Unity Aspect Ratio Research Articles

Double-reflection symmetry of thermal convection for Rayleigh number up to 1010

The Rayleigh–Bénard convection system exhibits certain known symmetries at low Rayleigh numbers that are broken as the Rayleigh number increases. In this study, we investigate the statistical symmetry of Rayleigh–Bénard convection at moderately high Rayleigh numbers through direct numerical simulations. The simulations are conducted for a fluid confined within two-dimensional walls, with an aspect ratio of unity and a fixed Prandtl number. Although elliptical large-scale circulations break both left-right and top-down reflection symmetries, we observe the emergence of a restored double-reflection symmetry. This symmetry is evident in the velocity and temperature fields, as well as in the variations of mean velocity and temperature profiles along the streamwise direction and the characteristics of the kinetic and thermal boundary layers. For Rayleigh numbers ranging between 107 and 1010, our results demonstrate a remarkable data collapse under this double-reflection transformation.

Numerical Simulation of Vertical Cyclic Responses of a Bucket in Over-Consolidated Clay

Multi-bucket foundations have become an alternative for large offshore wind turbines, with the expansion of offshore wind energy into deeper waters. The vertical cyclic loading–displacement responses of the individual bucket of the tripod foundation are relevant to the deflection of multi-bucket foundations and crucial for serviceability design. Finite element analyses are used to investigate the responses of a bucket subjected to symmetric vertical cyclic loading in over-consolidated clay. The Undrained Cyclic Accumulation Model (UDCAM) is adopted to characterize the stress–strain properties of clay, the parameters of which are calibrated through monotonic and cyclic direct simple shear tests. The performance of the finite element (FE) model combined with UDCAM in simulating vertical displacement amplitudes is evaluated by comparison with existing centrifuge tests. Moreover, the impact of the bucket’s aspect ratio on vertical displacement amplitude is investigated through a parametric study. A predictive equation is proposed to estimate the vertical displacement amplitudes of bucket foundations with various aspect ratios, based on the cyclic displacement amplitude of a bucket with an aspect ratio of unity.

Incremental Analysis of Magnetic Domains in Multiple Types of Ferromagnetic CoFe Nanolayer Patterns

In this article, the results of incremental analysis on the thickness, aspect ratio, and crystallographic substrate orientation dependence of magnetic domain formation in CoFe nanolayer patterns (NPs) on GaAs (001) substrates by magnetic force microscopy are reported. All the 35 nm thick CoFe NPs show multiple magnetic domains under as‐deposition condition whereas the 13 nm thick CoFe NPs have a single magnetic domain in the case of the patterns with a relatively small size and high aspect ratio. Subsequently, the magnetic fields are applied in the direction parallel to the <110> and <1–10> directions of the substrates to analyze a magnetization switching behavior in the patterns. The results reveal that the magnetic fields required for magnetization switching markedly tend to increase, with decreasing the thickness of the patterns and increasing their aspect ratio. A general tendency is obtained, which a higher magnetic field is needed for a higher aspect ratio and a thinner thickness of the NPs. Even in the case of the patterns with an aspect ratio of unity and a thickness of 35 nm (but, a smaller size), a single magnetic domain is formed at a relatively high applied magnetic field of 1500 Gauss.

Large eddy simulation of thermal stratification effects on tracer gas dispersion in a cavity

This paper assesses the effect of thermal stratification on the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large eddy simulation. The Reynolds number of the cavity flow, was 67 000. Thermal stratification was achieved through the heating or cooling of one or more of the walls within the cavity. When compared to an isothermal (neutral) case, unstable stratification from surface heating generally has a weak influence on the primary recirculating cavity vortex, except in the case where the windward wall is heated. For windward wall heating, a large secondary vortex appears at the corner of the windward wall and cavity floor. Unstable stratification has no significant influence on the removal of pollutant mass from the cavity. Stable stratification through surface cooling drastically alters the flow pattern within the cavity, pushing the cavity vortex towards the upper quadrant of the cavity. As a result, large regions of stagnant fluid are present within the cavity, reducing the effectiveness of the shear layer at removing pollutant concentration from the cavity. Some stable stratification configurations can increase the pollutant mass within the cavity by over a factor of five, when compared to the neutral case. Pollutant concentration flux maps show that, in stably stratified cases, the majority of pollutant transport from the cavity is the result of entrainment into the primary cavity vortex. The results show that pollutant concentrations in urban street canyon-type flows are substantially altered by diurnal heating and cooling, which may influence pedestrian management strategies in urban environments.

