simulation of steelgrade change in a water...

METAL 2007 22. – 24. 5. 2007 Hradec nad Moravicí

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SIMULATION OF STEELGRADE CHANGE IN A WATER MODEL

TUNDISH USING THE COMBINED DPIV/PLIF TECHNIQUE

Dipl.-Ing. Roger KOITZSCH*, PD Dr.-Ing. Hans-Jürgen ODENTHAL+,

Prof. Dr.-Ing. Herbert PFEIFER*

*Institute for Industrial Furnaces and Heat Engineering, RWTH Aachen University

Kopernikusstraße 16, 52074 Aachen, Germany. +SMS Demag AG, Eduard-Schloemann-Straße 4, 40237 Düsseldorf, Germany

*E-Mail: [email protected]

Abstract

The mixing process in a 1:3 scaled water model tundish for the production of stainless steel is

investigated using the combined DPIV/PLIF (Digital Particle Image Velocimetry/Planar

Laser Induced Fluorescence) technique. The velocities in the water model are measured in

different light sheet planes up to a size of 300 mm ⋅ 1100 mm by the conventional DPIV method. The variation of the time-dependent concentration field is measured in the same

plane by the PLIF method. The tracers are polyamide particles for DPIV and a rhodamine 6G

solution as fluorescent dye for PLIF. Due to the special calibration procedure of the

DPIV/PLIF system, the optical, geometrical and physical parameters do not have to be

determined analytically, thus leading to reliable results. The experiments have been carried

out with a turbulent Reynolds number of Re = 5000 and show that the mixing process

correlates with the quasi steady-state flow pattern. The residence time of some water region

in the tundish model is significantly longer than the mean residence time (θ < 5). Such information is important for the steel production, because the number of mixed slabs

produced during sequence casting with a grade change is closely related to the mixing of the

tundish melt. The results of the combined DPIV/PLIF measurements are used to validate

numerical simulations of the mixing processes in water models of metallurgical reactors.

1. INTRODUCTION

In the year 2006, the world wide crude steel production amounted to 1230 million tonnes, of which nearly 91 % were cast in continuous casting plants. With the production of 47.2 million tonnes crude steel annually, of which 96.3 % are continuously cast, this makes Germany the seventh largest steel maker in the world. Steel is more environmentally compatible than many other materials because it is produced with a minimum energy input and can be recycled without loss of quality.

A continuous casting plant primarily consists of the ladle turret, several steel ladles, tundish, and oscillating mould with lower rolls to support the strand. Figure 1 shows the typical set-up of a continuous casting plant and parameters influencing the steel quality. In order to cast multiple steel melts in sequence without interruption, the following, that means the (n+1)th ladle is quickly positioned above the casting platform. The secondary metallurgy (degassing, de-oxidation, alloying, temperature and cleanliness adjustments) taking place in the ladle is a discontinuous process, whereas the solidification of the steel melt in the mould to a strand is a continuous process. The tundish links the discontinuous secondary metallurgy with the continuous casting. It serves as steel melt buffer during the ladle change, distributes the steel


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melt to several strands and separates non-metallic particles (i. e. Al2O3, SiO2) into the top slag cover due to buoyancy forces.

Figure 1: Continuous casting line and parameters affecting the quality of steel [1,2].

Important demands on the tundish as metallurgical reactor are that the steel melt should be well mixed, but at the same time it should flow homogeneously to allow non-metallic particles to be separated. The density of the particles is lighter than the melt and rise to the free surface. Due to this, mixing in the tundish plays a major role in metallurgy because it affects the number of mixed slabs. The transient casting phase during ladle change must be kept as short as possible to minimise the number of mixed slabs. Accordingly, the duration until the steel melt of the nth ladle is completely replaced by that of the (n+1)th ladle is important.

Due to high temperatures of the steel melt, the flow and thermal phenomena are in a range for which no adequate measurement technique is available. For this reason, physical and numerical simulations have to be done. Water can be used for the physical simulation because the kinematic viscosities of steel melt and water are comparable, thus making the fluidic behaviour of both fluids similar (νst,1536°C = 8.26.10-7 m2/s, νw,20°C = 10.0.10-7 m2/s). Considering the similarity laws, the results for water can be transferred to the steel melt.


