Chemical Engineering Science
Volume 190,
23 November 2018
, Pages 320-332
Author links open overlay panel, ,
Abstract
The common design methods for mixers agitating non-Newtonian fluid flow are not suitable for developing a completely new geometrical shape. These design methods were originally intended only to scale an existing mixer with several correlation methods. For this, the dimensionless power characteristics of the mixer is first determined for agitating Newtonian fluid flow. Subsequently, for the desired operating conditions, the apparent viscosity of the non-Newtonian fluid is derived using the mentioned correlation principles. After setting the desired geometrical parameters, it is possible to calculate the apparent Reynolds number. By comparing the apparent Reynolds number with the dimensionless power characteristics, the estimated power consumption and, therefore, the engine to drive the mixer can be determined. This procedure comes with the assumption of a valid correlation between Newtonian and non-Newtonian fluid flow, which is not physical. Furthermore, the question of how to develop the geometric shape of a mixer for a considered operation point is still open. In this paper, a new method is introduced to develop the shape of a propeller mixer for arbitrary operating conditions in pseudo-plastic fluids by analytical methods. The method is based on the consequently implemented blade element momentum theory.
Introduction
Mixing procedures are widely distributed in many fields of the process industry. These procedures are often applied to agitate non-Newtonian fluid flow. The objective of the mixing process may be versatile, usually depends on the final product, and may range from increasing the heat transfer to generating high fluid-flow rates.
Especially for applications with high flow rates, the usage of propeller mixers is relevant (Zlokarnik, 1999). Propeller mixers are mostly arranged centrically, but an eccentric position is possible as well. They are included in the category of axial fluid machinery and are used for turbulent and highly viscous fluid flow. The typical viscosity reaches up to , but propeller mixers agitate fluids of even higher viscosity of about as well. The typical circumferential velocity is (Zlokarnik, 1999, Kraume, 2003). Due to these facts, propeller mixers are widely used in the field of wastewater treatment and biogas power plant technology.
The research of propellers, intended to be used as mixers, reaches far back in history. Among others, Stoops et al. and Rushton et al. investigated the application of propeller mixers in Newtonian fluid flow in the 1940s and 1950s (Stoops and Lovell, 1943, Rushton et al., 1950a, Rushton et al., 1950b). In the early 1960s, Metzner et al. expanded their research to non-Newtonian fluid flow (Metzner et al., 1961).
The mentioned research projects are restricted to power consumption and its scaling, only for several already available propellers. Generally, in industrial processes and, hence, even in research projects, the propeller geometry is designed by experience or taken from another application. In the aforementioned investigations, each research was performed with marine-type propellers. Therefore, it is clear that these propellers are not suitable for non-Newtonian fluid flow due to their water-application-based design.
Instead of offering robust analytic methods, recent directives only give rough hints about how to design the shape of a mixer (Rührer, 1992). In the literature on mixer design for agitating non-Newtonian fluid flow, mostly scale-up procedures can be found. These scale a given mixer geometry by taking the power consumption into account.
In many cases, these methods go back to the basic work of Metzner and Otto (1957), respectively of Rieger and Novak, 1972, Rieger and Novak, 1973, Rieger and Novak, 1974. Over time, a huge number of adjustments and extensions were developed, for instance by Henzler, 2007, Wassmer and Hungenberg, 2005, Reviol et al. (2014). But all derived methods have the same two problems: they are not able to identify the shape of a mixer for a given operation point and they include a pseudo-correlation between Newtonian and non-Newtonian fluids, which often leads to wrong results (Pawlowski, 2004). Nevertheless, a certain reliability of the method can be noted, e.g. for mixing creeping flow regime using the method given by Kelkar et al. (1973). More complex scale-up procedures based on more robust fundamentals also exist, but they have not been approved in practice due to their complexity (Böhme, 1988, Kluck, 2016).
The aim of this paper is to develop an easy-to-use method based on analytical methods. Therefore, a structured and transparent approach is introduced. The method has to be able to design a propeller mixer for an application in a non-Newtonian fluid for one given operating point. The design method has to calculate concrete output parameters such as power and thrust based on technical input parameters such as diameter and shaft speed. Furthermore, the method is required to be able to generate the specific geometrical shape of the propeller to realise this given operating point.
