AP_07_6.vp 1 Introduction A mechanically agitated system under a turbulent regime of flow with or without internals (radial baffles, draft tubes, coils etc.) consists of a broad spectrum of eddies from the size of the main (primary) circulation loop (PCL) of the agitated batch down to the dissipative vortices corresponding to mi- cro-scale eddies. This study deals with an experimental and theoretical analysis of the behaviour of the flow pattern, and mainly the PCL in an agitated liquid in a system with an axial flow impeller and radial baffles. Some characteristics of the inves- tigated behaviour are considered to be in correlation with the occurrence of flow macroinstabilities (FMIs), i.e. the flow macro-formation (vortex) appearing periodically in various parts of a stirred liquid. The flow macroinstabilities in a mechanically agitated system are large-scale variations of the mean flow that may affect the structural integrity of the vessel internals and can strongly affect both the mixing process and the measurement of turbulence in a stirred vessel. Their space and especially time scales considerably exceed those of the turbulent eddies that are a well known feature of mixing sys- tems. The FMIs occur in a range from several up to tens of seconds in dependence on the scale of the agitated system. This low-frequency phenomenon is therefore quite different from the main frequency of an incompressible agitated liquid corresponding to the frequency of revolution of the impeller. Generally, experimental detection of FMIs is based on fre- quency analysis of the oscillating signal (velocity, pressure, force) in long time series and frequency spectra, or more so- phisticated procedures (proper orthogonal decomposition of the oscillating signal, the Lomb period gram or the velocity decomposition technique) are used to determine the FMI frequencies. A theoretical method for finding FMIs could contribute significantly to a deeper understanding of fluid flow behaviour in stirred vessels, e.g. a description of the circulation patterns of a agitated liquid, application of the theory of deterministic chaos, knowledge of turbulent co- herent structures, etc. [1–10]. This study investigates oscillations of the primary circula- tion loop (the source of FMIs) in a cylindrical system with an axial flow impeller and radial baffles, aiming at a theoretical description of the hydrodynamical stability of the loop. How- ever, no integrated theoretical study of the MI phenomenon has been presented up to now. 2 Experimental The experiments were performed in a flat-bottomed cy- lindrical stirred tank of inner diameter T � 0.29 m filled with water at room temperature with the tank diameter height H � T. The vessel was equipped with four radial baffles (width of baffles b � 0.1 T) and stirred with a six pitched blade im- peller (pitch angle 45°, diameter D � T/3, width of blade W � D/5), pumping downwards. The impeller speed was ad- justed n � 400 rpm � 6.67 s�1 and its off-bottom clearance C was T/3 (see Fig. 1). © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 17 Acta Polytechnica Vol. 47 No. 6/2007 Dynamics of the Flow Pattern in a Baffled Mixing Vessel with an Axial Impeller O. Brůha, T. Brůha, I. Fořt, M. Jahoda This paper deals with the primary circulation of an agitated liquid in a flat-bottomed cylindrical stirred tank. The study is based on experiments, and the results of the experiments are followed by a theoretical evaluation. The vessel was equipped with four radial baffles and was stirred with a six pitched blade impeller pumping downwards. The experiments were concentrated on the lower part of the vessel, where the space pulsations of the primary loop, originated due to the pumping action of the impeller. This area is considered to be the birthplace of the flow macroinstabilities in the system – a phenomenon which has been studied and described by several authors. The flow was observed in a vertical plane passing through the axis of the vessel. The flow patterns of the agitated liquid were visualized by means of Al micro particles illuminated by a vertical light knife and scanned by a digital camera. The experimental conditions corresponded to the turbulent regime of agitated liquid flow. It was found that the primary circulation loop is elliptical in shape. The main diameter of the primary loop is not constant. It increases in time and after reaching a certain value the loop disintegrates and collapses. This process