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Papers by Andrea Boghi

Research paper thumbnail of Image-based quantification of soil microbial dead zones induced by nitrogen fertilization

Science of The Total Environment, Jul 1, 2020

Research paper thumbnail of Scaling the impact of rhizosphere processes - from imaged pore scale nutrient uptake to full field continuum models

Research paper thumbnail of Three-dimensional numerical simulation of a failed coronary stent implant at different degrees of residual stenosis. Part II: Apparent viscosity and wall permeability

Numerical Heat Transfer Part A-applications, Mar 19, 2017

The influence of the degree of residual stenosis (DOR) on the hemodynamics inside coronary arteri... more The influence of the degree of residual stenosis (DOR) on the hemodynamics inside coronary arteries is investigated through three-dimensional (3D) numerical simulations. The vascular wall permeability is investigated and the effect of the non-Newtonian viscosity discussed. The results agree in predicting an abrupt increase in wall permeability above 45% DOR, indicating that the implant could lead to a massive restenosis.

Research paper thumbnail of On a New Turbulent Energy Equation With Variable Thermal Conductivity

Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C, 2008

The present work investigates the energy equation of a general fluid, Newtonian or non-Newtonian,... more The present work investigates the energy equation of a general fluid, Newtonian or non-Newtonian, with variable thermal conductivity in turbulent flow. The usual energy equation, without the dissipation terms, is taken into account with the fluctuating terms in the temperature as well as in the thermal conductivity. The energy equation is written for the average temperature, for the fluctuating temperature one as well as for the square of the fluctuating temperature. Besides the usual Reynolds stresses, a new term appears, which is the product of the fluctuation of the thermal conductivity and the gradient of the temperature fluctuation. This new term is interpreted and introduced in the energy equation where the variable is the square of the temperature fluctuation where new terms appear. A possible physical interpretation is given to the different terms. Assuming a polynomial relation between thermal conductivity and temperature it is then possible to write an expression for the average and the fluctuating thermal conductivity. The expressions are then simplified on the basis of physical and mathematical considerations. Specifically, the heat flux due to the fluctuating thermal conductivity is then expressed as the product of the derivative of the thermal conductivity with the mean temperature to the gradient of the square of the temperature fluctuation. Further considerations allow to write a new energy equation of the average temperature which include the new term. The solution of this energy equation is possible with the coupled solution of the equation for the square of the fluctuating temperature. The introduction of this new term in the energy equation can be of some importance in problems related to liquid metals flowing in turbulent flow and/or in very low temperature applications where the thermal conductivity becomes very high.

Research paper thumbnail of Numerical Simulation of Blood Flow through Different Stents in Stenosed and Non-Stenosed Vessels

Numerical Heat Transfer Part A-applications, Apr 22, 2015

The fluid dynamics in two different stent configurations, peak-to-valley (S1) and peak-to-peak (S... more The fluid dynamics in two different stent configurations, peak-to-valley (S1) and peak-to-peak (S2), within a fully expanded situation and a 30% restenosis, is investigated. Numerical simulations are carried out in order to evaluate the conditions promoting atherosclerotic events when a selfexpanding bare metal stents (SE-BMS) is applied. The conclusions are that the two configurations, S1 and S2, have a similar fluid dynamic behavior, as far as the WSS is concerned, but OSI and RRT maps suggest that the peak-to-peak configuration, S2, has a better behavior than the peak-to-valley one, S1.

Research paper thumbnail of Three-Dimensional Numerical Simulation of Blood Flow in Two Coronary Stents

Numerical Heat Transfer Part A-applications, Feb 11, 2011

The aim of the present study is to carry out Computational Fluid Dynamics simulations in a realis... more The aim of the present study is to carry out Computational Fluid Dynamics simulations in a realistic three dimensional geometry of two stent under physiological conditions. The two stent, similar to real coronary ones, are both made of 12 rings but are differing as far as the position of the struts is concerned. One type has parallel-connectors and the other transverse-ones. The artery is modeled as rigid cylinder and the fluid is assumed as incompressible Newtonian fluid in laminar flow with the average physical properties of blood. The commercial computational fluid dynamic code FLUENT is used with the mesh made of non-uniform tetrahedrons. The mesh independence is proved using the steady state results of the wall shear stress. The parameters correlated to neo-intimal hyperplasia, such as wall shear stress, magnitude of wall shear stress gradient, and oscillatory shear index, are investigated. Time variation of the parameters is investigated with the conclusion that the stent with parallel-connectors has a better fluid dynamic behavior.

