Extension of the partially integrated transport modeling method to the simulation of passive scalar turbulent fluctuations at various Prandtl numbers

Chaouat, Bruno; Schiestel, Roland

doi:10.1016/j.ijheatfluidflow.2021.108813

Cited by 4 publications

(13 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A grid sensitivity study has been conducted to ensure that the grid resolution is adequate. In particular, in regard to DNS performed at the Reynolds number R τ = 395 for the Prandtl number P r = 10 (Chaouat 2018;Chaouat & Peyret 2019), the grid in the present case is more refined to compute the budgets of the transport equations for k θ and τ iθ involving higher-order statistics. Hence, the additional Mesh M 1 with an extremely high resolution 1024 × 512 × 1024, especially in the normal direction to the wall, has been used to capture adequately the correlation of the fluctuating scalar gradients (∂θ /∂x i )(∂θ /∂x i ) or even the correlation of the fluctuating velocity-scalar gradients (∂u i /∂x i )(∂θ /∂x i ) associated with the fine structures that evolve locally in time and space.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…The time step is adjusted to get a constant Courant-Friedrichs-Lewy number of unity. This combined time-space numerical scheme of high-order accuracy has shown very good numerical properties in performing DNS of turbulence with a passive scalar (Chaouat 2018;Chaouat & Peyret 2019). The computational fluid dynamics (CFD) code developed by Chaouat (2011) is based on the finite volume technique where the mean variables are evaluated at the centre of the computational cell whereas the convective and diffusive fluxes are computed at the interfaces surrounding the cell.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…where D/Dt = ∂/∂t + u k ∂/∂x k , P θ , P k and J k θ , J θ are the production and diffusion terms, c θθ 1 = 1, c θk 1 = 1/2, c θk 2 = 1/2 and c θθ 2 = 1.30 (Chaouat & Schiestel 2021b). Several formulations of the transport equation for θ have been proposed (Newmann, Launder & Lumley 1981;Jones & Musonge 1988;Nagano & Kim 1988;Yoshizawa 1988;Shikazono & Kasagi 1996) but (5.2) is one of the most general forms obtained in the spectral space by a theoretical formalism (Chaouat & Schiestel 2021b).…”

Section: The K θ − θ Transport Equationsmentioning

confidence: 99%

“…and dissipation of the scalar variance. This case was investigated more recently for the Reynolds number R τ = 395 and the Prandtl numbers P r = 0.01, 0.1, 1, 10 (Chaouat 2018;Chaouat & Peyret 2019). The results have revealed how the thermal characteristics of the flow evolve as the molecular Prandtl number varies from low to high values but the budgets of the scalar transport equations, the passive scalar to dynamic time-scale ratio R, amongst others, were not performed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Contribution of direct numerical simulations to the budget and modelling of the transport equations for passive scalar turbulent fields with wall scalar fluctuations

Chaouat

2023

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

We perform direct numerical simulations (DNS) of the fully developed turbulent channel flow with a passive scalar subjected to constant time-averaged scalar fluxes at the wall. The first case (case I) considers a constant time-averaged scalar flux $\left \langle q_w \right \rangle$ along with the specific condition of a non-fluctuating scalar $\theta _w$ imposed at the wall implying zero wall scalar fluctuation $\theta '_w=0$ and zero variance (isoscalar boundary condition) whereas the second case (case II) accounts for a constant instantaneous scalar flux $q_w$ in time and space leading to zero gradient of scalar fluctuation along the normal to the wall $(\partial \theta '/ \partial x_n)_w = 0$ (isoflux boundary condition) implying a non-zero variance. The friction Reynolds number takes on the value $R_\tau =395$ and the molecular Prandtl numbers considered are $P_r=0.01$ , 0.1, 1 and 10. The purpose is to investigate the effect of the wall scalar fluctuations on the scalar field. Emphasis is put on the mean passive scalar $\left \langle \theta \right \rangle$ , the half-scalar variance $k_\theta$ , the turbulent scalar fluxes $\tau _{i \theta }$ , the correlation coefficients $R_{i \theta }$ , the passive scalar to dynamic time-scale ratio $\mathcal {R}$ , the turbulent Prandtl number $Pr_t$ and higher-order scalar statistics. Systematic comparisons between these two scalar fields are undertaken. As a result of interest, it is found that the mean scalar remains almost the same whatever the type of the boundary layer condition but not the scalar variance. The budgets of transport equations for the half-scalar variance and turbulent fluxes reveal that some scalar quantities such as the dissipation-rate and the molecular diffusion terms are highly modified in the near-wall region but not really the production, diffusion and the scalar-pressure gradient correlation terms in a first approximation. Visualization of the instantaneous scalar fields indicates that the topology of the structures is strongly modified as the Prandtl number increases from $P_r=0.01$ up to $10$ . Finally, it is shown how to use this DNS database to devise and calibrate scalar flux equation models in the framework of both first and second moment closures. This study suggests that accounting for wall scalar fluctuations should be considered in the simulation of turbulent flows involving fluid and solid combinations at the interface and provides a useful high resolution DNS database.

