Unity Aspect Ratio Research Articles

Numerical simulation of turbulent Rayleigh-Bénard mercury convection in a circular cylinder with introducing small deviations from the axisymmetric formulation

Results of DNS are reported for turbulent Rayleigh-Bénard mercury convection (Pr = 0.025) in a cylindrical container with the aspect ratio of unity at the Rayleigh number of Ra = 106. The main goal of the study is to estimate the influence of small deviations from the axisymmetric formulation on the behavior of large-scale circulation (LSC) developing in the container. The deviations examined are a small tilt of the cylinder or prescribed sinusoidal disturbances of the bottom wall temperature. The effects of the computational grid structure in the central region of the flow are investigated as well. It has been shown that the azimuthal low-frequency reorientations of the LSC, which are typical for the axisymmetric problem setting, can be fully suppressed by imposing relatively small non-axisymmetric disturbances of various kinds. Time-averaged 3D velocity and temperature fields, as well as spatial non-uniformities of local heat transfer are analyzed for a “locked” LSC case.

Seismic Damage Analysis of Box Metro Tunnels Accounting for Aspect Ratio and Shear Failure

We performed a series of inelastic frame analyses for single, double, and triple reinforced concrete box tunnels to investigate their unique damage mechanisms. We focused our interest on the influence of the aspect ratio of box tunnels and the occurrence of a shear structural failure. This is a follow-up study of Lee et al. (2016), where damage analyses of box tunnels with an aspect ratio of unity were performed by considering only the flexural failure. We show that only flexural failures occurred in single box tunnels, whereas shear structural failures were produced at the inner column for double and triple box tunnels. The inner column failed in shear after flexural plastic hinges were formed at all four outer corners, and might cause a brittle collapse. A structural collapse was not observed in single box tunnels. An increase in the aspect ratio was demonstrated to cause associated increment in the seismic resistance. The moment and shear strains at which plastic hinges formed an increase by up to 5% and 20%, respectively. We proposed revised damage indices (DIs) corresponding to three damage states for single box tunnels, where DI is defined as the ratio of the elastic moment to the yield moment. The collapse damage state and corresponding DI for double and triple tunnels are newly presented.

Turbulent temperature fluctuations in a closed Rayleigh–Bénard convection cell

We report a systematic study of spatial variations of the probability density function (PDF) $P(\unicode[STIX]{x1D6FF}T)$ for temperature fluctuations $\unicode[STIX]{x1D6FF}T$ in turbulent Rayleigh–Bénard convection along the central axis of two different convection cells. One of the convection cells is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. By changing the distance $z$ away from the bottom conducting plate, we find the functional form of the measured $P(\unicode[STIX]{x1D6FF}T)$ in both cells evolves continuously with distinct changes in four different flow regions, namely, the thermal boundary layer, mixing zone, turbulent bulk region and cell centre. By assuming temperature fluctuations in different flow regions are all made from two independent sources, namely, a homogeneous (turbulent) background which obeys Gaussian statistics and non-uniform thermal plumes with an exponential distribution, we obtain the analytic expressions of $P(\unicode[STIX]{x1D6FF}T)$ in four different flow regions, which are found to be in good agreement with the experimental results. Our work thus provides a unique theoretical framework with a common set of parameters to quantitatively describe the effect of turbulent background, thermal plumes and their spatio-temporal intermittency on the temperature PDF $P(\unicode[STIX]{x1D6FF}T)$.

Rib Turbulator Heat Transfer Enhancements at Very High Reynolds Numbers

High-pressure stage gas turbine blades feature serpentine passages where rib turbulators are installed to enhance heat transfer between the relatively colder air bled off from the compressor and the hot internal walls. Most of the prior studies have been restricted to Reynolds number of 90,000 and several studies have been carried out to determine geometrically optimized parameters for achieving high levels of heat transfer in this range of Reynolds number. However, for land-based power generation gas turbines, the Reynolds numbers are significantly high and vary between 105 and 106. The present study is targeted toward these high Reynolds numbers where traditional rib turbulator shapes and prescribed optimum geometrical parameters have been investigated experimentally. A steady-state liquid crystal thermography technique is employed for measurement of detailed heat transfer coefficient. Five different rib configurations, viz., 45 deg, V-shaped, inverse V-shaped, W-shaped, and M-shaped have been investigated for Reynolds numbers ranging from 150,000 to 400,000. The ribs were installed on two opposite walls of a straight duct with an aspect ratio of unity. For very high Reynolds numbers, the heat transfer enhancement levels for different rib shapes varied between 1.4 and 1.7 and the thermal hydraulic performance was found to be less than unity.

