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1
Tenneti, Sudheer, Mohammad Mehrabadi, and Shankar Subramaniam. "Stochastic Lagrangian model for hydrodynamic acceleration of inertial particles in gas–solid suspensions." Journal of Fluid Mechanics 788 (January 12, 2016): 695–729. http://dx.doi.org/10.1017/jfm.2015.693.
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The acceleration of an inertial particle in a gas–solid flow arises from the particle’s interaction with the gas and from interparticle interactions such as collisions. Analytical treatments to derive a particle acceleration model are difficult outside the Stokes flow regime, but for moderate Reynolds numbers (based on the mean slip velocity between gas and particles) particle-resolved direct numerical simulation (PR-DNS) is a viable tool for model development. In this study, PR-DNS of freely-evolving gas–solid suspensions are performed using the particle-resolved uncontaminated-fluid reconcilable immersed-boundary method (PUReIBM) that has been extensively validated in previous studies. Analysis of the particle velocity variance (granular temperature) equation in statistically homogeneous gas–solid flow shows that a straightforward extension of a class of mean particle acceleration models (drag laws) to their corresponding instantaneous versions, by replacing the mean particle velocity with the instantaneous particle velocity, predicts a granular temperature that decays to zero, which is at variance with the steady particle granular temperature that is obtained from PR-DNS. Fluctuations in particle velocity and particle acceleration (and their correlation) are important because the particle acceleration–velocity covariance governs the evolution of the particle velocity variance (characterized by the particle granular temperature), which plays an important role in the prediction of the core annular structure in riser flows. The acceleration–velocity covariance arising from hydrodynamic forces can be decomposed into source and dissipation terms that appear in the granular temperature evolution equation, and these have already been quantified in the Stokes flow regime using a combination of kinetic theory closure and multipole expansion simulations. From PR-DNS data we show that the fluctuations in the particle acceleration that are aligned with fluctuations in the particle velocity give rise to a source term in the granular temperature evolution equation. This approach is used to quantify the hydrodynamic source and dissipation terms of granular temperature from PR-DNS results for freely-evolving gas–solid suspensions that are performed over a wide range of solid volume fraction ($0.1\leqslant {\it\phi}\leqslant 0.4$), Reynolds number based on the slip velocity between the solid and the fluid phase ($10\leqslant \mathit{Re}_{m}\leqslant 100$) and solid-to-fluid density ratio ($100\leqslant {\it\rho}_{p}/{\it\rho}_{f}\leqslant 2000$). The straightforward extension of drag law models does not give rise to any source in the granular temperature due to hydrodynamic effects. This motivates the development of better Lagrangian particle acceleration models that can be used in Lagrangian–Eulerian formulations of gas–solid flow. It is found that a Langevin equation for the increment in the particle velocity reproduces PR-DNS results for the stationary particle velocity autocorrelation in freely-evolving suspensions. Based on the data obtained from the simulations, the functional dependence of the Langevin model coefficients on solid volume fraction, Reynolds number and solid-to-fluid density ratio is obtained. This new Lagrangian particle acceleration model reproduces the correct steady granular temperature and can also be adapted to gas–solid flow computations using Eulerian moment equations.
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KERR, ROBERT M., and JACKSON R. HERRING. "Prandtl number dependence of Nusselt number in direct numerical simulations." Journal of Fluid Mechanics 419 (September 25, 2000): 325–44. http://dx.doi.org/10.1017/s0022112000001464.
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The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 104 < Ra < 107 and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated. For Nu there are good comparisons with experimental data and scaling laws for all the cases, including Ra2/7 laws at Pr = 0.7 and Pr = 7 and at low Pr, a Ra1/4 regime. Calculations at Pr = 0.3 predict a new Nu ∼ Ra2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.
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Song, Jiajun, Panxin Li, Lu Chen, Yuhang Zhao, Fengshi Tian, and Benwen Li. "Scaling Law of Flow and Heat Transfer Characteristics in Turbulent Radiative Rayleigh-Bénard Convection of Optically Thick Media." Energies 17, no. 19 (October 8, 2024): 5009. http://dx.doi.org/10.3390/en17195009.
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Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified Nu scaling law in small Pr range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large Pr. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the Nu of radiative RB convection.
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Fu, Jianhong, Sheng Chen, and Xiaochen Zhou. "Effect of heterogeneity on interphase heat transfer for gas–solid flow: A particle-resolved direct numerical simulation." Physics of Fluids 34, no. 12 (December 2022): 123317. http://dx.doi.org/10.1063/5.0130850.
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Particle-resolved direct numerical simulation (PR-DNS) of flow past a particle cluster is conducted to analyze the influence of heterogeneous particle distribution on the gas–solid heat transfer calculation. Then, the heat transfer rates calculated using Gunn's correlation are systematically compared with the DNS results for virtual computational fluid dynamics-discrete element method (CFD-DEM) grids with different levels of heterogeneity. The results show that, for a grid located at the interface between the dense cluster region and dilute region, Gunn's correlation significantly overestimates the heat transfer rate, especially at small Reynolds numbers. This is caused by the large temperature difference between the dense and dilute regions in the heterogeneous CFD-DEM grid. The value calculated by Gunn's correlation can be up to ten times the DNS result. For a homogeneous grid inside a dense region, the conventional Nusselt correlation fails to capture the rapid increase in the fluid temperature gradient around the near-interface particles when the grid approaches the cluster–fluid interface. Furthermore, even if the size of the CFD-DEM grid is reduced to twice the particle diameter, the heterogeneous particle distribution still leads to a remarkable error in the heat transfer calculation. Finally, modifications to Gunn's correlation are proposed for three typical cross-interface cases, which can well reflect the influence of the heterogeneous distribution of particles and yield a heat transfer rate close to the PR-DNS results. The mean relative deviations of the three fitted correlations are 5.8%, 14.3%, and 22.4%, respectively.
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Cui, Haihang, Qi Chang, Jianhua Chen, and Wei Ge. "PR-DNS verification of the stability condition in the EMMS model." Chemical Engineering Journal 401 (December 2020): 125999. http://dx.doi.org/10.1016/j.cej.2020.125999.
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Luo, Heng, Fengbin Zhang, Haibo Huang, Yong Huang, Zhendong Liu, Jianxi Yan, and Chicheng Yang. "The Effect of Ellipsoidal Particle Surface Roughness on Drag and Heat Transfer Coefficients Using Particle-Resolved Direct Numerical Simulation." Processes 12, no. 11 (November 7, 2024): 2473. http://dx.doi.org/10.3390/pr12112473.
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The purpose of this study is to estimate the effect of roughness layer thickness on the heat transfer and drag coefficients of ellipsoidal particles. Using an OpenFOAM-based particle-resolved direct numerical simulation (PR-DNS) method, we calculated the drag coefficient and Nusselt number for an isolated axisymmetric nonspherical particle with a rough surface in a uniform flow. The PR-DNS results indicate that the drag coefficient varies linearly with the effective roughness Sef at different angles, which can be expressed as CD=kSef−1+CD0. The changes in k are consistent with the Happel and Brenner equation. Furthermore, the influence of roughness on the heat transfer efficiency factor can be represented by Ef=Sef−65. The models for the drag coefficient and Nusselt number are valid within the ranges 1.25≤Ar≤2.5,1≤Sef≤2, and 10≤Rep≤200, thereby extending the applicability of the equations developed for smooth particles. These newly developed correlations for the drag coefficient and Nusselt number can be utilized for non-isothermal flows of particle mixtures containing materials with various rough-surfaced ellipsoids.
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Chilamkurti, Yesaswi N., and Richard D. Gould. "CFD-DEM and PR-DNS studies of low-temperature densely packed beds." International Journal of Heat and Mass Transfer 159 (October 2020): 120056. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2020.120056.
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Wu, X., and P. A. Durbin. "Numerical Simulation of Heat Transfer in a Transitional Boundary Layer With Passing Wakes." Journal of Heat Transfer 122, no. 2 (November 29, 1999): 248–57. http://dx.doi.org/10.1115/1.521485.
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Direct numerical simulation (DNS) has been used to investigate heat transfer and provide thermal statistics in a transitional flow in which turbulent wakes traversing the inlet periodically are swept downstream across a constant-temperature flat-plate. The same heat transfer problem was also computed using unsteady Reynolds-averaged Navier-Stokes (RANS) method with the v2-f turbulence model. During transition, the instantaneous Stanton number field exhibits spotlike structure, which in turn results in a strong streamwise modulation in the phase-averaged Stanton number distribution. At molecular Prandtl number Pr=0.7, the Reynolds analogy factor decreases in the transitional region but remains nearly constant afterwards. After the completion of transition, mean and second-order temperature statistics are in good agreement with previous experimental data from slightly heated turbulent flat-plate boundary layers. Throughout the transitional and turbulent regions the turbulent Prandtl number increases sharply as the wall is asymptotically approached. DNS results at a higher wake passing frequency are also presented to illustrate the effect of freestream turbulence. Unsteady RANS predictions of the time- and phase-averaged Stanton numbers as well as the enthalpy thickness are in reasonable agreement with the DNS. [S0022-1481(00)02002-8]
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Trane, D., M. Grespan, and D. Angeli. "Comparison between DNS and RANS approaches for liquid metal flows around a square rod bundle." Journal of Physics: Conference Series 2766, no. 1 (May 1, 2024): 012009. http://dx.doi.org/10.1088/1742-6596/2766/1/012009.