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Figure 2: General layout of the DPIV/PLIF facility consisting of laser, water model tundish and CCD cameras.

Although many authors [3-9] have carried out concentration and temperature measurements using the LIF (Laser Induced Fluorescence) technique, this approach has not yet been adapted to water models of metallurgical reactors. Measurements of the RTD (Residence Time Distribution) [10-13] have been carried out by dye injecting and monitoring the time-dependent dispersion of the tracer at certain sampling positions.

It is the objective of this work to apply the combination DPIV and PLIF technique to tundish water models. Melt flows in metallurgical reactors can also be numerically simulated (CFD - Computational Fluid Dynamics) [13-19]. This measurements are used to provide quantitative information of the concentration fields in water models of metallurgical reactors and using the results as validation criteria for CFD simulations.

2. EXPERIMENTAL SETUP

2.1. Principle of PLIF

Some naturally occurring materials glow under the influence of energy. The emitted radiation in the visible range is called luminescence. It is to be distinguished between fluorescence and phosphorescence. Fluorescence arises spontaneously and stops as soon as the input of energy stops (10-9 s < t < 10-6 s), whereas phosphorescence lasts substantially longer after the input of energy (10-4 s < t < 102 s). LIF uses the frequency shift of the light emitted by fluorescent substances to measure scalar quantities in fluids such as the concentration or temperature. One speaks of PLIF (Planar Laser Induced Fluorescence) technique, when the physical quantity is measured inside a thin laser light sheet plane. The fluorescence signal is recorded by CCD (Charged Couple Device) cameras, which are equipped with monochromatic filters to separate the fluorescence signal from the excitation light. PLIF is a non-intrusive in-situ-measurement technique with a high temporal and/or spatial resolution.

2.2. DPIV/PLIF experimental facilities.

DPIV (Digital Particle Image Velocimetry) is a method to record time-dependent velocity fields. It is based on the imaging, tracking and recording of seeding particles that move along together with the flow and thereby retain their individuality. The particles are illuminated inside a thin laser light sheet plane at defined intervals of time. The reflected light is observed perpendicularly to the light sheet plane by CCD-cameras and is evaluated using a cross-correlation algorithm.

For the present investigation a commercial DPIV system was used. It consists of two Quantel Twins Nd:YAG lasers each with a pulse energy of 140 mJ. Each laser is operated in a single

Q-switch mode so that the energy is emitted in 4.3 ns. The DPIV processor synchronises the time interval ∆tDPIV,min between the emission of light from each laser and controls the data acquisition process. The laser beam is guided through a flexible arm and is diverted by a cylindrical lens, Figure 2.

The DPIV measurement system is converted into a PLIF system by using different optical filters to detect the

emitted light of the fluorescent dye. These tracers should have a high quantum yield Φ, must be adapted to the light source and must be soluble in water. The used rhodamin 6G solution meets best to these demands.


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Table 1. Technical data of the Dantec FlowMap 2000 DPIV/PLIF system

Illumination system: Two Quantel Twins Nd:YAG laser, flexible arm with 1.8 m length wavelength λ 532 nm repetition rate f 15 Hz max. pulse energy Emax 140 mJ duration of each light pulse t 4.3 ns min. time between pulses ∆tDPIV,min 2 µs thickness of light sheet ∆y0 ≈ 2 mm energy variation between pulses ∆E 2.6 % and 4 %, respectively divergence angle of cylindrical lens α 15° Recording system: DPIV processor unit and two Kodak Megaplus ES 1.0 cameras with class-II-chip Light-sensitive pixels 1008 ⋅1018 repetition rate f (double exposure) 7 Hz pixel pitch lpp 9 x 9 µm pixel size lps 3.4 x 7 µm chip size lcs 9.07 mm x 9.16 mm

digital output 8 bit

Objective: Nikon Nikkor AF with monochromatic filters

focal length fo 24 mm

wavelength λo 570 nm

The laser light of the energy E0 and intensity I0, respectively, induces a decreased intensity IE inside the laser light sheet depends on the local position. The detected fluorescence intensity ID measured by the CCD camera at an arbitrary pixel element P can be assigned to the local concentration C [6,24]:

D 0 opt C CI = I f V A CΦ . (1)

The influence of the optical parameters is considered by the factor fopt. The quantity VC is the measuring volume of the laser light sheet. The quantum yield Φ is the aspect ratio of the average number of emitted and absorbed photons, whereas Φ is a function of the wavelength and the temperature. If the frequency ν0 of the excitation light source is not adapted to the relevant fluorescent dye, the molecules will be excited but will not emit photons. Thus, the quantum yield varies substantially. For many organic fluorescent dyes the temperature-dependency of Φ is negligible, so for rhodamine 6G. The absorption factor AC takes into account the decrease of the emitted intensity IE between the considered laser light sheet plane and the CCD camera:

LCCA = e−ε . (2)

The molar absorptivity ε describes the decrease of light intensity due to absorption and light scattering. To determine ε the decrease of intensity of the excitation light is measured on its way through a solution with given concentration. During the measurement, the temperature of the solution has to be kept constant. In general, the temperature dependency of ε is small. For rhodamine 6G the molar absorptivity is ε = 0.05 %/K. For low concentrations the absorption factor is found to be Ac ≈ 1.

If the quantum yield Φ does not depend on the temperature, or if the temperature is constant during the experiment, the concentration C of the fluid will be determined as follows [13]:


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D0

0

IC =

Iα , with 1

0 opt C C= f V A( )−α Φ . (3)

The proportional factor α0 considers optical, geometrical, and physical parameters. The quantity α0 is determined by a calibration, during which the detected fluorescence intensity ID is assigned to a known concentration C.

2.3. Water model tundish.

The DPIV/PLIF measurements have been carried out at a water model (scale 1:3) of a 16 tonnes single-strand tundish with flat bottom. In steelworks, the tundish without any flow control devices is used to produce stainless steels (X5CrNi18-9, AISI 304). Figure 3 shows the test rig of the water model tundish with the DPIV/PLIF system, flexible laser light arm with the CCD-cameras and the piping of the test rig. Table 2 contains the dimensions of both, original and model tundish.

The water model tundish can be operated either in an opened or closed circuit. If the closed circuit is used, the water will flow out of the tundish into the SEN (Submerged Entry Nozzle), through the pump, flow meter, throttle valve, valve 2, valve 1 and shroud back into the tundish. This operation is used during the calibration of the PLIF system. When operating in an open circuit, fresh water is supplied to the tundish through valve 1 (inlet), while the contaminated water is pumped out of the tundish into the discharge (outlet). The operation state and the filling level H remains constant when valves 1 and 2 are switched simultaneously (∆t < 0.5 s, sh SENV V=& & ) [25]. This operation mode is used after the calibration has been finished and the mixing process is simulated.

Figure 3: Water model tundish (scale 1:3) and DPIV/PLIF facilities and piping of the test rig


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Table 2: Dimensions of the original 16 tonnes tundish and the water model tundish (scale 1:3)

symbol original tundish

model tundish

volume of tundish at filling level H V in m3 2.275 0.084 tundish length L1 in m 3.140 1.047 tundish width B1 in m 0.780 0.26 inclination of the side walls γ in ° 7 7 filling level for steady-state casting H in m 0.8 0.266 distance shroud-bottom of tundish zsh 0.6 0.2 position of shroud Lsh 0.335 0.122 diameter of the shroud dsh in m 0.068 0.023 position of SEN LSEN 2.885 0.962 diameter of the SEN dSEN in m 0.070 0.023 cross section of the tundish A in m2 0.703 0.079 hydraulic diameter dhyd in m 1.175 0.691

The dimension analysis of the tundish flow shows that apart from the geometric similarity the similarity numbers Re, Fr, Ri, Str, and We play a predominating role in melt flows. However, for the quasi steady-state, isothermal, and single-phase flow of water in a tundish model only the Re and Fr criteria must be considered. In both cases, the hydraulic diameter dhyd of the tundish is used as characteristic length. The mean velocity u through the tundish during the steady-state casting sequence is used as characteristic velocity. With Re similarity considered, the volumetric flow rate in the water model tundish can be derived as follows:

hyd w ww st

hyd st st

dV V

d

ν=

ν& &

,

,

. (4)