Effect of local and upwind stratification on flow and dispersion inside and above a bi-dimensional street canyon

The effects of a stably-stratified boundary layer on flow and dispersion in a bi-dimensional street canyon with unity aspect ratio have been investigated experimentally in a wind tunnel in combination with differential wall heating. Laser-Doppler anemometry together with a fast flame ionisation detector and cold-wire anemometry were employed to sample velocities, concentration, temperatures and fluxes.A single-vortex pattern was observed in the isothermal case, preserved also when leeward wall was heated, but with a considerable increment of the vortex speed. Heating the windward wall, instead, was found to generate a counter-rotating vortex, resulting in the reduction of velocity within the canopy. The stable stratification also contributes reducing the speed, but only in the lower half of the canyon. The largest values of turbulent kinetic energy were observed above the canopy, while inside they were concentrated close to the windward wall, even when the leeward one was heated. An incoming stable stratification produced a significant and generalised turbulence reduction in all the cases. Windward heating was found to produce larger temperature increments within the canopy, while in the leeward case heat was immediately vacated above the canopy. A stable approaching flow reduced both the temperature and the heat fluxes.A passive tracer was released from a point source located at ground level at the centre of the street canyon. The resulting plume cross-section pattern was mostly affected by the windward wall heating, which produced an increment of the pollutant concentration on the windward side by breaking the main vortex circulation. The application of an incoming stable stratification created a generalised increment of pollutant within the canopy, with concentrations twice as large. Turbulent pollutant fluxes were found significant only at roof level and close to the source. On the other hand, in the windward wall-heated case the reduction of the mean flux renders the turbulent component relevant in other locations as well.The present work highlights the importance of boundary layer stratification and local heating, both capable of creating significant modifications in the flow and pollutant fields at microscale range.

Laminar Mixed Convection of Water-Based Alumina Nanofluid in a Cylindrical Enclosure with a Rotating End Wall: A Numerical Investigation

Steady-state laminar mixed convection of water-based alumina nanofluids in cylindrical enclosures with a rotating top cover has been numerically analyzed for different Reynolds numbers (500–3000), Richardson numbers (0–1) and nanoparticle volume fractions (1–5%) for an aspect ratio of unity. Two different configurations have been considered for this analysis in order to obtain physical insights into the fluid flow and heat transfer in cylindrical enclosures with a rotating end cover. In one configuration (i.e. C1 configuration), the rotating top wall is kept at a higher temperature than the bottom wall, whereas the bottom wall is heated in the second configuration (i.e. C2 configuration). The mean Nusselt number in the case of mixed convection has been found to assume higher values in the C2 configuration than in the C1 configuration for a given set of values of Reynolds number, Richardson number and nanoparticle volume fraction. It has also been found that mean Nusselt number monotonically decreases with increasing nanoparticle volume fraction regardless of Richardson number values in the C2 configuration, whereas the mean Nusselt number decreases (increases) with increasing nanoparticle volume fraction for fully forced convection (mixed convection) in the C1 configuration. The simulation data has been used to propose a correlation for the mean Nusselt number for both C1 and C2 configurations.

