| Summary: |
Turbulent flows of viscoelastic fluids based on polymeric and surfactant additives have industrial applications in flows of smart thermal fluids in district heating and cooling systems [1], in pipeline oil transport [2], and in oil and gas well-drilling. Duct flows of such fluids may show significant reductions in friction and heat transfer and this has motivated extensive research [3], but modern
predictive techniques associated to viscoelastic constitutive equations are almost exclusively based on Reynolds-averaged Navier-
predictive techniques associated to viscoelastic constitutive equations are almost exclusively based on Reynolds-averaged Navier-
Stokes equations (RANS) calibrated for wall flows [B]. However, it is well known that these models present inherent limitations in many engineering flows involving e.g. strong curvature, large-scale unsteadiness, or rotation [4]. Consequently, in complex new situations for which no calibration has been carried out RANS models may result in a substantial deviation from the actual flow statistics [4]. Moreover, some important flow data such as the dominating flow frequencies is not accessible in RANS [4]. For these reasons large-eddy simulations (LES) have been increasingly employed in engineering applications. In LES the largest energetic scales of motion are explicitly simulated and the effect of the smallest scales is modelled by using a subgrid-scale (SGS) model. Today, LES is the most advanced and accurate method for the simulation of turbulent flows of Newtonian fluids [5], but the possibility of using LES for non-Newtonian viscoelastic fluids remains elusive, as attested by the extremely small number of LES studies in such flows [6]. Moreover, some of these early attempts are extremely complex and computationally expensive, have only been calibrated for wall flows, and their behaviour in wall-free turbulent flows is unknown [6]. Thus, no SGS models are available today for routine engineering LES with n  |
Summary
Turbulent flows of viscoelastic fluids based on polymeric and surfactant additives have industrial applications in flows of smart thermal fluids in district heating and cooling systems [1], in pipeline oil transport [2], and in oil and gas well-drilling. Duct flows of such fluids may show significant reductions in friction and heat transfer and this has motivated extensive research [3], but modern
predictive techniques associated to viscoelastic constitutive equations are almost exclusively based on Reynolds-averaged Navier-
predictive techniques associated to viscoelastic constitutive equations are almost exclusively based on Reynolds-averaged Navier-
Stokes equations (RANS) calibrated for wall flows [B]. However, it is well known that these models present inherent limitations in many engineering flows involving e.g. strong curvature, large-scale unsteadiness, or rotation [4]. Consequently, in complex new situations for which no calibration has been carried out RANS models may result in a substantial deviation from the actual flow statistics [4]. Moreover, some important flow data such as the dominating flow frequencies is not accessible in RANS [4]. For these reasons large-eddy simulations (LES) have been increasingly employed in engineering applications. In LES the largest energetic scales of motion are explicitly simulated and the effect of the smallest scales is modelled by using a subgrid-scale (SGS) model. Today, LES is the most advanced and accurate method for the simulation of turbulent flows of Newtonian fluids [5], but the possibility of using LES for non-Newtonian viscoelastic fluids remains elusive, as attested by the extremely small number of LES studies in such flows [6]. Moreover, some of these early attempts are extremely complex and computationally expensive, have only been calibrated for wall flows, and their behaviour in wall-free turbulent flows is unknown [6]. Thus, no SGS models are available today for routine engineering LES with non-Newtonian viscoelastic fluids.
Arguably, the most important feature that any subgrid-scale model must represent is the kinetic energy flux from the resolved (or grid-scales), into the unresolved (or subgrid) scales [4,A]. In Newtonian fluids the development of subgrid-scale models is largely based on the Richardson-Kolmogorov energy cascade concept, according to which the smallest scales of motion are essentially isotropic, statistically universal and dynamically passive and simply dissipate whatever kinetic energy is injected into them from the large scales. This simple concept, which describes well the interscale interactions in turbulent Newtonian flows away from solid walls [A], explains much of the success of classical SGS models [4,5]. A key ingredient of this picture is the so-called equilibrium assumption, which states that all the kinetic energy transferred from the large into the smallest scales of motion is balanced (on average) by the viscous dissipation acting on the smallest scales. However, when dealing with non-Newtonian fluids one is immediately confronted with a much more challenging situation, because of the extremely complex SGS interactions arising there. Investigations of turbulent flow behaviour of viscoelastic fluids have focused on the Finitely Extensible Non-Linear Elastic constitutive model - with Peterlin's approximation (FENE-P) [7], a basic constitutive equation for viscoelastic fluids that displays all the main characteristics of an elastic fluid model. Fluid elasticity is associated with the deformability of some of the constituents of a fluid and its interaction with the turbulent structures significantly changes the energy distribution across scales. The present understanding of the physical mechanisms of these interactions is very limited, and even the most solid facts about the dynamics of the small scales are not observed in non-Newtonian inertio-elastic turbulence. For example, in a dilute solution of long polymer molecules, an important fraction of the kinetic energy transferred into the small scales is dissipated by the polymer [8,C], but in some cases one may observe the formation a polymer induced energy cascade that competes with the classical energy cascade [9,C]. Any future SGS model applied to non-Newtonian fluids will need to cope with this complex interplay between the existing scales of motion and the fluid rheology. The members of the research team have very recently uncovered much of this complexity by analysing the detailed large/small scale interactions in a viscoelastic flow, by using new direct numerical simulations (DNS) of isotropic turbulence for the FENE-P model[C].
The main objective of this project is (i) to develop SGS models for LES of turbulent flow of viscoelastic fluids represented by the FENE-P model allowing the simulation of new classes of engineering flows at high Reynolds numbers, and also (ii) to investigate the instabilities, transition and turbulence in viscoelastic turbulent jets. The investigation will rely on DNS carried out with high performance in-house codes and algorithms existing in the research team. |