Hedstrom number

Hedstrom number Nne t0D2 p /vHe — 2 Mx t0 = yield stress Pvc = limiting viscosity (Yield x inertia)/ viscous stresses Flow of Bingham plastics... 

The basic dimensionless variables for the Bingham plastic are the Reynolds number, the Hedstrom number, and the friction factor. Eliminating Dec from the Reynolds number and Eq. (7-25) (as above), the cost group is ... 

Dec can also be eliminated from the Hedstrom number by combining it with the Reynolds number ... 

With regard to the drag on a sphere moving in a Bingham plastic medium, the drag coefficient (CD) must be a function of the Reynolds number as well as of either the Hedstrom number or the Bingham number (7V Si = /Vne//VRe = t0d/fi V). One approach is to reconsider the Reynolds number from the perspective of the ratio of inertial to viscous momentum flux. For a Newtonian fluid in a tube, this is equivalent to... 

The product fReB is a unique function of the yield number [Hedstrom (1952)] and Govier (1959) has tabulated corresponding values of fReB and Y. A slightly different presentation is in terms of the Hedstrom number He, which is given by... 

Figure 3.10 shows a friction factor - Reynolds number chart for Bingham plastics at various values of the Hedstrom number. The turbulent flow line is that for Newtonian behaviour and is followed by some Bingham plastics with low values of the yield stress [Thomas (1962)]. 

Three dimensionless numbers contain the stirrer speed n. By combining two of them, we obtain a new number that is known as the Hedstrom number,... 

By keeping the Weissenberg number Wi (a pure material number) and the Hedstrom number He constant, measurements are performed and presented in a dimensionless frame ... 

Figure 11 depicts the power characteristics of a Rushton turbine stirrer in geometrically similar cylindrical vessels (///D = l D/J=2) without baffles. To keep the Hedstrom number constant at different scales, viscosity of the PAA solutions had to be fitted as discussed above. 

It is thus possible to calculate theoretically the relationship between the friction factor and Reynolds and Hedstrom numbers in the laminar-flow region. Beyond the laminar-flow region the relationships between these three dimensionless groups must be determined experimentally. 

In highly developed turbulent flow Govier and Winning (Gl) found experimental data to fall within 10% of the conventional Newtonian curve. This means that the effect of the Hedstrom number may be neglected beyond the end of the transition region. Their data were for five clay slurries in two pipe diameters and in. I.P.S.) for Reynolds numbers to 200,000 and Hedstrom numbers to 560,000. 

The other quantities have their usual significance. The first group is the product of the Reynolds and Hedstrom numbers the second is analogous to the tv/tw ratio of Eq. (6). Experimental data were used to support the mathematical development only in the case of the uniform-channel extruder. 

Bingham flow is represented by Figure 6.5(b) in terms of Reynolds and Hedstrom numbers. 

Hedstrom number He LHyp Pi Bingham Reynolds number x Bingham number Flow of Bingham plastics... 

Note that a new dimensionless parameter He, called the Hedstrom number, arises because in the constitutive relation there are two independent rheological parameters. Parameter He is essentially a dimensionless to. This multiplicity of dimensionless parameters in addition to the Re parameter is common to all non-Newtonian constitutive relations. 

The parameter Ca is called the Casson number and is analogous to the Hedstrom number He for the Bingham plastic and Herschel-Bulkley models. 

This parameter is defined to accommodate Herschel-Bulkley model fluids. In the limit To = 0, it reduces to an equivalent power law particle Reynolds number. In the limit n = 1, it reduces to a compound parameter involving the Bingham plastic particle Reynolds number and particle Hedstrom number. In both limits it reduces to the Newtonian particle Reynolds number. This correlation permits... 

Archimedes number Bingham number Bingham Reynolds number Blake number Bond number Capillary number Cauchy number Cavitation number Dean number Deborah number Drag coefficient Elasticity number Euler number Fanning friction factor Froude number Densometric Froude number Hedstrom number Hodgson number Mach number Newton number Ohnesorge number Peclet number Pipeline parameter... 

Laminar Flow. Theoretically derived equations for volumetric flow rate and friction factor are included for several models in Table 6.7. Each model employs a specially defined Reynolds number, and the Bingham models also involve the Hedstrom number,... 

TABLE 6.6 Laminar Flow Volumetric Flow Rate, Friction Factor, Reynolds Number, and Hedstrom Number... 

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