Eulerian-Lagrangian definition of coarse bed-load transport: Theory and verification with low-cost inertial measurement units

Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. This physical complexity has led to ambiguous definition of the reference frame (Lagrangian or Eulerian) in which sediment transport is analysed. A general Eulerian-Lagrangian approach accounts for inertial characteristics of particles in a Lagrangian (particle fixed) frame, and for the hydrodynamics in an independent Eulerian frame. The necessary Eulerian-Lagrangian transformations are simplified under the assumption of an ideal Inertial Measurement Unit (IMU), rigidly attached at the centre of the mass of a sediment particle. Real, commercially available IMU sensors can provide high frequency data on accelerations and angular velocities (hence forces and energy) experienced by grains during entrainment and motion, if adequately customized. IMUs are subjected to significant error accu- mulation but they can be used for statistical parametrisation of an Eulerian-Lagrangian model, for coarse sediment particles and over the temporal scale of individual entrainment events. In this thesis an Eulerian-Lagrangian model is introduced and evaluated experimentally. Absolute inertial accelerations were recorded at a 4 Hz frequency from a spherical instrumented particle (111 mm diameter and 2383 kg/m3 density) in a series of entrainment threshold experiments on a fixed idealised bed. The grain-top inertial acceleration entrainment threshold was approximated at 44 and 51 mg for slopes 0.026 and 0.037 respectively. The saddle inertial acceleration entrainment threshold was at 32 and 25 mg for slopes 0.044 and 0.057 respectively. For the evaluation of the complete Eulerian-Lagrangian model two prototype sensors are presented: an idealised (spherical) with a diameter of 90 mm and an ellipsoidal with axes 100, 70 and 30 mm. Both are instrumented with a complete IMU, capable of sampling 3D inertial accelerations and 3D angular velocities at 50 Hz. After signal analysis, the results can be used to parametrize sediment movement but they do not contain positional information. The two sensors (spherical and ellipsoidal) were tested in a series of entrainment experiments, similar to the evaluation of the 111 mm prototype, for a slope of 0.02. The spherical sensor entrained at discharges of 24.8 ± 1.8 l/s while the same threshold for the ellipsoidal sensor was 45.2 ± 2.2 l/s. Kinetic energy calculations were used to quantify the particle-bed energy exchange under fluvial (discharge at 30 l/s) and non-fluvial conditions. All the experiments suggest that the effect of the inertial characteristics of coarse sediments on their motion is comparable to the effect hydrodynamic forces. The coupling of IMU sensors with advanced telemetric systems can lead to the tracking of Lagrangian particle trajectories, at a frequency and accuracy that will permit the testing of diffusion/dispersion models across the range of particle diameters.

Heat transfer performance investigation of nanofluids flow in pipe

Different types of base fluids, such as water, engine oil, kerosene, ethanol, methanol, ethylene glycol etc. are usually used to increase the heat transfer performance in many engineering applications. But these conventional heat transfer fluids have often several limitations. One of those major limitations is that the thermal conductivity of each of these base fluids is very low and this results a lower heat transfer rate in thermal engineering systems. Such limitation also affects the performance of different equipments used in different heat transfer process industries. To overcome such an important drawback, researchers over the years have considered a new generation heat transfer fluid, simply known as nanofluid with higher thermal conductivity. This new generation heat transfer fluid is a mixture of nanometre-size particles and different base fluids. Different researchers suggest that adding spherical or cylindrical shape of uniform/non-uniform nanoparticles into a base fluid can remarkably increase the thermal conductivity of nanofluid. Such augmentation of thermal conductivity could play a more significant role in enhancing the heat transfer rate than that of the base fluid. Nanoparticles diameters used in nanofluid are usually considered to be less than or equal to 100 nm and the nanoparticles concentration usually varies from 5% to 10%. Different researchers mentioned that the smaller nanoparticles concentration with size diameter of 100 nm could enhance the heat transfer rate more significantly compared to that of base fluids. But it is not obvious what effect it will have on the heat transfer performance when nanofluids contain small size nanoparticles of less than 100 nm with different concentrations. Besides, the effect of static and moving nanoparticles on the heat transfer of nanofluid is not known too. The idea of moving nanoparticles brings the effect of Brownian motion of nanoparticles on the heat transfer. The aim of this work is, therefore, to investigate the heat transfer performance of nanofluid using a combination of smaller size of nanoparticles with different concentrations considering the Brownian motion of nanoparticles. A horizontal pipe has been considered as a physical system within which the above mentioned nanofluid performances are investigated under transition to turbulent flow conditions. Three different types of numerical models, such as single phase model, Eulerian-Eulerian multi-phase mixture model and Eulerian-Lagrangian discrete phase model have been used while investigating the performance of nanofluids. The most commonly used model is single phase model which is based on the assumption that nanofluids behave like a conventional fluid. The other two models are used when the interaction between solid and fluid particles is considered. However, two different phases, such as fluid and solid phases is also considered in the Eulerian-Eulerian multi-phase mixture model. Thus, these phases create a fluid-solid mixture. But, two phases in the Eulerian-Lagrangian discrete phase model are independent. One of them is a solid phase and the other one is a fluid phase. In addition, RANS (Reynolds Average Navier Stokes) based Standard κ-ω and SST κ-ω transitional models have been used for the simulation of transitional flow. While the RANS based Standard κ-ϵ, Realizable κ-ϵ and RNG κ-ϵ turbulent models are used for the simulation of turbulent flow. Hydrodynamic as well as temperature behaviour of transition to turbulent flows of nanofluids through the horizontal pipe is studied under a uniform heat flux boundary condition applied to the wall with temperature dependent thermo-physical properties for both water and nanofluids. Numerical results characterising the performances of velocity and temperature fields are presented in terms of velocity and temperature contours, turbulent kinetic energy contours, surface temperature, local and average Nusselt numbers, Darcy friction factor, thermal performance factor and total entropy generation. New correlations are also proposed for the calculation of average Nusselt number for both the single and multi-phase models. Result reveals that the combination of small size of nanoparticles and higher nanoparticles concentrations with the Brownian motion of nanoparticles shows higher heat transfer enhancement and thermal performance factor than those of water. Literature suggests that the use of nanofluids flow in an inclined pipe at transition to turbulent regimes has been ignored despite its significance in real-life applications. Therefore, a particular investigation has been carried out in this thesis with a view to understand the heat transfer behaviour and performance of an inclined pipe under transition flow condition. It is found that the heat transfer rate decreases with the increase of a pipe inclination angle. Also, a higher heat transfer rate is found for a horizontal pipe under forced convection than that of an inclined pipe under mixed convection.