Critical Richardson Number Research Articles

Conditions of Stabilization of the Plasma Jet in a Vortex Chamber

The stabilization of a plasma jet in a vortex chamber as a result of the return of the turbulent moles coming out of this jet and back into it was analyzed with account for the nonuniformity of the circumferential velocity of the vortex, the heat transfer, and the appearance of associated masses in this chamber. For the purpose of determining the dependence of the critical Richardson number in the indicated chamber on the physical and thermodynamic parameters of the moles and the vortex flow in it, a system of equations was derived and solved numerically. The calculation results obtained were compared with the corresponding experimental data.

Control of flow separation around bluff obstacles by superimposed thermal buoyancy

We analyze through numerical simulation the phenomena of suppression of flow separation around bluff obstacles by superimposed thermal buoyancy. For that purpose, we consider an unconfined flow of a Newtonian fluid around heated cylinders of circular and square cross-sections in a buoyancy-aided vertical flow configuration. The Reynolds numbers of the flow are kept intentionally low such that the flow remains steady and separated without imposition of the thermal buoyancy. When the buoyancy is added, it is observed that the flow separation diminishes gradually and at some critical value of the buoyancy parameter it completely disappears resulting a creeping flow like phenomena. Additionally, it is observed that the square cylinder requires more heating in comparison to its circular counterpart of equal linear dimension for complete suppression of flow separation. Although the phenomena is known, the exact quantification of the buoyancy parameter for which the flow separation around various types of bluff obstacles completely vanishes is unknown which is of tremendous fundamental importance. The major contribution is the determination of the critical Richardson numbers for the complete suppression of the flow separation around circular and square cylinders for the steady flow in the low Reynolds number laminar regime. Furthermore, the effect of Prandtl number on suppression of flow separation is also investigated and it is found that the high Prandtl number fluid requires less heating for suppression. The recirculation lengths and skin friction coefficients are computed to substantiate the above findings. Additionally, the Nusselt numbers are computed to predict the heat transfer rates from the obstacles under the superimposed thermal buoyancy condition.

Conversion of Energy Equation for Turbulent Motion and its Applications

Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number.

Effect of Side Ratio and Aiding/Opposing Buoyancy on the Aerodynamic and Heat Transfer Characteristics around a Rectangular Cylinder at Low Reynolds Numbers

A numerical investigation is carried out to understand the effect of side ratio, as well as aiding/opposing buoyancy on the aerodynamic and heat transfer characteristics around a rectangular cylinder in the vertical unconfined configuration. The representative vortex structures and isotherms patterns are presented and discussed. A correlation between the critical Richardson number for the buoyancy-induced breakdown of Kármán vortex street and the side ratio of the cylinder is obtained. The influence of side ratio and buoyancy on Strouhal number, drag and lift coefficient, the recirculation length, and heat transfer from the cylinder is also investigated.

The wind speed shear in the case of stable stratification and the scales of the similarity theory

The wind speed shear in the case of stable stratification in the linear part of the profile spreading high above the surface layer of constant flows is studied using the data of long-term sodar measurements in the atmospheric boundary layer. The wind speed shear in this part remains almost invariable during several hours at the significant change in parameters of the Monin-Obukhov theory. The length of this linear part can be associated with the layer of the critical Richardson number. In the case of the pronounced temperature inversion (with the positive gradient of more than 1°C per 100 m), the wind speed profile is close to the linear function in the most part of the nocturnal mixing layer. Proposed is a scale characterizing the height of the surface layer of constant flows.