Numerical Investigation of Flow and Dispersion over Two-Dimensional Semi-Open Street Canyon

A semi-open street canyon is able to protect pedestrians from unpleasant situations such as direct sunlight and rain. However, the protruding elements of the two opposite building facades that form the semi-open configuration can affect the air quality of the urban canopy layer (UCL). Therefore, this paper investigated the influence of the eave structures on the flow and pollutant dispersion over an idealized 2D street canyon with a unity aspect ratio. The length of the eaves was varied into 0.25H and 0.5H (H is the building height) and placed either on the leeward wall, the windward wall, or on both building facades located at the same elevation as the street canyon. Numerical simulations were performed using the steady-state Reynolds-averaged Navier-Stokes (RANS) equations in conjunction with Re-Normalization Group (RNG) k-ε as the turbulence closure model. The pollutant was released from a line source in the center of the bottom of the target canyon with uniform flow rate. Six different eave configurations were simulated in the wind direction perpendicular to the canyon axis, representing the worst condition of canyon ventilation. The evolution of the primary vortex, which occupied the entire canyon with the characteristic of skimming flow, showed less dependence on the length and position of the eave, except for the longest eave on the windward wall. However, the position of the vortex center depicted opposite results. The pollutant concentration is always higher near the leeward wall, but for the eave that protrudes from the windward wall with a length of 0.5H, the pollutant accumulates near the windward region. The ratio of pollutant concentration showed higher concentration in the semi-open configurations compared to the fully open layout as a result of limited penetration of shear flow into the canyon, which leads to deterioration of pollutant removal.

On the Performance of a Miniaturized Reactive Loaded Monopole Antenna for Ex Vivo Catheter Applications

In this paper, we propose a miniaturized series L-C loaded monopole antenna for catheter application in microwave ablation systems. Initially, a quarter wavelength long monopole antenna (Design1), having length 30 mm (≈ 0.24λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> where λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> represents the free-space wavelength at 2.4 GHz operating frequency) using series LC loading concept is designed. The initial design is further extended to a miniaturized version (Design2) having length 5 mm (≈ 0.04λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ), showing nearly 83% size reduction compared to its former.Both the antennas are designed and simulated by immersing inside high permittivity egg white phantom (ϵ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>r</i></sub> = 63.84). Antenna Design 1 and 2 exhibit good impedance matching ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> < –12 dB) at and around the operating frequency with uniform monopolar radiation pattern having co-to-cross isolation of nearly 30-35 dB. Further, the in-phantom Specific Absorption Rate (SAR) values for both antennas are evaluated using simulation and verified with the measured SAR values such as 22 W/kg and 19.6 W/kg for Design1 and 2 respectively, using an in-house experimental setup. Moreover, the microwave ablation property of the proposed antennas is studied using simulated transient thermal gradient which translates to ablation zone formation. Here, Design 2 shows the advantage of having a low invasive diameter of 1.5 mm and near unity aspect ratio (AR) for the ablation zone as compared to Design1.

Temperature statistics in turbulent Rayleigh–Bénard convection with a Prandtl number of Pr = 12.3

The transport of plumes in turbulent convective systems must be understood to study the mantle and various industrial applications. We measured the probability density function P(T) of the temperature at various radial and vertical positions in the bulk of a convection cell. The asymmetric-shaped distribution was decomposed into a turbulent background and plumes. The temperature of the turbulent background was fitted by a Gaussian function according to the peak of P(T). We proposed a simple quantity A ≡ (⟨T⟩ − Tbg) to describe the effective strength of the plume, where ⟨T⟩ is the time-averaged value of the local temperature. The hot plume diminishes as it rises in the cell. The plume strength varies logarithmically with the vertical position. For larger Ra, the plume along the centerline has a longer travel distance in terms of the thermal boundary layer. For a given Ra, the strength and travel distance of the plume increase as the measurements move closer to the sidewall. At the cell center, the temperature fluctuations can be decomposed into fluctuations due to the turbulent background σbg and fluctuations due to the plume. The value of σbg is so small that the relation between σbg and the vertical position can be fitted by a logarithmic function or a power law. The Ra dependence on these two fluctuations was also investigated. The measurements were collected in a cylindrical cell with a unity aspect ratio of 1, and FC72 was used as the working fluid.

