scholarly journals Local null controllability of a class of non-Newtonian incompressible viscous fluids

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pitágoras Pinheiro de Carvalho ◽  
Juan Límaco ◽  
Denilson Menezes ◽  
Yuri Thamsten
Keyword(s):  
Stokes Problem ◽  
Minimum Principle ◽  
Null Controllability ◽  
Pontryagin Minimum Principle ◽  
Shear Dependent Viscosity ◽  
Smooth Controls ◽  
Incompressible Viscous Fluids ◽  
Controllability Property ◽  
Dependent Viscosity ◽  
Quasi Newton

<p style='text-indent:20px;'>We investigate the null controllability property of systems that mathematically describe the dynamics of some non-Newtonian incompressible viscous flows. The principal model we study was proposed by O. A. Ladyzhenskaya, although the techniques we develop here apply to other fluids having a shear-dependent viscosity. Taking advantage of the Pontryagin Minimum Principle, we utilize a bootstrapping argument to prove that sufficiently smooth controls to the forced linearized Stokes problem exist, as long as the initial data in turn has enough regularity. From there, we extend the result to the nonlinear problem. As a byproduct, we devise a quasi-Newton algorithm to compute the states and a control, which we prove to converge in an appropriate sense. We finish the work with some numerical experiments.</p>

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

The Rheology of Saliva

1987 ◽  
Vol 66 (1_suppl) ◽  
pp. 660-666 ◽  
Author(s):  
W. H. Schwarz
Keyword(s):  
Salivary Gland ◽  
Rheological Properties ◽  
Medical Management ◽  
Artificial Saliva ◽  
Salivary Gland Dysfunction ◽  
Shear Dependent Viscosity ◽  
Saliva Analysis ◽  
Whole Saliva ◽  
Saliva Substitutes ◽  
Dependent Viscosity

The rheology of saliva affects the coating and lubrication of oral surfaces and the consistency of ingested foods. Salivary gland dysfunction can cause tissue damage and dysphagia. Therefore, we have considered the problem of designing a synthetic saliva for medical management. Also, we have measured certain rheological properties [shear-dependent viscosity η (k)] and the frequency-dependent moduli [G′(f) and η′(f)] of normal stimulated whole saliva. Analysis of the rheological data and consideration of requirements for using artificial saliva have resulted in a better understanding of the rheological functions of natural saliva and the desirable characteristics of synthetic saliva. In addition, we have measured rheological properties of two commercial saliva substitutes for comparison.

Stability of Shear-Thickening Liquids Between Rotating Cylinders

2010 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Dynamical Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Dependent Viscosity

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

Annular Frictional Pressure Losses During Drilling—Predicting the Effect of Drillstring Rotation

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Arild Saasen
Keyword(s):  
Rheological Properties ◽  
Pressure Loss ◽  
Drilling Fluid ◽  
Axial Flow ◽  
Drilling Fluids ◽  
Unstable Flow ◽  
Pressure Losses ◽  
Shear Dependent Viscosity ◽  
Water Based ◽  
Dependent Viscosity

Controlling the annular frictional pressure losses is important in order to drill safely with overpressure without fracturing the formation. To predict these pressure losses, however, is not straightforward. First of all, the pressure losses depend on the annulus eccentricity. Moving the drillstring to the wall generates a wider flow channel in part of the annulus which reduces the frictional pressure losses significantly. The drillstring motion itself also affects the pressure loss significantly. The drillstring rotation, even for fairly small rotation rates, creates unstable flow and sometimes turbulence in the annulus even without axial flow. Transversal motion of the drillstring creates vortices that destabilize the flow. Consequently, the annular frictional pressure loss is increased even though the drilling fluid becomes thinner because of added shear rate. Naturally, the rheological properties of the drilling fluid play an important role. These rheological properties include more properties than the viscosity as measured by API procedures. It is impossible to use the same frictional pressure loss model for water based and oil based drilling fluids even if their viscosity profile is equal because of the different ways these fluids build viscosity. Water based drilling fluids are normally constructed as a polymer solution while the oil based are combinations of emulsions and dispersions. Furthermore, within both water based and oil based drilling fluids there are functional differences. These differences may be sufficiently large to require different models for two water based drilling fluids built with different types of polymers. In addition to these phenomena washouts and tool joints will create localised pressure losses. These localised pressure losses will again be coupled with the rheological properties of the drilling fluids. In this paper, all the above mentioned phenomena and their consequences for annular pressure losses will be discussed in detail. North Sea field data is used as an example. It is not straightforward to build general annular pressure loss models. This argument is based on flow stability analysis and the consequences of using drilling fluids with different rheological properties. These different rheological properties include shear dependent viscosity, elongational viscosity and other viscoelastic properties.

