Optimizing the
energy consumption
of an agitator
transporting
wood chips
with the help of EDEM
C.P. Molhoek
Optimizing the
energy consumption
of an agitator
transporting
wood chips
with the help of EDEM
by
C.P. Molhoek
to obtain the degree of Master of Science in Mechanical Engineering at the Delft University of Technology
Student number: 1529250
Project duration: October 1, 2015 – December 19, 2015
Research committee: Dr. ir. D.L. Schott, TU Delft, supervisor MSc. M. Rackl, TU München, supervisor Prof. Dr. Ing. W. A. Günthner, TU München
Summary
Following the increasing demand for renewable energy, the demand for biomass has been rising over the years. This growth will continue as agreements are made in the EU and worldwide to decrease the use of non-renewable energy sources. From the different kind of biomasses, especially wood chips are used on a large scale to create energy. These wood chips are handled with the same equipment as coals and not much is known about the interaction of these wood chips and the handling equipment. Industry encounters jamming of the equipment, when working with wood chips in hoppers and therefore an agitator is put in place to prevent the wood chips from bridging and ensuring a continues flow of the material.
As the agitator uses extra energy, which makes the system less energy efficient, this research aims to decrease the power consumption of the agitator. The factors that are investigated and have influ-ence on the energy use of the agitator are: the angle of the blades relative to the agitator, the number of blades on the agitator, the speed of the agitator and the design of the blades.
To investigate these four factors on three different levels 81 experiments are needed. With the use of Design of Experiments this amount of experiments can be decreased from 81 to 27, by making use of a Box-Behnken design. This experimental plan was made with the software of R.
The experiments were done in a simulation environment with a Discreet Element Method program; EDEM2.7. The responses to be extracted form EDEM2.7 are: the torque of the agitator, from which the used energy can be deduced, the mass flow of the material to see if bridging takes place and to check on the performance and the amount of wood chips left in the bin, to make sure the bin is emptied. The results from EDEM were processed with Excel2010, MatlabR2013b and R. To verify the results, they are compared with the results of former research.
The energy consumption of an agitator transporting wood chips can be decreased by lowering the speed of the agitator and by creating a smaller surface of the blades, where the speed is the most influential. A smaller surface can be created by adjusting the angle of the blades, by adjusting the amount of blades and by the design of the blades. In non of the experiments bridging took place. The mass flow also was most influenced by the speed of the agitator, but reacted differently than the energy consumption on the other factors. A remarkable finding was that rounding the corners of the blades resulted in a lower mass flow. This is probably the result of the wood chips properties. All experiments were said to be efficient as less than 2% of the wood chips was left in the hopper. The found results were compared with former research and as the results matched the experiments are verified.
The design of the blades can be further investigated, not only different shapes, but also in terms of wear and forces acting upon the blades. Further it would be interesting to see the results when using a Central Composite Design instead of a Box-Behnken design for the experimental plan.
Contents
Summary iii
1 Introduction 1
1.1 Background: Increasing use of biomass . . . 1
1.2 Previous research . . . 1
1.3 Research questions . . . 2
2 Theory Design of Experiments (DoE) 5 2.1 Design of Experiments . . . 5
2.1.1 Mathematical models for DoE . . . 5
2.1.2 Factors and levels . . . 6
2.1.3 Full and fractional factorial designs . . . 6
2.1.4 Central Composite Design (CCD) and Box-Behnken Design (BBD) . . . 7
3 Methods 9 3.1 Application of DoE in this research . . . 9
3.1.1 Factors, levels and responses of this research . . . 9
3.1.2 The experimental design for this research . . . 10
3.2 Discrete Element Method (DEM) for the simulation of the experiments . . . 11
3.2.1 The material model in EDEM . . . 11
3.2.2 The geometry model in EDEM . . . 11
3.2.3 The simulation characteristics in EDEM . . . 14
3.3 Measurements with EDEM. . . 15
3.4 R . . . 15
4 Results 17 4.1 Convert EDEM data for Design of Experiments. . . 17
4.2 Energy usage of the agitator . . . 17
4.3 Mass flow of the wood chips . . . 19
4.4 Effectiveness of the different agitators . . . 21
4.4.1 Percentage left over of wood chips in the bin . . . 21
4.4.2 Bridging of the wood chips . . . 21
4.5 Influence of the individual factors on the responses . . . 21
4.6 Verification of the results compared to former research . . . 23
5 Discussion 29 5.1 Discussion of the factors influencing the energy use of the agitator . . . 29
5.2 Discussion of the factors influencing the mass flow of the wood chips . . . 30
5.3 Discussion of the effectiveness of the agitators . . . 30
5.4 Discussion about the influence of the individual factors . . . 30
5.5 Other points of interest for the discussion . . . 31
6 Conclusion 33 6.1 Conclusion . . . 33
6.2 Recommendations . . . 33
A Data for the Box Behnken Design in R 35
B R Analysis Data 37
C Response Surface Graphs 41
List of Figures 45
vi Contents
List of Tables 47
1
Introduction
This chapter will cover a lot of background information, both on the research as on the theory that will be used for the research. Section 1.1 shows the relevance of this research in a broader perspective. The increasing use of biomass worldwide, and especially in Europe, along with mall functioning of equipment support the field of research of biomass handling. From practical experience questions about the handling equipment for a special kind of biomass, the wood chips, arise. Section 1.2 gives the consequential research questions that will be covered in this research.
1.1. Background: Increasing use of biomass
Due to the 2020 targets of the EU to increase the use of renewable energy to 20% of the total amount of used energy, the demand for biomass increased over the past years. It is expected that this trend continues. From the used biomass the largest part consists of wood chips [13]. The European Envi-ronment Agency predicts a growth of the use of biomass of 6% per year until 2020 [15]. As the use of biomass for energy purposes gets more common, the handling equipment should adapt to this trend.
Problems encountered while handling biomass An ideal feeding system provides smooth and continuous feeding and allows for accurate control of the feed rate [4]. Unfortunately this is difficult to achieve when handling particulate bulk flows and even more difficult when working with biomass. According to industry biomass feeding systems have an 80% chance on significant problems [5]. Due to uncommon properties of particulate solid biomasses, both at particle and at bulk level, the flow reliability and control of these materials is even more unpredictable than that of other granular materials traditionally used by industry [2]. Since feeding systems for biomasses have been developed in an ’in the moment’ manner, often the result of an adjustment to existing equipment for traditional fuels, only a limited amount of information has been published on their design and operation. Systems are typically custom-designed for the specific application in mind [4]. Common design methods for storage units to ensure flow, based on Jenike analysis, have not yet been proven to work for biomass bulk solids [2]. According to Dai [5] the main problems for hopper flow, especially for biomasses, are bridging (i.e. arching) and formation of ratholes, stable voids that develop through a mass of static bulk material as the internal flow channel runs clear. Most hoppers in industrial applications are conical or wedge-shaped. The outlet should at least be twice the maximum particle dimension to prevent blockage. Especially for high-strength particles like wood chips, as they have the tendency to interlock and form bridges. To have a good discharge some hoppers are fitted with aids such as vibrators, air bladders, air injection and mechanical agitators. Passive flow aids are preferred over the active aids, like vibrators and agitators [5]. These active aids require more maintenance, add more uncertainties in promoting flow and cost more energy, due to extra moving parts in the system.
1.2. Previous research
At the Technical University München at the Institute for Materials Handling, Materials Flow and Logistics an experimental set-up of a hopper with agitator and a screw conveyor is used for research purposes.
