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Time-periodic non-Newtonian power-law flow across a triangular prism

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Abstract

The effects of non-Newtonian power-law fluids on the unsteady unconfined fluid flow characteristics of an equilateral triangular prism are investigated for Reynolds number (Re) ranging from 50 to 150 and power-law index (n) ranging from 0.4 to 1.8. The flow field around a triangular prism is represented by streamline contours. The output parameters such as root-mean-square values of lift and drag coefficients, time-averaged drag and lift coefficients and Strouhal number are calculated. A time-periodic behavior of the flow is observed for the entire range of control parameters studied. An increment in the time-averaged total drag coefficient is observed with the increase in Re for pseudo-plastic and Newtonian fluids. However, for dilatant fluids, a mixed trend is observed when time-averaged total drag coefficient is varied with n. There is an enhancement in the value of Strouhal number with the increase in Re for dilatant fluids, whereas a mixed trend of Strouhal number with Re is noticed for pseudo-plastic fluids.

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Abbreviations

B :

Side of an equilateral triangular prism (m)

C D :

Total drag coefficient (–)

\(\overline{{C_{\text{D}} }}\) :

Time-averaged drag coefficient (–)

C DF :

Friction drag coefficient (–)

C DP :

Pressure drag coefficient (–)

C Drms :

Rms value of the drag coefficient (–)

C L :

Total lift coefficient (–)

C Lrms :

Rms lift coefficient (–)

C p :

Pressure coefficient (–)

f :

Vortex shedding frequency (s−1)

F D :

Drag force per unit length of prism (Nm−1)

F DF :

Friction drag force per unit length of prism (Nm−1)

F DP :

Pressure drag force per unit length of prism (Nm−1)

F L :

Lift force per unit length of prism (Nm−1)

H :

Domain height (m)

I ij :

Second invariant of the strain tensor rate (s−2)

L :

Domain length (m)

m :

Power-law consistency index (Pa sn)

n :

Power-law index (–)

n s :

Direction vector normal to the surface of the prism (–)

n x :

x-Component of the direction vector normal to the surface of the prism (–)

p :

Dimensionless pressure (=p*/(ρ \(U_{\infty }^{2}\)))

Re:

Reynolds number (–)

s :

Surface of the triangular prism (–)

St:

Strouhal number (–)

t :

Time (s)

T:

Time period for one cycle (s)

\(U_{\infty }\) :

Uniform velocity at the inlet (m s−1)

U x :

x-Component of velocity (=U * x /\(U_{\infty }\))

U y :

y-Component of velocity (=U * y /\(U_{\infty }\))

U * x , U * y :

Velocity components in x- and y- directions, respectively (m s−1)

X d , X u :

Downstream and upstream distances, respectively (m)

x, y :

Dimensionless coordinates (=\(x^{*} /B\), \(y^{*} /B\))

x*, y* :

Cartesian coordinates (m)

ε :

Component of the strain tensor rate (s−1)

\({\varvec{\upsigma}}\) :

Stress tensor (Pa)

\({\varvec{\uptau}}\) :

Extra stress tensor (Pa)

η :

Fluid viscosity (Pa s)

ρ :

Density (kg m−3)

δ :

Smallest cell size (m)

\(\varphi_{\text{rms}}\) :

Rms value of any specific quantity (\(\varphi\))

rms:

Root mean square value

*:

Dimensional value

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    Richa Agarwal & Amit Dhiman

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  1. Richa Agarwal
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  2. Amit Dhiman
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Correspondence to Amit Dhiman.

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Technical Editor: Monica Feijo Naccache.

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Agarwal, R., Dhiman, A. Time-periodic non-Newtonian power-law flow across a triangular prism. J Braz. Soc. Mech. Sci. Eng. 38, 227–240 (2016). https://doi.org/10.1007/s40430-015-0332-6

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  • DOI: https://doi.org/10.1007/s40430-015-0332-6

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