The indices “w” and “st” refer to water and steel. With Fr similarity, the following applies:

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2hyd,w

w st

hyd,st

dV V

d=

& & . (5)

Eq. (4) and eq. (5) show that both similarities can not be kept simultaneously at downscaled water models even when νw ≈ νst. The experiments have been done at a turbulent Re number of Re = 5000, Table 3. Investigations at Re similarity could not be carried out at this downscaled water model because of too high flow velocities inside the model resulting in high surface wave amplitudes. Anyway, LDA and DPIV measurements show a strong similarity of the basic flow structure over a wide range of Re numbers as well as for different model scales [2,14].

Table 3. Boundary conditions for a typical steady-state casting sequence of the 16 tonnes tundish and the water model tundish

tundish original water model symbol Re similarity Fr similarity density 7038 998 kinematic viscosity ν in m2/s 8.72⋅10-7 10.06⋅10-7 volumetric flow rate V& in l/s 5.39 2.08 0.35

mean velocity through the tundish u in m/s 0.0077 0.0267 0.0052

velocity in the shroud |wsh| 1.49 2.42 0.973 mean residence time t in s 420 84 210 Reynolds number Re 10380 10380 2110 Froude number Fr 2.26⋅10-3 1.36⋅10-3 2.26⋅10-3


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Figure 4: Calibration curve of the left CCD camera: detected fluorescence intensity ID vs. concentration crh.

The mean residence time t of the water is

V

Vt =

&. (6)

After this time, the tundish volume will have been exchanged, if a homogeneous plug flow is assumed. In reality, the maximum residence time is larger than the mean residence time t due to mixing flow and dead water regions, while the minimum residence time is shorter due to short circuit flows. For example, mixing effects in dead water regions take place very slowly because the fluid is mixed mainly by diffusion.

2.4. Calibration of the PLIF system

The PLIF system is calibrated prior to the measurements. For this reason, eleven different, but known concentrations crh of rhodamine 6G in the water model tundish between crh = 0 and 100 % are recorded by the CCD camera. The concentration crh is then assigned to the detected fluorescence intensity ID for each pixel P(i,j) of the CCD camera (i = 1...1008, j = 1...1018). A linear correlation between ID and crh is found for small concentrations crh as eq. (3) denotes. Figure 4 shows the calibration curve ID = ID(crh) for the maximum pulse energy of E0 = 100 %. The calibration curve starts from a level different to zero, due to the luminosity in the laboratory. The correlation coefficient is R = 0.988. Thus, the calibration points are found to be on the curve within a range of 98.8 %.

If the concentration further increases, non-linear saturation effects will appear due to quenching. When using rhodamine 6G as fluorescent dye with a maximum concentration of Crh,max = 70 µgrh/lw, non-linear effects can be excluded. At the start of calibration, the test set-up with fresh water is operated in a closed circuit (crh = 0 %). A certain amount of rhodamine 6G is dissolved in 100 ml water and is added in steps of 10 ml. Subsequently, the tundish

volume is stirred for a sufficiently long duration (approx. 5 minutes) until a homogeneous concentration is reached. Because the laser power varies with time due to changing laboratory and laser conditions, the laser has not been turned off during the calibration and the concluding measurement to avoid thermal stresses on the optical set up caused by temperature changes. After the stirring time of approximately 5 minutes, each of the CCD camera takes ten images whereby the stored grey-tone values are averaged for each pixel. This way, the pulse to pulse fluctuations of the emitted laser power which are to be found within the range of 4 % can be compensated. The influence of the intensity variation is then reduced to

1.3 % (4 %/√10). At the end of the calibration, the maximum concentration in the water model tundish is crh = 100 % (Crh,max = 70 µgrh/lw), Figure 5. The stripe pattern belongs to the optical set up of the measurement system and of the test rig. Due to the calibration procedure of the DPIV/PLIF system, the optical, geometrical and physical parameters do not have to be determined. During the calibration procedure of approx. 55 minutes, the temperature of the water could be kept constant up to ± 1 K. Thus, the quantum yield varies about ∆Φ ≈ ± 4 %.