2 1. Introduction
This set-up was firstly used to investigate the influence of different grades of wood chips on the feeding performance [11]. The influence of three different wood chip grades and two blends on a biomass feeding system was investigated. Concluded was that the different wood chip qualities could influence the driving torque of the screw conveyor, the mass flow and the energy consumption considerably. The next step was to create a computer model of this set-up with the help of EDEM1, to be able to perform more experiments[16]. The simulation model of the set-up is displayed in figure 1.1. The red square indicates the factory where the wood chips are realised, the screw conveyor is dark blue and the agitator is the lighter blue. The low-quality wood chips were used [11] for the further research with the simulation model. For the simulations a material model of these wood chips had to be made, which was done in previous research [16]. This research also started the process of optimizing the set-up. Experiments with the agitator in different positions were conducted. At certain positions of the agitator the torque, and thus the energy use, was lower, but also the mass flow was lower at these positions. The agitator was moved horizontally, vertically and in both directions. The direction of rotation was investigated too, but not very extensive. Here the torque and mass flow showed the same pattern. As these factors are already investigated, they will not be included in this research.
Figure 1.1: The set-up configuration of the hopper, agitator and screw conveyor in EDEM
1.3. Research questions
As can be read in section 1.1 the addition of the agitator is needed to prevent the system from jam-ming. This agitator makes the system use more energy. Therefore the main research question for this research is:
• How can the energy consumption of an agitator transporting wood chips be decreased without
bridging of the wood chips?
Sub-questions To be able to answer the main question sub-questions will be made. This starts with an analysis of the main question. The energy consumption of the agitator will be defined as the power needed for the agitator to transport a certain amount of wood chips. As is commonly known:
𝑃 = 𝑇 × 𝜔 (1.1)
With P is mechanical power in Watt, T is the torque in Nm and �is the rotational speed in rad/s. When lowering the torque or lowering the rotational speed the power needed will decrease. The speed is one factor that influences the energy use. The torque that is needed can be influenced in
1.3. Research questions 3
several ways. The torque can be calculated as follows:
𝑇 = 𝐹 × 𝑟 (1.2)
With F is the force in N and the arm r in meters. The force or the arm can be adjusted. The arm is defined as the length of the blades of the agitator. The force that acts on the blades depends on several factors.
The material As described in section 1.2 the material properties of the material that is mixed have great influence on the energy consumption. This is the result of the resistance between the material and the agitator. This also implies that the material of the agitator itself will have influence. The material of the agitator is steel, the next chapter covers the properties. Steel is commonly used and also used in the former experiments. The wood chips will have the same properties as in the previous research [16]. Former research [11] proves that the material influences the torque, this factor will not be changed in this research.
Positioning of the agitator The position of the agitator can influence the mass flow and the torque as can be read in Rackl [16]. The conclusion is that the torque is lower at some positions, but the mass flow also is lower in those cases. This decreases the effect of the different positions. As all positions are already investigated, this factor will not be used.
The angle of the blades A factor that can influence the energy consumption is the position of the blades on the agitator. The angle influences the size of the surface that the force works on and therefore enlarges the force.
Number of blades The goal is to minimize the power consumption of the agitator without causing bridging. The less blades are used, the lower the total friction, as the surface of the blades is smaller, on the agitator and thus the less energy needed. But the number of blades needed to prevent the material from bridging in this set-up is unknown.
The design of the blades As Siraj [14] concludes the shape of the blades has influence on the fric-tion, which influences the force and thus energy consumption.
The four sub-questions
From the different factors described above the following sub-questions are derived:
1. What is the influence of the rotation speed of the agitator on the energy use of the agitator? 2. What is the influence of the angle of the blades on the energy use of the agitator?
3. What is the influence of the number of blades on the energy use of the agitator? 4. What is the influence on the design of the blades on the energy use of the agitator?
2
Theory Design of Experiments (DoE)
This chapter will give a theoretical background on design of experiments, or DoE. This mathematical method is used in the research to develop an experimental plan.
2.1. Design of Experiments
The definition of DoE by Antony [1] is as follows: ”DoE refers to the process of planning, designing
and analysing the experiment so that valid and objective conclusions can be drawn effectively and efficiently.” According to Wagner [17]: ”DoE is a technique or procedure to generate the required infor-mation with the minimum amount of experimentation.” Both definitions state that DoE is used to make
experiments more effective and even more efficient. DoE arises from the statistical methodologies to analyse data and is thus a mathematical tool. It is used for solving any technical problem when one would want to fully understand the response to different process or product variables that can be changed or controlled during the experimentation [17]. DoE uses statistical methods to greatly reduce the amount of needed experiments, without loosing their accuracy.
2.1.1. Mathematical models for DoE
The Response Surface Methodology (RSM) is used as a tool to investigate the effect of multiple fac-tors on the (multiple) response(s). In this way RSM can be used as an optimization tool [3]. To obtain response surfaces the full and fractional factorial designs and the more complex central composite, Box–Behnken, Doehlert and mixture designs are the most commonly used [8]. These are all experi-mental designs, with which mathematically and statistically the effects of the factors are determined.
The simplest mathematical model which can be used in RSM is a first order linear model [3][8][6]:
𝑦 = 𝛽 + ∑ 𝛽 𝑥 + 𝜖, (2.1)
This model shows no curvature and does not show the interaction effects of the factors. The second order linear model does show these aspects [3][8][6]:
𝑦 = 𝛽 + ∑ 𝛽 𝑥 + ∑ 𝛽 𝑥 𝑥 + 𝜖 (2.2)
To also be able to find the critical points, the maximum and minimum values of the factors, a quadratic model is used [3][8][6]:
𝑦 = 𝛽 + ∑ 𝛽 𝑥 + ∑ 𝛽 𝑥 + ∑ 𝛽 𝑥 𝑥 + 𝜖 (2.3)
6 2. Theory Design of Experiments (DoE)
Figure 2.1 shows graphs of the three mathematical models for the same data set. The first or-der linear model is shown in a, b shows the second oror-der model and c the quadratic model. These graphs show the difference and need for different models. To be able to find a maximum or minimum a quadratic model is necessary.
(a) (b) (c)
Figure 2.1: The first order model (a), the second order model (b) and the quadratic model (c), for each model the same dataset is used.
2.1.2. Factors and levels
When using DoE first the independent and dependent variables have to be defined. They are ad-dressed to as the factors and the responses respectively[7]. DoE finds the effects of the factors on the responses, depending on which method of DoE is used also second order effects, for example, can be found. The factors can be divided in quantitative and qualitative factors. The quantitative factors are factors as temperature, time, concentration etc.. The values these factors can hold are called levels. For example, when using three different temperatures in your experiment the factor temperature has three levels. Qualitative factors are discrete [17] [1]. They can represent the used material A and B, a type of catalyst etc.. The levels of the qualitative factors can also be called versions.
2.1.3. Full and fractional factorial designs
In general, there are three ways to obtain experimental data: one-factor-at-a-time, full factorial, and fractional factorial [12]. To investigate the influence of a factor on the response(s), experiments, in which that factor is changed, are performed. These experiments will be repeated for every level of the factor several times to mitigate the error. When investigating more factors, the experiments have to be repeated again but with changing other factors. This is the one-factor-at-a-time method and this method is mostly used. This method not only takes up a lot of time, but it also does not show if the factors may influence each other.
The advantage of factorial designs is that they also spot the interactions between the factors. In a factorial design the influences of all experimental variables, factors, and interaction effects on the response or responses are investigated. If the combinations of𝑘 factors are investigated at two levels, a full factorial design will consist of2 experiments [10]. When 𝑘 = 3, 2 or 8 experiments have to be done, when𝑘 = 5, 32 experiments are needed. With the amount of factors of 𝑘 = 10 a full factorial design with two levels already needs1024 experiments. If the amount of levels is raised by one, to a 3-level system, the amount of experiments is defined by3 . Which means that with 3 factors already 3 = 27, or with 5 factors 3 = 243 and with 10 factors 3 = 59049 experiments are needed. Needless to say that the amount of needed experiments increases exponential resulting in to much experiments. A full factorial experiment is practical if only a few factors (say, fewer than five) are being investigated. Beyond that, this design becomes time consuming and expensive [12].
