Among the various alternative fuels, vegetable-oil-based fuels have been attracting greater attention as a promising alternative to fossil diesel fuel in compression ignition (CI) engines. Fuel viscosity has a definite effect on fuel injection, spray development, and combustion processes of CI engines; hence, the viscosity estimation of new candidate fuels is significant. This paper discusses the methodologies used to estimate the viscosities of vegetable oil and biodiesel fuels, based on their fatty acid composition. While the methyl ester composition of biodiesel is directly related to the fatty acid composition of the oil, a basis for determining the triglyceride composition to estimate the straight vegetable oil viscosity is elucidated in the paper. The proposed methodologies are validated over a wide range of available viscosity data for vegetable oils and biodiesel fuels of varying composition and for varying temperatures. A comparison of the estimated viscosities with the measured values for 13 vegetable oils and 14 biodiesel samples shows an agreement within a predicted error of 10%.
Localized patches of turbulence frequently occur in geophysics, such as in the atmosphere and oceans. The effect of rotation, Ω, on such a region (a 'turbulent cloud') is governed by inhomogeneous dynamics. In contrast, most investigations of rotating turbulence deal with the homogeneous case, although inhomogeneous turbulence is more common in practice. In this paper, we describe the results of 512 3 direct numerical simulations (DNS) of a turbulent cloud under rotation at three Rossby numbers (Ro), namely 0.1, 0.3 and 0.5. Using a spatial filter, fully developed homogeneous turbulence is vertically confined to the centre of a periodic box before the rotation is turned on. Energy isosurfaces show that columnar structures emerge from the cloud and grow into the adjacent quiescent fluid. Helicity is used as a diagnostic and confirms that these structures are formed by inertial waves. In particular, it is observed that structures growing parallel to the rotation axis (upwards) have negative helicity and those moving antiparallel (downwards) to the axis have positive helicity, a characteristic typical of inertial waves. Two-dimensional energy spectra of horizontal wavenumbers, k ⊥ , versus dimensionless time, 2Ωt, confirm that these columnar structures are wavepackets which travel at the group velocities of inertial waves. The kinetic energy transferred from the turbulent cloud to the waves is estimated using Lagrangian particle tracking to distinguish between turbulent and 'wave-only' regions of space. The amount of energy transferred to waves is 40 % of the initial at Ro = 0.1, while it is 16 % at Ro = 0.5. In both cases the bulk of the energy eventually resides in the waves. It is evident from this observation that inertial waves can carry a significant portion of the energy away from a localized turbulent source and are therefore an efficient mechanism of energy dispersion.
In most numerical simulations of the Earth’s core the dynamo is located outside the tangent cylinder and, in a zero-order sense, takes the form of a classical $\unicode[STIX]{x1D6FC}^{2}$ dynamo. Such a dynamo usually requires a distribution of helicity, $h$, which is asymmetric about the equator and in the simulations it is observed that, outside the tangent cylinder, the helicity is predominantly negative in the north and positive in the south. If we are to extrapolate the results of these simulations to the planets, we must understand how this asymmetry in helicity is established and ask if the same mechanism is likely to operate in a planet. In some of the early numerical dynamos, which were too viscous by a factor of at least $10^{9}$, as measured by the Ekman number, the asymmetric helicity distribution was attributed to Ekman pumping. However, Ekman pumping plays much less of a role in more recent, and less viscous, numerical dynamos, and almost certainly plays no significant role in the core of a planet. So the question remains: what establishes the asymmetric helicity distribution in the simulations and is this mechanism likely to carry over to planetary cores? In this paper we review the evidence that planetary dynamos, and their numerical analogues, might be maintained by helical waves, especially inertial waves, excited in and around the equatorial regions. This cartoon arises from the observation that there tends to be a statistical bias in the buoyancy flux towards the equatorial regions, and so waves are preferentially excited there. Moreover, upward (downward) propagating inertial waves carry negative (positive) helicity, which leads naturally to a segregation in $h$.
Inertial waves are oscillations in a rotating fluid, such as the Earth's outer core, which result from the restoring action of the Coriolis force. In an earlier work, it was argued by Davidson that inertial waves launched near the equatorial regions could be important for the α 2 dynamo mechanism, as they can maintain a helicity distribution which is negative (positive) in the north (south). Here we identify such internally-driven inertial waves, triggered by buoyant anomalies in the equatorial regions in a strongly-forced geodynamo simulation. Using the time-derivative of vertical velocity, ∂u z /∂t, as a diagnostic for travelling wave-fronts, we find that the horizontal movement in the buoyancy field near the equator is well-correlated with a corresponding movement of the fluid far from the equator. Moreover, the azimuthally-averaged spectrum of ∂u z /∂t lies in the inertial wave frequency range. We also test the dispersion properties of the waves by computing the spectral energy as a function of frequency, ϖ, and the dispersion angle, θ. Our results suggest that the columnar flow in the rotation-dominated core, which is an important ingredient for the maintenance of a dipolar magnetic field, is maintained despite the chaotic evolution of the buoyancy field on a fast-time scale by internally-driven inertial waves.
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