scholarly journals Numerical study on the energy cascade of pulsatile Newtonian and power-law flow models in an ICA bifurcation

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245775
Author(s):  
Samar A. Mahrous ◽  
Nor Azwadi Che Sidik ◽  
Khalid M. Saqr
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Numerical Study ◽  
Carotid Bifurcation ◽  
Shear Thinning ◽  
Energy Cascade ◽  
Hemodynamic Parameters ◽  
Vortex Identification ◽  
Newtonian Viscosity ◽  
The Impact

The complex physics and biology underlying intracranial hemodynamics are yet to be fully revealed. A fully resolved direct numerical simulation (DNS) study has been performed to identify the intrinsic flow dynamics in an idealized carotid bifurcation model. To shed the light on the significance of considering blood shear-thinning properties, the power-law model is compared to the commonly used Newtonian viscosity hypothesis. We scrutinize the kinetic energy cascade (KEC) rates in the Fourier domain and the vortex structure of both fluid models and examine the impact of the power-law viscosity model. The flow intrinsically contains coherent structures which has frequencies corresponding to the boundary frequency, which could be associated with the regulation of endothelial cells. From the proposed comparative study, it is found that KEC rates and the vortex-identification are significantly influenced by the shear-thinning blood properties. Conclusively, from the obtained results, it is found that neglecting the non-Newtonian behavior could lead to underestimation of the hemodynamic parameters at low Reynolds number and overestimation of the hemodynamic parameters by increasing the Reynolds number. In addition, we provide physical insight and discussion onto the hemodynamics associated with endothelial dysfunction which plays significant role in the pathogenesis of intracranial aneurysms.

Heat Transfer Enhancement in Annular Shear-Thinning Flows Over a Sudden Pipe Expansion

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Power Law ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Transfer Enhancement ◽  
Heat Transfer Augmentation ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
The Impact

Heat transfer enhancement in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers, Nu, higher than the fully developed value, in the downstream pipe, is observed only for Pr = 10 and 100. Higher Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane. Heat transfer augmentation for Pr = 10 and 100, is more dramatic for suddenly expanding annular flows, in comparison with suddenly expanding pipe flow. For a given annular diameter ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, for both Newtonian and shear-thinning non-Newtonian flows.

Flow Inertia and Heat Transfer in Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Shear Thinning ◽  
Heat Transfer Augmentation ◽  
Flow And Heat Transfer ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
Annular Pipe ◽  
Flow Inertia ◽  
The Impact

The impact of flow inertia on flow and heat transfer in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. The equations governing conservation of mass, momentum, and energy, along with the power-law constitutive model are numerically solved using a finite-difference numerical scheme. The influence of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5}; n = {1, 0.6}; and Pr = {1, 10, 100}. Heat transfer augmentation, downstream the plane of expansion, is only observed for Pr = 10 and 100. The extent and intensity of recirculation in the corner region, increases with inflow inertia. Higher Reynolds and Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane.

LATTICE BOLTZMANN SIMULATION OF TWO-DIMENSIONAL WALL BOUNDED TURBULENT FLOW

2010 ◽  
Vol 21 (05) ◽  
pp. 669-680 ◽  
Author(s):  
GÁBOR HÁZI ◽  
GÁBOR TÓTH
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Power Laws ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulation ◽  
Decaying Turbulence

This paper reports on a numerical study of two-dimensional decaying turbulence in a square domain with no-slip walls. The generation of strong small-scale vortices near the no-slip walls have been observed in the lattice Boltzmann simulations just like in earlier pseudospectral calculations. Due to these vortices the enstrophy is not a monotone decaying function of time. Considering a number of simulations and taking their ensemble average, we have found that the decay of enstrophy and that of the kinetic energy can be described well by power-laws. The exponents of these laws depend on the Reynolds number in a similar manner than was observed before in pseudospectral simulations. Considering the ensemble averaged 1D Fourier energy spectra calculated along the walls, we could not find a simple power-law, which fits well to the simulation data. These spectra change in time and reveal an exponent close to -3 in the intermediate and an exponent -5/3 at low wavenumbers. On the other hand, the two-dimensional energy spectra, which remain almost steady in the intermediate decay stage, show clear power-law behavior with exponent larger than -3 depending on the initial Reynolds number.

Nonlinear Dynamics of Cattaneo–Christov Heat Flux Model for Third-Grade Power-Law Fluid

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Bhuvnesh Sharma ◽  
Sunil Kumar ◽  
Carlo Cattani ◽  
Dumitru Baleanu
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Power Law ◽  
Shear Thinning ◽  
Third Grade ◽  
Power Law Fluid ◽  
Conservation Of Energy ◽  
Flux Model ◽  
The Impact ◽  
Heat Flux Model

Abstract A rigorous analysis of coupled nonlinear equations for third-grade viscoelastic power-law non-Newtonian fluid is presented. Initially, the governing partial differential equations for conservation of energy and momentum are transformed to nonlinear coupled ordinary differential equations using exact similarity transformations which are known as Cattaneo–Christov heat flux model for third-grade power-law fluid. The homotopy analysis method (HAM) is utilized to approximate the systematic solutions more precisely with shear-thickening, moderately shear-thinning, and most shear-thinning fluids. The solution depends on various parameters including Prandtl number, power index, and temperature variation coefficient. A systematic analysis of boundary-layer flow demonstrates the impact of these parameters on the velocity and temperature profiles.

