Momentum Transport Equations Research Articles

A pair of entrapping or coalescing bubbles affected by convection during downward solidification

In this study, the development of solute concentration and velocity fields of a pair of entrapping or coalescing bubbles during downward solidification is provided. The gas-induced pores in the metal not only deteriorates the properties of the processed workpiece by causing stress concentration and defects within the material, but pore formation in sea ice also plays an important role in global warming. Using COMSOL Multiphysics version 5.2, the unsteady, two-dimensional transport equations of mass, momentum, energy, and concentration are solved. The results show that bubble coalescence is facilitated by decreasing solid thermal conductivity and interpore spacing. Unlike the symmetric distribution of concentration observed with a low Henry's law constant and liquid solute diffusivity, an asymmetric distribution occurs, with high and low concentration gradients near the leading and rear edges of each bubble, respectively, due to the liquid velocity from the upstream direction. An outward flow in the opposite direction occurs near the triple-phase line, resulting in an inflection region in the iso-concentration field. The thickness of the concentration boundary layer surrounding the pores also decreases with decreasing Henry's law constant and liquid solute diffusivity, as well as with increasing ambient pressure, gravitational acceleration, solid thermal conductivity, and surface tension. The predicted contact angle during solidification aligns well with Abel's equation. Solute segregation associated with the formation of multiple pores can be controlled.

A numerical study of double flow focusing micro-jets

Purpose Double flow-focusing nozzles (DFFNs) form a coaxial flow of primary liquid with micro-crystalline samples, surrounded by secondary liquid and focusing gas. This paper aims to develop an experimentally validated numerical model and assess the performance of micro-jets from a DFFN as a function of various operating parameters for the water–ethanol–helium system, revealing the jet's stability, diameter, length and velocity. Design/methodology/approach The physical model is formulated in the mixture-continuum formulation, which includes coupled mass, momentum and species transport equations. The model is numerically formulated within the finite volume method–volume of fluid approach and implemented in OpenFOAM to allow for a non-linear variation of the fluid's material properties as a function of the mixture concentration. The numerical results are compared with the experimental data. Findings A sensitivity study of jets with Reynolds numbers between 12 and 60, Weber numbers between 4 and 120 and capillary numbers between 0.2 and 2.0 was performed. It was observed that jet diameters and lengths get larger with increased primary and secondary fluid flow rates. Increasing gas flow rates produces thinner, shorter and faster jets. Previously considered pre-mixed and linear mixing models substantially differ from the accurate representation of the water–ethanol mixing dynamics in DFFNs. The authors demonstrated that Jouyban–Acree mixing model fits the experimental data much better. Originality/value The mixing of primary and secondary liquids in the jet produced by DFFN is numerically modelled for the first time. This study provides novel insights into mixing dynamics in such micro-jets, which can be used to improve the design of DFFNs.

Process intensification in the direct contact membrane distillation (DCMD) desalination by patterning membrane surface: A CFD study

In this research, the impact of pattern geometry on the intensification of the performance of surface patterned membranes for saline water desalination by direct contact membrane distillation (DCMD) is investigated by computational fluid dynamics (CFD) simulation. The Comsol Multiphysics software was applied to solve the governing transport equations for heat, momentum, and mass transfer. The result of the model was validated by the published experimental data, and the maximum deviation was <10 %. The target was to maximize the permeate flux by altering surface pattern geometry and dimensions. Based on the previous studies, a prism pattern was chosen in this work, and the influences of pattern type (3 types), pattern dimension (25–150 µm valley depth), and the distance between the valleys (0–400 µm) were studied on the temperature polarization coefficient (TPC) and DCMD permeate flux. The results showed that the pattern with a valley depth of 25 µm and a distance between the valleys of 300 µm had the best performance in DCMD operation. In this situation and feed temperature of 80 °C, a TPC of 0.78 and a water flux of 49.3 kg m-12.h were attained. The characteristics of flow close to the patterned membrane surface were also investigated, and it was observed that there are weak shear stresses in the lower zone of the valleys, while stronger shear stresses are created in the upper regions that are responsible for improving the TPC and water flux in the patterned membranes.

