Hydrodynamic Boundary Conditions Research Articles

A New Approach to Numerical Simulation of Small Sized Plate Heat Exchangers With Chevron Plates

A numerical and experimental study of heat transfer and fluid flow in a single pass counter flow plate heat exchanger with chevron plates has been presented in this paper. CFD analysis of small sized plate heat exchanger was carried out by taking the complete geometry of the heat transfer surface and more realistic hydrodynamic and thermal boundary conditions. A cold channel with two chevron plates and two halves of hot channels on either side having flat periodic boundaries was selected as the computational domain. The numerical model was validated with data from experiments and empirical correlations from literature. Heat transfer and pressure drop data were obtained experimentally with water as the working fluid, in the Reynolds number range 400–1300 and the Prandtl number range 4.4–6.3.

Infrared Imaging of a Solid Phase Surfactant Monolayer

A new method for visualizing solid phase surfactant monolayers is presented. This method utilizes infrared (IR) imaging of the surface of a warm subphase covered by the monolayer. When the subphase is deep, natural convection occurs, resulting in a complex surface temperature field that is easily visualized using an IR camera. The presence of a surfactant monolayer changes the hydrodynamic boundary condition at the interface, dramatically altering the surface temperature field, and permitting the differentiation of surfactant-covered and surfactant-free regions. In this work, solid phase monolayers are imaged using this IR method. Fractures in the monolayer are dramatically visualized because of the sudden elimination of surfactant in the region opened up by the crack. The method is demonstrated in a wind/water tunnel, where a stearic acid monolayer is deposited and a crack is created through shear on the surfactant surface, created by suddenly increasing the velocity of the air over the water.

Giant Amplification of Interfacially Driven Transport by Hydrodynamic Slip: Diffusio-Osmosis and Beyond

We demonstrate that "moderate" departures from the no-slip hydrodynamic boundary condition (hydrodynamic slip lengths in the nanometer range) can result in a very large enhancement--up to 2 orders of magnitude--of most interfacially driven transport phenomena. We study analytically and numerically the case of neutral solute diffusio-osmosis in a slab geometry to account for nontrivial couplings between interfacial structure and hydrodynamic slip. Possible outcomes are fast transport of particles in externally applied or self-generated gradient, and flow enhancement in nano- or microfluidic geometries.

Surface roughness and hydrodynamic boundary conditions

We report results of investigations of a high-speed drainage of thin aqueous films squeezed between randomly nanorough surfaces. A significant decrease in the hydrodynamic resistance force as compared with that predicted by Taylor's equation is observed. However, this reduction in force does not represent the slippage. The measured force is exactly the same as that between equivalent smooth surfaces obeying no-slip boundary conditions, but located at the intermediate position between peaks and valleys of asperities. The shift in hydrodynamic thickness is shown to be independent of the separation and/or shear rate. Our results disagree with previous literature data reporting very large and shear-dependent boundary slip for similar systems.

Hydrodynamic boundary condition in vibrofluidized granular systems

Granular media, fluidized by a vibrating wall, is studied in the high frequency ( ω → ∞ ) small amplitude ( A → 0 ) limit. It is shown that there exists an asymptotic regime such that if the product A ω 5 / 4 is kept constant, then the behavior of the fluid in the bulk remains independent of the actual value of the amplitude with the corresponding value of the frequency. Furthermore, we show that in this asymptotic regime the boundary condition associated to the vibrating wall can be replaced by a stationary heat source. The value of this heat flux proves to be proportional to A 2 ω 5 / 2 and depends on the fluid transport coefficients and on the wall oscillation waveform. Numerical solutions of the full hydrodynamic equations confirm these predictions.

Hydrodynamic effects in driven soft matter.

Recent theoretical works exploring the hydrodynamics of soft material in non-equilibrium situations are reviewed. We discuss the role of hydrodynamic interactions for three different systems: (i) the deformation and orientation of sedimenting semiflexible polymers, (ii) the propulsion and force-rectification with a nano-machine realized by a rotating elastic rod, and (iii) the deformation of a brush made of grafted semiflexible polymers in shear flow. In all these examples deformable polymers are subject to various hydrodynamic flows and hydrodynamic interactions. Perfect stiff nano-cylinders are known to show no orientational effects as they sediment through a viscous fluid, but it is the coupling between elasticity and hydrodynamic torques that leads to an orientation perpendicular to the direction of sedimentation. Likewise, a rotating stiff rod does not lead to a net propulsion in the Stokes limit, but if bending is allowed an effective thrust develops whose strength and direction is independent of the sense of rotation and thus acts as a rectification device. Lastly, surface-anchored polymers are deformed by shear flows, which modifies the effective hydrodynamic boundary condition in a non-linear fashion. All these results are obtained with hydrodynamic Brownian dynamics simulation techniques, as appropriate for dilute systems. Scaling analyses are presented when possible. The common theme is the interaction between elasticity of soft matter and hydrodynamics, which can lead to qualitatively new effects.