Synchronizing the helicity of Rayleigh–Bénard convection by a tide-like electromagnetic forcing

We present results on the synchronization of the helicity in a liquid-metal Rayleigh–Bénard experiment under the influence of a tide-like electromagnetic forcing with azimuthal wavenumber m = 2. We show that for a critical forcing strength the typical large-scale circulation in the cylindrical vessel of aspect ratio unity is entrained by the period of the tide-like forcing, leading to synchronized helicity oscillations with opposite signs in two half-spaces. The obtained experimental results are consistent with and supported by numerical simulations. A similar entrainment mechanism for the helicity in the solar tachocline may be responsible for the astonishing synchronization of the solar dynamo by the 11.07-year triple synodic alignment cycle of the tidally dominant planets Venus, Earth, and Jupiter.

Impact of moving traffic on pollutant transport in street canyons under perpendicular winds: A CFD analysis using large-eddy simulations

• One-way traffic has stronger influences on pollutant dispersion than two-way traffic • The influence of traffic motion is noticeable under a low approaching wind speed • At U 10 = 2 m/s, the net pollutant flow rate at the side can be increased by 14 times • Traffic density plays a much less role than traffic direction and wind speed • Considering traffic motion is essential for accurate predictions of urban pollutant In urban street canyons, wind and vehicle motions jointly influence the pollutant dispersion. The present study systematically investigated the impact of (i) traffic direction, (ii) traffic density, and (iii) approaching wind speed on the mechanism of pollutant dispersion. Large-eddy simulations were performed for a street canyon with an aspect ratio of unity under two-lane traffic flow. Results show that two-lane traffic moving in the opposite direction insignificantly affects the mean pollutant concentrations inside the canyon, with a change in the net pollutant flow rate by less than 7%. However, traffic moving in the same direction strongly modify the local mean pollutant concentration, especially under a low approaching wind speed. Under the wind with a 10-meter speed of 2 m⋅s −1 , one-way traffic plays a dominant role in determining the concentration pattern, shifting the region with the maximum pollutant concentration from the center to the corner downstream of the traffic direction. The absolute net pollutant outflow rate at the canyon's lateral opening downstream of the traffic direction is increased by about 14 times, which is caused by the outflow convective pollutant flux. Findings here suggest numerical studies that neglect traffic motion can erroneously predict the local pollutant concentration in street canyons.

Large Eddy simulation of tracer gas dispersion in a cavity

This paper assesses the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large Eddy simulation (LES). The flow Reynolds number was 67 000, based on the freestream velocity and cavity height. The flow upstream of the cavity was laminar, producing a cavity shear layer which underwent a transition to turbulence over the cavity. Three distinct meshes are used, with grid spacings of (coarse), (intermediate), and (fine) respectively. The Smagorinsky, WALE, and Germano-Lilly subgrid-scale models are used on each grid to quantify the effects of subgrid-scale modelling on the simulated flow. Coarsening the grid led to small changes in the predicted velocity field, and to substantial over-prediction of the tracer gas concentration statistics. Quantitative metric analysis of the tracer gas statistics showed that the coarse grid simulations yielded results outside of acceptable tolerances, while the intermediate and fine grids produced acceptable output. Interrogation of the fluid dynamics present in each simulation showed that the evolution of the cavity shear layer is heavily influenced by the grid and subgrid scale model. On the coarse and intermediate grids the development of the shear layer is delayed, inhibiting the entrainment and mixing of the tracer gas into the shear layer, reducing the removal of the tracer gas from the cavity. On the fine grid, the shear layer developed more rapidly, resulting in enhanced removal of the tracer gas from the cavity. Concentration probability density functions showed that the fine grid simulations accurately predicted the range, and the most probable value, of the tracer gas concentration towards both walls of the cavity. The results presented in this paper show that the WALE and Germano-Lilly models may be advantageous over the standard Smagorinsky model for simulations of pollutant dispersion in the urban environment.

