Effect of Load on the Thermal Efficiency of a Carburetor Engine
Abstract Generated abstract
This paper examines how load variation by throttling affects the thermal efficiency of an ideal carburetor engine cycle with heat supplied at constant volume. Using thermodynamic cycle calculations by the Grinevetskii, Mazing heat calculation method, the study compares cases with constant heat capacity and temperature dependent heat capacity for several fresh charge calorific values at a compression ratio of 5.26. The calculations indicate that with constant heat capacity the thermal efficiency is independent of load, whereas with variable heat capacity it increases as mean cycle pressure decreases, because lower expansion temperatures reduce heat capacity and raise the expansion adiabatic exponent. At full load the variable heat capacity efficiency is about 12 percent below the constant heat capacity value, but it approaches that value as load is reduced.
Full Text
Effect of Load on the Thermal Efficiency of a Carburetor Engine
A. S. Tsekhanov
(Submitted by Prof. V. K. Nechaev, Doctor of Technical Sciences)
To determine the principal regularities in the variation of the economy of a carburetor engine under throttling, the study of thermodynamic cycles is of considerable importance, since it makes it possible to establish the magnitude and the regularity of variation of the thermal efficiency as a function of load, which is important for comparison with the indicated efficiency of the engine.
As is known, at constant heat capacity of the working medium in the ideal cycle [2], the thermal efficiency of the cycle does not depend on load. The values of $\eta_t$ and of other cycle parameters at $C_v = \text{const.}$ for the example under consideration are given in Table 2.
However, in a cycle with variable heat capacity, the thermal efficiency decreases as the load increases.
Below are given the results of specific calculations, the purpose of which is to establish the degree of influence of quantitative control on the thermal efficiency with variable heat capacity of the working medium.
The throttling process, as a method of quantitative regulation of engine power, in the ideal cycle is manifested in a decrease in the pressure at the start of compression. Therefore, to study the effect of load on the thermal efficiency of the cycle of a carburetor engine, we shall use a thermodynamic ideal cycle with heat supplied at $v = \text{const.}$ (Fig. 1).
In view of the frontal character of combustion and the influence of residual gases, the limits of inflammability of the mixture in carburetor engines with respect to composition, i.e., with respect to quality, are very restricted. This necessitates the introduction of quantitative regulation of the mixture when the load on the engine is changed.
In a carburetor engine the working medium consists of two parts: fresh mixture and residual gases, the former being the carrier of heat. When the quantity of fresh mixture is regulated, the quantity of heat introduced by it into the cylinder per unit of working medium also changes. Accordingly, for the ideal cycle under investigation we shall divide the working medium into two parts (Fig. 1):
\[ M_a = M_r + M_o, \]
where $M_a$ is the number of moles of the working medium filling, in the given closed cycle, the entire cylinder volume $v_a$;
\(M_r\) — the number of moles of working medium filling the clearance volume \(v_c\) (residual gases),
\(M_o\) — the variable number of moles of fresh charge filling the working volume \(v_h\).
Quantitative regulation of the ideal cycle is carried out as follows. The cycles are considered closed for different amounts of working medium, which in the calculations is taken into account by varying the pressure at the start of compression \(p_a\). Heat is supplied with the fresh charge \(M_o\); a change in its amount causes a change also in the heat \(Q_1\) supplied to the entire working medium \(M_a\). It is convenient to evaluate the change in the amount of fresh charge by the filling coefficient \(\eta_v\), equal to
Fig. 1. Ideal cycle of a carburetor engine [4].
\[ \eta_v=\frac{G}{G_o}, \]
where \(G\) is the weight of the fresh charge \(M_o\) filling the working volume in the given closed cycle;
\(G_o\) is the weight of the charge \(M_o\) that can fill the same volume at the pressure and temperature of the surrounding medium.
The heat imparted to the working medium \(M_a\) in the given closed cycle is determined by the expression
\[ Q_1=M_o Q_o, \]
where \(Q_o\) is the calorific value of the fresh charge, i.e., the amount of heat, in kcal, supplied per 1 mole of charge \(M_o\).
In the calculations, the quantity \(Q_o\) is taken in the amounts that can theoretically be released during the combustion of 1 mole of the gasoline–air
mixture of the corresponding composition, less the theoretical incompleteness of combustion (Table 1).