Sweeping Jet Film Cooling on a Turbine Vane

The cooling performance of sweeping jet film cooling was studied on a turbine vane suction surface in a low-speed linear cascade wind tunnel. The sweeping jet holes consist of fluidic oscillators with an aspect ratio (AR) of unity and a hole spacing of Pd/D = 6. Infrared (IR) thermography was used to estimate the adiabatic film effectiveness at several blowing ratios and two different freestream turbulence levels (Tu = 0.3% and 6.1%). Convective heat transfer coefficient was measured by a transient IR technique, and the net heat flux benefit was calculated. The total pressure loss due to sweeping jet film cooling was characterized by traversing a total pressure probe at the exit plane of the cascade. Tests were performed with a baseline shaped hole (SH) (777-shaped hole) for comparison. The sweeping jet hole showed higher adiabatic film effectiveness than the 777-shaped hole in the near hole region. Although the unsteady sweeping action of the jet augments heat transfer, the net positive cooling benefit is higher for sweeping jet holes compared to 777 hole at particular flow conditions. The total pressure loss measurement showed a 12% increase in total pressure loss at a blowing ratio of M = 1.5 for sweeping jet hole, while 777-shaped hole showed a 8% total pressure loss increase at the corresponding blowing ratio.

Assessing Superspheroids in Modeling the Scattering Matrices of Dust Aerosols

AbstractAtmospheric dust particles are known to have diverse and irregular morphologies. In order to account for nonsphericity, the spheroidal model with an aspect ratio distribution has been extensively used for modeling the optical properties of dust. The spheroidal model is superior to the spherical shape assumption, but it requires further improvement. In this study, superspheroids' modeling capabilities were systematically examined by comprehensively comparing the spheroid's and superspheroid's scattering matrices. Superspheroids have one more degree of freedom than spheroids and can be nonspherical at an aspect ratio of unity. The invariant imbedding T‐matrix and the improved geometrical optics methods were employed to compute superspheroids' single‐scattering properties with a wide distribution of aspect ratios and a number of roundness parameters. We then assessed the spheroidal and superspheroidal models' applicability for simulating the scattering matrices of 25 dust samples from the Amsterdam‐Granada Light Scattering Database. It was found that extreme aspect ratios for spheroids in reproducing the measurements were unnecessary if superspheroids were used. Even with equi‐probable aspect ratio distribution, superspheroids with constrained roundness parameters (from 2.4 to 3.0) could achieve better performances in concurrently matching six nonzero scattering matrix elements from the laboratory measurements. Moreover, superspheroids demonstrated better performances than spheroids in achieving spectral consistency for modeling dust scattering matrices. Therefore, superspheroids appear to be highly promising for atmospheric radiative transfer and remote sensing applications.

The evolution of autoignition kernels in turbulent flames of dimethyl ether

Simultaneous planar laser-induced fluorescence (PLIF) imaging of CH2O and OH was performed at a repetition rate of 10.kHz, jointly with chemiluminescence to explore autoigniting dimethyl ether (DME) flames in a hot vitiated coflow burner. The focus of the study is the imaging of the flame stabilization region and the temporal evolution of ignition kernels upstream of the flame base. Results detail the evolution of kernels throughout their formation, growth and final merging with the flame base. The ignition events were explored for a range of different fuel premixing and dilution ratios over two coflow temperatures which result in different lift-off heights. Images of CH2O and OH over the entire flame length show that not only is the lift-off height much higher at low coflow temperatures, but that the fluctuations are more intense and the region of kernel formation is larger both radially and axially. In these autoignition stabilized flames, increased premixing leads to the lift-off height and location of the maximum kernel formation rate being further downstream. Transient 1-D simulations of hot coflow products opposed against jet fuel mixtures identify that the overlap of CH2O and OH PLIF signals are a reliable marker of heat release in autoignition kernels. Measurements indicate that for the high coflow temperature cases, on average, the heat release of individual kernels is low, despite the high total kernel formation rate. This can be correlated to the slow growth rate and elongated aspect ratio of the kernels. For low coflow temperature cases, kernels are growing faster and have high heat release rates with near unity aspect ratios.

