We present an overview of nowadays modeling capabilities and numerical challanges in the simulation of scalar dispersion phenomena in complex flows. Results from the simulation of a passive plume emitted from a line source downstream of a square obstacle are summarized to provide an example of a basic test case where the reliability of computational techniques can be carefully established

Iaccarino, G.

Rossi, R.

English

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DOI 10.1393/ncc/i2009-10405-9Colloquia: CSFI 2008IL NUOVO CIMENTO Vol. 32 C, N. 2 Marzo-Aprile 2009Computational aspects of scalar dispersion modeling andsimulation in complex flowsR. Rossi(1)(2) and G. Iaccarino(2)(1) Laboratorio di Termofluidodinamica ComputazionaleSeconda Facolta` di Ingegneria di Forl`ı, Universita` di BolognaVia Fontanelle 40, 47100 Forl`ı, Italy(2) Center For Turbulence ResearchDepartment of Mechanical Engineering, Stanford UniversityStanford CA 94305, United States(ricevuto il 4 Agosto 2009; pubblicato online il 25 Settembre 2009)Summary. — We present an overview of nowadays modeling capabilities and nu-merical challanges in the simulation of scalar dispersion phenomena in complex flows.Results from the simulation of a passive plume emitted from a line source down-stream of a square obstacle are summarized to provide an example of a basic testcase where the reliability of computational techniques can be carefully established.PACS 47.27.E- – Turbulence simulation and modeling.PACS 47.27.ek – Direct numerical simulations.PACS 47.27.em – Eddy-viscosity closures; Reynolds stress modeling.PACS 47.27.T- – Turbulent transport processes.1. – IntroductionThe theoretical understanding and modeling of scalar transport phenomena play akey role in several research fields, including basic fluid mechanics, heat and mass transferand meteorology [1]. In the framework of atmospheric dispersion, the analysis of scalartransport is typically connected with the problem of predicting the dispersal of pollu-tants emitted from localized sources. Despite simplified models are available to predictdispersion phenomena with reasonable accuracy at the level of the regional scale, whichis of the order of hundred kilometers, the analysis of scalar transport in urban areas isnoticeably complicated by the geometrical details arising at the street scale, which is ofthe order of hundred meters [2]. An example of this scenario is presented in fig. 1, wherelarge-scale computations in the city of Chicago are presented. The picture shows theeffect of displacing the scalar source from the original position (left panel) to a locationcloser to the Chicago river (right panel). It is clear from the iso-surface of scalar concen-tration how the predicted scalar field is significantly affected by the different interactionof the plume with the underlying flow field.c© Societa` Italiana di Fisica 257258 R. ROSSI and G. IACCARINOFig. 1. – Effect of scalar source displacement in large-scale computations of urban environments.Although experimental testing of urban dispersion has been pursued since more thanthree decades, Computational Fluid Dynamics (CFD) has also become a valuable andreliable tool to predict scalar transport phenomena. In this short paper, we present someresults from the numerical simulation of scalar dispersion in complex flows, with theaim to provide an example of nowadays modeling capabilities as well as the numericalchallanges that we still need to face in the upcoming future.2. – Mathematical and numerical modelsIn this paper we restrict our attention to the dynamics and modeling of non-reactingand non-buoyant scalars. In such conditions, the scalar advection can be approximatedto a passive mechanism, and the scalar field is governed by the following non-dimensionaladvection-diffusion equation:(1)∂C∂t+∂∂xj(UjC) =1ReSc∂2C∂xjxj,where Re is the flow Reynolds number and the Schmidt number Sc = ν/D gives the ratiobetween the momentum diffusivity of the fluid and the mass diffusivity of the scalar. Fromthe numerical point view, the most reliable prediction of turbulent scalar transport isobtained using Direct Numerical Simulations (DNS), that is, by solving eq. (1) directlyand thus without introducing further approximations into the mathematical model. Asis well known in the fluid mechanics community, the scaling arguments introduced bythe Kolmogorov theory of turbulence [3] show that DNS is affordable only at relative lowRe numbers. In the case of atmospheric dispersion, direct simulations become even moreproihibitive because of the wider range of turbulent scales occurring at large Schmidtnumbers. This is shown by the following estimate of the wave number characterizing thedissipative range of the scalar field, originally introduced by the work of Batchelor [4]:(2) kηc = (/νD2)1/4,COMPUTATIONAL ASPECTS OF SCALAR DISPERSION IN COMPLEX FLOWS 259Table I. – Computational cost of numerical tools.Tool No. EQs DIMs Grid size Time steps NCPUs Total timeDNS 5 3D 586.000 100.000 64 48 hRANS 