Simulation and Optimization of Cyclone Dust Separators

Schriftenreihe CIplus, Band 4/2013 Herausgeber: T. Bartz-Beielstein, W. Konen, H. Stenzel, B. Naujoks Simulation and Optimization of Cyclone Dust Separators Beate Breiderhoff, Thomas Bartz-Beielstein, Boris Naujoks, Martin Zaefferer, Andreas Fischbach, Oliver Flasch, Martina Friese, Olaf Mersmann and J¨org Stork Simulation and Optimization of Cyclone Dust Separators? Beate Breiderhoff, Thomas Bartz-Beielstein, Boris Naujoks, Martin Zaefferer, Andreas Fischbach, Oliver Flasch, Martina Friese, Olaf Mersmann, and Jörg Stork Faculty for Computer and Engineering Sciences Cologne University of Applied Sciences, 51643 Gummersbach, Germany [email protected] Abstract. Cyclone Dust Separators are devices often used to filter solid particles from flue gas. Such cyclones are supposed to filter as much solid particles from the carrying gas as possible. At the same time, they should only introduce a minimal pressure loss to the system. Hence, collection efficiency has to be maximized and pressure loss minimized. Both the collection efficiency and pressure loss are heavily influenced by the cyclones geometry. In this paper, we optimize seven geometrical parameters of an analytical cyclone model. Furthermore, noise variables are introduced to the model, representing the non-deterministic structure of the real-world problem. This is used to investigate robustness and sensitivity of solutions. Both the deterministic as well as the stochastic model are optimized with an SMS-EMOA. The SMS-EMOA is compared to a single objective optimization algorithm. For the harder, stochastic optimization problem, a surrogatemodel-supported SMS-EMOA is compared against the model-free SMS-EMOA. The model supported approach yields better solutions with the same run-time budget. 1 Introduction The reduction of emissions from coal-fired power plants is a demanding task. Cyclone separators are frequently used devices for filtering the flue gas of such plants. They remove dispersed particles from gas. Their advantages are simple structure, low costs and ease of operation. Collection efficiency and pressure loss are the two most important performance parameters. They are heavily influenced by the choice of several geometrical design parameters, like height or diameter. This results into a Multi-Objective Optimization (MOO) problem, the so called Cyclone Optimization Problem (COP). This study shows how a COP can be solved and analyzed, based on an analytical, deterministic model. Furthermore, the analytical model is extended by adding several noise ?This is the pre-print version of the following article: Breiderhoff, B.; Bartz-Beielstein, T.; Naujoks, B.; Zaefferer, M.; Fischbach, A.; Flasch, O.; Friese, M.; Mersmann, O. and Stork, J.: Simulation and Optimization of Cyclone Dust Separators, in Proceedings 23. Workshop Computational Intelligence, Hrsg. Hoffmann, F. and Hüllermeier, E., Karlsruhe, 2013. 2 Breiderhoff et al. variables. These enable to evaluate robustness of solutions, and yield a better estimate of how noisy real-world circumstances affect the problem. Techniques like a classical as well as a model-supported SMS-EMOA are used to handle the MOO problem. The remainder of the paper is structured as follows. Section 2 provides an overview on previous research and methods w.r.t. the modeling and the COP in particular as well as MOO. This section is followed by a short summary of the research questions and goals in Section 3. Section 4 describes the problem setup, introducing parameterizations for the COP. A sensitivity analysis of the problem is depicted in Section 5, which is followed by the description of the performed optimization experiments and their results in Section 6. A short summary and a discussion of the findings is given in Section 7. The paper closes with an outlook on future research in Section 8. 2 Previous Research and Methods 2.1 Cyclone Optimization Da Dt Be HeHe H ε Be Da Dt Front View Top View Fig. 1: Schematic representation of a cyclone dust separator. Cyclones exist in different shapes but the reverse flow cyclone represented in Fig. 1 is the most common design in industry. The principle of cyclone separation is simple: the Simulation and Optimization of Cyclone Dust Separators 3 gas-solid mixture enters at the top section tangentially. The cylindrical body induces a spinning, vortexed flow pattern to the gas-dustmixture. Centrifugal force separates the dust from the gas stream: the dust is moved to the walls of the cylinder and down the conical section to the dust outlet while the gas exits through the outlet pipe. Significant parameters of a cyclone Several characteristics constitute a COP. 1. Geometric shape Seven geometric parameters allow to describe the cyclone as shown in Fig. 1. 2. Fluid/Gas properties Parameters like viscosity or density describe the carrier substance. 3. Particle Properties Density, concentration and distribution of particle sizes describe the particle composition. 