Joule–Thomson Effects on the Flow of Liquid Water

We present a revised form of the energy balance for the coupled thermodynamics of liquid water flowing in porous media and give examples of situations where a commonly used formulation based on transport of enthalpy leads to erroneous results. Assuming negligible contribution from kinetic energy as well as sources and sinks such as energy from radioactive decay, total energy conservation is reduced to a balance between changes in internal energy, enthalpy, conductive heat flux, and gravitational potential energy. The Joule–Thomson coefficient is defined as the change in temperature with respect to an increase in pressure at constant enthalpy. Because liquid water has a negative Joule–Thomson coefficient at low temperatures, at a constant gravitational potential water cools as it compresses and heats as it expands. If one ignores the gravitational energy, transport of enthalpy alone leads to water heating by 2 \(^\circ \) C per kilometer as it is brought up from depth. The corrected energy balance transports methalpy, which is enthalpy plus gravitational potential energy. Although the simpler form leads to small changes in the temperature profile for typical simulations, there are several instances where this effect may prove to be important. The most important impact of the erroneous form is probably in the field of geothermal energy production, where the creation of a few degrees of heat in a simulation could lead to miscalculation of power plant efficiencies.     

Effect of Dynamic Prehistory on Aerodynamics of a Laminar Separated Flow in a Channel Behind a Rectangular Backward‐Facing Step

The effect of dynamic prehistory of the flow and the channelexpansion ratio on aerodynamics of a steady separated laminar flow behind a rectangular backwardfacing step located in a planeparallel channel is numerically studied. It is shown that the boundary layer upstream of the flow separation exerts a strong effect on flow characteristics behind the step. A decrease in the boundarylayer thickness in the cross section of the step leads to a decrease in the separationregion length, and an increase in the channelexpansion ratio with a fixed initial boundarylayer thickness and Reynolds number leads to an increase in the separationregion length.     

Vapor Flow with Evaporation–Condensation on Solid Particles

Strongly nonequilibrium vapor (gas) flows in a region filled by solid particles are considered with allowance for particlesize variation due to evaporation–condensation on the particle surface. The study is performed by directly solving the kinetic Boltzmann equation with allowance for the transformation of the distribution function of gas molecules due to their interaction with dust particles.     

Nonlinear Electrohydrodynamic Stability of a Poiseuille Two–Layer Flow

The long–wave stability of the Poiseuille two–layer flow of homogeneous viscous dielectrics between plate electrodes under a constant potential difference is studied in an electrohydrodynamic approximation. A linear asymptotic stability analysis shows that surface polarization forces are a destabilizing factor, in addition to viscous stratification. The method of many scales is used to obtain the Kuramoto—Sivashinsky equation governing the weakly nonlinear evolution of the interface between the dielectrics. Within the framework of the approaches used, it is shown that nonlinear interactions limit perturbation growth and the interface does not fail even for a rather large potential difference.     

Resonance Waves in a Model of a Two‐Layered Liquid

With allowance for surface interaction between phases, the behavior of longwave perturbations at the interface between two layers of dissimilar liquids, which form resonance triplets described by a pseudodifferential equation, is studied.     

Calculation of Linear Stability of a Stratified Gas–Liquid Flow in an Inclined Plane Channel

Linear stability of liquid and gas counterflows in an inclined channel is considered. The full Navier–Stokes equations for both phases are linearized, and the dynamics of periodic disturbances is determined by means of solving a spectral problem in wide ranges of Reynolds numbers for the liquid and vapor velocity. Two unstable modes are found in the examined ranges: surface mode (corresponding to the Kapitsa waves at small velocities of the gas) and shear mode in the gas phase. The wave length and the phase velocity of neutral disturbances of both modes are calculated as functions of the Reynolds number for the liquid. It is shown that these dependences for the surface mode are significantly affected by the gas velocity.     

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer–Viscous-Liquid-Layer System

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier–Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.     