Quasi-three-dimensional numerical simulation of a solid oxide fuel cell short stack: Effects of flow configurations including air-flow alternation

The effects of flow configuration in solid oxide fuel cell (SOFC) stacks are investigated using a quasi-three-dimensional numerical model. Flow configurations with alternated air flows in parallel and perpendicular to the fuel flows are considered in addition to the conventional co-, counter-, and cross-flow configurations. The stacks have eight cells with unity aspect ratio and an active area of 4900 mm2 and are compared at fuel utilization of 0.193, 0.386, 0.579, and 0.772. The numerical model is capable of analyzing both the streamwise and spanwise directions of the cells. Although the counter-flow stack achieves the highest voltage efficiency among the stacks with the conventional flow configurations, it has the highest dispersion of the current density distribution on the cells. Air-flow alternation is effective to achieve uniform and high cell temperature and hence low dispersion of the current density. Alternate air flows parallel to the fuel flows achieve the highest voltage efficiency of 0.797 at a fuel utilization of 0.772, while alternate air flows perpendicular to the fuel flows reduce the risk of local fuel depletion as compared with the cross-flow stacks. Appropriate selection of the air-flow configuration within stacks allows operation at higher efficiency without fuel depletion.

Effects of gravity and variable thermal properties on nanofluid convective heat transfer using connected and unconnected walls

In this paper, heat transfer characteristics of natural convection in an enclosure are investigated by considering variable thermal properties. The heated enclosure with an aspect ratio of unity is full of an alumina-water nanofluid. To analyze the effect of different thermal properties on the flow and temperature distributions, many comparisons are conducted for various cases at various Rayleigh numbers and volume fractions of nanoparticles (1–9.5%). The effect of low-gravity conditions on natural convection is investigated by using the gravity values of 0.25 g (2.45 m/s2), 0.5 g (4.9 m/s2), 0.75 g (7.35 m/s2) and 1.0 g (0.98 m/s2). It was found that larger temperature gradients near the heated and cold walls can be obtained by increasing the Rayleigh number. By increasing the value of gravity, the flow velocity increased along the y direction. This indicated that gravity has great influence on enhancement of heat transfer. The investigation of the volume fraction of nanoparticles shows that the variation of the Nusselt number for high volume fraction presented a more flat profile than for low volume fraction. The Nusselt number decreased with an increase of the volume fraction. Results for cases with connected and unconnected heated walls are presented. The results showed that heat transfer for the case with the nanoparticle volume fraction of 1% at 1.0 g increased by 89.9% using an unconnected heated wall compared to the connected heated wall.

Laminar mixed convection of power-law fluids in cylindrical enclosures with heated rotating top wall

Laminar mixed convection of inelastic non-Newtonian fluids obeying a power law model in a cylindrical enclosure with a heated rotating top cover has been investigated numerically in this study. The steady-state axisymmetric simulations have been carried out for a range of different nominal Reynolds, Prandtl, Richardson numbers (i.e. 500⩽Re⩽2000;10⩽Pr⩽500 and 0⩽Ri⩽1) and power-law index (i.e. 0.6⩽n⩽1.8) for an aspect ratio (height/radius) of unity (i.e. AR=1.0). It has been found that mean Nusselt number Nu‾ increases as Re and Pr increase, whereas Nu‾ decreases with increasing values of Ri for shear-thinning (i.e. n<1), Newtonian (i.e. n=1) and shear-thickening (i.e. n>1) fluids. It has also been observed that the variation of Nu‾ with n differs depending on the values of Re and Ri. For instance, for small values of Reynolds number, Nu‾ exhibits a non-monotonic trend (i.e. increases before reaching a maximum followed by a decreasing trend) with increasing n for small values of Richardson number, whereas Nu‾ monotonically increases with increasing values of n for high Richardson number cases. However, in the case of high Reynolds number, Nu‾ increases with n before reaching a maximum value which is followed by a decreasing trend for all values of Ri considered here. Detailed physical explanations are provided for the influences of Re, Pr, Ri, and n on Nu‾ based on an elaborate scaling analysis. Finally, the numerical findings have been used to propose a correlation for Nu‾ for the ranges of Re,Pr,Ri,n considered here.