The procedure is based on the blade element momentum theory, which has to be implemented in order to take into account the requirements of the non-Newtonian fluid patterns.
Hence, the propeller is developed in finite sections, while considering the local forces for each section. To fulfil the required forces, especially thrust, hydrodynamic profiles are automatically pre-selected for each considered section. Thus, the force coefficients of the considered profiles have to be known. For the selection, the knowledge of the Reynolds number for each considered section is necessary as well. Subsequently, an analysis of the force coefficients of the pre-selected profiles leads to the final selection of the hydrodynamic profiles, which best resolves the requirements in term of the needed force-coefficients. Finally, integrating over all sections leads to the whole blade of the propeller. Blade element momentum theory is used to form an algorithm out of the proceedings described above. This theory is well-researched and documented in literature and is the quasi-standard procedure to design this kind of fluid-machinery.
But the blade element momentum theory comes with one major problem: the method was introduced to handle fluid problems with purely Newtonian characteristics only. The method was never intended for non-Newtonian fluid flow and, therefore, cannot be adopted for non-Newtonian fluid flow. Hence, up to now, the method has never been used - or at least never been documented - for application in non-Newtonian fluid flow. In this context, several problems have to be solved first. These problems are divided into three categories:
- I.
The profile properties
A huge number of well-known airfoils are to be found in literature or several databases. For these airfoils, the aerodynamic patterns are excellently investigated and documented. These investigations have been performed within a Newtonian fluid - usually air. Thus, these data are not suitable for the present problem and cannot be used. Thus, to use the blade element momentum theory to design a propeller mixer for the agitation of non-Newtonian fluid flow, the whole procedure to elaborate the hydrodynamic patterns has to first be performed for several profiles.
- II.
The Reynolds number
Analysing the force coefficients of several profiles, as described above, leads to the further problem of how to compare the coefficients. Typically, the coefficients are plotted over the Reynolds number due to their significant dependency on this dimensionless number. But the Reynolds number is not easy to calculate when treating non-Newtonian fluids because of the dependency of the viscosity on the deformation. A suitable method to calculate the Reynolds number has to be found in order to compare the results. This problem is in line with scaling problems for a given agitator geometry. Therefore, existing approaches for representative Reynolds numbers can be used.
- III.
The design process
See AlsoInvestigation of propeller mixer for agitation of non-Newtonian fluid flow to predict the characteristics within the design processDiagnosis of wind turbine systematic yaw error through nacelle anemometer measurement analysisDiagnosis of wind turbine systematic yaw error through nacelle anemometer measurement analysisDue to the lack of knowledge regarding the profile chord length, the blade element momentum theory has to be solved iteratively - also for a constant apparent viscosity, which is not even the case here. Thus, in the scope of this research, the mentioned iteration process is more complex. An optimisation process has to be implemented in the design procedure to find the geometrical shape of the propeller to match the requirements. Hence, a numerical procedure is necessary to solve this issue. Furthermore, the inflow velocity depends on the process parameters; it is unknown due to the entrainment mass flow rate and has to be modelled in a suitable manner.
The aim of this paper is to develop the theoretical fundamentals of the design method and the numerical procedure to design the geometrical shape (q.v. III). Therefore, only these topics are explained in detail in Chapters 2 Fundamentals, 3 Developed algorithm. The result of an exemplarily designed propeller shape is given in Chapter 4 and a brief validation of this propeller is presented in Chapter 5. The essential profile data (q.v. I) and the intended method to calculate the Reynolds number (q.v. II) are briefly introduced in Chapter 2. In favour of the detailed presentation of the theoretical background, detailed results of the validation are omitted from this paper. The investigation of the utilised profile data can be found in Kluck et al. (in preparation). Several methods to calculate a suitable Reynolds number can be found in Kluck (2016) and Haldenwang et al. (2012). Finally, the particularised proof of the concept is presented in Reviol et al. (2018) and Wang et al. (2018).
