Non-Newtonian mixed convection flow from a horizontal circular cylinder with uniform surface heat flux

Mixed convection laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is investigated from a horizontal circular cylinder with uniform surface heat flux using a modified power-law viscosity model, that contains no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid temperature distributions, rate of heat transfer in terms of the local Nusselt number.

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

Influence of friction during forming processes-a study using a numerical simulation technique

Friction has an important influence in metal forming operations, as it contributes to the success or otherwise of the process. In the present investigation, the effect of friction on metal forming was studied by simulating compression tests on cylindrical Al-Mg alloy using the finite element method (FEM) technique. Three kinds of compression tests were considered wherein a constant coefficient of friction was employed at the upper die-work-piece interface. However, the coefficient of friction between the lower die-work-piece interfaces was varied in the tests. The simulation results showed that a difference in metal flow occurs near the interfaces owing to the differences in the coefficient of friction. It was concluded that the variations in the coefficient of friction between the dies and the work-piece directly affect the stress distribution and shape of the work-piece, having implications on the microstructure of the material being processed.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

Effect of inflow and outflow angles on the computational hemodynamics in abdominal aortic aneurysm

To help with the clinical screening and diagnosis of abdominal aortic aneurysm (AAA), we evaluated the effect of inflow angle (IA) and outflow bifurcation angle (BA) on the distribution of blood flow and wall shear stress (WSS) in an idealized AAA model. A 2D incompressible Newtonian flow is assumed and the computational simulation is performed using finite volume method. The results showed that the largest WSS often located at the proximal and the distal end of the AAA. An increase in IA resulted in an increase in maximum WSS. We also found that WSS was maximal when BA was 90°. IA and BA are two important geometrical factors, they may help with AAA risk assessment along with the commonly used AAA diameter.

Comparison between computational models of abdominal aortic aneurysm

Objective: To compare the differences in the hemodynamic parameters of abdominal aortic aneurysm (AAA) between fluid-structure interaction model (FSIM) and fluid-only model (FM), so as to discuss their application in the research of AAA. Methods: An idealized AAA model was created based on patient-specific AAA data. In FM, the flow, pressure and wall shear stress (WSS) were computed using finite volume method. In FSIM, an Arbitrary Lagrangian-Eulerian algorithm was used to solve the flow in a continuously deforming geometry. The hemodynamic parameters of both models were obtained for discussion. Results: Under the same inlet velocity, there were only two symmetrical vortexes in the AAA dilation area for FSIM. In contrast, four recirculation areas existed in FM; two were main vortexes and the other two were secondary flow, which were located between the main recirculation area and the arterial wall. Six local pressure concentrations occurred in the distal end of AAA and the recirculation area for FM. However, there were only two local pressure concentrations in FSIM. The vortex center of the recirculation area in FSIM was much more close to the distal end of AAA and the area was much larger because of AAA expansion. Four extreme values of WSS existed at the proximal of AAA, the point of boundary layer separation, the point of flow reattachment and the distal end of AAA, respectively, in both FM and FSIM. The maximum wall stress and the largest wall deformation were both located at the proximal and distal end of AAA. Conclusions: The number and center of the recirculation area for both models are different, while the change of vortex is closely associated with the AAA growth. The largest WSS of FSIM is 36% smaller than that of FM. Both the maximum wall stress and largest wall displacement shall increase with the outlet pressure increasing. FSIM needs to be considered for studying the relationship between AAA growth and shear stress.

Impact of coronary tortuosity on coronary pressure: Numerical simulation study

Background: Coronary tortuosity (CT) is a common coronary angiographic finding. Whether CT leads to an apparent reduction in coronary pressure distal to the tortuous segment of the coronary artery is still unknown. The purpose of this study is to determine the impact of CT on coronary pressure distribution by numerical simulation. Methods: 21 idealized models were created to investigate the influence of coronary tortuosity angle (CTA) and coronary tortuosity number (CTN) on coronary pressure distribution. A 2D incompressible Newtonian flow was assumed and the computational simulation was performed using finite volume method. CTA of 30°, 60°, 90°, 120° and CTN of 0, 1, 2, 3, 4, 5 were discussed under both steady and pulsatile conditions, and the changes of outlet pressure and inlet velocity during the cardiac cycle were considered. Results: Coronary pressure distribution was affected both by CTA and CTN. We found that the pressure drop between the start and the end of the CT segment decreased with CTA, and the length of the CT segment also declined with CTA. An increase in CTN resulted in an increase in the pressure drop. Conclusions: Compared to no-CT, CT can results in more decrease of coronary blood pressure in dependence on the severity of tortuosity and severe CT may cause myocardial ischemia.