Boundary layer fluctuations in turbulent Rayleigh–Bénard convection

We report a combined experimental and numerical study of the effect of boundary layer (BL) fluctuations on the scaling properties of the mean temperature profile$\unicode[STIX]{x1D703}(z)$and temperature variance profile$\unicode[STIX]{x1D702}(z)$in turbulent Rayleigh–Bénard convection in a thin disk cell and an upright cylinder of aspect ratio unity. Two scaling regions are found with increasing distance$z$away from the bottom conducting plate. In the BL region, the measured$\unicode[STIX]{x1D703}(z)$and$\unicode[STIX]{x1D702}(z)$are found to have the scaling forms$\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$and$\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$, respectively, with varying thermal BL thickness$\unicode[STIX]{x1D6FF}$. The functional forms of the measured$\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$and$\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$in the two convection cells agree well with the recently derived BL equations by Shishkinaet al.(Phys. Rev. Lett., vol. 114, 2015, 114302) and by Wanget al.(Phys. Rev. Fluids, vol. 1, 2016, 082301). In the mixing zone outside the BL region, the measured$\unicode[STIX]{x1D703}(z)$remains approximately constant, whereas the measured$\unicode[STIX]{x1D702}(z)$is found to scale with the cell height$H$in the two convection cells and follows a power law,$\unicode[STIX]{x1D702}(z)\sim (z/H)^{\unicode[STIX]{x1D716}}$, with the obtained values of$\unicode[STIX]{x1D716}$being close to$-1$. Based on the experimental and numerical findings, we derive a new equation for$\unicode[STIX]{x1D702}(z)$in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work demonstrates that the effect of BL fluctuations can be adequately described by the velocity–temperature correlation functions and the new BL equations capture the essential physics.

Experimental and Numerical Investigation of Sweeping Jet Film Cooling

A companion experimental and numerical study was conducted for the performance of a row of five sweeping jet (SJ) film cooling holes consisting of conventional curved fluidic oscillators with an aspect ratio (AR) of unity and a hole spacing of P/D = 8.5. Adiabatic film effectiveness (η), thermal field (θ), convective heat transfer coefficient (h), and discharge coefficient (CD) were measured at two different freestream turbulence levels (Tu = 0.4% and 10.1%) and four blowing ratios (M = 0.98, 1.97, 2.94, and 3.96) at a density ratio of 1.04 and hole Reynolds number of ReD = 2800. Adiabatic film effectiveness and thermal field data were also acquired for a baseline 777-shaped hole. The SJ film cooling hole showed significant improvement in cooling effectiveness in the lateral direction due to the sweeping action of the fluidic oscillator. An unsteady Reynolds-averaged Navier–Stokes (URANS) simulation was performed to evaluate the flow field at the exit of the hole. Time-resolved flow fields revealed two alternating streamwise vortices at all blowing ratios. The sense of rotation of these alternating vortices is opposite to the traditional counter-rotating vortex pair (CRVP) found in a “jet in crossflow” and serves to spread the film coolant laterally.

Large-eddy simulation of pollutant dispersion in a cavity at fine grid resolutions

This study validates large-eddy simulations (LESs) at fine grid resolutions to analyze the turbulent dispersion of pollutants in a cavity space, representing an urban street canyon. A pollution dispersion experiment was conducted using a physical model of a cavity with a height (H) of 1.0 m and an aspect ratio of unity (1:1). A line source at the bottom center of the cavity was used to deliver the tracer gas (a mixture of ethylene and synthetic air). The wind velocity was measured with a hot-wire anemometer. The tracer gas concentration was measured using a fast flame ionization detector. Following the physical experiment, LESs were conducted under the same model settings. Simple orthogonal grids were employed for the LESs with a grid spacing of H/200 and H/400. The LESs produced a good prediction of the mean and root-mean-square (RMS) velocity values. The LESs also predicted the mean, RMS, and percentiles of concentration well. However, a slight grid-dependency existed for the 95th and 99th concentration percentiles and the power spectral density of concentration at high-frequencies. The high percentiles were under predicted in the LESs as compared to the experiment near the source, especially in the coarser grid simulation.

