HYDRAULIC CHARACTERISTICS OF A CONTROL ELEMENT IN AN ENGINE COOLING SYSTEM

M. Kh. Dogin

To ensure optimal adjustment of an automatic-control system over a wide range of changes in engine load, the regulator control element must have a linear, or nearly linear, form of hydraulic characteristic.

As is known, the form of the curve of the hydraulic characteristic of a control element depends on the magnitude of the hydraulic resistance of the system. One and the same control element may have different characteristics depending on the magnitude of the resistance of the entire system. A considerable deviation of the characteristic from a linear form is observed at large system resistances. Therefore, it is necessary to consider the hydraulic characteristic of the control element in conjunction with the installation being automated, i.e., taking into account the hydraulic resistance of the entire system.

This article presents experimental data and a method for determining the hydraulic characteristics of a regulator valve in a system for automatic regulation of the cooling of internal-combustion engines.

In automated cooling systems for engines, a direct-acting temperature regulator, RTPD, manufactured by the “Tizpribor” plant [2], is used. The control element of the regulator is made in the form of a double-seat balanced valve. The dependence of the water flow rate on the amount of valve opening and its design are shown in Fig. 1.

Fig. 1

To determine the hydraulic characteristic of this control element in an engine cooling system, it is necessary to establish the change in the form of the characteristic as a function of the magnitude of the system resistance coefficient. The total head loss [1] in the engine system may be expressed as:

\[ \Delta H=\left(\xi_p+\xi_c\right)\frac{\gamma W^2}{2g}, \tag{1} \]

where

\(\xi_p\) — coefficient of resistance of the regulating element, referred to the cross-section of the pipeline before the valve;

\(\xi_c\) — coefficient of resistance of the system without the regulating element, referred to the same cross-section;

\(\Delta H\) — head loss in the entire system;

\(\gamma\) — specific weight of the liquid;

\(W\) — mean velocity of the water flow, referred to the cross-section of the pipeline before the valve;

\(g\) — acceleration due to gravity.

On the basis of expression (1), the weight flow rate of liquid through the regulating element is equal to:

\[ Q = F \sqrt{\frac{\Delta H \cdot 2g \cdot \gamma}{\xi_p + \xi_c}}, \tag{2} \]

and the flow coefficient is expressed by the formula:

\[ \mu = \frac{Q}{Q_{max}} = \sqrt{\frac{\xi_{pm} + \xi_{cm}}{\xi_p + \xi_c} \cdot \frac{\Delta H}{\Delta H_m}}, \tag{3} \]

where

\(\xi_{pm}\) and \(\xi_{cm}\) — resistance coefficients at the maximum flow rate \(Q_{max}\);

\(F\) — cross-sectional area of the pipeline before the valve;

\(\Delta H_m\) — head loss in the entire system at \(Q_{max}\).

As follows from this formula, in order to calculate the hydraulic characteristic \(\mu = f(n)\), the values of the resistance coefficients of the regulating element and of the system are required at various degrees of valve opening \((n)\), i.e., \(\xi_p = \varphi_1(n)\) and \(\xi_c = \varphi_2(n)\) must be known.

On the basis of the known dependence \(Q = F(n)\), the graph in Fig. 1, the graphical dependence \(\xi_p = \varphi_1(n)\) is readily determined; it is presented in Fig. 2. The resistance coefficient of the system \(\xi_c\) is determined from the experimentally found hydraulic resistances of the engine cooling system. The basic data for the engines whose hydraulic resistances were determined experimentally are presented in the tab-

Graph of the dependence of the resistance coefficient of the valve on the flow coefficients and the magnitude of opening

\[ \xi_p;\qquad \xi_c = f(n);\qquad \xi_p = \varphi(n);\qquad \mu(n) \]

Fig. 2

Table 1

where 1. The table also includes engines whose hydraulic resistances are known from TsNIDI data [3]. The results of measurements of the hydraulic resistances of the indicated engines are shown in Figs. 3 and 4.

Fig. 3

Fig. 4

As the curves of these graphs show, the head loss in the engine jacket as a function of water flow rate in the range from idle to full load is expressed with sufficient accuracy by the formula

\[ \Delta H = mQ^2, \tag{4} \]

where \(m\) is a constant coefficient which has its own value for each engine.

On the basis of this relation, the resistance coefficient of the engine cooling system will be equal to:

\[ \xi_c = \frac{\Delta H \cdot 2g}{\gamma W^2} = \frac{m \cdot 2g F^2}{\gamma} = \mathrm{const.}, \tag{5} \]

i.e., the resistance coefficient of the engine jacket does not depend on the water flow rate and has a definite value for each engine.

If, in addition, it is taken into account that the fluid pressure before the regulating element in the engine system is practically constant (depends little on the flow rate), then formula (3) takes the form:

\[ \mu = \sqrt{ \frac{\xi_{pm}+\xi_c}{\xi_p+\xi_c} }. \tag{6} \]

By assigning definite values of \(\xi_c\) and using the found dependence \(\xi_p=\varphi_1(n)\), one can, by formula (6), calculate the hydraulic characteristics of the regulating element in the system, i.e. \(\mu=f(n)\), for various values of \(\xi_c\).

The results of the calculations are presented graphically in the form of a map of hydraulic characteristics for the regulating element of the RTPD regulator (Fig. 5). In the calculation the following conditional values of the engine cooling-system resistances were adopted:

Fig. 5

\[ \xi_c = 0.1;\quad 1;\quad 3;\quad 4;\quad 10;\quad 700. \]

The values of the valve resistances \(\xi_p\) at various opening magnitudes \((n)\) were taken from Fig. 2.

On the basis of the compiled chart, it is possible to establish the hydraulic characteristic of the given control element in the cooling system of the engines under consideration. For these purposes, the resistance coefficient of the cooling system is first calculated by the formula:

\[ \xi_c=\frac{\Delta H_{dv}\cdot 2g}{\gamma\left(\dfrac{Q_{max}}{F}\right)} \tag{7} \]

The calculation results are summarized in Table 2.

Table 2

The chart and Table 2 show a considerable deviation of the hydraulic characteristics of the valve under consideration from linear ones. From the chart of control characteristics it follows that a dependence \(\mu=f(n)\) close to linear can be obtained with a system resistance coefficient \(\xi_c=3\div 4\).

Taking the system resistance coefficient equal to three, from formula (2) one can determine the valve cross-sectional area for the given engine. In calculating the liquid flow rate, the maximum value is taken. Thus, for an experimental installation with the MK engine, the valve cross section at maximum load should be \(60\ \text{mm}^2\).

Manufacturing a valve of standard design with such small dimensions presents great difficulties. Therefore, for this engine another design of the control element was made, in the form of a cylindrical spool with rectangular ports measuring \(6\times 10\ \text{mm}\).

Fig. 6

On the basis of the experimental curve \(Q=f(n)\) for this valve (Fig. 6), a chart of its hydraulic characteristics was calculated and constructed (Fig. 7).

On the same chart a dashed curve is plotted, obtained experimentally when blowing through the valve in the engine system. The curve obtained shows good agreement between the results of the calculation and the experimental data, and a sufficiently good approximation of the characteristic to a linear one.

Fig. 7

The installation of such a regulating element in the cooling system of the MK engine ensured the attainment of a stable process of automatic regulation of the temperature regime.

REFERENCES

1. Sokolov E. Ya., Shpeer M. G. — Operation of Heat Networks, Gosenergoizdat, 1940.
2. Instructions for the RTPD regulator, Tizpribor plant, 1949.
3. Diesel Engineering, 1934.