Entropy Generation in Third-Grade Non-Newtonian Fluid Flow and Heat Transport Through Porous Medium in a Horizontal Channel under Heat Generation

In this study, entropy production in flow along with heat transport of non-Newtonian fluid via porous medium, is analyzed. For fluid flow via porous medium, a modified Darcy resistance term, is taken in the momentum equation for third-grade fluid. Temperature-dependent viscosity is considered using Vogel’s model viscosity. Using adequate transformations, the momentum and heat transport equation are reduced to non-dimensional form and solved analytically invoking homotopy analysis method on MATHEMATICA software. Effects of parameters arising in the study are depicted by graphs on velocity distribution, temperature distribution, and entropy production with Bejan number and discussed. For validity of current findings, the values of velocity and temperature are computed for particular values of the parameters and equated with previously published results, excellent agreement achieved. Furthermore, skin-friction coefficient and Nusselt number values are expressed in tabular form for various values of relevant parameters and discussed. It is noticed that slip parameters $\left( \gamma \right)$ and $\left( \beta \right)$ reduce the entropy generation number $\left( NS \right)$. Also noticed that skin friction coefficient upsurges with rising velocity slip parameter $\left( \gamma \right)$ value while, effect of temperature slip parameter $\left( \beta \right)$ is observed to lessen Nusselt number in the absolute sense. HIGHLIGHTS Entropy production in third grade non-Newtonian fluid flow and heat transfer in a channel via porous medium is investigated in the presence of a heat source. Slip boundary conditions are applied. The resulting governing equations are solved analytically using the homotopy analysis method (HAM). Maximum entropy production observed near the lower wall of channel and Bejan number attains maximum value in middle of the channel. GRAPHICAL ABSTRACT

Three-dimensional thermal-electrochemical-hydrodynamic numerical study of vanadium redox flow battery with different flow fields and non-homogeneously compressed electrode

This paper presents a concise 3D numerical study of Vanadium Redox Flow Batteries (VRFBs) with different flow field designs and non-homogeneously compressed electrodes. The model integrates mass, momentum, charge, and energy transport equations, including reaction kinetics for vanadium species. Four flow field designs (conventional, parallel, serpentine, and interdigitated) are evaluated for heat distribution uniformity. The model accounts for non-uniform electrode properties due to compression. Numerical results are validated against experimental data, exploring the impact of operating parameters such as current density, flow rate, and temperature on thermal behavior. The study also compares heat generated by electrochemical reactions, ohmic losses, and chemical activation across different flow fields. The findings revealed the highest temperature gradient and non-uniformity (in terms of temperature) with conventional designs followed by interdigitated, parallel and serpentine. Importantly, the study consistently highlights elevated temperatures in the discharge condition across all configurations. This emphasizes the need for precise temperature control to prevent VO₂+ precipitation. These insights from VRFB optimization efforts are thoroughly presented in this paper.

Unsteady Dean flow between concentric circular cylinders in the presence of a uniform axial magnetic field

An analysis is carried out on the unsteady Dean flow of an incompressible electrically conducting viscous fluid between two concentric, stationary permeable circular cylinders in the presence of magnetic field of low intensity. The flow phenomenon is important in view of its biological as well as industrial applications, particularly in polymer industries for designing flows in cylindrical shaped pipes/tubes. The novelty of the study is to analyze the effect of electromagnetic body force which comes into play due to interaction of magnetic field with conducting fluid in flow. The cross flow due to suction/injection, azimuthal pressure gradient, and the Lorentz force (electromagnetic body force) are considered in the momentum transport equation. The mathematical model and the corresponding governing equations are solved in two methods; one is analytical using special function and another one is semi analytical approach, i.e. Laplace transform in conjuction with Riemann–Sum approximation for inversion. The study reveals the effects of magnetic parameter, suction/injection parameter and radii ratio of two concentric cylinders forming annular region. The striking outcomes which fulfills the design requirements are as follows. The applied radial magnetic field resulting electromagnetic body force on the flow, accelerates the circumferential velocity which energizes the industrial setup (flow model) to enhance faster productivity. Moreover, the curves of skin friction at R = λ posses critical points serving as benchmark for engendering flow instability.

