The Turbulent Schmidt Number for Transient Contaminant Dispersion in a Large Ventilated Room Using a Realizable k-εModel

Buildings with large open spaces in which chemicals are handled are often exposed to the risk of explosions.Computational fluid dynamics is a useful and convenient way to investigate contaminant dispersion in such large spaces.The turbulent Schmidt number(Sc_(t))concept has typically been used in this regard,and most studies have adopted a default value.We studied the concentration distribution for sulfur hexafluoride(SF_(6))assuming different emission rates and considering the effect of Sc_(t).Then we examined the same problem for a light gas by assuming hydrogen gas(H_(2))as the contaminant.When SF_(6) was considered as the contaminant gas,a variation in the emission rate completely changed the concentration distribution.When the emission rate was low,the gravitational effect did not take place.For both low and high emission rates,an increase in S_(ct) accelerated the transport rate of SF_(6).In contrast,for H_(2) as the contaminant gas,a larger S_(ct) could induce a decrease in the H_(2) transport rate.

Numerical Investigations on the Impact of Turbulent Prandtl Number and Schmidt Number on Supersonic Combustion

The flow field inside the combustor of a scramjet is highly complicated and the related turbulent Prandtl and Schmidt numbers have a significant impact on the effective numerical prediction of such dynamics.As in many cases researchers set these parameters on the basis of purely empirical laws,assessing their impact(via parametric numerical simulations)is a subject of great importance.In the present work,in particular,two test cases with different characteristics are selected for further evaluation of the role played by these non-dimensional numbers:Burrows-Kurkov case and DLR case.The numerical results indicate that these parameters influence ignition location.Moreover,the temperature distribution is more sensitive to them than to H2O mass fraction and velocity distributions.

Analysis of a Stagnation Point Flow with Hybrid Nanoparticles over a Porous Medium

The unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking sheet embedded in a porous medium with mass transpiration and chemical reactions is considered.The momentum and mass transfer problems are combined to form a system of partial differential equations,which is converted into a set of ordinary differential equations via similarity transformation.These ordinary differential equations are solved analytically to obtain the solution for velocity and concentration profiles in exponential and hypergeometric forms,respectively.The concentration profile is obtained for four different cases namely constant wall concentration,uniform mass flux,general power law wall con-centration and general power law mass flux.The effect of different physical parameters such as Darcy number Da^(1-1),mass transpiration parameter V_(C),stretching/shrinking parameter (d),chemical reaction parameter(β)and Schmidt number (Sc)on velocity and concentration profile is examined.Results show that,the axial velocity will decreases as the shrinking sheet parameter increases,regardless of whether the suction or injection case is examined.The concentration decreases with an increase in the shrinking sheet parameter and the chemical reaction rate parameter.

Families of Schmidt-number witnesses for high dimensional quantum states

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

Effects of Reynolds number and Schmidt number on variable density mixing in shock bubble interaction

Effects of Reynolds(Re)number and Schmidt(Sc)number on the flow structures and variable density mixing are numerically investigated through the canonical shock cylindrical bubble interaction.By determining the viscosity and diffusivity within a wide range,the controlling parameters,total vortex circulation,and compression rate,are conservative under a broad range of Re and Sc numbers(Re≈10^(3)-10^(5)and Sc≈0.1-5)in the same shock Mach(Ma)number condition(Ma=2.4).As for the Re number effect,the circulation of secondary baroclinic vorticity(SBV),induced by the main vortex centripetal acceleration,is observed to be higher in high Re number and vice versa.Based on the vorticity transport equation decomposition,a growth-inhibition vorticity dynamics balance mechanism is revealed:the vorticity viscous term grows synchronously with baroclinic production to inhibit SBV production in low Re number.By contrast,the viscous term terminates the baroclinic term with a time lag in high Re number,leading to the SBV production.Since the SBV reflects the local stretching enhancement based on the advection-diffusion equation,mixing is influenced by the Sc number in a different behavior if different Re numbers are considered.The time-averaged variable density mixing rate emerges a scaling law with Sc number asχ^(∗)=β·Sc^(−α),where the coefficientβ∼Re−0.2 and the scaling exponentα∼Re−0.385.The understanding of Re number and Sc number effect on variable density mixing provides an opportunity for mixing enhancement from the perspective of designing the viscosity and diffusivity of the fluid mixture.

