Thermal Vibrational Convection in a Two-phase Stratified Liquid

The response of a two-phase stratified liquid system subject to a vibration parallel to an imposed temperature gradient is analyzed using a hybrid thermal lattice Boltzmann method (HTLB). The vibrations considered correspond to sinusoidal translations of a rigid cavity at a fixed frequency. The layers are thermally and mechanically coupled. Interaction between gravity-induced and vibration-induced thermal convection is studied. The ability of applied vibration to enhance the flow, heat transfer and interface distortion is investigated. For the range of conditions investigated, the results reveal that the effect of vibrational Rayleigh number and vibrational frequency on a two-phase stratified fluid system is much different than that for a single-phase fluid system. Comparisons of the response of a two-phase stratified fluid system with a single-phase fluid system are discussed

Thermal Convection in Non-Fourier Fluids and Application to Liquid Helium II

This thesis examines different conditions for which non-Fourier effects can be significant in the flow of fluids. Non-Fourier fluids of dual-phase-lagging type (DPL) possess a relaxation time and a retardation time, reflecting the delay in the response of the heat flux and the temperature gradient with respect to one another. For non-Fourier fluids of single-phase-lagging type (SPL) the retardation time is zero. Non-Fourier fluids span a wide range of applications, including liquid helium, nanofluids and rarefied gases. The parallels between non-Fourier fluids and polymeric solutions are established. The instability of steady natural convection of a thin layer of non-Fourier fluid (SPL) between two horizontal (and vertical) surfaces maintained at different temperatures is studied. The SPL model is particularly relevant to liquid helium II, and nanofluids with high nanoparticle concentration. Linear stability analysis is employed to obtain the critical state parameters such as critical Rayleigh (Grashof) numbers. In both cases, as the fluid becomes more non-Fourier, oscillatory convection increasingly becomes the mode of preference, compared to both conduction and stationary convection. Critical Rayleigh (Grashof) number decreases for fluids with higher non-Fourier levels. By invoking the role of the eigenvectors to detect and quantify short-time behavior, transient growth of energy of disturbances in is studied. The energy of the perturbations is introduced in terms of the primary variables as a disturbance measure in order to quantify the size of the disturbance. It is found that nonlinearities are not required for the energy growth, and a significant energy growth can be observed even if the flow is stable. The post-critical convective state for Rayleigh-Benard convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered. Comparison with experimental results is made and a very good qualitative agreement is obtained

Studies In Small Scale Thermal Convection

The effect of non-Fourier heat transfer and partial-slip boundary conditions in Rayleigh-Bénard are analyzed theoretically. Non-Fourier fluids possess a relaxation time that reflects the delay in the response of the heat flux to a change in the temperature gradient while the partial slip boundary condition assumes that the fluid velocity and temperature are not equal to that of the wall. Both non-Fourier and partial-slip effects become important when small-scale heat transfer applications are investigated such as convection around micro- and nano-devices as suggested by the extended heat transport equations from kinetic theory. Other applications are also known to exhibit one or both of these effects such as low-temperature liquids, nanofluids, granular flows, rarefied gases and polymer flows. Small scale effects are measured by the Knudsen number. From this, non-Fourier effects can be estimated, measured non-dimensionally by the Cattaneo number and modelled using the frame indifferent Cattaneo-Vernotte equation which is derived from Oldroyd’s upper-convected derivative. Linear stability of non-Fourier fluids shows that the neutral stability curve possesses a stationary Fourier branch and an oscillatory branch intersecting at some wave number, where for small relaxation time, no change in stability is expected from that of a Fourier fluid. As the relaxation time increases to a critical value, both stationary and oscillatory convection become equally probable. Past this value, oscillatory instability is expected to occur at a smaller Rayleigh number and larger wave number than for a Fourier fluid. Non-linear analysis of weakly non-Fourier fluids shows that near the onset of convection, the convective roll intensity is stronger than for a Fourier fluid. The bifurcation to convection changes from subcritical to supercritical as the Cattaneo number increases and the instability of the convection state for a non-Fourier fluid is shown to occur via a Hopf bifurcation at lower Rayleigh number and higher Nusselt number than for a Fourier fluid. When hydrodynamic slip and temperature jump boundary conditions are considered, a significant reduction in the minimum critical Rayleigh number and corresponding wave number are found. Depending on the sign used for second-order coefficients, critical conditions can be greater than or less than that for first-order boundary conditions