As the name already suggests, fractional factorial designs only use a fraction of the experiments of a full fractional design. A full factorial design is the ideal design, through which information can be
2.1. Design of Experiments 7
obtained on all main effects and interactions. But because of the prohibitive number of the experiments, such designs are not practical to run [12]. Fractional factorial designs are used to determine which main effects are important and the effect of some interactions, while minimizing the number of experiments. Fractional factorials are normally one of the first steps in an evaluation procedure. The important variables can be identified and then evaluated in more detail [17].
2.1.4. Central Composite Design (CCD) and Box-Behnken Design (BBD)
In section 2.1.1 the quadratic models the Central Composite, Box–Behnken, Doehlert and mixture designs are mentioned. For this research the Central Composite and the Box-Behnken Design are further investigated as these two designs are mostly used for this kind of experiments in literature. These designs are response surface designs, just as the three-level full factorial designs, but they are more efficient. They are a special type of fractional factorial designs. Figure 2.1.4 shows a graphical representation of the three factor Central Composite and Box-Behnken design. It can be seen that the points of the CCD are at the corners of the square and in the middle of the plane. The points in the middle of the plane are at distance α from the center point. α is a value between 1 and√𝑘, with k the number of factors [8]. When α is 1, the CCD is a three-level design, otherwise the CCD is a five-level design. The points in the BBD are at the center of the ribs. This means they all have the same distance to the center point and there are no extremes. It also indicates that all BBD are three-level designs [9].
(a) Central Composite Design (b) Box-Behnken Design Figure 2.2: Design for three factors with three levels [3] [7]
Both CCD and the BBD are more efficient than the full factorial designs and the BBD is slightly more efficient than the CCD. Its efficiency rises with more factors. With three factors a BBD needs 12 experiments, where the CCD already needs 14 runs, both need a not yet defined amount of center-runs [8]. Another difference is that the BBD does not have combinations for which all factors are at their highest or lowest levels, the corner points of the square. Especially in experimental design it can be an advantage not to include these extreme conditions [7], as they can cause a mall functioning experiment. Sometimes it can be physical impossible to experiment with all the factors at their extreme values. Table 2.1 shows the scheme of a Box-Behnken and a Central Composite design with four factors. For the Box-Behnken design at least one of the factors is 0, which means that an extreme combination is never the case. The CCD shows that the extremes are included. The CCD also needs slightly more runs. Because CCD uses the distance α, it can occur that the points will lay out of bounds. As an example; A factor can vary between 5 and 15, it can be lower than 5, although this is not preferable, but it cannot be higher than 15. When using a CCD with a large α this number can exceed the max of 15 in the CCD and can give an optimal value of 20, while in the physical experiments this is not possible. This is also something to take into account when choosing a design and, when needed, an α.
8 2. Theory Design of Experiments (DoE)
Box-Behnken Design Central Composite Design 1 -1 -1 0 -1 -1 -1 2 1 -1 0 1 -1 -1 3 -1 1 0 -1 1 -1 4 1 1 0 1 1 -1 5 -1 0 -1 -1 -1 1 6 1 0 -1 1 -1 1 7 -1 0 1 -1 1 1 8 1 0 1 1 1 1 9 0 -1 -1 -α 0 0 10 0 1 -1 α 0 0 11 0 -1 1 0 -α 0 12 0 1 1 0 α 0 13 0 0 0 0 0 -α 14 0 0 0 0 0 α 15 0 0 0 0 0 0 16 0 0 0 17 0 0 0
3
Methods
For this research the experimental set-up used in previous researches could be modified to obtain the answers to the research questions. As this will be a time consuming and expensive project, it is chosen to use simulation. Simulation will be cheaper, faster and easier to modify. Although, the outcomes of the simulations should always be verified by real experiments. This research uses EDEM1, a discrete
element method program that is designed to cope with solid particulate materials. The experimental plan and the analysis of a large part of the data will be done by the Design of Experiments method. A mathematical and statistical method that helps designing and analysing experiments. The analysis, by the rules of Design of Experiments, will be done with the help of R2and Matlab3. To use R for Design of Experiments the package RcmdrPlugin.DoE4is used.
3.1. Application of DoE in this research
In chapter 2 the theory of Design of Experiments is explained. This section tells how DoE is used in this research.
3.1.1. Factors, levels and responses of this research
Before the right design for the experiments of this research can be chosen, first the factors and re-sponses have to be defined. From the research questions stated in section 1.2 the factors can be determined. Only the levels have yet to be thought of. The levels are based on the original config-uration of the set-up as seen in previous research [11] [16]. The agitator in the original set-up had 7 rectangular blades placed in an 45° angle on a square beam. The agitator had a rotational speed of 1,339 rad/s. When using 2 levels only linear effects can be found. To also include non-linear effects at least 3 levels are needed. To minimize the amount of experiments 3 levels should be sufficient to show non-linear effects and enough to be able to answer the questions of this research. Table 3.1 shows the factors and their levels.
Factor level -1 level 0 level 1
Angle of blades (°) 0 45 90
Number of blades 3 5 7
Rotation Speed𝜔(𝑟𝑎𝑑/𝑠) 0,5 1 1,5
Design of blades 3 1 2
Table 3.1: Factors and their levels
Of the defined factors 3 are quantitative factors: the angles of the blades, the number of the blades and the rotation speed. The other factor, the design of the blades, is a qualitative factor.
1EDEM 2.7 , http://www.dem-solutions.com/.
2R version 3.2.2 was used. R is a free software environment for statistical computing and graphics, https://www.r-project.org/. 3MATLAB version R2013b was used, www.mathworks.com/products/matlab/.
4RcmdrPlugin.DoE version 0.12-3 was used. It is an R Commander Plugin for (industrial) Design of Experiments.
10 3. Methods
There will be 3 responses to check. 1. Energy use of the agitator 2. Mass flow of the wood chips
3. Amount of wood chips left in the bin at the end of the experiment
The first is the already mentioned energy use of the agitator. The second and third response will evaluate the efficiency and effectiveness of the factors. One of these responses is the mass flow; the higher the flow, the faster the bin will be empty and the larger its efficiency. This response is also important so the research can be compared with previous ones. When checking the percentage of wood chips that is left in the bin when the system has got a steady state, it can be seen how effective the system is. The steady state of the system is when the mass flow out of the system is 0 kg/s. The system is not transporting any wood chips any more at this state. A conclusion when combining these two responses could for example be, that an agitator with 3 blades is more energy efficient, but leaves more wood chips in the system and is thus not so effective.
3.1.2. The experimental design for this research
As can be read in chapter 2, there will be two possible experimental designs: the Central Composite design and the Box-Behnken design. Here is chosen for a Box-Behnken design. The Central Compos-ite design with an αof 1 was also possible. Both designs would need 27 experiments when using four factors. According to Ferreira [8] this design can be used when experimenting with both quantitative and qualitative factors. Table 3.2 shows the values the factors will have in which experiments, the table is randomized. In appendix A the values that belong with each experiment can be seen.
Exp. nr. Angle Blade Speed Design Angle [°] Blades [#] Speed [rad/s] Design
1 0 0 1 1 45 5 1,5 2 2 0 -1 -1 0 45 3 0,5 1 3 -1 0 0 1 0 5 1 2 4 1 0 0 1 90 5 1 2 5 0 -1 0 -1 45 3 1 3 6 0 0 0 0 45 5 1 1 7 0 1 0 1 45 7 1 2 8 1 -1 0 0 90 3 1 1 9 1 0 -1 0 90 5 0,5 1 10 0 -1 0 1 45 3 1 2 11 0 1 1 0 45 7 1,5 1 12 -1 0 -1 0 0 5 0,5 1 13 -1 1 0 0 0 7 1 1 14 0 0 1 -1 45 5 1,5 3 15 1 0 0 -1 90 5 1 3 16 -1 0 0 -1 0 5 1 3 17 0 1 -1 0 45 7 0,5 1 18 0 -1 1 0 45 3 1,5 1 19 -1 -1 0 0 0 3 1 1 20 0 0 0 0 45 5 1 1 21 0 0 0 0 45 5 1 1 22 0 1 0 -1 45 7 1 3 23 -1 0 1 0 0 5 1,5 1 24 1 0 1 0 90 5 1,5 1 25 1 1 0 0 90 7 1 1 26 0 0 -1 -1 45 5 0,5 3 27 0 0 -1 1 45 5 0,5 2
3.2. Discrete Element Method (DEM) for the simulation of the experiments 11
3.2. Discrete Element Method (DEM) for the simulation of the
ex-periments
EDEM uses Discrete Element Method (DEM) software for bulk material flow simulation. EDEM is used for the ‘virtual testing’ of equipment that handles or processes bulk materials in the mining, equipment manufacturing and process industries.