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Abstract The thermal-hydraulic characteristics of liquid metal flows around rod bundles are of great interest for the research and design of fourth generation nuclear reactors. Currently, a large research effort is aimed at the development of accurate numerical models for low Prandtl number fluid flows, since the data available in the literature are quite scarce. Direct Numerical Simulation (DNS) is undoubtedly the most accurate approach, but its large requirements of computational resources and time make it less practical than other simplified methods such as the Reynolds-Average Navier Stokes (RANS) approach. The present paper provides a comparison between numerical results of a flow of liquid Lead-Bismuth Eutectic (LBE) at Pr=0.031 around four vertical cylindrical rods arranged in a square lattice, obtained by DNS and RANS. Several turbulence models are considered, including the standard k−ε, k−ω SST, and two Reynolds stress models, namely the ones by Launder, Reece and Rodi (LRR), and Speziale, Sarkar and Gatski (SSG). The accuracy of these models is assessed by comparing the mean Nusselt number, the pressure drop, and local field distributions with those obtained by DNS.
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Lakehal, D., M. Fulgosi, G. Yadigaroglu, and S. Banerjee. "Direct Numerical Simulation of Turbulent Heat Transfer Across a Mobile, Sheared Gas-Liquid Interface." Journal of Heat Transfer 125, no. 6 (November 19, 2003): 1129–39. http://dx.doi.org/10.1115/1.1621891.
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The impact of interfacial dynamics on turbulent heat transfer at a deformable, sheared gas-liquid interface is studied using Direct Numerical Simulation (DNS). The flow system comprises a gas and a liquid phase flowing in opposite directions. The governing equations for the two fluids are alternately solved in separate domains and then coupled at the interface by imposing continuity of velocity and stress. The deformations of the interface fall in the range of capillary waves of waveslope ak=0.01 (wave amplitude a times wavenumber k), and very small phase speed-to-friction velocity ratio, c/u*. The influence of low-to-moderate molecular Prandtl numbers Pr on the transport in the immediate vicinity of the interface is examined for the gas phase, and results are compared to existing wall-bounded flow data. The shear-based Reynolds number Re* is 171 and Prandtl numbers of 1, 5, and 10 were studied. The effects induced by changes in Pr in both wall-bounded flow and over a gas-liquid interface were analyzed by comparing the relevant statistical flow properties, including the budgets for the temperature variance and the turbulent heat fluxes. Overall, Pr was found to affect the results in very much the same way as in most of the available wall flow data. The intensity of the averaged normal heat flux at high Prandtl numbers is found to be slightly greater near the interface than at the wall. Similar to what is observed in wall flows, for Pr=1 the turbulent viscosity and diffusivity are found to asymptote with z+3, where z+ is the distance to the interface, and with z+n, where n>3 for Pr=5 and 10. This implies that the gas phase perceives deformable interfaces as impermeable walls for small amplitude waves with wavelengths much larger than the diffusive sublayers. Moreover, high-frequency fluctuating fields are shown to play a minor role in transferring heat across the interface, with a marked filtering effect of Pr. A new scaling law for the normalized heat transfer coefficient, K+ has been derived with the help of the DNS data. This law, which could be used in the range of Pr=1 to 10 for similar flow conditions, suggests an approximate Pr−3/5 relationship, lying between the Pr−1/2 dependence for free surfaces and the Pr−2/3 law for immobile interfaces and much higher Prandtl numbers. A close inspection of the transfer rates reveals a strong and consistent relationship between K+, the frequency of sweeps impacting the interface, the interfacial velocity streaks, and the interfacial shear stress.
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Avsarkisov, V., M. Oberlack, and S. Hoyas. "New scaling laws for turbulent Poiseuille flow with wall transpiration." Journal of Fluid Mechanics 746 (March 28, 2014): 99–122. http://dx.doi.org/10.1017/jfm.2014.98.
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AbstractA fully developed, turbulent Poiseuille flow with wall transpiration, i.e. uniform blowing and suction on the lower and upper walls correspondingly, is investigated by both direct numerical simulation (DNS) of the three-dimensional, incompressible Navier–Stokes equations and Lie symmetry analysis. The latter is used to find symmetry transformations and in turn to derive invariant solutions of the set of two- and multi-point correlation equations. We show that the transpiration velocity is a symmetry breaking which implies a logarithmic scaling law in the core of the channel. DNS validates this result of Lie symmetry analysis and hence aids establishing a new logarithmic law of deficit type. The region of validity of the new logarithmic law is very different from the usual near-wall log law and the slope constant in the core region differs from the von Kármán constant and is equal to 0.3. Further, extended forms of the linear viscous sublayer law and the near-wall log law are also derived, which, as a particular case, include these laws for the classical non-transpiring case. The viscous sublayer at the suction side has an asymptotic suction profile. The thickness of the sublayer increase at high Reynolds and transpiration numbers. For the near-wall log law we see an indication that it appears at the moderate transpiration rates ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}0.05<v_0/u_{\tau }<0.1$) and only at the blowing wall. Finally, from the DNS data we establish a relation between the friction velocity$u_{\tau }$and the transpiration$v_0$which turns out to be linear at moderate transpiration rates.
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SHISHKINA, OLGA, and ANDRÉ THESS. "Mean temperature profiles in turbulent Rayleigh–Bénard convection of water." Journal of Fluid Mechanics 633 (August 25, 2009): 449–60. http://dx.doi.org/10.1017/s0022112009990528.
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We report an investigation of temperature profiles in turbulent Rayleigh–Bénard convection of water based on direct numerical simulations (DNS) for a cylindrical cell with unit aspect ratio for the same Prandtl number Pr and similar Rayleigh numbers Ra as used in recent high-precision measurements by Funfschilling et al. (J. Fluid Mech., vol. 536, 2005, p. 145). The Nusselt numbers Nu computed for Pr = 4.38 and Ra = 108, 3 × 108, 5 × 108, 8 × 108 and 109 are found to be in excellent agreement with the experimental data corrected for finite thermal conductivity of the walls. Based on this successful validation of the numerical approach, the DNS data are used to extract vertical profiles of the mean temperature. We find that near the heating and cooling plates the non-dimensional temperature profiles Θ(y) (where y is the non-dimensional vertical coordinate), obey neither a logarithmic nor a power law. Moreover, we demonstrate that the Prandtl–Blasius boundary layer theory cannot predict the shape of the temperature profile with an error less than 7.9% within the thermal boundary layers (TBLs). We further show that the profiles can be approximated by a universal stretched exponential of the form Θ(y) ≈ 1 − exp(−y − 0.5y2) with an absolute error less than 1.1% within the TBLs and 5.5% in the whole Rayleigh cell. Finally, we provide more accurate analytical approximations of the profiles involving higher order polynomials in the approximation.
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Chadil, Mohamed-Amine, Stéphane Vincent, and Jean-Luc Estivalèzes. "Gas-Solid Heat Transfer Computation from Particle-Resolved Direct Numerical Simulations." Fluids 7, no. 1 (December 30, 2021): 15. http://dx.doi.org/10.3390/fluids7010015.
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Particle-Resolved simulations (PR-DNS) have been conducted using a second order implicit Viscous Penalty Method (VPM) to study the heat transfer between a set of particles and an incompressible carrier fluid. A Lagrange extrapolation coupled to a Taylor interpolation of a high order is utilized to the accurate estimate of heat transfer coefficients on an isolated sphere, a fixed Faced-Centered Cubic array of spheres, and a random pack of spheres. The simulated heat transfer coefficients are compared with success to various existing Nusselt laws of the literature.
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Mannix, P. M., and A. J. Mestel. "Weakly nonlinear mode interactions in spherical Rayleigh–Bénard convection." Journal of Fluid Mechanics 874 (July 9, 2019): 359–90. http://dx.doi.org/10.1017/jfm.2019.440.
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In an annular spherical domain with separation $d$, the onset of convective motion occurs at a critical Rayleigh number $Ra=Ra_{c}$. Solving the axisymmetric linear stability problem shows that degenerate points $(d=d_{c},Ra_{c})$ exist where two modes simultaneously become unstable. Considering the weakly nonlinear evolution of these two modes, it is found that spatial resonances play a crucial role in determining the preferred convection pattern for neighbouring modes $(\ell ,\ell \pm 1)$ and non-neighbouring even modes $(\ell ,\ell \pm 2)$. Deriving coupled amplitude equations relevant to all degeneracies, we outline the possible solutions and the influence of changes in $d,Ra$ and Prandtl number $Pr$. Using direct numerical simulation (DNS) to verify all results, time periodic solutions are also outlined for small $Pr$. The $2:1$ periodic signature observed to be general for oscillations in a spherical annulus is explained using the structure of the equations. The relevance of all solutions presented is determined by computing their stability with respect to non-axisymmetric perturbations at large $Pr$.
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Wang, Dong, Tai Jin, Kun Luo, Junhua Tan, and Jianren Fan. "Analysis of the particles-induced turbulence in confined gas-solid fluidized beds by PR-DNS." International Journal of Multiphase Flow 141 (August 2021): 103655. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2021.103655.
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Mehrabadi, M., J. A. K. Horwitz, S. Subramaniam, and A. Mani. "A direct comparison of particle-resolved and point-particle methods in decaying turbulence." Journal of Fluid Mechanics 850 (July 4, 2018): 336–69. http://dx.doi.org/10.1017/jfm.2018.442.
