Richardson Number Ri Research Articles

The combined effect of coriolis and centrifugal buoyancy forces on internal cooling of turbine blades with modified ribs using Large Eddy Simulation (LES)

Cooling of turbine blades is necessary for longer durability and better thermal efficiency of the turbines. Turbine blade cooling is fulfilled by passing a coolant through the serpentine channel roughened with turbulators. In this work, the combined effect of the centrifugal buoyancy and the Coriolis force on heat transfer of a square duct roughened with ribs is studied using Large Eddy Simulation (LES). Simulations are carried for a Reynolds number based on bulk velocity of 20,000 with staggered square (SQ) rib, Backward step (BS) rib, and Forward step (FS) rib on the leading and trailing wall. The heat transfer performance of the square duct roughened with ribs is compared at rotation numbers Ro=0.35,0.67 and Richardson numbers Ri=0.0,12.0,28.0. The heat transfer augmentation for SQ-, BS-, and FS-ribs for Ro=0.67 and Ri=28 is 4.2%, 8.6% and 14.9%, respectively, higher than that without the effects of buoyancy. The friction coefficient for SQ-, BS-, and FS-ribs for Ro=0.67 and Ri=28 is 12.8%, 14.8% and 13.3% respectively higher than that without buoyancy.

On the flame width of turbulent fire whirls

Flame shape is a fundamental property of flames and is critical for scaling the flame size, heat release rate, and radiative heat flux. This paper presents a combined analytical and experimental effort to reveal the effect of imposed circulation on the flame width of turbulent fire whirls. Experiments of free buoyant flame without rotation were performed for comparison using propane burner diameters of 0.30 m and 0.40 m with heat release rates of 25–300 kW to ensure substantially turbulent flow. The turbulent fire whirl experiments used propane (0.30 m in burner diameter) and heptane (0.15–0.50 m in pool size) as fuels, and the heat release rates ranged from 25 kW to 669 kW. Results showed that the imposed circulation strongly restricts the flame pulsations in fire whirls compared to free buoyant flames with equal heat release rates. The turbulence suppression in fire whirls is quantified by the turbulent diffusivity that is expressed as a decreasing function of the Richardson number (Ri). Based on the concepts of equal axial convection and radial diffusion times and turbulence suppression, a semi-physical model of the mean flame width is derived, which couples the known heat release rate, Richardson number, turbulence viscosity parameter, and axial velocity parameters. The model predictions are in good agreement with experimental data of turbulent fire whirl and free buoyant flame. Turbulence suppression was found to play a dominant role in the radial flame contraction of a turbulent fire whirl compared to a free buoyant flame with the same fire size.

A comparative study of turbulent stratified shear layers: effect of density gradient distribution

Direct numerical simulations are performed to compare the evolution of turbulent stratified shear layers with different density gradient profiles at a high Reynolds number. The density profiles include uniform stratification, two-layer hyperbolic tangent profile and a composite of these two profiles. All profiles have the same initial bulk Richardson number (Ri_{b,0}); however, the minimum gradient Richardson number and the distribution of density gradient across the shear layer are varied among the cases. The objective of the study is to provide a comparative analysis of the evolution of the shear layers in term of shear layer growth, turbulent kinetic energy as well as the mixing efficiency and its parameterization. The evolution of the shear layers in all cases shows the development of Kelvin–Helmholtz billows, the transition to turbulence by secondary instabilities followed by the decay of turbulence. Comparison among the cases reveals that the amount of turbulent mixing varies with the density gradient distribution inside the shear layer. The minimum gradient Richardson number and the initial bulk Richardson number do not correlate well with the integrated TKE production, dissipation and buoyancy flux. The bulk mixing efficiency for fixed Ri_{b,0} is found to be highest in the case with two-layer density profile and lowest in the case with uniform stratification. However, the parameterizations of the flux coefficient based on buoyancy Reynolds number and the ratio of Ozmidov and Ellison scales show similar scaling in all cases.