Breaking Surface Wave Effects on River Plume Dynamics during Upwelling-Favorable Winds

Abstract This study examines the dynamics of a buoyant river plume in upwelling-favorable winds, concentrating on the time after separation from the coast. A set of idealized numerical simulations is used to examine the effects of breaking surface gravity waves on plume structure and cross-shore dynamics. Inclusion of a wave-breaking parameterization in the two-equation turbulence submodel causes the plume to be thicker and narrower, and to propagate offshore more slowly, than a plume in a simulation with no wave breaking. In simulations that include wave breaking, the plume has much smaller vertical gradients of salinity and velocity than in the simulation without breaking. This leads to decreased importance of shear dispersion in the plumes with wave breaking. Much of the widening rate of the plume is explained by divergent Ekman velocities at the off- and onshore edges. Some aspects of plume evolution in all cases are predicted well by a simple theory based on a critical Richardson number and an infinitely deep ocean. However, because the initial plume in these simulations is in contact with the sea floor in the inner shelf, some details are poorly predicted, especially around the time that the plume separates from the coast.

On the nonlinear destabilization of stably stratified shear flow

AbstractA weakly nonlinear analysis of the bifurcation of the stratified Ekman boundary-layer flow near a critical bulk Richardson number is conducted and compared to a similar analysis of a continuously stratified parallel shear flow subject to Kelvin–Helmholtz instability. Previous work based on asymptotic expansions and predicting supercritical bifurcation at Prandtl number $Pr\lt 1$ and subcritical bifurcation at $Pr\gt 1$ for the parallel base flow is confirmed numerically and through fully nonlinear temporal simulations. When applied to the non-parallel Ekman flow, weakly nonlinear analysis and fully nonlinear calculations confirm that the nature of the bifurcation is dominantly controlled by $Pr$, although a sharp threshold at $Pr= 1$ is not found. In both flows the underlying physical mechanism is that the mean flow adjusts so as to induce a viscous (respectively diffusive) flux of momentum (respectively buoyancy) that balances the vertical flux induced by the developing instability, leading to a weakening of the mean shear and mean stratification. The competition between the former nonlinear feedback, which tends to be stabilizing, and the latter, which is destabilizing and strongly amplified as $Pr$ increases, determines the supercritical or subcritical character of the bifurcation. That essentially the same competition is at play in both the parallel shear flow and the Ekman flow suggests that the underlying mechanism is valid for complex, non-parallel stratified shear flows.

The effect of small viscosity and diffusivity on the marginal stability of stably stratified shear flows

AbstractThe effect of non-zero, but small, viscosity and diffusivity on the marginal stability of a stably stratified shear flow is examined by making perturbations around the neutral solution for an inviscid and non-diffusive flow. The results apply to turbulent flows in which horizontal and vertical turbulent transports of momentum and buoyancy are represented by eddy coefficients of viscosity and diffusivity that vary in the vertical ($z$) direction. General expressions are derived for the modified phase speed and the growth rate of small disturbances as a function of wavenumber. To first order in their coefficients, the effect on the phase speed of adding viscosity and diffusivity is zero. Growth rates are found for two mean flows when the horizontal or vertical coefficients of viscosity and diffusivity vary in $z$ in such a way that the rates can be found analytically. The first flow, denoted as a ‘Holmboe flow’, has a velocity and density interface: the mean horizontal velocity and the density are both proportional to $\tanh az$, where $a$ is proportional to the inverse of the interface thickness. The second, ‘Drazin flow’, has a similar velocity variation in $z$ but uniform density gradient. The analytical results compare favourably with numerical calculations. Small horizontal coefficients of viscosity and diffusivity may affect disturbances to the flow in opposite ways. Although the effect of uniform vertical coefficients of viscosity is to decrease the growth rates, and uniform vertical coefficients of diffusivity increase them, cases are found in which, with suitably chosen $z$ dependence, vertical coefficients of viscosity (or diffusivity) may cause a previously neutral disturbance to grow (or to diminish); viscosity may destabilize a stably stratified shear flow. The introduction of viscosity and diffusivity may consequently increase the critical Richardson number to a value exceeding $1/ 4$. While some patterns of behaviour are apparent, no simple rule appears to hold about whether flows that are neutral in the absence of these effects (viscosity or diffusivity) will be stabilized or destabilized when they are added. One such rule, namely our conjecture that viscosity is always stabilizing and that diffusivity is destabilizing, is explicitly refuted.