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We use particle-resolved direct numerical simulation (PR-DNS) as a model-free physics-based numerical approach to validate particle acceleration modelling in gas-solid suspensions. To isolate the effect of the particle acceleration model, we focus on point-particle direct numerical simulation (PP-DNS) of a collision-free dilute suspension with solid-phase volume fraction $\unicode[STIX]{x1D719}=0.001$ in a decaying isotropic turbulent particle-laden flow. The particle diameter $d_{p}$ in the suspension is chosen to be the same as the initial Kolmogorov length scale $\unicode[STIX]{x1D702}_{0}$ ($d_{p}/\unicode[STIX]{x1D702}_{0}=1$) in order to overlap with the regime where PP-DNS is valid. We assess the point-particle acceleration model for two different particle Stokes numbers, $St_{\unicode[STIX]{x1D702}}=1$ and 100. For the high Stokes number case, the Stokes drag model for particle acceleration under-predicts the true particle acceleration. In addition, second moment quantities which play key roles in the physical evolution of the gas–solid suspension are not correctly captured. Considering finite Reynolds number corrections to the acceleration model improves the prediction of the particle acceleration probability density function and second moment statistics of the point-particle model compared with the particle-resolved simulation. We also find that accounting for the undisturbed fluid velocity in the acceleration model can be of greater importance than using the most appropriate acceleration model for a given physical problem.
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Kravets, B., D. Schulz, R. Jasevičius, S. R. Reinecke, T. Rosemann, and H. Kruggel-Emden. "Comparison of particle-resolved DNS (PR-DNS) and non-resolved DEM/CFD simulations of flow through homogenous ensembles of fixed spherical and non‐spherical particles." Advanced Powder Technology 32, no. 4 (April 2021): 1170–95. http://dx.doi.org/10.1016/j.apt.2021.02.016.
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Panagiotou, Constantinos F., Fotos S. Stylianou, Elias Gravanis, Evangelos Akylas, and Constantine Michailides. "An Explicit Algebraic Closure for Passive Scalar-Flux: Applications in Channel Flows at a Wide Range of Reynolds Numbers." Journal of Marine Science and Engineering 8, no. 11 (November 13, 2020): 916. http://dx.doi.org/10.3390/jmse8110916.
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In this paper, we propose an algebraic model for turbulent scalar-flux vector that stems from tensor representation theory. The resulting closure contains direct dependence on mean velocity gradients and quadratic products of the Reynolds stress tensor. Model coefficients are determined from Direct Numerical Simulations (DNS) data of homogeneous shear flows subjected to arbitrary mean scalar gradient orientations, while a correction function was applied at one model coefficient based on a turbulent channel flow case. Model performance is evaluated in Poiseuille and Couette flows at several Reynolds numbers for Pr=0.7, along with a case at a higher Prandtl number (Pr=7.0) that typically occurs in water–boundary interaction applications. Overall, the proposed model provides promising results for wide near-wall interaction applications. To put the performance of the proposed model into context, we compare with Younis algebraic model, which is known to provide reasonable predictions for several engineering flows.
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Shishkina, Olga, Susanne Horn, and Sebastian Wagner. "Falkner–Skan boundary layer approximation in Rayleigh–Bénard convection." Journal of Fluid Mechanics 730 (August 1, 2013): 442–63. http://dx.doi.org/10.1017/jfm.2013.347.
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AbstractTo approximate the velocity and temperature within the boundary layers in turbulent thermal convection at moderate Rayleigh numbers, we consider the Falkner–Skan ansatz, which is a generalization of the Prandtl–Blasius one to a non-zero-pressure-gradient case. This ansatz takes into account the influence of the angle of attack $\beta $ of the large-scale circulation of a fluid inside a convection cell against the heated/cooled horizontal plate. With respect to turbulent Rayleigh–Bénard convection, we derive several theoretical estimates, among them the limiting cases of the temperature profiles for all angles $\beta $, for infinite and for infinitesimal Prandtl numbers $\mathit{Pr}$. Dependences on $\mathit{Pr}$ and $\beta $ of the ratio of the thermal to viscous boundary layers are obtained from the numerical solutions of the boundary layers equations. For particular cases of $\beta $, accurate approximations are developed as functions on $\mathit{Pr}$. The theoretical results are corroborated by our direct numerical simulations for $\mathit{Pr}= 0. 786$ (air) and $\mathit{Pr}= 4. 38$ (water). The angle of attack $\beta $ is estimated based on the information on the locations within the plane of the large-scale circulation where the time-averaged wall shear stress vanishes. For the fluids considered it is found that $\beta \approx 0. 7\mathrm{\pi} $ and the theoretical predictions based on the Falkner–Skan approximation for this $\beta $ leads to better agreement with the DNS results, compared with the Prandtl–Blasius approximation for $\beta = \mathrm{\pi} $.
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Garai, Anirban, Jan Kleissl, and Sutanu Sarkar. "Flow and heat transfer in convectively unstable turbulent channel flow with solid-wall heat conduction." Journal of Fluid Mechanics 757 (September 19, 2014): 57–81. http://dx.doi.org/10.1017/jfm.2014.479.
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AbstractMost turbulent coherent structures in a convectively unstable atmospheric boundary layer are caused by or manifested in ascending warm fluid and descending cold fluids. These structures not only cause ramps in the air temperature timeseries, but also imprint on the underlying solid surface as surface temperature fluctuations. The coupled flow and heat transport mechanism was examined through direct numerical simulation (DNS) of a channel flow allowing for realistic solid–fluid thermal coupling. The thermal activity ratio (TAR; the ratio of thermal inertias of fluid and solid), and the thickness of the solid domain were found to affect the solid–fluid interfacial temperature variations. The solid–fluid interface with large (small) thermal activity ration behaves as an isoflux (isothermal) boundary. For the range of parameters considered here (Grashof number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Gr} = 3\times 10^5\text {--} 325\times 10^5$; $\textit {TAR} = 0.01\text {--}1$; solid thickness normalized by heat penetration $\text {depth} = 0.1\text {--}10$), the solid thermal properties and thickness influence the fluid temperature only in the viscous or conduction region while the convective forcing influences the turbulent flow. Flow structures influence the interfacial temperature more effectively with increasing TAR and solid thickness compared with a constant temperature boundary condition. The change of channel flow structures with increasing convective instability is examined and the concomitant change of thermal patterns is quantified. Despite large differences in friction Reynolds and Richardson number between the DNS and atmospheric observations, similarities in the flow features were observed.
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Zhang, Hao, Bo Xiong, Xizhong An, Chunhai Ke, and Guangchao Wei. "Prediction on drag force and heat transfer of spheroids in supercritical water: A PR-DNS study." Powder Technology 342 (January 2019): 99–107. http://dx.doi.org/10.1016/j.powtec.2018.09.051.
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Zhang, Hao, Lixing Zhang, Xizhong An, and Aibing Yu. "PR-DNS on the momentum and heat transfer of a rotating ellipsoidal particle in a fluid." Powder Technology 373 (August 2020): 152–63. http://dx.doi.org/10.1016/j.powtec.2020.06.030.
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Kolla, H., E. R. Hawkes, A. R. Kerstein, N. Swaminathan, and J. H. Chen. "On velocity and reactive scalar spectra in turbulent premixed flames." Journal of Fluid Mechanics 754 (August 7, 2014): 456–87. http://dx.doi.org/10.1017/jfm.2014.392.
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AbstractKinetic energy and reactive scalar spectra in turbulent premixed flames are studied from compressible three-dimensional direct numerical simulations (DNS) of a temporally evolving rectangular slot-jet premixed flame, a statistically one-dimensional configuration. The flames correspond to a lean premixed hydrogen–air mixture at an equivalence ratio of 0.7, preheated to 700 K and at 1 atm, and three DNS are considered with a fixed jet Reynolds number of 10 000 and a jet Damköhler number varying between 0.13 and 0.54. For the study of spectra, motivated by the need to account for density change, which can be locally strong in premixed flames, a new density-weighted definition for two-point velocity/scalar correlations is proposed. The density-weighted two-point correlation tensor retains the essential properties of its constant-density (incompressible) counterpart and recovers the density-weighted Reynolds stress tensor in the limit of zero separation. The density weighting also allows the derivation of balance equations for velocity and scalar spectrum functions in the wavenumber space that illuminate physics unique to combusting flows. Pressure–dilatation correlation is a source of kinetic energy at high wavenumbers and, analogously, reaction rate–scalar fluctuation correlation is a high-wavenumber source of scalar energy. These results are verified by the spectra constructed from the DNS data. The kinetic energy spectra show a distinct inertial range with a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}-5/3$ scaling followed by a ‘diffusive–reactive’ range at higher wavenumbers. The exponential drop-off in this range shows a distinct inflection in the vicinity of the wavenumber corresponding to a laminar flame thickness, $\delta _L$, and this is attributed to the contribution from the pressure–dilatation term in the energy balance in wavenumber space. Likewise, a clear spike in spectra of major reactant species (hydrogen) arising from the reaction-rate term is observed at wavenumbers close to $\delta _L$. It appears that in the inertial range classical scaling laws for the spectra involving the Kolmogorov scale are applicable, but in the high-wavenumber range where chemical reactions have a strong signature the laminar flame thickness produces a better collapse. It is suggested that a full scaling should perhaps involve the Kolmogorov scale, laminar flame thickness, Damköhler number and Karlovitz number.