An existence result for fluids with shear dependent viscosity — Steady flows

1997 ◽  
Vol 30 (5) ◽  
pp. 3041-3049 ◽  
Author(s):  
Jens Frehse ◽  
Josef Málek ◽  
Mark Steinhauer
Keyword(s):  
Existence Result ◽  
Steady Flows ◽  
Shear Dependent Viscosity ◽  
Dependent Viscosity

scholarly journals Application and benchmarking of a direct method to optimize the fuel consumption of a diesel electric locomotive

2018 ◽  
Vol 232 (9) ◽  
pp. 2272-2289 ◽  
Author(s):  
V Macian ◽  
C Guardiola ◽  
B Pla ◽  
A Reig
Keyword(s):  
Optimal Control ◽  
Direct Method ◽  
Minimum Principle ◽  
Optimization Technique ◽  
Direct Methods ◽  
Optimization Methods ◽  
Computational Time ◽  
Electric Locomotive ◽  
Pontryagin Minimum Principle ◽  
A Direct Method

This paper addresses the optimal control of a long-haul passenger train to deliver minimum-fuel operations. Contrary to the common Pontryagin minimum principle approach in railroad-related literature, this work addresses this optimal control problem with a direct method of optimization, the use of which is still marginal in this field. The implementation of a particular direct method based on the Euler collocation scheme and its transcription into a nonlinear problem are described in detail. In this paper, this optimization technique is benchmarked with well-known optimization methods in the literature, namely dynamic programming and the Pontryagin minimum principle, by simulating a real route. The results showed that the direct methods are on the same level of optimality compared with other algorithms while requiring reduced computational time and memory and being able to handle very complex dynamic systems. The performance of the direct method is also compared to the real trajectory followed by the train operator and exhibits up to 20% of fuel saving in the example route.

scholarly journals Development of Global Optimization Algorithm for Series-Parallel PHEV Energy Management Strategy Based on Radau Pseudospectral Knotting Method

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3268
Author(s):  
Kegang Zhao ◽  
Jinghao Bei ◽  
Yanwei Liu ◽  
Zhihao Liang
Keyword(s):  
Global Optimization ◽  
Energy Management ◽  
Computational Efficiency ◽  
Management Strategy ◽  
Hybrid Electric Vehicles ◽  
Minimum Principle ◽  
Management Strategies ◽  
Energy Management Strategy ◽  
Pontryagin Minimum Principle ◽  
Component Sizing

The powertrain model of the series-parallel plug-in hybrid electric vehicles (PHEVs) is more complicated, compared with series PHEVs and parallel PHEVs. Using the traditional dynamic programming (DP) algorithm or Pontryagin minimum principle (PMP) algorithm to solve the global-optimization-based energy management strategies of the series-parallel PHEVs is not ideal, as the solution time is too long or even impossible to solve. Chief engineers of hybrid system urgently require a handy tool to quickly solve global-optimization-based energy management strategies. Therefore, this paper proposed to use the Radau pseudospectral knotting method (RPKM) to solve the global-optimization-based energy management strategy of the series-parallel PHEVs to improve computational efficiency. Simulation results showed that compared with the DP algorithm, the global-optimization-based energy management strategy based on the RPKM improves the computational efficiency by 1806 times with a relative error of only 0.12%. On this basis, a bi-level nested component-sizing method combining the genetic algorithm and RPKM was developed. By applying the global-optimization-based energy management strategy based on RPKM to the actual development, the feasibility and superiority of RPKM applied to the global-optimization-based energy management strategy of the series-parallel PHEVs were further verified.

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