Influence of Turbulence Schmidt Number on Exit Temperature Distribution of an Annular Gas Turbine Combustor using Flamelet Generated Manifold

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS(Reynoldsaveraged Navier–Stokes)simulations,where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer.This concept,applied to a lean premixed combustion system,was assessed in this paper in terms of exit temperature distribution.Because of the isotropic assumption involved in this analogy,the prediction in some flow condition,such as jet cross flow mixing,would be inaccurate.In this study,using Flamelet Generated Manifold as reaction model,some of the numerical results,obtained from an annular combustor configuration with the turbulent Schmidt number varying from 0.85 to 0.2,were presented and compared with a benchmark atmospheric test results.It was found that the Schmidt numberσt in mean mass fraction f transport equation had significant effect on dilution air mixing process.The mixing between dilution air and reaction products from the primary zone obviously improved asσt decreased on the combustor exit surface.Meanwhile,the sensitivity ofσt in three turbulence models including Realizable k-ε,SST(Shear Stress Transport)and RSM(Reynolds Stress Model)has been compared as well.Since the calculation method of eddy viscosity was different within these three models,RSM was proved to be less sensitive than another two models and can guarantee the best prediction of mixing process condition.On the other hand,the results of dilution air mixing were almost independent of Schmidt number Sct in progress variable c transport equation.This study suggested that for accurate prediction of combustor exit temperature distribution in steady state reacting flow simulation,the turbulent Schmidt number in steady state simulation should be modified to cater to dilution air mixing process.

Construction and Validation of an Urban Area Flow and Dispersion Model on Building Scales

This paper presents a numerical model that simulates the wind fields, turbulence fields, and dispersion of gaseous substances in urban areas on building to city block scales. A Computational Fluid Dynamics（CFD） approach using the steady-state, Reynolds-Averaged Navier-Stokes（RANS） equations with the standard k-ε turbulence model within control volumes of non-uniform cuboid shapes has been employed. Dispersion field is computed by solving an unsteady transport equation of passive scalar. Another approach based on Gaussian plume model is used to correct the turbulent Schmidt number of tracer, in order to improve the dispersion simulation. The experimental data from a wind tunnel under neutral conditions are used to validate the numerical results of velocity, turbulence, and dispersion fields. The numerical results show a reasonable agreement with the wind tunnel data. The deviation of concentration between the simulation with corrected turbulent Schmidt number and the wind tunnel experiments may arise from 1） imperfect point sources, 2） heterogeneous turbulent difusivity, and 3） the constant turbulent Schmidt assumption used in the model.

Penetration efficiency of nanoparticles in a bend of circular cross-section

In order to quantify the losses of nanoparticles in a bend of circular cross-section, the penetration efficiency of nanoparti- cles of sizes ranging from 5.6 nm to 560 nm in diameter is determined as a function of the Dean number, the Schmidt number and the bend angle. It is shown that the effect of the Dean number on the penetration efficiency depends on the particle size. The Dean number has a stronger effect on the penetration efficiency for small particles than for large particles. There exists a critical value of the Dean number beyond which the penetration efficiency turns from increasing to decreasing with the increase of the Dean number, and this critical value is dependent on the particle size and the bend length. The penetration efficiency increases abruptly when the Schmidt number changes from 7 500 to 25 000. Finally, a theoretical relation between the penetration efficiency and the Dean number, the Schmidt number and the bend length is derived.

Chaos,Transport and Mesh Convergence for Fluid Mixing

Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids （as considered here）, this interface is defined as a 50% mass concentration isosurface. For shock wave induced （Richtmyer-Meshkov） instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.

Prediction of uniaxial compressive strength of rock based on lithology using stacking models

Uniaxial compressive strength(UCS)of rock is an essential parameter in geotechnical engineering.Point load strength(PLS),P-wave velocity,and Schmidt hammer rebound number(SH)are more easily obtained than UCS and are extensively applied for the indirect estimation of UCS.This study collected 1080 datasets consisting of SH,P-wave velocity,PLS,and UCS.All datasets were integrated into three categories(sedimentary,igneous,and metamorphic rocks)according to lithology.Stacking models combined with tree-based models and linear regression were developed based on the datasets of three rock types.Model evaluation showed that the stacking model combined with random forest and linear regression was the optimal model for three rock types.UCS of metamorphic rocks was less predictable than that of sedimentary and igneous rocks.Nonetheless,the proposed stacking models can improve the predictive performance for UCS of metamorphic rocks.The developed predictive models can be applied to quickly predict UCS at engineering sites,which benefits the rapid and intelligent classification of rock masses.Moreover,the importance of SH,P-wave velocity,and PLS were analyzed for the estimation of UCS.SH was a reliable indicator for UCS evaluation across various rock types.P-wave velocity was a valid parameter for evaluating the UCS of igneous rocks,but it was not reliable for assessing the UCS of metamorphic rocks.

Numerical investigation of two-dimensional and axisymmetric unsteady flow between parallel plates

In this study,heat and mass transfer in a viscous fluid which is squeezed between parallel plates Is investigated numerically using the fouith-order Runge-Kutta method.The numerical investigation is carried out for different governing parameters namely;the squeeze number,Prandtl number,Eckert number,Schmidt number and the chemical reaction parameter.Results show that Nusselt number has direct relationship with Prandtl number and Eckert number but it has reverse relationship with the squeeze number.Also it can be found that Sherwood number increases as Schmidt number and chemical reaction parameter increases but it decreases with increases of the squeeze number.