Table 1
Calorific value of the charge \(M_o\)
| \(Q_o\) | kcal/mol | \(\bar a\) |
|---|---|---|
| \(Q_o^{I}\) | 17840 | 0.8 |
| \(Q_o^{II}\) | 19940 | 1.0 |
| \(Q_o^{III}\) | 16650 | 1.2 |
As the working medium we take air, whose initial parameters are \(p_0 = 1\ \text{kg}/\text{cm}^2\) and \(T_0 = 288^\circ\) abs. The pressure and temperature of the residual part of the working medium \(M_r\) (point \(r\)) are taken equal to \(p_0\) and \(T_o\). Hence the temperature at the beginning of compression of the charge \(T_a\) is equal to \(T_o\). The compression ratio was taken as \(\varepsilon = 5.26\), equal to the compression ratio of the engine on which the experimental investigations were subsequently carried out. As the load indicator of the ideal cycle we shall regard the mean cycle pressure \(p_t\) [2, 3]. The compression and expansion processes are taken to be adiabatic. The parameters of the cycles under consideration were determined by the Grinevetskii–Mazing method of heat calculation [1], both with constant and with variable heat capacities. The dependence of heat capacity on temperature was taken as linear [4]. The calculation results are given in Tables 2 and 3.
Taking into account the dependence of the heat capacity of the working medium on temperature, let us determine the influence of this factor on the thermal efficiency of the cycle as a function of \(p_t\).
Calculations of the cycle showed (Table 3, Fig. 2) that, under quantity control, as \(p_t\) decreases the thermal efficiency increases. The increase in the thermal efficiency \(\eta_t'\) with decreasing \(p_t\) is caused by a decrease in the heat capacity of the working medium during the expansion process, or, correspondingly, by an increase in the exponent of the expansion adiabat \(\kappa_2\) (Fig. 3).
During the compression process the heat capacity of the charge, and consequently the exponent of the compression adiabat \(\kappa_1\), does not change, and therefore it does not affect the change in the economy of the cycle. This is explained by the fact that heat removal from the working medium occurs, according to condition [4], down to the ambient temperature \(T_o\). Therefore the temperature at the beginning of compression \(T_a\), irrespective of the amount of the working medium, is equal to \(T_o\), and hence the temperature at the end of compression likewise does not change. With decreasing \(p_t\) under quantity control, despite the constant calorific value of the fresh charge \(M_o\), the amount of heat supplied to the whole working medium \(M_a\) decreases because of the increase in the relative amount of the residual part of the working medium \(M_r\). In view of this, the temperature at the end of heat addition \(T_z\) (Fig. 3), and together with it the degree of pressure rise \(\lambda\), decrease, and the heat capacity of the working medium decreases. This decrease in heat capacity causes an increase in the exponent \(\kappa_2\), whence the degree of temperature change during the expansion process \(\delta^{\kappa_2-1}\), and leads to an increase in the thermal efficiency by 3.5–4.5%. With a change in the calorific value of the fresh charge \(Q_o\), the temperature also changes.
Table 2
Calculated data of the ideal cycle under quantitative control,
\(c_v = \mathrm{const.},\ \varepsilon = 5.26\).