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When starting the measurements, the piping is switched from the closed to the open circuit and fresh water is supplied to the tundish model via valve 1. From this time on, the temporal decrease of the rhodamine 6G concentration is measured.

Figure 5: Calibration: average of 10 images for typical concentrations crh for the left CCD camera.

As an example, Figure 6 shows the grey-tone distribution of the detected fluorescence intensity ID for the left CCD camera as well as the accompanying concentration distribution determined by means of the calibration curve.

Figure 6: Image of the left DPIV/PLIF camera, a) grey-tone distribution of the detected fluorescence intensity ID, b) concentration distribution crh converted using the calibration curve in Figure 7.

The described procedure for the calibration and measuring processes has substantial advantages. A certain amount of fluorescent dye is gradually added to a known volume of fresh water during the calibration process. Thus, the maximum, known concentration in the water model arises at the end of the calibration. This process is carried out for a thin object and laser light sheet plane, respectively so that optical, geometrical, and physical parameters have not to be determined. This way, one can forego the theoretical determination of the spatially varying intensity IE inside the laser light sheet plane.

3. RESULTS AND DISCUSSION

3.1. DPIV velocity measurements.

DPIV has been used to measure the velocities in longitudinal and cross planes in the water model tundish to determine the flow structure. The velocity distributions in the centre plane (y/B1 = 0), side wall plane (y/B1 = -0.5), and a cross plane (x/L1 = 0.5) are shown in Figure 7. Each diagram consists of an average of 100 double exposures. The time interval between a double exposure used for a cross correlation is ∆tDPIV = 2 ms, the time interval between a burst is ∆tA = 333 ms. Each interrogation area has a size of 64 pixel ⋅ 64 pixel with an overlap of 75 %. Thus, the spatial resolution of an interrogation area is 25 mm ⋅ 25 mm.

The shroud jet with a velocity of |wsh| = 2.42 m/s enters the tundish with a relatively high momentum, reaches the bottom of the tundish and is reversed toward the side walls, Figure 7a. A recirculating region develops at the bottom finding its origin in the transient shear layer of the shroud jet and the positive pressure gradient (dp/dx > 0). The centre of the recirculating region is located at x/L1 = 0.53 and z/H = 0.20. The maximum back flow velocity is four times higher than the mean velocity u = 0.0128 m/s through the tundish. At y/B1 = -0.5, Figure 7b, a short-circuit flow along the side wall can be seen. In reality, short-circuit flows in steel melt can transport non-metallic particles directly into the mould. The


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Figure 7: DPIV measurements in the water model tundish, Re = 5000, Fr = 6.56 . 10-3, average of 100 images, ∆tDPIV = 2 ms, ∆tA = 333 ms, a) y/B1 = 0, b) y/B1 = -0.5, c) x/L1 = 0.5.

maximum horizontal velocity within the short-circuit flow is twelve times higher than u . Figure 7c shows results in the cross plane of the tundish at x/L1 = 0.5. The predominating flow structure is a vortex pair of counter rotating vortices induced by the momentum of the shroud jet. The centres of these vortices are at y/B1 = -0.35, z/H = 0.74 and y/B1 = 0.33, z/H = 0.70. A considerable amount of fluid is transported in negative x-direction through the centres of these vortices. In general, the lowest velocities are found in the edges as well as in the outlet region of the tundish below the free surface. Detailed laser-optical investigations for a larger tundish model, at a scale of 1:1.7 and different Re numbers, show similar results [2,14]. The fundamental flow structure found in the water model tundish is sketched in Figure 8.

3.2. PLIF concentration measurement

Figure 11 exemplary show results of PLIF concentration measurements at different times. The time t has been normalised with the mean residence time t 84 s= according to Equation

(6). At θ = 0, the valves 1 and 2, see Figure 3, are switched and fresh water (crh = 0) flows

Figure 8: General fluid flow structures in the water model tundish.