Assessment of an accidental hydrogen leak from a vehicle tank in a confined space

This study aims to characterize some safety aspects by examining the geometries of the infrastructure, currently used by societies, against the accumulation of hazardous hydrogen clouds during an accidental leak in areas with limited ventilation. Using ANSYS FLUENT as a modeling tool, the influence of garage roof shape; pyramidal and domed roof compared with the basic model (flat roof), for different leak times, on dispersion and stratification of hydrogen layers, is analyzed. As a result, the domed roof promotes to have a lower hydrogen concentration and presents two remarkable peaks of the Richardson number (Ri) with the highest value more than 2 × 105, which is three times higher than the flat roof. Besides, the influence of the leak time on the dynamic of the flow, concentration, and stratification process are observed: the mole fraction of hydrogen is more than 0.25 after 1 h of leak, whereas it is lower than 0.05 after 100 s. The volume flow and therefore the flammable volume increase. This study highlights the importance of geometrical and sizing parameters on the characteristics of hydrogen leaks and subsequently gives insights to establish performance standards for the availability and reliability of safety critical systems.

Study on the combined effect of wind and buoyancy on cross-unit contamination around a high-rise residential building

• Cross-unit contamination around a high-rise building is studied by CFD method. • The risks of air contaminant under various environmental conditions are evaluated. • Temperature differences between windward/leeward surface and ambient air are studied. • Multiple cases for Richardson numbers range from 0 to 14.0 are investigated. In this paper, the characteristics of air cross-contamination around a high-rise building under the combined effect of wind and buoyancy are numerically studied. A 1:1 typical multi-unit building model is constructed and the risks of air contaminant building ingress under various environmental conditions are quantitatively evaluated. Firstly, the reentry ratios are quantified to evaluate the possible cross-unit dispersion without considering thermal effects. Then, the flow field and dispersion behavior are further analyzed considering the effect of wall surface temperature rise. The simulated concentration fields in three intervals of generally recognizes Richardson number (Ri) are investigated from the combined effect of wind and buoyancy. It is found that reentry ratios in multiple cases can reach 10.0%, which indicates that the air cross-contamination is an important route that cannot be neglected when a highly infectious airborne disease outbreak in high-densely residential environment. And the largest reentry ratio is detected when the windward surface temperature difference is 15 K above the ambient air at the wind speed of 1.0 m/s, with Ri=14. This study helps deepen our understanding of the mechanisms of cross-contamination under the influence of solar radiation, and will be useful for the prevention and control of accidental infectious diseases outbreaks.

Mixed convection in an insulated rectangular enclosure with two obstacles subject to various configurations using multi-relaxation-time lattice Boltzmann method

Mix convection heat transfer is studied in a rectangular lid-driven cavity comprising two obstacles. One of the obstacles is isothermally heated and the other is isothermally cooled. The mass flow and transfer are simulated, taking regular, incompressible, Newtonian, and viscid fluid using Numerical techniques. The fluid follows the Boussinesq approximation. The effect of pertinent parameters like Richardson number (Ri = 0.01, 0.1, 1, 5, 10, 100), Grashof number (), and Prandtl number (Pr = 0.71, 1, 7) is studied. Two aspect ratios of the lid-driven cavity are taken to study the fluid behavior. The effect of centric and eccentric locations of the heated blockages and the effect of different sizes of the obstruction on the fluid flow and thermal transportation are reported. and models of MRT-LBM are implemented for the simulation of flow and heat transfer regimes respectively. Also, Local and Average Nusselt numbers along the walls of a heated obstacle for different dimensionless parameters are calculated. The contour plots for the flow's horizontal and vertical velocity profiles are also discussed. The validation of our result is also checked by the grid independence test. The convergence of against different grid sizes shows that our code is valid.

Scaling the Mixing Efficiency of Sediment‐Stratified Turbulence

AbstractThe flux Richardson number Rf, also called the mixing efficiency of stratified turbulence, is important in determining geophysical flow phenomena such as ocean circulation and air‐sea transports. Measuring Rf in the field is usually difficult, thus parameterization of Rf based on readily observed properties is essential. Here, estimates of Rf in a strongly turbulent, sediment‐stratified estuarine flow are obtained from measurements of covariance‐derived turbulent buoyancy fluxes (B) and spectrally fitted values of the dissipation rate of turbulent kinetic energy (ε). We test scalings for Rf in terms of the buoyancy Reynolds number (Reb), the gradient Richardson number (Ri), and turbulent Froude number (Frt). Neither the Reb‐based nor the Ri‐based scheme is able to describe the observed variations in Rf, but the Frt‐based parameterization works well. These findings support further use of the Frt ‐ based parameterization in turbulent oceanic and estuarine environments.

