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Research Papers: Heat and Mass Transfer

# Heat Transfer Modulation by Inertial Particles in Particle-Laden Turbulent Channel Flow

[+] Author and Article Information
Caixi Liu

Department of Mechanical Engineering,
University of Minnesota,
Minneapolis, MN 55455;
Shanghai Institute of Applied Mathematics and
Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: liux3755@umn.edu

Shuai Tang

Department of Mechanical Engineering,
University of Minnesota,
Minneapolis, MN 55455;
Shanghai Institute of Applied Mathematics and
Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: tangx701@umn.edu

Yuhong Dong

Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: dongyh@staff.shu.edu.cn

Lian Shen

St. Anthony Falls Laboratory,
Department of Mechanical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: shen@umn.edu

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 22, 2017; final manuscript received May 12, 2018; published online August 3, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(11), 112003 (Aug 03, 2018) (16 pages) Paper No: HT-17-1101; doi: 10.1115/1.4040347 History: Received February 22, 2017; Revised May 12, 2018

## Abstract

We study the effects of particle-turbulence interactions on heat transfer in a particle-laden turbulent channel flow using an Eulerian–Lagrangian simulation approach, with direct numerical simulation (DNS) for turbulence and Lagrangian tracking for particles. A two-way coupling model is employed in which the momentum and energy exchange between the discrete particles and the continuous fluid phase is fully taken into account. Our study focuses on the modulations of the temperature field and heat transfer process by inertial particles with different particle momentum Stokes numbers ($St$), which in a combination of the particle-to-fluid specific heat ratio and the Prandtl number results in different particle heat Stokes numbers. It is found that as $St$ increases, while the turbulent heat flux decreases due to the suppression of wall-normal turbulence velocity fluctuation, the particle feedback heat flux increases significantly and results in an increase in the total heat flux. The particle thermal feedback effect is illustrated using the instantaneous structures and statistics of the flow and temperature fields. The mechanisms of heat transfer modulation by inertial particles are investigated in detail. The budget of turbulent heat flux is examined. Moreover, by taking advantage of the ability of numerical simulation to address different momentum and heat processes separately, we investigate in detail the two processes of particles affecting heat transfer for the first time, namely the direct effect of particle thermal feedback to the fluid (i.e., heat feedback) and the indirect effect of the modulation of turbulent velocity field induced by the particles (i.e., momentum feedback). It is found that the contribution of heat transfer from turbulent convection is reduced by both heat and momentum feedback due to the decrease of the turbulent heat flux. The contribution of heat transfer from particle transport effects is barely influenced by the momentum feedback, even if $St$ is large and is mainly affected by the heat feedback. Our results indicate that both heat and momentum feedback are important when the particle inertia is large, suggesting that both feedback processes need to be taken into account in computation and modeling.

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## Figures

Fig. 4

(a) The relative temperature between the particles and the surrounding fluid (<Tp−Tf>), and (b) the particle thermal feedback term (Qp)

Fig. 1

Configuration of nonisothermal turbulent channel flow

Fig. 13

Temperature statistics in particle-free and particle-laden flows with only H-feedback: (a) fluid temperature fluctuation (Trms) and (b) turbulent heat flux (qT(y))

Fig. 5

Instantaneous iso-surfaces of turbulent heat flux. The green color denotes positive turbulent heat flux with −T′u′2=0.07, and the blue color denotes negative turbulent heat flux with −T′u2′=−0.07: (a) particle-free flow, (b) St=25,Rcp=2 (case A1), (c) St=75,Rcp=2 (case B1), and (d) St=125,Rcp=2 (case C1).

Fig. 6

Instantaneous quasi-streamwise vortices identified by the Q criterion (Q = 70): (a) particle-free flow, (b) St=25,Rcp=2 (case A1), (c) St=75,Rcp=2` (case B1), and (d) St=125,Rcp=2 (case C1)

Fig. 2

Heat flux in particle-free flow and particle-laden flows with various St: (a) turbulent heat flux (qT(y)), (b) particle feedback heat flux (qp(y)), and (c) molecular heat flux (qv(y))

Fig. 3

(a) Wall-normal fluid velocity fluctuation (u2,rms), (b) fluid temperature fluctuation (Trms), and (c) correlation between fluid wall-normal velocity and temperature (Ru2′T′)

Fig. 10

Budget terms of turbulent heat flux: (a) production (P2T), (b) pressure-temperature gradient correlation (Π2T), (c) dissipation (ε2T), (d) turbulent diffusion (T2T), (e) molecular diffusion (D2T), and (f) particle feedback (B2T)

Fig. 11

(a) The gradient of pressure fluctuation along the wall-normal direction (∂p′/∂y), (b) correlation between the particle wall-normal momentum feedback and fluid temperature (fp,2′T′/(fp,2rmsTrms)), and (c) correlation between the particle thermal feedback and fluid wall-normal velocity (Qp′u2′/(Qp,rmsu2,rms))

Fig. 12

(a) Fluid temperature fluctuation (Trms), (b) streamwise velocity fluctuation (u1,rms), and (c) turbulent heat flux (qT(y))

Fig. 7

Quadrant contributions to heat flux from (a) Q2 events and (b) Q4 events

Fig. 8

Instantaneous particle thermal feedback to turbulence, with the green color denoting the iso-surfaces of Qp=0.6: (a) St=25,Rcp=2 (case A1), (b) St=75,Rcp=2 (case B1); (c) St=125,Rcp=2 (case C1); and (d) St=125,Rcp=0.4 (case C4)

Fig. 9

Budget terms of turbulent heat flux in the particle-free flow:production (P2T); pressure-temperature gradient correlation (Π2T); dissipation (ε2T); turbulent diffusion (T2T); and molecular diffusion (D2T)

Fig. 17

(a) Particle feedback heat flux (qp(y)) and (b) particle thermal feedback term (Qp) in particle-laden flows with M&H-feedback and with only H-feedback

Fig. 14

Budget terms of fluid temperature: (a) production (PT), (b) particle feedback (BT), and (c) correlation between the particle thermal feedback and fluid temperature (Qp′T′/(Qp,rmsTrms))

Fig. 15

Temperature statistics in particle-laden flows with M&H-feedback and with only M-feedback: (a) fluid temperature fluctuation (Trms) and (b) turbulent heat flux (qT(y))

Fig. 16

Temperature statistics in particle-laden flows with M&H-feedback and with only H-feedback: (a) fluid temperature fluctuation (Trms) and (b) turbulent heat flux (qT(y))

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