is characterized by a certain periodicity and its period proved to be correlated to the occurrence of flow macroinstability. The instability of the loop can be explained by a dissipated energy balance. When the primary loop reaches the level of disintegration, the whole impeller power output is dissipated and under this condition any flow alteration requiring additional energy, even a very small vortex separation, causes the loop to collapse. Keywords: mixing, axial impeller, primary circulation loop, oscillation, macroinstability. Fig. 1: Pilot plant experimental equipment The flow under the parameters mentioned above was turbulent, with the impeller Reynolds number value ReM � 6.22·10 4. The flow was observed in a vertical plane passing through the vessel (vertical section of the vessel) in front of the adja- cent baffles. The flow patterns of the agitated liquid were visu- alized by means of Al micro particles 0.05 mm in diameter spread in water and illuminated by a vertical light knife 5 mm in width, see Fig. 2. 18 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 47 No. 6/2007 Fig. 2: Experimental technique of flow visualization Fig. 3: Visualization of the PCL Fig. 4: Visualization of flow macro formation The visualized flow was scanned by a digital camera; series of shots were generated with a time step of 0.16 s and were an- alyzed by appropriate graphic software. The total length of the analyzed record was 30.24 s. The characteristics observed and analyzed were: a) the shape and sizes of the PCL, b) the size of the PCL core, c) the positions of the top of the flow macro formation and the corresponding functions were obtained: a) the height of the PCL hci � hci(t) (see Fig. 3), b) the width of the PCL sci � sci(t) (see Fig. 3), c) the equivalent mean diameter of the PCL core rc,av i � rc,av i(t) (see Fig. 3), d) the height of the top of the flow macro formation hFMI,i � hFMI,i(t) (see Fig. 4). 3 Results of experiments The analysis of the experiments provided the following findings: The PCL can be described as a closed stream tube with a vertical section elliptical in shape with a core. The flow in the elliptical annular area is intensive and streamlined, while the core is chaotic and has no apparent streamline characteristics. The flow in the remaining upper part is markedly steadier. This is in agreement with the earlier observations of some au- thors [6, 7]. The flow process is characterized by three stages. In the first stage, the PCL grows to a certain size (its shape can be ap- proximated as elliptical). Then a quasi-steady stage follows, when the PCL remains at a constant size for a short time. In the next stage the PCL collapses into very small flow forma- tions (vortices) or disintegrates into chaotic flow, see Fig. 5a–c. © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 19 Acta Polytechnica Vol. 47 No. 6/2007 a) b) c) Fig. 5: a) PCL growing, b) PCL at maximum height, c) PCL after its collapse 0 20 40 60 80 100 120 0 5 10 15 20 25 30 35 t (s) P C L in c id e n c e (% ) Fig. 6: Dependence of PCL incidence on time for the whole analyzed time The process (oscillation of the PCL) is apparently charac- terized by a certain periodicity. The function of the incidence of the PCL in time is illustrated in Fig. 6, which shows that the PCL incidence ratio approaches 80 % of the considered time. The graph in Fig. 7 (vertical dimension of the PCL as a function of time) illustrates this process for the whole ana- lysed time of 30.24 s. 20 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 47 No. 6/2007 0 0.05 0.1 0.15 0.2 0.25 0 5 10 15 20 25 30 35 t (s) h c i (m ) Fig. 7: Dependence of the vertical dimension of PCL hci on time for the whole analyzed time Fig. 8: Time evolution of the height of the PCL (average cycle time tc,av � 1.59 s, maximum height hc,max � 0.181 m, hc, max/H � 0.62) for one cycle of PCL oscillation Fig. 9: Dependence of the mean rising velocity ur of the PCL on time (ur � dh/dt � 0.042 m/s � const., t > 0.77 s) The calculated average time of one cycle (the time be- tween the origin of the PCL and its collapse) is tc,av � 1.59 s. This means that the frequency of the PCL oscillations is fosc � 1/tc,av � 0.63 Hz and dimensionless frequency Fosc � fosc/n � 0.094. This dimensionless frequency is markedly higher than the value detected earlier in the interval 0.02–0.06 [8–10]. This corresponds to our finding that only some of the flow formations generated by one PCL cycle result