| \(\eta_v\) | \(T_c\) | \(T_z\) | \(T_v\) | \(r\) | \(\lambda\) | \(p_a\) | \(p_c\) | \(p_z\) | \(p_v\) | \(p_t\) | \(\eta_t\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) | \(Q_o^I = 17840\ \mathrm{kcal/mol}\ (a = 0.8)\) |
| 1,00 | 560 | 3480 | 1788 | 0,235 | 6,22 | 1,000 | 10,24 | 63,60 | 6,22 | 15,17 | 0,486 |
| 0,80 | 560 | 3346 | 1720 | 0,294 | 5,98 | 0,838 | 8,58 | 51,30 | 5,01 | 12,13 | 0,486 |
| 0,60 | 560 | 3150 | 1618 | 0,391 | 5,63 | 0,676 | 6,92 | 38,94 | 3,80 | 9,11 | 0,486 |
| 0,40 | 560 | 2826 | 1452 | 0,587 | 5,05 | 0,514 | 5,26 | 26,55 | 2,59 | 6,06 | 0,486 |
| 0,20 | 560 | 2212 | 1137 | 1,174 | 3,95 | 0,352 | 3,60 | 14,23 | 1,39 | 3,03 | 0,486 |
| \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) | \(Q_o^{II} = 19940\ \mathrm{kcal/mol}\ (a = 1.0)\) |
| 1,00 | 560 | 3820 | 1962 | 0,235 | 6,82 | 1,000 | 10,24 | 69,85 | 6,82 | 16,96 | 0,486 |
| 0,80 | 560 | 3670 | 1885 | 0,295 | 6,55 | 0,838 | 8,58 | 56,20 | 5,49 | 13,57 | 0,486 |
| 0,60 | 560 | 3455 | 1775 | 0,391 | 6,17 | 0,676 | 6,92 | 42,70 | 4,17 | 10,17 | 0,486 |
| 0,40 | 560 | 3096 | 1590 | 0,587 | 5,58 | 0,514 | 5,26 | 29,10 | 2,84 | 6,78 | 0,486 |
| 0,20 | 560 | 2411 | 1238 | 1,174 | 4,31 | 0,352 | 3,52 | 15,52 | 1,52 | 3,39 | 0,486 |
| \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) | \(Q_o^{III} = 16650\ \mathrm{kcal/mol}\ (a = 1.2)\) |
| 1,00 | 560 | 3285 | 1688 | 0,235 | 5,7 | 1,000 | 10,24 | 60,00 | 5,87 | 14,16 | 0,486 |
| 0,80 | 560 | 3160 | 1623 | 0,294 | 5,64 | 0,838 | 8,58 | 48,40 | 4,73 | 11,32 | 0,486 |
| 0,60 | 560 | 2978 | 1528 | 0,391 | 5,32 | 0,676 | 6,92 | 36,80 | 3,59 | 8,49 | 0,486 |
| 0,40 | 560 | 2681 | 1377 | 0,587 | 4,79 | 0,514 | 5,26 | 25,20 | 2,46 | 5,66 | 0,486 |
| 0,20 | 560 | 2108 | 1083 | 1,174 | 3,72 | 0,352 | 3,52 | 13,37 | 1,31 | 2,83 | 0,486 |
the end of heat addition, the heat capacity of the working medium and the exponent \(k_2\) (Table 3), which affects the value of \(\eta_t\). With an increase in the heating value of the fresh charge \((Q_0^{II} > Q_0^I)\), the thermal efficiency decreases, and the curve \(\eta_t'\) (Fig. 2) runs lower than for \(Q_0^I\).
Comparison of cycles with constant and variable heat capacities of the working medium showed the following (Fig. 4).
With a decrease in \(p_t\), owing to the reduction in temperatures, the heat capacity of the working medium decreases and the exponent \(k_2\) increases. Therefore, the thermodynamic losses decrease with decreasing \(p_t\) when the heat capacity is variable. The thermal efficiency \(\eta_t\), increasing like the exponent \(k_2\), approaches its maximum value for constant heat capacity of the working medium. In this case the thermal efficiency \(\eta_t'\) is 12–8.5% lower than the values of the thermal efficiency \(\eta_t\) for the same loads with constant heat capacity of the working medium.
The investigation carried out for the ideal cycle makes it possible to draw the following conclusions.