The applicability of physical optics in the millimetre and sub-millimetre spectral region. Part II: Application to a three-component model of ice cloud and its evaluation against the bulk single-scattering properties of various other aggregate models

The bulk single-scattering properties of various randomly oriented aggregate ice crystal models are compared and contrasted at a number of frequencies between 89 and 874 GHz. The model ice particles consist of the ten-branched plate aggregate, five-branched plate aggregate, eight-branched hexagonal aggregate, Voronoi ice aggregate, six-branched hollow bullet rosette, hexagonal column of aspect ratio unity, and the ten-branched hexagonal aggregate. The bulk single-scattering properties of the latter two ice particle models have been calculated using the light scattering methods described in Part I, which represent the two most extreme members of an ensemble model of cirrus ice crystals. In Part I, it was shown that the method of physical optics could be combined with the T-matrix at a size parameter of about 18 to compute the bulk integral ice optical properties and the phase function in the microwave to sufficient accuracy to be of practical value. Here, the bulk single-scattering properties predicted by the two ensemble model members and the Voronoi model are shown to generally bound those of all other models at frequencies between 89 and 874 GHz, thus representing a three-component model of ice cloud that can be generally applied to the microwave, rather than using many differing ice particle models. Moreover, the Voronoi model and hollow bullet rosette scatter similarly to each other in the microwave. Furthermore, from the various comparisons, the importance of assumed shapes of the particle size distribution as well as cm-sized ice aggregates is demonstrated.

Surface obstacles in pulsatile flow

Flows past obstacles mounted on flat surfaces have been widely studied due to their ubiquity in nature and engineering. For nearly all of these studies, the freestream flow over the obstacle was steady, i.e., constant velocity, unidirectional flow. Unsteady, pulsatile flows occur frequently in biology, geophysics, biomedical engineering, etc. Our study is aimed at extending the comprehensive knowledge base that exists for steady flows to considerably more complex pulsatile flows. Characterizing the vortex and wake dynamics of flows around surface obstacles embedded in pulsatile flows can provide insights into the underlying physics in all wake and junction flows. In this study, we experimentally investigate the wake of two canonical obstacles: a cube and a circular cylinder with an aspect ratio of unity. Our previous studies of a surface-mounted hemisphere in pulsatile flow are used as a baseline for these two new, more complex geometries. Phase-averaged PIV and hot-wire anemometry are used to characterize the dynamics of coherent structures in the wake and at the windward junction of the obstacles. Complex physics occur during the deceleration phase of the pulsatile inflow. We propose a framework for understanding these physics based on self-induced vortex propagation, similar to the phenomena exhibited by vortex rings.

A priori study of subgrid-scale features in turbulent Rayleigh-Bénard convection

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Bénard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and π spanwise open-ended distance are used at two Rayleigh numbers Ra∈{108,1010} [Dabbagh et al., “On the evolution of flow topology in turbulent Rayleigh-Bénard convection,” Phys. Fluids 28, 115105 (2016)]. First, DNS at Ra = 108 is used to assess the performance of eddy-viscosity models such as QR, Wall-Adapting Local Eddy-viscosity (WALE), and the recent S3PQR-models proposed by Trias et al. [“Building proper invariants for eddy-viscosity subgrid-scale models,” Phys. Fluids 27, 065103 (2015)]. The outcomes imply that the eddy-viscosity modeling smoothes the coarse-grained viscous straining and retrieves fairly well the effect of the kinetic unfiltered scales in order to reproduce the coherent large scales. However, these models fail to approach the exact evolution of the SGS heat flux and are incapable to reproduce well the further dominant rotational enstrophy pertaining to the buoyant production. Afterwards, the key ingredients of eddy-viscosity, νt, and eddy-diffusivity, κt, are calculated a priori and revealed positive prevalent values to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. The topological analysis suggests that the effective turbulent diffusion paradigm and the hypothesis of a constant turbulent Prandtl number are only applicable in the large-scale strain-dominated areas in the bulk. It is shown that the bulk-dominated rotational structures of vortex-stretching (and its synchronous viscous dissipative structures) hold the highest positive values of νt; however, the zones of backscatter energy and counter-gradient heat transport are related to the areas of compressed focal vorticity. More arguments have been attained through a priori investigation of the alignment trends imposed by existing parameterizations for the SGS heat flux, tested here inside RBC. It is shown that the parameterizations based linearly on the resolved thermal gradient are invalid in RBC. Alternatively, the tensor-diffusivity approach becomes a crucial choice of modeling the SGS heat flux, in particular, the tensorial diffusivity that includes the SGS stress tensor. This and other crucial scrutinies on a future modeling to the SGS heat flux in RBC are sought.

