Determination of Optimum Body Diameter of Air

ENVIRONMENTAL ENGINEERING SCIENCE Volume 23, Number 4, 2006 © Mary Ann Liebert, Inc.

Determination of Optimum Body Diameter of Air Cyclones Using a New Empirical Model and a Neural Network Approach Kaan Yetilmezsoy* Yildiz Technical University Faculty of Civil Engineering Department of Environmental Engineering 34349, Yildiz, Besiktas, Istanbul, Turkey

ABSTRACT This paper presents a new empirical model and a two-layer neural network approach for the determination of optimum body diameter (OBD) of air cyclones. OBD values were calculated by help of a MATLAB® algorithm for 505 different artificial scenarios given in a wide range of five main operating variables. The predicted results obtained from each proposed approach were compared with the wellknown Kalen and Zenz’s model. The computational analysis showed that the empirical model and neural network outputs obviously agreed with the Kalen and Zenz’s model, and all the predictions proved to be satisfactory, with a correlation coefficient of about 0.9998 and 1, respectively. The maximum diameter deviations from Kalen and Zenz’s model were recorded as only 61.3 cm and 6 0.0022 cm for the proposed model and NN outputs, respectively. In addition to proposed approaches, the pressure drop problem was controlled using a MATLAB® algorithm, and results were obtained rapidly and practically for varying data used in the cyclone design. Key words: cyclone separators; optimum body diameter; neural network; Kalen and Zenz’s model; pressure drop; MATLAB®

INTRODUCTION HE SEPARATION of solid particles from the waste air streams is required in many industrial processes. For this purpose, cyclone separators are widely used as the most common devices. Conventionally, cyclone separators have been used as precleaning devices for the removal of particles bigger than 10 mm from the carrier

T

gas in both air pollution control and other processes. Because of their adaptability, simple design and low costs in terms of maintenance, construction, and operation make cyclones ideal for use in the various stages of industrial applications (Yang and Yoshida, 2004). Cyclones are also used as bio-aerosol samplers in air quality applications and hospitals in addition to chemical, metallurgical, and petroleum industries (Pant et al., 2002). In

*Corresponding author: Yildiz Technical University, Faculty of Civil Engineering, Department of Environmental Engineering, 34349, Yildiz, Besiktas, Istanbul, Turkey. Phone: 190 212 259 7070 (2730); Fax: 190 212 261 90 41; E-mail: [email protected]

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OPTIMUM BODY DIAMETER OF AIR CYCLONES

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extreme conditions, a cyclone separator can be used as a spray dryer or a gasification reactor. With growing concern for the environmental effects of particulate pollution, it becomes increasingly important to be able to optimize the design of pollution control systems (Wang et al., 2003). There are a number of different designs of the cyclone that are in use for different purposes, such as straight-through, uniflow, and the reverse-flow cyclones (Ingham and Ma, 2002). It is generally known that the most common cyclone design has a tangential inlet and reverse flow. In cyclone separators, a centrifugal force generated by a spinning gas stream is employed for the separation of dispersed particles. A certain number of revolutions made by the gas spirals increase the inlet velocity (Kim et al., 2001). For a given design, higher inlet velocities give higher collection efficiencies (h), but this also increases the pressure drop (DP) across the cyclone. The design and performance of a cyclone separator are generally characterized by two parameters: collection efficiency of particles, and pressure drop through the cyclone. Pressure drop and collection efficiency are the two major criteria used to evaluate cyclone performance (Ramachandran et al., 1991). Because of the relation between these parameters and operating cost, an accurate prediction should be made to get more benefits in cyclone design. Due to the pressure drop problem across the cyclone, an optimization between collection efficiency and pressure drop becomes inevitable in the design procedure. Hence, a number of modification steps can improve collection efficiencies of particles and reduce the pressure drop problem generated in conventional cyclones. In this study, an empirical model was developed to provide a new scientific contribution in modeling of air cyclones. Engineers, designers, researchers, manufacturers, and end-users may not have enough time to calculate all variables in different functions and to control required iterative calculations. Hence, a number of attempts in developing a representative model including lesser variables can promote the existing calculation method and give favorable results for desired values. It was aimed to determine the optimum body diameter (OBD) of air cyclones by using a new empirical equation and to provide a new reference for other theoretical and experimental future diameter models, and also to be helpful for separation–equipment engineers, designers, and other researchers concerned with the separation processes. The artificial neural network (ANN) techniques have successfully been applied to many application fields such as modeling, simulation, learning, recognition, and forecasting (Goktepe et al., 2005). ANNs are intended to interact with the objects of the real world in the same way as a biological nervous system (Kohonen, 1993). The advantage of ANNs is to perceive complex interactions be-

