1、Non-Newtonian Fluids,Non-Newtonian Flow,GoalsDescribe key differences between a Newtonian and non-Newtonian fluidIdentify examples of Bingham plastics (BP) and power law (PL) fluidsWrite basic equations describing shear stress and velocities of non-Newtonian fluidsCalculate frictional losses in a no
2、n-Newtonian flow system,Non-Newtonian Fluids,Newtonian Fluid,Non-Newtonian Fluid, is the apparent viscosity and is not constant for non-Newtonian fluids., - Apparent Viscosity,The shear rate dependence of categorizes non-Newtonian fluids into several types.,Power Law Fluids:Pseudoplastic (viscosity)
3、 decreases as shear rate increases (shear rate thinning)Dilatant (viscosity) increases as shear rate increases (shear rate thickening)Bingham Plastics: depends on a critical shear stress (t0) and then becomes constant,Non-Newtonian Fluids,Newtonian,Bingham Plastic:,Pseudoplastic:,Dilatant:,sludge, p
4、aint, blood, ketchup,latex, paper pulp, clay solns.,quicksand,Modeling Power Law Fluids,Oswald - de Waele,where:K = flow consistency indexn = flow behavior index,Note: Most non-Newtonian fluids are pseudoplastic n1.,Modeling Bingham Plastics,Rigid,Frictional Losses Non-Newtonian Fluids,Recall:,Appli
5、es to any type of fluid under any flow conditions,Laminar Flow,Mechanical Energy Balance,0,0,0,MEB (contd),Combining:,Momentum Balance,0,0,Power Law Fluid,Boundary Condition,Velocity Profile of Power Law FluidCircular Conduit,Upon Integration and Applying BC,Power Law (contd),Need bulk average veloc
6、ity,Power Law Results (Laminar Flow), Hagen-Poiseuille (laminar Flow) for Power Law Fluid ,Recall,Power Law Fluid Behavior,Power Law Reynolds Number and Kinetic Energy Correction,Laminar Flow Friction FactorPower Law Fluid,Turbulent Flow Friction Factor Power Law Fluid (Smooth Pipe),Power Law Fluid
7、Example,A coal slurry is to be transported by horizontal pipeline. It has been determined that the slurry may be described by the power law model with a flow index of 0.4, an apparent viscosity of 50 cP at a shear rate of 100 /s, and a density of 90 lb/ft3. What horsepower would be required to pump
8、the slurry at a rate of 900 GPM through an 8 in. Schedule 40 pipe that is 50 miles long ?,P = 1atm,P = 1atm,L = 50 miles,Friction Factor (Power Law Fluid),Bingham Plastics,Bingham plastics exhibit Newtonian behavior after the shear stress exceeds to. For flow in circular conduits Bingham plastics be
9、have in an interesting fashion.,Bingham Plastics,Unsheared Core,Sheared Annular Region,Laminar Bingham Plastic Flow,Hedstrom Number,(Non-linear),Turbulent Bingham Plastic Flow,Drilling Rig Fundamentals,Bingham Plastic Example,Drilling mud has to be pumped down into an oil well that is 8000 ft deep.
10、The mud is to be pumped at a rate of 50 GPM to the bottom of the well and back to the surface through a pipe having an effective diameter of 4 in. The pressure at the bottom of the well is 4500 psi. What pump head is required to pump the mud to the bottom of the drill string ? The drilling mud has the properties of a Bingham plastic with a yield stress of 100 dyn/cm2, a limiting (plastic) viscosity of 35 cP, and a density of 1.2 g/cm3.,P = 4500 psi,P = 14.7 psi,L = 8000 ft,
