Abstract
Basic equations describing steady, two-directional, isothermal and fully developed drag-pressure flow of generalized Newtonian fluid between parallel plates assumed as the appropriate flow model in flat, shallow screw channel, are given. It is shown that the flow output for any generalized Newtonian fluid in the two-directional case can be described by a simple expression with a few parameters depending in a complicated way on pressure gradient, channel geometry and constants of the constitutive model. The expression is also valid for unidirectional flow as the limiting case of the two-directional flow. The parameters must be determined as a rule with numerical methods. To simplify the practical calculations, a few (semi)analytical methods of parameters determination for unidirectional power law flow are discussed first. These methods make possible to calculate analytically the pressure gradient for known output that is typical of screw flow characterization. The results obtained for the unidirectional flow 1-D were generalized to describe the two-directional flow 2-D, which takes into account both longitudinal and transverse velocity components. The generalization is based on translation and dilation of the 1-D flow characteristics by introducing a few additional parameters, which are only dependent on the helix angle and power law exponent. It was found a very good agreement between exact numerical and approximate ( semi)analytical characteristics for both flows.
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