Alternative fuels and green aviation - Biomass as Energy Source: Resources, Systems and Applications - page 182

Figure 11.4. Experimentally measured density and viscosity of jet fuel, petroleum diesel and biodiesel.
(a) Density of two samples of Jet A; and (b) viscosity of two samples of Jet A, petrodiesel and
several biodiesels derived from various vegetable oils. Data adapted from Bruno and Huber
(2010) for jet fuel; and Freitas et al . (2011) for petrodiesel and biodiesel.

accompanying increases in exhaust smoke and emissions. On the other hand, low-viscosity fuels
may not provide enough lubrication for moving engine components to work properly.
Viscosity decreases with increasing temperature, but the form of the functionality is not as
simple as for density. Many mathematical descriptions for viscosity as a function of temperature
have been proposed, and the form of that functionality differs among the models. To complicate
matters further, there are two commonly used definitions for viscosity: kinematic viscosity ν
measured in units of L 2 t − 1 and dynamic (or absolute) viscosity (usually denoted as µ or η ,
depending on the discipline) measured in MLt 1 . The viscosities can be converted back and forth
through the density ρ , i.e., ν = µ / ρ . Strictly speaking, the dynamic viscosity is the factor that
relates fluid response to shear stress, but the kinematic viscosity comes in handy since this
converted parameter can simplify the form of the equations of fluid motion in some cases. From a
physics standpoint, the dynamic viscosity of a typical Newtonian liquid should obey anArrhenius-
type expression in temperature T , i.e., an exponential, µ ∝ exp( − A/T ). The constant A is specific
to the type of liquid under consideration. Since density is inversely proportional to temperature,
µ ∝ 1 /T , we should expect that µ ∝ T · exp( − A/T ). However, over small temperature ranges,
even a linear approximation may be sufficient. Near the freezing point, the viscosity behavior
becomes more sensitive to temperature decrease, and the viscosity shoots up (Kerschbaum and
Rinke, 2004). Freitas and co-workers evaluate several viscosity models against experimental
measurements of diesel and biodiesel, shown in Figure 11.4b, that vary substantially over a range
of temperature and the fuel's hydrocarbon content (Freitas et al. , 2011).
In Figure 11.4b, experimental data on two samples of Jet A (the two traces at the bottom)
shows that the temperature dependence is not linear between 20 and 100 ◦ C, but it is not grossly
nonlinear. However, viscosity does not behave linearly over the broad range of temperatures
encountered during aircraft operations, particularly at low temperatures. Note that, in Figure
11.4b, the petrodiesel (third frombottom) and biodiesels (clustered above the petrodiesel curve) all
exhibit increasing sensitivity to lower temperatures. In this case, the petrodiesel was a commercial
product suitable for automotive use, and the biodiesel was comprised of pure methyl esters from a
variety of vegetable oils. For jet fuels, the WFSP found that the temperature dependence became
markedly nonlinear when the temperature approached

40 ◦ C and below (Hadaller and Johnson,
2006). For the purposes of fuel qualification, all of the fuel in the WFSP survey easily met the
specification at the upper bound, 8mm 2 /s at -20 ◦ C. For other discussions on the temperature
dependence of diesel-grade fuel viscosity, see Freitas et al. (2011), Pratas et al. (2011a,b), Yuan
et al. (2003, 2005, 2009), and Hansen and Zhang (2003).

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