Modified Peclet Number Research Articles

Effects of non-Darcy mixed convection over a horizontal cone with different convective boundary conditions incorporating gyrotactic microorganisms on dispersion

This paper investigates the influence of dispersion impact on mixed convection flow over a horizontal cone within a non-Darcy porous medium. Multiple convective boundary conditions are applied to address the heat, mass and motile microorganism transfer phenomena. This paper incorporates the dispersion effect for gyrotactic microorganisms due to biological and environmental applications. By imposing appropriate similarity transformations, the nonlinear partial differential equations governing flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations & then solved using the MATLAB BVP4C function. The computation of grid independence test is analyzed for different flow profiles to show the precision of the points. In a few instances, our present numerical data is compared with previously published works, leading to excellent agreement. The non-Darcy effect, as well as mixed convection values from 0.1 to 0.9 and buoyancy parameters from 0.2 to 0.8, all significantly affects the velocity profile. The reduction in the microorganism profile is brought on by the increase in the bioconvection Lewis parameter and bio convection peclet number between 0.3 and 1. In the absence of dispersion, the variation of Biot numbers between 0.5 and 2, favor heat, mass, and motile microorganism transfer the most in the range of mixed convection parameter 0.5 to pure forced convection 1. Thermal, solutal and microorganism dispersion coefficients a, b, c that lie between frac{1}{7} and frac{1}{3} and higher values of modified peclet number ranges from 2 to 10 cause increased dispersion effects which lower flow transfer rates mostly in forced convection regime.

Effect of conjugate heat transfer on the thermo-electro-hydrodynamics of nanofluids: entropy optimization analysis

We investigate, in this analysis, the entropy generation characteristics associated with the transport of nanofluid in a microfluidic channel under the combined influences of applied pressure gradient and electrical forcing. In our study, the nanofluid is subjected to an asymmetric cooling at the channel walls, while the conductive transport of heat through the channel walls is also taken into account. We show that the underlying thermo-electro-hydrodynamics of nanofluids in the channel lead to entropy generation, attributed to the irreversibilities associated with heat transfer, viscous dissipation, and Joule heating effects. We establish that a non-trivial interplay among these irreversibilities gives rise to an optimum value of the geometrical parameter, viz. the channel wall thickness ( $$ \delta $$ ), and the thermophysical parameters, viz. the thermal conductivity of the wall $$ (\gamma ) $$ , Biot number (Bi), and the modified Peclet number ( $$ \overline{\text{Pe}} $$ ), leading to a minimum entropy generation rate of the system. Also, we unveil through this study that changes in the electroosmotic parameter $$ \bar{\kappa } $$ (representative of the EDL thickness) or the composition of the fluid ( $$ \phi $$ , the volume fraction of nanoparticles agglomerates) non trivially alter the optimum values of these parameters. Inferences drawn from this analysis may have consequences in the optimum design of thermal systems/devices, typically used for thermal management in micro-heat exchangers, micro-reactors, and micro heat pipes.

Numerical investigation of a porous media combustor in a small-scale diesel engine

The application of porous media in compression ignition engines has significant effects on its combustion behavior. In this work, a Computational Fluid Dynamics (CFD) analysis of combustion in diesel engine is performed for 100% load, and the effects of porous media addition in the combustion chamber are quantified. With a porosity of 66.7%, silicon carbide is applied as porous media of cylindrical shape in the modified piston bowl in the conventional engine. The combustion analysis outputs include average cylinder-pressure, temperature; Nitrogen Oxides (NOX), mean mixture fraction, turbulent kinetic energy, total energy and modified Peclet number. The results of the CFD study for the cases of non-porous media are validated against the performed baseline experimental analysis, whereas porous media predictions are compared to the state-of-the-art studies available in the literature. In presence of porous media, the average peak pressure and temperature are found to drop by ∼26 bar and ∼550 K, respectively, as compared to that of non-porous media. Furthermore, NOX emissions are significantly reduced up to 97%. The generation of turbulent kinetic energy is enhanced by 86% for PM leading to an increment of ∼36% in the thermal energy conversion than without a porous media.

A rheological model to predict viscosity of dispersions as a function of the modified Peclet number

The suspensions and emulsions are important products and raw materials for various industrial production and processing branches. The knowledge concerning the rheological properties of such substances is of key importance for many manufacturing processes. Many dependences can be found within the literature but there is lack of model that takes into account the influence of inner phase concentration, share rate, and diameters of the dispersed phase particles on a viscosity of these systems. The presented work goal was to obtain a rheological equation containing the modified form of Peclet number, which would provide the relation between the viscosity, the volume fraction, and the shear rate. The theory of Kozeny-Carman, which transforms the granular structure into a bunch of the torturous capillary tubes, was the base of this model. The proposed model has been verified for data available in the literature and for the data obtained in authors own experiments.