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STEVENS, RICHARD J. A. M., ROBERTO VERZICCO, and DETLEF LOHSE. "Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection." Journal of Fluid Mechanics 643 (January 15, 2010): 495–507. http://dx.doi.org/10.1017/s0022112009992461.
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Results from direct numerical simulation (DNS) for three-dimensional Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 106 to 2 × 1011. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall.
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Peeters, J. W. R. "Modelling turbulent heat transfer in rough channels using phenomenological theory." Journal of Physics: Conference Series 2116, no. 1 (November 1, 2021): 012025. http://dx.doi.org/10.1088/1742-6596/2116/1/012025.
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Abstract Rough walls are often encountered in industrial heat transfer equipment. Even though it is well known that a rough wall affects velocity fields and thermal fields differently (and therefore also skin friction factors and Stanton or Nusselt numbers), predicting the effect of rough walls on turbulent heat transfer remains difficult. A relation between the scalar spectrum and the Stanton number is derived for channels with both smooth and rough walls. It is shown that the new relation agrees reasonably well with recent DNS experiments for wall roughness sizes of k + < 150 and when Pr = 0.7 − 1.0. Under these conditions, a thermal analogue of Moody’s diagram can be created using the newly developed relation.
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Miao, Haishan, Hao Zhang, Yuhang Wu, Yang Wang, and Xizhong An. "PR-DNS investigation on momentum and heat transfer of two interactive non-spherical particles in a fluid." Powder Technology 427 (September 2023): 118791. http://dx.doi.org/10.1016/j.powtec.2023.118791.
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Wan, Zhen-Hua, Ping Wei, Roberto Verzicco, Detlef Lohse, Guenter Ahlers, and Richard J. A. M. Stevens. "Effect of sidewall on heat transfer and flow structure in Rayleigh–Bénard convection." Journal of Fluid Mechanics 881 (October 24, 2019): 218–43. http://dx.doi.org/10.1017/jfm.2019.770.
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In Rayleigh–Bénard convection experiments, the thermal coupling between the sidewall and fluid is unavoidable. As a result, the thermal properties of the sidewall can influence the flow structure that develops. To get a better understanding of the influence of the sidewall, we performed a one-to-one comparison between experiments and direct numerical simulations (DNS) in aspect ratio (diameter over height) $\unicode[STIX]{x1D6E4}=1.00$ samples. We focus on the global heat transport, i.e. the Nusselt number $Nu$, and the local vertical temperature gradients near the horizontal mid-plane on the cylinder axis and close to the sidewall. The data cover the range $10^{5}\lesssim Ra\lesssim 10^{10}$ where $Ra$ is the Rayleigh number. The $Nu$ number obtained from experimental measurements and DNS, in which we use an adiabatic sidewall, agree well. The experiments are performed with several gases, which have widely varying thermal conductivities, but all have a Prandtl number $Pr\approx 0.7$. For $Ra\gtrsim 10^{7}$, both experiments and DNS reveal a stabilizing (positive) temperature gradient at the cylinder axis. This phenomenon was known for high $Pr$, but had not been observed for small $Pr\approx 0.7$ before. The experiments reveal that the temperature gradient decreases with decreasing $Ra$ and eventually becomes destabilizing (negative). The decrease appears at a higher $Ra$ when the sidewall admittance, which measures how easily the heat transfers from the fluid to the wall, is smaller. However, the simulations with an adiabatic sidewall do not reproduce the destabilizing temperature gradient at the cylinder axis in the low $Ra$ number regime. Instead, these simulations show that the temperature gradient increases with decreasing $Ra$. We find that the simulations can reproduce the experimental findings on the temperature gradient at the cylinder axis qualitatively when we consider the physical properties of the sidewall and the thermal shields. However, the temperature gradients obtained from experiments and simulations do not agree quantitatively. The reason is that it is incredibly complicated to reproduce all experimental details accurately due to which it is impossible to reproduce all experimental measurement details. The simulations show, in agreement with the models of Ahlers (Phys. Rev. E, vol. 63 (1), 2000, 015303) and Roche et al. (Eur. Phys. J. B, vol. 24 (3), 2001, pp. 405–408), that the sidewall can act as an extra heat conductor, which absorbs heat from the fluid near the bottom plate and releases it into the fluid near the top plate. The importance of this effect decreases with increasing $Ra$. A crucial finding of the simulations is that the thermal coupling between the sidewall and fluid can strongly influence the flow structure, which can result in significant changes in heat transport. Since this effect goes beyond a simple short circuit of the heat transfer through the sidewall, it is impossible to correct experimental measurements for this effect. Therefore, careful design of experimental set-ups is required to minimize the thermal interaction between the fluid and sidewall.
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Salehipour, H., W. R. Peltier, and A. Mashayek. "Turbulent diapycnal mixing in stratified shear flows: the influence of Prandtl number on mixing efficiency and transition at high Reynolds number." Journal of Fluid Mechanics 773 (May 20, 2015): 178–223. http://dx.doi.org/10.1017/jfm.2015.225.
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Motivated by the importance of small-scale turbulent diapycnal mixing to the closure of the large-scale meridional overturning circulation (MOC) of the oceans, we focus on a model problem which allows us to address the fundamental fluid mechanics that is expected to be characteristic of the oceanographic regime. Our model problem is one in which the initial conditions consist of a stably stratified parallel shear flow which evolves into the turbulent regime through the growth of a Kelvin–Helmholtz wave to finite amplitude followed by transition to turbulence. Through both linear stability analysis and direct numerical simulations (DNS), we investigate the secondary instabilities and the turbulent mixing at a fixed high Reynolds number and for a range of Prandtl numbers. We demonstrate that the oceanographically expected high value of the Prandtl number has a profound influence on the nature of the secondary instabilities that govern the transition process. Specifically through non-separable linear stability analysis, we discover new characteristics for the shear-aligned convective instability such that it is modified into a mixed mode that is driven both by static instability and by shear. The growth rate and ultimate strength of this mode are both strongly enhanced at higher $\mathit{Pr}$ while the growth rate and ultimate strength of the stagnation point instability (SPI), which may compete for control of the transition process, are simultaneously impeded. Of equal importance is the fact that, for higher $\mathit{Pr}$, the characteristic length scales associated with the dominant mixed mode of instability decrease and therefore there ceases to be a strong scale selectivity. In the limit of much higher $\mathit{Pr}$, we conjecture that a wide range of spatial scales become equally unstable so as to support an ‘ultraviolet catastrophe’, in which a direct injection of energy occurs into a broad range of scales simultaneously. We further establish the validity of these analytical results through a series of computationally challenging DNS analyses, and provide a detailed analysis of the efficiency of the turbulent mixing of the density field that occurs subsequent to transition and of the entrainment of fluid into the mixing layer from the high-speed flanks of the shear flow. We show that the mixing efficiency decreases monotonically with increase of the molecular value of the Prandtl number and the expansion of the shear layer is reduced as such entrainment diminishes.
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Lluesma-Rodríguez, F., S. Hoyas, and M. J. Perez-Quiles. "Influence of the computational domain on DNS of turbulent heat transfer up to Reτ=2000 for Pr=0.71." International Journal of Heat and Mass Transfer 122 (July 2018): 983–92. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.02.047.
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Plumley, Meredith, Keith Julien, Philippe Marti, and Stephan Stellmach. "The effects of Ekman pumping on quasi-geostrophic Rayleigh–Bénard convection." Journal of Fluid Mechanics 803 (August 16, 2016): 51–71. http://dx.doi.org/10.1017/jfm.2016.452.
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Numerical simulations of three-dimensional rapidly rotating Rayleigh–Bénard convection are performed by employing an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parametrized Ekman pumping boundary conditions and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier–Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct numerical simulations (DNS) and laboratory experiments. Results from these methods have established Ekman pumping as the mechanism responsible for significantly enhancing the vertical heat transport. This asymptotic model demonstrates excellent agreement over a range of thermal forcing for Prandtl number $Pr\approx 1$ when compared with results from experiments and DNS at maximal values of their attainable rotation rates, as measured by the Ekman number ($E\approx 10^{-7}$); good qualitative agreement is achieved for $Pr>1$. Similar to studies with stress-free boundaries, four spatially distinct flow morphologies exists. Despite the presence of frictional drag at the upper and/or lower boundaries, a strong non-local inverse cascade of barotropic (i.e. depth-independent) kinetic energy persists in the final regime of geostrophic turbulence and is dominant at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries, Ekman friction is found to attenuate the efficiency of the upscale energy transport and, unlike the case of stress-free boundaries, rapidly saturates the barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is strong enough to prevent the development of a coherent dipole vortex condensate. Instead, vortex pairs are found to be intermittent, varying in both time and strength. For all combinations of boundary conditions, a Nastrom–Gage type of spectrum of kinetic energy is found, where the power-law exponent changes from ${\approx}-3$ to ${\approx}-5/3$, i.e. from steep to shallow, as the spectral wavenumber increases.
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Salehipour, Hesam, and W. R. Peltier. "Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence." Journal of Fluid Mechanics 775 (June 26, 2015): 464–500. http://dx.doi.org/10.1017/jfm.2015.305.