4. Collection efficiency (CE) The overall CE of the cyclone describes the amount of particles filtered from the gas. 5. Pressure Loss (PL) The Pressure Loss is the difference in pressure between inlet and outlet. These different characteristics are summarized in Table 1. Pressure loss and collection efficiency are the main criteria used to evaluate cyclone performance. Both are functions of the cyclone dimensions. Normally, the goal of cyclone design is to maximize collection efficiency and to minimize pressure loss by adjusting the geometric parameters. Previous Optimization Studies A first multi objective optimization of cyclone separators was performed by Ravi et al. [2]. They used the Non Dominated Sorting Genetic Algorithm NSGA II to optimize an analytical model by Mothes and Löffler [1], minimizing pressure loss and maximizing total collection efficiency for eight geometrical parameters. Elsayed and Lacor [3] optimized four geometrical parameters using computational fluid dynamics CFD models and the a model based on work by Barth [4]. They minimized pressure loss only, using the response surface methodology. Pishbin and Moghiman [5] optimized seven geometry parameters with a genetic algorithm, minimizing pressure loss and maximizing efficiency. They used a CFD model to construct the fitness function. The bi-objective problem was transferred to a single-objective problem using weights. Elsayed and Lacor [6] minimized pressure drop and cut-off diameter. They used a Pareto optimization approach, utilizing a Radial Basis Function Neural Network RBFNN. The RBFNN was trained with data from literature. A similar approach was taken by Safikhani et al. [7], where the data for trained neural network stemmed from CFD simulations. The herein presented work uses the analytical model based on work by Barth [4] and Muschelknautz [8]. In contrast to previous approaches, we introduce a stochastic simulation based on the analytical model, where several parameters are assumed to be 4 Breiderhoff et al. Table 1: Table of fluid, particle and geometrical parameters used in the experiments. Most values are taken from an example by Löffler [1]. Parameter Symbol Default Unit Geometry Cyclone diameter Da1260 mm Cyclone height H 2500 mm Outlet pipe diameter Dt420 mm Outlet pipe immersion Ht640 mm Cyclone cone angle 13.134 ◦ Inlet height He600 mm Inlet width Be200 mm Fluid Viscosity µ18.5·10−6P a ·s Flow Rate Vp5000 m3 h Gas density ρf1.86 kg l Particle Particle density ρp2kg l Particle concentration ce50 g m3 Output Pressure Loss PL 2564 P a Collection Efficiency CE 0.89 (without unit) noisy. This allows to investigate robustness of solutions. Furthermore the more recent SMS-EMOA is used to solve the multi-objective COP. In case of the stochastic cyclone simulation, the model-free SMS-EMOA compared to a model-supported SMS-EMOA, using a Kriging surrogate model. 2.2 Analytical Models for Dust Separation Barth [4] and Muschelknautz [8] proposed a simple model based on a force balance, as presented by Löffler [1]. This model enables to obtain the collection efficiency and pressure loss. The principle of calculation is based on the fact that a particle carried by the vortex is influenced by two forces: a centrifugal force and a flow resistance. They are expressed at the outlet pipe radius riwhere the highest tangential velocity occurs. The model represents a reverse flow cyclone with a tangential rectangular inlet. This is a simple and still useful model, by which friction was first introduced in cyclone modeling. Collection Efficiency The cyclone geometry, together with flow rate, defines the cutsize of the cyclone. Cut-size defines the particle size that will be collected with 50% efficiency. Smaller particles are collected with lower efficiency, larger with higher efficiency. Barth [4] developed a mathematical model for the cut-size as follows: xGr =s18µvrri (%p−%)v2 φi (1) Simulation and Optimization of Cyclone Dust Separators 5 where riis the outlet pipe radius, vris the radial gas velocity on the outlet pipe and vφi is the cyclone inlet velocity. The fractional efficiency curve assigns an efficiency to the particle diameter as shown in Fig. 2. Larger particles are collected more efficiently than smaller particles. The fractional efficiency curve is described by: T(x) = 1 + 2 x xGr 3,564 !−1.235 (2) where xis the particle size and xGr equals to Eq. (1). The overall collection efficiency 0 5 10 15 20 25 30 35 0.0 0.2 0.4 0.6 0.8 1.0 Particle Size [µm] Fractional Efficiency Fig. 2: Fractional efficiency curve. is predicted according to: E=Zxmax xmin T(x)qe(x)dx = xmax X xmin T( ˜xi)∆Qe(xi)(3) where xmin is the lower bound of the particle size, xmax is the upper bound of the particle size, ˜xiis the mean particle size, ∆Qe(xi)is the change in distribution of particle sizes and qe(x) = ∆Qe(xi) ∆xi. Pressure Loss Pressure loss is defined as the difference in pressure between two points of a fluid carrying body. It occurs with frictional forces. It relates directly to operation cost. Therefore an exact prediction is very important. Total pressure loss equals to: ∆p =ρ 2v2 i(ξe−a+ξa−i+ξi−m)(4) where ξe−ais the friction coefficient for the loss within the inlet (equals zero because of the tangential rectangular inlet) , ξa−iis the friction coefficient for the loss within the cyclone body, ξi−mis the friction coefficient for the loss within the outlet pipe and ρ 2v2 iis the relationship between pressure and velocity. 