7–10 2D 63.000 200 2 0.5 hwhere  denotes the dissipation of the kinetic energy associated with the momentumturbulence. Therefore, although has been proven that reliable DNS of turbulent scalartransport can be performed using numerical schemes suitable for complex geometries [5],this numerical tool can be only used to improve the basic understanding of the physicalphenomenon or to establish very accurate numerical database.Since large-scale computations of the type shown in fig. 1 cannot be afforded by directsimulations, we are forced to introduce some level of modeling in order to ameliorate therequested computational effort. The most common and less demanding approach is givenby taking an ensamble average of eq. (1), which leads to the RANS (Reynolds-AveragedNavier-Stokes) formulation of the scalar transport equation(3)∂C∂t+∂∂xj(U jC) =1ReSc∂2C∂xjxj− ∂∂xj(ujc),where the overline denotes averaged quantities and lowercase letters represent fluctuatingvalues of primitive variables. The new unknown ujc at the right hand side of eq. (3) isusually termed the vector of turbulent scalar fluxes. It originates from the averagingoperation and represents the effect of turbulent motions on the mean scalar field. Mostof empirical models developed in the past to provide an approximation to ujc relied onthe analogy with molecular transport phenomena. This leads to the so-called gradient-transport type closures(4) uic = −Dtij∂C∂xj,where Dtij represents the turbulent-diffusivity tensor. Despite the simplicity of such typeof models, recent studies have shown that they can be applied successfully to scalar dis-persion in complex flows when a suitable estimate of velocity fluctuations uj is availableand retaining the anisotropic character of the diffusivity tensor Dtij [6]. In the next sec-tion, we present briefly some results from the numerical simulation of scalar dispersiondownstream of a square obstacle fully immersed in a turbulent boundary layer. Thecomputations are performed using DNS as well as RANS models, while numerical dis-cretization is carried out using unstructured finite-volume schemes. Table I provides asummary of the computational effort required by the different simulation techniques.3. – ResultsThe turbulent dispersion of a passive plume emitted from a line source downstream asquare obstacle provides a basic test case to establish the reliability of computational tech-niques. The obstacle is fully immersed in a turbulent boundary layer and flow separationoccurs behind it. The flow Reynolds number is 700, based on the free-stream velocityand the obstacle height H.260 R. ROSSI and G. IACCARINO−4 −2 0 2x 10−300.511.522.53−1 0 1 2x 10−300.511.522.53(a) (b)Fig. 2. – Profiles of turbulent scalar fluxes in a passive plume emitted downstream of a squareobstacle: (a) streamwise flux, (b) vertical flux; ––– DNS, – · – anisotropic scalar flux model, – – –isotropic scalar flux model, ◦ measurements [7].Since accurate predictions of mean scalar concentration require reliable estimationsof turbulent scalar fluxes, the computed profiles of ujc using DNS and scalar flux modelsof the type (4) are compared in fig. 2 to experimental measurements [7]. The resultsgiven by DNS show that unstructured finite-volume schemes can be applied successfullyto scalar dispersion in complex flows. However, the analysis of several inflow conditions,not reported here for the sake of brevity, has shown that the generation of realisticvelocity fluctuations in the approaching flow is mandatory in order to get satisfactoryresults [8].Although the modeling of momentum turbulence is always of prime concern in theframework of RANS modeling, fig. 2 also shows that isotropic models, which are cus-tomary in the CFD community, are not consistent with experimental and DNS results.Therefore, a significant effort should be also directed toward the improvement of scalarflux modeling.∗ ∗ ∗The research project has been supported by the Marco Polo program of the Universityof Bologna. The financial support from the Army High Performance Computing ResearchCenter at Stanford is also gratefully acknowledged.REFERENCES[1] Warhaft Z., Annu. Rev. Fluid Mech., 32 (2000) 203.[2] Britter R. E. and Hanna S. R., Annu. Rev. Fluid Mech., 35 (2003) 465.[3] Kolmogorov A. N., Proc. R. Soc. London, Ser. A, 434 (1980) 15.[4] Batchelor G. K., The Theory of Homogeneous Turbulence (Cambridge University Press)1953.[5] Rossi R., J. Comput. Phys., 228 (2009) 1639.[6] Rossi R. and Iaccarino G., Atmos. Environ., 43 (2009) 2518.[7] Vinc¸ont J.-Y., Simo¨ens S., Ayrault M. and Wallace M., J. Fluid Mech., 424 (2000)127.[8] Rossi R. and Iaccarino G., Annual Research Briefs, Center for Turbulence Research,Stanford University and NASA-Ames (2008) pp. 287-312.

Computational aspects of scalar dispersion modeling and

simulation in complex flows

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Computational aspects of scalar dispersion modeling and simulation in complex flows

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