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Development of inflow turbulence in microscale urban atmospheric environment

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Abstract

The sensitivity of turbulence-development to inflow turbulent statistics is investigated in microscale urban atmospheric environment flows. Large-eddy simulations (LESs) are carried out, in which the inflow error is brought in by transforming a fully developed turbulent field according to the Reynolds stress or energy spectra. A theoretical analysis is performed by neglecting the diffusion term in the budget equations of the turbulent kinetic energy. The results show that, (i) the error caused by the Reynolds stress decays until the fully developed level is achieved, and (ii) the error caused by the characteristic length scale increases immediately and then decreases. The streamwise changing rate of the inflow error weakens when the vertical coordinate increases. Further testing of the effects of the inflow inner- and outer-layer data shows that, the inflow inner-layer data dominate the near field, and the inflow outer-layer data dominate the far field.

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Abbreviations

A f :

frontal area ratio

A p :

projection area ratio

\({D_{{k^0}}}\) :

diffusion term in the turbulent kinetic energy budget equation in the baseline case

\({D_{{k^e}}}\) :

diffusion term in the turbulent kinetic energy budget equation in the testing case

E :

(k e/k 0)1/2

E uu :

wave spectrum of the streamwise velocity

h :

side length of the cubical roughness

k 0 :

turbulent kinetic energy in the baseline case

k e :

turbulent kinetic energy in the testing case

L x , L y , L z :

domain sizes in the streamwise, lateral, and vertical directions

l 0 (z) :

characteristic length scale in the baseline case

l e (z) :

characteristic length scale in the testing case

\({P_{{k^0}}}\) :

production term in the turbulent kinetic energy budget equation in the baseline case

\({P_{{k^e}}}\) :

production term in the turbulent kinetic energy budget equation in the testing case

p̂ :

filtered pressure

R 0 ij (z) :

Reynolds stress in the baseline case

R e ij (z) :

Reynolds stress in the testing case

Ŝ ij :

deformation tensor of the resolved velocity

P :

averaged mean pressure

ν :

kinematic viscosity coefficient

U, V, W :

averaged mean velocities in the streamwise, lateral, and vertical directions, respectively

u e :

characteristic turbulent velocity in the testing case

u 0 :

characteristic turbulent velocity in the baseline case

û, v̂, ŵ :

filtered velocities in the streamwise, lateral, and vertical directions

δ :

boundary layer depth

ρ :

air density

x, y, z :

coordinate in the streamwise, lateral, and vertical directions

ν t :

subgrid-scale eddy-viscosity

ϕij :

redistribution term in the budget equation of 〈u′ i u′ j 〉

τ ij :

subgrid-scale stress

\({\varepsilon _{{k^0}}}\) :

dissipation term in the turbulent kinetic energy budget equation in the baseline case

\({\varepsilon _{{k^e}}}\) :

dissipation term in the turbulent kinetic energy budget equation in the testing case

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Authors and Affiliations

  1. School of Aerospace, Tsinghua University, Beijing, 100084, China

    Haifeng Li, Guixiang Cui & Zhaoshun Zhang

Authors
  1. Haifeng Li
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  2. Guixiang Cui
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  3. Zhaoshun Zhang
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Corresponding author

Correspondence to Guixiang Cui.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11132005, 11490551, and 11322221)

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Li, H., Cui, G. & Zhang, Z. Development of inflow turbulence in microscale urban atmospheric environment. Appl. Math. Mech.-Engl. Ed. 38, 1377–1396 (2017). https://doi.org/10.1007/s10483-017-2247-6

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  • DOI: https://doi.org/10.1007/s10483-017-2247-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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