Dave Dickey Forum Moderator 283 Posts
Re: How do I calculate Reynolds Number?25 January 2013 at 3:12pm
The answer to this question comes with some qualifications, which require some additional explanation. The calculation of an impeller Reynolds number is based more on a definition than a comprehensive property that can be applied with equal significance to different types of impellers.
Impeller Reynolds number is by definition the impeller diameter squared times the rotational speed times the liquid density divided by the fluid viscosity. The dimensions of each variable must be consistent or conversion factors must be applied so the result is dimensionless. Thus a value of the Reynolds number is the same, independent of the size, shape, or type of impeller, which only provides a means of relating impeller operation to the fluid properties. In effect, the Reynolds number provides a ratio of inertial to viscous forces applied to the fluid, not an evaluation of the impeller performance.
The impeller Reynolds number is by definition independent to the impeller type, number of blades, blade width, etc. Results of the impeller design may be different. In this case, while the form of the correlation for the inside heat transfer film coefficient may be the same for different impeller types, at least the coefficient in the correlation may not be the same. Most correlations for heat transfer coefficients equate a Nusselt number, which includes the film coefficient, a key dimension of the heat transfer surface, and the thermal conductivity of the fluid, to the mixer dimensions and fluid property variables. The correlated Nusselt number is typically expressed as a function of a constant times the Reynolds number raised to a power times the Prandtl number raised to a another power times other geometry ratios and fluid property ratios. The differences associated with impeller types appears in the constants, sometimes in the exponents and rarely in the other factors.
The real qualification comes with respect to the effectiveness of the different impellers. This question implies that the impellers are of different sizes, yet turning at the same speed. Because impeller diameter has a large effect on power (impeller diameter to the fifth power for turbulent impeller conditions) one impeller could be doing most of the mixing and therefore most of the heat transfer. Trying to use heat transfer correlations in the literature for impellers different from those tested will be difficult, if not impossible. Even good heat transfer correlations estimate film coefficients within only +/- 15%, so precision may not give a better answer.
Since you have impellers for which heat transfer correlations probably don't exits, my recommendation is to do an equivalent calculation with a known type of impeller. Calculate or measure the power required to turn the existing impellers. Calculate the size of a 4-blade, pitched-blade impeller that would require the same power at the same speed as the total of the actual two impellers. Then do a heat transfer correlation based on the equivalent pitched-blade impeller. The only way to improve on that calculation would be to conduct a heat transfer test with water or other known fluid and derive the overall heat transfer coefficient.