Flow boundary conditions for chain-end adsorbing polymer blends

Using the phenol-terminated polycarbonate blend as an example, we demonstrate that the hydrodynamic boundary conditions for a flow of an adsorbing polymer melt are extremely sensitive to the structure of the epitaxial layer. Under shear, the adsorbed parts (chain ends) of the polymer melt move along the equipotential lines of the surface potential whereas the adsorbed additives serve as the surface defects. In response to the increase of the number of the adsorbed additives the surface layer becomes thinner and solidifies. This results in a gradual transition from the slip to the no-slip boundary condition for the melt flow, with a nonmonotonic dependence of the slip length on the surface concentration of the adsorbed ends.

Hydrodynamic slip boundary condition at chemically patterned surfaces: A continuum deduction from molecular dynamics

We investigate the slip boundary condition for flows past a chemically patterned surface. Molecular dynamics simulations show that fluid forces and stresses vary laterally along the patterned surface. A subtraction scheme is developed to verify the validity of the Navier slip boundary condition, locally, for the patterned surface. A continuum hydrodynamic model is formulated using the Navier-Stokes equation and the Navier boundary condition, with a slip length varying along the patterned surface. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from molecular simulations.

Transient Free Convection Fluid Flow in a Vertical Microchannel as Described by the Hyperbolic Heat Conduction Model

The transient hydrodynamics and thermal behaviors of fluid flow in an open-ended vertical parallel-plate microchannel are investigated analytically under the effect of the hyperbolic heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in this study. The effects of Knudsen number Kn and thermal relaxation time τ on the microchannel hydrodynamics and thermal behaviors are investigated using the hyperbolic and the parabolic heat conduction models. It is found that as Kn increases, the slip in the hydrodynamic and thermal boundary condition increases. Also, this slip increases as τ decreases.

Boundary Slip on Smooth Hydrophobic Surfaces: Intrinsic Effects and Possible Artifacts

We report an accurate determination of the hydrodynamic boundary condition of simple liquids flowing on smooth hydrophobic surfaces using a dynamic surface force apparatus equipped with two independent subnanometer resolution sensors. The boundary slip observed is well defined and does not depend on the scale of investigation from one to several hundreds of nanometers, nor on shear rate up to 5 x 10(3)s(-1). The slip length of 20 nm is in good agreement with theory and numerical simulations concerning smooth nonwetting surfaces. These results disagree with previous data in the literature reporting very high boundary slip on similar systems. We discuss possible origins of large slip length on smooth hydrophobic surfaces due to their contamination by hydrophobic particles.

Extending Uncertainty Analysis of a Hydrodynamic-Water Quality Modelling System using High Level Architecture (HLA)

Abstract This paper illustrates the coupling of water quality model components in High Level Architecture (HLA), a computer architecture for constructing distributed simulations. HLA facilitates interoperability among different simulations and simulation types and promotes reuse of simulation software modules. It was originally developed for military applications but the platform is finding increasing applicability for civilian purposes. The models from the Water Quality Analysis Simulation Program (WASP5) were implemented in HLA to extend its Monte Carlo uncertainty analysis capabilities. The models include DYNHYD (hydrodynamics), EUTRO (phytoplankton and nutrient dynamics) and TOXI (sediment and micropollutant transport). The uncertainty analysis investigated the impact of errors in the hydrodynamic parameters (weir discharge and roughness coefficients) and boundary conditions (upstream and tributary discharge) on the uncertainty in the water quality output variables. It was found that the contribution of the hydrodynamic parameter error to the water quality output uncertainty is comparable to that obtained from the error in the water quality parameters. The error in the boundary condition input data is also an important contributor to model uncertainty.