- With variable heat capacity of the working medium, for the adopted compression ratio \((\varepsilon = 5.26)\) and full-load operation \((\eta_v = 1)\), the therme-
Table 3
Calculated data for the ideal cycle under quantitative control,
\(C_v = f(T),\ \varepsilon = 5.26.\)
| \(\eta_v\) | \(T_c\) | \(T_z\) | \(T_v\) | \(\gamma\) | \(\lambda\) | \(\kappa_1\) | \(\kappa_2\) | \(P_a\) | \(P_c\) | \(p_z\) | \(p_v\) | \(p_t\) | \(\eta_t\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(Q_0^I = 17840\) kcal/mol \((\alpha = 0.8)\) | |||||||||||||
| 1,00 | 554 | 2960 | 1777 | 0,235 | 5,34 | 1,393 | 1,307 | 1,000 | 10,10 | 54,00 | 6,16 | 13,60 | 0,436 |
| 0,80 | 554 | 2863 | 1710 | 0,294 | 5,17 | 1,393 | 1,310 | 0,838 | 8,46 | 43,70 | 4,97 | 10,88 | 0,436 |
| 0,60 | 554 | 2725 | 1618 | 0,391 | 4,92 | 1,393 | 1,314 | 0,676 | 6,83 | 33,60 | 3,79 | 8,25 | 0,441 |
| 0,40 | 554 | 2480 | 1455 | 0,587 | 4,48 | 1,393 | 1,321 | 0,514 | 5,19 | 23,23 | 2,60 | 5,53 | 0,443 |
| 0,20 | 554 | 2000 | 1142 | 1,174 | 3,61 | 1,393 | 1,337 | 0,352 | 3,55 | 12,83 | 1,39 | 2,81 | 0,451 |
| \(Q_0^{II} = 19940\) kcal/mol \((\alpha = 1.0)\) | |||||||||||||
| 1,00 | 554 | 3191 | 1940 | 0,235 | 5,76 | 1,393 | 1,300 | 1,000 | 10,10 | 58,20 | 6,73 | 14,66 | 0,428 |
| 0,80 | 554 | 3095 | 1870 | 0,294 | 5,59 | 1,393 | 1,303 | 0,838 | 8,46 | 47,30 | 5,44 | 12,05 | 0,431 |
| 0,60 | 554 | 2930 | 1755 | 0,391 | 5,29 | 1,393 | 1,308 | 0,676 | 6,83 | 36,10 | 4,12 | 9,07 | 0,439 |
| 0,40 | 554 | 2670 | 158 | 0,587 | 4,82 | 1,393 | 1,315 | 0,514 | 5,19 | 25,00 | 2,81 | 6,12 | 0,439 |
| 0,20 | 554 | 2150 | 1238 | 1,174 | 3,88 | 1,393 | 1,332 | 0,352 | 3,55 | 13,80 | 1,51 | 3,11 | 0,446 |
| \(Q_0^{III} = 16650\) kcal/mol \((\alpha = 1.2)\) | |||||||||||||
| 1,00 | 554 | 2810 | 1625 | 0,235 | 5,07 | 1,393 | 1,311 | 1,000 | 10,10 | 51,20 | 5,80 | 12,74 | 0,437 |
| 0,80 | 554 | 2725 | 1617 | 0,294 | 4,92 | 1,393 | 1,314 | 0,838 | 8,46 | 41,60 | 4,69 | 10,20 | 0,437 |
| 0,60 | 554 | 2575 | 1517 | 0,391 | 4,65 | 1,393 | 1,318 | 0,676 | 6,83 | 31,75 | 3,55 | 7,67 | 0,438 |
| 0,40 | 554 | 2370 | 1382 | 0,587 | 4,28 | 1,393 | 1,325 | 0,514 | 5,19 | 22,20 | 2,46 | 5,19 | 0,445 |
| 0,20 | 554 | 1918 | 1080 | 1,174 | 3,46 | 1,393 | 1,340 | 0,352 | 3,55 | 12,30 | 1,33 | 2,65 | 0,455 |
...the efficiency is less than the corresponding values for \(C_v = \mathrm{const.}\) by 12%.
- With a decrease in the mean pressure of the cycle under quantitative control, owing to the dependence of heat capacity on temperature, the thermal efficiency increases, approaching in its limit the thermal efficiency for constant heat capacity of the working medium.
Fig. 2. Dependence of the thermal efficiency \(\eta_t\) on the mean cycle pressure \(p_t\) under quantitative control; \(C_v = f(T)\),
\(Q_0^I = 17840\) kcal/mol; \(Q_0^{II} = 19940\) kcal/mol.
Fig. 3. Dependence of the temperature at the end of heat addition \(T_z\) and of the adiabatic exponents of compression \(\kappa_1\) and expansion \(\kappa_2\) on the mean cycle pressure \(p_t\) under quantitative control; \(C_v=f(T)\); \(Q_0^{II}=19940\ \text{kcal/mole}\).
Fig. 4. Dependence of the thermal efficiency and of the adiabatic exponent of expansion of the ideal cycle on the mean cycle pressure under quantitative control; \(Q_0^{I}=17840\ \text{kcal/mole}\); \(Q_0^{II}=19940\ \text{kcal/mole}\); ----- \(C_v=\text{const.}\); — \(C_v=f(T)\).
3. The temperature at the end of heat addition and the degree of pressure rise in the ideal cycle, both with variable and with constant heat capacity of the working fluid, at constant calorific value of the fresh charge, decrease with decreasing load, owing to the decrease in the heat supplied per unit of working fluid because of the relative increase in the residual portion of the working fluid corresponding to the residual gases.
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