in macro- -flow formation causing a surface level eruption, detected as “macroinstability”. The function hc � hc(t) for one cycle is shown in Fig. 8. This function was obtained by regression of the experimental data hci(t), where the individual cycle intervals were recalculated for an average time cycle tc,av � 1.59 s. Fig. 8 shows that the mean maximum height of the PCL hc,max reaches a value of 0.181 m, which is 62 % of surface level height H. This agrees with earlier findings [11] that hc,max� 2/3 H. The function hc � hc(t) was used for calculating the PCL rising velocity, see Fig. 9. Finally, the average rising time of flow macro formation generated by PCL was calculated from the time function hFMI � hFMI(t) (time between generating and disintegration), and the value obtained was tav, FMI � 1.0 s. The regression curve hFMI,i � hFMI,i(t) corresponding to the experimental data for one cycle (development of one macro-formation, the time recalculated for average rising time tav,FMI) is illustrated in Fig. 10. To specify the PCL characteristics more deeply, the vol- ume of the PCL (active volume of the primary circulation) was calculated. This was assumed as a toroidal volume around its elliptical projection in the r-z plane of the mixing vessel. The function of the ratio of the PCL volume to vessel volume Vc/V � (Vc/V) (t) for one cycle is illustrated in Fig. 11, where © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 21 Acta Polytechnica Vol. 47 No. 6/2007 Fig. 10: Dependence of the height of the top of the flow macro formation hFMI, i on the time for one cycle Fig. 11: Dependence of the ratio of the PCL volume to the vessel volume Vc,max/V on time for one cycle of the PCL oscillation V t T h t s t T r tc c c c, av( ) ( ) ( ) ( )� � � � � � � � 2 2 2 4 (1) is calculated from the corresponding regression curves hc � hc(t), sc � sc(t) and rc,av(t). Fig. 11 shows that the mean maximum ratio of the PCL volume to the vessel volume Vc,max/V reaches a value of 0.326. 4 Theoretical calculation of energy balance An energy balance for the PCL was carried out with a view to explaining the reasons for the flow field behaviour (pre- dominantly PCL oscillations). As mentioned above, there are three different stages in the flow process. The energy balance was carried out for the quasi-steady stage under conditions when the PCL reaches its top position, i.e. hc = hc, max, see Fig. 12. This stage directly follows (precedes) the collapse and is assumed to have a critical influence on the flow disintegration. The impeller power input N is dissipated in the PCL by the following components: I) Mechanical energy losses: 1) Nturn – lower turn of the primary circulation loop about 180° from downwards to upwards. 2) Nwall – friction of the primary circulation loop along the vessel wall. II) Turbulence energy dissipation: 1) Ndisch – dissipation in the impeller discharge stream just below the impeller. 2) Nup – dissipation in the whole volume of the agitated liquid above the impeller rotor region, i.e. in the space occupied by both the primary and secondary flow. It is expected that under quasi-steady state conditions (just before the PCL collapses) these components are in bal- ance with the impeller power output. This means that no spare power is available, and that no alternative steady state formation is possible. The individual power components and quantities can be calculated when the validity of the following simplifying assumption for the flow in the PCL is considered: 1) The system is axially symmetrical around the axis of symmetry of the vessel and impeller. 2) The primary circulation loop can be considered as a closed circuit. 3) The cross section of the primary circulation loop (stream tube) is constant. 4) The conditions in the primary circulation loop are isobaric. 5) The liquid flow regime in the whole agitated system is fully turbulent. 6) The character of the turbulence in the space above the impeller rotor region is homogeneous and isotropic. 