tween the input and output, without requiring a mathematical model. Briefly, neural networks are tools that can quantify pattern recognition (Stanley, 1988). A neural network model was selected as an iterative process in this study. Because they do not require any prior knowledge of a solution, neural networks have been applied to many environmental problems (McCann, 2004) such as prediction of ground level SO2 concentration (Saral and Erturk, 2003), prediction of tropospheric ozone concentration (Abdul-Wahab and Al-Alawi, 2002), forecasting of river flow rate during low flow periods (Campolo et al., 1999), determination of the effects of water pollution of aquacultures (Sengorur and Oz, 2002), modeling of outdoor noise levels (Avsar et al., 2004), forecasting of daily river flow (Kisi, 2004, 2005), eutrophication modeling (Karul et al., 2000), mathematical water quality modeling (Karul et al., 1998), estimation of phytoplankton production (Scardi, 1996), prediction of algal bloom (Yabunaka et al., 1997), statistical characterization of atmospheric PM10 and PM2.5 concentrations (Karaca et al., 2005), modeling of residual chlorine in urban drinking water systems (Rodriguez and Sérodes, 1999), regional flood frequency analysis (Hall and Minns, 1998), modeling of the rainfall runoff process (Hsu et al., 1995), optimization of groundwater remediation (Rogers and Dowla, 1994), forecasting of

Figure 1. clone.

A schematic diagram of a classical reverse-flow cy-

ENVIRON ENG SCI, VOL. 23, NO. 4, 2006

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YETILMEZSOY Main operating and design parameters selected in computational analysis.

Table 1.

Operating parameters Gas flow rate Q (m3/h) 25000

Design parameters

Density of particles

Temperature (°C)

Design Parameter 1

Design Parameter 2

rp (gr/cm3) 1.50

T 230

Ka 0.5

Kb 0.2

salinity in a river (Maier and Dandy, 1998), suspended sediment estimation for rivers (Cigizoglu, 2002), rainfallrunoff forecasting models (Anctil et al., 2004), prediction of wastewater treatment plant performance (Hamed et al., 2004), modeling of SO2 concentration (Nunnari et al., 2004), determination of the relationship between sewage odour and biological oxygen demand (BOD) (Onkal-Engin et al., 2005), estimation of sanitary flows (Djebbar and Alila, 1998), and controlling of leachate flow rate (Karaca and Ozkaya, 2005). Nevertheless, very little information is available in the literature on OBD of air cyclones using ANN approach. The objectives of this study are:

The inlet pipe (rectangular inlet) of the cyclone is generally mounted tangentially onto the side of the cylindrical part of the cyclone body. The exit tube, usually called the vortex finder, is fixed on the top of the cyclone (Ma et al., 2000). The size of a cyclone separator can be characterized in terms of its body diameter. OBD values were calculated from the optimum cyclone diameter model proposed by Kalen and Zenz (1974) for these different operating conditions. According to Kalen and Zenz’s model, optimum cyclone diameter was expressed by the following formula:

1. to calculate the body diameter of air cyclones using the proposed approaches defined in a different function of main operating parameters and compare results with the well-known Kalen and Zenz’s model; 2. to control the pressure drop using a MATLAB® algorithm for various operating data; 3. to assess the impact of the proposed approaches for designers, researchers, engineers, manufacturers, and end-users concerned with separation processes and provide a reference for other future diameter models.

where D is the optimum cyclone diameter (ft), Q is the gas flow rate (ft3/s), rf is the gas density (lb/ft3), m is the viscosity (lb/ft/s), rp is the particle density (lb/ft3), and Ka and Kb are design parameters. Depending on the temperature values, gas viscosity (mG) and gas (air) density (rG) were calculated from the following equations:

Kalen and Zenz’s model A schematic diagram of a classical reverse-flow cyclone is illustrated in Fig. 1. The cyclone consists of four main parts (Altmeyer et al., 2004): the inlet, the separation chamber, the dust chamber, and the vortex finder.

