Effect of non-Newtonian fluid rheology on an arterial bypass graft: A numerical investigation guided by constructal design

In post-operative scenarios of arterial graft surgeries to bypass coronary artery stenosis, fluid dynamics plays a crucial role. Problems such as intimal hyperplasia have been related to fluid dynamics and wall shear stresses near the graft junction. This study focused on the question of the use of Newtonian and non-Newtonian models to represent blood in this type of problem in order to capture important flow features, as well as an analysis of the performance of geometry from the view of Constructive Theory. The objective of this study was to investigate the effects rheology on the steady-state flow and on the performance of a system consisting of an idealized version of a partially obstructed coronary artery and bypass graft. The Constructal Design Method was employed with two degrees of freedom: the ratio be- tween bypass and artery diameters and the junction angle at the bypass inlet. The flow problem was solved numerically using the Finite Volume Method with blood modeled employing the Carreau equation for viscosity. The Computational Fluid Dynamics model associated with the Sparse Grid method generated eighteen response surfaces, each representing a severe stenosis degree of 75% for specific combinations of rheological parameters, dimensionless viscosity ratio, Carreau number and flow index at two distinct Reynolds numbers of 150 and 250. There was a considerable dependence of the pressure drop on rhe- ological parameters. For the two Reynolds numbers studied, the Newtonian case presented the lowest value of the dimensionless pressure drop, suggesting that the choice of applying Newtonian blood may underestimate the value of pressure drop in the system by about 12.4% ( Re = 150) and 7.8% ( Re = 250). Even so, results demonstrated that non-Newtonian rheological parameters did not influence either the shape of the response surfaces or the optimum bypass geometry, which consisted of a diameter ratio of 1 and junction angle of 30 °. However, the viscosity ratio and the flow index had the greatest im- pact on pressure drop, recirculation zones and wall shear stress. Rheological parameters also affected the recirculation zones downstream of stenosis, where intimal hyperplasia is more prevalent. Newto- nian and most non-Newtonian results had similar wall shear stresses, except for the non-Newtonian case with high viscosity ratio. In the view of Constructal Design, the geometry of best performance was in- dependent of the rheological model. However, rheology played an important role on pressure drop and flow dynamics, allowing the prediction of recirculation zones that were not captured by a Newtonian model

Otimização de design do duto ramificado em forma de T com escoamento de fluido newtoniano e paredes impermeáveis

Este artigo apresenta os resultados de escoamentos em dutos em forma de “T”. O problema consiste em encontrar as resistências ao escoamento em estruturas tridimensionais (3D) cujos sistemas têm diferentes relações homotética entre tamanhos (diâmetros e comprimentos) dos dutos de entrada e saída de fluído. O método utilizado é denominado “Constructal Design” e é fundamentado na “Teoria Constructal”. Este método baseia-se na minimização da resistência global sujeito a restrições geométricas, que no presente estudo são o volume e área ocupada pelos dutos considerados constantes. O escoamento nos dutos é considerado tridimensional, laminar, incompressível, e em regime permanente e com propriedades uniformes e constantes. Os resultados obtidos numericamente em geometrias 3D é validado por comparação com os resultados analíticos bidimensional disponíveis na literatura. A geometria será estudada para diferentes relações D1 / D0 e L1 / L0, para diferentes número de Reynolds

Constructal design of an arterial bypass graft

Arterial bypass grafts tend to fail after some years due to intimal hyperplasia\u2014an abnormal proliferation of smooth muscle cells that leads to stenosis and graft occlusion. In this regard and on the basis of the constructal design method, this study seeks to investigate the effect of geometric parameters\u2014stenosis degree, junction angle, and diameter ratio\u2014on the flow through a bypass graft circumventing an idealized, partially stenosed coronary artery. The computational model assumes a steady\u2010state Newtonian fluid flow through an artery stenosis degree from 25% to 75%. A computational fluid dynamics model and a response surface methodology were employed to assess the effects of the project parameters on pressure drop. As diameter ratio increases to 1 and the junction angle decreases to 30\ub0, the pressure drop decreases and there is a considerable dependence of pressure drop on the stenosis degree. The effects of the diameter ratio are more pronounced than those of junction angle on the velocity field and wall shear stress. The application of the constructal design method in hemodynamicsmight be a good alternative to provide configurations with enhanced performance and to provide valuable results to the understanding of biological flows

