaust gases.
Fig. 2
in some experiments (as already indicated above) \(SO_2\) contents greater than possible were obtained.
In general it must be admitted that it is not possible to obtain a reliable determination of \(SO_2\), owing to its possible dissolution in the water condensing in the sampling tubes; the method used for determining CO, however, proved sufficiently sensitive and reliable.
The results of processing the materials of the experiments under consideration are summarized in Table III. In addition to establishing the combustion characteristics by the author’s formulas (29–32), the same quantities were also calculated on the basis of the theory of incomplete combustion due to soot formation, using the formulas of Prof. Masing and Dr. Akkerman.
A comparison of the results of these calculations clearly confirms the propositions established above, namely that the theory of incomplete combustion due only to soot formation gives somewhat understated values of the excess-air coefficient and a greatly exaggerated estimate of the incompleteness of combustion, the error in which, owing to neglect of the presence of CO in the exhaust gases, in individual cases reaches almost 50%.
Composition of exhaust gases from the experiments of the “CO” series as a function of \(\alpha\)
Fig. 3
For comparison, the most interesting data are the results of processing the material of experiments conducted at the same load, but with
with variable injector pressure, are presented as curves in Fig. 4. Here the intensive increase of the total relative incompleteness of combustion \(x\) and of the relative incompleteness of combustion into soot \(x_2\), while the values of the relative incompleteness of combustion into CO—\(x_1\)—remain almost constant, is very characteristic. The curves corresponding to the values of the relative incompleteness of combustion (only into soot) according to the formulas of Mazing and Ackermann almost coincide, but pass considerably above the curve \(x\).
The same graph (Fig. 4) also presents, for comparison, the curve of variation of the conditional indicator of combustion incompleteness \(z\) from soot deposits, determined in accordance with the method developed by the author [4].
Fig. 5 graphically presents the dependence of heat loss due to incomplete combustion (total per kilogram of fuel—\(q\), due to formation
Main results of the experiments of series “CO”
Fig. 4
Heat losses from incomplete combustion according to the experiments of series “CO”
Fig. 5
of soot—\(q_c\), and due to formation of CO—\(q_{\mathrm{co}}\)), as well as the hourly expenditure of heat from incomplete combustion \(Q\) cal/hour, on the injector pressure \(p_\phi\). For comparison, the corresponding curves are plotted that were obtained as a result of calculating heat loss according to the formulas of Mazing and Ackermann. The character of the dependencies here remains almost the same as for the relative characteristics of combustion incompleteness (Fig. 3).
Consideration of the experimental materials obtained, their processing, and analysis of the results make it possible to state that the applicability of the relationships established above to the determination of combustion incompleteness and the heat losses caused by it (on the basis of analysis of the engine exhaust gases and comparison of it with data on the elemental composition of the fuel), as well as the inadmissibility, demonstrated above, of disregarding the presence of carbon monoxide in the engine exhaust gases, are confirmed by the practice of operating a Diesel engine on heavy liquid fuel.
Conclusion
On the basis of the theoretical investigations carried out in the present work, confirmed by numerical examples based on practical data, and, finally, from the results of testing the application of the established
...conclusions and methods to the particular case covering a sufficiently wide range of Diesel-engine operation, the following principal conclusions may be drawn.
-
Determination of all the principal kinds of incomplete combustion by comparing the data of exhaust-gas analysis with the elemental composition of the fuel is entirely possible; for this purpose, however, it is necessary, in addition to the usual determinations of \(CO_2[RO_2]\) and \(O_2\) in the engine exhaust gases, also to establish quantitatively their content of \(CO\) and \(SO_2\).
-
Allowance for possible incomplete combustion of sulfur is not necessary, since the error obtained from assuming its complete combustion (in estimating the total loss from incomplete combustion of ordinary liquid fuels) is scarcely perceptible and does not exceed the limits of the usual accuracy of observations and calculations. Consequently, the need to determine \(SO_2\) in the exhaust gases disappears.