Instability structures during periods of large Richardson number (Ri > ): Evidence of parametric instability

AbstractThe commonly used criteria for shear and convective instabilities were developed for steady horizontally uniform background flows. However, the formalism that rigorously addresses the instability of waves on a basic state modulated by a primary wave is Floquet theory in which the basic state includes a wave. A Floquet system supports parametric instabilities when conventional Richardson number (Ri) criteria indicate that the system is stable. In a study of small‐scale instability structures during the Maui MALT campaign, Hecht et al. (2005) noted that there were occurrences of ripple (instability) structure when the conventional criteria indicated stable conditions. We have followed up this work with a detailed survey of the occurrence of ripple structure over Maui during periods that were both stable and unstable according to conventional criteria. Values of Ri were calculated from lidar data. We have found frequent occurrence of ripple structure when Ri > . We have focused on a period when there are clear indications of waves and ripple structure exhibiting two‐dimensional instability structure when Ri ~ 1 or greater. These results are analyzed in terms of Floquet theory and interpreted as parametric instabilities occurring for modest primary wave amplitudes.

Secondary instability of the stably stratified Ekman layer

AbstractThe Ekman flow, an exact solution of the Boussinesq equations with rotation, is a prototype flow for both atmospheric and oceanic boundary layers. The effect of stratification on the finite-amplitude longitudinal rolls developing in the Ekman flow and their three-dimensional stability is studied by means of linearized and nonlinear numerical simulations. Similarities and differences with respect to billows developing in the Kelvin–Helmholtz (KH) unidirectional stratified shear flow are discussed. Prandtl number effects are investigated as well as the role played by the buoyant-convective instability. For low Prandtl number, the amplitude of the saturated rolls vanishes at the critical bulk Richardson number, while at high Prandtl number, finite-amplitude rolls are found. The Prandtl number also affects how the growth rate of the secondary instability evolves as the Richardson number is increased. For low Prandtl number, the growth rate decreases as the Richardson number increases while it remains significant for large Prandtl number over the range of stratification studied. This behaviour is likely a result of the differing amplitudes of the roll vortices. Furthermore, the most unstable wave vector is much lower than for the secondary instability of KH billows. Examination of the energetics of the secondary instability shows that buoyant-convective instability is present locally at high Reynolds and Prandtl numbers but plays an overall minor role despite the presence in the base flow of statically unstable regions characterized by a high Richardson number.

Observations of Barotropic Oscillations and Their Influence on Mixing in the Faroe Bank Channel Overflow Region

Abstract Observations of hydrography, currents, and microstructure are presented together with sea surface height (SSH) patterns from concurrent satellite tracks to describe the subinertial oscillations in the region downstream of the Faroe Bank Channel overflow. Energetic oscillations with a dominant 3–5-day period have previously been observed in the dense bottom layer and found to be consistent with topographic Rossby waves. Here, the authors present evidence that the oscillations extend over the whole water column and are connected to a wave-like pattern in SSH along the continental slope. The waves are observed in two satellite tracks running parallel to the slope and indicate a wavelength of 50–75 km, an amplitude of about 5 cm, and a phase speed of 15–20 cm s−1. The pattern extends at least 450 km along the slope. Repeat occupations of a section through a 4-day period show a barotropic velocity anomaly that is associated with an increase in plume transport [from 0.5 to 2.5 Sv (1 Sv ≡ 106 m3 s−1)] and interface height (from 100 to 200 m) as well as changes in dissipation rates and mixing. Estimates of entrainment velocity wE vary with a factor of 102 over the oscillation period, and there is an inverse relation between wE and plume thickness, that is, mixing is most intense when the dense bottom layer is thin. High values of wE coincide with a large percentage of critical Richardson numbers in the interfacial layer. The rotational motion, or the horizontal “stirring,” is observed to bring water from the south, traceable because of its low oxygen concentrations, into the plume.

