Abstract
Based on the governing equations of the inner cyinder of the unsteady flow of the power law fluid in eccentric annuli with the inner cylinder reciprocating axially in bipolar coordinate system, the calculation formulae of tangential force were established, and the relevant numerical calculation method was given. Taking the aqueous solution of partially hydrolyzed polyacrylamides (HPAM) for examples, the tangential forces were calculated by using the formulae and numerical calculation method mentioned above; the curves of the tangential force on the wall of the inner cylinder of HPAM aqueous solution were plotted; and the effects on the tangential force of the flow behavior index of the power law fluid, the stroke and the stroke frequency of the inner cylinder were analyzed.
Highlights
At present in our country, there is few theoretical research on the tangential force on the wall of the inner cylinder of the power law fluid flowing in eccentric annuli with the inner cylinder reciprocating axially
W(ξo,ζ,t) = 0 (1d) where η ( I2 ) is the viscosity function of the power law fluid; I2 is the second invariant of the component of the first order Rivlin-Ericksen tensor; ξ, ζ are the dipolar coordinates, and ξ < 0, ζ ≥ 0 ; ρ is the density of the power law fluid; t is the time; p is the pressure gradient; wp (ξ,ζ ) is the velocity distribution of the power law fluid in eccentric annuli with the motionless inner cylinder; W is the amplitude of the velocity of the inner cylinder reciprocating axially; f is the stroke frequency of the inner cylinder
Take hydrolyzed polyacrylamides (HPAM) aqueous solution as an example, the radius of the inner cylinder of annulus Ro = 2.960 × 10−2 m, the radius of the inner cylinder Ri = 0.885 × 10−2 m, the pressure gradient of the aqueous solution P = 61.061 Pa/m and by using the calculation method mentioned above, the tangential forces on the wall of the inner cylinder of the HPAM aqueous solution are calculated and the relevant distribution curves are plotted as Figure 1 to Figure 4
Summary
At present in our country, there is few theoretical research on the tangential force on the wall of the inner cylinder of the power law fluid flowing in eccentric annuli with the inner cylinder reciprocating axially. This force for sucker rod eccentric wear research has an important influence.
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