3.2.1. The material model in EDEM
In this research the same wood chips as used in the previous researches, as can be seen in section 1.2, will be used. This will make the research comparable and time is saved on making a good material model. The wood chips are modelled as spheres, to save computation time. The material of the experimental set-up is steel, so the simulation set-up will be modelled as steel. Table 3.3 shows all needed material properties. For the properties of steel the standard values, also used by EDEM, are used. The properties of the wood chips are copied from previous research [16].
Property Value
Wood chip diameter 𝐷 29, 3𝑚𝑚
Poisson’s ratio wood chips 𝜈 0, 3
Poisson’s ratio steel 𝜈 0, 3
Shear modulus wood chips 𝐺 3, 85 ⋅ 10 𝑃𝑎
Shear modulus steel 𝐺 7 ⋅ 10 𝑃𝑎
Density wood chips 𝜌 496𝑘𝑔/𝑚
Density steel 𝜌 7900𝑘𝑔/𝑚
Coefficient of restitution wood-wood 𝑒 0, 5
Coefficient of restitution wood-steel 𝑒 0, 3 Coefficient of static friction wood-wood 𝜇 0, 874 Coefficient of static friction wood-steel 𝜇 0, 691 Coefficient of rolling friction wood-wood 𝜇 0, 0264 Coefficient of rolling friction wood-steel 𝜇 0, 0143
Gravity 𝑔 9, 81𝑚/𝑠
Both material interaction models Hertz-Mindlin (no slip)
Table 3.3: All material values used in the simulation
3.2.2. The geometry model in EDEM
In figure 3.1 the dimensions of the geometry are shown. All parts of the geometry are made with AutoCAD5 and than imported into EDEM. The screw driver consists of two parts, as can be seen in
figure 3.1. The first part𝐿 the pitch width is 160𝑚𝑚, the pitch width of the second part 𝐿 is 140𝑚𝑚. In the front view of the figure the letters A and B stand for the agitator and screw driver respectively.
12 3. Methods
(a) Side view (b) Front view Figure 3.1: Dimensions of the experimental set-up and the simulation model [11]
As seen in the research questions some adjustments to the agitator will be made. In figure 3.2.2 different agitators are shown. The angle of the blades, the number of blades and the design of the blades are varied. How the different agitators, that will be used in the experiments, exactly will look like, will be known after the experimental plan is designed. This plan will be made in the following section and will give the combinations to be experimented with. The base of the agitator is a square beam of40𝑚𝑚 by 40𝑚𝑚 and 800𝑚𝑚 long.
(a) Angle 0°, 7 blades, design 1 (b) Angle 45°, 5 blades, design 2
(c) Angle 90°, 3 blades, design 1 (d) Angle 45°, 5 blades, design 3 Figure 3.2: Different possible designs of the agitator
Design of the blades Three different blade models are needed, as the factor has to be varied on three levels. The first design will be the existing configuration. The second design will be based on Siraj [14], where is stated that a blade design with rounded corners uses less energy. As it is assumed that the surface of the blades has a large influence on the energy consumption, the third design will be
3.2. Discrete Element Method (DEM) for the simulation of the experiments 13
designed as a rod, with a very small surface. All blade designs will have the same length of 100𝑚𝑚 and the same width of8𝑚𝑚.
100 mm 50 mm Design 1 0 8 mm Design 3 -1 8 mm 75 mm 50 mm Design 2 1 50 mm
Figure 3.3: Designs of the blades displayed in level order
Angle of the blades The next figure shows the three different angles of the blades.
0° 45° 90°
-1 0 1
ω
Figure 3.4: Different angles of the blades
Particle factory and measurement tools Part of the geometry are also the factory, which generates the particles, and the geometries that are needed to measure. Table 2.4 shows the characteristics of the factory and the dynamics of the agitator and screw conveyor. These values are again based on or copied from previous research. When using values that lie close to the values of previous research, the results will be comparable. In this research one grid bin is used to measure the weight of the particles in the bin. The grid bin encloses the hopper, as can be seen in figure 2.4. Next to the grid bin a flow meter is placed. This flow meter measures the mass flow in kg/s of the wood chips. Both measurement tools measure at every time step.
14 3. Methods
Wood chip factory
Factory type dynamic
Total mass 46,37 kg
Target mass 10 kg/s
Start time 1e-12 s
Attempts to place particle 20
Type Wood chip
Size One size
Position random
Velocity fixed, Z: -2 m/s
X,Y: 0 m/s
Orientation random
Angular fixed; X,Y and Z: 0 rad/s
Geometry dynamics
Agitator start time 6 s
Screw conveyor start time 6 s
Agitator and screw conveyor end time no end time
Agitator velocity varies
Screw conveyor initial velocity 1,339 rad/s
Table 3.4: The geometry dynamics
Domain
Grid bin
Flow meter
Figure 3.5: The position of the grid bin and flow meter
3.2.3. The simulation characteristics in EDEM
As many simulations have to run, it is faster and more simple to run the simulations in a batch file. Due to former experiences the estimated time per simulation was 30 hours. The average time of the simulations was 10 hour per simulation. Only a few simulations took 14 hours. This was very different from the expectations. This difference will be discussed in the discussion section of chapter 4. The needed data could be extracted by the batch file. This resulted in Excel files with the total torque on the agitator, the total mass flow through the flow meter and the total mass in the grid bin, all per time step. Table 2.5 shows the used simulation data. It is advised not to exceed the 35% of the Rayleigh fixed time step.
3.3. Measurements with EDEM 15
EDEM simulation settings
Rayleigh fixed time step 35%
Total simulation time 615 s
Target save interval 0,2 s
Selective save Particle: Base particle data and velocity Geometry and Interaction: all
Full data save every 5 intervals (1 s)
Cell size 2 R min
Number of cores 37
Table 3.5: The simulation settings in EDEM
3.3. Measurements with EDEM
The simulations will be run within a batch file. This will make the simulations faster, as no window has to be open, and the simulations will be able to run all day without waiting time. When running these batch files also data from the simulations can be subtracted. The data acquired for this research is listed in table 3.3.
Name Tool Unit
MassFlowRate Average Particle Mass Flow Rate flow meter kg/s Torque_total Total Geometry Torque Magnitude - Nm TotalMass_bin Total Particle Mass grid bin kg
Table 3.6: The measurements done in EDEM and their tool and unit
3.4. R
According the website ”R is a language and environment for statistical computing and graphics”. Here R was used to create the random generation of the Box-Behnken design. R will be used to analyse the data and will show the effects of the factors on the responses.
4
Results
In this chapter the results of the simulations are given. The first section covers the conversion of the data, so the data can be used for analyses. In the next sections the mathematical models of the responses, obtained by R, and some Response Surface models are shown. After these sections, the influence of the individual factors on the responses power consumption and mass flow are given. Section 4.6 shows the verification of the data, by making the data comparable to previous researches. All simulations took around 10 to 12 hours to run.