Modeling and simulation of hybrid Casson nanofluid mixed convection in a partly heated trapezoidal enclosure

The current article aimed to model and analyze hybrid Casson nanofluid mixed convection in the partly heated enclosure using the finite element method. In this model, Al203−Cu hybrid nanofluid is considered. The computations are carried out for a variety of model parameters, including the Richardson number (between 0.1 and 100), the parameter of Casson fluid (between 0.1 and 1), and the volume fraction of hybrid nanoparticles (between 0% and 2%). The solution domain is discretized using a finite element mesh with uniform triangular elements. The unknown values of the governing equations were approximated using interpolation functions within those finite elements. It is scrutinized that, the plot of temperature contours varies when the Richardson number Ri changes. The contours of the temperature are more concentrated at the bottom wall than on the non-parallel side walls, due to the presence of hot temperature at the bottom wall of the enclosure. The inclusion of hybrid nanoparticles demonstrates that the stream function drops to some amount as the volume percentage of hybrid nanoparticles increases. Further, when the small value of Ri is considered, the heat transfer rate is found to be minimum due to lower fluid inertia and then heat transfer behaviors change rapidly by increasing Ri which is caused by the domination of fluid inertia.

Hybrid forced-buoyancy convection in a channel with a backward facing step

The present work integrates and expands the line of inquiry started in Inam and Lappa (2021), Int. J. of Heat and Mass Transfer, 173, 121267 for unsteady mixed forced-buoyancy convection in a channel with a forward facing step by addressing the mirror case where the fluid flowing in a duct undergoes a sudden expansion (i.e., a channel with a backward facing step). By alternatively setting some portions of the lower boundary of the system as isothermal (heated) or adiabatic surfaces, the interplay of forced and buoyancy convection is investigated numerically for a fixed expansion ratio (ER = 2) and a variety of conditions corresponding to extended intervals of the Rayleigh number Ra and several values of the Richardson number Ri (Ra≥O(104) and Ri≥O(1)). It is shown that the emerging dynamics involve a variety of concurrent mechanisms, which range from the standard hydrodynamic phenomena typical of isothermal fluids, to specific effects of buoyant nature (driven by the instability of thermal boundary layers and the ensuing emergence of thermal plumes in various parts of the domain). Comparison with the equivalent forward facing step configuration indicates that, besides the differences, these two systems display interesting analogies.

Mixed convection heat transfer effects in a lid driven square cavity

This investigation numerically explored the parameters of mixed convection heat transfer in a square cavity with a bottom heated wall. The upper horizontal wall of the cavity is Tc, while the heated lower wall is Th, while the surfaces of the left and right walls are adiabatic. The main approach here is to solve numerically the mass, momentum, and energy flow equation using Galerkin weighted residual finite element method. Here, the Prandtl number (Pr), Richardson number (Ri), and Reynolds number (Re) effects have been investigated. The factors mentioned above have been found to have a significant impact on the temperature and flow fields.

Fluid flow over a vertical stretching surface within a porous medium filled by a nanofluid containing gyrotactic microorganisms

In this paper, the boundary layer flow of a nanofluid containing gyrotactic microorganisms over a vertical stretching surface embedded in a porous medium. The fluid contains gyrotactic microorganisms. Nonlinear velocity stretches the surface, and the surface is isothermal. The governing boundary layer equations for steady, laminar, and two-dimensional are transformed into ordinary differential equations using a suitable similarity transformation. The fourth/fifth-order Runge–Kutta method solved the system of equations after linearization. The shooting method guesses the missing boundary conditions. Pertinent results are presented graphically and discussed quantitatively with respect to variation in the controlling parameters such as bioconvection Lewis number (Lb), Lewis number (Le), Peclet Lewis number (Pe), buoyancy ratio parameter (Nr), bioconvection Rayleigh number(Rb), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Richardson number (Ri), motile parameter (sigma), porosity parameter (user2{ }lambda), and Prandtl number (Pr) on dimensionless velocity, temperature, nanoparticle concentration, and microorganisms conservation. It is observed that increasing the porosity parameter retards the thermal boundary layer thickness which from application point of view, it is obvious that the surface cooling effect is enhanced and thus nanofluids are appropriate as heat transfer fluids. The comparison with the previous validates the applied numerical scheme.

