NUMERICAL EXPERIMENTS WITH AN ALGORITHM FOR PROCESSING EXPERIMENTAL DATA TO DETERMINE THE PARAMETERS OF A RHEOLOGICAL MODEL OF A LIQUID WITH THE EFFECT OF «SOLIDIFICATION»

Предложена методика обработки экспериментальных данных и алгоритм для ее реализации по определению параметров реологической модели вязкопластической жидкости, которая демонстрирует проявление эффекта «отвердевания». С целью проверки работоспособности алгоритма проведены численные эксперименты с наборами генерируемых случайным образом “псевдоэкспериментальных” данных с заранее заданной величиной максимальной относительной погрешности. Проведен анализ влияния максимальной относительной погрешности исходных “псевдоэкспериментальных” данных на величину относительной погрешности определяемых в ходе численных экспериментов параметров реологической модели. По итогам проведенных экспериментов показано, что относительная погрешность определения параметров реологической модели соизмерима с максимальной погрешностью генерируемых “псевдоэкспериментальных” данных. Рассмотрен пример обработки экспериментальных данных для суспензии частиц карбоната кальция на основе полиэтиленгликоля. A technique for processing experimental data and an algorithm for its implementation to determine the parameters of a rheological model of a viscoplastic fluid, which demonstrates the manifestation of the "hardening" effect, are proposed. In order to test the algorithm's operability, numerical experiments were carried out with sets of randomly generated "pseudo-experimental" data with a predetermined maximum relative error. The analysis of the influence of the maximum relative error of the initial “pseudo-experimental” data on the value of the relative error of the parameters of the rheological model determined during numerical experiments was carried out. Based on the results of the conducted experiments, it is shown that the relative error in determining the parameters of the rheological model is commensurate with the maximum error of the generated “pseudo-experimental” data. An example of processing experimental data for a suspension of calcium carbonate particles based on polyethylene glycol is considered.

THE METHOD OF PROCESSING EXPERIMENTAL DATA AND THE ALGORITHM FOR ITS IMPLEMENTATION TO DETERMINE THE PARAMETERS OF THE RHEOLOGICAL MODEL OF A DILATANT LIQUID WITH THE EFFECT OF «SOLIDIFICATION»

В различных технических приложениях применяются рабочие среды типа суспензий, которые при достаточно высокой концентрации частиц твердой фазы демонстрируют аномалии вязкости. Существо этих аномалий заключается в том, что при приближении скорости сдвига к некоторому пороговому значению наблюдается явление резкого возрастания вязкости жидкости. При этом в соответствующих зонах течения рабочая среда начинает вести себя подобно твердому телу. Механическое поведение такой рабочей среды может быть описано в рамках реологической модели вязкопластической жидкости, которая позволяет учитывать проявление эффекта“упрочнения” или “отвердевания”. Рассмотрена методика определения параметров такой реологической модели на основе обработки экспериментальных данных зависимости касательного напряжения от скорости сдвига. Предложен алгоритм для реализации этой методики. In various technical applications, working media such as suspensions are used, which, at a sufficiently high concentration of solid phase particles, demonstrate viscosity anomalies. The essence of these anomalies lies in the fact that when the shear rate approaches a certain threshold value, the phenomenon of a sharp increase in the viscosity of the liquid is observed. At the same time, in the corresponding flow zones, the working medium begins to behave like a solid. The mechanical behavior of such a working medium can be described within the framework of a rheological model of a viscoplastic fluid, which allows for the manifestation of the effect of “hardening” or “solidification”. The method of determining the parameters of such a rheological model based on the processing of experimental data on the dependence of the shear stress on the shear rate is considered. An algorithm for the implementation of this technique is proposed

Secondary Consolidation Characteristics of Organic Soil Modified by Biological Enzymes Based on Gibson Model

In order to study the secondary consolidation characteristics of organic soil modified by enzyme, the secondary consolidation tests of organic soil modified by enzyme were carried out. Firstly, the consolidation coefficient Cv, secondary consolidation coefficient Ca and compression index Cc of modified organic soil under different levels of loads and different enzyme contents were obtained according to the analysis of experimental data. Then, the parameters of Gibson rheological model were fitted respectively according to the experimental results. Finally, the relationship between rheological model parameters, Ca/Cc, secondary consolidation coefficient Ca and loading was analyzed under different enzyme contents. The results show that: (1) The rheological model parameters of organic soil modified by enzyme are negatively correlated with the enzyme content, and positively correlated with the load value. When the enzyme content is 0.01%, some parameters reach the maximum value; (2) The secondary consolidation coefficient is related to the load. The secondary consolidation coefficient of samples with different enzyme contents shows a certain rule under all levels of load. With the increasing of load, the final secondary consolidation coefficient Ca approaches a stable value; (3) The Ca/Cc values of the samples of the modified organic soil with different enzyme contents are between 0.042 and 0.1 under different loads. The results show that the model is suitable for describing the secondary consolidation creep characteristics of organic soil, and can be used to guide the long-term deformation prediction of organic soil foundation.

Rheological Model to Describe the Cyclic Load-Bearing Behaviour of Strain-Hardening Cement-Based Composites (SHCC)

The mechanical behaviour of strain-hardening cement-based composites (SHCC) under monotonic tensile loading has been the subject of research for many years. The recent research on the SHCC’s performance under cyclic loading has enabled the identification of a wide variety of damage phenomena different to those observed under monotonic loading. The article at hand first summarises the experimental evidence of such phenomena in the context of the material performance observed. On this basis, the mechanisms behind these phenomena are discussed and explained using rheological modelling.

Non fourier heat transfer enhancement in power law fluid with mono and hybrid nanoparticles

Several polymers like ethylene glycol exhibit non-Newtonian rheological behavior. Ethylene glycol is a world-widely used engine coolant and therefore, investigation of thermal enhancement by dispersing mono and hybrid nanoparticles in ethylene glycol is worthful. Since ethylene glycol has shear rate-dependent viscosity and it obeys the power-law rheological model. Therefore, based on these facts, the power-law rheological model with thermophysical properties is augmented with basic law of heat transfer in fluid for the modeling of the considered physical situation. $$Mo{S}_{2}$$ M o S 2 are taken as mono-nanoparticles where $$Mo{S}_{2}$$ M o S 2 and $$Si{O}_{2}$$ S i O 2 are taken as hybrid nanoparticles. Comparative study for the enhancement of thermal performance of MoS2 ethylene glycol and $$Mo{S}_{2}$$ M o S 2 −$$Si{O}_{2}$$ S i O 2 – ethylene glycol is done. For energy conservation, non-Fourier’s law of Cattaneo–Christov is used. The power-law fluid becomes more heat generative due to the dispersion of $$Mo{S}_{2}$$ M o S 2 and $$Si{O}_{2}$$ S i O 2 . However, $$Mo{S}_{2}$$ M o S 2 −power-law fluid is less heat generative relative to $$Mo{S}_{2}$$ M o S 2 − $$Si{O}_{2}$$ S i O 2 -nanofluid. Thermal relaxation time is found proportional to the ability of the fluid to restore its thermal equilibrium.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

Giesekus fluid flow past a sphere in a pipe

A numerical simulation of a viscoelastic fluid flow past a sphere in a round pipe is carried out. The four mode Giesekus model is taken as a rheological model. By the example of a polymer melt flow, the features of the flow around a sphere in comparison with the flow around a cylinder are revealed. Velocity and stress profiles for polymer melt and polymer solution fluid flow around a sphere at the same Weissenberg numbers are analyzed.