Weakened energy cascade in elastoinertial turbulence.

Newtonian turbulence is characterized by interscale transport of energy from the forcing scales to the dissipation scales. In elastoinertial turbulence, this interscale energy flux is weakened. Here, we explain this phenomenon by numerically showing that elastoinertial energy is predominantly dissipated through polymer chain relaxation. As opposed to Newtonian dissipation, chain relaxation is neither restricted to small nor to large scales but instead it is effective on all the scales. Chain relaxation does not therefore require interscale transport of elastoinertial energy from the forcing scales to the dissipation scales.

Modeling the Microstructure and Stress in Dense Suspensions under Inhomogeneous Flow.

Under inhomogeneous flow, dense suspensions exhibit behavior that violates the conventional homogeneous rheology. Specifically, one finds flowing regions with a macroscopic friction coefficient below the yielding criterion, and volume fraction above the jamming criterion. We demonstrate the underlying physics by incorporating shear rate fluctuations into a recently proposed tensor model for the microstructure and stress, and applying the model to an inhomogeneous flow problem. The model predictions agree qualitatively with particle-based simulations.

Constitutive Model for Time-Dependent Flows of Shear-Thickening Suspensions.

We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent materials with ideas developed previously to explain the steady flow of shear-thickening ones, whereby friction proliferates among compressive contacts at large particle stresses. We apply our model to shear reversal, and find good qualitative agreement with particle-level, discrete-element simulations whose results we also present.

Two-Dimensional Decaying Elastoinertial Turbulence.

We numerically simulate two-dimensional, decaying elastoinertial turbulence using the finitely extensible, nonlinear, elastic spring model. We vary the polymer concentration over seven decades, and observe two turbulent elastoinertial regimes. In the weakly coupled regime only the small scale structures change, while in the strongly coupled regime all structures change. This regime is dominated by elastoinertial shock waves with drag reduction properties; i.e., the energy decay rate decreases when the polymer concentration increases.

Stabilizing the thermal lattice Boltzmann method by spatial filtering.

We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

Boundary conditions for surface reactions in lattice Boltzmann simulations.

A surface reaction boundary condition in multicomponent lattice Boltzmann simulations is developed. The method is applied to a test case with nonlinear reaction rates and nonlinear density profiles. The results are compared to the corresponding analytical solution, which shows that the error of the method scales with the square of the lattice spacing.

Lattice-Boltzmann-based two-phase thermal model for simulating phase change.

A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum limit one recovers the well known macroscopic energy conservation equation for the mixtures. Heats of reaction, the enthalpy change associated with the phase change, and the diffusive transport of enthalpy are all taken into account; but the dependence of enthalpy on pressure, which is usually a small effect in most nonisothermal flows encountered in chemical reaction systems, is ignored. The energy equation is coupled to the LB equations for species transport and pseudopotential interaction forces through the EOS by using the filtered local pseudotemperature field. The proposed scheme is validated against simple test problems for which analytical solutions can readily be obtained.

Viscoelastic flow simulations through an array of cylinders.

Polymer solution flow is studied numerically in a periodic, hexagonal array of cylinders as a model for a porous medium. We use a lattice Boltzmann method supplemented by a polymer stress, where the polymers are modeled as finitely extensible, nonlinear, elastic dumbbells. The simulated, nonmonotonic behavior of the effective viscosity µ(eff) as a function of the Weissenberg number We is in qualitative agreement with experiments in the literature. An analytical model, which replaces the flexible polymers by rods and that replaces the flow field in the porous medium by a superposition of shear and elongation, correctly reproduces the simulated µ(eff) as a function of the polymer extensibility parameter b in the limit of large We.

Maximum drag reduction simulation using rodlike polymers.

Simulations of maximum drag reduction (MDR) in channel flow using constitutive equations for suspensions of noninteracting rods predict a few-fold larger turbulent kinetic energy than in experiments using rodlike polymers. These differences are attributed to the neglect of interactions between polymers in the simulations. Despite these inconsistencies the simulations correctly reproduce the essential features of MDR, with universal profiles of the mean flow and the shear stress budgets that do not depend on the polymer concentration.

Polymer flexibility and turbulent drag reduction.

Polymer-induced drag reduction is the phenomenon by which the friction factor of a turbulent flow is reduced by the addition of small amounts of high-molecular-weight linear polymers, which conformation in solution at rest can vary between randomly coiled and rodlike. It is well known that drag reduction is positively correlated to viscous stresses, which are generated by extended polymers. Rodlike polymers always assume this favorable conformation, while randomly coiling chains need to be unraveled by fluid strain rate in order to become effective. The coiling and stretching of flexible polymers in turbulent flow produce an additional elastic component in the polymer stress. The effect of the elastic stresses on drag reduction is unclear. To study this issue, we compare direct numerical simulations of turbulent drag reduction in channel flow using constitutive equations describing solutions of rigid and flexible polymers. When compared at constant phi r2, both simulations predict the same amount of drag reduction. Here phi is the polymer volume fraction and r is the polymer aspect ratio, which for flexible polymers is based on average polymer extension at the channel wall. This demonstrates that polymer elasticity plays a marginal role in the mechanism for drag reduction.