Ali Mani

On the propagation of concentration polarization from microchannel-nanochannel interfaces. Part I: Analytical model and characteristic analysis.

We develop two models to describe ion transport in variable-height micro- and nanochannels. For the first model, we obtain a one-dimensional (unsteady) partial differential equation governing flow and charge transport through a shallow and wide electrokinetic channel. In this model, the effects of electric double layer (EDL) on axial transport are taken into account using exact solutions of the Poisson-Boltzmann equation. The second simpler model, which is approachable analytically, assumes that the EDLs are confined to near-wall regions. Using a characteristics analysis, we show that the latter model captures concentration polarization (CP) effects and provides useful insight into its dynamics. Two distinct CP regimes are identified: CP with propagation in which enrichment and depletion shocks propagate outward, and CP without propagation where polarization effects stay local to micro- nanochannel interfaces. The existence of each regime is found to depend on a nanochannel Dukhin number and mobility of the co-ion nondimensionalized by electroosmotic mobility. Interestingly, microchannel dimensions and axial diffusion are found to play an insignificant role in determining whether CP propagates. The steady state condition of propagating CP is shown to be controlled by channel heights, surface chemistry, and co-ion mobility instead of the reservoir condition. Both models are validated against experimental results in Part II of this two-paper series.

On the Propagation of Concentration Polarization from Microchannel-Nanochannel Interfaces Part II. Numerical and Experimental Study

We present results of a combined computational and experimental study of the propagation of concentration polarization (CP) zones in a microchannel-nanochannel system. Our computational model considers the combined effects of bulk flow, electromigration, and diffusion and accurately captures the dynamics of CP. Using wall charge inside the nanochannel as a single fitting parameter, we predict experimentally observed enrichment and depletion shock velocities. Our model can also be used to compute the existence of CP with propagating enrichment and depletion shocks on the basis of measured ion mobility and wall properties. We present experiments where the background electrolyte consists of only a fluorescent ion and its counterion. These results are used to validate the computational model and to confirm predicted trends from an analytical model presented in the first of this two-paper series. We show experimentally that the enrichment region concentration is effectively independent of the applied current, while the enrichment and depletion shock velocities increase in proportion to current density.

Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface

We present a comprehensive analysis of transport processes associated with electrohydrodynamic chaos in electrokinetic systems containing an ion-selective surface. The system considered is an aqueous symmetric binary electrolyte between an ion-selective surface and a stationary reservoir. Transport is driven by an external electric field. Using direct numerical simulations (DNS) of the coupled Poisson–Nernst–Planck and Navier–Stokes equations in 2D we show significant transitions in flow behavior from coherent vortex pairs to fully chaotic multi-layer vortex structures with a broadband energy spectrum. Additionally, we demonstrate that these vortices can eject both positive and negative free charge density into the bulk of the domain and completely disrupt the structure of the traditionally described extended space charge region. The resulting dynamical behavior poses a challenge for traditional asymptotic modeling that relies on the quasi-electroneutral bulk assumption. Furthermore, we quantify for the first time the relative importance of energy dissipation due to viscous effects in various transport regimes. Finally, we present a framework for the development of ensemble-averaged models (similar to Reynolds Averaged Navier–Stokes equations) and assess the importance of the unclosed terms based on our DNS data.

Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks

The artificial bulk viscosity method to numerically capture shocks is investigated for large-eddy simulation (LES). Different variations of this method are tested on a turbulent flow over a cylinder at Reynolds number of 10,000 and free-stream Mach number of 0.85. The artificial bulk viscosity model by Cook and Cabot, which is parameterized by the strain rate magnitude, is found to provide unnecessary bulk viscosity in turbulent regions away from shocks. While developed turbulent structures are found unaffected, this extra bulk viscosity is shown to significantly damp the sound field. An alternative formulation of the model which is parameterized by the rate of dilatation is proposed. This formulation is shown to avoid the unnecessary bulk viscosity and enhance the sound-prediction capability of the model. It was found that standard LES combined with artificial bulk viscosity is a promising approach for simulation of turbulent flows with shocks. The formulation of the model on curvilinear coordinates is presented in the appendix.

Analysis and optimization of numerical sponge layers as a nonreflective boundary treatment

The aim of this work is to provide practical guidelines for designing sponge layers considering applications in computational fluid dynamics and computational aeroacoustics. We present the analysis of sponge/flow interactions and provide a characterization of its basic reflectivity mechanisms. While sponges are perfect absorbers in one-dimensional systems, they can cause their own reflection when encountering oblique sound or oblique vorticity waves. To minimize this adverse effect, sponge strength and profile need to be selected optimally. Also for a fixed desired accuracy, sponge length should be above a minimum threshold. Our analysis quantifies these requirements for a wide range of conditions in terms of inflow/outflow Mach number, incident frequencies, incident angles, and desired accuracy, and covers main concerns with sponges such as sound/sponge interactions and vortex/sponge interactions. As a test case, we present a nonlinear Euler calculation of a convecting vortex interacting with sponges with different lengths. We show that sponges designed by our guidelines achieve accuracies comparable to perfectly matched layers for the same cost, over moderate to high accuracy demands. The results of the presented analysis can be used to determine sponge requirements for a wide range of CFD applications. A summary of these guidelines are listed in the paper.

