Abstract:
Fluid
ows are constitutive to a wide variety of scienti c and engineering problems, owing to the
fact that they encompass a vast range of spatial and temporal scales. An accurate prediction of
the
uid
ow has innumerable commercial applications in turbomachinery, petrochemical industries,
hydraulic machines, inkjet printing, as well as is of great scienti c interest for multiphase
ows, non-Newtonian
ows, hydrodynamic instability and transition to turbulence (Dixon &
Hall, 2013; Oliemans, 2012; Batchelor, 2000; Leal, 2007). Fluid dynamics becomes crucial during
scenarios that require knowledge of
ows over an aortic stenosis, designing arti cial heart
valves, and predicting extreme weather patterns such as cyclones,
oods, hurricanes. Additionally,
a quick prediction of the atmospheric
ows can lead to the prior knowledge of the expected
rainfall, which will reduce losses in the regions that are dependent on the rain for the purpose
of agricultural irrigation.
Although seemingly disparate, the various
ows in the continuum regime, irrespective of
the spatial and temporal scales, are similar and are governed by the Navier-Stokes-Fourier
(NSF) equations (Batchelor, 2000). These equations can be simpli ed and solved to obtain a
closed form solution for a large class of problems (Leal, 2007). However, they do not render a
general solution for many realistic engineering and scienti c problems, particularly in the case of
turbulent
ows where the nonlinearity of the NSF equations gives rise to chaotic beahviour. One
has to, therefore, resort to numerical methods to solve them. The direct numerical simulations
(DNS), where all the scales of the
ow are resolved, are the most reliable numerical approaches
for solving the NSF equations. However, the DNS of many realistic
ows such as the turbulent
ows requires grid sizes that are often too large (Pope, 2000). With the existing approaches, it is
widely accepted that DNS of turbulent
ows will be feasible only after a decade (Thantanapally
et al., 2013a; Slotnick et al., 2014; Larsson & Wang, 2014). Thus, one looks for viable alternates
to it such as the turbulence models. They reduce the computational load by modeling the subgrid
phenomena and projecting it onto a coarse grid. However, the choice of these turbulence model
is problem speci c and hence these models lack universality.