4

0.454

(1)

mG 5 0.0234 1 0.0001464 (T1 1 273)

(2)

P MG rG 5 }} R(T1 1 273)

(3)

The proposed model The empirical model was developed based on five main variables: gas flow rate, temperature, particle den-

Relationship between cyclone diameter and main variables used in the computational analysis.

Variable parameters Q (ft3/sec) rp (lb/ft3) T (°K) Ka Kb

3

where mG is the gas viscosity (kg/m ? s), T1 is the operating temperature (°C), rG is the gas density (kg/m3), P is the gas pressure (atm), MG is the molecular weight of the gas (kg/kmol), and R is the universal gas constant (0.082 m3 ? atm/mol ? K).

DEFINITION OF THE PROPOSED MODELS

Table 2.

(Q)(rf)2(1 2 Kb) D 5 0.0502 }}} (mG)(rp)(Ka)(Kb)2.2

Constant parameters rp Q Q Q Q

5 5 5 5 5

93.5174 lb/ft3 245.0524 ft3/sec 245.0524 ft3/sec 245.0524 ft3/sec 245.0524 ft3/sec

T T rp rp rp

5 5 5 5 5

Parameter equations 503°K 503°K 93.5174 lb/ft3 93.5174 lb/ft3 93.5174 lb/ft3

Ka Ka Ka T T

5 5 5 5 5

0.50 0.50 0.50 503°K 503°K

Kb Kb Kb Kb Ka

5 5 5 5 5

0.20 0.20 0.20 0.20 0.50

D D D D D

5 5 5 5 5

0.3286 Q0.454 31.35 rp20.454 9119.4 T21.2431 2.916 Ka20.454 0.6519 Kb21.1263

OPTIMUM BODY DIAMETER OF AIR CYCLONES Table 3.

Input variables and their operating ranges considered in the scenarios.

Variables Gas flow rate (Q1) Temperature (T1) Particle density (rp1) Ka Kb

Units

Minimum

Maximum

[m3/h/cyclone] [°C] [gr/cm3] Dimensionless Dimensionless

108.98 130 1.20 0.400 0.180

24000 300 2.10 0.600 0.260

sity, and two design parameters, which are Ka and Kb. Main operating and design parameters used in the computational analysis were presented in Table 1. The computational analysis was carried out for 32 different gas flow rates (Q), 17 different particle densities (rp), 21 different temperatures (T), 11 different Ka, and 8 different Kb values. In the first step of the computational analysis, gas flow rates were selected between 300–25,000 m3/h (2.9406–245.0524 ft3/s). Temperatures and particle densities were run between 130–230°C (403–503°K) and 1.20–2.00 g/cm3 (74.8139–124.6899 lb/ft3). The values of Ka and Kb were considered between 0.4–0.6 and 0.19–0.25, respectively. In the second step, five parameter equations presented in Table 2 were developed based on the power-law correlation for results obtained from the computational analysis. Parameter equations given in Table 2 were combined [Equation (4)], and new results were calculated computationally for different operating and design parameters selected in the first step of the computational analysis.

Table 4.

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The combined equation developed from parameter equations was given as follows:

3 1

1 2 21 21

Q 0.454 D 5 178582.89955 } nC 1 1 1 } } } r 0.454 T1.2431 Ka0.454 p

1

2 1 } 24 K 1.1263 b

0.2

(4)

where D is the cyclone diameter (ft), Q is the gas flow rate (ft3/s), nC is the number of cyclones used, rP is the particle density (lb/ft3), T is the operating temperature (K), and Ka and Kb are design values. In the last step, new results obtained from the computational analysis were corrected for main operating and design parameters, and five correction equations were formed. Maximum deviations between the combined equation and Kalen and Zenz’s model were determined, and five correction equations in terms of main parameters (Q, rP, T, Ka, and Kb) were set up. The correction equations were transferred to the combined equation, and the proposed model was obtained [Equation (5)]. The proposed model was rewritten as a function of gas flow rate (Q1), number of cyclones (nC), temperature (T1), particle

