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Numerical investigation of flow and heat transfer behind a two-dimensional backward-facing step equipped with a semi-porous baffle

流体在带半多孔挡板的二维后向台阶后方流动与传热的数值研究

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Abstract

The backward-facing step is a critical problem existing in many engineering and industrial applications. In this study, a semi-porous baffle (the root of the baffle is a porous medium and the tip is solid) is placed behind the step. The effects of the length of the porous part, and the baffle location on the energy transfer and pressure drop are studied in different Reynolds numbers (Re=100, 200, 300, 400, 500). The effect of the Darcy number of the porous medium on the aforementioned parameters is also investigated. Both the local maximum and average relative Nusselt numbers (divided by the Nusselt of the base case with no baffle at the same Reynolds) and relative pressure drop (calculated as the relative Nusselt number) are reported. The results show that by adoption of the proper length of the porous medium, the average relative and maximum local Nusselt numbers could be enhanced by 20% and 90%, respectively. Low permeable porous media give better energy transfer. For example, porous media with Da=10−5 give 30% better maximum local Nusselt number and about 7% higher average Nusselt number with respect to the same case with Da=10−2.

摘要

后向台阶是工程和工业应用中普遍存在的一个关键问题。在本研究中,在台阶后方放置半多孔挡板(挡板根部是多孔的,顶端是实心的),研究了不同雷诺数(Re=100、200、300、400、500)下多孔部分长度和挡板位置对能量传递和压降的影响,研究了多孔介质达西数对上述参数的影响,得到局部最大和平均相对努塞尔数(努塞尔数除以相同雷诺数下无挡板的情况下的努塞尔数)和相对压降(计算为相对努塞尔数)。结果表明,采用适当多孔介质长度可使平均相对努塞尔数和努塞尔数分别提高20% 和90%。低渗透性的多孔介质提供更好的能量传递。例如,Da=10−5的多孔介质比Da=10−2的多孔介质的最大局部努塞尔数提高了30%,平均努塞尔数提高了约7%。

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Abbreviations

b :

The depth of domain (m)

C :

Inertia coefficient

C p :

Thermal capacity (J/(kg·K))

Da :

Darcy number

g :

Gravitational acceleration (m/s2)

H :

Total height of the channel (m)

h :

Heat transfer coefficient (W/(m2·K))

S :

Height of the step (m)

H* :

H/S

K :

Permeability of the porous medium(m2)

k :

Thermal conductivity (W/(m·K))

L :

Total length of the channel (m)

L* :

L/S

L :

The channel length before the step (m)

L 1 * :

L 1 /S

ṁ :

Mass flow rate (kg/s)

Nu :

Nusselt number

P :

Pressure (Pa)

q″:

Heat flux (W/m2)

Re :

Reynolds number

T :

Temperature (K)

T b :

Bulk temperature (K)

T in :

Inlet temperature (K)

T w :

Wall temperature (K)

u :

x-component of the velocity vector (m/s)

V :

Velocity vector (m/s)

v :

y-component of the velocity vector (m/s)

V* :

Nondimensionalized velocity magnitude

w 1 :

The position of the baffle (m)

W 1 * :

w1/S

w 2 :

Height of porous portion (m)

W 2*:

w2/S

w 3 :

Height of solid portion (m)

α :

Thermal diffusion (m2/s)

γ :

Binary parameter

ε :

Porosity

θ :

Dimensionless Temperature

μ :

Dynamic viscosity (Pa • s)

μ′:

Apparent viscosity (Pa • s)

ν :

kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

ave:

Average

b:

Related to bulk temperature

eff:

Effective

f:

Fluid

in:

Inlet

s:

Solid

w:

Wall

x:

Local value

*:

Dimensionless form

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  1. Department of Mechanical Engineering, Qom University of Technology, Qom, 37195, Iran

    Hamid-Reza Bahrami

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Bahrami, HR. Numerical investigation of flow and heat transfer behind a two-dimensional backward-facing step equipped with a semi-porous baffle. J. Cent. South Univ. 28, 3354–3367 (2021). https://doi.org/10.1007/s11771-021-4860-1

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