Research paper thumbnail of Numerical simulation of magnetic nano drug targeting in a patient-specific coeliac trunk

Journal of Magnetism and Magnetic Materials, Sep 1, 2017

Magnetic nano drug targeting, through the use of an external magnetic field, is a new technique f... more Magnetic nano drug targeting, through the use of an external magnetic field, is a new technique for the treatment of several diseases, which can potentially avoid the dispersion of drugs in undesired locations of the body. Nevertheless, due to the limitations on the intensity of the magnetic field applied, the hydrodynamic forces can reduce the effectiveness of the procedure. This technique is studied in this paper with the Computational Fluid Dynamics (CFD), focusing on the influence of the magnetic probe position, and the direction of the circulating electric current. A single rectangular coil is used to generate the external magnetic field. A patient-specific geometry of the coeliac trunk is reconstructed from DICOM images, with the use of VMTK. A new solver, coupling the Lagrangian dynamics of the nanoparticles with the Eulerian dynamics of the blood, is implemented in OpenFOAM to perform the simulations. The resistive pressure, the Womersley's profile for the inlet velocity and the magnetic field of a rectangular coil are implemented in the software as boundary conditions. The results show the influence of the position of the probe, as well as the limitations associated with the rectangular coil configuration.

Research paper thumbnail of A three dimensional exact equation for the turbulent dissipation rate of Generalised Newtonian Fluids

International Communications in Heat and Mass Transfer, Apr 1, 2012

The Flow of inelastic Non-Newtonian fluids is involved in many biological and industrial applicat... more The Flow of inelastic Non-Newtonian fluids is involved in many biological and industrial applications like nanofluids. Despite many years have passed since the beginning of the study of turbulent Non-Newtonian fluids, most of the studies carried out focus the attention on viscoelastic-fluids. In order to make accurate and low-cost prediction on turbulent inelastic Non-Newtonian fluids flow, a RANS Generalized Newtonian Fluid (GNF) turbulence model is required based on exact transport equation of turbulent variables. In a previous paper [52] we achieved the exact transport equations for turbulent kinetic energy and dissipation rate through the introduction of an apparent viscosity transport equation in 2D case for sake of simplicity. The object of this paper is to extend the results given in [52] in 3D case giving the full mathematical demonstration of the exact-equations. The modelling of the unknown terms it is left for a future work.

Research paper thumbnail of New transport equations for turbulent flow with variable transport properties: biomedical applications of non-Newtonian blood flow in coronary stent and stenosed carotid artery

INTRODUCTION 1.1 Variable Physical properties 1.2 Turbulence Modeling 1.3 Second Order Turbulence... more INTRODUCTION 1.1 Variable Physical properties 1.2 Turbulence Modeling 1.3 Second Order Turbulence Closures Nomenclature for Second Order Moments Equations 1.4 Second Order Moments equations 1.5 Computational Methods References of Chapter 1 2 NUMERICAL METHOD 2.1 Finite Volume Method (FVM) in a two-dimensional flow 2.

Research paper thumbnail of On a phase-field model for a miscible drop in a spinning drop tensiometer

Bulletin of the American Physical Society, Nov 20, 2011

Submitted for the DFD11 Meeting of The American Physical Society On a phase-field model for a mis... more Submitted for the DFD11 Meeting of The American Physical Society On a phase-field model for a miscible drop in a spinning drop tensiometer 1 ANDREA BOGHI, ANATOLIY VOROBEV, University of Southampton-We examine shape transformations of a solute droplet immersed into a solvent-filled and sealed capillary tube subject to fast rotations around its axis, i.e. the configuration of the spinning drop tensiometer. Despite the fact, that a droplet is miscible, its dissolution occurs rather slowly, and under rotations a droplet becomes elongated, which is used to measure the dynamic surface tension of the solute/solvent interface. The Boussinesq approximation [1] of the full (quasicompressible) Cahn-Hilliard-Navier-Stokes is used as a theoretical model to capture the droplet evolution. We found that the behaviour of a miscible droplet contained in a closed enclosure is strongly different from an immiscible one. Miscible droplets in general are thermodynamically unstable and ultimately dissolve, large partially miscible droplets however may remain stable with the size determined by the total mass balance. In the limit of high Prandtl numbers, droplet's shape changes quickly (on a convective time scale), so that quasi-stable droplets are observed with only weak hydrodynamic flows present. Such states remain thermodynamically unstable: droplets lose their mass and the droplet's interface properties changes on a long diffusive time scale.

Research paper thumbnail of On a New Passive Scalar Equation With Variable Mass Diffusivity

ABSTRACT The present work investigates the mass conservation equation of a Newtonian and non-Newt... more ABSTRACT The present work investigates the mass conservation equation of a Newtonian and non-Newtonian fluid in turbulent flow with variable mass diffusivity. The mass conservation equation is considered with the fluctuating terms in the concentration as well as in the mass diffusivity and is written for the average concentration, for the fluctuating concentration one as well as for the square of the fluctuating concentration. A new term appears in the form of product of the fluctuating mass diffusivity to the space gradient of the concentration fluctuation. This new term is interpreted and introduced in the mass conservation equation of the square of the fluctuating concentration where other new terms are also appearing. A possible physical interpretation is given to the different terms. Assuming several relations between mass diffusivity and concentration it is then possible to write expressions for the average and the fluctuating mass concentration which can be simplified on the basis of physical and mathematical considerations. Specifically, the mass flux is then expressed as the product of the derivative of the mass diffusivity to the gradient of the square of the mass fluctuation. Further considerations make possible to write a new mass conservation equation of the average concentration which include a new term which takes into account the space gradient of the mass flux. The mass conservation equation can be solved with the coupled solution of the equation of the square of the concentration fluctuation.