Vortex-shedding suppression in two-dimensional mixed convective flows past circular and square cylinders

Vortex-shedding suppression in two-dimensional mixed convective flows past circular and square cylinders is investigated numerically at two supercritical Reynolds numbers, Re = 60 and 100, at a fixed Prandtl (Pr) number of 0.71. The Richardson number (Ri) and free-stream orientation (α) are varied in the range [0, 1.6] and [0, π/2], respectively. The investigations involve the numerical solutions of mass, momentum, and energy equations subject to Boussinesq approximation in generalized curvilinear body-fitted coordinates. The critical Richardson numbers corresponding to the onset of suppression of vortex-shedding are determined for different free-stream orientations using the numerical data and the Stuart-Landau theory. For the case of circular cylinder, the critical Richardson number exhibits a “cosine-law” with respect to the free-stream orientation, while a non-monotonic trend is observed for the case of the square cylinder. By examining the near critical steady flow field data, two distinct components of the baroclinic vorticity generation rate are identified that appear to control the shedding suppression laws (relationships between the critical Richardson number and free-stream orientation) in theRi-α parametric space for the circular and the square cylinders. Supported by numerical experiments, the plausible roles of these baroclinic vorticity generation rate components are identified and utilized to theoretically deduce the functional forms of the shedding suppression laws that agree with the laws observed in the numerical experiments.

An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows

AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

Improving Stable Boundary-Layer Height Estimation Using a Stability-Dependent Critical Bulk Richardson Number

For many decades, attempts have been made to find the universal value of the critical bulk Richardson number (\(Ri_{Bc}\); defined over the entire stable boundary layer). By analyzing an extensive large-eddy simulation database and various published wind-tunnel data, we show that \(Ri_{Bc}\) is not a constant, rather it strongly depends on bulk atmospheric stability. A (qualitatively) similar dependency, based on the well-known resistance laws, was reported by Melgarejo and Deardorff (J Atmos Sci 31:1324–1333, 1974) about forty years ago. To the best of our knowledge, this result has largely been ignored. Based on data analysis, we find that the stability-dependent \(Ri_{Bc}\) estimates boundary-layer height more accurately than the conventional constant \(Ri_{Bc}\) approach. Furthermore, our results indicate that the common practice of setting \(Ri_{Bc}\) as a constant in numerical modelling studies implicitly constrains the bulk stability of the simulated boundary layer. The proposed stability-dependent \(Ri_{Bc}\) does not suffer from such an inappropriate constraint.

A mesoscale simulation of coastal circulation in the Guadalquivir valley (southwestern Iberian Peninsula) using the WRF-ARW model

Located in the southwest of the Iberian Peninsula, the Guadalquivir valley is a site of frequent problems related to air pollution. The atmospheric dynamics of this region is poorly characterised but is fundamental to understanding the chemical and photochemical processes that contribute to the pollution problems. In this work, the atmospheric mesoscale Weather Research and Forecasting (WRF-ARW) model was used to study the horizontal and vertical development of the two sea–land breeze patterns (pure and non-pure) that are identified in the coastal area as being responsible for many of the air pollution events. In addition, data from five meteorological stations within the valley were used to validate and compare the model results.The FNL archives were used to define the initial and boundary conditions of the model. Four domains with a grid resolution of 81, 27, 9 and 3km and 40 sigma pressure levels in each domain were defined. The Medium Range and Forecast (MRF) parameterisation scheme was used with new values for both the bulk critical Richardson number and the coefficient of proportionality. This new configuration was obtained from the sensitivity exercises.Several periods were modelled for both breeze patterns, focusing on the wind, the potential temperatures and the specific humidity fields. For the pure breeze, the horizontal movement along the valley was conditioned by the arrival of a Mediterranean flow in the Guadalquivir valley that limits the horizontal extension of the breeze to 20–40km inland. In contrast, the non-pure pattern was only identified in the coastal area; although motivated by the entrance of southwestern flows, a marine air mass transport along the valley was detected and reached inland areas located approximately 200km from the coast line.In both cases, the model results indicated the formation of a thermal internal boundary layer with a vertical development of less than 500m for the pure sea breeze while for the non-pure breeze can reach a vertical extension of 1km. In the case of the non-pure pattern, the model forecast for the Atmospheric Boundary Layer (ABL) height distribution along the valley revealed a homogeneous pattern related to the entrance of the southwestern flows, in contrast with the clear division of the valley observed for the pure pattern motivated by the arrival of Mediterranean flows.