Section snippets
Free-jet kinematics
To design a fluid-flow machine with free axial outflow, a suitable control room around the machine is typically chosen. The outline of the control room is equivalent to a stream tube that overflows the whole fluid-flow machine. Thus, in theory, no perpendicular velocity components exist on the shell surface of the stream tube. That means that for the calculation of the mass balance, only inlet and outlet planes have to be taken into account. Subsequently, for relevant locations within the
Developed algorithm
The aforementioned fundamentals are combined in an iteratively working algorithm that accesses the preliminary and parallel processed work introduced in Kluck, 2016, Kluck et al., in preparation, and Urban (2008). As already mentioned, the aim of this paper, apart from the theoretical fundamentals, is the development and description of the algorithm with references to relevant preliminary or parallel processed work. For any further details about these, please refer to the appropriate references
Selected design parameter
The algorithm, as described in Chapter 3, is utilised for an exemplarily specified operating point. With respect to the validating experimental investigations to be performed later, the initial design parameters are specified in accordance with the provided test bench. The experimental investigations to validate the described procedure and their analysis are not discussed in detail here, as pointed out earlier. Only a brief overview is given in see Chapter 5. For a detailed discussion of the
Validation
Although the focus of this paper lies on both the formulation of the underlying theoretical fundamentals and the developed algorithm, the validation of the method is important as well. Thus, a brief overview of the measurement results is presented in the following, without much details. For further details and a particularised discussion, please refer to Reviol et al. (2018) and Wang et al. (2018).
The propeller designed in this chapter and finally presented in Fig. 12 is experimentally
Conclusion
In this paper, a comprehensive design procedure to develop a propeller mixer to agitate non-Newtonian fluid flow is presented. The procedure is based on analytical fundamentals; hence, the whole design process is transparent.
In principle, the design process is very similar to the commonly known blade element momentum theory. But to adopt this procedure for non-Newtonian fluid flow, some different tasks have to be undertaken. First, the identification of suitable hydrofoils and their profile
Acknowledgements
The authors would like to thank the ’Rhineland-Palatinate of innovation’ foundation (Stiftung ’Rheinland-Pfalz für Innovation’) of Germany for supporting this project.
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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.
Many different procedures to design mixers have been investigated in research literature. The methods are either typically based on empiricism or already available mixers are scaled to adjust them to different but similar operating conditions, as considered in the original design process. For the most part the power characteristics of such a design of mixer has been proven through empirical methods, or is estimated within the mentioned scale-up methodology. The estimation of the power consumption has been shown as especially prone to error. The practice of estimation is associated with uncertainties, due to the determination of the power consumption in a late step of the design technique, or just simply has a low reliability. In this paper, a method will be derived in order to predict the full power characteristic without performing any experimental investigations within the design process. A new blade element momentum theory based design method will be taken and enhanced to calculate the power consumption by actually inverting the entire design procedure.
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FAQs
What are propeller mixers used for mixing? ›
A propeller mixer is used for mixing liquids and dissolving solids within liquids.
What is the construction of propeller agitator? ›Propeller agitator is a specialized of various types of substances. It consists of three basic components which are the shaft, blade and the vessel. In the construction, mild steel was chosen due to it’s inherent properties.
What is a propeller mixer? ›Propeller mixers are used for mixing liquids in a wide range of viscosities. They are suitable for the formation of low-viscosity emulsions, for dissolving applications and for liquid-phase reactions.
At what speed does the propeller of propeller mixer rotate? ›They rotate at high speed (from 500 to several thousand r.p.m). The propellers are not very effective if they are mounted on vertical axes located in the center of the mixing tank. Both the radial and longitudinal components generally contribute to the mixing, but not always the rotary component.
What is the flow pattern of impeller mixers? ›The most common flow patterns in mixing are axial (down and up) and radial (side to side) flow. These flow patterns also describe the generic classes of impellers: axial and radial.
What is the flow pattern of propeller agitator? ›Agitator impellers can be classified based on the flow pattern they produce. These flow patterns are axial, radial, and tangential flows.
What are the 4 types of materials used in propeller construction? ›The materials used for making marine propellers are an alloy of aluminium and stainless steel. Other popular materials used are alloys of nickel, aluminium and bronze which are 10~15 % lighter than other materials and have higher strength.
What are the three types of propeller systems? ›There are three basic types of an aircraft propeller, each with its own variations – the fixed pitch propeller, constant speed propeller or the ground adjustable propeller.
What is the maximum speed of propeller mixer in rpm? ›The high-torque electric motors allow for propeller speed ranges from 300-400 rpm, depending on the size.