Research paper thumbnail of On a New Passive Scalar Equation With Variable Mass Diffusivity: Flow Between Parallel Plates

Journal of Fluids Engineering-transactions of The Asme, Nov 1, 2010

The present work investigates mass conservation equations in turbulent flow between parallel plat... more The present work investigates mass conservation equations in turbulent flow between parallel plates with variable mass diffusivity. Species conservation equations are relative to the average concentration, as well as to the concentration variance. The product of fluctuating mass diffusivity and space gradient of concentration fluctuation is appearing in the equation of mean and concentration variance. A physical interpretation is given to the different terms. The assumption of a relation between mass diffusivity and concentration allows writing expressions for average and fluctuating mass diffusivity, which can be simplified on the basis of theoretical considerations. The new mass flux is expressed as a function of mass diffusivity and a gradient of concentration variance. Further considerations make it possible to model the new terms appearing in the concentration variance equation. The mass conservation equation can be solved when coupled to the equation of concentration variance. The equations are solved numerically for flow between parallel plates in order to evaluate the influence of the new terms.

Research paper thumbnail of Two new differential equations of turbulent dissipation rate and apparent viscosity for non-newtonian fluids

International Communications in Heat and Mass Transfer, Jul 1, 2011

A new equation for the dissipation rate of turbulent kinetic energy is derived exactly in conserv... more A new equation for the dissipation rate of turbulent kinetic energy is derived exactly in conservative form for a Generalized Newtonian Fluid (GNF). The transport equations for mass, momentum, and turbulent kinetic energy are written along to the transport equation for the shear rate. A new transport equation for the apparent viscosity is derived assuming the viscosity as dependent only on the shear rate. The assumption is of incompressible two-dimensional GNF flow.

Research paper thumbnail of Phase-field modelling of a miscible system in spinning droplet tensiometer

Journal of Colloid and Interface Science, Nov 1, 2016

The spinning drop tensiometry is used for measurements of surface tension coefficients, especiall... more The spinning drop tensiometry is used for measurements of surface tension coefficients, especially, when interfaces are characterised by low and ultra-low interfacial stresses. A droplet of lighter liquid is introduced into a rotating capillary that was initially saturated with another heavier liquid. The tube is subject to axial rotation that results in droplet's elongation along the tube's axis. The equilibrium shape of the droplet is used to determine the surface tension coefficient. In this work, the evolution of a slowly miscible droplet introduced into a spinning capillary is investigated. This technique is frequently employed for studies of the dynamics of miscible systems, even despite the fact that a strict equilibrium is never achieved in a mixture of fully miscible liquids. The numerical modelling of a miscible droplet is fulfilled on the basis of the phase-field (Cahn-Hilliard) approach. The numerical results are compared against the experimental data pursuing two objectives: (i) to verify the use of the phase-field approach as a consistent physics-based approach capable of accurate tracking of the short-and long-term evolution of miscible systems, and (ii) to estimate the values of the phenomenological parameters introduced within the phase-field approach, so making this approach a practical tool for modelling of thermohydrodynamic changes in miscible systems within various configurations.

Research paper thumbnail of Significance of root hairs at the field scale – modelling root water and phosphorus uptake under different field conditions

Plant and Soil, Dec 6, 2019

Background and aims Root hairs play a significant role in phosphorus (P) extraction at the pore s... more Background and aims Root hairs play a significant role in phosphorus (P) extraction at the pore scale. However, their importance at the field scale remains poorly understood. Methods This study uses a continuum model to explore the impact of root hairs on the large-scale uptake of P, comparing root hair influence under different agricultural scenarios. High vs low and constant vs decaying P concentrations down the soil profile are considered, along with early vs late precipitation scenarios. Results Simulation results suggest root hairs accounted for 50% of total P uptake by plants. Furthermore, a delayed initiation time of precipitation potentially limits the P uptake rate by over 50% depending on the growth period. Despite the large differences in the uptake rate, changes in the soil P concentration in the domain due to root solute uptake remains marginal when considering a single growth season. However, over the duration of 6 years, simulation results showed that noticeable differences arise over time. Conclusion Root hairs are critical to P capture, with uptake efficiency potentially enhanced by coordinating irrigation with P application during earlier growth stages of crops.