Numerical and Experimental Investigation of Liquid Residue in 90° Bend Microchannel Based on Gas–Liquid Two-Phase Flow

The microfluidic chip for nucleic acid detection in vitro is an essential application of microfluidic technology to the process of in vitro diagnosis. The 90° bend microchannels in chip designed for facilitating assay reagent delivery may cause reagent residues and cast mutual contamination between detection reagents, which significantly affects the detection accuracy. In this paper, a two-dimensional gas–liquid two-phase flow model is constructed to simulate the liquid residue phenomenon. Using the results of simulation, the residual liquid generation can be observed and the area of residual liquid can be obtained. The accuracy of the numerical simulation is verified by comparison with the experimental results. The effects of the fillet radius R, the diameter ratio d₁/d₂ of the vertical to horizontal sections, the flow velocity v, and the surface roughness R_a on the residual amount are studied. We find that the fillet radius is inversely proportional to the residual amount within the range v = 20–100 mm/s and there is almost no liquid residue in the channel when the radius increases to R = 1 mm. When the channel diameter ratio d₁/d₂ increases, the liquid residual amount also increases by approximately 98%. The increased surface roughness R_a significantly increases the residual amount. The results of this study provide a reference for the optimal design of microchannels on chips.

     

Steady Flow of a Navier–Stokes Liquid Past an Elastic Body

We perform a mathematical analysis of the steady flow of a viscous liquid, L{\mathcal{L}} , past a three-dimensional elastic body, B{\mathcal{B}} . We assume that L{\mathcal{L}} fills the whole space exterior to B{\mathcal{B}} , and that its motion is governed by the Navier–Stokes equations corresponding to non-zero velocity at infinity, v _∞. As for B{\mathcal{B}} , we suppose that it is a St. Venant–Kirchhoff material, held in equilibrium either by keeping an interior portion of it attached to a rigid body or by means of appropriate control body force and surface traction. We treat the problem as a coupled steady state fluid-structure problem with the surface of B{\mathcal{B}} as a free boundary. Our main goal is to show existence and uniqueness for the coupled system liquid-body, for sufficiently small |v _∞|. This goal is reached by a fixed point approach based upon a suitable reformulation of the Navier–Stokes equation in the reference configuration, along with appropriate a priori estimates of solutions to the corresponding Oseen linearization and to the elasticity equations.     

Effect of Inertial Terms on Fluid–Porous Medium Flow Coupling

The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundary-layer flow overlying the Darcy–Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different short-wave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.     

Effect of Allowance for Small‐Scale Perturbations of the Carrier Phase on Properties of the System of Equations of a Two‐Fluid Flow with Incompressible Phases

The effect of the fluctuating components of kinetic energy and stress tensor of the carrier phase, which were previously obtained by the cell technique, on the properties of the system of equations of a gas–liquid flow with incompressible phases is considered. It is shown that the characteristic properties of this system and also the possibility of modeling the Zuber–Findlay empirical relation are determined by the tensor of fluctuating stresses of the carrier phase.     

Effect of Transitional Nonequilibrium on the Molecular–Dissociation Rate in a Hypersonic Shock Wave

The problem of the influence of a nonequilibrium (non–Maxwellian( distribution of translational energy over the degrees of freedom of molecules on the rate of their dissociation in a hypersonic shock wave is considered. An approximate beam—continuous medium model, which was previously applied to describe a hypersonic flow of a perfect gas, was used to study translational nonequilibrium. The degree of dissociation of diatomic molecules inside the shock–wave front, which is caused by the nonequilibrium distribution over the translational degrees of freedom, is evaluated. It is shown that the efficiency of the first inelastic collisions is determined by the dissociation rate exponentially depending on the difference in the kinetic energy of beam molecules and dissociation barrier.     

Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow

The influence of small cylindrical bluntness of the leading edge of a flat plate on formation of spatial structures in a nominally two-dimensional supersonic compression corner flow at the Mach number M∞ ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperature-sensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 · 10⁶–2.55 · 10⁶) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces spanwise oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum deviations of the Stanton number reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of spanwise oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of three-dimensional Navier–Stokes equations are obtained for some test conditions. The computed results are in good agreement with experimental data, which points to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.     

The Effect of the Walls of an Arbitrary Tank in the Problem of Separation–Free Impact on a Floating Body

An algorithm for constructing an asymptotic power series for large depths is proposed. It allows one to use the well–known solution of the problem of impact on a rigid body floating on the surface of a fluid half–space to obtain an approximate solution of the impact problem for the same body floating on the surface of a fluid in a bounded basin. The case where the domain occupied by the fluid has two perpendicular planes of symmetry is considered. Asymptotic expressions are given for the velocity potential on the wetted part of the body surface and for the added mass. Examples of solutions are considered.     