-
Neglecting the presence of carbon monoxide in the engine exhaust gases, when one wishes to determine incomplete combustion with any quantitative accuracy, is inadmissible, since the results obtained from the relations established on the basis of this assumption in most cases give a very noticeable reduction in the estimate of incomplete combustion and of the heat loss corresponding to it.
-
The quantitative determination of carbon monoxide in the engine exhaust gases, required for a correct estimate of incomplete combustion in the small amounts that occur here, can be carried out under practical conditions by using the method of further oxidation of \(CO\) to \(CO_2\) in the presence of a catalyst, such as mercuric oxide at \(100^\circ C\), with accuracy sufficient for this purpose.
-
Separate determination of the oxygen and nitrogen content in liquid fuel is not necessary for the present purposes, since the error obtained by replacing the maximum possible quantities of nitrogen by oxygen is scarcely perceptible. In this connection, the formulas established for determining the principal losses from incomplete combustion are appreciably simplified, and they can readily be nomographed.
These conclusions also resolve the tasks posed by the author.
LITERATURE
-
E. K. Mazing. Application of exhaust-gas analysis to the investigation of liquid-fuel engines with determination of incomplete combustion from soot. Bulletin of NAGI, 1923.
-
Dr. Ing. Ackermann. Das Verbrennungsdreieck bei Russbildung. V.D.I. Forschungsheft—366. Mai–Juni 1934. Abstract in “Dieselestroenie,” No. 3, 1936.
-
Dr.-Ing. B. Wenzel. Combustion and burning processes in non-compressor Diesels. Forschungsheft 336, 1934. Translation in vol. III of the monograph “Internal-Combustion Engines.”
-
Assoc. Prof. Yu. N. Sokolov. Determination of incomplete combustion in oil engines from soot deposits. “Dieselestroenie,” Nos. 7 and 8, 1939.
Noted Misprints
| Page | Line | Printed | Should be |
|---|---|---|---|
| 89 | Fig. 3 | (Figure inverted) | |
| 92 | 7 from bottom | $o_2$ | $-i_{02}$ |
| 95 | 19 from bottom | $Z$ | $Z_T$ |
| 97 | In equation (27), $x$ is the exponent | ||
| 98 | 19 from bottom | $Z_m \Delta$ | $Z_m \gamma$ |
| 101 | 15 from bottom | surrounding | circumferences |
| 178 | 17 from bottom | $$s=\frac{n}{n}$$ | $$s=\frac{n}{n_0}$$ |
| 193 | 4 from top | $$I_2^{\,2}=\frac{E}{1+Z^2}$$ | $$I_2^{\,2}=\frac{\varepsilon}{1+Z^2}$$ |
| 203 | 12 from top | $$I=I_M\left(1-e^{-\frac{r_M}{L_M}}\right)=\cdots$$ | $$I=I_M\left(1-e^{-\frac{r_M}{L_M}t}\right)=\cdots$$ |
| 203 | 17 from bottom | concluding | concluding |
| 214 | 8 from bottom | (28) | (26) |
| 221 | 4 from top | $$\ldots \frac{i_0^{\,2}-i''_a}{i_{01}-i''_a}$$ | $$\ldots \frac{i_{02}-i''_a}{i_{01}-i''_a}$$ |
| 318 | Caption to Fig. 5 | Heat losses from incomplete combustion. | Heat losses due to incomplete combustion. |
| 318 | 14 from bottom | (fig. 3) | (fig. 4) |
| 323 | 1 from top | ature | perature |
| 323 | 1 from top | $r=58^\circ$ | $r=587$ |
| 325 | In Fig. 6 | $q'_{\mathrm{water}}$ and $q''_{\mathrm{water}}$ | $q'_{\mathrm{water}}$ and $q''_{\mathrm{water}}$ |
| 326 | 33 from top | $/2\ 3+25=293\ \mathrm{K},$ | $/273+25=293\ \mathrm{K}/,$ |