Inflow Conditions and Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Inflow Velocity ◽  
Flow Recirculation ◽  
Shear Thinning Fluids ◽  
Power Law Index ◽  
The Impact ◽  
Inflow Conditions

The impact of inflow conditions on the flow structure and evolution characteristics of annular flows of Newtonian and shear-thinning fluids through a sudden pipe expansion are studied. Numerical solutions to the elliptic form of the governing equations along with the power-law constitutive equation were obtained using a finite-difference scheme. A parametric study is performed to reveal the influence of inflow velocity profiles, annular diameter ratio, k, and power-law index, n, over the following range of parameters: inflow velocity profile = {fully-developed, uniform}, k = {0, 0.5, 0.7} and n = {1, 0.8, 0.6}. Flow separation and entrainment, downstream of the expansion plane, creates central and a much larger outer recirculation regions. The results demonstrate the influence of inflow conditions, annular diameter ratio, and rheology on the extent and intensity of both flow recirculation regions, the wall shear stress distribution, and the evolution and redevelopment characteristics of the flow downstream the expansion plane. Fully-developed inflows result in larger reattachment and redevelopment lengths as well as more intense recirculation, within the central and corner regions, in comparison with uniform inflow conditions.

Pulse dynamics in a power-law falling film

2014 ◽  
Vol 747 ◽  
pp. 460-480 ◽  
Author(s):  
M. Pradas ◽  
D. Tseluiko ◽  
C. Ruyer-Quil ◽  
S. Kalliadasis
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Thin Liquid Film ◽  
Small Strain ◽  
Shear Thinning ◽  
Final State ◽  
Local Flow ◽  
Stability Dynamics ◽  
The Stability ◽  
Low Dimensional

AbstractWe examine the stability, dynamics and interactions of solitary waves in a two-dimensional vertically falling thin liquid film that exhibits shear-thinning effects. We use a low-dimensional two-field model that describes the evolution of both the local flow rate and the film thickness and is consistent up to second-order terms in the long-wave expansion. The shear-thinning behaviour is modelled via a power-law formulation with a Newtonian plateau in the limit of small strain rates. Our results show the emergence of a hysteresis behaviour as the control parameter (the Reynolds number) is increased which is directly related to the shear-thinning character of the liquid and can be quantified with both linear analysis arguments and a physical interpretation. We also study pulse interactions, observing that two pulses may attract or repel each other either monotonically or in an oscillatory manner. In large domains we find that for a given Reynolds number the final state depends on the initial condition, a consequence of the presence of multiple solutions.

Numerical study of the effect of blockage ratio in forced convection confined flows of shear-thinning fluids

2021 ◽  
Vol 929 ◽  
Author(s):  
O. Ruz ◽  
E. Castillo ◽  
M. Cruchaga
Keyword(s):  
Case Studies ◽  
Power Law ◽  
Numerical Study ◽  
Three Dimensional ◽  
Shear Thinning ◽  
Time Dependent ◽  
Blockage Ratio ◽  
Chaotic Flows ◽  
Nusselt Numbers ◽  
Wide Range

In this work, the fluid dynamics and heat transfer of time-dependent flows with shear-thinning behaviour over two confined square cylinders in tandem arrangement are studied numerically. The case studies include two- and three-dimensional flows under a wide range of power-law indices, $0.25\leq n \leq 1.0$ , and blockage ratios, $\beta =0.50$ , 0.66 and 0.80, for a fixed Reynolds number of $Re=100$ and Prandtl number of $Pr=10$ . The fluid dynamic analysis includes detailed qualitative and quantitative comparisons between the different fluids and blockage ratios, where streamlines, viscosity fields, and lift and drag coefficients are presented. Moreover, a detailed study of the route from laminar time-dependent to chaotic flows is included. It was determined that the flow exhibits a transition from laminar to chaotic by decreasing the power-law index ( $n$ ) and increasing the blockage ratio ( $\beta$ ). With respect to the thermal analysis, isotherms and Nusselt numbers are compared between the different case studies. This analysis demonstrates that the average Nusselt numbers increased in chaotic flows. The three-dimensional cases confirmed the results proposed for the two-dimensional case.

Numerical Simulation of the Steady-State Herschel-Bulkley Fluid Flow in a Channel with Sudden Expansion

2017 ◽  
Vol 743 ◽  
pp. 474-479
Author(s):  
Efim Hegaj ◽  
Evgeny Borzenko
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Steady State ◽  
Power Law ◽  
Simple Procedure ◽  
Sudden Expansion ◽  
Bingham Number ◽  
Power Law Index ◽  
The Impact

In this paper, the steady-state flow of non-Newtonian fluid in a planar channel with sudden expansion is investigated. The rheological behavior of this media is described by the Herschel-Bulkley model. To determine both steady-state velocity and pressure fields, a numerical algorithm based on the relaxation method and SIMPLE procedure is used.The mathematical problem statement includes three non-dimensional parameters: the Reynolds number, the Bingham number (non-dimensional viscoplasticity parameter), and the power-law index. The results of numerical simulation are obtained in a range of the Reynolds number 1 ≤ Re ≤ 40, Bingham number 0 ≤ Se ≤ 2, and power-law index 0.4 ≤k ≤ 2 (for shear thinning, Newtonian, and shear thickening fluids).The distribution of the main fluid flow characteristics and localization of the two-dimensional region in an expansion zone is presented. The impact of main parameters of the problem on a dead zone distribution in the fluid flow is shown.

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