4.1. Convert EDEM data for Design of Experiments
The data provided by EDEM is automatically put into an Excel file. EDEM gives the total torque on the agitator per time step. This is a lot of data as the time step is 0,2 seconds and the simulation takes 615 seconds. Also, when using R for DoE, only one number (per response) per experiment is needed. Therefore the data has to be converted into one number that makes it possible to compare the experi-ments. When the torque in all time steps is added, the total torque the agitator used for that experiment is known. However, this number can not be compared between the experiments, as the moved mass of wood chips might be different per experiment. EDEM gives also the mass that is in the bin per time step. The first 6 seconds, this number goes up as the bin is filled. After 6 seconds, when the agitator an screw start working, this number goes down again. In all experiments there was some residue in the bin at the end of the experiment. It can be concluded that this residue would not come out, as the mass flow out of the bin has been 0𝑘𝑔/𝑠 for multiple time steps. This was also measured by EDEM. Within Excel 2010 the difference between the maximum total mass in the bin and the residue was calculated. The total torque was then divided by this mass, getting a number in𝑁𝑚/𝑘𝑔, which is equal to 𝐽/𝑘𝑔. For every experiment the rotational speed𝜔(𝑟𝑎𝑑/𝑠) of the agitator was fixed and known. This speed was multiplied with the torque/mass. The results are shown in appendix A. So to be able to make an accurate comparison between the experiment the energy is defined as the power needed to move 1
kilogram of wood chips𝑊/𝑘𝑔.
From this data also the average mass flow per experiment and the percentage of wood chips that are left in the bin can be defined. These results will be used to see if the energy needed and the mass flow are affected by one another and to see how the different factors affect the efficiency of the system. These numbers can also be found in appendix A.
These data points are then imported into R, which analyses the results according to the Box-Behnken Design. The results are presented in the next sections.
4.2. Energy usage of the agitator
In 4.1 is described which unit (𝑊/𝑘𝑔) is used to express the energy use of the agitator. Here the results of the Box-Behnken Design are shown. Equation 4.1 gives the influence of the factors on the energy use𝑦. Table 4.1 shows which factor belongs to which unit.
18 4. Results 𝑦 = Response 𝑥 = Angle of blades 𝑥 = Number of blades 𝑥 = Rotation Speed 𝑥 = Design of blades
Table 4.1: The factors, used in all the results
𝑦 = 1139 − 149𝑥 + 228𝑥 + 575𝑥 + 162𝑥 −58𝑥 𝑥 − 110𝑥 𝑥 − 29𝑥 𝑥 + 169𝑥 𝑥 + 72𝑥 𝑥 + 119𝑥 𝑥 −103𝑥 + 64𝑥 − 2𝑥 − 240𝑥
(4.1)
It can be seen that in equation 4.1 the third factor, that is 𝑥 the rotation speed, has the largest influence on the energy use of the agitator. The quadratic term−2𝑥 is very small and shows that the influence of the speed is almost linear. Secondly the number of blades has the most influence. Figure 4.1 shows the influence of both factors together on the energy consumption in a Response Surface Plot. From this figure it can also be seen that the slope of the rotation speed is almost twice as steep when the agitator has 7 blades (this is at 1 on the blade axis) instead of 3. The other way around, the slope of the number of blades is more steep at a higher speed. Apparently, when the speed is low, it does not matter to much how many blades are on the agitator. This becomes different at higher rotation speeds.
3
5
7
0,5
1
1,5
rad/s
Figure 4.1: The influence of the speed of the agitator and number of the blades on the agitator on the energy consumption ( / )
The boxplot in figure 4.2 shows that only one experiment, experiment 18, had an outcome not in line with the other experiments. In the discussion chapter it will be discussed why this experiment lies
4.3. Mass flow of the wood chips 19
out of bound with the others. But when interpreting the boxplot one has to be careful. A Box-Behnken Design does not take into account the extremes. So probably with a different design such as the Central Composite Design, there would have been more outliers or the boxplot would have had a larger reach.
Figure 4.2: A boxplot showing the power in / needed per experiment.
4.3. Mass flow of the wood chips
Equation 4.2 gives the values for the factors when analysing the mass flow of the wood chips. It can be seen that the combination of the angle of the blades and the rotation speed has the largest influence on the mass flow. As a single factor the angle of the blades has the largest influence. The factor is also parabolic. Again the influence of the speed is close to linear.
𝑦 = 0, 0861 − 0, 0051𝑥 + 0, 0007𝑥 + 0, 0034𝑥 − 0, 0018𝑥 −0, 0093𝑥 𝑥 − 0, 0110𝑥 𝑥 − 0.0016𝑥 𝑥 − 0, 0022𝑥 𝑥 + 0, 0022𝑥 𝑥 + 0, 00009𝑥 𝑥 +0, 0044𝑥 + 0, 0018𝑥 − 0, 0005𝑥 − 0, 0025𝑥
(4.2)
Figure 4.3 shows the Response Surface plot of the angle of the blades and the rotation speed on the mass flow. The graph shows that the two factors influence each other in an opposite way. When the angle 0°is the slope of the speed is positive, but when the angle is 90°the slope is less steep and negative. The boxplot in figure 4.4 shows that experiments 4 and 17 have a very high mass flow.
20 4. Results
0
45
90
0,5
1
1,5
rad/s
Figure 4.3: The influence of the speed of the agitator and the angle of the blades on the agitator on the mass flow( / )
4.4. Effectiveness of the different agitators 21
4.4. Effectiveness of the different agitators
The effectiveness is divided in two categories: The amount of wood chips that never leave the bin and the bridging tendency of the wood chips with different agitators. The less wood chips stay behind the more effective the system. Also, when the agitator cannot prevent the wood chips from bridging, the system is really not effective.
4.4.1. Percentage left over of wood chips in the bin
Equation 4.4.1 gives the percentage left over wood chips in the bin. It is better to address the boxplot from figure 4.5. Here it can easily been seen that the percentages are all under 2%, which is very small. Therefore it will be said that all different systems are qualified for the work they have to do, and none of them is non-effective.
𝑦 = 1, 400 − 0, 002𝑥 + 0, 020𝑥 + 0, 015𝑥 − 0, 101𝑥 −0, 007𝑥 𝑥 − 0, 032𝑥 𝑥 − 0, 0606𝑥 𝑥 − 0, 011𝑥 𝑥 − 0, 056𝑥 𝑥 − 0, 342𝑥 𝑥 −0, 040𝑥 + 0, 061𝑥 + 0, 022𝑥 + 0, 045𝑥
(4.3)
Figure 4.5: The boxplot shows the percentage of wood chips that are left in the bin at the end of the experiment.
4.4.2. Bridging of the wood chips
Bridging can be found in two ways: by visual inspection of the simulation and by looking at the mass flow. When the mass flow suddenly drops to 0 kg/s at a point at which this is not expected, not at the end of the simulation, this can indicate bridging. No drop of mass flow was found in any simulation and also visual inspection did not indicate bridging. Therefore no bridging took place and all experiments were effective.
4.5. Influence of the individual factors on the responses
When using a Box-Behnken Design and the response surface models in R, it is not possible to create graphs for just one factor. The following graphs are thus made with equations 4.1 and 4.2 in Matlab. The influence of the single factors will be shown one by one.
22 4. Results
Angle of the blades Figure 4.6 shows the influence of one factor, the angle, on the power consump-tion and on the hight of the mass flow. As can be seen, when the angle is 0°, the power and mass flow are high. When the angle is 45°, the power consumption is high, but the mass flow is low. With an angle of 90°the mass flow is low and the agitator uses less energy than the previous levels.
Figure 4.6: The effect of the angle of the blades on the power and mass flow
Number of blades As can be seen in figure 4.7 the power consumption of the agitator rises with the number of blades. On the contrary, the mass flow seems to stay behind. There is little difference in mass flow rates between the different levels.
Figure 4.7: The effect of the number of blades on the agitator on the power and mass flow
Speed of the agitator As expected from equation 4.1 and 4.2 the influence of the speed on the power and mass flow gives steep slopes as shown in figure 3.8. With increasing speed, also the power and mass flow significantly increase.
