Buoyancy Term Research Articles

Surface Layer Turbulent Characteristics over the Complex Terrain of the Loess Plateau Semiarid Region

Surface layer turbulence has an important influence on land-air interactions and pollutant dispersion, and studying the characteristics of surface layer turbulence in complex terrain can contribute to understanding land-air interactions, improving model surface layer parameterization, and enhancing pollution prediction capabilities. The surface layer turbulence observations from the Semi-Arid Climate and Environment Observatory (SACOL) of Lanzhou University in 2008 were processed in this study. High-quality turbulence parameters were calculated, the statistical and transfer characteristics of turbulence were analyzed, and the formation of turbulence was assessed in terms of dynamics and thermodynamics. The atmospheric stability in the semiarid region of the Loess Plateau is basically dominated by neutral/near-neutral and weakly unstable/weakly stable conditions; this pattern is significantly different from the preponderance of unstable and stable layers at other sites. The turbulence intensity differs significantly in both the horizontal and vertical directions and basically shows the relationship I u ≈ I v > I w . The mean values of I u and I v are 0.42 and 0.40, respectively, and the mean value of I w is 0.14, which is different from the general pattern of I u > I v > I w , indicating that the turbulence intensity at SACOL is characterized by a large lateral wind contribution. The dimensionless standard deviations of the nonneutral wind velocity components satisfy the “1/3rd law,” and the dimensionless standard deviations of u, v , and w components are 3.35, 2.98, and 1.26, respectively, in the semiarid Loess Plateau. These values are larger than those over flat terrain. The contribution of the shear term to the formation of turbulence is greater than that of the buoyancy term, and the mean annual values of the shear term and the buoyancy in the kinetic energy budget equation in SACOL are 47.94 × 10−4 m2·s−3 and 11.32 × 10−4 m2·s−3, respectively. The annual mean values of the momentum transfer coefficient C D and the heat transfer coefficient C H under near-neutral conditions are 8.54 × 10−3 and 2.52 × 10−3, respectively.

Study on the characteristics of the pressure fluctuations and their contribution to turbulence kinetic energy

In this study, the integral and microscopic turbulent statistical characteristics of pressure fluctuations, applicability of the pressure gradient and pressure flux divergence to the Monin-Obukhov similarity theory (MOST), and contribution of the pressure transport term to turbulence kinetic energy (TKE) were analyzed using the turbulence observational data obtained from a field observational station over the Horqin Sandy Land in Inner Mongolia, China. The normalized standard deviations of the pressure fluctuations have no obvious relationship with the dimensionless stability parameter (z/L). The turbulent variance spectra of pressure fluctuations Sp(n) follow the n−2 scaling law with a peak frequency of approximately one to two orders of magnitude lower than that of the wind speed and temperature. The spectral gap also shifts to lower frequencies, and the transition from turbulent scale to the larger scale is sharper. The normalized vertical pressure gradient (κzp∗∂p¯∂z) has no significant relationship with z/L. The non-dimensional pressure transport term (φp=κzρ¯u∗3∂w'p'¯∂z) represents the pressure flux divergence and is well related to the z/L with expressions of φp = ± (1 − 14.5z/L) for unstable stratifications and φp = ± (1 + 15.0z/L) for stable stratifications. The relative importance of pressure transport term in the TKE budget equation with respect to the shear production and buoyancy terms is larger at larger scales. The pressure transport term is averagely one order of magnitude larger than the sum of these two terms at scales above 5 min. The contribution of the pressure transport term to the TKE is non-negligible.