Research paper thumbnail of Preliminary numerical solutions of the evolution of free jets. IMECE2012-86730

ABSTRACT The present paper presents preliminary numerical solutions of the flow evolution of a tw... more ABSTRACT The present paper presents preliminary numerical solutions of the flow evolution of a two dimensional rectangular free jet. The numerical simulations in a two-dimensional domain are carried out with Open-FOAM, the open-source code, and compare the numerical results with the experimental visualizations performed in the same laboratory with the shadowgraph technique. The evolution of a two-dimensional submerged free jet is reported in the literature by the presence of two regions of flow: the potential core, where the centerline velocity maintains equal to that on the slot exit, and the turbulent or mixing region, where the centerline velocity decreases with the distance from the exit. Previous anemometric measurements, carried out in this laboratory with an air jet emerging from a rectangular channel, showed the presence of a region of flow, just outside the exit and before the potential core, where velocity and turbulence remain almost equal to those measured on the exit, and it has been called “undisturbed region of flow” because is present also in turbulent conditions. Previous and present shadowgraph visualizations show a jet which has the same height along the undisturbed region of flow and increases its height afterwards. The length of the undisturbed region depends on the Reynolds number of the flow and on the presence of turbulence promoters, e.g. metallic grids, at the exit of the slot. The undisturbed region is becoming nil with the increase of the Reynolds numbers, in agreement to the literature. The present two dimensional numerical solutions, carried out at Re numbers equal to 25,000 and 60,000 confirm the results obtained with the shadow visualizations.

Research paper thumbnail of Heat transfer on a flat wall due to a rectangular turbulent jet

International Communications in Heat and Mass Transfer

Research paper thumbnail of Further results on the mean mass transfer and fluid flow in a turbulent round jet

International Communications in Heat and Mass Transfer

Research paper thumbnail of Passive scalar diffusion in three-dimensional turbulent rectangular free jets with numerical evaluation of turbulent Prandtl/Schmidt number

International Communications in Heat and Mass Transfer, 2018

The passive scalar spreading of fluids with laminar Prandtl or Schmidt number, , Pr Sc , equal to... more The passive scalar spreading of fluids with laminar Prandtl or Schmidt number, , Pr Sc , equal to 1 in turbulent rectangular submerged free jets is analyzed by means of numerical simulation and theoretical analysis in the Reynolds number range 5000-40,000. The numerical investigation is carried out by means of a three-dimensional (3D) Large Eddy Simulation (LES) approach with the dynamic Smagorinsky model. A new mathematical model allows to obtain a simplified description of the passive scalar spreading in the largest area of the flow field, the Fully Developed Region (FDR). The present three-dimensional (3D) investigation shows that the passive scalar spreading follows a self-similarity law in the Fully Developed Region (FDR), as well as in the mean Undisturbed Region of Flow (URF) and in the Potential Core Region (PCR), similarly to what found in the Near Field Region (NFR) of rectangular submerged free jets, investigated with a two-dimensional (2D) approach. The turbulent Prandtl or Schmidt number is evaluated numerically and is found to be inversely proportional to the mean velocity gradient in the PCR. The present 3D numerical results show that the turbulent Prandtl or Schmidt number is zero in most part of the mean URF, and PCR, while it assumes different values outside. In the FDR the turbulent Prandtl or Schmidt number is constant and approximately equal to 0.7, in agreement with the literature, showing that turbulence affects momentum and passive scalar in a different way.

Research paper thumbnail of On a phase-field model for a miscible drop in a spinning drop tensiometer

Bulletin of the American Physical Society, 2011

ABSTRACT We examine shape transformations of a solute droplet immersed into a solvent-filled and ... more ABSTRACT We examine shape transformations of a solute droplet immersed into a solvent-filled and sealed capillary tube subject to fast rotations around its axis, i.e. the configuration of the spinning drop tensiometer. Despite the fact, that a droplet is miscible, its dissolution occurs rather slowly, and under rotations a droplet becomes elongated, which is used to measure the dynamic surface tension of the solute/solvent interface. The Boussinesq approximation [1] of the full (quasi- compressible) Cahn-Hilliard-Navier-Stokes is used as a theoretical model to capture the droplet evolution. We found that the behaviour of a miscible droplet contained in a closed enclosure is strongly different from an immiscible one. Miscible droplets in general are thermodynamically unstable and ultimately dissolve, large partially miscible droplets however may remain stable with the size determined by the total mass balance. In the limit of high Prandtl numbers, droplet's shape changes quickly (on a convective time scale), so that quasi- stable droplets are observed with only weak hydrodynamic flows present. Such states remain thermodynamically unstable: droplets lose their mass and the droplet's interface properties changes on a long diffusive time scale.[4pt] [1] A. Vorobev, PRE 82, 056312 (2010).