Hydrothermal and Entropy Investigation of Nanofluid Natural Convection in a Lid-Driven Cavity Concentric with an Elliptical Cavity with a Wavy Boundary Heated from Below.

This work investigates mixed convection in a lid-driven cavity. This cavity is filled with nanofluid and subjected to a magnetic field. The concentric ovoid cavity orientation 0–90°, and undulation number (N), 1–4, are considered. The Richardson number (Ri) varies between 1 and 100. The nanofluid volume fraction () ranges between 0 and 0.08%. The effect of the parameters on flow, thermal transport, and entropy generation is illustrated by the stream function, isotherms, and isentropic contours. Heat transfer is augmented and the Nusselt number rises with higher Ri, , N, and . The simulations show that the heat transfer is responsible for entropy generation, while frictional and magnetic effects are marginal.

Magneto-bioconvection flow of hybrid nanofluid in the presence of oxytactic bacteria in a lid-driven cavity with a streamlined obstacle

This work explores the magneto-bioconvection flow of silver(Ag)‑magnesium oxide(MgO)-water hybrid nanoliquid in a porous cavity considering the effect of gyrotactic microorganisms. The novelty of this work is to examine the magnetic force on bioconvection flow in a porous cavity containing obstacle, oxytactic bacteria and occupied by a hybrid nanofluid. A streamlined square obstacle is inserted in the flow field. For the modeling of porous medium, Brinkman-Forchheimer extended Darcy's model is considered. In order to simulate the governing system of dimensionless equations, a higher Galerkin finite element method (GFEM) is implemented. The resulting discrete algebraic systems are treated using the adaptive Newton's method. The validity and reliability of designed solver is ensured by recomputing the numerical and experimental data available in the literature. The flow structure, heat and mass transport are analyzed for the controlling parameters such as Hartmann number (Ha = 0 − 100), bioconvection Rayleigh number (Rb = 10 − 100), Peclet number (Pe = 0.1 − 1), Richardson number (Ri = 0.1 − 5), Lewis number (Le = 1 − 10) and Darcy number (Da = 10−5 − 10−2). The obtained numerical approximations demonstrated that the variation of heat transfer becomes almost constant for varying the Peclet number. Whilst the Sherwood number is a decreasing function of Peclet number. The dimensions of streamlined obstacle can serve as a control parameter and it makes opposite impact on heat and mass transport.

Physical specifications of MHD mixed convective of Ostwald-de Waele nanofluids in a vented-cavity with inner elliptic cylinder

The present work investigates heat transmission and stable MHD (magneto-hydrodynamic) mixed convective flowing in a ventilated porous enclosed space with a heated elliptic inner cylinder filled with MWCNT (multi-wall carbon nanotube)/CMC (carboxymethylcellulose) nanofluid. The enclosure is surrounded by a homogeneous magnetic field. By employing Galerkin finite element method (GFEM), the governing equations are confirmed. Simulations are performed for various ranges of pertinent parameters such as power law index (between 0.8 and 1.4), Hartmann number (between 0 and 100), elliptic cylinder inclination (between 0∘ and 90∘), and Richardson number (between 0.1 and 100). The numerical findings are given in bounds of isotherms, Nusselt numbers, and streamlines, which are critical governing factors for heat convective and enclosure flow. The data demonstrate that average Nusselt numbers Nuavg increases when Richardson number Ri and porosity ratio, increases. Hartman number works with the induced Lorentz force to make fluidity dominates the lower-level fluidity in the enclosure which reflects in isothermal displays. Even if the higher power law indexing operates against the fluidity by triggering shear force, it appears to be constructive in terms of heat transmission.