CONSTRUCTAL DESIGN OF FINS IN COOLED CAVITIES BY NON-NEWTONIAN FLUIDS

The present work investigates the Construtal Design of fins inserted in cavities submitted to mixed convection by non-Newtonian fluids. The objective is to obtain the optimum aspect ratio for the fin considering different flow conditions and variations in the rheological parameters of the fluid. The phenomena of flow and heat transfer are modeled by mass balance, momentum and energy equations, and by the generalized Newtonian liquid constitutive equation. The viscosity is modeled as that of a pseudoplastic fluid, using the Carreau function. The optimization problem consists in maximizing heat transfer from the fin using the average Nusselt number. The investigated project variable is the aspect ratio between the edges of the rectangular plane fin profile. The restrictions are the volume of the cavity and the fin. The results are obtained numerically using a finite volume code and a two-dimensional geometry, through exhaustive searching. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, such as was shown in previous studies. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, as was shown in previous studies. It was also found that the Nusselt number increases as the increase in flow intensity, represented by the parameter p, and that the result of the maximum Nusselt number does not change monotonically with the non-Newtonian dimensionless viscosity and with the flow index, showing that the pseudoplasticity of the fluid implies optimal configurations very different from those predicted for Newtonian fluids

COMPUTATIONAL FLUID DYNAMICS OF A FLUID BED EMPLOYING TUNED GAS-SOLID DRAG MODELS

Fluidized beds are devices in which a fluid flows from the bottom through a bed of particles, keeping them under suspension. Fluidized beds find many applications as reactors for combustion and gasification of solid fuels. For a given fluid-particulate combination, there is a minimum fluidization velocity (U mf) which exerts a drag force that equals the weight of the bed, fluidizing the system. Therefore, it is possible to calculate gas-solid drag forces parameters from a minimum fluidization velocity (Umf) obtained experimentally. In the present work, the objective was to tune gas-solid drag correlations to be used in the Computational Fluid Dynamics (CFD) of a fluidized bed employing the Umf and to analyze the improvement of CFD results. The particles employed were one of Geldart-B (sand-like) and two of Geldart-D (spoutable) types, fluidized in a cylindrical riser with 0.114 m internal diameter. The CFD multiphase model employed was the Two-Fluid-Model (TFM). In this model both gas and solid phases are assumed interpenetrating continua, mapped along the domain via its volume fraction, and the Kinetic Theory of Granular Flows (KTGF) is used to model solids phase viscosity term. The force interactions between phases are modeled using gas-solid drag correlations, which in this work were based on Syamlal-O'Brien and Di Felice models. A finite volume method CFD code was used to perform the simulations. The simulations for superficial velocity of 1.5 Umf was performed in order to confront experimental and numerical results of pressure drop and bed height. So far tuned models were better than the original ones in the prediction of fluidization curves (pressure drop versus superficial velocity), and in the prediction of bed expansion and bubble formation

GALERKIN LEAST-SQUARES APPROXIMATIONS FOR FLOWS OF CASSON FLUIDS THROUGH AN EXPANSION

Among non-Newtonian fluid models, purely viscous constitutive equations play an important role in industrial applications regardless their lack of accuracy in non-viscometric flows. In this work we are concerned with the flow of viscoplastic shear-thinning fluids in complex geometry. Viscoplastic fluids are those that behave as extremely high viscosity materials when submitted to low stresses and that flow when submitted to stresses higher than a yield stress value. Usually, they also present shearthinning behavior. Fluids such as molten chocolate, xanthan gum solutions, blood, wastewater sludges, muds, and polymer solutions present viscoplastic shear-thinning features. In order to approximate numerically viscoplastic shear-thinning flows we first describe a mechanical model based on continuum mechanics conservation laws of mass and momentum. The description of material behavior is such as to respect certain principles of objectivity and generality in continuum mechanics. The Generalized Newtonian Liquid constitutive equation with Casson viscosity function is able to predict viscoplasticity and shear-thinning. The numerical approximation of the equations is performed by a finite element method. To prevent the model from pathologies known for the classic Galerkin method, we employ a stabilized method based on a Galerkin least-squares (GLS) scheme, which is designed to circumvent Babuška-Brezzi condition and deal with the asymmetry of the advective operator. We present approximations for the flow through a planar 4:1 sudden expansion. We investigate the influence of Reynolds and Casson numbers on the flow dynamics

Pulsatile flow through an idealized arterial bypass graft: an application of the constructal design method

Bypass grafts promote blood flow impaired by a partial obstruction (stenosis) of arteries by fat accumulation. This type of system’s computational modeling is used to understand the flow characteristics and look for reasons and solutions for postoperative failures. The present work deals with the effects of changes in geometry in the performance of a system consisting of an idealized partially obstructed artery and a bypass graft. The constructal design method has been employed in previous works in the analysis of such system assuming steady-state flow. In the present work, blood flow is modeled as transient and pulsatile. The constructal design method is used to determine the performance indicator (dimensionless pressure drop), constraints (system volume and stenosis degrees–50% and 75%) and degrees of freedom: junction angle (30º ≤ α ≤ 70º) and diameter ratio (0.5 ≤ D1/ D ≤ 1). The response surface methodology was used to evaluate the conditions of minimum pressure drop in transient conditions. As the junction angle decreased to 30º, and the diameter ratio increased to 1, the pressure drop decreased, and there was a considerable dependence of pressure drop on the stenosis degree. The effects of the diameter ratio were more pronounced than those of the junction angle. A resistance model based on an analogy with an electronic circuit was introduced, resulting in a correlation for the pressure drop due to the bypass. This correlation confirmed that the point (, D1∕D) = (30◦, 1) is a point of minimization of flow resistance. The application of the constructal design method in hemodynamics might be an excellent alternative to configuring enhanced performance and providing valuable results to the understanding of biological flows