Collective effect of thermal plumes on temperature fluctuations in a closed Rayleigh–Bénard convection cell

We report a systematic study of the collective effect of thermal plumes on the probability density function (p.d.f.) $P(\delta T)$ of temperature fluctuations $\delta T(t)$ in turbulent Rayleigh–Bénard convection. By decomposing $\delta T(t)$ into four basic fluctuation modes associated with single and multiple warm and cold plumes and a turbulent background, we derive an analytic form of $P(\delta T)$ based on the convolutions of the five independent modes. To test the derived form of $P(\delta T)$ in the multiple-plume regions, where the thermal plumes are heavily populated, we conduct time series measurements of temperature fluctuations in two convection cells; one is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. For a given normalized position in most regions of the convection cell, all of the measured p.d.f.s $P(\delta T)$ for different Rayleigh numbers fall onto a single master curve, once $\delta T$ is normalized by its root-mean-square (r.m.s.) value $\sigma _T$ . It is found that the measured $P(\delta T/\sigma _T)$ at different locations along the symmetric horizontal and vertical axes of the convection cells can all be well described by the derived form of $P(\delta T/\sigma _T)$ . The fitted values of the parameters associated with the number of plumes in multiple plume clusters and their relative strengths and degrees of intermittency are closely linked to the spatial distribution of thermal plumes and local dynamics of the large-scale circulation in a closed convection cell. Our work thus provides a unified theoretical approach for understanding scalar p.d.f.s in a turbulent field, which is very useful not only for the present study but also for the study of many turbulent mixing problems of practical interest.

Endwall heat transfer characteristics of octahedron family lattice-frame materials

Recent studies on traditional metal foam thick blocks suggest that much of the foam volume remains unused in heat dissipation and that the thinner configurations are more efficient in forced convection scenarios. Single cell thick lattice-frame configurations are attractive solutions to the problem of unused foam volume and can also be additively manufactured through Direct Metal Laser Sintering process while also offering superior load bearing capabilities. Due to the inherent nature of such single cell thick configurations, their unit cell topologies' footprint at the enclosing walls has significant effect in both local heat transfer coefficient distribution and net overall heat dissipation. This study presents detailed endwall heat transfer coefficient measurements for lattice-frame structure of Octet unit cell topology and compares its thermal performance with two other members of the Octahedron family, viz. Octa and V-Octet. Developing heat transfer was measured through transient liquid crystal thermography at the endwalls of a unity aspect ratio duct featuring five consecutive interconnected unit cells at a Reynolds number of 37,200. Relative to a smooth channel, the cell-based averaged Nusselt numbers for Octet, Octa and V-Octet were 2.96, 2.78 and 3.05 times, respectively.

Cross Sections of Coronal Loop Flux Tubes

Abstract Coronal loops reveal crucial information about the nature of both coronal magnetic fields and coronal heating. The shape of the corresponding flux tube cross section and how it varies with position are especially important properties. They are a direct indication of the expansion of the field and of the cross-field spatial distribution of the heating. We have studied 20 loops using high spatial resolution observations from the first flight of the Hi-C rocket experiment, measuring the intensity and width as a function of position along the loop axis. We find that intensity and width tend to either be uncorrelated or to have a direct dependence, such that they increase or decrease together. This implies that the flux tube cross sections are approximately circular under the assumptions that the tubes have nonnegligible twist and that the plasma emissivity is approximately uniform along the magnetic field. The shape need not be a perfect circle and the emissivity need not be uniform within the cross section, but subresolution patches of emission must be distributed quasi-uniformly within an envelope that has an aspect ratio of order unity. This raises questions about the suggestion that flux tubes expand with height, but primarily in the line-of-sight direction so that the corresponding (relatively noticeable) loops appear to have roughly uniform width, a long-standing puzzle. It also casts doubt on the idea that most loops correspond to simple warped sheets, although we leave open the possibility of more complex manifold structures.

Comparison of two and three-dimensional Rayleigh-Bénard convection of power-law fluids in cylindrical and annular enclosures

