Abstract
In this study, the presence of Bingham fluid between two parallel plane annuli with constant squeeze motion is theoretically analyzed. The effect of radius of separation on core thickness, pressure distribution, and squeeze force for different values of Bingham number has been investigated. By considering equilibrium of an element of the core in the fluid, thickness of the rigid plug core has been calculated numerically. The properties of the squeeze film are investigated through the non-Newtonian effects on the squeeze force of the plane for various annular spaces.
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Abbreviations
- \(h^{*}\) :
-
Squeeze film thickness
- \(H = {{h^{*} } \mathord{\left/ {\vphantom {{h^{*} } {h^{*} = 1}}} \right. \kern-0pt} {h^{*} = 1}}\) :
-
Dimensionless squeeze film thickness
- \(r^{*}\) :
-
Radial coordinate
- \(r = {{r^{*} } \mathord{\left/ {\vphantom {{r^{*} } {r_{2}^{*} }}} \right. \kern-0pt} {r_{2}^{*} }}\) :
-
Dimensionless radial coordinate
- \(z^{*}\) :
-
Axial coordinate
- \(z = z^{*} /h^{*}\) :
-
Dimensionless axial coordinate
- \(r_{1}^{*}\) :
-
Inner radius
- \(r_{2}^{*}\) :
-
Outer radius
- \(v_{\text{r}}^{*}\) :
-
Radial velocity component
- \(v_{\text{z}}^{*}\) :
-
Axial velocity component
- \(p^{*}\) :
-
Pressure
- \(p\) :
-
Dimensionless pressure
- \(\dot{h}^{*} = - v_{\text{s}}\) :
-
Squeeze velocity
- \(r_{0}^{*}\) :
-
Radius of separation
- \(\lambda = r_{0}^{*} /r_{2}^{*}\) :
-
Dimensionless radius of separation
- \(k = r_{1}^{*} /r_{2}^{*}\) :
-
Ratio of inner and outer radius
- \(p_{\text{a}}^{*}\) :
-
Ambient pressure
- \(p_{\text{a}}\) :
-
Dimensionless ambient pressure
- \(\tau_{rz}\) :
-
Dimensionless shear stress
- \(\tau_{0}\) :
-
Yield stress
- \(\mu\) :
-
Newtonian viscosity
- \(B = \frac{{\tau_{0} (h^{*} )^{2} }}{{\mu v_{\text{s}} r_{2}^{*} }}\) :
-
Bingham number
- \(h_{{1_{1} }}^{*} ,h_{{2_{1} }}^{*}\) :
-
Boundaries of core thickness in \(r_{1}^{*} \le r^{*} \le r_{0}^{*}\)
- \(h_{{1_{2} }}^{*} ,h_{{2_{2} }}^{*}\) :
-
Boundaries of core thickness in \(r_{0}^{*} \le r^{*} \le r_{2}^{*}\)
- \(h_{{c_{1} }}^{*}\) :
-
Core thickness in the region \(r_{1}^{*} \le r^{*} \le r_{0}^{*}\)
- \(h_{{c_{2} }}^{*}\) :
-
Core thickness in the region \(r_{0}^{*} \le r^{*} \le r_{2}^{*}\)
- \(H_{1} ,H_{2}\) :
-
Dimensionless boundaries of the core thickness
- \(H_{{1_{1} }} ,H_{{2_{1} }}\) :
-
Dimensionless boundaries of the core thickness in \(k \le r \le \lambda\)
- \(H_{{1_{2} }} ,H_{{2_{2} }}\) :
-
Dimensionless boundaries of the core thickness in \(\lambda \le r \le 1\)
- \(H_{c} = H_{{{c}_{1} }}\) :
-
Dimensionless core thickness in the region \(k \le r \le \lambda\)
- \(H_{c} = H_{{{c}_{2} }}\) :
-
Dimensionless core thickness in the region \(\lambda \le r \le 1\)
- \(w^{*}\) :
-
Squeeze force
- \(w\) :
-
Dimensionless squeeze force
- \(w(k,N)\) :
-
Dimensionless squeeze force of Newtonian fluid
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Pavan Kumar, S., Vishwanath, K.P. (2018). Squeezing of Bingham Fluid Between Two Plane Annuli. In: Singh, M., Kushvah, B., Seth, G., Prakash, J. (eds) Applications of Fluid Dynamics . Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-5329-0_28
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DOI: https://doi.org/10.1007/978-981-10-5329-0_28
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