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On the Performance of Various Reynolds Stress Models in Resolving Non-equilibrium Features of Turbulent In-cylinder Engine Flows

  • Research Article - Mechanical Engineering
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Abstract

In highly transient turbulent flows, the energy cascade and related dissipation rate of energy are key factors which must be modeled precisely to obtain the accurate computational predictions. The flow in diesel engines specifically during compression stroke is quite transient, so most commonly used eddy viscosity based turbulence models fail to predict the transitional characteristics of these types of flow. This paper focuses on performance appraisal of three versions of Reynolds stress turbulence models in resolving non-equilibrium features and transitional characteristics of turbulent in-cylinder engine flows. Results indicate that although these turbulence models give the same prediction of averaged quantities of turbulent flows (i.e. mean flow kinetic energy), their results are totally different in calculating non-equilibrium features and the turbulent length scales. According to calculated results, incompressible Launder–Reece–Rodi and Naot second-moment closure models give unreal estimations of the turbulent integral length scale during compression stroke, while the modified Launder–Reece–Rodi model predictions have more similarity with physical trends.

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Abbreviations

a i j :

Reynolds stress anisotropy

C D :

Droplet drag coefficient

C P :

Specific heat capacity (J K−1)

D d,k :

Droplet diameter (m)

D i j :

Reynolds stress diffusion (kgm−1 s−3)

f :

Evaporated fuel mass (kg)

h :

Gas phase enthalpy (J kg−1)

k :

Turbulent kinetic energy (m2 s−2)

k d :

Turbulence effects of gas phase on droplets (s−1)

N d,k :

Number of droplets in a parcel

n i :

Normal-to-the-wall unit vector

P :

Near wall temperature field correction function

P :

Static pressure (pa)

P i j :

Reynolds stress production (kgm−1 s−3)

\({\dot{{q}_{\rm w}}}\) :

Wall heat flux (W)

r :

Radial coordinate (m)

r d :

Droplet radial coordinate (m)

S hd :

Droplet source term in gas phase energy equation (Jm−3 s−1)

S i j :

Mean flow strain rate (s−1)

S md :

Converted mass from liquid to gas (kg s−1)

S u :

Droplet source term in gas phase axial momentum equation (kgm−2 s−2)

S ud :

Droplet source term in gas phase axial momentum equation (kgm−2 s−2)

S v :

Droplet source term in gas phase radial momentum equation (kgm−2 s−2)

S vd :

Droplet source term in gas phase radial momentum equation (kgm−2 s−2)

t :

Time (s)

T k,D :

Droplet temperature (K)

T w :

Wall temperature (K)

T + :

Non-dimensional temperature

u :

Gas phase axial velocity (ms−1)

u d :

Droplet axial component velocity (ms−1)

U + :

Non-dimensional velocity

u′:

Gas phase axial component velocity fluctuations (ms−1)

\({\overline {{{u}^{\prime}{u}^{\prime}}}}\) :

Reynolds stress (m2 s−2)

\({\overline {{{u}^{\prime}{v}^{\prime}}}}\) :

Reynolds stress (m2 s−2)

U τ :

Frictional velocity (ms−1)

v :

Gas phase radial component velocity (ms−1)

V rel :

Relative velocity (ms−1)

v′:

Gas phase radial component velocity fluctuations (ms−1)

\({\overline {{{v}^{\prime}{v}^{\prime}}}}\) :

Reynolds stress (m2 s−2)

x :

Axial coordinate (m)

x d :

Droplet axial coordinate (m)

y + :

Non-dimensional distance from wall

θ :

Void fraction

ρ :

Gas phase density (kgm−3)

μ :

Gas phase viscosity (kgm−1 s−1)

\({\varepsilon}\) :

Eddy dissipation rate (m2 s−3)

\({\Pi _{{\rm ij}}}\) :

Reynolds stress pressure–strain correlation

\({\Pi _{{\rm ij1}}}\) :

Reynolds stress pressure–strain “slow term” correlation (kgm−1 s−3)

\({\Pi _{{\rm ij2}}}\) :

Reynolds stress pressure–strain “rapid term” correlation (kgm−1 s−3)

\({\Pi _{{\rm ijw}}}\) :

Reynolds stress pressure–strain “wall-echo” (kgm−1 s−3)

\({\Omega _{{\rm ij}}}\) :

Rotational term (s−1)

τ w :

Wall shear Stress (kgm−1 s−2)

σ h,t :

Turbulent Prandtl number

σ h :

Prandtl number

μ t :

Eddy viscosity (kgm−1 s−1)

ρ d :

Droplet density (kgm−3)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

    Hamid Motamedi Zoka & Hassan Khaleghi

  2. Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran

    Amir Omidvar

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  1. Hamid Motamedi Zoka
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  2. Amir Omidvar
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  3. Hassan Khaleghi
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Correspondence to Hamid Motamedi Zoka.

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Zoka, H.M., Omidvar, A. & Khaleghi, H. On the Performance of Various Reynolds Stress Models in Resolving Non-equilibrium Features of Turbulent In-cylinder Engine Flows. Arab J Sci Eng 38, 2891–2900 (2013). https://doi.org/10.1007/s13369-012-0477-x

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