A Three-Dimensional Model of Two-Phase Flows in a Porous Medium Accounting for Motion of the Liquid–Liquid Interface

A new three-dimensional hydrodynamic model for unsteady two-phase flows in a porous medium, accounting for the motion of the interface between the flowing liquids, is developed. In a minimum number of interpretable geometrical assumptions, a complete system of macroscale flow equations is derived by averaging the microscale equations for viscous flow. The macroscale flow velocities of the phases may be non-parallel, while the interface between them is, on average, inclined to the directions of the phase velocities, as well as to the direction of the saturation gradient. The last gradient plays a specific role in the determination of the flow geometry. The resulting system of flow equations is a far generalization of the classical Buckley–Leverett model, explicitly describing the motion of the interface and velocity of the liquid close to it. Apart from propagation of the two liquid volumes, their expansion or contraction is also described, while rotation has been proven negligible. A detailed comparison with the previous studies for the two-phase flows accounting for propagation of the interface on micro- and macroscale has been carried out. A numerical algorithm has been developed allowing for solution of the system of flow equations in multiple dimensions. Sample computations demonstrate that the new model results in sharpening the displacement front and a more piston-like character of displacement. It is also demonstrated that the velocities of the flowing phases may indeed be non-collinear, especially at the zone of intersection of the displacement front and a zone of sharp permeability variation.     

Effect of Free‐Stream Turbulence on the Flow Structure near a Wedge and the Windward Side of an Airfoil

The flow structure behind wire grids is studied for flows with a low subsonic velocity, and the effect of grids on the boundarylayer flow structure is considered. It is shown that the meanvelocity inhomogeneity induced by the grid does not disappear until a distance of 925 calibers downstream of the grid is reached. Liquidcrystal thermography combined with hotwire measurements made it possible to find the source of steady largescale streamwise vortex structures in the boundary layer on a wedge and on an airfoil and to determine the parameters of these structures.     

Effect of Varying Test Parameters on Elastic–plastic Properties Extracted by Nanoindentation Tests

A systematic experiment was performed in an effort to investigate how the levels of certain test parameters affect the values of elastic modulus, hardness, yield stress, and strain hardening constant obtained using nanoindentation test. Maximum applied load, loading (unloading) rate, and hold time at maximum load were varied at three levels. The effects of these testing parameters were investigated through a three-level, full factorial design of experiment. The experiments were conducted on ultrafine Al-Mg specimens that were mechanically extruded. Both longitudinal and transverse extrusion directions were examined to investigate effects of anisotropy on mechanical properties and evaluate the persistence of observed variations due to test parameters on different materials orientations. An indentation size effect (ISE) was observed demonstrating that maximum load—and thereby maximum indentation depth—can have a significant effect on values of hardness and elastic modulus. Hardness values decreased with higher loading rates, and higher rates of unloading resulted in higher values of elastic modulus (5–10 GPa increases). Strain-hardening exponent showed a decreasing trend with increasing loading rate while yield stress exhibited a consistent correlation to hardness across all studied parameters. The material exhibited very little creep during the hold period, and values of the calculated properties were not significantly altered by varying the length of the hold time. Anisotropy effect was observed, particularly in the values of yield strength. This is attributed to the preferred grain orientation due to extrusion.     

Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow

In this work we study the long time inviscid limit of the two dimensional Navier–Stokes equations near the periodic Couette flow. In particular, we confirm at the nonlinear level the qualitative behavior predicted by Kelvin’s 1887 linear analysis. At high Reynolds number Re, we prove that the solution behaves qualitatively like two dimensional Euler for times \({{t \lesssim Re^{1/3}}}\), and in particular exhibits inviscid damping (for example the vorticity weakly approaches a shear flow). For times \({{t \gtrsim Re^{1/3}}}\), which is sooner than the natural dissipative time scale O(Re), the viscosity becomes dominant and the streamwise dependence of the vorticity is rapidly eliminated by an enhanced dissipation effect. Afterwards, the remaining shear flow decays on very long time scales \({{t \gtrsim Re}}\) back to the Couette flow. When properly defined, the dissipative length-scale in this setting is \({{\ell_D \sim Re^{-1/3}}}\), larger than the scale \({{\ell_D \sim Re^{-1/2}}}\) predicted in classical Batchelor–Kraichnan two dimensional turbulence theory. The class of initial data we study is the sum of a sufficiently smooth function and a small (with respect to Re^?1) L² function.