Study on the dynamic characteristics of the overflow advection and diffusion of trailing suction hopper dredgers based on CFD

Trailing suction hopper dredgers (TSHDs) are the main type of ship used for dredging projects. However, the release of low concentration slurry poses challenges for the development of environmentally focused dredging engineering. Therefore, to effectively reduce the influence of the overflow released by a TSHD, a numerical simulation study based on a combination of the volume of fluid (VOF) and large eddy simulation (LES) methods is carried out to explore the overflow advection and diffusion process near the hull, and the results are agreed well with the experimental results. The results show that the overflow regimes are different under different Richardson numbers (Ri) and velocity ratios (ζ). Surface plumes that are disastrous for sea wildlife mostly occur under a high ζ or low Ri flow. In addition, the influence of the hull tail structure and the propeller produces additional energy disturbances that aggravate the turbulence in the flow field, and the addition of the release frequency causes pulsation, which could destroy the flow state of the main flow. All these factors cause more surface plumes. Furthermore, the effects of different external conditions on the overflow advection and diffusion are more obvious at low towing speeds.

Mixed bioconvection flow of Ag-MgO/water in the presence of oxytactic bacteria and inclined periodic magnetic field

In this paper, a numerical investigation on mixed bioconvection flow of silver(Ag)-magnesium oxide(MgO)-water hybrid nanofluid in a trapezoidal porous cavity under the effect of inclined periodic magnetic field is carried out. Brinkman–Forchheimer-extended Darcy model for the porous medium is adopted. Galerkin weighted residual finite element method is implemented to simulate the governing steady dimensionless equations. The resulting discrete nonlinear algebraic systems are treated using the adaptive Newton's method. The fluid flow, heat and mass transfer behavior are examined in variation of parameters as Hartmann number (Ha=0−100), angle of periodic magnetic field (θ=0∘−90∘), period of periodic magnetic field (Λ=0.1−1), bioconvection Rayleigh number (Rb=10−100), Richardson number (Ri=0.1−5), Lewis number (Le=1−10) and Peclet number (Pe=0.1−1). The rise in Hartmann number has a weakening effect on both transfer of heat and mass. When θ=0∘, convective heat and mass transfer is the smallest at Λ=1 where the most reduction in the average Nusselt and Sherwood numbers is 9.14% and 6.98% as Λ is raised from 0.1 to 1, respectively, and occurs at Ha=100. The significant decrement in the average Nusselt number is 42.57% at Ha=75 and in the Sherwood number is 10.4% at Ha=50 when θ is changed from 0∘ to 90∘.

MHD quadratic mixed convective Eyring-Powell nanofluid flow with multiple diffusions

In many industrial processes such as metal extrusion, paper manufacture, glass fibre production, metal and polymer extrusion, the process design engineers are concerned with efficient heat and mass transfer near the bounding surfaces of the fluid machineries. The applied magnetic field and nanoparticle additives in the fluid are often employed as control mechanisms for efficient heat and mass transport in the presence of multiple diffusive species. Further, the rheological behaviour of the industrial fluids is non-Newtonian behaviour. In this paper, the main objective is to investigate the magnetohydrodynamic triple diffusive quadratic combined convective Eyring-Powell nanoliquid flow over a moving vertical plate in the presence of diffusing liquid hydrogen and oxygen. The mathematical study of such flows is yet to be reported in the open literature. The present mathematical analysis reveals the fluid flow characteristics in terms of many physical parameters that could serve as process design parameters. The governing nonlinear coupled partial differential equations (NCPDEs) and boundary constraints that model the flow problem are converted into dimensionless equations by utilising non-similar transformations. The quasilinearization of the resulting dimensionless governing equations, followed by their implicit finite difference approximation, leads to a block tri-diagonal system, which is solved using Varga's algorithm. The numerical results for fluid velocity, temperature, species concentration, nanoparticle volume fraction distributions, and corresponding gradients correlate with the various physical parameters graphically. The computations have been performed for several values of physical parameters: quadratic mixed convective parameterγ(0≤γ≤1), thermophoresis parameterNt(0≤Nt≤1), Magnetic field parameter M(0≤M≤1), Eckert number Ec(−0.1≤Ec≤0.1), Lewis number Le(2≤Le≤10), Richardson number Ri(−1≤Ri≤10), Brownian diffusion parameterNb(0≤Nb≤1), Eyring-Powell fluid material parameters α*(0≤α*≤2) and β*(0≤β*≤2). The analysis of the numerical results has shown that the enhancing values of quadratic combine convection parameter enhance the magnitude of surface drag coefficient and heat transport rate. At the same time, it decreases for the Eyring-Powell fluid characteristics compared to that for a Newtonian liquid. Finally, the computed values of the heat transport coefficient in the present study are consistent with the previously published results in the literature.

