Academic literature on the topic 'Unsteady tube stretching'

Hydro turbines operating at partial flow conditions usually have vortex ropes in the draft tube that generate large pressure fluctuations. This unsteady flow phenomenon is harmful to the safe operation of hydropower stations. This paper presents numerical simulations of the internal flow in the draft tube of a Francis turbine with particular emphasis on understanding the unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the air and the vortices. The pressure fluctuations induced by the vortex rope are alleviated by air admission from the main shaft center, with the water-air two phase flow in the entire flow passage of a model turbine simulated based on the homogeneous flow assumption. The results show that aeration with suitable air flow rate can alleviate the pressure fluctuations in the draft tube, and the mechanism improving the flow stability in the draft tube is due to the change of vortex rope structure and distribution by aeration, i.e. a helical vortex rope at a small aeration volume while a cylindrical vortex rope with a large amount of aeration. The preferable vortex rope distribution can suppress the swirl at the smaller flow rates, and is helpful to alleviate the pressure fluctuation in the draft tube. The analysis based on the vorticity transport equation indicates that the vortex has strong stretching and dilation in the vortex rope evolution. The baroclinic torque term does not play a major role in the vortex evolution most of the time, but will much increase for some specific aeration volumes. The present study also depicts that vortex rope is mainly associated with a pair of spiral vortex stretching and dilation sources, and its swirling flow is alleviated little by the baroclinic torque term, whose effect region is only near the draft tube inlet.

The conditions and mechanisms of events in a moving fluid are analyzed, leading to the apparent disorder of unsteady flow, known as turbulence. The method of analysis is the use of different forms of equations of motion and transfer of characteristics, the selection of stable formations in the flow structure and a description of the interaction between them. The non-trivial results of previous works are used. The transfer and transformation of disturbances of a vortex distributed in the flow is analyzed, the conditions under which insulated tubes with a helical flow appear inside the shear flow. An important condition is the short duration of vortex disturbances. Equations are obtained that describe the interaction of the main shear flow and the vortex tube, the features of which lead to flow instability. The existence of two mechanisms for the development of turbulence is shown - the autogeneration of local decelerations and the instability of stretching of vortex tubes. The self-generation mechanism is the transfer of kinetic energy from the main flow to an annular vortex with the generation of a new annular vortex. This is the main mechanism that ensures the propagation of instability downstream, arises first when the Re number increases. The tensile instability leads to the splitting of the vortex tube into independent sections, the generation of many annular vortices that fill the space and drift in it. The vortex multiplication factor in each generation increases with the Re number and can reach many thousands. The role of ordered unsteady flows in the initiation of turbulence is shown.

The water-based single- and multiple-wall carbon nanotubes nanofluid over the surface of an unsteady stretched cylinder has been studied. The thin film of the carbon-nanotube nanofluid has been focused for the heat transfer enhancement applications. The well-known thermal conductivity model for the revolving tube materials like single- and multiple-walled carbon nanotubes defined by Xue were used. The modeled problem has been solved through the optimal homotopy analysis method using the BVPh 2.0 package. The distribution of the thin layer has been regulated through the pressure term using the variable thickness of the nanoliquid. The entropy generation has mainly focused during the motion of the thin layer for the both sorts of carbon nanotubes. The important features of the entropy generation and Bejan number under the influence of the physical constraints have been compared for the both types of single-wall carbon nanotubes and multiple-wall carbon nanotubes and discussed. The well-known BVPh 2.0 package of the optimal homotopy analysis method has been used to find the outcomes.

In this study, the heat and mass transfer of the blood flow, particularly in a capillary tube having a porous lumen and permeable wall in the presence of external magnetic field are considered. The velocity, temperature and concentration of blood flow become unsteady due to the time dependence of the stretching velocity, surface temperature and surface concentration. The thermal and mass buoyancy effect on blood flow, heat transfer and mass transfer are taken into account in the presence of thermal radiation. This analysis is very much useful in the treatment of cardiovascular disorders. The equations governing the flow under some assumptions are complex in nature, but capable of presenting the realistic model of blood flow using the theory of boundary layer approximation and similarity transformation. First, the system of coupled partial differential equations (PDEs) is converted into a system of coupled ordinary differential equations (ODEs). Then the solutions are obtained by Runge-Kutta method of 4thorder with shooting technique. The effects of various parameters such as Hartman number, radiation parameter, unsteadiness parameter, permeable parameter, thermal buoyancy parameter, Prandtl number, mass buoyancy parameter, velocity slip parameter, thermal slip parameter, Schmidt number on velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are depicted through graphs. Local Sherwood number enhances because of increase in Schmidt number. Moreover, some of the important results, which are discussed in the present study and have an impact on diseases like hyperthermia, stoke and moyamoya in human body.