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In order that it be correctly characterized, irreversible turbulent mixing in stratified fluids must distinguish between adiabatic ‘stirring’ and diabatic ‘mixing’. Such a distinction has been formalized through the definition of a diapycnal diffusivity, $K_{{\it\rho}}$ (Winters & D’Asaro, J. Fluid Mech., vol. 317, 1996, pp. 179–193) and an appropriate mixing efficiency, $\mathscr{E}$ (Caulfield & Peltier, J. Fluid Mech., vol. 413, 2000, pp. 1–47). Equivalent attention has not been paid to the definitions of a corresponding momentum diffusivity $K_{m}$ and hence an appropriately defined turbulent Prandtl number $\mathit{Pr}_{t}=K_{m}/K_{{\it\rho}}$. In this paper, the diascalar framework of Winters & D’Asaro (1996) is first reformulated to obtain an ‘Osborn-like’ formula in which the correct definition of irreversible mixing efficiency $\mathscr{E}$ is shown to replace the flux Richardson number which Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89) assumed to characterize this efficiency. We advocate the use of this revised representation for diapycnal diffusivity since the proposed reformulation effectively removes the simplifying assumptions on which the original Osborn formula was based. We similarly propose correspondingly reasonable definitions for $K_{m}$ and $\mathit{Pr}_{t}$ by eliminating the reversible component of the momentum production term. To explore implications of the reformulations for both diapycnal and momentum diffusivity we employ an extensive series of direct numerical simulations (DNS) to investigate the properties of the shear-induced density-stratified turbulence that is engendered through the breaking of a freely evolving Kelvin–Helmholtz wave. The DNS results based on the proposed reformulation of $K_{{\it\rho}}$ are compared with available estimations due to the mixing length model, as well as both the Osborn–Cox and the Osborn models. Estimates based upon the Osborn–Cox formulation are shown to provide the closest approximation to the diapycnal diffusivity delivered by the exact representation. Through compilation of the complete set of DNS results we explore the characteristic dependence of $K_{{\it\rho}}$ on the buoyancy Reynolds number $\mathit{Re}_{b}$ as originally investigated by Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193–214) in their idealized study of homogeneous stratified and sheared turbulence, and show that the validity of their results is only further reinforced through analysis of the turbulence produced in the more geophysically relevant Kelvin–Helmholtz wave life-cycle ansatz. In contrast to the results described by Shih et al. (2005) however, we show that, besides $\mathit{Re}_{b}$, a vertically averaged measure of the gradient Richardson number $\mathit{Ri}_{b}$ may equivalently characterize the turbulent mixing at high $\mathit{Re}_{b}$. Based on the dominant driving processes involved in irreversible mixing, we categorize the intermediate (i.e. $\mathit{Re}_{b}=O(10^{1}{-}10^{2})$) and high (i.e. $\mathit{Re}_{b}>O(10^{2})$) range of $\mathit{Re}_{b}$ as ‘buoyancy-dominated’ and ‘shear-dominated’ mixing regimes, which together define a transition value of $\mathit{Ri}_{b}\sim 0.2$. Mixing efficiency varies non-monotonically with both $\mathit{Re}_{b}$ and $\mathit{Ri}_{b}$, with its maximum (on the order of 0.2–0.3) occurring in the ‘buoyancy-dominated’ regime. Unlike $K_{{\it\rho}}$ which is very sensitive to the correct choice of $\mathscr{E}$ (i.e. $K_{{\it\rho}}\propto \mathscr{E}/(1-\mathscr{E})$), we show that $K_{m}$ is almost insensitive to the choice of $\mathscr{E}$ (i.e. $K_{m}\propto 1/(1-\mathscr{E})$) so long as $\mathscr{E}$ is not close to unity, which implies $K_{m}\approx \mathit{Ri}_{b}\mathit{Re}_{b}$ for the entire range of $\mathit{Re}_{b}$. The turbulent Prandtl number is consequently shown to decrease monotonically with $\mathit{Re}_{b}$ and may be (to first order) simply approximated by $\mathit{Re}_{b}$ itself. Assuming $\mathit{Pr}_{t}=1$, or $\mathit{Pr}_{t}=10$ (as is common in large-scale numerical models of the ocean general circulation), is also suggested to be a questionable assumption.
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Zhang, Xuan, and Oleg Zikanov. "Mixed convection in a horizontal duct with bottom heating and strong transverse magnetic field." Journal of Fluid Mechanics 757 (September 19, 2014): 33–56. http://dx.doi.org/10.1017/jfm.2014.473.
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AbstractMixed convection in a horizontal duct with imposed transverse horizontal magnetic field is studied using direct numerical simulations (DNS) and linear stability analysis. The duct’s walls are electrically insulated and thermally insulated with the exception of the bottom wall, at which constant-rate heating is applied. The focus of the study is on flows at high Hartmann ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ha}\le 800$) and Grashof ($\mathit{Gr}\le 10^9$) numbers. It is found that, while conventional turbulence is fully suppressed, the natural convection mechanism leads to the development of large-scale coherent structures. Two types of flows are found. One is the ‘low-$\mathit{Gr}$’ regime, in which the structures are rolls aligned with the magnetic field and velocity and temperature fields are nearly uniform along the magnetic field lines outside of the boundary layers. Another is the ‘high-$\mathit{Gr}$’ regime, in which the convection appears as a combination of similar rolls oriented along the magnetic field lines and streamwise-oriented rolls. In this case, velocity and temperature distributions are anisotropic, but three-dimensional.
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van der Poel, Erwin P., Roberto Verzicco, Siegfried Grossmann, and Detlef Lohse. "Plume emission statistics in turbulent Rayleigh–Bénard convection." Journal of Fluid Mechanics 772 (April 28, 2015): 5–15. http://dx.doi.org/10.1017/jfm.2015.176.
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Direct numerical simulations (DNS) of turbulent thermal convection in a $\mathit{Pr}=0.7$ fluid up to $\mathit{Ra}=10^{12}$ are used to study the statistics of thermal plumes. At various vertical locations in a cylindrical set-up with aspect ratio ${\it\Gamma}=\text{width}/\text{height}=1/3$, plumes are identified and their properties extracted. It is found that plumes are much less likely to be emitted from plate regions with large wind shear. Close to the plates, the plumes have a unimodal log–normal distribution, whereas at more central locations the distribution becomes weakly bimodal, which can be traced back to clustering of the plumes and influence of the large-scale circulation. The number of hot plumes decreases with height. The width of the plumes scales with $\mathit{Ra}$ approximately as $\mathit{Nu}^{-1}$, indicating that it is determined by the thermal boundary layer thickness.
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Luhar, M., A. S. Sharma, and B. J. McKeon. "On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis." Journal of Fluid Mechanics 751 (June 16, 2014): 38–70. http://dx.doi.org/10.1017/jfm.2014.283.
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AbstractWe generate predictions for the fluctuating pressure field in turbulent pipe flow by reformulating the resolvent analysis of McKeon and Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) in terms of the so-called primitive variables. Under this analysis, the nonlinear convective terms in the Fourier-transformed Navier–Stokes equations (NSE) are treated as a forcing that is mapped to a velocity and pressure response by the resolvent of the linearized Navier–Stokes operator. At each wavenumber–frequency combination, the turbulent velocity and pressure field are represented by the most-amplified (rank-1) response modes, identified via a singular value decomposition of the resolvent. We show that these rank-1 response modes reconcile many of the key relationships among the velocity field, coherent structure (i.e. hairpin vortices), and the high-amplitude wall-pressure events observed in previous experiments and direct numerical simulations (DNS). A Green’s function representation shows that the pressure fields obtained under this analysis correspond primarily to the fast pressure contribution arising from the linear interaction between the mean shear and the turbulent wall-normal velocity. Recovering the slow pressure requires an explicit treatment of the nonlinear interactions between the Fourier response modes. By considering the velocity and pressure fields associated with the triadically consistent mode combination studied by Sharma and McKeon (J. Fluid Mech., vol. 728, 2013, pp. 196–238), we identify the possibility of an apparent amplitude modulation effect in the pressure field, similar to that observed for the streamwise velocity field. However, unlike the streamwise velocity, for which the large scales of the flow are in phase with the envelope of the small-scale activity close to the wall, we expect there to be a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\pi /2$ phase difference between the large-scale wall-pressure and the envelope of the small-scale activity. Finally, we generate spectral predictions based on a rank-1 model assuming broadband forcing across all wavenumber–frequency combinations. Despite the significant simplifying assumptions, this approach reproduces trends observed in previous DNS for the wavenumber spectra of velocity and pressure, and for the scale-dependence of wall-pressure propagation speed.
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Baharanchi, Ahmadreza Abbasi, Seckin Gokaltun, and George Dulikravich. "Performance improvement of existing drag models in two-fluid modeling of gas–solid flows using a PR-DNS based drag model." Powder Technology 286 (December 2015): 257–68. http://dx.doi.org/10.1016/j.powtec.2015.07.001.
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Wagner, Sebastian, and Olga Shishkina. "Heat flux enhancement by regular surface roughness in turbulent thermal convection." Journal of Fluid Mechanics 763 (December 11, 2014): 109–35. http://dx.doi.org/10.1017/jfm.2014.665.
