the effect of the particle size distribution on non-newtonian turbulent ...

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Chapter 2 Literature Review Page 2.34 The area ratio A, is thus given by: 1 + :y n] A r = 2 [ 0 1 + n ' and hence <strong>the</strong> viscous sub-layer thickness is: (2.64) (2.65) where 0" and 0",. are equivalent Newtonian and non-Newtonian viscous sub-layer thicknesses respectively. The velocity <strong>distribution</strong> is given by: u -=251n V. ' [ PV.y] p.' + 5,5 + 11,6 (A, - 1) - 2,5 In(A,) . The mean velocity is given by: V V N - = - + 11 6 (A - 1) - 2 5 In A - {} V V' r ' r' . . where V N is <strong>the</strong> mean velocity for <strong>the</strong> equivalent Newtonian fluid and n is given by: {} = -2,5 In [1 _T y ] _ 2,5 T y [1 + 0,5 T y ] • To TO TO 2.11.5 The Slatter Model (2.66) (2.67) (2.68) As mentioned in Chapter 1 Slatter (1994) is one <strong>of</strong> <strong>the</strong> few researchers to have taken into account <strong>the</strong> <strong>size</strong> <strong>of</strong> <strong>the</strong> <strong>particle</strong> contained in <strong>the</strong> fluid for turbulent flow analysis. A new Reynolds number was developed for predicting <strong>the</strong> onset <strong>of</strong> turbulence. It was modelled using <strong>the</strong> assumption that <strong>the</strong> unsheared plug present due to <strong>the</strong> yield stress acts as a solid at <strong>the</strong> pipe axis and inhibits turbulence (Figure 2.14).
Chapter 2 Literature Review Page 2.35 I Pipe wall Sheared annulus The Reyno1ds number is given by where and D ohear = D - D p,ug • Annular velocity Figure 2.14: Unsheared plug geometry Plug diameter Pipe diameter Slatter (1994) used <strong>the</strong> following precepts as <strong>the</strong> basis <strong>of</strong> his turbulent flow model: (2.69) (2.70) (2.71) • The velocity <strong>distribution</strong> is logarithmic and similar to <strong>the</strong> classic Newtonian turbulent velocity <strong>distribution</strong> over <strong>the</strong> entire core region. • A roughness <strong>effect</strong> is caused by <strong>the</strong> solid <strong>particle</strong>s.
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THE EFFECT OF THE PARTICLE SIZE DIS
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