Research paper thumbnail of Image-based quantification of soil microbial dead zones induced by nitrogen fertilization

Science of The Total Environment, Jul 1, 2020

Research paper thumbnail of Scaling the impact of rhizosphere processes - from imaged pore scale nutrient uptake to full field continuum models

Research paper thumbnail of Three-dimensional numerical simulation of a failed coronary stent implant at different degrees of residual stenosis. Part II: Apparent viscosity and wall permeability

Numerical Heat Transfer Part A-applications, Mar 19, 2017

The influence of the degree of residual stenosis (DOR) on the hemodynamics inside coronary arteri... more The influence of the degree of residual stenosis (DOR) on the hemodynamics inside coronary arteries is investigated through three-dimensional (3D) numerical simulations. The vascular wall permeability is investigated and the effect of the non-Newtonian viscosity discussed. The results agree in predicting an abrupt increase in wall permeability above 45% DOR, indicating that the implant could lead to a massive restenosis.

Research paper thumbnail of On a New Turbulent Energy Equation With Variable Thermal Conductivity

Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C, 2008

The present work investigates the energy equation of a general fluid, Newtonian or non-Newtonian,... more The present work investigates the energy equation of a general fluid, Newtonian or non-Newtonian, with variable thermal conductivity in turbulent flow. The usual energy equation, without the dissipation terms, is taken into account with the fluctuating terms in the temperature as well as in the thermal conductivity. The energy equation is written for the average temperature, for the fluctuating temperature one as well as for the square of the fluctuating temperature. Besides the usual Reynolds stresses, a new term appears, which is the product of the fluctuation of the thermal conductivity and the gradient of the temperature fluctuation. This new term is interpreted and introduced in the energy equation where the variable is the square of the temperature fluctuation where new terms appear. A possible physical interpretation is given to the different terms. Assuming a polynomial relation between thermal conductivity and temperature it is then possible to write an expression for the average and the fluctuating thermal conductivity. The expressions are then simplified on the basis of physical and mathematical considerations. Specifically, the heat flux due to the fluctuating thermal conductivity is then expressed as the product of the derivative of the thermal conductivity with the mean temperature to the gradient of the square of the temperature fluctuation. Further considerations allow to write a new energy equation of the average temperature which include the new term. The solution of this energy equation is possible with the coupled solution of the equation for the square of the fluctuating temperature. The introduction of this new term in the energy equation can be of some importance in problems related to liquid metals flowing in turbulent flow and/or in very low temperature applications where the thermal conductivity becomes very high.

Research paper thumbnail of Numerical Simulation of Blood Flow through Different Stents in Stenosed and Non-Stenosed Vessels

Numerical Heat Transfer Part A-applications, Apr 22, 2015

The fluid dynamics in two different stent configurations, peak-to-valley (S1) and peak-to-peak (S... more The fluid dynamics in two different stent configurations, peak-to-valley (S1) and peak-to-peak (S2), within a fully expanded situation and a 30% restenosis, is investigated. Numerical simulations are carried out in order to evaluate the conditions promoting atherosclerotic events when a selfexpanding bare metal stents (SE-BMS) is applied. The conclusions are that the two configurations, S1 and S2, have a similar fluid dynamic behavior, as far as the WSS is concerned, but OSI and RRT maps suggest that the peak-to-peak configuration, S2, has a better behavior than the peak-to-valley one, S1.

Research paper thumbnail of Three-Dimensional Numerical Simulation of Blood Flow in Two Coronary Stents

Numerical Heat Transfer Part A-applications, Feb 11, 2011

The aim of the present study is to carry out Computational Fluid Dynamics simulations in a realis... more The aim of the present study is to carry out Computational Fluid Dynamics simulations in a realistic three dimensional geometry of two stent under physiological conditions. The two stent, similar to real coronary ones, are both made of 12 rings but are differing as far as the position of the struts is concerned. One type has parallel-connectors and the other transverse-ones. The artery is modeled as rigid cylinder and the fluid is assumed as incompressible Newtonian fluid in laminar flow with the average physical properties of blood. The commercial computational fluid dynamic code FLUENT is used with the mesh made of non-uniform tetrahedrons. The mesh independence is proved using the steady state results of the wall shear stress. The parameters correlated to neo-intimal hyperplasia, such as wall shear stress, magnitude of wall shear stress gradient, and oscillatory shear index, are investigated. Time variation of the parameters is investigated with the conclusion that the stent with parallel-connectors has a better fluid dynamic behavior.