Effect of Bejan and Prandtl numbers on the design of tube arrangements in forced convection of shear thinning fluids: A numerical approach motivated by constructal theory

In this work, the effects of the pressure drop (i.e. the Bejan number in dimensionless term) and of the Prandtl number have been investigated with reference to optimal geometries for maximizing the heat transfer density under forced convection of shear thinning fluids. Constructal Design associated with Design of Experiments and Response Surface methodologies have been employed to search computationally for the optimals. More specifically, after having fixed the power law index value, n, equal to 0.4, we studied the effect of the Bejan number, Be, ranging from 10(4) to 10(5) (for Pr = 1) and the effect of the Prandtl number, Pr, ranging from 1 to 10 (for Be = 10(5)) on the maximum dimensionless heat transfer density. The optimal geometries here detected differ much from those referred to Newtonian fluids, as a consequence of the non-linear stress behavior with respect to strain rate. We observed that the optimal aspect ratio of the elliptical tubes, r(opt) highlights different (opposite) behaviours with the augmentation of Be and Pr: while r(opt) decreases as Be increases, it augments with higher Pr, suggesting that for flows characterized by thermal diffusivity the tubes should be more slender horizontally for better heat transfer performance. In the meantime, assigned r(opt), the dimensionless optimal distance between tubes, (S)over-tilde(0), proved to be practically independent of all the tested values of Bejan number and Prandtl number

Dimensionless pressure drop number for non-newtonian fluids applied to Constructal Design of heat exchangers

This paper introduces a dimensionless group for pressure drop, named Bejan number (Be), to be used with non-Newtonian fluids. When defining Be for non-Newtonian fluids, it is necessary to choose a characteristic apparent viscosity to compose this dimensionless group. In non-Newtonian fluid dynamics, the viscosity at a characteristic shear rate is usually chosen as reference, with the latter given as the reference velocity divided by the reference length. When the flow rate is not known, a reference velocity may be taken as the square root of the pressure drop divided by the mass density. Thus, a characteristic apparent viscosity may be defined for any non-Newtonian model, even for one that does not present a characteristic viscosity defined explicitly in the viscosity function, such as the power-law model. The non-dimensionalization of motion equations for the crossflow of a power-law fluid between two aligned cylinders was performed using this philosophy. Some numerical tests were performed to corroborate the idea that the introduced form for Be is a good alternative to be used in experiments to predict and evaluate the heat transfer density in the context of Constructal Design of heat exchangers tube bundles

Geometric optimization of a rectangular isothermal block inside a lid-driven cavity by means of constructal design

The present work applies the Constructal Design method to analyze the performance of a rectangular isothermal block (IB) - inside an adiabatic lid-driven cavity with an isothermal lid - submitted to mixed convection heat transfer with unstable stratification. The effect of IB configuration on heat transfer performance is investigated via numerical simulation of heat and flow dynamics. The modeling for numerical simulations involves steady, laminar, and incompressible flow in a two-dimensional domain filled with a Newtonian fluid (air). Equations of mass, momentum, and energy balance are solved using numerical simulations based on the finite volume method (FVM). The main purpose of employing the Constructal Design method is to maximize the dimensionless heat transfer rate (q⁎) between the IB and the surrounding fluid. The constraint are the cavity area and the IB/cavity area fraction (φ = 1/4, 1/8, 1/16, and 1/32), while the IB aspect ratio and its horizontal position are the degrees of freedom (DOF). The behavior of the system is investigated for different operational conditions given by the Richardson Number (Ri = 0.1, 1.0, and 10), for fixed Grashof (GrA = 105) and Prandtl (Pr = 0.71) numbers. Considering all possible combinations of the analyzed parameters, 162 different geometric configurations were tested (54 for each Ri). The results indicate that higher heat transfer rates are associated with the largest aspect ratio tested for each IB-cavity area fraction. For φ = 1/16 and Ri = 0.1 – when the IB assumes a tall shape – q⁎ is 143.2% greater than the square shape. Considering all cases, the highest q⁎ is related to the flow dominated by forced convection (Ri = 0.1) and the IB placed to the right, where the IB-cavity area fraction and the IB aspect ratio are 1/4 and 3.0, respectively