Prediction of Sound Generated by Complex Flows at Low Mach Numbers

We present a computational aeroacoustics method to evaluate sound generated by low Mach number flows in complex configurations in which turbulence interacts with arbitrarily shaped solid objects. This hybrid approach is based on Lighthills acoustic analogy in conjunction with sound source information from an incompressible calculation. In this method, Lighthills equation is solved using a boundary element method that allows the effect of scattered sound from arbitrarily shaped solid objects to be incorporated. We present validation studies for sound generated by laminar and turbulent flows over a circular cylinder at Re = 100 and 10,000, respectively. Our hybrid approach is validated against directly computed sound using a high-order compressible flow solver as well as the solution of the Ffowcs Williams and Hawkings equation in conjunction with compressible sound sources. We demonstrate that the sound predicted by a second-order hybrid approach is as accurate as sound directly computed by a sixth-order compressible flow solver in the frequency range in which low-order numerics can accurately resolve the flow structures. As an example of an engineering problem, we calculated the sound generated by flow over an automobile side-view mirror and compared it to experimental measurements.

Overlimiting current and shock electrodialysis in porous media.

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electroosmotic flow also contribute to ionic flux. In this article, we report experimental evidence for surface-driven overlimiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with a 500 nm mean pore size) in an aqueous electrolyte (CuSO4 or AgNO3) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electroosmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM to 1.0 M) after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water (≈10 μM) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5 mm across the outlet. The results suggest the feasibility of shock electrodialysis as a new approach to water desalination and other electrochemical separations.

Computational study of optical distortions by separated shear layers and turbulent wakes

The flow over a circular cylinder at Re D = 3900 and 10000 and M = 0.4 is considered a platform to study the aero-optical distortions by separated shear layers and turbulent wakes. The flow solution is obtained by large eddy simulation (LES) and validated against previous experimental and numerical results. The fluctuating refractive index obtained from LES is used in a ray-tracing calculation to determine wavefront distortions after the beam passes through the turbulent region. Free-space propagation to the far field is computed using Fourier optics. The optical statistics are analysed for different conditions in terms of optical wavelength, aperture size and the beam position. It is found that there exists an optimal wavelength which maximizes the far-field peak intensity. Optical results at both Reynolds numbers are compared. The optical distortion by the downstream turbulent wake is found to be Reynolds number insensitive. However, due to their different transition mechanisms, distortions by the near wake regions are different in the two flows. The aero-optical effects of different flow scales are examined using filtering and grid refinement. Through a grid convergence study it is confirmed that an adequately resolved LES can capture the aero-optics of highly aberrating flows without requiring additional subgrid scale model for the optics.

On the Dynamical Regimes of Pattern-Accelerated Electroconvection

Recent research has established that electroconvection can enhance ion transport at polarized surfaces such as membranes and electrodes where it would otherwise be limited by diffusion. The onset of such overlimiting transport can be influenced by the surface topology of the ion selective membranes as well as inhomogeneities in their electrochemical properties. However, there is little knowledge regarding the mechanisms through which these surface variations promote transport. We use high-resolution direct numerical simulations to develop a comprehensive analysis of electroconvective flows generated by geometric patterns of impermeable stripes and investigate their potential to regularize electrokinetic instabilities. Counterintuitively, we find that reducing the permeable area of an ion exchange membrane, with appropriate patterning, increases the overall ion transport rate by up to 80%. In addition, we present analysis of nonpatterned membranes, and find a novel regime of electroconvection where a multivalued current is possible due to the coexistence of multiple convective states.

Resolution requirements for aero-optical simulations

Analytical criteria are developed to estimate the error of aero-optical computations due to inadequate spatial resolution of refractive index fields in high Reynolds number flow simulations. The unresolved turbulence structures are assumed to be locally isotropic and at low turbulent Mach number. Based on the Kolmogorov spectrum for the unresolved structures, the computational error of the optical path length is estimated and linked to the resulting error in the computed far-field optical irradiance. It is shown that in the high Reynolds number limit, for a given geometry and Mach number, the spatial resolution required to capture aero-optics within a pre-specified error margin does not scale with Reynolds number. In typical aero-optical applications this resolution requirement is much lower than the resolution required for direct numerical simulation, and therefore, a typical large-eddy simulation can capture the aero-optical effects. The analysis is extended to complex turbulent flow simulations in which non-uniform grid spacings are used to better resolve the local turbulence structures. As a demonstration, the analysis is used to estimate the error of aero-optical computation for an optical beam passing through turbulent wake of flow over a cylinder.