4.1 Calculation of basic quantities Impeller power input P Po n D� � 3 5, (2) where the impeller power number Po � 1.7 for ReM>10 4 [12], n � 6.67 s�1, D � 0.0967 m, � � 1000 kg/m3. Then P � 4.25 W. The impeller power output can be calculated for known impeller hydraulic efficiency �h (�h=0.48 for a four 45° pitched blade impeller [14]). N Ph� �� 2 04. W . (3) Impeller pumping capacity Qp can be calculated from the known flow rate number NQp (NQp � 0.94 for ReM>10 4 [13]). Q N n Dp Qp m s l s� � � � � �3 3 3 1 15 66 10 5 66. . (4) The mass flow rate is m Qp p� �� 5 66. kg s �1 (� � 1 kg l �1). (5) The axial impeller discharge velocity is equal to the aver- age circulation velocity of the PCL (assuming a constant aver- age circulation velocity in the loop): w Q D c,av p � � 4 2 � 0.77 m s�1, (6) where �D2/4 is the cross sectional area of the impeller rotor region, i.e. the cylinder circumscribed by the rotary mixer. Then the primary circulation loop is a closed stream tube consisting of the set of stream lines passing through the im- peller rotor region. 4.2 Calculation of turbulent dissipation below the impeller rotor region, Ndisch The energy dissipation rate per unit mass is [14] � � �A q L 3 2 , (7) where � � � � � � � A 2 3 3 2 (8) and the integral length of turbulence [14] is L D � 10 . (9) 22 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 47 No. 6/2007 Fig. 12: Schematic view of the PCL under its top position (hc = hc, max) The kinetic energy of turbulence per unit of mass is q w w wz r� � � � � � � � � � � 1 2 2 2 2 � . (10) According to [14] the average value of q in the impeller discharge stream is q0 � 0.226 m 2s�2 for the conditions de- scribed in [14]: a four pitched blade impeller with a pitch angle of 45°, D0 � 0.12 m, T0 � 0.24 m, n0 � 6.67 s �1, Po0 � 1.4, ReM,0 � 44 10 4, P0 � 10.3 W, L0 � 0.012 m. We have from Eq. (7) �0 � 6.029 m 2 s�3. The energy dissipation per unit mass � related to the experimental system used in this study is � � � � �� � �0 0 0 0 0 0 0 P m P m P V P V , ( ) (11) and after substitution V � 0.0192 m3, P0 � 10.3 W, V0 � 0.0109 m3 we obtain � � 1.384 m2 s�3. Using N Vdisch disch� � � , (12) where the dissipation volume below the impeller rotor region Vdisch � 0.000330 m 3 (see Fig. 13). We obtain Ndisch � 0.46 W. 4.3 Calculation of dissipation in the whole volume above the impeller region, Nup According to [15] N Pup up� �� 0.60 W, (13) where the portion of the impeller power input dissi- pated above the impeller rotor region �up = 0.14 for a six 45° pitched blade impeller (D/T = C/T = 1/3, H = T) and ReM>10 4. When calculating the quantity Nup, the validity of intro- duced assumption No. 6 is considered. Moreover, because of the momentum transfer between the primary flow and the secondary flow out of the PCL the rate of energy dissipation above the impeller rotor region is related to the whole vol- ume, consisting of both the primary and secondary flows. 4.4 Calculation of the dissipation in the lower turns of the PCL, Nturn According to [16] N w mj j turn c,av 2 p2 � � . (14) Substituting the sum of loss coefficients � j j � 0.50 for bend of turn of the PCL � � 180° as well as the values of the average circulation velocity of the PCL wc,av , and the mass flow rate mp, we obtain Nturn � 0.84 W. 4.5 Calculation of the dissipation by the wall friction along the PCL, Nwall Using the relation for mechanical energy loss due to the friction along the wall, from [17] N l w d m e wall c,av 2 p� 2 , (15) where equivalent diameter is defined as d S O D T D Te � � � 4 4 4 2 2 � � (16) and the friction factor for a smooth wall � �0 3164 0 25. Re . (17) where Re � w Dc,av � � . (18) Then we can calculate the rate of energy dissipation in the flow along the smooth vessel wall after substitution: � � 1 m Pa s, length of the PCL along the wall l h h� �c,max turn where hc,max � 0.181 m, (see Fig. 8), hturn � 0.051 m, so l � 0.13 m, and values de � 0.032 m, © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 23 Acta Polytechnica Vol. 47 No. 6/2007 Fig. 13: Dissipation volume below the impeller rotor region Vdisc before the first turn of the loop (D � T/3 � 0.0967 m, z � 0.045 m) Re � 7.45 104 and � 0.020 obtained from Eqs. (16)–(18) to Eq. (15), we get Nwall � 0.14 W. 4.6 Energy balance in the quasi-steady stage of the PCL The sum of all dissipated power components considered here is N N N N Ni � � � � turn wall disch up, (19) Ni � � � � �0 84 014 0 46 0 60 2 04. . . . . W. (19a) The value in Eq. (19a) is in good agreement with the im- peller power output from Eq. (3), N � 2.04 W, though the data used for the calculations come from six independent litera- ture sources. This result means that in the quasi-steady phase of the PCL oscillation cycle, all the impeller power output is consumed by dissipation. No power is available, either for increasing the PCL kinetic energy or for any changes in flow formation resulting in a higher energy level. However, it