Research paper thumbnail of Numerical simulation of magnetic nano drug targeting in a patient-specific coeliac trunk

Journal of Magnetism and Magnetic Materials, Sep 1, 2017

Magnetic nano drug targeting, through the use of an external magnetic field, is a new technique f... more Magnetic nano drug targeting, through the use of an external magnetic field, is a new technique for the treatment of several diseases, which can potentially avoid the dispersion of drugs in undesired locations of the body. Nevertheless, due to the limitations on the intensity of the magnetic field applied, the hydrodynamic forces can reduce the effectiveness of the procedure. This technique is studied in this paper with the Computational Fluid Dynamics (CFD), focusing on the influence of the magnetic probe position, and the direction of the circulating electric current. A single rectangular coil is used to generate the external magnetic field. A patient-specific geometry of the coeliac trunk is reconstructed from DICOM images, with the use of VMTK. A new solver, coupling the Lagrangian dynamics of the nanoparticles with the Eulerian dynamics of the blood, is implemented in OpenFOAM to perform the simulations. The resistive pressure, the Womersley's profile for the inlet velocity and the magnetic field of a rectangular coil are implemented in the software as boundary conditions. The results show the influence of the position of the probe, as well as the limitations associated with the rectangular coil configuration.

Research paper thumbnail of A three dimensional exact equation for the turbulent dissipation rate of Generalised Newtonian Fluids

International Communications in Heat and Mass Transfer, Apr 1, 2012

The Flow of inelastic Non-Newtonian fluids is involved in many biological and industrial applicat... more The Flow of inelastic Non-Newtonian fluids is involved in many biological and industrial applications like nanofluids. Despite many years have passed since the beginning of the study of turbulent Non-Newtonian fluids, most of the studies carried out focus the attention on viscoelastic-fluids. In order to make accurate and low-cost prediction on turbulent inelastic Non-Newtonian fluids flow, a RANS Generalized Newtonian Fluid (GNF) turbulence model is required based on exact transport equation of turbulent variables. In a previous paper [52] we achieved the exact transport equations for turbulent kinetic energy and dissipation rate through the introduction of an apparent viscosity transport equation in 2D case for sake of simplicity. The object of this paper is to extend the results given in [52] in 3D case giving the full mathematical demonstration of the exact-equations. The modelling of the unknown terms it is left for a future work.

Research paper thumbnail of New transport equations for turbulent flow with variable transport properties: biomedical applications of non-Newtonian blood flow in coronary stent and stenosed carotid artery

INTRODUCTION 1.1 Variable Physical properties 1.2 Turbulence Modeling 1.3 Second Order Turbulence... more INTRODUCTION 1.1 Variable Physical properties 1.2 Turbulence Modeling 1.3 Second Order Turbulence Closures Nomenclature for Second Order Moments Equations 1.4 Second Order Moments equations 1.5 Computational Methods References of Chapter 1 2 NUMERICAL METHOD 2.1 Finite Volume Method (FVM) in a two-dimensional flow 2.

Research paper thumbnail of On a phase-field model for a miscible drop in a spinning drop tensiometer

Bulletin of the American Physical Society, Nov 20, 2011

Submitted for the DFD11 Meeting of The American Physical Society On a phase-field model for a mis... more Submitted for the DFD11 Meeting of The American Physical Society On a phase-field model for a miscible drop in a spinning drop tensiometer 1 ANDREA BOGHI, ANATOLIY VOROBEV, University of Southampton-We examine shape transformations of a solute droplet immersed into a solvent-filled and sealed capillary tube subject to fast rotations around its axis, i.e. the configuration of the spinning drop tensiometer. Despite the fact, that a droplet is miscible, its dissolution occurs rather slowly, and under rotations a droplet becomes elongated, which is used to measure the dynamic surface tension of the solute/solvent interface. The Boussinesq approximation [1] of the full (quasicompressible) Cahn-Hilliard-Navier-Stokes is used as a theoretical model to capture the droplet evolution. We found that the behaviour of a miscible droplet contained in a closed enclosure is strongly different from an immiscible one. Miscible droplets in general are thermodynamically unstable and ultimately dissolve, large partially miscible droplets however may remain stable with the size determined by the total mass balance. In the limit of high Prandtl numbers, droplet's shape changes quickly (on a convective time scale), so that quasi-stable droplets are observed with only weak hydrodynamic flows present. Such states remain thermodynamically unstable: droplets lose their mass and the droplet's interface properties changes on a long diffusive time scale.

Research paper thumbnail of On a New Passive Scalar Equation With Variable Mass Diffusivity

ABSTRACT The present work investigates the mass conservation equation of a Newtonian and non-Newt... more ABSTRACT The present work investigates the mass conservation equation of a Newtonian and non-Newtonian fluid in turbulent flow with variable mass diffusivity. The mass conservation equation is considered with the fluctuating terms in the concentration as well as in the mass diffusivity and is written for the average concentration, for the fluctuating concentration one as well as for the square of the fluctuating concentration. A new term appears in the form of product of the fluctuating mass diffusivity to the space gradient of the concentration fluctuation. This new term is interpreted and introduced in the mass conservation equation of the square of the fluctuating concentration where other new terms are also appearing. A possible physical interpretation is given to the different terms. Assuming several relations between mass diffusivity and concentration it is then possible to write expressions for the average and the fluctuating mass concentration which can be simplified on the basis of physical and mathematical considerations. Specifically, the mass flux is then expressed as the product of the derivative of the mass diffusivity to the gradient of the square of the mass fluctuation. Further considerations make possible to write a new mass conservation equation of the average concentration which include a new term which takes into account the space gradient of the mass flux. The mass conservation equation can be solved with the coupled solution of the equation of the square of the concentration fluctuation.

