pronounced variation of viscosity with temperature, as shown in Figure 2.8.
Figure 2.8 Qualitative representation of the viscosity index (VI).
Table 2.6 Typical values for the viscosity index.
Source: OelCheck [21].
| Oil type | Viscosity index |
|---|---|
| Mineral oil | 95–105 |
| Multi‐grade oil | 140–200 |
| Synthetic oils | 200–400 |
The VI was originally defined as a dimensionless value on a 0–100 scale, being 100 the best VI. Nowadays, thanks to the progress in the formulation of VI improvers, much higher values can be achieved as shown in Table 2.6.
2.6.2 Viscosity as a Function of Pressure
For liquids, the viscosity increases with pressure. While this effect can be negligible for limited pressure variations (<200 bar), it might be relevant for hydraulic systems working at high pressure (>200 bar). A formula that can be used to approximate the variation of fluid viscosity with pressure is given by
where μ0 is the dynamic viscosity at atmospheric pressure (at a given temperature), p is the fluid pressure (in bar), and b is a coefficient that depends on the fluid. For mineral‐based oils, b = 1.7 · 10−3 bar−1; for HFC oils, b = 3.5 · 10−4 bar−1; and for HFD oils b = 2.2 · 10−3 bar−1. Relation (2.21) is plotted in Figure 2.9. As the reader can notice from the figure, for a mineral oil, there is an increase in viscosity of about 40% from atmospheric conditions to 200 bar.
Figure 2.9 Viscosity as a function of pressure.
2.7.1 Entrained Air
In some circumstances, the hydraulic fluid can entrain some air from the environment that can lead to suction condition issues for the pump(s). This is commonly referred as pseudo‐cavitation.
This usually can occur in the reservoir (Figure 2.10a) or when gas leakages are present in low‐pressure hydraulic lines, such as suction lines (Figure 2.10b). For example, the return line entering the reservoir might present a non‐submerged pipe or a design creating a high amount of turbulence. In both cases the hydraulic fluid can entrap air that is then carried within the flow and can enter the hydraulic system. If the bubbles of air do not have enough time to settle within the reservoir, foam can accumulate on the surface.
The entrained air can lead to cavitation of the pump or to erratic phenomena such as a slow response of some functions. For this reason, it is always recommended to adopt all possible measures to avoid or limit the air entrainment.
2.7.2 Gas Solubility
All liquids, including hydraulic fluids, normally contain dissolved incondensable gases (typically air taken from the environment).
The liquid absorbs the gas from the surroundings until the saturation state is reached. As long as the gas is dissolved, it does not influence the main properties of the fluid, particularly in terms of compressibility or viscosity.
The (maximum) volume of air dissolved in the liquid can be determined by the following equation, derived from the well‐known Henry–Dalton law:
It is important to remark that Vair, d represents the volume of air measured at the reference pressure p0. This law states that the volume of air that the liquid can dissolve proportionally increases with pressure. For mineral oils, the coefficient αa is also known as Bunsen coefficient and can vary from 0.06 to 0.09. This is not much affected by temperature or viscosity [22]. For water, the Bunsen coefficient is 0.04, which means that mineral‐based oils tend to dissolve more air than water. To better understand the meaning of αa and quantify the actual amount of incondensable gas that a hydraulic fluid can dissolve, one can consider the atmospheric pressure as the reference condition, p0. This is the condition of most hydraulic fluids inside a reservoir open to atmosphere. In this situation, considering p = p0 in Eq. (2.22), a volume of air corresponding to 6%, up to 9%, of the volume of the fluid V0 could be held by the fluid. This amount of air is in equilibrium with the liquid, and it is not released unless the pressure of the fluid is reduced.
Figure 2.10 Typical causes of entrained air within the hydraulic fluid: (a) in a reservoir; (b) in a suction line.
The air release phenomenon is similar to what anyone experiences when opening a bottle of carbonated drink. Before opening the bottle, the fluid in the bottle appears as uniform liquid; however, while opening the bottle, bubbles of gas can be observed while the internal pressure decreases. This means that before opening the bottle, the gas was in equilibrium with the liquid, entirely dissolved. As the pressure decreases, a certain amount of gas gets released, and bubbles start appearing within the liquid.
Considering the gas solubility of the fluid, three possible equilibrium states can be identified. These are graphically represented in Figure 2.11: Above the saturation pressure pSAT, all the air is dissolved in the liquid without affecting the main properties of the fluid. However, below the saturation pressure, only a portion of the air remains