6 Breiderhoff et al. 2.3 Model Alternatives The above described analytical model is used as a predictor for collection efficiency and pressure loss. Several other analytical models of the cyclone separator exist [9]. Although all these methods have had a remarkable success, more advanced ideas are needed to model cyclones. Unsteadiness and asymmetry are for example two features not considered in classical cyclone theory that may affect the velocity distribution to a great extent, thus changing the model of the separation mechanism. On the other hand, as in many other fields, CFD currently emerges as a potentially accurate modeling technique. Still, analytical models provide a good starting point for first investigations. Such models usually are not as precise as the more complex CFD models, but are much faster with respect to calculation time and other resources. 2.4 Multi Objective Optimization In classical optimization methods only one objective is investigated. This is different in Multi Objective Optimization (MOO) where more than one objective can be optimized in parallel. However, new concepts had to be developed because these objectives are often conflicting, i.e. an improvement in one objective automatically leads to a deterioration in other objectives. Here, the concept of Pareto dominance comes into play. It says that solution adominates solution bif ais not worse in any objective and better than bin at least one objective. Formally, in case of minimization it reads adominates b⇔ ∀i:fi(a)≤fi(b)∧ ∃j:fj(a)< fj(b) for a fitness function fof multiple objectives, f(x) := (f1(x), f2(x), . . . )Based on this concept, an optimization process searches for solutions that are not dominated by any other solution. This results into a set of non-dominated solutions, called the Pareto front. The performance of an optimization process can therefore only be expressed in relation to a set of solution, rather than the quality of a single best solution. Evolutionary Algorithms (EA) have become a standard tool for solving MOO problems. These algorithms are based on sets of solutions. This coincides well with the challenge of finding a set of solutions in MOO problems. Optimization Algorithms (EMOA) are modern MOO techniques that optimize the space that is covered by a Pareto front with respect to a predefined reference point. Maximizing this space, also called the hypervolume, pushes solutions more and more towards the desired objective values. Moreover, the hypervolume rewards a high diversity of solutions, i.e. a wide spread, and a smooth distribution of solutions along the border to the non-dominated area. All these properties are highly appreciated in MOO. One of the techniques employing hypervolume maximization is the SMS-EMOA (cf. Beume et al. [10]), which is also employed here. 2.5 Expensive Optimization Problems In general, industrial design tasks can not be optimized by manufacturing multiple design instances and deciding for the best alternative afterwards. In almost all cases, this Simulation and Optimization of Cyclone Dust Separators 7 procedure would simply be too expensive. As a consequence, models are considered to estimate the performance of different designs before the actual manufacturing process. These simulations or models themselves can become time-consuming to evaluate. Developing surrogate approaches is the most important solution to that issue. In such approaches, the optimization problem (e.g. the cyclone model) is replaced by a cheaper, or easier to optimize surrogate model. A comprehensive survey of surrogate modeling in optimization was provided by Jin [11]. A methodical framework for surrogate model based optimization of noisy and deterministic problems is Sequential Parameter Optimization (SPO) introduced by BartzBeielstein et al. [12]. SPO has been developed for solving expensive algorithm tuning problems but can be directly employed for solving real world engineering problems as well. One of the most often used surrogate-models is Kriging. This is partly due to the fact that it poses an excellent predictor of smooth, continuous problem landscapes. Moreover, it provides an uncertainty estimate of its own prediction, which can be used to calculate the Expected Improvement (EI) of a solution. This was used in Efficient Global Optimization by Jones et al. [13] to balance exploitation and exploration in the optimization process. In MOO, several approaches employ surrogate modeling. An overview of surrogate modeling in MCO is given by Knowles and Nakayama [14]. EGO has also been extended for MOO problems, as in the ParEGO Algorithm by Knowles [15] or the SMSEGO approach suggested by Ponweiser et al. [16]. Emmerich et al. [17] show how the EI in hypervolume can be calculated exactly. 