The influence of pore geometry and orientation on the strength and stiffness of porous rock

The geometry of voids in porous rock falls between two end-members: very low aspect ratio (the ratio of the minor to the major axis) microcracks and perfectly spherical pores with an aspect ratio of unity. Although the effect of these end-member geometries on the mechanical behaviour of porous rock has received considerable attention, our understanding of the influence of voids with an intermediate aspect ratio is much less robust. Here we perform two-dimensional numerical simulations (Rock Failure Process Analysis, RFPA2D) to better understand the influence of pore aspect ratio (from 0.2 to 1.0) and the angle between the pore major axis and the applied stress (from 0 to 90°) on the mechanical behaviour of porous rock under uniaxial compression. Our numerical simulations show that, for a fixed aspect ratio (0.5) the uniaxial compressive strength and Young's modulus of porous rock can be reduced by a factor of ∼2.4 and ∼1.3, respectively, as the angle between the major axis of the elliptical pores and the applied stress is rotated from 0 to 90°. The influence of pore aspect ratio on strength and Young's modulus depends on the pore angle. At low angles (∼0–10°) an increase in aspect ratio reduces the strength and Young's modulus. At higher angles (∼40–90°), however, strength and Young's modulus increase as aspect ratio is increased. At intermediate angles (∼20–30°), strength and Young's modulus first increase and then decrease as pore aspect ratio approaches unity. These simulations also highlight that the influence of pore angle on compressive strength and Young's modulus decreases as the pore aspect ratio approaches unity. We find that the analytical solution for the stress concentration around a single elliptical pore, and its contribution to elasticity, are in excellent qualitative agreement with our numerical simulations. The results of our numerical modelling are also in agreement with recent experimental data for porous basalt, but fail to capture the strength anisotropy observed in experiments on sandstone. We conclude that the alignment of grains or platy minerals such as clays exerts a greater influence on strength anisotropy in porous sandstones than pore geometry. Finally, we show that the strength anisotropy that arises as a result of preferentially aligned elliptical pores is of a similar magnitude to that generated by bedding in porous sandstones and foliation in low-porosity metamorphic rocks. The modelling presented herein shows that porous rocks containing elliptical pores can display a strength and stiffness anisotropy, with implications for the preservation and destruction of porosity and permeability, as well as the distribution of stress and strain within the Earth's crust.

Numerical investigation of mixed convection of Bingham fluids in cylindrical enclosures with heated rotating top wall

The steady-state laminar mixed convection of yield stress fluids obeying the Bingham model in a cylindrical enclosure with a heated rotating top cover has been numerically analysed based on axisymmetric incompressible flow simulations. Yield stress effects on heat and momentum transport have been investigated for an aspect ratio (height/radius) of unity (i.e. AR=1) for a range of different values of nominal Prandtl, Richardson and Reynolds numbers given by 10⩽Pr⩽500, 0⩽Ri⩽1 and 100⩽Re⩽3000. The mean Nusselt number Nu‾ has been found to decrease sharply with increasing Bingham number Bn, but subsequently Nu‾ approaches asymptotically to a value of unity, which is indicative of conduction-driven transport. It has also been found that Nu‾ increases with increasing values of Prandtl and Reynolds numbers for both Newtonian (i.e. Bn=0) and Bingham fluids. In contrast, Nu‾ decreases with increasing Ri for both Newtonian and Bingham fluids for small values of Bingham number, whereas Nu‾ remains insensitive to the variation of Ri for large values of Bingham number. The variation of torque coefficient CT, which gives a quantitative measure of power consumption, has also been investigated. The torque coefficient CT has been found to increase with increasing Bn whereas it decreases with increasing Re. It has also been found that CT decreases slightly with increasing Ri for small values of Bn, whereas it becomes insensitive to the variation of Ri for large Bingham numbers. For the fully forced convection (Ri=0) case, Pr does not have a significant influence on CT. However, in the case of mixed convection CT increases with increasing Pr. The simulation data has been used in conjunction with a detailed scaling analysis to propose a correlation for Nu‾ for the range of Re,Ri and Pr considered here.