Mixed convection from a heated sphere in power-law fluids

In this work, the steady, laminar, mixed convection heat transfer from a heated sphere immersed in power-law fluids has been investigated in the so-called aiding-buoyancy configuration. The momentum and thermal energy equations have been solved numerically over the following ranges of conditions: Richardson number, 0≤Ri≤2, power-law index, 0.2≤n≤2, sphere Reynolds number, 1≤Re≤100 and the generalized Prandtl number, 1≤Pr≤100. The detailed kinematics of the flow and temperature fields are visualized in terms of the streamline (stream trace) and isotherm contours in the close proximity of the heated sphere. Further insights are provided in terms of the distribution of pressure coefficient and local Nusselt number along the surface of the heated sphere over wide ranges of conditions from weak to strong free convection flow. Finally, the overall macroscopic characteristics are reported in terms of the individual and total drag coefficients and the surface average Nusselt number as functions of the pertinent dimensionless parameters. The drag coefficient is seen to increase monotonically with the Richardson and Prandtl numbers at low Reynolds numbers and the type of dependence changes at a critical Richardson number. Similarly, the average Nusselt number shows a positive dependence on the Reynolds number, Prandtl number and Richardson number. Broadly, shear-thinning viscosity (n<1) promotes heat transfer over and above that in Newtonian fluids otherwise under identical conditions and, as expected, shear-thickening behaviour (n>1) somewhat impedes it. Finally, the present numerical results have been correlated in terms of the modified Reynolds and Prandtl numbers thereby enabling interpolation of the present results for the intermediate values of the governing parameters.

The Performance of Different Boundary-Layer Parameterisations in Meteorological Modelling in a Southwestern Coastal Area of the Iberian Peninsula

The performance of four atmospheric boundary layer (ABL) schemes in reproducing the diurnal cycles of surface meteorological parameters as well as the ABL structure and depth over a coastal area of southwestern Iberia was assessed using the mesoscale meteorological Weather Research and Forecasting (WRF) model. The standard configuration of the medium-range forecast (MRF) and the Yonsei University (YSU) ABL schemes were employed. Modified versions of each, in which the values of the bulk critical Richardson number () and the coefficient of proportionality () were varied, were also used. The results were compared to meteorological measurements representative of SW-NW and NE synoptic flows. The WRF model in its basic configuration was found to yield satisfactory forecasting results for nearly all near-surface atmospheric variables. Modifications in and did not influence the simulation of surface meteorological parameters. Both parameterisations appeared to be optimal predictors of ABL structure, and all four ABL schemes tended to produce a cold ABL during both periods, although this ABL was drier in the SW-NW flow season and wetter in the NE flow season. Considering all the parameters analysed, the MRF ABL parameterisation with the lowest values of and coefficients tested (0.25 and 0.0, resp.) tends to show a realistic simulation.

The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both of the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a 'critical value' of about 0.20 - 0.25, the inertial subrange associated with the Richardson-Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson-Kolmogorov energy cascade weakens; therefore, the applicability of local Monin-Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri_cr and Rf < Rf_cr. However, it is found that Rf_cr = 0.20 - 0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin-Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson-Kolmogorov cascade) have been filtered out.

