How to use solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media

ResumenLas soluciones de la Ecuación de Advección-Dispersión son usadas frecuentemente para describir el transporte de solutos a través de medios porosos, considerando adsorción en equilibrio, de tipo lineal y reversible. Para indicar algunas sugerencias acerca de este tema, se hizo una revisión de las soluciones analíticas disponibles. Hay soluciones para Problemas con Condiciones de Frontera, de primer y tercer-tipo en la entrada así como de primer y segundo-tipo a la salida. Se analiza el comportamiento de las soluciones equivalentes, para sistemas finitos y semi-infinitos, observando que las soluciones de los sistemas semi-infinitos se aproximan a las correspondientes de los sistemas finitos conforme la condición de frontera de salida en el infinito se aproxima a la ubicación de medición del sistema finito. Solamente se presentan las soluciones analíticas con condiciones de frontera de segundo-tipo a la salida, ya que son iguales a las correspondientes soluciones analíticas con frontera de primer-tipo a la salida, para ambos tipos de condiciones de frontera de entrada usadas. Un análisis paramétrico, basado en el número de Peclet, muestra que todas las soluciones convergen cuando el número de Peclet es mayor que veinte. Los sistemas investigados deben tener un número de Peclet mayor que cinco para usar con confianza las soluciones de la Ecuación de Advección-Dispersión para describir el transporte de soluto en medios porosos.Palabras Clave: Ecuación de Advección-Difusión, Soluciones Analíticas, Transporte de Solutos Reactivos, Medios Porosos.AbstractThe solutions of Advection-Dispersion Equation are frequently used to describe solute transport through porous media when considering lineal and reversible equilibrium adsorption. To notice some warnings about this item, a review of analytical solutions available was done. There are solutions for Boundary Value Problems with first and third-type inlet boundary conditions as well as first and second-type outlet boundary condition. The behavior of equivalent solutions for finite and semi-infinite systems are analyzed, observing that semi-infinite system solutions approximates to the corresponding finite ones as the “infinite” outlet boundary condition approach to the finite measurement location. Because the analytical solutions with a first-type outlet boundary condition are equal to the corresponding analytical solutions with a second-type one, for both inlet boundary condition type used, only the latter is presented. A parametric analysis based on Peclet number shows that all solutions converge for Peclet number greater than twenty. Systems under research must have Peclet number greater than five to use confidently the solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media.Keywords: Advection-Diffusion Equation, Analytical solutions, Reactive Solute Transport, Porous Media.

Evaluation of Pulmonary Arterial Hypertension Using Computational Fluid Dynamics Simulation

In silico study of the relationships between flow conditions, arterial surface shear stress, and pressure was investigated in a patient with pulmonary arterial hypertension (PAH), using multi-detector Computed Tomography Angiography (CTA) images and Computational Fluid Dynamics (CFD). The CTA images were converted into 3D models and transferred to CFD software for simulations, allowing for patient-specific comparisons between in silico results with clinical right heart catheterization pressure data. The simulations were performed using two different methods of outlet boundary conditions: zero traction and lumped parameter model (LPM) methods. Outlet pressures were set to a constant value in zero traction method, which can produce flow characteristics solely based on the segmented distal arteries, while the lumped parameter model used a three-element Windkessel lumped model to represent the distal vasculature by accounting for resistance, compliance, and impedance of the vasculature. Considering existing limitations with both approaches, it was found that the lumped parameter Windkessel outlet boundary condition provides a better correlation with the clinical RHC pressure results than the zero traction constant pressure outlet boundary condition.