Numerical study of mixed convection and entropy generation of Water-Ag nanofluid filled semi-elliptic lid-driven cavity

In this study, laminar mixed convection of water/Ag nanofluid with volume fraction of nanoparticles φ = 0, 2, 4, and 6% and Grashof numbers Gr = 50,000, 150,000, 250,000 and 400,000 and Richardson numbers Ri = 0.1, 1, and 10 are simulated using finite volume method. Obtained results indicate that adding a higher volume fraction of nanoparticles at lower Richardson numbers leads to the enhancement of heat transfer and Nusselt number. Streamlines behavior in the cavity is under the influence of two main factors including lid-driven motion (which is the basic factor) and the viscosity of fluid (which transfers the fluid motion to bottom layers and affects the flow domain). Every factor stimulating the flow domain causes uniform temperature distribution in the cavity. The increase of Richardson number leads to the enhancement of lid-driven velocity, temperature penetration and a better mixture of fluid layers, and by increasing Grashof number; this issue can have a great effect on uniform temperature distribution.

Stability of an Electrically Conducting Fluid Flow between Coaxial Cylinders under Magnetic field

This research aims to investigate the vortex breakdown zone, the stability margin, and the fluid layers of the rotating flow between two vertical coaxial cylinders under the effect of thermal gradient and an axial magnetic field. The governing Navier-Stokes, temperature, and potential equations are solved using the finite-volume method. Three combinations of aspect ratios (γ) and Reynolds numbers (Re) are compared. The pumping action sets up a secondary circulation along the meridional plane of the annular gap. For certain combinations, the vortex breakdown bubble occurred near the inner wall. Bifurcation in form of multiple fluid layers becomes apparent when the temperature difference exceeds a critical value. These fluid layers play the role of thermal insulation and limit the heat transfer between the hot top and cold bottom of the coaxial cylinders. Both the vortex breakdown and fluid layers could be suppressed by the magnetic field; the increasing of Hartmann number (Ha) would reduce the number of fluid layers. Diagrams represent the effect of increasing Richardson number (Ri) on fluid layers are established. Then stability diagrams corresponding to the transition from the multiple fluid layers zone to the one fluid layer zone for increasing Prandtl number (Pr) are obtained.

Impact of green walls on ventilation and heat removal from street canyons: Coupling of thermal and aerodynamic resistance

Green walls are considered a sustainable and environmental technology for improving the local urban microclimate. The presented wind tunnel measurements reveal the coupling effect of aerodynamic and thermal resistance of green walls in flat and steep street canyons in a simplified urban neighborhood model. The building and ground surfaces are set to thermal conditions at a series of Richardson numbers (Ri) ranging from 0 to 2.07. Green walls induce flow resistance due to their high skin friction and large volume-specific surface areas, which leads to the formation of a thick boundary layer near green walls, where hot air is trapped. These boundary layers weaken the convective heat transfer from building surfaces to the canyon, leading to an air temperature reduction in the canyon. The lower temperature reduces the strength of buoyancy, which, together with the aerodynamic resistance, results in the reduction of air flow speed, turbulence kinetic energy (TKE), and air ventilation in the canyon. The reduction of air ventilation is more significant in non-isothermal conditions, particularly for the steep canyon, where the air entrainment at the roof level is reduced by 32.4% in the isothermal condition, and air removal is reduced by up to 91.5% in the non-isothermal conditions (Ri of the steep canyon, Ris = 2.07). Green walls alter the flow structures by suppressing the strength of the downward flow, canyon-wide vortical flow, and ascending buoyant flow.