In the present study, three-dimensional steady-state laminar Rayleigh-Bénard convection (RBC) of power-law fluids in cylindrical and annular enclosures with a square cross-section has been investigated numerically. The simulations have been carried out for a range of power-law exponents for different non-dimensional parameters such as nominal Rayleigh number (Ra) (from 103 to 105), internal radius to enclosure height ratio (ri/L) (from 0 to 2), for a single representative value of Prandtl number (i.e. Pr=102) and an aspect ratio of unity together with Dirichlet boundary conditions. It has been found that convection augments with decreasing n values due to the shear-thinning character of viscosity. As a reflection of this, the mean Nusselt number (Nu¯) increases with decreasing n values and the flow patterns show multiple torus like structures. These findings have been compared with previous findings where the same analysis has been conducted for two-dimensional axisymmetric simulations of cylindrical enclosures. It has been revealed that the results of the two-dimensional analysis are not representative for a three-dimensional configuration in terms of flow pattern and the Nusselt number at Ra > 104 for both the Newtonian (i.e. n=1.0) and shear-thinning (i.e. n < 1) fluids for high values of Rayleigh number. Additionally, the values of critical Rayleigh numbers Racrit (RaNu¯=1) (where Nu¯ values deviate from unity for n ≤ 1 (n > 1)) have been found to be almost insensitive to the change in ri/L, but they decrease with decreasing value of n. Finally, a new correlation for Nu¯, Racrit and RaNu¯=1 has been proposed for the range of parameters considered in this study, based on three-dimensional analysis, which can be very useful for practical applications.

The Influence of Computational Parameterization on Mean Flow and Turbulence Statistic in 2D Idealized Street Canyon: Computational Domain

The use of Computational Fluid Dynamics (CFD) as a research tool has been utilized in many ways to predict the turbulent flow nature and pollution dispersion in an urban environment such as street canyon. Apart from the advance advantages offered by this method, some problems can be arising on respect to accurate prediction of data and uncertainties of the assumption that are made in numerical modelling. The execution and evaluation of the CFD studies need to undergo validation and generic sensitivity analyses to minimize the computational error and have an accurate prediction of data. This study performs a series of large eddy simulation (LES) to investigate the flow fields within and above a two-dimensional idealized street canyon with a unity aspect ratio (ratio of street width, W to building height, H). The effect of domain size on turbulent statistics is evaluated through the implementation of three different domain sizes i.e. varied streamwise lengths with fixed spanwise length and vertical height for different grid resolution (coarse, medium and fine). Comparison with the available experimental results shown a good agreement for mean velocity profiles. However, current LES underestimates the higher-order turbulent statistics. For the mean flow, the LES predicts the streamwise flow in the upper part and reversed flow in the lower part of the canyon, indicating the well-known flow regime of skimming flow. The value of mean velocities for all cases of the run have almost matching profile inside and above the canyon. For all cases, the maximum values of standard deviation in the streamwise and vertical directions are located approximately near the roof-level windward wall represent the occurrence of velocities fluctuation. In contrast, the Reynold shear stress for all cases shows some discrepancy where the peaked of turbulence intensity near the roof height is not smoothly captured in the current LES. Study shows that the LES cannot properly simulate those statistics accurately when the streamwise domain is limited to 10H even with the increasing of grid resolution sizes. Nevertheless, these results are expected to provide additional information relevant to uncertainty estimation upon execution of computational fluid dynamics (CFD) simulation.

From Rayleigh–Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure

We perform a numerical study of the heat transfer and flow structure of Rayleigh-B\'enard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $\phi$ in the flow properties during the transition process from the traditional RB convection with $\phi=1$ (so no obstacles included) to Darcy-type porous-media convection with $\phi$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities $\phi$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonously as a function of $\phi$; namely, with decreasing $\phi$, it first increases, before it decreases for $\phi$ approaching 0. The non-monotonous behaviour of $Nu(\phi)$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $\phi$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ vs $Ra$, namely, a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux, and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.

Flow regimes of Rayleigh–Bénard convection in a vertical magnetic field

The effects of a vertical static magnetic field on the flow structure and global transport properties of momentum and heat in liquid metal Rayleigh–Benard convection are investigated. Experiments are conducted in a cylindrical convection cell of unity aspect ratio, filled with the alloy GaInSn at a low Prandtl number of . Changes of the large-scale velocity structure with increasing magnetic field strength are probed systematically using multiple ultrasound Doppler velocimetry sensors and thermocouples for a parameter range that is spanned by Rayleigh numbers of and Hartmann numbers of . Our simultaneous multi-probe temperature and velocity measurements demonstrate how the large-scale circulation is affected by an increasing magnetic field strength (or Hartmann number). Lorentz forces induced in the liquid metal first suppress the oscillations of the large-scale circulation at low , then transform the one-roll structure into a cellular large-scale pattern consisting of multiple up- and downwellings for intermediate , before finally expelling any fluid motion out of the bulk at the highest accessible leaving only a near-wall convective flow that persists even below Chandrasekhar’s linear instability threshold. Our study thus proves experimentally the existence of wall modes in confined magnetoconvection. The magnitude of the transferred heat remains nearly unaffected by the steady decrease of the fluid momentum over a large range of Hartmann numbers. We extend the experimental global transport analysis to momentum transfer and include the dependence of the Reynolds number on the Hartmann number.