Comparison of eight backpropagation (BP) algorithms

Backpropagation (BP) Algorithms

Acronyms

R-values

Mean squared error (MSE)

Iteration Number

Resilient backpropagation (Rprop) Fletcher-Reeves conjugate gradient backpropagation Polak-Ribiere conjugate gradient backpropagation Powell-Beale conjugate gradient backpropagation Levenberg-Marquardt backpropagation Scaled Conjugate Gradient backpropagation BFGS Quasi-Newton backpropagation One Step Secant backpropagation

RP CGF

0.997 0.997

0.00407027 0.00470985

75 41

CGP

0.997

0.0592127

42

CGB

0.999

0.00193771

66

LM

1.000

0.000337671

40

SCG

0.999

0.000911033

91

BFG

0.998

0.00326695

34

OSS

0.998

0.0025302

100


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YETILMEZSOY

Neural network (NN) approach

Figure 2. The flow chart of MATLAB® algorithm used for controlling of pressure drop.

Operating parameters which are effective in the determination of OBD of air cyclones, such as gas flow rate, temperature, particle density, and design parameters (Ka and Kb) were taken as model input. Diameter values calculated from Kalen and Zenz’s model were used as a target vector for the neural network (NN) model. The NN model used back-propagation (BP) algorithm to predict diameter values based on inputs vector (5 3 505) of five main operating variables and target vector (1 3 505) obtained from Kalen and Zenz’s model. Five input variables and their operating ranges considered in the scenarios are defined in Table 3. Diameter values were selected as output in the NN model. Data were divided into a p (input) matrix and a t (target) matrix. In the first step, data were loaded into the workspace. Original network inputs and targets given in the matrices p and t were normalized. The normalized inputs and targets, pn and tn gained zero means and unity standard deviation. The mean and standard deviations of the original inputs and targets were defined before the network had been trained. Moreover, the matrices containing the transformed input vectors and the principal component transformation matrix were defined, respectively. All these vectors were used in transformation for future inputs. In the next step, principal component analysis was performed as an effective procedure for the determination of input parameters. Principal components that contribute less than 0.1% to the total variation in the data set

density (rP1), and Ka and Kb values in an SI unit system (kg-meter-second) and given in Equation (6). By using the proposed model, gas viscosity (mG) and gas density (rG) used in Kalen and Zenz’s model were eliminated. Transferring correction equations to the combined equation yields the predicted equation given as follows: D5 }21}}21} }21}}24 3178582.899551}n}2 1} r T K K 25000 230 0.5 0.2 1.5 }} }} }} }} 1 Q 2 1 T 2 1 K 2 1 K 2 1}r }2 Q

0.454

0.3632

1

1

1

0.454 P 20.3864

C

1

1

1.2431

0.454 a 20.883

20.363

a

b

1

0.2

1.1263 b 20.363

(5)

P1

Equation (5) was rewritten as a function of gas flow rate (Q1 [5] m3/h), number of cyclones (nC), temperature (T1 [5] °C), particle density ( rP1[5] g/cm3), and Ka and Kb values. Combining and transforming the predicted equation in a new function yields: D5

1 2

Q 0.454 (0.2279) }}1 nC }}}}} (rp1 Ka)0.4538 (T1 1 273)0.2486 T10.3864 Kb1.1083

(6)

Figure 3. Relationship between OBD values obtained from Kalen and Zenz’s model and the proposed model for 505 different artificial operating data.


Figure 4.

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Agreement between predicted values and Kalen and Zenz’s model.

were eliminated, or it can be said that principal components which accounted for 99.9% of the variation were used in the data set. It was observed that there was no redundancy in the data set and size of the transformed data after the computation. Most of the neural network models are characterized by the summation function, activation function, network topol-

Figure 5.

ogy, and learning rule they employ (Massong and Wang, 1990). In this study, a two-layer NN with tangent sigmoid transfer function (tan-sig) at a hidden layer and a linear transfer function (purelin) at an output layer were used. Data were divided into training, validation, and test subsets. Onefourth of the data was taken for the validation set, onefourth for the test set, and one-half for the training set.

The comparison between backpropagation algorithms.