Distributed Sensitivity Analysis of Flood Inundation Model Calibration

Uncertainties in hydrodynamic model calibration and boundary conditions can have a significant influence on flood inundation predictions. Uncertainty analysis involves quantification of these uncertainties and their propagation through to inundation predictions. In this paper the inverse problem of sensitivity analysis is tackled, in order to diagnose the influence that model input variables, together and in combination, have on the uncertainty in the inundation model prediction. Variance-based global sensitivity analysis is applied to simulation of a flood on a reach of the River Thames (United Kingdom) for which a synthetic aperture radar image of the extent of flooding was available for model validation. The sensitivity analysis using the method of Sobol' quantifies the significant influence of variance in the Manning channel roughness coefficient in raster-based flood inundation model predictions of flood outline and flood depth. The spatial influence of the Manning channel roughness coefficient is analyzed by dividing the channel into subreaches and calculating variance-based sensitivity indices for each subreach. Replicated Latin hypercube sampling is used for sensitivity analysis with correlated input variables. The methodology identifies subreaches of channel that have the most influence on variance in the model predictions, demonstrating how far boundary effects propagate into the model and indicating where further data acquisition and nested higher-resolution model studies should be targeted.

Hydrodynamic Boundary Conditions Effects on Soret-Driven Thermosolutal Convection in a Shallow Porous Enclosure

Hydrodynamic Boundary Conditions Effects on Soret-Driven Thermosolutal Convection in a Shallow Porous Enclosure

Solvent Effect on Rotational Correlation Times of Symmetric Tetraalkylammonium Ions

The overall rotational correlation times of symmetric tetraalkylammonium ions, R4N+ (R = ethyl, n-propyl, n-butyl, and n-pentyl), in various solvents were determined by the measurements of the 13C NMR spin-lattice relaxation times and the nuclear Overhauser enhancement factors of each α-carbon, considering the contribution of the internal rotation around the N—C bond. Except in water, the observed solvent dependencies of the rotational correlation times, τr, showed good correlations with those predicted from an electrohydrodynamic (Hubbard–Onsager–Felderhof) model. The correlation times of R4N+ increased as the size of the alkyl groups became larger. In the case of the n-Bu4N+ and the n-Pen4N+ ion, the τ r values were similar to or even higher than those predicted by the HOF model under the stick hydrodynamic boundary condition, in spite of the fact that the ions were too small to allow the solvent to be regarded as a hydrodynamic or a dielectric continuum. A comparison of the results with the rotations of other pseudotetrahedral ions, e.g., tetraphenylborate and tetraphenylarsenium ions and with the translation of the R4N+ ions suggests that a considerable part of the rotational friction for R4N+ is brought about by pushing aside the solvent in the spaces between the alkyl groups of R4N+. A significant slowing in the rotation in water was observed for the n-Pr4N+, n-Bu4N+, and n-Pen4N+ions; the extent of this effect increased with increasing size of the alkyl group. The increase in friction was related to the hydrophobic hydration of the R4N+ ions.

Brownian Motion of a Rough Sphere and the Stokes−Einstein Law

Using molecular dynamics computer simulation, we have calculated the velocity autocorrelation function and diffusion constant for a variety of solutes in a dense fluid of spherical solvent particles. We explore the effects of surface roughness of the solute on the resulting hydrodynamic boundary condition as we naturally approach the Brownian limit (when the solute becomes much larger and more massive than the solvent particles). We find that when the solute and solvent interact through a purely repulsive isotropic potential, in the Brownian limit the Stokes−Einstein law is satisfied with slip boundary conditions. However, when surface roughness is introduced through an anisotropic solute−solvent interaction potential, we find that the Stokes−Einstein law is satisfied with stick boundary conditions. In addition, when the attractive strength of a short-range isotropic solute−solvent potential is increased, the solute becomes dressed with solvent particles, making it effectively rough, and so stick boundary conditions are again recovered.

Transport properties of nitrogen in single walled carbon nanotubes.

Transport properties including collective and tracer diffusivities of nitrogen, modeled as a diatomic molecule, in single walled carbon nanotubes have been studied by equilibrium molecular dynamics at different temperatures and as a function of pressure. It is shown that while the asymptotic decay of the translational and rotational velocity autocorrelation function is algebraic, the collective velocity decays exponentially with the relaxation time related to the interfacial friction. The tracer diffusivity in the nanochannel, which is comparable in magnitude with diffusivity in the equilibrium bulk phase, depends only weakly on the conditions at the fluid-solid interface, whereas the collective diffusivity is a strong function of the hydrodynamic boundary conditions and is found to be three orders of magnitude higher than self-diffusivity in carbon nanotubes and for the comparatively rough surface of the rare-gas tube it is one order of magnitude greater. A relationship between the collective diffusivity and the Maxwell coefficient describing wall collisions is obtained. The transport coefficients appear to be insensitive to the long-range details of the potential function.