Determining efficiency of removal of dispersed phase from gases and modernization of scrubbers using high-performance packings

A solution to the problem of modeling the removal of a finely dispersed phase from stack gases and process gases at power engineering and petrochemical enterprises using a column apparatus filled with new highly efficient random and structured packings is considered.The use of diffusion and cell models of the flow structure for calculating a concentration profile of particles settling on a liquid fi lm in apparatuses filled with various packings is shown. Accounting for the deposition of finely dispersed particles from gases on the interfacial surface of the liquid fi lm flowing down along the packing is carried out using a bulk source of mass. The model of turbulent-inertial sedimentation of particles is adopted. The main parameters of the model are the coefficient of turbulent migration of particles to the fi lm surface on contact devices, a modified Peclet number with a backmixing coefficient, and the number of complete mixing cells. This approach can be generalized to a wide class of fi lm-type apparatuses for wet gas cleaning with the aim of designing them or choosing modernization options. Expressions are obtained for calculating the efficiency of aerosol separation on packings as well as the required depth of the packed bed for a given efficiency.Results of calculating the efficiency of gas purification from aerosols with the use of various types of packings in scrubbers as well as the required depth of the packed bed for a given efficiency are presented. A graphical dependence of the power spent on gas cleaning in apparatuses with different packings is given. Results of solving the production problem of cleaning pyrogas from coke and tar by circulating water in a modernized scrubber with new highperformance packings are shown.Expressions for calculating the rate of turbulent particle migration for random and structured packings as well as modified Peclet numbers are presented. A distinctive feature of these expressions is the calculation based on the known hydraulic resistance of contact devices.

Efficiency of the Process of Heating of Fuels and Oils in Intensified Heat Exchangers

Processes that arise in the course of heating of liquid hydrocarbon mixtures in the channels of heat exchangers containing process intensifiers are considered. Random metal packings and coiled elements are used as the intensifiers. Using a cellular model of the flow structure, an expression is derived for calculating the temperature profile of the heated medium along the length of the channel. Formulas for calculating the Nusselt number in a channel containing intensifiers as well as the modified Peclet number of the flow structure are presented. Sample calculations of the process of heating of turbine oils and marine diesel oil are provided. A significant increase in the efficiency of heat transfer (more than eight-fold) and the force factor (more than fivefold) is demonstrated.

Study of Flow Structure in Apparatus with Suspended Transportable Bed of Granular Material

The hydrodynamic regime used in apparatuses with suspended transportable bed of granular material (ASTB) occupies an intermediate place between fluidization and pneumatic transport. To select the basic method of calculation of ASTB, it is essential to determine which apparatuses they are close to in flow structure. In this context, studies of the flow structure in the ASTB and determination of the basic design and technological parameters affecting this characteristic are urgent. The results of determination of the modified Peclet number and the longitudinal mixing coefficient in a wide range of variation of ASTB operation conditions are presented. The obtained results confirm the closeness of the flow structure in ASTBs and pneumatic tubular driers.

On the flame height of circulation-controlled firewhirls with variable density

A theoretical analysis on the flame height of circulation-controlled firewhirls is presented with emphasis on studying the influence of variable density that was ignored in most previous studies. A circulation-controlled firewhirl is approximated as a non-premixed flame, with variable density and temperature-dependent diffusivities in a steady and axisymmetric Burgers vortex. A coupling-function-based formulation is established to describe the firewhirl by invoking the assumption of unity Lewis number. By virtue of a Howarth-Dorodnitsyn-like coordinate transformation, the transport equations for the coupling functions can be solved analytically to result in the well-known linear relation between the normalized flame height and the modified Peclet number. The variable density effect in enhancing the flame height is characterized by a dimensionless temperature factor multiplied to the linear relation. For the firewhirls supplied by a fuel in condensed phase, the boundary conditions at the fuel surface are specified by considering the physical mechanism of Stefan flow.