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YETILMEZSOY

Hence, 253 input sets were used for the training and 126 input sets were used for the validation and test, respectively. Optimization of an NN is an important task of NNbased studies (Almasri and Kaluarachchi, 2005). This operation plays an important role in the performance of the network. Hence, an optimization was carried out between the neuron number and mean squared error (MSE). Then, the two-layer neural network were evaluated by the best BP algorithm, selected as the best of eight BP algorithms for training (Table 4). In the last step, some analysis of the network response was carried out. The entire data set was put through the network (training, validation, and test), and a linear regression between the network outputs and the corresponding targets was performed. First, the trained network was simulated. In the next step, the network outputs were unnormalized and converted back into the original units. Briefly, the unnormalized network outputs (a) was obtained in the same units as the original targets (t).

Controlling of the pressure drop Pressure drop is one of the major criteria used to evaluate cyclone performance (Zhao, 2004). It is a function of the cyclone geometrical dimensions and flow parameters. Pressure losses through the cyclone is a key pa-

Figure 6.

rameter on the performance of the cyclone, and directly related to energy consumption. In order to emphasize the usefulness of a proposed diameter model, controlling of pressure drop is needed. Hence, predictive capabilities of proposed diameter models should be examined by pressure drop control. This optimization will provide better estimations in cyclone design. In this study, a MATLAB® algorithm was also used to control pressure drop problems in addition to prediction models developed for OBD of air cyclones. In operating conditions, pressure drop was controlled by the following equation: DP 5 0.00330 r9f uT2 NH 5 0.00330

1

Q [rf 1 c(rp 2 rf)] }} (DKa)(DKb)

2

2

NH (7)

where DP is the pressure drop across the cyclone (inch), uT is the inlet velocity (ft/s), NH is the pressure drop parameter (inlet velocity heads), rf is the gas density (lb/ft3), c is the ratio between the particle volume, and gas volume, rp is the particle density, uT is the inlet velocity (ft/s), Q is the gas flow rate (ft3/s), D is the optimum body diameter (ft), a is the inlet height (ft), b is the inlet width (ft), and Ka and Kb are design parameters. In computational analysis, values higher than 10 inches were determined rapidly and practically using the MATLAB® al-

The dependence between MSE and number of neurons.


Figure 7.

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Optimal neural network structure for prediction of OBD values.

gorithm. Controlling of pressure drop was followed by calculation of collection efficiency (h) for operating data giving a pressure drop less than 10 inches. The flow chart of MATLAB® algorithm is illustrated in Fig. 2.

RESULTS AND DISCUSSIONS The proposed empirical model was solved by the MATLAB® algorithm for 505 different artificial scenarios given in a wide range of operating variables. Scenarios were run for the gas flow rate between 108.98 and 24,000 m3/h/cyclone (1.07 and 235.25 ft3/s/cyclone), for temperatures between 130 and 300°C (403 and 573 K), for particle densities between 1.20 and 2.10 g/cm3 (74.90 and 130.92 lb/ft3), for Ka values between 0.400 and 0.600, and for Kb values between 0.180 and 0.260. Results obtained from the predicted model agreed very well with the OBD model given by Kalen and Zenz. The relationship between the proposed model and Kalen and Zenz’s model shows an excellent correlation for various operating conditions. The linear regression between the proposed model and Kalen and Zenz’s model is shown in Fig. 3. Figure 4 illustrates the agreement between two models for 505 artificial scenarios given in a wide range of operating data. The proposed model predicts very well OBD values for air cyclones, and can be used in cyclone design for various operating and design conditions. In computational calculations, very small-diameter deviations were recorded, with a maximum deviation of about 61.3 cm from Kalen and Zenz’s model. The relationship between the proposed model and Kalen and Zenz’s model shows an excellent correlation (R2 5 0.9998) for OBD values calculated computationally.

In an NN study, a two-layer network was formed and trained after the definition of subsets. Eight BP algorithms were compared to select the best fitting BP algorithm. For all BP algorithms, a two-layer network with a tan-sig transfer function at the hidden layer and a purelin at the output layer, were used. Nine neurons were used at the hidden layer for all BP algorithms. The LevenbergMarquardt algorithm (LMA), with a MSE was selected as the best of eight BP algorithms (Table 4). The comparison between BP algorithms was shown in Fig. 5.