What happens when a propeller spins too fast? ›Just like wings, propellers generate force using differences in air pressure and angle of attack. But, unlike wings, propellers have different angles of attack along their blades. Because of this, spinning a propeller too fast can cause it to generate more drag than lift.
What makes a prop faster? ›
Change Your Propeller
If you are running an aluminum prop, changing to even a basic stainless steel prop will usually improve top speed. Because stainless steel is stronger than aluminum, the blades on a stainless prop can be thinner, which reduces drag in the water.
Advantages of the propeller agitator at a glance:
Efficient stirring due to high circulation. Low power input. Low maintenance and suitable for continuous operation. Uncomplicated & easy cleaning.
- Airfoil. Generally most efficient because it produces the maximum pumping with the lowest shear. ...
- Pitch Blade. Ideal for viscous mixtures and for applications requiring a combination of pumping and shearing. ...
- Radial Blade. ...
- Marine-Type Propellers.
The SpeedMixer works by using Dual Asymmetric Centrifuge (DAC), simultaneously spinning the cup/material in 2 different directions. The opposing forces cause the material to quickly mix and remove bubbles.
What are the three 3 main attachments of mixers? ›Every mixer comes with a flat beater, dough hook, and wire whip.
What are the three main functions of a mixer? ›Mixers help automate the repetitive tasks of stirring, whisking or beating. When the beaters are replaced by a dough hook, a mixer may also be used to knead.
Which impeller is best for mixing? ›Radial flow impellers are efficient in applications like gas/liquid mixing and dispersion.
What is the difference between an impeller and a propeller mixer? ›Impellers are often contained within a pump housing and use vanes to draw in fluid, while propellers use blades to push liquid away. In centrifugal pumps, impellers are often used to create pressure to move slurries through pump housing.
Which impeller is used in liquid agitation? ›Propellers: The marine propeller is a relatively small, high speed impeller widely used in low viscosity liquid systems.
What are the different types of agitation? ›Agitated behaviors can be divided into physical and verbal, aggressive and non-aggressive.
What are the different types of flow in impellers? ›
Impeller types can be categorized into two basic categories: axial flow, and radial flow.
What is the difference between a 4 way agitator and impeller? ›Washing machines with agitators use a central post that twists back and forth, rubbing against clothes to help break apart stains. In contrast, washing machines with impellers use a low-profile cone or disc that spins/rotates to rub clothes against each other to get them clean.
What is the most efficient type of propeller design in use today? ›Large propeller designs can become less effective operating at the axial velocity. The most efficient designs are those which maintain a pitch to diameter ratio of 1:1.
What is the most efficient type of propeller? ›Theoretically the most efficient propeller is a large diameter, slowly turning single blade propeller. Here, think the Osprey or helicopters. In both cases, large diameter, slowly turn- ing, compared to typical fixed wing aircraft, propellers are used.
What are the different types of propeller cavitation? ›The cavitation patterns which occur on marine propellers are usually referred to as comprising one or more of the following types for model propellers: sheet, bubble, cloud, tip vortex or hub vortex cavitation.
What are the two types of propeller configuration? ›Aircraft have had two types of propeller configurations: pusher propellers and tractor propellers.
What are the 4 propeller effects? ›Torque, spiraling slipstream, P-factor, and gyroscopic precession are commonly referred to as the four left-turning tendencies, because they cause either the nose of the aircraft or the wings to rotate left. Although they create the same result, each force works in a unique way.
What are the two main methods of propeller ice control system? ›Aircraft and engine ice protection systems are generally of two designs: either they remove ice after it has formed, or they prevent it from forming.
In what position is the motor mounted in most of the mixers? ›A horizontal foot mounted motor is fitted above the main mixer frame on a steel mounting plate which allows adjustment for correct belt tensioning.
What is the best propeller RPM? ›For example, Lycoming advises that, when fixed pitch propellers are used with their engines, the static rpm should be 2300 plus or minus 50 rpm for all engines rated at 2700 rpm.
What is the fastest prop speed? ›
Martindale's breaking 620 mph (1,000 km/h) (Mach 0.92) in the same aircraft in April 1944. It should however, be noted that while not FAI certified, the results from Martindale's flight are more than claims. The Royal Aircraft Establishment was a scientific body with the capability to record such events.
What causes propeller failure? ›Causes. Propeller blade separation can almost always be attributed to a combination of significant centrifugal force due to the high rotational speed of the propeller and one or more of: Material fatigue. Cracks.