Efficient implementation of multi-moment methods in gas-liquid two-phase flows and heat transfer

Numerical simulations are a vital tool for understanding gas-liquid two-phase flows, and robust numerical methods are essential for this purpose. In this regard, a code library was developed using C++ for the numerical simulation of three-dimensional gas-liquid two-phase flows and heat transfer. The code is written based on a framework of numerical methods namely; Volume/Surface Integrated Average-Based Multi- Moment Method (VSIAM3) including Constrained Interpolation Profile-Conservative semi-Lagrangian (CIPCSL) methods, Coupled Level-Set and Volume-of-Fluid (CLSVOF) method, and density scaled CSF model. VSIAM3 is a numerical method for compressible and incompressible flows based on the multi-moment concept. VSIAM3 employs CIP-CSL schemes for solving the conservation equation. The CLSVOF is an interface capturing method that is well suited for two-phase flows with surface tension. The density scaled CSF model is used for the surface tension computation. An efficient implementation of the numerical methods was investigated through the discretisation techniques of the conservation equation in VSIAM3. These techniques were studied through the lid-driven cavity, shock tube problems, two-dimensional explosion test, and droplet splashing on a superhydrophobic substrate. It has been found that the use of a less oscillatory CIP-CSL method is essential for robust numerical simulation of compressible and incompressible flows using VSIAM3 and that the numerical results are sensitive to the discretization techniques of the velocity divergence term in the conservation equation. A parallel code library was also developed using Open MPI (the Message-Passing InAbstract iv terface) for the three-dimensional numerical simulation of gas-liquid two-phase flows and heat transfer. The parallel performance has been evaluated, and a good scalability was obtained. The code library was further validated through the numerical simulation of equilibrium drop, single rising bubble, Kelvin-Helmholtz instability, and turbulent channel flow. The numerical results were reasonable. Validations of VSIAM3 for heat transfer problems were also conducted through singlephase and two-phase Rayleigh-Benard convection. We found that solving the diffusion term of the Navier-Stokes equation and the conduction term of the energy equation for all the moments in VSIAM3 is essential for robust numerical simulation of heat transfer problems using VSIAM3. In addition to that, using Time Evolution Converting (TEC) for computing the boundary values of the temperature in VSIAM3 as suggested in the literature influences the robustness of VSIAM3. In conclusion, an efficient implementation of VSIAM3 for gas-liquid two-phase flows and heat transfer using VSIAM3 and CLSVOF was developed and validated through single-phase and gas-liquid two-phase flows and heat transfer problems. The established code library is suitable for the numerical simulation of gas-liquid two-phase flows and heat transfer

