On the Calculation of Safety Fluid Couplings at Reynolds Numbers Equal to or Less Than Its Critical Value
Abstract Generated abstract
This paper examines the applicability of similarity-law recalculation for predicting the mechanical characteristics of low-power safety fluid couplings operated at pump-wheel speeds different from those used in testing, particularly when Reynolds numbers are near or below the critical value. Using an asymmetric, partially filled coupling with an active diameter of 280 mm and industrial oil as the working fluid, experimental torque characteristics at 1440, 950, and 725 rpm are compared with values calculated from a known characteristic. The comparison indicates satisfactory agreement only at low filling, about 60 percent, and on working portions at higher fillings, while at fillings of 65 percent and above substantial deviations occur. The study concludes that similarity-based recalculation can produce significant errors, up to 100 percent, for such safety couplings outside limited operating conditions.
Full Text
On the Calculation of Safety Fluid Couplings at Reynolds Numbers Equal to or Less Than Its Critical Value
A. V. Murin
(Presented by the scientific seminar of the Department of Applied Mechanics)
Often one and the same fluid coupling, for which mechanical characteristics have been obtained at some definite rotational speed of the pump wheel, has to be used at other speeds of its driving member. For single-cavity fluid couplings with a symmetrical profile of the working cavity, a method is known for obtaining mechanical characteristics in such a case [1, 2]. Calculations of mechanical characteristics for other nominal speeds of the pump wheel of a fluid coupling from an available characteristic are possible only for dynamically similar regimes of the circulation flow [3]. Calculations based on the law of similarity are also applied to safety fluid couplings with asymmetrical profiles of the working wheels [4, 5]. Such couplings, as is known, operate with partial filling of their working cavity.
To ensure similar regimes in geometrically similar fluid couplings operating with partial fillings and with different numbers of revolutions of the pump wheel, equality of slips, relative fillings, and Reynolds numbers must be observed [6]. However, with an unchanged active diameter and the use of the same working fluid for geometrically identical fluid couplings operating at different speeds of the pump wheel, only kinematic similarity can be ensured [3]. At large Re, exceeding its critical value, self-similar regimes are ensured, and changes in this number may be neglected [3, 6]. For low-power fluid couplings \((N < 5\ \text{kW})\), when oils commonly used as the working fluid are employed, the values of Re are either close to, or even less than, its critical value. For hydrodynamic transmissions it is recommended to calculate the Reynolds number from the relation [3, 7, 8]
\[ \operatorname{Re}=\frac{nD^{2}}{\nu}, \]
where
\(n\) is the angular velocity;
\(D\) is the active diameter of the hydrodynamic transmission;
\(\nu\) is the kinematic coefficient of viscosity.
Self-similarity of regimes for single-cavity fluid couplings with symmetrical profiles of the working wheels is ensured at values of the Reynolds criterion, calculated from this relation with the dimension of
speeds, rad/sec, equal to \(Re > 10^6\) [9, 10]. Moreover, the indicated value of \(Re\) is necessary for ensuring similar regimes at \(i=\dfrac{n_2}{n_1}\) close to unity; at large slips, smaller values of this number are necessary [10].
For an experimental verification of the suitability of the aforementioned method for calculating mechanical characteristics at other pump-wheel speeds, as applied to low-power safety fluid couplings with an asymmetric profile of the working cavity and an additional volume on the driving-link side, a coupling of the stated type with an active diameter of 280 mm [11] was used. Industrial oil 12 (GOST 1707-51) served as the working fluid. Mechanical characteristics of this coupling were obtained at an almost constant pump-wheel speed equal, respectively, to 1440, 950,
Fig. 1. Relative values of the torques (referred to their values at a pump-wheel speed of 1440 rpm), transmitted by the safety fluid coupling, obtained on the basis of the similarity law (straight lines 1, 2) and experimentally (curves 3, 4), \(1\) and \(3\)—\(n_1\)-const \(=950\) rpm; \(2\) and \(4\)—\(n_1\)-const \(=725\) rpm.
725 rpm and at different fillings. The Reynolds number at a working-fluid temperature of 50–70°C and at these speeds was, respectively, about \(1.2\times 10^6\), \(0.8\times 10^6\), \(0.6\times 10^6\). Figure 1 gives the relative values of the torques at such speeds (in relation to their values at \(n_1=1440\) rpm), obtained by calculation (straight lines 1 and 2) and on the basis of experimental data (curves 3 and 4).
As is evident from the graphical dependences presented, only at low fillings \((q = 60\%)\) do the values of the relative torques obtained by calculation and on the basis of experimental data agree quite well, which evidently indicates the self-similarity of the regimes at the indicated Reynolds numbers.
It should be borne in mind that recalculation of the mechanical characteristic to other pump-wheel speeds according to the law of similarity is not entirely accurate even for single-cavity fluid couplings with symmetrical impeller profiles [1]. In this connection, at pump-wheel speeds differing by 30–40% from the speed at which the characteristic used for recalculation was obtained, in order to refine the calculations A. P. Kudryavtsev [1] recommends introducing a correction by means of the dependence he obtained. Dependences for an analogous purpose are also proposed by other authors [7].
Thus, the method of constructing the mechanical characteristics of safety fluid couplings of the above-named type at various \(n_1\) on the basis of the law of similarity from a known characteristic obtained at \(\mathrm{Re} > \mathrm{Re}_{\mathrm{cr}}\) gives satisfactory agreement with experiment only at a filling of \(q = 60\%\) \((\mathrm{Re} = (0.8—0.6) \times 10^6)\) and on the working portions at higher fillings. On the remaining part of the characteristics at \(q \geqslant 65\%\) this method gives significant errors (up to 100%).
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