What happens if a propeller is not twisted? ›The twist is necessary to maintain a more or less constant angle of attack along the length of the blade. Like a wing, propeller performance is degraded when it is not at its optimum angle of attack.
What happens if your propeller is too big? ›Overpitched and oversized propellers can cause an engine to work harder and hotter than it should and not allow it to reach optimal cruising rpm, resulting in poor performance and decreased engine life.
What is the strongest force acting on a propeller? ›Centrifugal force is a physical force that tends to throw the rotating propeller blades away from the hub. This is the most dominant force on the propeller.
Which factor has the greatest effect on Propspeed? ›RPM. One of the most important factors affecting propeller efficiency is the revolutions per minute (RPM). RPM represents the number of full rotations a propeller makes within a minute.
What increases propeller efficiency? ›Generally, propulsive efficiency can be increased by installing propellers with large diameters. However, the diameter behind the ship is limited by the draught of the vessel. Optimization of propeller design is done to meet the balance.
Why propellers are used in mixing? ›Whenever high mixing capacity is needed, propellers are used. Their maximum viscosity can be 2 Pa. s or less, making them very effective for mixing liquids.
What is the use of impeller mixer? ›Impeller mixers are simple but versatile equipment used widely in the process industries to mix a liquid with another liquid, a gas or solids using forced convection (flow). A variety of impeller designs is available but their classification is not unique.
What is the function of impeller in mixer? ›The purpose of an impeller is to deliver the necessary flow inside the mixing vessel. It does this by transferring energy from the motor to the impeller head and into the liquid, creating a specific flow pattern to achieve optimum consistency of the product.
What is the difference between impeller and propeller mixer? ›
Impellers are often contained within a pump housing and use vanes to draw in fluid, while propellers use blades to push liquid away. In centrifugal pumps, impellers are often used to create pressure to move slurries through pump housing.
What are the three types of materials used on propellers? ›Propellers for commercial boats are typically made from either a stainless steel alloy, a nickel-aluminum-bronze alloy, or a manganese bronze alloy. The costliest material, stainless steel, is very easily repaired and stands up to quite a bit of abuse. The hardest alloy is nickel-aluminum-bronze.
What are propellers for liquid mixing? ›Propeller is a device which is used for liquid-liquid mixing. It consists of a propeller rod attached to the propeller blades, Propeller blades used are generally like blades of a fan and are called marine types. The blades are arranged in different ways to force the liquid in different directions.
What are the pros and cons of agitator vs impeller? ›| Cleaning Features | Agitator Washing Machine | Impeller Washing Machine |
|---|---|---|
| Wash Cycle Speed? | Faster | Slower |
| More Space for Large and Bulky Loads? | Not typically, unless you choose a high capacity machine | Yes |
| Energy Efficiency? | Good | Best |
A washing machine with an impeller uses less motion and water than a washer with an agitator. Designed so laundry has more room to move, it drives clothes from the outer rim of the wash basket to the center, using a small amount of water to optimize the friction. This is what helps deliver a gentle, yet thorough clean.
What is the difference between agitate and impeller? ›Washing machines with agitators use a central post that twists back and forth, rubbing against clothes to help break apart stains. In contrast, washing machines with impellers use a low-profile cone or disc that spins/rotates to rub clothes against each other to get them clean.
How does impeller affect flow rate? ›As the impeller diameter decreases, added clearance between the impeller and the fixed pump casing increases internal flow recirculation, causes head loss, and lowers pumping efficiency.
Which type of impeller is most efficient? ›A closed impeller is the most efficient form and is ideal for handling clean liquids with low viscosity. Consisting of two plates (known as shrouds) either side of the impeller vanes and a boss, extending from the front shroud into the pump suction to guide the liquid into the impeller eye.
Which type of propeller is most efficient? ›Theoretically the most efficient propeller is a large diameter, slowly turning single blade propeller. Here, think the Osprey or helicopters. In both cases, large diameter, slowly turn- ing, compared to typical fixed wing aircraft, propellers are used.
Which casting method is best for impeller? ›In addtion, stainless steel casting can customize impellers in different specifications and sizes according to different uses. So, it is undoubtedly a good choice to produce impeller by stainless steel casting.