Research paper thumbnail of On a New Passive Scalar Equation With Variable Mass Diffusivity: Flow Between Parallel Plates

Journal of Fluids Engineering-transactions of The Asme, Nov 1, 2010

The present work investigates mass conservation equations in turbulent flow between parallel plat... more The present work investigates mass conservation equations in turbulent flow between parallel plates with variable mass diffusivity. Species conservation equations are relative to the average concentration, as well as to the concentration variance. The product of fluctuating mass diffusivity and space gradient of concentration fluctuation is appearing in the equation of mean and concentration variance. A physical interpretation is given to the different terms. The assumption of a relation between mass diffusivity and concentration allows writing expressions for average and fluctuating mass diffusivity, which can be simplified on the basis of theoretical considerations. The new mass flux is expressed as a function of mass diffusivity and a gradient of concentration variance. Further considerations make it possible to model the new terms appearing in the concentration variance equation. The mass conservation equation can be solved when coupled to the equation of concentration variance. The equations are solved numerically for flow between parallel plates in order to evaluate the influence of the new terms.

Research paper thumbnail of Two new differential equations of turbulent dissipation rate and apparent viscosity for non-newtonian fluids

International Communications in Heat and Mass Transfer, Jul 1, 2011

A new equation for the dissipation rate of turbulent kinetic energy is derived exactly in conserv... more A new equation for the dissipation rate of turbulent kinetic energy is derived exactly in conservative form for a Generalized Newtonian Fluid (GNF). The transport equations for mass, momentum, and turbulent kinetic energy are written along to the transport equation for the shear rate. A new transport equation for the apparent viscosity is derived assuming the viscosity as dependent only on the shear rate. The assumption is of incompressible two-dimensional GNF flow.

Research paper thumbnail of Phase-field modelling of a miscible system in spinning droplet tensiometer

Journal of Colloid and Interface Science, Nov 1, 2016

The spinning drop tensiometry is used for measurements of surface tension coefficients, especiall... more The spinning drop tensiometry is used for measurements of surface tension coefficients, especially, when interfaces are characterised by low and ultra-low interfacial stresses. A droplet of lighter liquid is introduced into a rotating capillary that was initially saturated with another heavier liquid. The tube is subject to axial rotation that results in droplet's elongation along the tube's axis. The equilibrium shape of the droplet is used to determine the surface tension coefficient. In this work, the evolution of a slowly miscible droplet introduced into a spinning capillary is investigated. This technique is frequently employed for studies of the dynamics of miscible systems, even despite the fact that a strict equilibrium is never achieved in a mixture of fully miscible liquids. The numerical modelling of a miscible droplet is fulfilled on the basis of the phase-field (Cahn-Hilliard) approach. The numerical results are compared against the experimental data pursuing two objectives: (i) to verify the use of the phase-field approach as a consistent physics-based approach capable of accurate tracking of the short-and long-term evolution of miscible systems, and (ii) to estimate the values of the phenomenological parameters introduced within the phase-field approach, so making this approach a practical tool for modelling of thermohydrodynamic changes in miscible systems within various configurations.

Research paper thumbnail of Significance of root hairs at the field scale – modelling root water and phosphorus uptake under different field conditions

Plant and Soil, Dec 6, 2019

Background and aims Root hairs play a significant role in phosphorus (P) extraction at the pore s... more Background and aims Root hairs play a significant role in phosphorus (P) extraction at the pore scale. However, their importance at the field scale remains poorly understood. Methods This study uses a continuum model to explore the impact of root hairs on the large-scale uptake of P, comparing root hair influence under different agricultural scenarios. High vs low and constant vs decaying P concentrations down the soil profile are considered, along with early vs late precipitation scenarios. Results Simulation results suggest root hairs accounted for 50% of total P uptake by plants. Furthermore, a delayed initiation time of precipitation potentially limits the P uptake rate by over 50% depending on the growth period. Despite the large differences in the uptake rate, changes in the soil P concentration in the domain due to root solute uptake remains marginal when considering a single growth season. However, over the duration of 6 years, simulation results showed that noticeable differences arise over time. Conclusion Root hairs are critical to P capture, with uptake efficiency potentially enhanced by coordinating irrigation with P application during earlier growth stages of crops.