3 Questions and Goals Real-world industrial multi-objective test cases are highly appreciated by the MOO research community because these allow for a comparison of methods apart from artificial test cases. The latter are usually used in the community but do not yield the complexity or significance of real-world applications. The COP is presented as a MOO test case and first results are presented. Moreover, the MOO results are compared to results from a single objective optimization approach to determine a possible lack of performance due to involving multiple objectives in parallel. Therefore, the single objective optimization results are compared to the extreme Pareto non-dominant solutions. The cyclone model assumes a certain distribution of particle sizes as well as fixed, undisturbed settings of all other relevant variables. In practice, variables like the inflow speed or particle sizes will be noisy. That noise can be simulated by repeated sampling from random distributions, each sample leading to a new evaluation of the cyclone model. The repeated evaluation with different samples leads to a more time consuming target function for the optimization algorithm. To alleviate this issue, surrogate models can be introduced to support the optimization process. Therefore, the goals of this study are to: –test the deterministic COP as a MOO problem. –compare a single-objective and a multi-objective approach. 8 Breiderhoff et al. –analyze the influence of noise on the solution quality. –determine influence of geometry, fluid and particle parameters. –compare a model-free and a model-supported SMS-EMOA in case of optimizing a stochastic cyclone simulation. 4 Problem Setup 4.1 Parameters of the Deterministic Cyclone Model The herein described experiments are based on an example by Löffler [1]. This example uses the geometrical, fluid-specific, and particle-specific parameters summarized in Table 1. The geometrical parameters to be optimized are varied in fixed boundaries, which are ±10 % of the default values from Table 1. Geometrical parameters could be varied in a much wider range, however, this range would not necessarily be fitting to the given fluid and particle parameters. Therefore, the 10% deviation was chosen as a typical experimental setup. A two-dimensional case (with Daand Honly) as well as a seven dimensional case with all seven parameters are investigated. 4.2 Stochastic Cyclone Simulation In addition to the parameters from the deterministic model, three noise sources are introduced. That is, flow rate Vp, particle density ρp, and the particle sizes xiused in the collection efficiency calculation can be subject to noise. The flow rate is allowed to vary in between ±10% of the default value, while particle density varies within ±5%. In both cases, a uniform distribution is used. For the collection efficiency calculation, one sample is drawn in each of the intervals from Table 2, instead of simply using the midst of each interval. That is, the particle size in each interval is determined randomly with a uniform distribution. These values are then inserted in Eq. (3), to calculate the overall collection efficiency. Simulation and Optimization of Cyclone Dust Separators 15 time restriction makes pure exploitation the more desirable choice. This result into a run-time of roughly 210 seconds, consistent with the model-free run-time. Here, the main contributors to run-time are the training of the Kriging model, and the subsequent optimization on the Kriging model. Both the SMS-EMOA and the Kriging-supported SMS-EMOA are run 20 times. The quality of each point in the resulting Pareto front estimates are validated by 10,000 runs of the stochastic simulation. To compare, the hypervolume indicator is used with a reference point of 5000 PL and zero CE. Results from Stochastic Optimization Runs The optimization results are summarized in Fig. 10. For the model-free SMS-EMOA, increasing the number of evaluations per point seems to yield no improvement. Exploring more points is at least as profitable as estimating the quality of each point more accurately. Still, it can be seen, that the model supported SMS-EMOA clearly outperforms the model-free SMS-EMOA. This is despite of the fact, that the model uses a much smaller budget than the SMS-EMOA. The run-time of both approaches is about equal. The Kriging model seems to deal well with the remaining noise in the objective function, yielding a more easy to optimize surrogate. This is especially interesting since the target-function is not exactly expensive, which would be the usual case where Kriging surrogates work well. Still, 1000 evaluations of each point make this a semi-expensive problem. One explanation for the ●● ●● ● ●● SMS−EMOA, 1 evaluation SMS−EMOA, 10 evaluations SMS−EMOA, 100 evaluations SMS−EMOA, 1000 evaluations Krig+SMS−EMOA, 1000 evaluations 3120 3140 3160 3180 3200 3220 3240 Hypervolume Fig. 10: Boxplots for the optimization experiments with the stochastic simulation. The x-axis shows hypervolume of the estimated fronts, validated by 10,000 runs for each point. Higher values are better. Evaluation numbers refer to the repeated evaluation of each point. excellent performance of the model-based SMS-EMOA, besides its ability to smoothen the noisy landscape, may be, that even in the seven-dimensional case, the true front is spread along several boundaries of the decision space. This could already be observed for the deterministic model, and holds here as well. That may lead to a situation, where the surrogate model does not have to have high accuracy over the whole search space because it suffices to predict decreasing values towards the boundaries. 