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AbstractDirect numerical simulations (DNS) of turbulent thermal convection in a box-shaped domain with regular surface roughness at the heated bottom and cooled top surfaces are conducted for Prandtl number $\mathit{Pr}=0.786$ and Rayleigh numbers $\mathit{Ra}$ between $10^{6}$ and $10^{8}$. The surface roughness is introduced by four parallelepiped equidistantly distributed obstacles attached to the bottom plate, and four obstacles located symmetrically at the top plate. By varying $\mathit{Ra}$ and the height and width of the obstacles, we investigate the influence of the regular wall roughness on the turbulent heat transport, measured by the Nusselt number $\mathit{Nu}$. For fixed $\mathit{Ra}$, the change in the value of $\mathit{Nu}$ is determined not only by the covering area of the surface, i.e. the obstacle height, but also by the distance between the obstacles. The heat flux enhancement is found to be largest for wide cavities between the obstacles which can be ‘washed out’ by the flow. This is also manifested in an empirical relation, which is based on the DNS data. We further discuss theoretical limiting cases for very wide and very narrow obstacles and combine them into a simple model for the heat flux enhancement due to the wall roughness, without introducing any free parameters. This model predicts well the general trends and the order of magnitude of the heat flux enhancement obtained in the DNS. In the $\mathit{Nu}$ versus $\mathit{Ra}$ scaling, the obstacles work in two ways: for smaller $\mathit{Ra}$ an increase of the scaling exponent compared to the smooth case is found, which is connected to the heat flux entering the cavities from below. For larger $\mathit{Ra}$ the scaling exponent saturates to the one for smooth plates, which can be understood as a full washing-out of the cavities. The latter is also investigated by considering the strength of the mean secondary flow in the cavities and its relation to the wind (i.e. the large-scale circulation), that develops in the core part of the domain. Generally, an increase in the roughness height leads to stronger flows both in the cavities and in the bulk region, while an increase in the width of the obstacles strengthens only the large-scale circulation of the fluid and weakens the secondary flows. An increase of the Rayleigh number always leads to stronger flows, both in the cavities and in the bulk.
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Rosevear, Madelaine G., Bishakhdatta Gayen, and Ross W. Griffiths. "Turbulent horizontal convection under spatially periodic forcing: a regime governed by interior inertia." Journal of Fluid Mechanics 831 (October 13, 2017): 491–523. http://dx.doi.org/10.1017/jfm.2017.640.
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Differential heating applied at a single horizontal boundary forces ‘horizontal convection’, even when there is no net heat flux through the boundary. However, almost all studies of horizontal convection have been limited to a special class of problem in which temperature or heat flux differences were applied in only one direction and over the horizontal length of a box (the Rossby problem; Rossby, Deep-Sea Res., vol. 12, 1965, pp. 9–16). These conditions strongly constrain the flow. Here we report laboratory experiments and direct numerical simulations (DNS) extending the results of Griffiths & Gayen (Phys. Rev. Lett., vol. 115, 2015, 204301) for horizontal convection forced by boundary conditions imposed in a two-dimensional periodic array at a horizontal boundary. The experiments use saline and freshwater fluxes at a permeable base with the imposed boundary salinity having a horizontal length scale one quarter of the width of the box. The flow reaches a state in which the net boundary buoyancy flux vanishes and the bulk of the fluid shows an inertial range of turbulence length scales. A regime transition is seen for increasing water depth, from an array of individual coherent plumes on the forcing scale to convection dominated by emergent larger scales of overturning. The DNS explore the analogous thermally forced case with sinusoidal boundary temperature of wavenumber $n=4$, and are used to examine the Rayleigh number ($Ra$) dependence for shallow- and deep-water cases. For shallow water the flow transitions with increasing $Ra$ from laminar to turbulent boundary layer regimes that are familiar from the Rossby problem and which have normalised heat transport scaling as $Nu\sim Ra^{1/5}$ and $Nu\sim (Ra\,Pr)^{1/5}$, with $Nu$ the Nusselt number and $Pr$ the Prandtl number, in this case maintaining a stable array of coherent turbulent plumes. For deep-water and large $Ra$ the laminar scaling transitions to $Nu\sim (Ra\,Pr)^{1/4}$, with the scales of turbulence extending to the dimensions of the box. The $1/4$ power law regime is explained in terms of the momentum of symmetric, inviscid large scales of motion in the interior coupled to diffusive loss of heat through stabilised parts of the boundary layer. The turbulence production is predominantly by shear instability rather than convection, with viscous dissipation distributed throughout the bulk of the fluid. These conditions are not seen in the highly asymmetric flow in the Rossby problem even at Rayleigh numbers up to six orders of magnitude greater than the transition found here. The new inertial interior regime has the rate of supply of available potential energy, and its removal by mixing of density, increasing as $Ra^{5/4}$, which is faster than $Ra^{6/5}$ in the Rossby problem. Irreversible mixing is confined close to the forcing boundary and is very much larger than the viscous dissipation, which is proportional to $Ra$.
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Fu, Hao, Juan Chen, Yanjun Tong, Sifan Peng, Fang Liu, Xuefeng Lyu, and Houjian Zhao. "New Nusselt Number Correlation and Turbulent Prandtl Number Model for Turbulent Convection with Liquid Metal Based on Quasi-DNS Results." Energies 18, no. 3 (January 24, 2025): 547. https://doi.org/10.3390/en18030547.
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Liquid metal is widely used as the primary coolant in many advanced nuclear energy systems. Prandtl number of liquid metal is much lower than that of the conventional coolant of water or gas. Based on the Reynolds analogy, the turbulent Prandtl number is assumed to be a constant around unity. For the turbulent convection of liquid metal, dissipations of half the temperature variance are larger than those of turbulent kinetic energies. The dissimilarity between the thermal and momentum fields increases as Pr decreases. The turbulent Prandtl number is larger than one for the liquid metal. In the current investigation, the turbulent convection of liquid metal in the channel is quasi-directly simulated with OpenFOAM-7. The turbulent statistics of the momentum and the thermal field are compared with the existing database to validate the numerical model. The power law for dimensionless temperature distribution with different Prandtl numbers is obtained by regression analysis of numerical results. A new Nusselt number correlation is derived based on the power law. The new Nusselt number correlation agrees well with the DNS results in the literature. The momentum mixing process between different layers in the cross section is compared with the thermal mixing process. The effects of the Prandtl number on the difference between the turbulence time scale and scalar time scale are analyzed. A new turbulent Prandtl number model with local parameters is obtained for turbulent convection with liquid metal. Combined with the k−ω model, the temperature distributions with the new turbulent Prandtl number model agree well with the DNS results in the literature. The new turbulent Prandtl number model can be used for turbulent convection with different Prandtl and different Reynolds numbers.
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Deusebio, Enrico, G. Brethouwer, P. Schlatter, and E. Lindborg. "A numerical study of the unstratified and stratified Ekman layer." Journal of Fluid Mechanics 755 (August 26, 2014): 672–704. http://dx.doi.org/10.1017/jfm.2014.318.
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AbstractWe study the turbulent Ekman layer at moderately high Reynolds number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}1600 < \mathit{Re} = \delta _{E}G/\nu < 3000$, using direct numerical simulations (DNS). Here, $\delta _{E} = \sqrt{2\nu /f}$ is the laminar Ekman layer thickness, $G$ the geostrophic wind, $\nu $ the kinematic viscosity and $f$ is the Coriolis parameter. We present results for both neutrally, moderately and strongly stably stratified conditions. For unstratified cases, large-scale roll-like structures extending from the outer region down to the wall are observed. These structures have a clear dominant frequency and could be related to periodic oscillations or instabilities developing near the low-level jet. We discuss the effect of stratification and $\mathit{Re}$ on one-point and two-point statistics. In the strongly stratified Ekman layer we observe stable co-existing large-scale laminar and turbulent patches appearing in the form of inclined bands, similar to other wall-bounded flows. For weaker stratification, continuously sustained turbulence strongly affected by buoyancy is produced. We discuss the scaling of turbulent length scales, height of the Ekman layer, friction velocity, veering angle at the wall and heat flux. The boundary-layer thickness, the friction velocity and the veering angle depend on $Lf/u_\tau $, where $u_\tau $ is the friction velocity and $L$ the Obukhov length scale, whereas the heat fluxes appear to scale with $L^+=L u_\tau /\nu $.
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Sun, Bo, Sudheer Tenneti, Shankar Subramaniam, and Donald L. Koch. "Pseudo-turbulent heat flux and average gas–phase conduction during gas–solid heat transfer: flow past random fixed particle assemblies." Journal of Fluid Mechanics 798 (June 1, 2016): 299–349. http://dx.doi.org/10.1017/jfm.2016.290.
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Fluctuations in the gas-phase velocity can contribute significantly to the total gas-phase kinetic energy even in laminar gas–solid flows as shown by Mehrabadi et al. (J. Fluid Mech., vol. 770, 2015, pp. 210–246), and these pseudo-turbulent fluctuations can also enhance heat transfer in gas–solid flow. In this work, the pseudo-turbulent heat flux arising from temperature–velocity covariance, and average fluid-phase conduction during convective heat transfer in a gas–solid flow are quantified and modelled over a wide range of mean slip Reynolds number and solid volume fraction using particle-resolved direct numerical simulations (PR-DNS) of steady flow through a random assembly of fixed isothermal monodisperse spherical particles. A thermal self-similarity condition on the local excess temperature developed by Tenneti et al. (Intl J. Heat Mass Transfer, vol. 58, 2013, pp. 471–479) is used to guarantee thermally fully developed flow. The average gas–solid heat transfer rate for this flow has been reported elsewhere by Sun et al. (Intl J. Heat Mass Transfer, vol. 86, 2015, pp. 898–913). Although the mean velocity field is homogeneous, the mean temperature field in this thermally fully developed flow is inhomogeneous in the streamwise coordinate. An exponential decay model for the average bulk fluid temperature is proposed. The pseudo-turbulent heat flux that is usually neglected in two-fluid models of the average fluid temperature equation is computed using PR-DNS data. It is found that the transport term in the average fluid temperature equation corresponding to the pseudo-turbulent heat flux is significant when compared to the average gas–solid heat transfer over a significant range of solid volume fraction and mean slip Reynolds number that was simulated. For this flow set-up a gradient-diffusion model for the pseudo-turbulent heat flux is found to perform well. The Péclet number dependence of the effective thermal diffusivity implied by this model is explained using a scaling analysis. Axial conduction in the fluid phase, which is often neglected in existing one-dimensional models, is also quantified. As expected, it is found to be important only for low Péclet number flows. Using the exponential decay model for the average bulk fluid temperature, a model for average axial conduction is developed that verifies standard assumptions in the literature. These models can be used in two-fluid simulations of heat transfer in fixed beds. A budget analysis of the mean fluid temperature equation provides insight into the variation of the relative magnitude of the various terms over the parameter space.