Research paper thumbnail of Preliminary numerical solutions of the evolution of free jets. IMECE2012-86730

ABSTRACT The present paper presents preliminary numerical solutions of the flow evolution of a tw... more ABSTRACT The present paper presents preliminary numerical solutions of the flow evolution of a two dimensional rectangular free jet. The numerical simulations in a two-dimensional domain are carried out with Open-FOAM, the open-source code, and compare the numerical results with the experimental visualizations performed in the same laboratory with the shadowgraph technique. The evolution of a two-dimensional submerged free jet is reported in the literature by the presence of two regions of flow: the potential core, where the centerline velocity maintains equal to that on the slot exit, and the turbulent or mixing region, where the centerline velocity decreases with the distance from the exit. Previous anemometric measurements, carried out in this laboratory with an air jet emerging from a rectangular channel, showed the presence of a region of flow, just outside the exit and before the potential core, where velocity and turbulence remain almost equal to those measured on the exit, and it has been called “undisturbed region of flow” because is present also in turbulent conditions. Previous and present shadowgraph visualizations show a jet which has the same height along the undisturbed region of flow and increases its height afterwards. The length of the undisturbed region depends on the Reynolds number of the flow and on the presence of turbulence promoters, e.g. metallic grids, at the exit of the slot. The undisturbed region is becoming nil with the increase of the Reynolds numbers, in agreement to the literature. The present two dimensional numerical solutions, carried out at Re numbers equal to 25,000 and 60,000 confirm the results obtained with the shadow visualizations.

Research paper thumbnail of Heat transfer on a flat wall due to a rectangular turbulent jet

International Communications in Heat and Mass Transfer

Research paper thumbnail of Further results on the mean mass transfer and fluid flow in a turbulent round jet

International Communications in Heat and Mass Transfer

Research paper thumbnail of Passive scalar diffusion in three-dimensional turbulent rectangular free jets with numerical evaluation of turbulent Prandtl/Schmidt number

International Communications in Heat and Mass Transfer, 2018

The passive scalar spreading of fluids with laminar Prandtl or Schmidt number, , Pr Sc , equal to... more The passive scalar spreading of fluids with laminar Prandtl or Schmidt number, , Pr Sc , equal to 1 in turbulent rectangular submerged free jets is analyzed by means of numerical simulation and theoretical analysis in the Reynolds number range 5000-40,000. The numerical investigation is carried out by means of a three-dimensional (3D) Large Eddy Simulation (LES) approach with the dynamic Smagorinsky model. A new mathematical model allows to obtain a simplified description of the passive scalar spreading in the largest area of the flow field, the Fully Developed Region (FDR). The present three-dimensional (3D) investigation shows that the passive scalar spreading follows a self-similarity law in the Fully Developed Region (FDR), as well as in the mean Undisturbed Region of Flow (URF) and in the Potential Core Region (PCR), similarly to what found in the Near Field Region (NFR) of rectangular submerged free jets, investigated with a two-dimensional (2D) approach. The turbulent Prandtl or Schmidt number is evaluated numerically and is found to be inversely proportional to the mean velocity gradient in the PCR. The present 3D numerical results show that the turbulent Prandtl or Schmidt number is zero in most part of the mean URF, and PCR, while it assumes different values outside. In the FDR the turbulent Prandtl or Schmidt number is constant and approximately equal to 0.7, in agreement with the literature, showing that turbulence affects momentum and passive scalar in a different way.

Research paper thumbnail of On a phase-field model for a miscible drop in a spinning drop tensiometer

Bulletin of the American Physical Society, 2011

ABSTRACT We examine shape transformations of a solute droplet immersed into a solvent-filled and ... more ABSTRACT We examine shape transformations of a solute droplet immersed into a solvent-filled and sealed capillary tube subject to fast rotations around its axis, i.e. the configuration of the spinning drop tensiometer. Despite the fact, that a droplet is miscible, its dissolution occurs rather slowly, and under rotations a droplet becomes elongated, which is used to measure the dynamic surface tension of the solute/solvent interface. The Boussinesq approximation [1] of the full (quasi- compressible) Cahn-Hilliard-Navier-Stokes is used as a theoretical model to capture the droplet evolution. We found that the behaviour of a miscible droplet contained in a closed enclosure is strongly different from an immiscible one. Miscible droplets in general are thermodynamically unstable and ultimately dissolve, large partially miscible droplets however may remain stable with the size determined by the total mass balance. In the limit of high Prandtl numbers, droplet's shape changes quickly (on a convective time scale), so that quasi- stable droplets are observed with only weak hydrodynamic flows present. Such states remain thermodynamically unstable: droplets lose their mass and the droplet's interface properties changes on a long diffusive time scale.[4pt] [1] A. Vorobev, PRE 82, 056312 (2010).