7 Summary and Discussion This paper presents a multi objective optimization problem, based on a deterministic, analytical model of a cyclone dust separator. Noise influence was added, thus generating 16 Breiderhoff et al. a stochastic simulation model. This allowed not only to optimize, but also to investigate robustness of solutions, against uncertainty in the noisy variables. In case of the deterministic model, users can choose preferable results from the Pareto front, depending on their preference of CE and PL combinations. Preferred design points can be further analyzed with the stochastic simulation model. For instance, a user might choose the knee of the Pareto front (see right plot in Fig. 9) and an extreme point on the upper left part of the Pareto front, as summarized in Table 3. Those settings could be reevaluated with the stochastic model, yielding resulting variance estimates as depicted in Fig. 11. In practice, it may occur, that a user would prefer the extreme solution. While this solution has a worse expected value for CE, there is strong overlap between both solutions. On the other hand, the PL values show clearly a significant difference, thus leading to the potential preference of the extreme point. It was also shown, that the stochastic simulation can be optimized directly. While the Table 3: Two Points from the Pareto front found by SMS-EMOA on the deterministic model, with all seven geometrical parameters considered. The whole front is shown in Fig. 9 on the right. Parameter Point 1 (knee) Point 2 (extreme) Da1134 1134 H 2750 2750 Dt462 462 Ht576 576 13.92 12.81 He540 660 Be180 220 PL 2103.87 1375.90 CE -0.921 -0.86 high noise level makes this more costly for a simple SMS-EMOA, a surrogate model based approach seems to handle the issue more efficiently. The classical, single objective Nelder-Mead is able to identify the optima of the deterministic objective, but fails in case of the noisy simulation. The presented cyclone model representations are of comparativly simple structure, and thus are good candidates for real-world based multi objective test problems. Simulation and Optimization of Cyclone Dust Separators 17 Knee Extreme 1200 1400 1600 1800 2000 2200 2400 2600 Pressure Loss ●●●●● ●● ●●● ●● ● ●● ●● ●● ●●●●●● ● ● ●●● ●●●● ●● ●● ●● ●● ●● ● ●● ●●● ● ● ●● ● ●●● ● ● ●●● ●● ●● ●●● ● ● ●● ●●● ●● ●● ●●●●●● ●● ●●● Knee Extreme −0.9 −0.8 −0.7 −0.6 Collection Efficiency Fig. 11: Boxplots for the knee, and an extreme point of the Pareto front found for the deterministic model. Corresponding to the parameters in Table 3, reevaluated 1000 times with the stochastic simulation. Lower values are better. 8 Outlook While the analytical cyclone model does pose an interesting MOO problem, it lacks any information about quality of non-standard problems and solutions. That means, whenever particle, fluid or geometry attributes stray to far from the standard, the models quality deteriorates. For instance, the model is unable to represent non-centric positions of the outlet or slanted inlets. Still, such changes to geometry are of high interest to practitioners in industry. To get a better quality estimate of these geometries, CFD models are used. CFD models offer a wide variety to model the dynamics of particles in any kind of flow. However, such models need different preliminaries like the discretization of the considered space (meshing) and a solver for the resulting set of (partial) differential equations. This results in rather time-consuming and thus expensive simulations for each design alternative. However, such simulations can be very precise, mapping the real process with a very high accuracy and thus might be worth the effort. To support the optimization of such time consuming simulations, the analytical model may still be of use. It can be used for multi-fidelity optimization of such CFD models, using techniques like Co-Kriging [20]. 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K¨oln, Januar 2012 Herausgeber / Editorship Prof. Dr. Thomas Bartz-Beielstein, Prof. Dr. Wolfgang Konen, Prof. Dr. Horst Stenzel, Dr. Boris Naujoks Institute of Computer Science, Faculty of Computer Science and Engineering Science, Cologne University of Applied Sciences, Steinm¨ullerallee 1, 51643 Gummersbach url: www.ciplus-research.de Schriftleitung und Ansprechpartner/ Contact editor’s office Prof. Dr. Thomas Bartz-Beielstein, Institute of Computer Science, Faculty of Computer Science and Engineering Science, Cologne University of Applied Sciences, Steinm¨ullerallee 1, 51643 Gummersbach phone: +49 2261 8196 6391 url: http://www.gm.fh-koeln.de/~bartz/ eMail: [email protected] ISSN (online) 2194-2870