Association between aneurysm shoulder stress and abdominal aortic aneurysm expansion: A longitudinal follow-up study

Background Aneurysm expansion rate is an important indicator of the potential risk of abdominal aortic aneurysm (AAA) rupture. Stress within the AAA wall is also thought to be a trigger for its rupture. However, the association between aneurysm wall stresses and expansion of AAA is unclear. Methods and Results Forty-four patients with AAAs were included in this longitudinal follow-up study. They were assessed by serial abdominal ultrasonography and computed tomography scans if a critical size was reached or a rapid expansion occurred. Patient-specific 3-dimensional AAA geometries were reconstructed from the follow-up computed tomography images. Structural analysis was performed to calculate the wall stresses of the AAA models at both baseline and final visit. A nonlinear large-strain finite element method was used to compute the wall-stress distribution. The relationship between wall stresses and expansion rate was investigated. Slowly and rapidly expanding aneurysms had comparable baseline maximum diameters (median, 4.35 cm [interquartile range, 4.12 to 5.0 cm] versus 4.6 cm [interquartile range, 4.2 to 5.0 cm]; P=0.32). Rapidly expanding AAAs had significantly higher shoulder stresses than slowly expanding AAAs (median, 300 kPa [interquartile range, 280 to 320 kPa] versus 225 kPa [interquartile range, 211 to 249 kPa]; P=0.0001). A good correlation between shoulder stress at baseline and expansion rate was found (r=0.71; P=0.0001). Conclusion A higher shoulder stress was found to have an association with a rapidly expanding AAA. Therefore, it may be useful for estimating the expansion of AAAs and improve risk stratification of patients with AAAs.

Computed wall stress may predict the growth of abdominal aortic aneurysm

Growth rate of abdominal aortic aneurysm (AAA) is thought to be an important indicator of the potential risk of rupture. Wall stress is also thought to be a trigger for its rupture. However, stress change during the expansion of an AAA is unclear. Forty-four patients with AAAs were included in this longitudinal follow-up study. They were assessed by serial abdominal ultrasonography and computerized tomography (CT) scans if a critical size was reached or a rapid expansion occurred. Patient-specific 3-dimensional AAA geometries were reconstructed from the follow-up CT images. Structural analysis was performed to calculate the wall stresses of the AAA models at both baseline and final visit. A non-linear large-strain finite element method was used to compute the wall stress distribution. The average growth rate was 0.66cm/year (range 0-1.32 cm/year). A significantly positive correlation between shoulder tress at baseline and growth rate was found (r=0.342; p=0.02). A higher shoulder stress is associated with a rapidly expanding AAA. Therefore, it may be useful for estimating the growth expansion of AAAs and further risk stratification of patients with AAAs.

Impact of calcification and intraluminal thrombus on the computed wall stresses of abdominal aortic aneurysm

Background: Increased biomechanical stresses within the abdominal aortic aneurysm (AAA) wall contribute to its rupture. Calcification and intraluminal thrombus can be commonly found in AAAs, but the relationship between calcification/intraluminal thrombus and AAA wall stress is not completely described. Methods: Patient-specific three-dimensional AAA geometries were reconstructed from computed tomographic images of 20 patients. Structural analysis was performed to calculate the wall stresses of the 20 AAA models and their altered models when calcification or intraluminal thrombus was not considered. A nonlinear large-strain finite element method was used to compute the wall stress distribution. The relationships between wall stresses and volumes of calcification and intraluminal thrombus were sought. Results: Maximum stress was not correlated with the percentage of calcification, and was negatively correlated with the percentage of intraluminal thrombus (r = -0.56; P = .011). Exclusion of calcification from analysis led to a significant decrease in maximum stress by a median of 14% (range, 2%-27%; P < .01). When intraluminal thrombus was eliminated, maximum stress increased significantly by a median of 24% (range, 5%-43%; P < .01). Conclusion: The presence of calcification increases AAA peak wall stress, suggesting that calcification decrease the biomechanical stability of AAA. In contrast, intraluminal thrombus reduces the maximum stress in AAA. Calcification and intraluminal thrombus should both be considered in the evaluation of wall stress for risk assessment of AAA rupture.