is well known that vortex disintegration in smaller formations or even a very small vortex separation from a primary flow is a process that consumes energy (according to the law of angular momentum conservation). The experiments proved that vor- tex separations (small and large) occur in all the stages, thus also in the quasi-steady stage. This seems to provide an expla- nation for the PCL collapse: in the quasi-steady stage, the energy necessary for vortex separation or for other changes in flow formation cannot be supplied by the impeller, but energy is exhausted from the ambient flow field. And then, even a very small energy deficit can result in a qualitative flow field change appearing as the PCL collapse. It should be noted that the PCL collapse can be followed by a noticeable rise in the surface level, classified as a macroinstability. How- ever, not every collapse reaches the level and is observed as a macroinstability. This corresponds to this disagreement between the PCL oscillation frequency determined experi- mentally in this study and the macroinstability frequency presented. The phenomenon observed here affects the processes tak- ing place in an agitated charge , especially on the macro level, i.e., when miscible liquids blend and when solids suspend in liquids. Oscillations of the macroflow contribute to attain a so called “macroequilibrium” in an agitated batch, i.e., better homogeneity both in a pure liquid (blending) and in a solid- -liquid suspension (distribution of solid particles in a liquid). These processes can be observed predominantly in the subre- gion of low liquid velocity above the impeller rotor region, corresponding to approx. One third of the volume of the agi- tated charge. Oscillations of the primary circulation of an agitated liquid can contribute to the forces affecting the body of the impeller as well as the mixing vessel and its internals. This low frequency phenomenon probably need not have fa- tal consequences, because the standard design of industrial mixing equipment should have sufficient margins for unex- pected events during processes running in an industrial unit. 5 Conclusions a) The average circulation velocity in the primary circulation loop is more than one order of magnitude higher than the rising velocity of the loop. b) The frequency of the primary loop oscillations is about one order of magnitude lower than the revolution frequence of the impeller. c) The top of the disintegration of the primary circulation loop is a birthplace of macroinstabilities in the region of secondary flow. d) The primary circulation loop collapses owing to disequilib- rium between the impeller power output and the rate of dissipation of the mechanical energy in the loop. A small change (e.g. a small turbulent vortex or a small increase in the primary circulation loop) can have a great effect. Acknowledgments The authors of this paper are grateful for financial sup- port from the following Czech Grants Agencies: 1. Czech Grant Agency Grant No. 104/05/2500. 2. Czech Ministry of Education Grant No. 1P05 LA 250. 3. Czech Ministry of Education Grant No. MSM6046137306. List of symbols b width of baffle, m C off-bottom clearance, m de equivalent diameter, m D impeller diameter, m fosc frequency of PCL oscillations, Hz Fosc dimensionless frequency of oscillations hc value of height of the PCL obtained by regres- sion, m hci experimental value of height of the PCL, m hc, max maximal height of the PCL, m hc,min minimal height of the PCL, m hFMI value of height of the top of macro formation obtained by regression, m hFMI,i experimental value of height of the top of the flow macro formation, m hturn height of turn of the PCL, m H height of water level, m l length of the PCL adjacent to wall, m L integral length scale of turbulence, m m mass of liquid in a stirred tank, kg mp mass flow rate, kg s �1 n impeller speed, s�1 N impeller power output, W Ndisch turbulent dissipation below the impeller rotor region, W NQp impeller pumping number Nturn dissipation in lower turns of the PCL, W Nup dissipation in the whole volume above the im- peller rotor region, W 24 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 47 No. 6/2007 Nwall dissipation by the wall friction of the PCL, W P impeller power input, W Po impeller power number q kinetic energy of turbulence per unit of mass, m2s�2 Qp impeller pumping capacity, m 3s�1 rc,av equivalent mean diameter value of the PCL core, obtained by regression, m