Impacts of Varying Concentrations of Cloud Condensation Nuclei on Deep Convective Cloud Updrafts—A Multimodel Assessment

AbstractThis study presents results from a model intercomparison project, focusing on the range of responses in deep convective cloud updrafts to varying cloud condensation nuclei (CCN) concentrations among seven state-of-the-art cloud-resolving models. Simulations of scattered convective clouds near Houston, Texas, are conducted, after being initialized with both relatively low and high CCN concentrations. Deep convective updrafts are identified, and trends in the updraft intensity and frequency are assessed. The factors contributing to the vertical velocity tendencies are examined to identify the physical processes associated with the CCN-induced updraft changes. The models show several consistent trends. In general, the changes between the High-CCN and Low-CCN simulations in updraft magnitudes throughout the depth of the troposphere are within 15% for all of the models. All models produce stronger (~+5%–15%) mean updrafts from ~4–7 km above ground level (AGL) in the High-CCN simulations, followed by a waning response up to ~8 km AGL in most of the models. Thermal buoyancy was more sensitive than condensate loading to varying CCN concentrations in most of the models and more impactful in the mean updraft responses. However, there are also differences between the models. The change in the amount of deep convective updrafts varies significantly. Furthermore, approximately half the models demonstrate neutral-to-weaker (~−5% to 0%) updrafts above ~8 km AGL, while the other models show stronger (~+10%) updrafts in the High-CCN simulations. The combination of the CCN-induced impacts on the buoyancy and vertical perturbation pressure gradient terms better explains these middle- and upper-tropospheric updraft trends than the buoyancy terms alone.

Seasonal characteristics of boundary layer over a high-altitude rural site in Western India: implications on dispersal of particulate matter.

The temporal variability of the planetary boundary layer height (PBLH) over Mahabaleshwar was studied for a period of 1 year from 1 December 2015 to 30 November 2016 using microwave radiometer (MWR) observations. The PBLH over Mahabaleshwar was found to be the highest during the pre-monsoon (March-May) season and lowest during the winter (December-February) season. The seasonal mean of PBLH was estimated to be 339±88 m during winter, 485±70 m during pre-monsoon, 99±153 m during monsoon, and 438±24 m during post-monsoon season. Frequency distribution analysis of PBLH during pre-monsoon season revealed that the formation of turbulence internal boundary layer (TIBL) is evident. In contrast, cold and moist air mass during the monsoon season enhances the wind shear with lower buoyancy term which results in lowering of PBLH. The comparison of PBLH between MWR and radiosonde observations shows a good correlation (r2 = 0.66, p=0.001). The growth rate was observed to be 388 m/h during pre-monsoon, 206 m/h during winter, 57 m/h during monsoon, and 167 m/h during post-monsoon season. The seasonal mean concentration of PM2.5 was found to be 42.3±4.6 μg/m3during winter, 33.4±8.7 μg/m3 during pre-monsoon, 6.6±2.2 μg/m3 during monsoon, and 26.1±1.7 μg/m3during post-monsoon season. The effect of higher loading of scattering-type aerosol (dust particle) was also investigated as a case study. The analysis reveals the inverse relationship between the PBL height variability and the particulate loading indicating the importance of aerosol direct effect. Analysis of the ventilation coefficient (Vc) revealed that the dissipation potential was higher (1736 m2/s) during pre-monsoon season as compared to (1191 m2/s, 455m2/s, and 1580 m2/s) winter, monsoon, and post-monsoon seasons.

In-depth analysis of mixing characteristics of stratified gases during spray operation in the TOSQAN Test 113 using OpenFOAM

During the severe accident of a nuclear power plant, the hydrogen is generated by the reactor core oxidation which may be stratified or distributed in the containment building. There are risks such as hydrogen explosion at a certain concentration of hydrogen, and therefore a detailed analysis is needed to assess the hydrogen risk. Meanwhile, the spray system operates as part of a severe accident strategy, and the dynamic effects of spray, in particular, are expected to have a significant impact on the gas entrainment and global mixing. Some parameters such as a buoyancy term in a turbulence model and particle diameter affecting the global behavior, have been reported in the previous researches. However, the detailed mechanisms of the dynamic aspect of spray were not described. Thus, the present study aims to perform an in-depth analysis of the effect of the buoyancy term in a turbulence model and the droplet size on the mixing characteristics (mixing tendency and mixing time) in TOSQAN 113 test.