show abstract

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: The K θ − θ Transport Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Contribution of direct numerical simulations to the budget and modelling of the transport equations for passive scalar turbulent fields with wall scalar fluctuations

Chaouat

2023

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Various applications were tackled, such as flow in a plane channel with appreciable fluid injection through a permeable wall corresponding to the propellant burning in solid rocket motors [170], rotating channel flows encountered in turbomachinery [176], flow over periodic hills with separation and reattachment of the boundary layer at several Reynolds numbers as shown in Figure 5 [177,178] corresponding to the experiment reference [179], airfoil flows [180], flow in small axisymmetric contraction [181]. The PITM method has been recently extended to the turbulent transfer of a passive scalar including transport of variance and its dissipation rate [182].…”

Section: Subfilter Stress Transport Modelmentioning

confidence: 99%

Turbulence modeling and simulation advances in CFD during the past 50 years

Schiestel¹,

Chaouat²

2022

Comptes Rendus. Mécanique

Self Cite

View full text Add to dashboard Cite

show abstract

Energy Partitioning Control in the PITM Hybrid RANS/LES Method for the Simulation of Turbulent Flows

Chaouat

Schiestel

2021

Flow Turbulence Combust

Self Cite

View full text Add to dashboard Cite

The partially integrated transport modeling (PITM) method first introduced in Ref. [R. Schiestel and A. Dejoan, "Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations ", Theor. Comput. Fluid Dyn. 18, 443 (2005)] and in Ref.[B. Chaouat and R. Schiestel, "A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows ", Phys. Fluids 17, 065106 ( 2005)] provides a continuous approach for hybrid RANS-LES simulations. Inspired from the multiple scale approach, the basis of the development of the method is the spectral space in quasi-homogeneous turbulence.The PITM method embodies a partitioning control function that monitors the ratio of subfilter energy to total turbulent energy by reference to the cutoff wavenumber location. How this procedure behaves in inhomogeneous flows is an important question. The present paper demonstrates that the same control function can be used both in homogeneous and in non-homogeneous flows as well.Further on, an analysis of the effect of anisotropic filters generally used for wall flows is conducted for computing the equivalent cutoff wavenumber suitable for determining the subfilter energy of the spectrum and see how it interferes with control function. Illustrations in the turbulent plane channel flow are given that confirm the efficiency of the procedure and DNS data have been used to support and supplement the discussion.

show abstract

Extension of the partially integrated transport modeling method to the simulation of passive scalar turbulent fluctuations at various Prandtl numbers

Cited by 4 publications

References 49 publications

Contribution of direct numerical simulations to the budget and modelling of the transport equations for passive scalar turbulent fields with wall scalar fluctuations

Contribution of direct numerical simulations to the budget and modelling of the transport equations for passive scalar turbulent fields with wall scalar fluctuations

Turbulence modeling and simulation advances in CFD during the past 50 years

Energy Partitioning Control in the PITM Hybrid RANS/LES Method for the Simulation of Turbulent Flows

Contact Info

Product

Resources

About