Unstructured Conservative Level-Set (UCLS) method for reactive mass transfer in bubble swarms at high density ratio

This research presents a parallel Unstructured Conservative Level-Set (UCLS) method for reactive mass transfer in bubbles with a high-density ratio. This method uses the multiple-marker UCLS approach to circumvent the numerical coalescence of bubbles, combined with the finite-volume method to discretize transport equations on 3D collocated unstructured meshes. The fractional-step projection method solves the pressure-velocity coupling. The central difference scheme discretizes the diffusive term, whereas convective term within the momentum transport equation, level-set advection equations, and mass transfer equation are discretized by unstructured flux-limiters schemes. Such a combination of numerical techniques preserves the numerical stability in bubbly flows with a high Reynolds number and high-density ratio. Numerical and physical findings on the effect of physical properties ratios on the reactive mass transfer are reported, including their effect on the Reynolds number, interfacial area and Sherwood number.

DNS of Marangoni effects on a suspension of droplets in microgravity using the unstructured conservative level-set method

The multi-marker unstructured conservative level-set (UCLS) method for two-phase flow with variable surface tension is used for the Direct Numerical Simulation of thermocapillary-driven motion of a bi-dispersed suspension of droplets in microgravity. The so-called Marangoni stresses induced by surface tension gradients on the interface lead to a coupling of the momentum transport equation and the thermal energy transport equation. The finite-volume method discretizes the transport equations on three-dimensional collocated unstructured meshes. The UCLS method performs interface capturing with mass conservation of the fluid phases, whereas the multiple marker approach circumvents the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters schemes discretize the convective term in transport equations. Numerical and physical findings are reported.

Heat transfer model analysis of fractional Jeffery-type hybrid nanofluid dripping through a poured microchannel

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

Entropy generation for thermo-magnetic fractional order convective flow in complex porous enclosures: a numerical study

PurposeThis study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.Design/methodology/approachIn the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (Sff), heat transfer (Sht) and magnetic field (Smf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102≤Ra≤104), Hartmann number (0≤Ha≤20) and fractional order parameter (0<α<1) with respect to time.FindingsIt has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Beht), fluid friction (Beff) and magnetic field (Bemf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 102 to 104 shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf→1 shows the dominance of the magnetic field irreversibility in the total entropy generation.Practical implicationsRecently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.Originality/valueThe fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

Analysis of particle dispersion and cavity formation during bulk particle water entry using fully coupled CFD-DEM-VOF approach

This paper presents the development and validation of a fully coupled computational fluid dynamics—discrete element method—volume of fluid (CFD-DEM-VOF) model to simulate the complex behavior of particle-laden flows with free surfaces. The coupling between the fluid and particle phases is established through the implemented continuity, momentum, and alpha transport equation. The coupled particle forces such as drag, pressure gradient, dense virtual mass, viscous, and interface forces are also integrated, with drag and dense virtual mass forces being dependent on local porosity. The integrated conservative alpha transport equation ensures phase volume conservation during interactions between particles and water. Additionally, we have implemented a trilinear interpolation method designed to operate on unstructured hexahedral meshes. This method has been tested for its ability to properly resolve the coupling effects in the numerical simulations, particularly in cases with a relatively low cell-size ratio. The model is validated through three distinct test cases: single particle water entry, dam break with particles, and water entry of a group of particles case. The experimental setup is built to study the dynamics of the water entry of a group of particles, where three key flow features are analyzed: the evolution of average particle velocity, cavity shape, and particle dispersion cloud profiles in water. The tests involve four different scenarios, including two different water levels (16.1 and 20.1 cm) and two different particle densities (2650 and 4000 kg/m3). High-speed videometry and particle tracking velocimetry (using ImageJ/TrackMate) methods are employed for experimental data acquisition. It is demonstrated that numerical results are in excellent agreement with theoretical predictions and experimental data. The study highlights the significance of vortices in cavity shaping and particle dispersion. The validated CFD-DEM-VOF model constitutes a robust tool for simulating particle-laden flows, contributing valuable insights into the complex interplay between particles and fluids.