4.6. Verification of the results compared to former research 23
Figure 4.8: The effect of the speed of the agitator on the power and mass flow
Design of the blades The design of the blades is the one qualitative factor, therefore this graph is different from the others.
Figure 4.9: The effect of the design of the blades on the power and mass flow
4.6. Verification of the results compared to former research
This section will show the data in different graphs, which are in the same format as other research to see if the data is comparable [11][16]. An average is shown of all data, the blue line, an average of only the three reference experiments (with all factors at 0), the green line and the sigma of the standard deviation difference for all the data are shown in graphs 4.10, 4.11 and 4.12. The average values are in the same value ranges as the previous researches. The sigma interval is a lot larger than the interval with former experiments. This is also fairly easy to explain as other experiments did not investigate the influence of many factors. More factors and higher differences in their values will result in a broader spectrum of response data. 𝑡 is the time when the wood chips start falling out of the screw driver.
24 4. Results
For all graphs a ’rloess’ of 70 is used to smooth the data. For the standard deviation plots the fuction ’confplot’ is used. All graphs are made with Matlab.
Figure 4.10: The average mass flow of all experiments, the blue line, the average of the three reference experiments (with all factors at 0), the green line, and the standard deviation are shown over time.
Figure 4.11: The average torque of all experiments, the blue line, the average of the three reference experiments (with all factors at 0), the green line, and the standard deviation are shown over time.
4.6. Verification of the results compared to former research 25
Figure 4.12: The average power of all experiments, the blue line, the average of the three reference experiments (with all factors at 0), the green line, and the standard deviation are shown over time.
As seen in the boxplots ?? ?? ?? there are some outliers within all the responses. To see what influence these outliers have on the data the graph in figure 4.13 is made. This graph contains all data except the data from the two experiments that fell out of bound. As can be seen the influence of these data points, which were higher than all other values, is neglectable. This means that the data set was large enough.
Figure 4.13: Average mass flow over time without the extreme values, which can be seen in the boxplot, fig ??.
26 4. Results
from seven experiments that had the highest average power consumptions. The green line shows the average data from the seven experiments that had the lowest average power consumption. The black line is the average of the three reference experiments. This leaves ten experiments in the middle, that are combined in the blue line. As can be seen the experiments with the highest power consumption also have the highest mass flow. The experiments with the lowest power consumption have the lowest mass flow. Only the middle segment, the black and blue line, are not consistent.
Figure 4.14: The power consumption over time, with the 7 experiments with the highest power consumption combined in the red line and the 7 experiments with the lowest power consumption combined in the green line.
4.6. Verification of the results compared to former research 27
Figure 4.15: The mass flow over time, with the 7 experiments with the highest power consumption combined in the red line and the 7 experiments with the lowest power consumption combined in the green line. The dotted lines represent the average value of the experiments.
5
Discussion
This chapter contains a discussion and is built up in the same way as chapter 3. First the factors ’energy use’ and ’mass flow’ will be discussed. Hereafter the individual factors follow. The last section contains other discussion points, that cannot be placed in the former sections.
5.1. Discussion of the factors influencing the energy use of the
ag-itator
The height of the power usage is dominated by one factor: the speed. The other factors are less influential.
Influential factors From equation 3.1 it can be seen that the factor speed has the largest influence on the energy use. The relation is almost linear. When the speed is lower, the energy use is lower. The second most influential factor is the number of blades: the more blades, the higher the energy use. This factor has a small curvature shown in figure 3.7. When the amount of blades gets higher the power rises quickly, while as the number of blades gets lower at some point the power stays the same. The boxplot in figure 4.2 shows that experiment number 18 is an outlier. Experiment number 18 is the randomized experiment number 11 from table 3.2, which has a speed of 1,5 rad/s and 7 blades on the agitator. This experiment confirms the findings that these two factors are the most influential. The combination of these factors, figure 3.1, tells that the slope of the speed is steeper when the agitator has more blades. When the agitator has more blades, it means it has more surface. It can be said that with a bigger surface the consumed power is higher.
Less influential factors The angle of the blades and the design of the blades both have an influence on the power consumption, but a small influence compared with the other two factors. Still the influence is considerable, when for example the speed and the number of blades cannot be changed.
Angle When the angle is 0°the surface of the blade that interacts with the wood chips, as a force, is the largest. The surface at 90°is the smallest. The surface at 90°has more surface for sliding friction as the blade stands in line with to the rotation direction. The surface of the blade at 45°was exactly in between the other two. The power consumption does not show a big difference when using the largest surface or half of it, but shows a large decline to the smaller surface. As the material is pushed away as well as downwards, when the blades have an angle smaller than 90°, the material accumulates at one side of the hopper. The movement of the material to the one side of the hopper is less when the angle is higher, so there is less time and material to make accumulation happen. This results in a lower power consumption when dealing with smaller surfaces.
Design The design should be assessed more carefully as this is a qualitative factor. The three different designs stand alone and there is no design for all values between -1 and 1. Therefore only the power consumption values for -1, 0 and 1 are taken into account. From the graph in figure 3.9 it can
30 5. Discussion
be seen that design 3 has the lowest power consumption and design 2 and 1 almost have the same consumption. This confirms the assumption that the surface area of the blades has most influence on the energy use. The surfaces of designs 1 and 2 do not differ much, but the surface of design 3 is very small.
5.2. Discussion of the factors influencing the mass flow of the wood
chips
The angle of the blades and the speed combined have the highest influence on the mass flow. As a single factor the angle of the blades has the largest influence. The mass flow is highest at 0°when the blade is perpendicular to the rotation direction and the surface of the blade is the largest. The mass flow declines quickly when the blade loses surface.Further the higher the speed the higher the mass flow, which can be seen in figure 3.8. Here the response surface model in figure 3.3 gives an extra dimension. When the angle is 0°the mass flow indeed increases with higher speed, but with an angle of 90°the mass flow becomes smaller with a higher speed. This could be because the surface at that angle is very small and therefore the amount of moved wood chips is also smaller. As this amount of moved chips is small, at a high speed the chips have less time to fill the gaps, causing a smaller mass flow when the surface is small and the speed high.
The boxplot in figure 4.4 shows experiments 4 and 17, which are the randomized experiments 23 and 13 from table 3.2, as outliers. These outliers have different speeds, 1,5 and 1 rad/s and an angle of 45°. This figure does not show the same results as described above. This deviation cannot be explained, except that all values are close together and that maybe something else was of influence.
When looking at the influence of only the design on the mass flow in figure 3.9, design 2 gives the smallest mass flow. Design 1 and 3 have almost the same mass flow. This is odd as the surfaces of design 1 and 2 are more the same. Thus it is probably the design. The corners of the blades in design 2 are rounded and as wood chips tend to interlock, the rounded corners may not pull the chips out of the mass.
5.3. Discussion of the effectiveness of the agitators
As section 3.4 already points out, all bins of all experiments have less than 2% wood chips left overs. Therefore all systems are qualified as effective.
5.4. Discussion about the influence of the individual factors
Where the previous sections considered the responses and which factors are most influential, this section will consider the influence of the individual factors on more responses. This will provides a broader view.
Angle of the blades When looking at the graph in figure 3.6 it can be seen that the power usage and mass flow curves are the opposite. When the angle is 0°and the surfaces is largest and creating the largest normal force, the power consumption is high as is the mass flow. In the middle, at 45°, the power consumption is still high but the mass flow low. This was in previous section 5.1 described as a result of pushing the material to the side of the bin instead of down to the screw conveyor. At 90°both power consumption and mass flow are lower. The conclusion would be; when power consumption is most important the angle should be 90°, when mass flow is more important the angle should be 0°. 45°seems the least attractive option.
