A numerical study of peristaltic flow
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Peristaltic flow is a transport mechanism primarily used in the human body to transport fluids. This form of transport is characterised by the contraction and relaxation of flexible tubes. Many studies have been undertaken to investigate this phenomenon. Factors such as amplitude ratio, wave number and the Reynolds number have been studied to identify their effects on peristaltic flow. In this work, the peristaltic flow of power-law fluids under non-isothermal conditions is investigated using the Computation Fluid Dynamics (CFD) methodology. The effect of temperature on peristaltic flow will be investigated in various conditions, for example, in Newtonian fluid (a special case of power-law fluids), non-Newtonian fluid of power-law type and different values of coefficient a1 (a1 being exponential coefficient of the temperature dependent viscosity). Pelistaltic flow for possible industrial applications will be considered, with fluid properties thus corresponding to those of an oil and a wider range of the Reynolds numbers (1-1 000) than for biological applications. Comparison of isothennal versus non-isothermal flow shall also be shown. Flow will be studied in the reference frame which moves with the wave (the wave frame). In this reference frame, the flow becomes steady. Firstly, isothermal flow models are shown to produce comparable results with previous works from the literature, therefore proving the validity of the present computational methodology. These conditions were then applied to non-isothermal models. After this confidence has been established, non-isothermal flow is then investigated. This in turn affects whole flow field including factors such as change of viscosity and shear stress due to temperature change. Streamline patterns, velocity profiles and pressure drop per wavelength are presented to show the effect of temperature in peristaltic flow. Pressure drop in non-isothermal flow is shown to be significantly less than that for isothermal case. Thus, for example, in the case of isothermal Newtonian flow, pressure drop per wavelength is 6305.2 Pa with conditions of the Reynolds number Re=10, wave number (α) = 0.25 and amplitude ratio (∅) = 0.5. On the other hand, in the case of non-isothermal flow, pressure drop per wavelength becomes 2054.7 Pa with the same conditions. Influence of temperature is then considered in flow of non-Newtonian fluids of the power-law type. Consistent flow conditions are modelled to give a reasonable comparison. It is found that Newtonian and shear-thickening fluids are influenced by temperature strongly. However, in the case for shear thinning fluid, the effect of temperature is relatively small. Thus, for example, in table 5.2 (chapter 5), pressure drop per wavelength in a case for shear thinning fluids is very similar, at 49.153 Pa and 55.892 Pa corresponding to viscosity exponential coefficient a1 = -0.034°C-1 and a1 = 0°C-1 respectively. The role of coefficient a1 in power-law fluid is clarified in this research. Different values of a1 are used and the corresponding results presented. They show that a1 has stronger influence on the flow at regions adjacent to walls. Vorticity patterns are also presented to show the effect of temperature. Especially, for Newtonian fluids, temperature affects vorticity differently at the crest and trough sections. The effect of temperature on peri static flow in different geometry is shown by streamline patterns, pressure drops and velocity profile. The variable, h (the mean distance of the wall from the axis of symmetry) is utilised to produce a model that shows the effect of the geometry in isothermal flow. After the geometry is changed and resulting effect plotted, non-isothermal flow model is considered to prove the presence of thermal effects. The results gained by the models indicate that the temperature effect is stronger at the region adjacent to the wall in different geometries and the effect of temperature reduced the effect of geometry in pressure drop. The above study was carried out in order to simulate realistic peristaltic flow. The addition of temperature by modelling non-isothermal flow has been shown to reduce the impact of the Reynolds number therefore changing the streamline pattern. This effect has been visualised in a number of special fluid applications to give a variety of results. The effects shown visually by CFD represent what peristaltic flow in industrial applications could look like.
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