rc,av i experimental value of equivalent mean diame- ter of the PCL core, m Re Reynolds number ReM impeller Reynolds number S cross section, m2 sc value of width of the PCL, obtained by regres- sion, m sci experimental value of width of the PCL, m T diameter of stirred tank, m tc,av average time of the PCL cycle, s tav, FMI average rising time of flow macro formation, s ur rising velocity of the PCL, m s �1 ur,av mean rising velocity of the PCL, m s �1 V volume of stirred tank, m3 Vc calculated volume of the PCL, m 3 Vc,max maximum value of calculated volume of the PCL, m3 Vdisch volume of dissipation below the impeller rotor region, m3 W width of blade, m wc,av axial impeller discharge velocity, m s �1 �wz, �wr, �w� turbulent velocity fluctuations in individual axis directions, m s�1 z height of cylindrical volume of dissipation be- low the impeller rotor region, m � bend of turn of the PCL, 1 � energy dissipation rate per unit mass, m2s�3 � dynamic viscosity, Pa.s �h impeller hydraulic efficiency �up portion of the impeller power input dissipated above the impeller rotor region friction factor � density of liquid, kg m�3 �j loss coefficient References [1] Roussinova, V. 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[6] Fořt, I., Gračková, Z., Koza, V.: Flow Pattern in a System With Axial Mixer and Radial Baffles. Collection of Czechoslovak Chemical Communications, Vol. 37 (1972), p. 2371–2385. [7] Kresta, S. M., Wood, P. E.: The Mean Flow Field Pro- duced by a 45° Pitched Blade Turbine: Changes in the Circulation pattern Due to off Bottom Clearance. The Canadian Journal of Chemical Engineering, Vol. 71 (1993), p. 52–42. [8] Brůha, O., Fořt, I., Smolka, P.: Phenomenon of Turbu- lent Macro-Instabilities in Agitated Systems. Collection of Czechoslovak Chemical Communications, Vol. 60 (1995), p. 85–94. [9] Hasal, P., Montes, J-L., Boisson, H. C., Fořt, I.: Macro- -instabilites of Velocity Field in Stirred Vessel: Detection and Analysis. Chemical Engineering Science, Vol. 55 (2000), p. 391–401. [10] Paglianti, A., Montante, G., Magelli, F.: Novel Ex- periments and Mechanistic Model for Macroinstabilities in Stirred Tanks. AICHE Journal, Vol. 52 (2006), p. 426–437. [11] Bittorf, K. V., Kresta, S. M.: Active Volume of Mean Circulation for Stirred Tanks Agitated with Axial Im- pellers. Chemical Engineering Science, Vol. 55 (2000), p. 1325–1335. [12] Medek, J.: Power Characteristics of Agitators with Flat Inclined Blades. International Chemical Engineering, Vol. 20 (1985), p. 664–672. [13] Brůha, O., Fořt, I., Smolka, P., Jahoda, M.: Experimen- tal Study of Turbulent Macroinstabilities in an Agitated System with Axial High-speed Impeller and Radial Baf- fles. Collection of Czechoslovak Chemical Communications, Vol. 61 (1996), p. 856–867. [14] Zhou, G., Kresta, S. M.: Distribution of Energy Between Convective and Turbulent Flow for Three Frequently Used Impellers. Trans I ChemE, Vol. 74 (Part A) (1996), p. 379–389. [15] Jaworski, Z., Fořt, I.: Energy Dissipation Rate in a Baffled Vessel with Pitched Blade Turbine Impeller. Col- lection of Czechoslovak Chemical Communications, Vol. 56 (1991), p. 1856–1867. © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 25 Acta Polytechnica Vol. 47 No. 6/2007 [16] Perry, J. H.: Chemical Engineer’s Handbook (Fourth Edi- tion). New York: McGraw–Hill Book Comp., 1963. [17] Brodkey, R. S.: The Phenomenon of Fluid Motions. Read- ing: Adison-Wesley Publishing Comp., 1967. Doc. Ing. Oldřich Brůha, CSc. phone, fax: +420 251 560 040 mobil: +420 777 895 766 e-mail: enex@atlas.cz Department of Physics Czech Technical University in Prague Faculty of Mechanical Engineering Technická 4 166 07 Prague 6, Czech Republic Ing. Tomáš Brůha phone, fax: +420 251 560 040 mobil: +420 777 895 762 e-mail: enex@volny.cz Department of Chemical and Process Engineering Institute of Chemical Technology, Prague Technická 5 166 28 Prague 6, Czech Republic Doc. Ing. Ivan Fořt, DrSc. phone: +420 224 352 713 fax: +420 224 310 292 e-mail: Ivan.Fořt@fs.cvut.cz Department of Process Engineering Czech Technical University in Prague Faculty of Mechanical Engineering Technická 4 166 07 Prague 6, Czech Republic Doc. Dr. Ing. Milan Jahoda phone: +420 220 443 223 fax: +420 220 444 320 e-mail: Milan.Jahoda@vscht.cz Department of Chemical and Process Engineering Institute of Chemical Technology, Prague Technická 5 166 28 Prague 6, Czech Republic 26 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 47 No. 6/2007