Rayleigh–Taylor instability with gravity reversal

We present results from Direct Numerical Simulations (DNS) of Rayleigh–Taylor instability at Atwood numbers up to 0.9. After the layer width had developed substantially, additional branched simulations have been run under reversed and zero gravity conditions. We focus on the modifications of the mixing layer structure and turbulence in response to the acceleration change. After the gravity reversal, the flow undergoes a complex transient process in which the vertical mass flux changes sign multiple times and, consequently, the buoyancy term in the turbulent kinetic energy transport equation changes its role back and forth from production to destruction. This behavior is examined in detail using the turbulent kinetic energy and mass flux transport equations and time instances when the vertical mass at the centerline crosses zero and reaches local minima and maxima. While the transient process significantly affects the flow anisotropy at all scales, other turbulence characteristics, like the alignment between the vorticity and eigenvectors of the strain rate tensor, retain their fully developed turbulence behavior in the interior of the layer. In addition, after the gravity reversal, the edges of the layer also exhibit characteristics closer to those of the turbulent interior, even as the fluids become more mixed. None of these changes affects the mean density profile, which still collapses among various cases. Such significant changes in some turbulence quantities and not others are difficult to capture with existing turbulence models.

A thermal fluid dynamics framework applied to multi-component substrates experiencing fusion and vaporisation state transitions

The fluid dynamics of multi-component alloy systems subjected to high energy density sources of heat largely determines the local composition, microstructure, and material properties. In this work a multi-component thermal fluid dynamics framework is presented for the prediction of alloy system development due to melting, vaporisation, condensation and solidification phenomena. A volume dilation term is introduced into the continuity equation to account for the density jump between liquid and vapour species, conserving mass through vaporisation and condensation state changes. Mass diffusion, surface tension, the temperature dependence of surface tension, buoyancy terms and latent heat effects are incorporated. The framework is applied to describe binary vapour collapse into a heterogeneous binary liquid, and a high energy density power beam joining application; where a rigorous mathematical description of preferential element evaporation is presented.

Heat transfer analysis of mixed convection flow in a vertical microchannel with electrokinetic effect

In this article, the transient/steady mixed convective flow formation inside a vertical microchannel subjected to uneven wall zeta potentials in the presence of an electric body force is carried out theoretically. Employing the Navier–Stokes, Poisson–Boltzmann and energy equations, the velocity profile, electric potential and temperature distributions respectively governing flow formation and heat transfer in dimensional form are presented. Using appropriate dimensionless parameters, the corresponding dimensionless form of the governing equations are obtained. At the transient state, the Laplace transform technique is utilized while at the steady-state, direct integration as well as undetermined coefficients are employed to obtain solutions to governing equations. To justify solutions obtained, the steady state solution is found and compared with the implicit finite difference method at large time; this comparison gives an excellent agreement. Graphical simulations show that the skin-friction could have incurred an error of up to 19% if the buoyancy term in the momentum equation had been neglected. In addition, it is established that for a large electric double layer, the interval of no reverse flow at the microchannel walls is significantly extended.

Improvements of turbulence model for analysis of hydrogen stratification erosion by turbulent buoyant jet

Light gas stratification erosion by steam turbulent buoyant jet is the typical phenomenon about containment thermal hydraulics and hydrogen safety. Overprediction of stratification erosion rate has been observed in computational fluid dynamics (CFD) analysis by using current turbulence model based on simple gradient diffusion hypothesis (SGDH). To solve this problem, the effects of buoyancy term, coefficient and turbulent Schmidt number are discussed and a modified k-ε model with buoyancy term based on generalized gradient diffusion hypothesis (GGDH) which contains vertical and horizontal density gradient is developed. In modified k-ε model, besides the value of coefficient, the buoyancy term based on SGDH is modified into GGDH. The strain tensor is modified into rotating tensor to suppress the overestimated local turbulent kinetic energy generated in flow stagnation zone. Comparison between analysis results and experimental data shows that improvement effect of modified model on prediction of light gas stratification erosion rate is significant.