A proper analytical analysis of annular step porous fins for determining maximum heat transfer

The annular stepped fin is a common choice for enhancing heat transfer from a cylindrical primary surface. This typical fin shape is easy in manufacturing compared to the taper shape. There is still effort required to increase the heat transfer rate per unit mass of a step fin. With this design point of view, the present study has been carried out. There may be two design aspects to be adopted to satisfy the above design requirement. With consideration of the porous material and moving condition of fins, heat transfer can be increased for a constraint mass of a fin. In the present study, an appropriate analytical method has been developed for an annular step fin of porous material under a moving condition. The effect of internal heat generation in the fin and the radiation mode of heat transfer on the fin performance have been studied elaborately. Unlike previous literature for moving fins, the performance design parameter is dependent on the modified Peclet number instead of the conventional Peclet number. The double differential transform method has been used for the analytical analysis. The optimization analysis has been demonstrated for the maximization of heat transfer through an annular step porous fin (ASPF) under a design constraint of mass of a fin. A comparative study has also been made between the porous and solid fins for an equal mass of fins. It was highlighted that the porous fin transfer always more heat at an optimum condition compared to the solid fin which is a profitable design aspect for selecting the porous condition. The moving condition is also a better approach to increase heat transfer rate and it is clearly demonstrated in the present study. The formulation of the present work is suitable for stationary and annular disk porous fins also by considering an appropriate design variable.

Gas hold-up distribution and mixing time in gas–liquid stirred tanks

In this work, the gas–liquid dispersion in a stirred tank equipped with different impellers is investigated by Electrical Resistance Tomography (ERT). The main goal of the study is to provide detailed information on the spatial distribution of the gas phase and on the effect of bubbles on the liquid homogenisation dynamics. The analysis is carried out under variable gas flow rates and impeller speeds, thus covering different regimes of gas–impeller interaction, as obtained by Rushton Turbines, Pitched Blade Turbines pumping upwards and Lightnin A310. The experimental technique allows us to overcome the typical limitations of optical methods and to gain insight into the complex behaviour of sparged stirred tanks without restriction on the upper value of overall gas hold-up, that is of great interest for several chemical and biochemical processes. Besides, the experimental data can be adopted as a benchmark for advanced modelling techniques based on CFD methods, whose scant validation is often due to limited information on the local dispersion features.The analysis of experimental results allows us to suggest simple correlations for the prediction of the prevailing flow regime based on the dimensionless Froude and flow numbers. Finally, the definition of a modified Peclet number is also suggested, as a simple parameter for the interpretation of both the gas hold-up distribution and the dimensionless mixing time.

A model for knickpoint migration in first‐ and second‐order streams

AbstractWe introduce a new theoretical framework for knickpoint migration in unventilated flows prevalent in channelized semicohesive first‐ and second‐order streams characterized by a sequence of constrictions and expansions in the channel cross section. A key feature of the framework is the inclusion of shear‐induced fluvial erosion due to flow suction at the nappe as the key mechanism driving migration. Channel surveys, water stage, time‐lapse photography, and laser scans from Mud Creek, Iowa, USA, confirm this unventilated erosive mechanism and reveal a dual advective‐diffusive mode of retreat. We treat the fluvial bed shear stress as being similar to the flow on the lee side of a submerged obstacle and derive a governing equation which is a generalized Burgers' equation. The equation is solved to successfully simulate knickpoints monitored in two sites (Iowa and Mississippi), and a modified Peclet number is used to analyze the advective‐diffusive nature of the knickpoint migration.

Generalized criterion for the onset of particle deposition in crossflow microfiltration via DOTM – Modeling and experimental validation

The concept of a critical permeation flux for the onset of particle deposition in crossflow microfiltration (CFMF) is well-established. However, the critical flux is known to be a function of process parameters such as the particle size, bulk concentration and crossflow velocity. In the present study, the critical modified Peclet number (Pecrit) is explored instead as a generalized criterion for the onset of particle deposition that incorporates the effects of these process parameters as well as the axial position along the membrane. A proper determination of Pecrit requires an accurate prediction of the concentration polarization boundary layer thickness δc and shear-induced diffusion coefficient Ds. The classical Lévêque model is adapted to allow for the effect of the permeation flux on the velocity profile. Moreover, the assumptions of a constant concentration at the membrane surface cw and constant Ds that have been made in prior studies are relaxed in an improved numerical solution to the convective diffusion equation that is used to predict δc and Ds. The critical permeation flux is determined from particle deposition data taken for 6 and 10μm latex spheres via Direct Observation Through the Membrane (DOTM) characterization. A constant value of Pecrit=4.00±0.08 is found to characterize the effects of particle diameter, bulk concentration and crossflow velocity as well as axial position on the onset of particle deposition.