Figure 8. The graphical output of the network outputs plotted versus the targets for the Levenberg-Marquardt algorithm. A: Network outputs, T: Targets.


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YETILMEZSOY

Figure 9.

Agreement between 126 test outputs and Kalen and Zenz’s model.

In optimization of the network, five neurons were used in the hidden layer as an initial guess. With increasing of neuron number, the network gave several local minimum values, and different MSE values were obtained for the training set. However, increasing neuron numbers to more than 11 caused an unrealistic result, and the mean squared began to increase. Hence, the optimal neuron number for the LMA algorithm was found to be 11 neurons (MSE 4.52821e-005/0). Figure 6 illustrates the dependence between the neuron number and MSE. Finally, the optimal NN structure for prediction of diameter values was shown in Fig. 7: a two-layer network, with tansig function at the hidden layer with 11 neurons and a purelin at the output layer.

Figure 10.

The training was stopped after 40 iterations (TRAINLM, Epoch 40/100) for the Levenberg-Marquardt algorithm because the differences between training error and validation error started to increase. The linear regression between the network outputs and the corresponding targets showed that the NN outputs (predicted values) obviously agreed with Kalen and Zenz’s model. The LMA was selected as the best of eight BP algorithms. The optimal neuron number for the LMA was obtained to be 11. Hence, a two-layer network structure with a tan-sig transfer function at the hidden layer with 11 neurons and a purelin at the output layer were used to predict OBD of air cyclones. Figure 8 illustrates the graphical output of the network

Residual errors (diameter deviations) between 126 test outputs and Kalen and Zenz’s model.


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outputs plotted vs. the targets as open circles. The best linear fit was indicated by a dashed line. Figure 9 shows the agreement between 126 test outputs (predicted values) and Kalen and Zenz’s model. NN outputs showed a negligible diameter deviations with a maximum deviation of about 60.0022 cm from Kalen and Zenz’s model (Fig. 10). The R2 value was almost 1. It is believed that ANN techniques, which have recently been applied to various problems, may provide a good alternative to statistical and theoretical techniques and also iterative problems because of their speed and capability of learning, robustness, predictive capabilities, nonlinear characteristics, nonparametric regression capabilities, generalization properties, and easiness of working with high-dimensional data. In the last decade, it is shown that this technology can provide useful tools for solving practical engineering problems (Rath, 1988; Stevenson 1991).

searchers concerned with separation processes. The proposed approaches presented in this study can provide realistic results for the OBD of air cyclones. It is expected that the information given here will be useful for many cyclone applications in relevant calculations for designers, researchers, manufacturers, separation–equipment engineers and end-user industries.

CONCLUSIONS In this paper, a two-layer NN approach and a mathematical model that can predict the OBD of air cyclones have been described. Five hundred five different artificial scenarios given in a wide range of five main operating variables were solved based on proposed empirical equation and a two-layer NN model. Results obtained from these two categories were compared with Kalen and Zenz’s model, and significant points of the proposed approaches were evaluated. Both developing a new mathematical model and creating a NN model on OBD values promoted the existing calculation method, and gave favorable results for desired values. The OBD equation was written as a different function of gas flow rate, number of cyclones, temperature, particle density, and Ka and Kb values in a different unit system. The gas density (rf) and gas viscosity (mG) variables used in Kalen and Zenz’s model were eliminated by using the proposed OBD model. Both the proposed model and NN outputs showed a good prediction on OBD values under 505 different artificial scenarios. Choosing an appropriate data set depending on the ranges of input variables showed a good performance for stochastic modeling approaches presented in this study. It can be concluded that the stochastic approaches given in this study can be evaluated as a new approach, and a new scope of calculation to predict the OBD values in cyclone design. Results obtained from this study will provide a new reference for other theoretical and experimental future diameter models and be helpful for separation–equipment engineers, designers, and other re-

ACKNOWLEDGMENTS The author would like to thank Assist. Prof. Dr. Bestamin Ozkaya for his useful comments and suggestions. The author also wish to thank Prof. Dr. Ferruh Erturk and Assist. Prof. Dr. Arslan Saral for their helpful discussions.

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