Buoyancy Effects in the Turbulence Kinetic Energy Budget and Reynolds Stress Budget for a Katabatic Jet over a Steep Alpine Slope

Katabatic winds are very frequent but poorly understood or simulated over steep slopes. This study focuses on a katabatic jet above a steep alpine slope. We assess the buoyancy terms in both the turbulence kinetic energy (TKE) and the Reynolds shear-stress budget equations. We specifically focus on the contribution of the slope-normal and along-slope turbulent sensible heat fluxes to these terms. Four levels of measurements below and above the maximum wind-speed height enable analysis of the buoyancy effect along the vertical profile as follow: (i) buoyancy tends to destroy TKE, as expected in stable conditions, and the turbulent momentum flux in the inner-layer region of the jet below the maximum wind-speed height $$z_j$$ ; (ii) results also suggest buoyancy contributes to the production of TKE in the outer-layer shear region of the jet (well above $$z_j$$ ) while consumption of the turbulent momentum flux is observed in the same region; (iii) In the region around the maximum wind speed where mechanical shear production is marginal, buoyancy tends to destroy TKE and our results suggest it tends to increase the momentum flux. The present study also provides an analytical condition for the limit between production and consumption of the turbulent momentum flux due to buoyancy as a function of the slope angle, similar to the condition already proposed for TKE. We reintroduce the stress Richardson number, which is the equivalent of the flux Richardson number for the Reynolds shear-stress budget. We point out that the flux Richardson number and the stress Richardson number are complementary stability parameters for characterizing the katabatic flow apart from the region around the maximum wind-speed height.

The Effect of Gravity Modulation on Double Diffusive Convection in the Presence of Applied Magnetic Field and Internal Heat Source

We have investigated the study of double diffusive stationary convection in the presence of applied magnetic field and internal heating. A weakly nonlinear stability analysis has been performed using the finite amplitude Ginzburg-Landau model. This finite amplitude of convection is obtained at third order of the system. It is assumed that the buoyancy term has two parts, steady and oscillatory parts. The second part is varying sinusoidally with time and vibrates the system with finite amplitude δ1 and frequency ω. The effects of δ1 and on heat/mass transports have been analysed and depicted graphically. The studies are established that the heat/mass transports can be controlled effectively by gravity modulation. Further, it is found that internal Rayleigh number Ri is to enhance heat transfer and reduces the mass transfer in the system.

CFD Modelling of Particle-Driven Gravity Currents in Reservoirs

Reservoir sedimentation results in ongoing loss of storage capacity all around the world. Thus, effective sediment management in reservoirs is becoming an increasingly important task requiring detailed process understanding. Computational fluid dynamics modelling can provide an efficient means to study relevant processes. An existing in-house hydrodynamic code has been extended to model particle-driven gravity currents. This has been realised through a buoyancy term which was added as a source term to the momentum equation. The model was successfully verified and validated using literature data of lock exchange experiments. In addition, the capability of the model to optimize venting of turbidity currents as an efficient sediment management strategy for reservoirs was tested. The results show that the concentration field during venting agrees well with observations from laboratory experiments documented in literature. The relevance of particle-driven gravity currents for the flow field in reservoirs is shown by comparing results of simulations with and without buoyant forces included into the model. The accuracy of the model in the area of the bottom outlet can possibly be improved through the implementation of a non-upwind scheme for the advection of velocity.

Computational Analysis of Natural Convection Heat Transfer on a Vertical Plate With Discrete Heat Sources

In the present study, buoyancy driven free convection flow along the vertical plate with discrete heat sources is analyzed. To illustrate free convection heat transfer along a vertical plate with finite discrete heat sources a 2-D steady-state model is considered. The thermos-physical properties of fluid are assumed constant except for the buoyancy terms, which are computed using the Boussinesq approximation of Navier-stokes equation. The two-dimensional Navier-stokes equations are solved using SIMPLER algorithm. The dimensionless equations are descretised and solved by using central difference finite difference approach. The development of the air flow caused by buoyancy induced free convective heat transfer has been studied through the progression of velocity and temperature fields. The results are obtained for various Grashof numbers Gr=103 , 104 and 5x 104 , and the influence of Grashof number on flow field has been studied. Average Nusselt number at the plate is also obtained. The effect of variation of Prandtl number at a given Grashof number is also studied.