EXPERIMENTAL CHARACTERIZATION OF THERMAL DISPERSION IN FIBROUS POROUS MEDIA

When a hot fluid is injected into a cold fibrous porous media or vice versa, energy is convected by the movement of fluid particles not only in the direction of the averaged velocity but also in the transverse direction because of the undulating flow path. This heat dispersion phenomenon can be modeled by increasing the effective transverse thermal conductivity to account for the enhancement in heat transfer. In this work, we have developed a new characterization setup to measure the heat transfer enhancement for a variety of flow rates and fiber volume fractions and introduced a modified Peclet number to describe the heat-transfer enhancement. In the experiment a cold resin is introduced in a heated mold containing fibrous media. The temperature history at the inlet, exit, and at six locations on the mold walls and three locations within the porous media is measured, and the transverse thermal conductivity in the model is varied, until all the temperature profiles recorded from the experiments match with the predicted values at all the thermocouple locations. This is repeated for various fiber volume fractions, flow rates, and two different preform architectures to develop a constitutive relationship between thermal dispersion and the modified Peclet number.

Determination of the effective radial mass diffusivity in tubular reactors under non-Newtonian laminar flow using residence time distribution data

Residence time distribution (RTD) plays an important role in the performance of a laminar flow reactor (LFR). The theoretical E-curve can be derived for the tube flow of a power law non-Newtonian fluid; however, in practice, the streamline flow can be disturbed by the use of corrugated tubes or coils or by the presence of mechanical vibration, high wall relative roughness, pipe fittings or curves. Moreover, stagnation or recirculation zones reduce the active volume of the reactor. The integration of the measured RTD with the process model for flow, heat transfer and reaction can be challenging. The approach proposed in this work is to introduce an effective radial mass diffusivity in the model to take into account the enhanced dispersion and to use the mean residence time as characteristic time. The LFR with radial diffusion was modeled and the simulation results showed the transition from ideal laminar flow to intense radial dispersion according to the modified Peclet number. The measured RTD of a tubular system with high wall relative roughness running with a Newtonian fluid and a pseudo-plastic fluid was compared with the simulated results in order to determine the effective radial diffusivity and the active volume. With these parameters, the LFR model would provide a more reliable prediction of the RTD, hence preventing the representation of complex flow distributions in the reactor.

Natural Circulation and Linear Stability Analysis for Liquid-Metal Reactors with the Effect of Fluid Axial Conduction

The effect of fluid axial thermal conduction on one-dimensional liquid metal natural circulation and its linear stability was performed through nondimensional analysis, steady-state assessment, and linear perturbation evaluation. The Nyquist criterion and a root-search method were employed to find the linear stability boundary of both forward and backward circulations. The study provided a relatively complete analysis method for one-dimensional natural circulation problems with the consideration of fluid axial heat conduction. The results suggest that fluid axial heat conduction in a natural circulation loop should be considered only when the modified Peclet number is [approximately]1 or less, which is significantly smaller than the practical value of a lead liquid metal-cooled reactor.

Fundamentals of membrane transport

A review is presented to give a generalized membrane transport theory based on the principles of nonequilibrium thermodynamics. This theory is then used to develop specific flux equations for gas separation, pervaporation, osmosis, reverse osmosis, nanofiltration, ultrafiltration, microfiltration, dialysis, and electrodialysis. All membrane processes suffer from boundary layer mass transfer resistances caused by concentration polarization. The convective motions parallel and perpendicular to the membrane surface are distinguishable, and the former becomes more relevant than the latter in the boundary layer mass transfer. The modified Peclet number is introduced and its importance is discussed in characterizing the boundary layer mass transfers of various membrane processes. Many different transport mechanisms through membrane itself are reviewed including the solution-diffusion model, pore model, permeation through composite membranes, and transport through inorganic membranes. Finally, the differences between membrane mass transfer and other mass transfer are delineated, including a discussion of negative mass transfer coefficient.

Quantifying Transcription of Clinically Relevant Immobilized DNA within a Continuous Flow Microfluidic Reactor

Flow-through reactors are commonly used to control and optimize reagent delivery and product removal. Although recent research suggests that transcription reactions using picogram quantities of cDNA produce RNA efficiently in a flow-through microreactor, there has not been a detailed study on the mass transport and reagent dependence of microfluidic transcription reactions. We present a novel microreactor that contains H5 influenza cDNA immobilized directly onto the reactor walls to study the kinetics and reagent dependence of in vitro transcription reactions on a microfluidic platform. Enzyme and the rNTP substrate continuously flow over the cDNA and create RNA, which flows to a downstream collection well. Using nanogram quantities of cDNA, we found that enzyme limiting conditions caused by the concentration of cDNA in a small-volume microreactor channel may be partially overcome as the enzyme binds and concentrates near the channel wall. Kinetics confirm this phenomenon and show that the timescale for enzyme binding can be approximated by t(f) = cDNA/Q[E]. Surprisingly, on-chip transcription reactions have a strong dependence on the rNTP concentration from 5 to 9 mM despite a low consumption rate of rNTP molecules that is largely independent of the flow rate. Faster flow rates decrease the time it takes to fill DNA promoter sites with enzyme while additionally refreshing rNTP and MgCl(2) to allow for a greater consumption of rNTP. These two effects cause reactions with higher concentrations of cDNA in the reactor channel to have a greater dependence on the flow rate. At high flow rates (>0.37 nL/s), the reaction rate begins to drop, likely because of the release and escape of enzyme molecules from the cDNA layer. This critical flow rate can be predicted by a new modified Peclet number, Pe(m) = L(c)V/D, where L(c) is the full length of the tightly packed cDNA molecules, V is the velocity at the DNA/fluid interface, and D is the diffusivity of the enzyme molecule. Together, these insights can inspire reactor designs for a variety of applications.