A NUMERICAL STUDY ON THE REDUCTION OF GREENHOUSE GASEOUS COMPONENT (CO2) DUE TO THE ADDITION OF H2 IN THE FUEL STREAM OF THE COUNTERFLOW CH4/AIR DIFFUSION FLAME

In this study, a series of 1-D and steady-state numerical simulations have been performed for the prediction of the effect of the addition of H2 on the characteristics of a non-sooting counterflow CH4/Air diffusion flame using detailed chemical reaction model, which is composed of 325 elementary chemical reactions and 53 chemical species. Under the steady-state assumption, a set of one-dimensional transport equations of mass, momentum, species, and energy along with the equation of state has been solved numerically at the atmospheric conditions over the counterflow configuration by exploiting an efficient numerical code, OPPDIF (a Fortran Program for Computing Opposed-Flow Diffusion Flames). The grid adaption technique has been used to achieve better convergence as well as to ensure the maximum accuracy of the simulated results. It is found that the flame temperature is increased due to the addition of H2 with CH4, which is injected into the fuel stream. The elevation in the temperature is caused by the augmentation of the integrated heat release rate of the elementary reactions supported by the active radicals (H, O, and OH), which are generated by the higher reactivity of H2. Besides, it is found that the mole fractions of H2O are increased as the percentage of H2 in the loading fuel (CH4) is increased and also, it is identified that the chain propagating reaction, OH + H2 =&gt; H2O + H is dominating one which produces highest amount of H2O. Furthermore, it is noticed that the indirect greenhouse gas or precursor, CO is reduced when H2 is added to CH4. Consequently, the mole fraction of the principle greenhouse gas, CO2 is decreased significantly when the fuel, CH4 percentage is modified by the higher percentage of H2. The sensitivity analysis of elementary reactions reveals the fact that the chemical reaction: OH + CO =&gt; H + CO2 is a dominating reaction in producing a lower amount of CO2 when the volume fraction of H2 is increased in the fuel (CH4) stream. In the presence of 75 % H2 in CH4, the pressure-dependent reaction, O + CO (+M) =&gt; CO2 (+M) appears as another chemical route that also generates greenhouse gas, CO2 but its contribution is negligibly small.

CFD simulation of osmotic membrane distillation using hollow fiber membrane contactor: Operating conditions and concentration polarization effects

Inorganic salts, when present in high concentrations, can disrupt the osmotic balance of aquatic organisms, leading to physiological and ecological harm. Osmotic membrane distillation (OMD) is an emerging technique for recovering inorganic salts from wastewater. The process involves the transfer of water vapor from a feed solution (FS) to a permeate stream due to the difference in vapor pressure across a hydrophobic membrane. It thus results in a concentrated solution at the feed outlet and purified water at the permeate side. OMD is preferred due to its straightforward scale-up and low energy requirements. In this research, a steady state 2-D axisymmetric computational fluid dynamics (CFD) model is developed to study the recovery of sodium carbonate (Na2CO3) from aqueous feed solution through OMD in a hollow fiber membrane contactor (HFMC). Aqueous sodium chloride (NaCl) solution was taken as an osmotic solution (OS). The numerical convection-diffusion mass, momentum transport, and Happel equations were scripted in COMSOL Multiphysics™ version 6.0 software. The model computed the water transport from FS to OS. Computed water flux well matched with the literature based experimental results. Simulations were carried out to investigate the parametric effects, including Reynold’s number, FS and OS concentration and the module geometrical parameters to establish an optimized operating conditions and module geometry and to achieve the desired FS concentration. Results showed that a 2-fold rise in OS concentration increased the transmembrane water flux 4-fold. However, the flow rates of both FS and OS did not significantly affect the flux. On the other hand, concentration polarization (CP) showed dependence on the FS concentration, tortuosity, and Reynolds number. A membrane tortuosity of 1.6, feed concentration of 75 g L−1, OS concentration of 300 g L−1, and a FS Reynolds number in the turbulent flow range can result in higher transmembrane flux and lower chances of CP development.