In this study, the heat and mass transfer of the blood flow, particularly in a capillary tube having a porous lumen and permeable wall in the presence of external magnetic field are considered. The velocity, temperature and concentration of blood flow become unsteady due to the time dependence of the stretching velocity, surface temperature and surface concentration. The thermal and mass buoyancy effect on blood flow, heat transfer and mass transfer are taken into account in the presence of thermal radiation. This analysis is very much useful in the treatment of cardiovascular disorders. The equations governing the flow under some assumptions are complex in nature, but capable of presenting the realistic model of blood flow using the theory of boundary layer approximation and similarity transformation. First, the system of coupled partial differential equations (PDEs) is converted into a system of coupled ordinary differential equations (ODEs). Then the solutions are obtained by Runge-Kutta method of 4thorder with shooting technique. The effects of various parameters such as Hartman number, radiation parameter, unsteadiness parameter, permeable parameter, thermal buoyancy parameter, Prandtl number, mass buoyancy parameter, velocity slip parameter, thermal slip parameter, Schmidt number on velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are depicted through graphs. Local Sherwood number enhances because of increase in Schmidt number. Moreover, some of the important results, which are discussed in the present study and have an impact on diseases like hyperthermia, stoke and moyamoya in human body.

The present study explores three-dimensional vortex-dynamics past a wall-attached bluff body kept in a variable velocity field with numerical simulations. A trapezoidal pulse of mean velocity, consisting of acceleration phase from rest followed by constant velocity phase and deceleration phase to rest, is imposed at the inlet of the computational domain similar to the experimental study of Das et al. [“Unsteady separation and vortex shedding from a laminar separation bubble over a bluff body,” J. Fluids Struct. 40, 233–245 (2013)]. For a wide range of Reynolds numbers ([Formula: see text]), acceleration Reynolds numbers ([Formula: see text]), and deceleration Reynolds numbers ([Formula: see text]), different stages of flow evolution are systematically analyzed. The flow evolution starts with the formation of a primary vortex followed by a two-dimensional circular array of spanwise vortex tubes by inflectional shear-layer instability. At a sufficiently high Reynolds number, the shear layer vortices originated from two-dimensional fluctuations deformed by three-dimensional instabilities, giving fragmented streamwise vorticity. In addition, long-wavelength “tongue-like structures” and short-wavelength “rib-like structures” are evident near the top wall and the bluff body, respectively. The streamwise vorticity generation equation indicates that the spanwise vortex tubes initially tilt, resulting in streamwise vorticity, further amplified by the vortex stretching process. The distinct flow features, including mode shape, frequency, and growth rate associated with the shear-layer instability, are identified using the dynamic mode decomposition (DMD) algorithm. Using the maximum growth rate criteria, the DMD technique successfully separates the coherent shear layer modes associated with two-dimensional shear layer instability from the flow field.

Mathematical modelling is used to examine the unsteady problem of heating and pulling an axisymmetric cylindrical glass tube with an over-pressure applied within the tube to form tapers with a near uniform bore and small wall thickness at the tip. To allow for the dependence of viscosity on temperature, a prescribed axially varying viscosity is assumed. Our motivation is the manufacture of emitter tips for mass spectrometry which provide a continuous fluid flow and do not become blocked. We demonstrate, for the first time, the feasibility of producing such emitters by this process and examine the influence of the process parameters, in particular the pulling force and over-pressure, on the geometry. There is not a unique force and over-pressure combination to achieve the desired geometry at the tip but smaller over-pressure (hence force) yields a more uniform bore over the entire length of the emitter than does a larger over-pressure (and force). However, the sensitivity of the geometry to small fluctuations in the parameters increases as the over-pressure decreases. The best parameters depend on the accuracy of the puller used to manufacture the tapers and the permissible tolerances on the geometry. The model has wider application to the manufacture of other devices.

Nanoelectrospray ionisation (nESI) is a useful technology for assessing the chemical composition of various liquid samples using mass spectrometry (MS). Signi cant e orts have been made in the design of nESI emitters, as their shape and geometry are critical to the electrospray performance and subsequent MS detection. In the actual manufacturing of these emitters through the heat and draw process, the desired geometry cannot, at present, be achieved. In particular, the inner channel reduces in size, which is not desirable. To improve the sensitivity of biological and chemical mass spectrometry and avoid clogging of the tip, a small near-uniform bore of 10 - 20 m is desirable with the external wall tapering over a length of around 5mm from 75 - 150 m in radius to a sharp end with a radius around 8 - 15 m. Through mathematical modelling, we demonstrate, for the rst time, the feasibility of producing such emitters using the heat and draw process with the addition of pressure in the channel to prevent any reduction in size. In this thesis, we consider the unsteady problem of heating and pulling of an axisymmetric cylindrical glass tube, using asymptotic methods to exploit the slenderness of the tube and over-pressure applied within the inner channel, to form tapers with a near uniform bore and small wall thickness at the tip. This is an unsteady extensional ow problem. As the glass temperature increases, the viscosity reduces until the central heated region extends and thins rapidly to yield an hour-glass shape. During stretching, the cross-sectional geometry will also deform under the e ects of surface tension and applied pressure, with the pressure counteracting the closure of the channel by surface tension and, perhaps, further expanding it. When cooled and cut transversely at the centre, two identical tapered capillaries are obtained. In this thesis, we assume molten glass is a Newtonian uid, and develop coupled ow and energy models to examine in detail the in uence of the process parameters on the geometry, namely the pulling force, pressure, temperature, and surface tension. The use of an over-pressure in the channel, to counteract the reduction in its size as the crosssectional area decreases due to pulling and the channel closes due to surface tension, is of particular interest. The model and solution method described in this thesis enable determination of a pulling force, channel over-pressure, and draw time to achieve tapers with the desired internal diameter and wall thickness at the very tip from a given tubular bre for a temperature dependent viscosity.
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2022