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Gayen, Bishakhdatta, Ross W. Griffiths, and Graham O. Hughes. "Stability transitions and turbulence in horizontal convection." Journal of Fluid Mechanics 751 (June 25, 2014): 698–724. http://dx.doi.org/10.1017/jfm.2014.302.
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AbstractRecent results have shown that convection forced by a temperature gradient along one horizontal boundary of a rectangular domain at a large Rayleigh number can be turbulent in parts of the flow field. However, the conditions for onset of turbulence, the dependence of flow and heat transport on Rayleigh number, and the roles of large and small scales in the flow, have not been established. We use three-dimensional direct numerical simulation (DNS) and large-eddy simulation (LES) over a wide range of Rayleigh numbers,$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}Ra\sim 10^8\mbox{--}10^{15}$, for Prandtl number$Pr=5$and a small aspect ratio, and show that a sequence of several stability transitions at$Ra \sim 10^{10}\mbox{--} 10^{11}$defines a change from laminar to turbulent flow. The Prandtl number dependence too is examined at$Ra = 5.86 \times 10^{11}$. At the smallest$Ra$considered the thermal boundary layer is characterized by a balance of viscous stress and buoyancy, whereas inertia and buoyancy dominate in the large-$Ra$regime. The change in the momentum balance is accompanied by turbulent enhancement of the overall heat transfer, although both laminar and turbulent regimes give$Nu\sim Ra^{1/5}$. The results support both viscous and inviscid theoretical scaling models from previous work. The mechanical energy budget for an intermediate range of Rayleigh numbers above onset of instability ($10^{10}<Ra<10^{13}$) reveals that the small scales of motion are produced predominantly by thermal convection, whereas at$Ra \ge 10^{14}$shear instability of the large-scale flow begins to play a dominant role in sustaining the small-scale turbulence. Extrapolation to ocean conditions requires knowledge of the inertial regime identified here, but the simulations show that the corresponding asymptotic balance has not been fully realized by$Ra \sim 10^{15}$.
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Biferale, L., A. S. Lanotte, R. Scatamacchia, and F. Toschi. "Intermittency in the relative separations of tracers and of heavy particles in turbulent flows." Journal of Fluid Mechanics 757 (September 23, 2014): 550–72. http://dx.doi.org/10.1017/jfm.2014.515.
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AbstractResults from direct numerical simulations (DNS) of particle relative dispersion in three-dimensional homogeneous and isotropic turbulence at Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathit{Re}}_{\lambda } \sim 300$ are presented. We study point-like passive tracers and heavy particles, at Stokes number $\mathit{St}=0.6,1$ and 5. Particles are emitted from localised sources, in bunches of thousands, periodically in time, allowing an unprecedented statistical accuracy to be reached, with a total number of events for two-point observables of the order of ${10^{11}}$. The right tail of the probability density function (PDF) for tracers develops a clear deviation from Richardson’s self-similar prediction, pointing to the intermittent nature of the dispersion process. In our numerical experiment, such deviations are manifest once the probability to measure an event becomes of the order of – or rarer than – one part over one million, hence the crucial importance of a large dataset. The role of finite-Reynolds-number effects and the related fluctuations when pair separations cross the boundary between viscous and inertial range scales are discussed. An asymptotic prediction based on the multifractal theory for inertial range intermittency and valid for large Reynolds numbers is found to agree with the data better than the Richardson theory. The agreement is improved when considering heavy particles, whose inertia filters out viscous scale fluctuations. By using the exit-time statistics we also show that events associated with pairs experiencing unusually slow inertial range separations have a non-self-similar PDF.
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TRIAS, F. X., M. SORIA, A. OLIVA, and C. D. PÉREZ-SEGARRA. "Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4." Journal of Fluid Mechanics 586 (August 14, 2007): 259–93. http://dx.doi.org/10.1017/s0022112007006908.
Full textAbstract:
A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.
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Ibe, Akihiro, Kazuo Saito, Mitsuo Nakazato, Yoko Kikuchi, Kenji Fujinuma, and Taichiro Nishima. "Quantitative Determination of Amines in Wine by Liquid Chromatography." Journal of AOAC INTERNATIONAL 74, no. 4 (July 1, 1991): 695–98. http://dx.doi.org/10.1093/jaoac/74.4.695.
Full textAbstract:
Abstract A liquid chromatographic (LC) procedure is described for the determination by dansylation of the following 16 kinds of biogenic amines found In wine: monomethylamine (MM), ethylamine (EM), iso- and n-propylamlne (Pr), iso- and n-butylamine (Bu), iso- and n-amylamlne (Am), pyrrolidine (PY), 2- phenethylamine (PH), tryptamine (TR), putresclne (PU), cadaverine (CA), histamine (HI), tyramine (TY), and spermidine (SP). The amines In white and red wine were applied to a column of Amberllte CG-50 type I resin (Na-form) after the column had been washed with water and eluted with 1N hydrochloric acid. This eluate was evaporated to dryness under reduced pressure and derivatized with dansyl chloride (DNS). LC separations were performed on Finepak SIL C18S and LiChrosorb RP-8 columns with an acetonitrile-water elution gradient. In the survey of commercial wines by this method, most of the samples were found to contain 12 amines, including iso-Am, CA, PU, TY, and others. The highest levels of these amines were 4.84 μg PU/mL in red wine, and 5.11 μg Iso-Am/mL in white wine. The total levels of amines in red wine were comparatively higher than in white wine.
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Varaksin, Aleksey Yu, and Sergei V. Ryzhkov. "Mathematical Modeling of Gas-Solid Two-Phase Flows: Problems, Achievements and Perspectives (A Review)." Mathematics 11, no. 15 (July 26, 2023): 3290. http://dx.doi.org/10.3390/math11153290.
Full textAbstract:
Mathematical modeling is the most important tool for constructing theories of different kinds of two-phase flows. This review is devoted to the analysis of the introduction of mathematical modeling to two-phase flows, where solid particles mainly serve as the dispersed phase. The main problems and features of the study of gas-solid two-phase flows are included. The main characteristics of gas flows with solid particles are discussed, and the classification of two-phase flows is developed based on these characteristics. The Lagrangian and Euler approaches to modeling the motion of a dispersed phase (particles) are described. A great deal of attention is paid to the consideration of numerical simulation methods that provide descriptions of turbulent gas flow at different hierarchical levels (RANS, LES, and DNS), different levels of description of interphase interactions (one-way coupling (OWC), two-way coupling (TWC), and four-way coupling (FWC)), and different levels of interface resolution (partial-point (PP) and particle-resolved (PR)). Examples of studies carried out on the basis of the identified approaches are excluded, and they are also excluded for the mathematical modeling of various classes of gas-solid two-phase flows.
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Horn, Susanne, and Olga Shishkina. "Toroidal and poloidal energy in rotating Rayleigh–Bénard convection." Journal of Fluid Mechanics 762 (December 2, 2014): 232–55. http://dx.doi.org/10.1017/jfm.2014.652.
Full textAbstract:
AbstractWe consider rotating Rayleigh–Bénard convection of a fluid with a Prandtl number of $\mathit{Pr}=0.8$ in a cylindrical cell with an aspect ratio ${\it\Gamma}=1/2$. Direct numerical simulations (DNS) were performed for the Rayleigh number range $10^{5}\leqslant \mathit{Ra}\leqslant 10^{9}$ and the inverse Rossby number range $0\leqslant 1/\mathit{Ro}\leqslant 20$. We propose a method to capture regime transitions based on the decomposition of the velocity field into toroidal and poloidal parts. We identify four different regimes. First, a buoyancy-dominated regime occurring while the toroidal energy $e_{tor}$ is not affected by rotation and remains equal to that in the non-rotating case, $e_{tor}^{0}$. Second, a rotation-influenced regime, starting at rotation rates where $e_{tor}>e_{tor}^{0}$ and ending at a critical inverse Rossby number $1/\mathit{Ro}_{cr}$ that is determined by the balance of the toroidal and poloidal energy, $e_{tor}=e_{pol}$. Third, a rotation-dominated regime, where the toroidal energy $e_{tor}$ is larger than both $e_{pol}$ and $e_{tor}^{0}$. Fourth, a geostrophic regime for high rotation rates where the toroidal energy drops below the value for non-rotating convection.