Analytical and numerical solutions for alternative overpressuring processes: Application to the Callovo‐Oxfordian sedimentary sequence in the Paris basin, France

Previous studies that made use of basin models have shown that the normal geological evolution of the Paris basin does not generate the observed, albeit weak, excess pressures in some shale layers of the basin. Other processes that may have created the overpressures, currently neglected in such models, are investigated here. Terms accounting for osmotic effects and tectonic stress changes are successively added to the diffusivity equation. The effect of changes in outcrop boundary conditions is also calculated with a pseudo‐two‐dimensional analytical solution. These solutions are applied to the Callovo‐Oxfordian shale formation in the eastern part of the Paris basin, France. It is shown that a long‐term transient osmotic effect starting in the Tertiary could explain in part the observed excess pressures in the Callovo‐Oxfordian shale assuming effective diffusion coefficients of 1–5 × 10−12 m2 s−1 in line with the measurements and a pore radius b around 20 Å for the shales. However, because of the uncertainty on the value of the shale pore radius, additional head measurements and osmotic experiments on samples should be made to fully establish the possibility of an osmotic process. Our study also shows that recent changes in hydrodynamic boundary conditions could also explain excess pressure distribution in this shale layer. It is plausible that a combination of the two processes could best explain the distribution and intensity of the “overpressures.” Tectonic stress changes do not appear to be important; it is shown that for such processes, to maintain high pressures, strong and recent increase in tectonic compressive stress would be required.

Simulating two-dimensional thermal channel flows by means of a lattice Boltzmann method with new boundary conditions

Thermal boundary conditions for a doubled-populations BGK model are introduced and numerically demonstrated. The unknown thermal distribution functions at the boundary are assumed to be equilibrium distribution functions, with a counter-slip internal energy density which is determined consistently with Dirichlet and/or Neumann boundary constraints. The hydrodynamic boundary conditions are adapted to situations of engineering interest, and viscous heating effects are taken in account. The method is used to simulate channel flows; numerical results and theoretical solutions are found in satisfactory agreement for both hydrodynamic and thermal fields.

Surface roughness and interfacial slip boundary condition for quartz crystal microbalances

The response of a quartz crystal microbalance (QCM) is considered using a wave equation for the substrate and the Navier-Stokes equations for a finite liquid layer under a slip boundary condition. It is shown that when the slip length to shear wave penetration depth is small, the first-order effect of slip is only present in the frequency response. Importantly, in this approximation the frequency response satisfies an additivity relation with a net response equal to a Kanazawa liquid term plus an additional Sauerbrey “rigid” liquid mass. For the slip length to result in an enhanced frequency decrease compared to a no-slip boundary condition, it is shown that the slip length must be negative so that the slip plane is located on the liquid side of the interface. It is argued that the physical application of such a negative slip length could be to the liquid phase response of a QCM with a completely wetted rough surface. Effectively, the model recovers the starting assumption of additivity used in the trapped mass model for the liquid phase response of a QCM having a rough surface. When applying the slip boundary condition to the rough surface problem, slip is not at a molecular level, but is a formal hydrodynamic boundary condition which relates the response of the QCM to that expected from a QCM with a smooth surface. Finally, possible interpretations of the results in terms of acoustic reflectivity are developed and the potential limitations of the additivity result should vapor trapping occur are discussed.

Random fields of water surface waves using Wiener–Hermite functional series expansions

Random motions of irrotational gravity water surface waves on deep water are formulated using the so-called Wiener–Hermite functional series expansion, based on the ‘ideal random process’, i.e. the white noise. Such a procedure is known to differ fundamentally from moment expansions such as Gram–Charlier or Edgeworth series. The applications concern ‘free waves’ which are homogeneous in the horizontal plane and stationary in time. Starting from the basic hydrodynamic equation and boundary conditions, the general procedure for obtaining the equations for the deterministic kernels is described. First, the expansion is carried out with no approximation of the hydrodynamic equations but the expansion is limited to the first order. This defines the Gaussian part of the wave field. As expected, the nonlinearity of the hydrodynamic equations has effects on the dispersion relation through explicit frequency and acceleration terms whose physical interpretations are discussed. No attempt is made to solve the highly complicated coupled nonlinear integral kernels equations. Instead, Dirac kernel functions are chosen a priori as an approach to a narrowband random wave field. In this case, the nonlinearity is found to be characterized by a ‘statistical wave steepness’ having an upper limit value of order 0.42. As a second example, a non-Gaussian field is determined on the basis of the hydrodynamic equations truncated at second order in the wave amplitude. In the case of Dirac first-order kernels, the second-order nonlinear effect results in the generation of the second harmonic of the fundamental wave component. The ratio between the energy levels of these two components is found to compare well with standard results from laboratory experiments.