A seepage outlet boundary condition in hemodynamics modeling

Background:In computational fluid dynamics (CFD) models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions.Objective:As an important part of the arterial circulation, microcirculation plays important roles in many aspects, such as substance exchange, interstitial fluid generation and inverse flow. It is necessary to consider microcirculation in hemodynamics modeling. This is a methodological paper to test and validate a new type of boundary condition never applied to microcirculation before.Methods:In order to address this issue, we introduce microcirculation as a seepage outlet boundary condition in computational hemodynamics. Microcirculation is treated as a porous medium in this paper. Numerical comparisons of the seepage and traditional boundary conditions are made.Results:The results show that the seepage boundary condition has significant impacts on numerical simulation. Under the seepage boundary condition, the fluctuation range of the pressures progressively rises in the artery zone. The results obtained from the traditional boundary condition show that the pressure fluctuation range gradually falls. In addition, the wall shear stresses under the traditional outlet boundary condition are much higher than those under the seepage outlet boundary condition.Conclusions:The proposed boundary condition is more suitable in hemodynamics modeling.

VALIDATION OF LOSS-COEFFICIENT-BASED OUTLET BOUNDARY CONDITIONS FOR SIMULATING AORTIC FLOW

Flow in a polyurethane model of a human aorta, driven by a heart-lung machine, is analyzed experimentally and computationally for antegrade and retrograde perfusion. The purpose of the analysis is the validation of the previously proposed loss-coefficient-based outlet boundary condition for aortic branches. This model is claimed to be commonly applicable to different perfusion modes of the aorta, unlike the alternative straightforward constant-pressure outlet boundary condition. First, the antegrade perfusion is analyzed computationally and experimentally. This step delivers the loss-coefficients that are to be used in any other perfusion mode of the aorta. Subsequently, a retrograde perfusion is applied to the same aorta, where the flow rates at the outlets of the aortic branches are measured and predicted by applying the loss-coefficient-based outlet boundary conditions. A very good agreement of the predictions with the measurements is observed. The predictions delivered by the standard constant-pressure outlet boundary condition are observed, on the contrary, to be highly in error. Thus, the advocated loss-coefficient-based outlet boundary condition is experimentally validated. It is shown that it is applicable to different perfusion modes with a quite good accuracy, which is much higher compared to the straightforward constant-pressure outlet boundary condition.

A Novel Numerical Scheme for Outlet Boundary Conditions in Large Density Ratio Lattice Boltzmann Model

In the past decades, the Lattice Boltzmann method has gained much success in variety fields especially in multiphase flow, porous media flow, and other complex flow, and become a promising method for computational fluid dynamic (CFD). The outlet boundary condition (OBC) and its numerical scheme are critical issues in CFD, which may influence the accuracy and stability of the calculation. The common OBCs i.e. Neumann boundary condition (NBC), extrapolation boundary condition (EBC), and convection boundary condition (CBC), which have been widely investigated in single-phase LB model, have rarely been investigated in multiphase LB model. The previous research on the OBCs for two-phase LB model only aims at small density ratio. While in most industrial applications, the density ratio often ranges from a hundred to a thousand, and a large density ratio would bring some problems such as parasitic current and bad stability in LB method. Lee and Fischer have proposed an improved LB model which is suitable for large density ratio two-phase flow. In order to assess the OBCs for large density ratio LB model, the OBCs are investigated. And it is found that the existing OBC numerical scheme cannot be directly applied to the large density ratio LB model. In present study, a novel numerical scheme for the OBCs is proposed assuming that the outlet velocity is gained by the outlet boundary condition instead of the momentum equation which is an improvement of previous scheme, and it can be used in large density ratio LB model. The performance of the proposed OBC scheme is examined for different density ratios. The results show that the proposed OBC scheme could converge in a stable manner. Comparing with the reference flow condition, the CBC scheme shows a better performance than the NBC scheme and the EBC scheme. The NBC scheme would lead a large droplet deformation, large velocity peaks at the outlet, and large errors for both small and large density ratio. And the EBC scheme keeps a good droplet shape, but it would lead large velocity peaks at the outlet and large error when large density ratio is considered. The CBC scheme always shows superior performance including a good droplet shape, smooth outlet velocity profile, and small errors no matter whether the density ratio is small or large. Hence the CBC scheme could be applied in large density ratio LB model for the outlet boundary condition, which has a good accuracy and stability in the calculation.