Investigation of propeller mixer for agitation of non-Newtonian fluid flow to predict the characteristics within the design process (2023)

In many technical disciplines there is a wide set of applications for the mixing of non-Newtonian fluid flows, especially in the process industry but also in waste water treatment or biogas power plants (Zlokarnik, 1999, Kaltschmitt and Hartmann, 2001, Hellmann and Riegler, 2003, Stieß, 2009).

The depth of knowledge about the power consumption has been driven by the importance of improving the process efficiency of the applied mixers. Whilst vertical aligned mixers are preferred in the process industry, waste water treatment and biogas power plants often utilize mixers with a horizontal aligned shaft (Zlokarnik, 1999, Kaltschmitt and Hartmann, 2001, Kraume, 2003). In this second subfield, the utilization of a combination of propeller mixers and submersible electric motors has been proven as a strong method as it can reach a high mass flow rate together with the capability for a high viscous fluid flow that is typically connected to common applications (Zlokarnik, 1999).

However, the design of the deployed propellers can cause critical operating points to occur. As aforementioned the power consumption of the applied mixers is important to the efficiency of the mixer. However, the power consumption is also related to the heat development of the electric motor and so a poorly designed propeller mixer can cause overheating when operating beyond or even at the specified design point and hence a total breakdown of the mixing process may well occur.

Thus, a well designed mixer and the knowledge about its full characteristics is of high importance to efficiency and reliability conditions. But until today, there has been no fully clear and comprehensible design technique for mixers that is theoretically substantiated. Hence, in the scope of this work, an alternative design procedure, which is based on analytical models will be considered. Nevertheless, to underline the difference of this method to the common procedures developed in the past, these procedures will be summarized quickly in the following section.

The geometrical shape of a mixer is often designed by experience or taken from related subfields. Subsequently, the mixer is scaled to the desired operating point by different methods that have been proven in practice.

One of these methods to scale mixers was introduced in 1957 by Metzner and Otto (1957). Another method was developed in the 1970s by Rieger and Novak, 1972, Rieger and Novak, 1973, Rieger and Novak, 1974. In the past, both procedures were often applied and also improved or enhanced. But in general most of the enhancements are directly related to one or both of the mentioned origin methods.

Many improvements can be found throughout related literature. A method introduced by Henzler and Obernosterer (1991) is seen to be close to the method of Metzner and Otto but with one key difference: instead of the shaft speed, the power of the mixer is taken into account. The concept developed by Wassmer et al. is very close to Henzler’s concept (Wassmer, 2005), but was derived from experimental investigations. Reviol also discovered a power based concept. Reviol regarded an analytic formulation of an abstracted mixing process and confirmed his model by experimental investigations (Reviol, 2010, Reviol and Böhle, 2013, Reviol et al., 2014). Both the concepts of Wassmer et al. and Reviol can be applied and transformed into each other. A detailed summary of such established methods are gathered in various pieces of research literature e.g. in Kraume (2003) and Henzler (2007).

Although the original design methods are more than 50 years old, these procedures are still state of the art due to their simplicity (Wichterle et al., 1971) and their suitability when applied to many technical processes. In order to prove the suitability, many researchers discovered these methods. While the concept by Rieger and Novak has been confirmed for creeping flow by e.g. Kelkar et al., 1972, Kelkar et al., 1973, especially the dependency of Metzner’s and Otto’s concept on the mixed fluid was criticized in the past (Ulbrecht and Wichterle, 1967, Höcker et al., 1980, Tanguy et al., 1996), but also the lack of dimensional accuracy (Pawlowski, 2004), which possibly leads to wrong power calculation (Böhme, 1988). Thus, despite of the high acceptance of the mentioned methods, the fundamentals of these methods were often under criticism. More complex scale-up procedures related to theoretical considerations also exist but have not been approved in practice due to this complexity, see e.g. (Böhme, 1988, Kluck, 2016).

Criticism of the original methods was often driven by unsatisfactory results when applied to scale-up procedures or their enhancements. This is made clear as the considered mixer was designed for a point that is now no longer the operating point after having scaled the mixer. If deviation between these two points is too great and, thus non-modelled aspects are relevant within the process, then the scale-up procedure can be said to have come to the wrong power predictions. This can directly cause the aforementioned overheating or at least an inefficient mixing process.

Furthermore, a scale-up procedure always requires the presence of a mixer, because of the inability of these methods to develop the geometrical shape of the mixer. Hence, the design procedures, developed in the past, despite them having been accepted and proven in practice for many mixing processes, has to be complemented by a fully understandable and transparent design process.

In Reviol et al. (2018), such a technique to design propeller mixer is presented. In contrast to the previously presented methods, the technique is based on analytical methods. Within this process, that only needs simple design parameters, all relevant output data is generated. The output contains the geometrical shape of the propeller mixer for a preselected operating point as well as power consumption, thrust and efficiency for this point. Since fluid machines are often operating beyond this previously considered design point, the in Reviol et al. (2018) presented technique leads to incomplete knowledge for practical use, due to the validity of the results for only one single operating point and this method leads to unsatisfactory results too and has to be enhanced.

In the present paper, a method is introduced to generate the characteristics of a propeller mixer based on its geometrical data, its design parameters and the factual operating parameters. The method is based on the design process introduced by Reviol et al. (2018) and includes this process, but is also applicable to propeller mixers, that were not designed by the aforementioned technique, provided that the mentioned input parameters are known for the propeller.

The technique is expected to calculate the complete characteristic diagram, depending on shaft speed and containing non-Newtonian properties of different fluids, which were not taken into account within the design process. In combination with (Reviol et al., 2018) the new designed propeller mixer is fully known.

Consequently, a full and completely clear design process to develop propeller mixers is now available. All relevant data is calculated within the design technique. Hence, subsequently performed experimental examinations to derive the power consumption or other data are no longer necessary.

Method fundamentals

The method to calculate the full power characteristics of a propeller mixer, which is introduced in this paper, is in general based on the new design technique, that was presented in Reviol et al. (2018). The calculation procedure is not actual a stand-alone procedure, but rather an extension and a logical enhancement of the mentioned design technique. Thus, a brief overview of the design procedure, presented in Reviol et al. (2018), is given.

Considered hydraulic systems

In the scope of this paper, two propeller mixers are designed via the in Reviol et al. (2018) presented method. With regard to these two propellers, the chapter Section 2.2 introduced an inverse procedure to calculate the whole power characteristic that is connected to the design point as well as the calculation of the characteristics for a differing operation point that will be validated by experimental methods. It is worth mentioning that the first propeller is explicitly designed neglecting

Experiments

In this chapter all performed experiments will be presented. At first, investigations for Propeller A are shown before the results of Propeller B are elucidated.

Discussion

The presentation of the results in chapter Section 4 elucidated the inability of the introduced algorithm to confirm the experimental investigation of Propeller A, while the algorithm predicted the experimental data for Propeller B with high accuracy.

Furthermore, the non-continuous course of the numerically calculated characteristics is striking for Propeller A as well as for Propeller B. It is obvious, that this course is not physical and that the reason for the non-continuous course has to be

Acknowledgements

The authors would like to thank the foundation “Rhineland-Palatinate of innovation” of Germany (Stiftung “Rheinland-Pfalz für Innovation”) for the support of this project.