Number of blades Figure 3.7 shows the effect of the number of blades on the power consumption and the mass flow. Here there the mass flow curve is interesting. There seems to be an optimal amount of blades on the agitator. 4 or 5 blades on the agitator provide the worst mass flow rates. The mass flow goes quickly up when using more blades, but also the power usage. When using less blades the mass flow goes up again, but power gets less. So less blades provide less power use and more mass flow. Although attention should be paid to the bridging problem. Without any blades the mass flow should
5.5. Other points of interest for the discussion 31
be high and power consumption very low, but this graph cannot show that maybe bridging can occur. Therefore it can be said that in these experiments in this research the optimum amount of blades is 3.
Speed of the agitator This graph in figure 3.8 is straight forward: A lower power consumption means a lower mass flow, a higher power consumption means a higher mass flow. When looking at the values, the power consumption has a difference of1000𝑊/𝑘𝑔. Compared to the power differences at the other factors this is large, as the others are around300𝑊/𝑘𝑔 or 400𝑊/𝑘𝑔. The mass flow however differs only 0, 007𝑘𝑔/𝑠, where the influence of the other factors on the mass flow varies from 0, 005𝑘𝑔/𝑠 to 0, 01𝑘𝑔/𝑠. When wanting to lower the energy consumption, lowering the speed gives the best result.
Design of the blades In the graph in figure 3.9 not the curves are judged but only the points at -1, 0 and 1. As there cannot be a design at 0,4 etc.. The form of the curve does influence the exact values at these points, but here it will be assumed that the influence is not too large. It can be seen that design 2 has a low mass flow and a high energy consumption. Design 2 is not the design with the smallest surface, therefore the low mass flow was not expected. As stated in section 5.2 this is probably the result of the rounded corners of this design. The conclusion here is that design 3 is the best blade design of the three used designs in this research and that this is the result of the limited surface area. The design appeared to be a difficult factor. This factor does have influence on the energy con-sumption and on the mass flow, but the exact influence remains unclear. It is assumed that the rounded corners are the cause of the lower mass flow, but it is not proven. This cannot be answered with this research. From this research only the most favourable design of the used three can be chosen.
5.5. Other points of interest for the discussion
Mass flow versus power consumption Other factors can also influence the energy use: a lower mass flow for example. As mass flow is also one of the investigated responses, it is possible to com-pare these two. Graphs 4.13 and 4.14 in the previous chapter show that with an increased mass flow also the torque increases. Only the relation in the middle section is not conclusive. The high and lower values do show a relation. When using R to test for correlations, the Pearson correlation gives a value of 0,35. This low value contradicts the possible correlation found in the graphs.
Also the boxplot in figure 4.4 shows high mass flows for experiments 4 and 17, but these experiments do not have a particularly high power consumption. Based on all these findings not much can be said about the relation between the mass flow and power consumption
Surface of the blades When the surface of the blades is larger, the power consumption is also larger when looking at the factor graphs of the angle and number of blades (figures 4.6 and 4.7). Only, the design (figure 4.8) shows something different.
Design and angle In appendix C the rest of the response surface graphs are displayed. When looking at the graph of the influence of the angle and design on power consumption, it can be seen that the power consumption changes at design 3 (at design = -1) when changing the angle. This is strange as design 3 is a rod and the angle should have no influence, as the rod remains the same at every point. This is also the case when looking at the response surface graph of the two factors with the mass flow. Therefore it can be discussed if the chosen designs were correct or if a response surface method was the right way to get information about this factor (or combination of factors). The curves of the graph made by the other two designs influenced the outcome of the third design. That the design of the blades is a qualitative factor makes the interpretation of the results not easier. Therefore it is advised to asses these two factors separately and not together as in the response surface graph.
Simulation time All simulations took between 9 to 14 hours to run. It was expected that the sim-ulations would take more or less 30 hours, as this was the case in former research. The one thing that can explain this difference is the Rayleigh time step. In former research it was set at 25%, in this
32 5. Discussion
research 35% was used. This can explain a difference in simulation time, but not such a large differ-ence. Another reason for the time difference was not found. The number of used cores in EDEM was comparable and when using 20 cores or more the difference in simulation time is not that large [16].
6
Conclusion
This chapter contains the found conclusion of this research and some recommendations for future research.
6.1. Conclusion
The answer to the main question is: The energy consumption of an agitator transporting wood chips
can be decreased by lowering the speed of the agitator and by creating a smaller surface of the blades.
The speed of the agitator has the largest influence on the power consumption. The higher the speed, the higher the power consumption, this relation is almost linear. The relations between the power consumption and the other factors; the angle of the blades, the number of blades and the de-sign, are not linear. It can be said that a larger surface area, by means of more blades or the angle of the blades i.a., causes a larger power consumption.
The mass flow shows a different pattern and a larger surface does not necessarily leads to a larger mass flow. The most remarkable fact is the way how the design of the blades influence the mass flow. Here is found that blades with rounded corners have a negative influence on the mass flow. Again the speed is the most influential factor.
Bridging of the wood chips was not found in any of the experiments.
6.2. Recommendations
Here are some recommendations for future research.
Design of the blades As there was some discussion about the designs, this is something to consider to investigate. The shape of the blades should be investigated, but also extra factors such as the forces on the blades. The rods used in this research are small and may not be strong enough to overcome the forces acting upon it. Also wear can be taken into account, wear on the blade itself and on its connection to the agitator.
Length of the blades In section 1.3 some formulas are given. Formula 1.2 suggests that the arm, the length of the blade, influences the power consumption. This is indeed the case, but the length of the blades was not used as a factor in this research. One would assume, when surface is an important factor, that a shorter arm can drive down the power consumption. This factor can be investigated in the future. Here it is also important to keep the wood chips from bridging.
Box-Behnken and Central Composite Design It would be interesting to see the results when using a CCD. As it is not yet known which of the two designs would be the best to cover this kind of research.
34 6. Conclusion
BBD leaves out the extremes, but a CCD does not. This can give new insights in the problem and will maybe help in the future to chose the right tool for the experimental design.
A
Data for the Box Behnken Design in R
Factors Average
Exp. Random Angle Blades Speed Design Nm/kg=J/kg Power (W/kg) %leftover kg/s
1 45 5 1,5 2 1158 1737 1,015 0,088193 2 45 3 0,5 1 807 403,5 1,466 0,086233 3 0 5 1 2 966 966 1,325 0,080067 4 90 5 1 2 852 852 1,325 0,082002 5 45 3 1 3 641 641 1,452 0,091927 6 45 5 1 1 1121 1121 1,353 0,082097 7 45 7 1 2 1359 1359 1,339 0,090371 8 90 3 1 1 731 731 1,297 0,088796 9 90 5 0,5 1 760 380 1,381 0,088253 10 45 3 1 2 859 859 1,494 0,084081 11 45 7 1,5 1 1573 2359,5 1,564 0,079873 12 0 5 0,5 1 1018 509 1,325 0,084989 13 0 7 1 1 1630 1630 1,579 0,11212 14 45 5 1,5 3 728 1092 1,987 0,084356 15 90 5 1 3 709 709 1,691 0,094454 16 0 5 1 3 706 706 1,451 0,086401 17 45 7 0,5 1 1342 671 1,494 0,086241 18 45 3 1,5 1 945 1417,5 1,579 0,088598 19 0 3 1 1 1105 1105 1,409 0,087018 20 45 5 1 1 1159 1159 1,311 0,095866 21 45 5 1 1 1136 1136 1,536 0,080527 22 45 7 1 3 852 852 1,522 0,089474 23 0 5 1,5 1 1225 1837,5 1,339 0,120671 24 90 5 1,5 1 847 1270,5 1,268 0,080024 25 90 7 1 1 1023 1023 1,438 0,076777 26 45 5 0,5 3 680 340 1,254 0,077556 27 45 5 0,5 2 1022 511 1,649 0,077842
Table A.1: Experiments and their given and obtained values
B
R Analysis Data
This appendix consists of data obtained by R. The formulas used in chapter 3 are composed with values found in these tables.