Effect of Thermal Buoyancy on the Two-Dimensional Upward Flow and Heat Transfer Around a Square Cylinder

The effect of aiding/opposing buoyancy on the two-dimensional upward flow and heat transfer around a heated/cooled cylinder of square cross section is studied in this work. The finite-volume-based commercial computational fluid dynamics (CFD) software FLUENT is used for the numerical simulation. The influence of aiding/opposing buoyancy is studied for Reynolds and Richardson numbers ranges of 50 to 150 and –1 to 1, respectively, and the blockage parameters of 2% and 25%. The flow exhibits unsteady periodic characteristics in the chosen range of Reynolds numbers (except for Reynolds number of 50 and blockage parameter of 25%) for the forced convective cases (Richardson number of 0). However, the vortex shedding is observed to stop completely at some critical value of Richardson number for a particular Reynolds number, below which the shedding of vortices into the stream is quite prominent. Representative streamlines and isotherm patterns for different blockage parameters are systematically presented and discussed. The critical Richardson and average Nusselt numbers are plotted against the Reynolds and Richardson numbers, respectively, to elucidate the role of thermal buoyancy on flow and heat transfer characteristics. It is observed that the vortex shedding frequency (Strouhal number) increases with increased heating and suddenly reduces to zero at the critical Richardson number. The critical Richardson number is again found to increase with Reynolds number for a particular blockage ratio, and the higher the blockage ratio, the less is the critical Richardson number. The results obtained from the commercial solver are extensively validated with the available numerical results in the literature and an excellent agreement is observed.

Preface for the special issue on computational heat transfer

The special issue reports the current advancements in the field of computational heat transfer. The area has witnessed rapid strides in the last four decades and the world has seen an explosive growth in the number, range of applicability and robustness of newer computational tools and their increasing application to problems of practical importance in thermal sciences. This issue carries articles that propose better than the state-of-the-art techniques for solving fluid flow and heat transfer problems, those that consider novel variants to existing techniques and demonstrate their use in engineering problems and also those that have employed well known techniques to very complex problems in fields ranging from chemical engineering to nuclear thermal hydraulics. The first paper in the issue by Yadav et al. reports the results of steady state simulations of a three dimensional model of a super critical CO2 based natural convection loop with end heat exchangers. The study shows that even for a small temperature difference of 18 K, buoyancy is powerful enough to result in high heat transfer rates. Nandakumar et al. in their paper studied the thermal hydraulics of sodium heated once through steam generator of a nuclear reactor by three dimensional simulations and used these results in a one dimensional analysis. The results from the study provide an estimate of a key engineering quantity, namely differential thermal expansion of shells and tubes in the steam generator. Amit Kumar and Malhotra formulated a two dimensional numerical model of downward flame over a thin solid fuel and solved it to study the effect of a gas phase heat sink (a wire mesh) on the flame spread and flame extinction. The numerical results were validated with experiments and both of them showed that the wire mesh was effective in reducing the flame spread when placed at a distance of 5 mm. Sengupta et al. carried out a three dimensional conjugate heat transfer analysis of the BeO reflector assemblies of a 2 W upgraded Apsara nuclear reactor. The key challenge here is the accomplishment of heat transfer purely by natural convection and the results indicate that the maximum air gap between the aluminium side and BeO blocks should not be more than 0.3 mm to keep the temperatures within safe limits. Biswas et al. considered a new sub-grid model pertaining to large eddy simulation (LES) methodology, namely shear improved Smagorinsky model that can take into account the mean shear arising out of the anisotropy of the flow. The model was tested for the lid driven cavity flow and the predictions were seen to agree well with the experiments as well as the LES model. Kalyana Raman et al. employed the immersed boundary method (IBM) under mixed convection at Re = 100 for an elliptic cylinder. The advantage of the IBM was the use of a simple Cartesian grid in the simulations. The critical Richardson number at which shedding gets suppressed was determined for different aspect ratios of the elliptic cylinder. Phongthanapanich and Dechaumpai proposed a new second order accurate characteristic based finite volume element method for analyzing time-dependent scalar convection–diffusionreaction equation in two dimensions. The method combined the finite volume and the finite element methods. It was seen that the method reduces spurious oscillations and does not require an artificial diffusion to improve the solution stability. Song and Tafti evaluated the use of a wall model for the LES of a rotating ribbed duct and compared the C. Balaji (&) Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India e-mail: balaji@iitm.ac.in