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Pagliarini, L., R. Corsini, E. Stalio, and F. Bozzoli. "RANS representation of transition and separation over a low-Re number blade section at high angle of attack." Journal of Physics: Conference Series 2766, no. 1 (May 1, 2024): 012086. http://dx.doi.org/10.1088/1742-6596/2766/1/012086.
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Abstract Systems based on wind energy harvesting can successfully meet part of the increasing green energy demand worldwide. However, wind turbines operation might be undermined by varying atmospheric conditions, which could result in an increase of angle of attack and consequent onset of flow separation phenomena, especially at low Reynolds numbers. Such conditions are strongly influenced by blades geometry, and they negatively affect structural integrity and power output of wind turbines. For this reason, it is crucial to define a tool capable of swiftly allowing numerical investigations on different geometrical configurations to delay and mitigate flow separation occurrence. The present work aims at modelling laminar-turbulent transition and turbulent flow separation over a wind turbine blade section operating at angle of attack = 15°, Re = 66000 and Pr = 0.71 by means of a steady RANS approach. Turbulence is treated by means of the Transition SST k-ω and the Transition k-kL-ω models. The main aerodynamic and thermal coefficients are evaluated and compared against a high-order accurate DNS database for validation. The results highlight, for the present test case, a better capability of the Transition SST k-ω of perceiving the main thermo-fluid dynamic features of the separated flow over the blade section.
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Masi, Enrica, Josette Bellan, Kenneth G. Harstad, and Nora A. Okong’o. "Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition." Journal of Fluid Mechanics 721 (March 19, 2013): 578–626. http://dx.doi.org/10.1017/jfm.2013.70.
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AbstractA model is developed for describing mixing of several species under high-pressure conditions. The model includes the Peng–Robinson equation of state, a full mass-diffusion matrix, a full thermal-diffusion-factor matrix necessary to incorporate the Soret and Dufour effects and both thermal conductivity and viscosity computed for the species mixture using mixing rules. Direct numerical simulations (DNSs) are conducted in a temporal mixing layer configuration. The initial mean flow is perturbed using an analytical perturbation which is consistent with the definition of vorticity and is divergence free. Simulations are performed for a set of five species relevant to hydrocarbon combustion and an ensemble of realizations is created to explore the effect of the initial Reynolds number and of the initial pressure. Each simulation reaches a transitional state having turbulent characteristics and most of the data analysis is performed on that state. A mathematical reformulation of the flux terms in the conservation equations allows the definition of effective species-specific Schmidt numbers $(\mathit{Sc})$ and of an effective Prandtl number $(\mathit{Pr})$ based on effective species-specific diffusivities and an effective thermal conductivity, respectively. Because these effective species-specific diffusivities and the effective thermal conductivity are not directly computable from the DNS solution, we develop models for both of these quantities that prove very accurate when compared with the DNS database. For two of the five species, values of the effective species-specific diffusivities are negative at some locations indicating that these species experience spinodal decomposition; we determine the necessary and sufficient condition for spinodal decomposition to occur. We also show that flows displaying spinodal decomposition have enhanced vortical characteristics and trace this aspect to the specific features of high-density-gradient magnitude regions formed in the flows. The largest values of the effective species-specific $\mathit{Sc}$ numbers can be well in excess of those known for gases but almost two orders of magnitude smaller than those of liquids at atmospheric pressure. The effective thermal conductivity also exhibits negative values at some locations and the effective $\mathit{Pr}$ displays values that can be as high as those of a liquid refrigerant. Examination of the equivalence ratio indicates that the stoichiometric region is thin and coincides with regions where the mixture effective species-specific Lewis number values are well in excess of unity. Very lean and very rich regions coexist in the vicinity of the stoichiometric region. Analysis of the dissipation indicates that it is dominated by mass diffusion, with viscous dissipation being the smallest among the three dissipation modes. The sum of the heat and species (i.e. scalar) dissipation is functionally modelled using the effective species-specific diffusivities and the effective thermal conductivity. Computations of the modelled sum employing the modelled effective species-specific diffusivities and the modelled effective thermal conductivity shows that it accurately replicates the exact equivalent dissipation.
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Ahlers, Guenter, Eberhard Bodenschatz, and Xiaozhou He. "Logarithmic temperature profiles of turbulent Rayleigh–Bénard convection in the classical and ultimate state for a Prandtl number of 0.8." Journal of Fluid Mechanics 758 (October 9, 2014): 436–67. http://dx.doi.org/10.1017/jfm.2014.543.
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AbstractWe report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh–Bénard convection for a cylindrical sample with an aspect ratio (diameter $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}D$ over height $L$) equal to 0.50, in both the classical and the ultimate state. The measurements are for Rayleigh numbers $\mathit{Ra}$ from $6\times 10^{11}$ to $10^{13}$ in the classical and $7\times 10^{14}$ to $1.1\times 10^{15}$ (our maximum accessible $\mathit{Ra}$) in the ultimate state. The Prandtl number was close to 0.8. Although to lowest order the bulk is often assumed to be isothermal in the time average, we found a ‘logarithmic layer’ (as reported briefly by Ahlers et al., Phys. Rev. Lett., vol. 109, 2012, 114501) in which the reduced temperature $\varTheta = [\langle T(z) \rangle - T_m]/\Delta T$ (with $T_m$ the mean temperature, $\Delta T$ the applied temperature difference and $\langle {\cdots } \rangle $ a time average) varies as $A \ln (z/L) + B$ or $A^{\prime } \ln (1-z/L) + B^{\prime }$ with the distance $z$ from the bottom plate of the sample. In the classical state, the amplitudes $-A$ and $A^{\prime }$ are equal within our resolution, while in the ultimate state there is a small difference, with $-A/A^{\prime } \simeq 0.95$. For the classical state, the width of the log layer is approximately $0.1L$, the same near the top and the bottom plate as expected for a system with reflection symmetry about its horizontal midplane. For the ultimate state, the log-layer width is larger, extending through most of the sample, and slightly asymmetric about the midplane. Both amplitudes $A$ and $A^{\prime }$ vary with radial position $r$, and this variation can be described well by $A = A_0 [(R - r)/R]^{-0.65}$, where $R$ is the radius of the sample. In the classical state, these results are in good agreement with direct numerical simulations (DNS) for $\mathit{Ra} = 2\times 10^{12}$; in the ultimate state there are as yet no DNS. The amplitudes $-A$ and $A^{\prime }$ varied as ${\mathit{Ra}}^{-\eta }$, with $\eta \simeq 0.12$ in the classical and $\eta \simeq 0.18$ in the ultimate state. A close analogy between the temperature field in the classical state and the ‘law of the wall’ for the time-averaged downstream velocity in shear flow is discussed. A two-sublayer mean-field model of the temperature profile in the classical state was analysed and yielded a logarithmic $z$ dependence of $\varTheta $. The $\mathit{Ra}$ dependence of the amplitude $A$ given by the model corresponds to an exponent $\eta _{th} = 0.106$, in good agreement with the experiment. In the ultimate state the experimental result $\eta \simeq 0.18$ differs from the prediction $\eta _{th} \simeq 0.043$ by Grossmann & Lohse (Phys. Fluids, vol. 24, 2012, 125103).
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Intana, Warin, Prisana Wonglom, Nakarin Suwannarach, and Anurag Sunpapao. "Trichoderma asperelloides PSU-P1 Induced Expression of Pathogenesis-Related Protein Genes against Gummy Stem Blight of Muskmelon (Cucumis melo) in Field Evaluation." Journal of Fungi 8, no. 2 (February 4, 2022): 156. http://dx.doi.org/10.3390/jof8020156.
Full textAbstract:
Gummy stem blight caused by Stagonosporopsis cucurbitacearum is the most destructive disease of muskmelon cultivation. This study aimed to induce disease resistance against gummy stem blight in muskmelon by Trichoderma asperelloides PSU-P1. This study was arranged into two crops. Spore suspension at a concentration of 1 × 106 spores/mL of T. asperelloides PSU-P1 was applied to muskmelon to investigate gene expression. The expression of PR genes including chitinase (chi) and β-1,3-glucanase (glu) were determined by reverse transcription quantitative polymerase chain reaction (RT-qPCR), and enzyme activity was assayed by the DNS method. The effects of T. asperelloides PSU-P1 on growth, yield, and postharvest quality of muskmelon fruit were measured. A spore suspension at a concentration of 1 × 106 spore/mL of T. asperelloides PSU-P1 and S. cucurbitacearum was applied to muskmelons to determine the reduction in disease severity. The results showed that the expression of chi and glu genes in T. asperelloides PSU-P1-treated muskmelon plants was 7–10-fold higher than that of the control. The enzyme activities of chitinase and β-1,3-glucanase were 0.15–0.284 and 0.343–0.681 U/mL, respectively, which were higher than those of the control (pathogen alone). Scanning electron microscopy revealed crude metabolites extracted from T. asperelloides PSU-P1-treated muskmelon plants caused wilting and lysis of S. cucurbitacearum hyphae, confirming the activity of cell-wall-degrading enzymes (CWDEs). Application of T. asperelloides PSU-P1 increased fruit weight and fruit width; sweetness and fruit texture were not significantly different among treated muskmelons. Application of T. asperelloides PSU-P1 reduced the disease severity scale of gummy stem blight to 1.10 in both crops, which was significantly lower than that of the control (2.90 and 3.40, respectively). These results revealed that application of T. asperelloides PSU-P1 reduced disease severity against gummy stem blight by overexpressed PR genes and elevated enzyme activity in muskmelon plants.