Mixed convection in gravity-driven thin nano-liquid film flow with homogeneous–heterogeneous reactions

A modified nanofluid model for homogeneous–heterogeneous reactions in a gravity-driven liquid film is proposed based on the assumptions of the homogeneous reaction governed by isothermal cubic autocatalytic kinetics and the heterogeneous reaction given by first-order kinetics. The Buongiorno model is introduced to describe behaviors of nanofluids with the Boussinesq approximation being used for simplification of the buoyancy term. Multiple solutions are captured, whose stabilities are checked and discussed based on the theory of Sturm–Liouville. The influence of various physical parameters on important physical quantities is presented for different cases, including buoyancy assisting, no buoyancy, and buoyancy opposing. Different from previous studies on chemical reactions in which reactants are presumed in nanometer scale, we assume that the chemical species are of regular size, which react with each other in a nanofluid. This configuration makes our model physically more realistic than previous ones.

Non-Newtonian fluid flow around a Y-shaped fin embedded in a square cavity

This study investigates the free convection of Casson fluid inside a square cavity with intruded Y-shaped fin at the bottom surface. The Casson fluid is a non-Newtonian fluid and has an infinite viscosity at zero rates of shear. This is the first time that this fluid is used in the square cavity containing Y-shaped fin at the bottom surface. The Y-shaped fin helps in understanding the constructal theory and enhancing the heat transfer rate from the fin. The main objective of using this fin is to increase the convective heat transfer surface area. The sidewalls of the cavity are kept at cold temperature, the bottom surface at a hot temperature, and the top surface as adiabatic. The tips of the Y-shaped fin are considered as hot, cold, and adiabatic. The effects of the magnetic field and radiation are included in the momentum and energy equations. The influence of viscous heating is neglected. The buoyancy term is included in the momentum equation using Boussinesq approximation. The dimensionless governing equations are solved numerically using a Galerkin weighted residual technique of the finite element method. The effects of Rayleigh number (Ra = 104–106), radiation parameter (Rd = 0–103), Hartmann number (Ha = 0–103), and Casson parameter (γ = 0.1–1) on streamlines, isotherms, dimensionless velocity components, temperature, and local Nusselt numbers along the fin and the bottom heated wall are investigated and presented graphically. It is demonstrated that, in the presence of Y-shaped fin, all the pertinent parameters and dimensionless numbers help in enhancing the heat transfer rate along the bottom surface.

A Lorenz Model for Almost Compressible Fluids

Starting from the almost compressible 2-D Oberbeck–Boussi nesq system, characterized by an extra buoyancy term which is pressure-dependent, we write the corresponding Lorenz system and observe a larger instability with respect to the classical model in which the buoyancy is proportional to the temperature deviation only.

A comparison of entrainment in turbulent line plumes adjacent to and distant from a vertical wall

We present simultaneous two-dimensional measurements of the velocity and buoyancy fields on a central vertical plane in two-dimensional line plumes: a free plume distant from vertical boundaries and a wall plume, adjacent to a vertical wall. Data are presented in both an Eulerian and a plume coordinate system that follow the instantaneous turbulent/non-turbulent interface (TNTI) of the plume. We present measurements in both coordinate systems and compare the entrainment in the two flows. We find that the value of the entrainment coefficient in the wall plume is greater than half that of the free plume. The reduction in entrainment is investigated by considering a decomposition of the entrainment coefficient based on the mean kinetic energy where the relative contributions of turbulent production, buoyancy and viscous terms are calculated. The reduced entrainment is also investigated by considering the statistics of the TNTI and the conditional vertical transport of the ambient and engulfed fluid. We show that the wall shear stress is non-negligible and that the free plume exhibits significant meandering. The effect of the meandering on the entrainment process is quantified in terms of the stretching of the TNTI where it is shown that the length of the TNTI is greater in the free plume and, further, the relative vertical transport of the engulfed ambient fluid is observed to be 15 % greater in the free plume. Finally, the turbulent velocity and buoyancy fluctuations, Reynolds stresses and the turbulent buoyancy fluxes are presented in both coordinate systems.