Modeling of toroidal momentum transport induced by neoclassical toroidal viscosity torque for ITER scenarios

Neoclassical toroidal viscosity (NTV) torque caused by resonant magnetic perturbation (RMP) and the induced toroidal momentum transport are investigated for International Thermonuclear Experimental Reactor (ITER) scenarios through numerical modeling. The NTV torque is calculated using the NTVTOK code including the bounce-drift resonant effect, and the toroidal rotation evolution is modeled by solving a toroidal momentum transport equation that couples momentum source (NTV torque) and the momentum diffusion effect. The variation of RMP coil phasing (defined as toroidal phase difference between different rows of RMP coils) results in different types of plasma response and hence different features of NTV torque and toroidal momentum transport. The bounce-drift resonant effect enhances NTV torque and induces more significant toroidal rotation variation than simulations that adopt the bounce-averaged NTV model. With the initial rotation of the ITER design, plasma rotation is braked by NTV torque, but it may be sustained at moderate amplitude due to electron contributions to NTV torque. It is also found that initially static or slowly rotating plasma can be accelerated by NTV torque either toward co- Ip or counter- Ip ( Ip indicates plasma current) direction, indicating that NTV torque can be regarded as a momentum source for plasma with low torque injection; for instance, radio-frequency heated plasma.

Reduced-order-modeling of the transient starting in supersonic passages

Characterizing the time scales of starting in supersonic passages is essential for future aerospace propulsion systems, such as supersonic intakes, Rotating Detonation Engines, and power generation systems based on Organic Rankine Cycles. This paper first compares 2D URANS results with 1D Euler results to identify the equations that govern the acceleration and deceleration of the strong shock during the starting process's time evolution. Secondly, we characterized the effect of the frequency of pulsating flows on the starting process; intermediate frequencies around 1 kHz show best startability while higher and much lower frequencies can cause unstarting. Finally, using the governing terms for the shock acceleration and deceleration in the momentum transport equation, a reduced-order model was developed and coupled with an optimization algorithm to enable rapid designs with improved flow starting capability. An optimized design demonstrated dominant startability using URANS simulations in comparison to two other geometries. The developed method represents an essential tool for reduced time-to-market solutions for aerospace propulsion components, such as inlets, supersonic turbomachinery, and nozzles.

Mixed convection flow in a channel with a dimpled section and adiabatic cylindrical obstacle under the influence of magnetic and Joule effects

This study investigates the mixed convection flow in a channel with a dimpled section and an adiabatic cylindrical obstacle under the influence of a magnetic field. The channel has a heated dimpled portion, while the flat horizontal walls are adiabatic. The energy equation considers the Joule heating effect, and the resulting momentum and thermal transport equations are numerically solved using the Galerkin weighted residual finite element method. The study discusses the flow and heat transfer characteristics for different values of the Joule heating parameter, Reynolds, Hartman, and Rayleigh numbers. The results show that increasing Hartmann and Joule heating parameters reduce average heat transfer rates while increasing Prandtl, Reynolds, and Rayleigh numbers enhances it. This analysis's outcomes will help design Ohmic heating systems like magnetic fluid power actuators and thermal processing gadgets for particulate food products. The novel quantitative findings in this study include enhancement in heat transfer with increasing Prandtl, Reynolds, and Rayleigh numbers. Furthermore, the adiabatic cylindrical obstacle near the dimpled section significantly affects the heat transfer rates, resulting in complex flow patterns. The results of this study can be used in magnetic fluid power actuators, thermal processing gadgets for particulate food products, and heat exchangers.

Transient mixed convection in a cylindrical cavity with a rotating finned cylinder

This article presents a numerical study of horizontal ring mixed convection with a heated inner cylinder equipped with two fins. Thermal buoyancy forces are maintained by considering the inner and outer cylinders at different uniform temperatures. The flow is generated by the rotation of the inner cylinder with a constant angular velocity (ω) in the counter-clockwise direction while the outer cylinder is held fixed. A finite volume scheme is adopted using the SIMPLE algorithm to solve the transport equations for continuity, momentum and energy. Simulations are made for various combinations of rotating Reynolds (Re = 0 to 1500) and Grashof numbers (Gr = 10 to 106). First, we focused on the criteria and parameters controlling the fully developed periodic regime. Thereafter, the heat transfer rates analyzed through the averaged Nusselt number (instant and over a period) highlights a complex phenomenon. For moderate Grashof numbers (Gr ≤ 103) the overall Nusselt number is not affected by Gr further, Re = 750 constitute a limit for the improvement of the heat transfer beyond which it decreases strongly. For larger Gr (>103), the reverse phenomenon occurs, i.e., the overall mean Nusselt number grows with Gr as Re < 750, then decreases for higher values.