Power
Estimate Std. Error t value Pr(>|t|) (Intercept) 1138.6667 81.6912 13.9387 8.968e-09 *** x1 -149.0000 40.8456 -3.6479 0.0033395 ** x2 228.1250 40.8456 5.5851 0.0001189 *** x3 574.9583 40.8456 14.0764 8.020e-09 *** x4 162.0000 40.8456 3.9662 0.0018724 ** x1:x2 -58.2500 70.7466 -0.8234 0.4263637 x1:x3 -109.5000 70.7466 -1.5478 0.1476331 x1:x4 -29.2500 70.7466 -0.4134 0.6865718 x2:x3 168.6250 70.7466 2.3835 0.0345416 * x2:x4 72.2500 70.7466 1.0212 0.3272841 x3:x4 118.5000 70.7466 1.6750 0.1197768 x1 -102.8542 61.2684 -1.6787 0.1190296 x2 63.7083 61.2684 1.0398 0.3189199 x3 -1.6667 61.2684 -0.0272 0.9787452 x4 -239.7292 61.2684 -3.9128 0.0020619 **
Table B.1: Results from R: influence of the factors on power consumption and their significance
— Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Multiple R-squared: 0.9609, Adjusted R-squared: 0.9152 F-statistic: 21.05 on 14 and 12 DF, p-value: 2.701𝑒 − 06
Df Sum Sq Mean Sq F value Pr(>F) FO(x1, x2, x3, x4) 4 5172757 1293189 64.5937 5.147e-08 TWI(x1, x2, x3, x4) 6 255742 42624 2.1290 0.124979 PQ(x1, x2, x3, x4) 4 471946 117987 5.8933 0.007332 Residuals 12 240244 20020 Lack of fit 10 239512 23951 65.3808 0.015156 Pure error 2 733 366
Table B.2: Analysis of variance for the power consumption
38 B. R Analysis Data
Analysis of Variance Table Stationary point of response surface:
x1 x2 x3 x4
-0.3677004 -3.7048003 1.2698973 0.1158938
Stationary point in original units:
Angle Blades Speed Design
-0.3677004 -3.7048003 1.2698973 0.1158938 Eigenanalysis: values [1] 145.7729 -45.3693 -126.4000 -254.5453 vectors [,1] [,2] [,3] [,4] x1 0.2279977 0.3407098 0.91206644 0.008288623 x2 -0.7583428 0.6474810 -0.05180395 -0.054780081 x3 -0.5865816 -0.6726858 0.39981720 -0.208715171 x4 -0.1698682 -0.1103585 0.07481552 0.976405868
Massflow
Estimate Std. Error t value Pr(>|t|) (Intercept) 0.08616354 0.00497596 17.3160 7.449e-10 *** x1 -0.00508005 0.00248798 -2.0418 0.06378 . x2 0.00068359 0.00248798 0.2748 0.78818 x3 0.00338346 0.00248798 1.3599 0.19886 x4 -0.00180078 0.00248798 -0.7238 0.48306 x1:x2 -0.00928023 0.00430930 -2.1535 0.05231 . x1:x3 -0.01097779 0.00430930 -2.5475 0.02558 * x1:x4 -0.00152951 0.00430930 -0.3549 0.72880 x2:x3 -0.00218331 0.00430930 -0.5066 0.62158 x2:x4 0.00218579 0.00430930 0.5072 0.62119 x3:x4 0.00088799 0.00430930 0.2061 0.84020 x1 0.00435143 0.00373197 1.1660 0.26627 x2 0.00184360 0.00373197 0.4940 0.63022 x3 -0.00049135 0.00373197 -0.1317 0.89743 x4 -0.00250442 0.00373197 -0.6711 0.51488
Table B.3: Results from R: influence of the factors on mass flow and their significance
— Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Multiple R-squared: 0.6402, Adjusted R-squared: 0.2204 F-statistic: 1.525 on 14 and 12 DF, p-value: 0.2348
39 Df Sum Sq Mean Sq F value Pr(>F)
FO(x1, x2, x3, x4) 4 0.00049158 1.2289e-04 1.6545 0.2246 TWI(x1, x2, x3, x4) 6 0.00087723 1.4621e-04 1.9683 0.1498 PQ(x1, x2, x3, x4) 4 0.00021713 5.4283e-05 0.7308 0.5881 Residuals 12 0.00089136 7.4280e-05
Lack of fit 10 0.00074891 7.4891e-05 1.0515 0.5813 Pure error 2 0.00014245 7.1226e-05
Table B.4: Analysis of variance for the mass flow
Analysis of Variance Table Stationary point of response surface:
x1 x2 x3 x4
0.2524642 0.3628227 -0.5177662 -0.3700753 Stationary point in original units:
Angle Blades Speed Design
0.2524642 0.3628227 -0.5177662 -0.3700753 Eigenanalysis: values [1] 0.009654174 0.002036679 -0.002649546 -0.005842053 vectors [,1] [,2] [,3] [,4] x1 0.8029543 0.1358856 0.13366321 -0.5647422 x2 -0.4367996 0.7731900 -0.07710602 -0.4532528 x3 -0.3919667 -0.6107402 0.09869679 -0.6808947 x4 -0.1040804 0.1034837 0.98308075 0.1095931
Percentage left over
Estimate Std. Error t value Pr(>|t|) (Intercept) 1.4000000 0.0658764 21.2519 6.857e-11 *** x1 -0.0023333 0.0329382 -0.0708 0.944692 x2 0.0199167 0.0329382 0.6047 0.556661 x3 0.0152500 0.0329382 0.4630 0.651656 x4 -0.1008333 0.0329382 -3.0613 0.009875 ** x1:x2 -0.0072500 0.0570506 -0.1271 0.900982 x1:x3 -0.0317500 0.0570506 -0.5565 0.588081 x1:x4 -0.0600000 0.0570506 -1.0517 0.313656 x2:x3 -0.0107500 0.0570506 -0.1884 0.853689 x2:x4 -0.0562500 0.0570506 -0.9860 0.343613 x3:x4 -0.3417500 0.0570506 -5.9903 6.310e-05 *** x1 -0.0399583 0.0494073 -0.8088 0.434399 x2 0.0606667 0.0494073 1.2279 0.243029 x3 0.0216667 0.0494073 0.4385 0.668792 x4 0.0445417 0.0494073 0.9015 0.385049
Table B.5: Results from R: influence of the factors on the percentage left overs and their significance
— Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Multiple R-squared: 0.8132, Adjusted R-squared: 0.5954 F-statistic: 3.733 on 14 and 12 DF, p-value: 0.01393
40 B. R Analysis Data Df Sum Sq Mean Sq F value Pr(>F)
FO(x1, x2, x3, x4) 4 0.12962 0.032406 2.4891 0.099162 TWI(x1, x2, x3, x4) 6 0.49893 0.083156 6.3872 0.003263 PQ(x1, x2, x3, x4) 4 0.05177 0.012943 0.9941 0.447690 Residuals 12 0.15623 0.013019 Lack of fit 10 0.12760 0.012760 0.8915 0.636507 Pure error 2 0.02863 0.014313
Table B.6: Analysis of variance for the percentage of left overs
Analysis of Variance Table Stationary point of response surface:
x1 x2 x3 x4
0.093997901 -0.180565218 -0.280260152 0.006033756 Stationary point in original units:
Angle Blades Speed Design
0.093997901 -0.180565218 -0.280260152 0.006033756 Eigenanalysis: values [1] 0.20681638 0.06137461 -0.03094158 -0.15033274 vectors [,1] [,2] [,3] [,4] x1 -0.04434437 0.012303900 0.95829348 -0.2820564 x2 -0.11530882 -0.986847539 -0.02517786 -0.1104621 x3 -0.66914464 0.161009475 -0.23504589 -0.6863489 x4 0.73279118 -0.007516449 -0.16060237 -0.6611864