Vesiculation and crystallization under instantaneous decompression: Numerical study and comparison with laboratory experiments

Vesiculation and crystallization in ascending magmas are key processes that control the eruption behavior, and they interplay each other through the water exsolution process. We conducted a numerical study in order to quantitatively understand the water exsolution and crystallization processes in natural eruptions (decompression history is unknown) and in laboratory experiments (the amount of decompression is constant with time). The numerical results, which take into account homogeneous or heterogeneous nucleation and growth of bubbles with varying diffusivity of water, viscosity, and the amount of decompression, provide a quantitative understanding of their control on bubble formation and water exsolution in the constant amount of decompression. The bubble nucleation in the homogeneous nucleation can be divided into two regimes – the diffusion control regime and viscosity control regime – depending on the modified Peclet number and the effective supersaturation. In the cases of both homogeneous and heterogeneous nucleations, the bubble growth is controlled by diffusion or viscosity, depending on the modified Peclet number and bubble number density. The water exsolution rate, which is controlled by the modified Peclet number in the viscosity control regime and by the bubble number density and diffusive driving force in the diffusion control regime, acts as an effective cooling rate in a decompression-induced crystallization process. A comparison of the numerical results with the results of laboratory experiments suggests that water exsolution proceeds by the diffusion-limited growth of bubbles under disequilibrium vesiculation through the heterogeneous nucleation of bubbles, and this in turn controls the crystallization kinetics of microlite with the homogeneous nucleation of microlite and the diffusion-limited growth of crystal. The several orders of variation of microlite number density with the amount of decompression in laboratory experiments can be interpreted as the effect of the amount of decompression on the driving force for the diffusive bubble growth that controls the water exsolution rate.

Heterogeneous Drying of Colloidal Polymer Films: Dependence on Added Salt

Using magnetic resonance profiling coupled with dynamic light scattering, we have investigated the mechanisms leading to the formation of a partly coalesced surface layer, or "open skin", during film formation from waterborne polymer dispersions. We present the first use of the skewness of the distribution of free water as a model-free indicator of the spatial nonuniformity of drying. The skewness reaches a maximum at the same time at which a strong, static component, presumably originating from a skin at the film/air interface, appears in the light scattering data. Addition of salt to the dispersion increases both the skewness of the distribution of free water and the propensity for skin formation. Surprisingly, the drying is influenced not only by the concentration and valency of the ions in the salt but also by the particular ion. At intermediate particle densities, added salt strongly lowers the cooperative diffusion coefficient, Dcoop. When the particles reach close packing, Dcoop sharply increases. If the particles readily coalesce, the effects of the increased diffusivity will be counteracted, thereby inducing the formation of a skin. A modified Peclet number, Pe, using Dcoop, is proposed, so that the presence of salt is explicitly considered. This modified Pe is able to predict the nonuniformity in drying that leads to skin formation.

Dissipative particle dynamics simulation of on-chip hydrodynamic chromatography

Separations of flexible polymers using on-chip hydrodynamic chromatography (HDC) have been studied with dissipative particle dynamic simulations, a novel computational technique that fully accounts for hydrodynamic interactions among polymer segments and with walls. The current study focuses on comparisons of simulation results on elution times with that predicted by earlier theoretical models for HDC separation. The elution times obtained in simulation are found to compare reasonably well with the theoretical prediction when chain stretching is not significant. Deviation from the theoretical prediction occurs when the chain stretching becomes significant. We observe a reversal in elution order and the reversal occurs at a Deborah number about 8, slightly larger than the Deborah number at the onset of chain stretching. The simulations also confirm the applicability of the Aris–Taylor equation for the convective dispersion of small solutes and for solutes like polymer chains, except the latter requires the use of a modified Peclet number.