Mixed convection of power-law fluids in cylindrical enclosures with a cold rotating top cover and a stationary heated bottom wall

Steady-state laminar mixed convection in cylinders with a rotating top cold cover and a heated bottom has been numerically analysed for inelastic shear-thinning/shear-thickening fluids by applying power-law model of viscosity. In this analysis, axisymmetric incompressible flow simulations have been conducted for a range of different values of Reynolds, Richardson, Prandtl numbers (i.e. 500≤Re≤2000;0≤Ri≤1.0; 10≤Pr≤1000) and power-law index (i.e. 0.6≤n≤1.8) for an aspect ratio (height/radius) of unity (i.e. AR=1.0). The thermal convective transport has been found to strengthen with increasing Re and Pr, which in turn gives rise to an increase in the mean Nusselt number Nu‾. By contrast, an increase in Ri leads to a mild increase in Nu‾ for small Richardson number values but Nu‾ becomes insensitive to the changes in Ri for large Richardson numbers within the range of 0≤Ri≤1.0 for all values of n considered here. The mean Nusselt number Nu‾ exhibits a non-monotonic trend (i.e. increases before reaching a maximum followed by a decreasing trend) with the variation of n. The influences of Ra,Pr and Ri on the mean Nusselt number Nu‾ have been explained in terms of scaling arguments. The scaling relations along with the numerical findings have been utilised to propose a correlation for the mean Nusselt number for the configuration and the parameter range considered here.

New Supersonic Loss Model for the Preliminary Design of Transonic Turbine Blades and the Influence of Pitch

Abstract In order to produce a more efficient design of a compact turbine driving a cryogenic engine turbo-pump for a satellite delivering rocket, a new supersonic loss model is proposed. The new model was constructed based on high-quality published data, composed of Schlieren photographs and experimental measurements, that combined provided a unique insight into the mechanisms driving supersonic losses. Using this as a cornerstone, model equations were formulated that predict the critical Mach number and shock loss and shock-induced mixing loss as functions of geometrical (i.e., blade outlet and uncovered turning angle and trailing edge thickness) and operational parameters (i.e., exit Mach number). A series of highly resolved CFD numerical simulations were conducted on an in-house designed state-of-the-art transonic turbine rotor row (around unity aspect ratio (AR)) to better understand changes in the shock system for varying parameters. The main outcome showed that pitch to chord ratio has a powerful impact on the shock system, and thus on the manner by which shock loss and shock-induced mixing loss is distributed to compose the overall supersonic losses. The numerical loss estimates for two pitch to chord ratios—t⁄c = 0.70 and t⁄c = 0.98—were compared with absolute loss data of a previously published similar blade with satisfactory agreement. Calibrated equations are provided to allow hands-on integration into existing overall turbine loss models, where supersonic losses play a key role, for further enhancement of preliminary turbine design.

Experimental investigation of turbulent Rayleigh-Bénard convection of water in a cylindrical cell: The Prandtl number effects for Pr &amp;gt; 1

We report an experimental study of turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio unity, focusing on the effects of the Prandtl number (Pr). Purified water was used as the convecting fluid. Five different Pr between 3.58 and 9.40 were achieved by changing the mean temperature of water, and the measurements were carried out over the Rayleigh number range 2.63 × 108 ≤ Ra ≤ 3.89 × 1010. Over the present parameter range, the measured Nusselt number Nu is found to scale as Nu ∼ Raβ with β = 0.30 and to be independent of Pr. Based on the oscillation period of the measured temperature, the Reynolds number Re scales as Re ∼ Ra0.47Pr−0.72. The local temperature fluctuations at the cell center and near the cell’s sidewall were measured, and their relations with Ra and Pr were studied. Our results further reveal that the non-Oberbeck-Boussinesq effects of water have a relatively small influence on the measured scaling relation Nu ∼ Raβ.