Existence and nonlinear stability of convective solutions for almost compressible fluids in Bénard problem

We study the nonlinear almost compressible 2D Oberbeck-Boussinesq system, characterized by an extra buoyancy term where the density depends on the pressure, and a corresponding dimensionless parameter β, proportional to the (positive) compressibility factor β0. The local in time existence of the perturbation to the conductive solution is proved for any “size” of the initial data. However, unlike the classical problem where β0 = 0, a smallness condition on the initial data is needed for global in time existence, along with smallness of the Rayleigh number. Removing this condition appears quite challenging, and we leave it as an open question.We study the nonlinear almost compressible 2D Oberbeck-Boussinesq system, characterized by an extra buoyancy term where the density depends on the pressure, and a corresponding dimensionless parameter β, proportional to the (positive) compressibility factor β0. The local in time existence of the perturbation to the conductive solution is proved for any “size” of the initial data. However, unlike the classical problem where β0 = 0, a smallness condition on the initial data is needed for global in time existence, along with smallness of the Rayleigh number. Removing this condition appears quite challenging, and we leave it as an open question.

Evaluation of RANS k – ε calculations for turbulent stably stratified layers based on GEMIX experiments using the CUPID code

In the present study, the prediction capability of RANS k − ε turbulence models implemented in the CUPID code which has been developed by KAERI for nuclear safety assessment was evaluated based on GEMIX (GEneric MIxing eXperiment) experiments.The present study is a part of the work participating in the International Benchmark Exercise based on the GEMIX experiment done by OECD/NEA and PSI. The GEMIX experiment performed by PSI is focused on the basic turbulent mixing mechanisms in unstratified and stably stratified conditions.For both the unstratified and stably stratified conditions considered, the RANS k − ε turbulence model calculations show reasonably good agreement with experimental data for time-averaged axial velocity. However, the turbulent kinetic energy measured in the GEMIX experiment was not well predicted by RANS k − ε model, which becomes worse in the stably stratified conditions.The influence of grid resolution and the inclusion of buoyancy terms in k − ε model were not significant. Also, the different RANS models such as SST and RST showed similar results to k − ε model, which indicates the fact that the drawbacks of k − ε model such as the isotropic feature do not play significant role of underestimation of turbulent kinetic energy in the present GEMIX benchmark problems. On the other hand, with the tuning of the model constant Cμ based on the experimental data of k and uv¯, the prediction capability of RANS turbulence models is shown to improve the estimation of the turbulent kinetic energy in stably stratified conditions, which is consistent with the turbulence modeling theory reported in the literature. The present sensitivity approach for Cμ could be elaborated by a calibration approach in order to improve the prediction capability of the current RANS k − ε calculations. As has been seen by the RANS society, such a pragmatic modeling could be a successful means.

Theory of fully developed mixed convection including flow reversal: A nonlinear Boussinesq approximation approach

AbstractIn this article, an exact solution is obtained to investigate the role of nonlinear Boussinesq approximation on mixed convection flow in a vertical channel subject to asymmetric wall heating. The nonlinear density variation with temperature (NDT) in the buoyancy term is introduced to the momentum equation and solved exactly by direct integration. During the course of graphical and numerical computations, results show that the role of NDT is to increase fluid velocity as well as skin‐friction while it reduces the rate of heat transfer. In addition, reverse flow formation at the walls is increased due to the inclusion of NDT (nonlinear Boussinesq approximation).