Double population cascaded lattice boltzmann method

Lattice Boltzmann Methods (LBM) are powerful numerical tools to simulate heat and mass transfer problems. Instead of directly integrating the N-S equations, LBM solves the discretized form of the Boltzmann Transport Equation (BTE), keeping track of the microscopic description of the systems. Therefore, LBM can solve fluid flows with great stability and computational efficiency, especially complex geometry fluid flows. For thermal flows, double distribution function (DDF) LBM scheme is the most popular and successful approach. But it is evident from the literature that existing double distribution function (DDF) LBM approaches, which use two collision operators, involve collision schemes which violate Galilean invariance, therefore producing instabilities for flows with high Re and Ra numbers. In this thesis, a double population cascaded lattice Boltzmann method is developed to improve the DDF LBM scheme from this drawback. The proposed method reduces the degree of violation of Galilean invariance, increasing the stability and accuracy of the LBM scheme. The scheme was implemented to simulate advection-diffusion, forced convection and natural convection heat transfer problems. The proposed scheme was also successfully tested for turbulent flow regimes and 3-D fluid flow in porous media. The results obtained from this work are in strong agreement with those available in the literature obtained through other numerical methods and experiments.Os métodos de ”Lattice”Boltzmann (LBM) são potentes ferramentas numéricas para simular problemas de transferência de massa e calor. Ao invés de integrar diretamente as equações de Navier-Stokes, o método LBM resolve, de forma discretizada, a equação de transporte de Boltzmann, acompanhando a descrição microscópica dos sistemas. O método LBM pode solucionar fluxo de fluidos com grande estabilidade e eficiência computacional, especialmente fluxos em geometrias complexas. Para fluxos térmicos, o esquema LBM de dupla função de distribuição (DDF) é a abordagem mais popular e bem sucedida. Mas é evidente, a partir da literatura, que as abordagens LBM de dupla função de distribuição (DDF), as quais utilizam dois operadores de colisão, envolvem esquemas de colisão que violam a invariância de Galileu, produzindo instabilidades para fluxos com números Re e Ra altos. Nesta tese, o método de ”Lattice”Boltzmann em cascata de dupla população em cascata é desenvolvido para corrigir o esquema DDF LBM. O método proposto reduz o grau de violação da invariância de Galileu, aumentando a estabilidade e acurácia do método LBM. O método foi implementado para simular problemas de advecção, difusão, convecções natural e forçada típicos de transferências de calor. O esquema proposto foi também bem sucedido em regimes de fluxo turbulento e em escoamentos 3-D em meios porosos. Os resultados obtidos neste trabalho estão fortemente de acordo com experimentos e métodos numéricos disponíveis na literatura

Microgravity science and applications bibliography, 1989 revision

This edition of the Microgravity Science and Applications (MSA) Bibliography is a compilation of government reports, contractor reports, conference proceedings, and journal articles dealing with flight experiments utilizing a low gravity environment to elucidate and control various processes, or with ground based activities that provide supported research. It encompasses literature published but not cited in the 1988 Revision and that literature which has been published in the past year. Subdivisions of the Bibliography include: electronic materials, metals, alloys, and composites; fluids, interfaces, and transport; glasses and ceramics; biotechnology; combustion science; experimental technology, facilities, and instrumentation. Also included are publications from the European, Soviet, and Japanese programs

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

Computational fluid dynamics using Graphics Processing Units: Challenges and opportunities

A new paradigm for computing fluid flows is the use of Graphics Processing Units (GPU), which have recently become very powerful and convenient to use. In the past three years, we have implemented five different fluid flow algorithms on GPUs and have obtained significant speed-ups over a single CPU. Typically, it is possible to achieve a factor of 50-100 over a single CPU. In this review paper, we describe our experiences on the various algorithms developed and the speeds achieved

A study of pressure-driven displacement flow of two immiscible liquids using a multiphase lattice Boltzmann approach

The pressure-driven displacement of two immiscible fluids in an inclined channel in the presence of viscosity and density gradients is investigated using a multiphase lattice Boltzmann approach. The effects of viscosity ratio, Atwood number, Froude number, capillary number, and channel inclination are investigated through flow structures, front velocities, and fluid displacement rates. Our results indicate that increasing viscosity ratio between the fluids decreases the displacement rate. We observe that increasing the viscosity ratio has a non-monotonic effect on the velocity of the leading front; however, the velocity of the trailing edge decreases with increasing the viscosity ratio. The displacement rate of the thin-layers formed at the later times of the displacement process increases with increasing the angle of inclination because of the increase in the intensity of the interfacial instabilities. Our results also predict the front velocity of the lock-exchange flow of two immiscible fluids in the exchange flow dominated regime. A linear stability analysis has also been conducted in a three-layer system, and the results are consistent with those obtained by our lattice Boltzmann simulations