Assessment of carotid plaque vulnerability using structural and geometrical determinants

Background Because many acute cerebral ischemic events are caused by rupture of vulnerable carotid atheroma and subsequent thrombosis, the present study used both idealized and patient-specific carotid atheromatous plaque models to evaluate the effect of structural determinants on stress distributions within plaque. Methods and Results Using a finite element method, structural analysis was performed using models derived from in vivo high-resolution magnetic resonance imaging (MRI) of carotid atheroma in 40 non-consecutive patients (20 symptomatic, 20 asymptomatic). Plaque components were modeled as hyper-elastic materials. The effects of varying fibrous cap thickness, lipid core size and lumen curvature on plaque stress distributions were examined. Lumen curvature and fibrous cap thickness were found to be major determinants of plaque stress. The size of the lipid core did not alter plaque stress significantly when the fibrous cap was relatively thick. The correlation between plaque stress and lumen curvature was significant for both symptomatic (p = 0.01; correlation coefficient: 0.689) and asymptomatic patients (p = 0.01; correlation coefficient: 0.862). Lumen curvature in plaques of symptomatic patients was significantly larger than those of asymptomatic patients (1.50±1.0mm-1 vs 1.25±0.75 mm-1; p = 0.01). Conclusion Specific plaque morphology (large lumen curvature and thin fibrous cap) is closely related to plaque vulnerability. Structural analysis using high-resolution MRI of carotid atheroma may help in detecting vulnerable atheromatous plaque and aid the risk stratification of patients with carotid disease.

Does calcium deposition play a role in the stability of atheroma? Location may be the key

Background: Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The role of calcium deposition and its contribution to plaque stability is controversial. This study uses both an idealized and a patient-specific model to evaluate the effect of a calcium deposit on the stress distribution within an atheromatous plaque. Methods: Using a finite-element method, structural analysis was performed on an idealized plaque model and the location of a calcium deposit within it was varied. In addition to the idealized model, in vivo high-resolution MR imaging was performed on 3 patients with carotid atheroma and stress distributions were generated. The individual plaques were chosen as they had calcium at varying locations with respect to the lumen and the fibrous cap. Results: The predicted maximum stress was increased by 47.5% when the calcium deposit was located in the thin fibrous cap in the model when compared with that in a model without a deposit. The result of adding a calcium deposit either to the lipid core or remote from the lumen resulted in almost no increase in maximal stress. Conclusion: Calcification at the thin fibrous cap may result in high stress concentrations, ultimately increasing the risk of plaque rupture. Assessing the location of calcification may, in the future, aid in the risk stratification of patients with carotid stenosis.

Instability of laminated composite thin-walled open-section beams

Instability of thin-walled open-section laminated composite beams is studied using the finite element method. A two-noded, 8 df per node thin-walled open-section laminated composite beam finite element has been used. The displacements of the element reference axis are expressed in terms of one-dimensional first order Hermite interpolation polynomials, and line member assumptions are invoked in formulation of the elastic stiffness matrix and geometric stiffness matrix. The nonlinear expressions for the strains occurring in thin-walled open-section beams, when subjected to axial, flexural and torsional loads, are incorporated in a general instability analysis. Several problems for which continuum solutions (exact/approximate) are possible have been solved in order to evaluate the performance of finite element. Next its applicability is demonstrated by predicting the buckling loads for the following problems of laminated composites: (i) two layer (45°/−45°) composite Z section cantilever beam and (ii) three layer (0°/45°/0°) composite Z section cantilever beam.

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.

Monoblock cylinder internally pressurised under asymmetric end constraints Some aspects of design

The finite element method is used to analyse stresses and displacements in a monoblock cylinder open at one end only. The cylinder is internally pressurised. The analysis shows that the minimum pressure required to cause yield in the cylinder decreases rapidly with increasing cylinder height until the height is about the same as the outer radius of the cylinder, beyond which the decrease is marginal. Introduction of a fillet at the internal corner enhances the design pressure substantially while a fillet at the outer corner affects this pressure only marginally.