Derivation of acoustical streaming equations for nonlinear and dispersive fluids

The equations of streaming generated by an acoustic mod propagating in a nonlinear dispersive medium (exhibiting absorption and dispersion of phase sound speed) are derived with an arbitrarily shaped incident acoustical field assumed. This field may be periodic or non-periodic. A general dispersion model represented by a convolution operator taking into account relaxation effects was taken into account. Making the assumption of a periodic acoustic field from the general streaming equation.The quasi-stationary flow is driven by a force given by the average value of the dispersion operator with respect to the velocity and acoustic pressure fields. In the spectral representation, it is given by the weighted spectral power density distribution of the acoustic field. The weight of the distribution is the dispersion coefficient - the eigenvalue of the dispersion operator. A new result also reveals the effect of the refractive index deviation on the driving force of streaming. The possibility of generalizing the description of streaming in the simplest case of a non-Newtonian fluid was analyzed. The Reiner-Revlin model of a simple liquid was assumed. It was also noted that the streaming model in the Maxwell liquid is analytically solvable. It was found that asymptotic states of streaming in this model and the Navier-Stokes model are identical.The derivations use new methods different from those used so far. They are based on the separation of nonlinear modes in the momentum transport equation and on the properties of the Gauss-Weierstrass function for the Fick diffusion operator. So far, the method of successive approximations has been used. The consistency of the obtained equations with the assumptions was checked. The obtained formulas generalize the known descriptions of the form of forces driving streaming and extend their application to the case of nonlinear propagation.

Closure modeling for the conditional pressure gradient in turbulent premixed combustion

In turbulent premixed combustion, turbulence is affected by both the influence of combustion heat release and turbulent shear effects. At low Karlovitz number, heat release effects are more dominant than turbulent shear effects, but, at high Karlovitz number, turbulent shear effects dominate the turbulence dynamics. Closure models for the velocity and scalar fields that only account for one of those effects are incapable of generally describing combustion-turbulence interactions at any finite Karlovitz number. A manifold-based turbulence model that solves the conditional mean momentum transport equation conditioned on a progress variable has the potential to provide such a general description, but closure models for the equation are required. Among the unclosed terms, the conditional mean pressure gradient is significant at both low and high Karlovitz numbers but has fundamentally different behaviors in each regime. In this work, a general closure model is developed to capture the conditional pressure gradient in both Karlovitz number regimes by considering heat release and turbulent shear effects. The deviation of the conditional pressure gradient from the unconditional pressure gradient is modeled with two components. One represents the pressure decrease across the flame due to combustion heat release, and the other represents the hydrodynamic pressure fluctuations due to turbulent shear. The heat release component depends on the heat release rate and the flame-normal vector, and the turbulent shear component depends on the conditional Reynolds stresses and the gradient of the progress variable probability density function. The model is validated against Direct Numerical Simulations of spatially-evolving turbulent premixed hydrogen/air planar jet flames at low and high Karlovitz numbers. The proposed model well captures the conditional pressure gradient at both Karlovitz numbers and shows a natural transition of its dominant term: the heat release component at low Karlovitz number and the turbulent shear component at high Karlovitz number.

Heat and mass diffusion to williamson fluid streaming through a tube with multiple stenoses while subjected to periodic body acceleration

This article examines a mathematical framework that describes the versatile behavior of heat and mass exchange in blood flowing through a narrowed vessel having multiple stenoses. The geometry of a channel having multiple stenoses with an asymmetrical axial axis and a symmetrical radial axis can be visualized by applying a suitable mathematical expression. The geometry of the chosen model considers the height and shape of stenoses. The modification in shape parameter is used to capture variations in the shape of the stenoses in the artery. The blood is supposed to be isochoric (incompressible), while its rheological behavior is characterized by Williamson’s fluid model. The transfer of momentum is analyzed using the equation of motion in cooperation with the continuity equation. In addition, the equations of heat conduction and diffusion are utilized, respectively, to illustrate the distributions of heat and mass. Simplified forms of momentum, mass, and heat transport equations are achieved by incorporating dimensionless quantities and moderate stenosis conditions. A well-known explicit finite difference approach is utilized to solve the emergent non-linear system of governing equations numerically. The influence of different evolving parameters on the flow field along with mass and heat distributions is illustrated through various plots.