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into the tundish. In principle, this should simulate the ladle change between the nth ladle and (n+1)th ladle. The facts that the ladle shroud jet enters a tundish with dropping down melt level ( shV 0=& , SENV 0≠& ) and that the temperature increases remain unconsidered. In the diagrams, the local concentration of fresh water in the tundish is shown. The concentration of rhodamine 6G in the tundish model is crh = 100 % at θ = 0 and crh = 0 % for θ → ∞. Already at θ = 0.3 the concentration in the inlet region of the water model tundish has decreased to crh = 50 – 60 %, Figure 9a.

Figure 9: PLIF measurement in the centre plane (y/B1 = 0) of the water model tundish, Re = 5000, Fr = 6.56 . 10-3.


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The high flow velocities in the inlet region of the tundish cause an intensive mixing. The turbulent character of the shroud jet which impacts on the bottom and is redirected to the side walls of the tundish can be clearly seen. The time-dependent and spatial expansion of the fresh water correlates with the convective mass and momentum transport, characterised by the quasi steady-state flow structure in Figure 8. The fresh water flows along the bottom of the tundish toward the SEN up to x/L1 = 0.5 - 0.6. This bottom-based flow transports fresh water into the recirculating region. Because the mass and momentum exchange between the recirculating region and the ambience takes place very slowly, the concentration inside the recirculating region remains low for a while, Figure 9b. For θ = 1.5, Figure 9c, the tundish can be roughly separated into three zones. A low concentration of crh ≈ 15 % is to be found in the inlet region of the tundish (0 ≤ x/L1 < 0.33). In the middle region (0.33 ≤ x/L1 < 0.66) the concentration of crh ≈ 25 % is quite high as well. In the outlet region (0.66 ≤ x/L1 < 1), and in particular below the free surface, clearly lower concentrations of crh ≈ 50 % can be found. From the outlet region of the tundish, water is transported inside the counter-rotating vortices back toward the inlet zone.

Even for θ > 2, Figure 9d, the concentration below the free surface remains noticeably high. The current PLIF investigations emphasise that the total volume has been exchanged not until θ = 5. If this time is transferred from the physical model to the steel melt tundish using the data from Table 4, this will lead to a mixing time of approx. 35 minutes.

As an example, Figure 10 shows RTD curves for the water model tundish determined by the conventional dye injection, the PLIF approach and the CFD simulation. In the case of dye injection, a certain amount of dye is introduced into the shroud at steady-state flow conditions and the dispersion of the tracer is optically monitored inside the SEN. The measurement has been repeated three times and the results have been averaged. In the case of PLIF, the local concentration of rhodamine 6G is detected just above the SEN by the CCD camera. The CFD simulation is based on the RANS equations with the Realizable k-ε turbulence model and standard wall functions [20,21]. An additional scalar equation for the concentration has been solved. It can be seen, that the numerical results fit best the physical simulations if a turbulent Schmidt number of Sctub = 0.8 is used.

0

0,2

0,4

0,6

0,8

1

1,2

0 1 2 3 4 5

θ

con

cen

tr. c

norm

color dye measurement average

PLIF measurement

cfd-simulation Sc = 0.8

Figure 10 RTD curves for the water model tundish at Re = 5000, Fr = 6.56 . 10-3, a) dye injection, b) PLIF measurement, c) CFD simulation.

4. CONCLUSION

At present, dye injection into water models of metallurgical reactors to predict mixing processes is state of the art. In this case, the response signal to a tracer pulse input is measured at the outlet of the physical domain. The RTD curve yields the specific volumes, i. e. plug,


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mixing and dead water volume of the reactor. However, the concentration can only be detected at certain locations inside the model without emphasizing on the complex process of turbulent mixing. Within the scope of this paper, the large scale mixing in a water model tundish at a scale of 1:3 is quantitatively investigated for the first time using the combined DPIV/PLIF technique. A simple calibration technique is used which does not need optical, geometrical and physical parameters. For a turbulent tundish flow of Re = 5000, the velocities in several planes of the water model with a size of up to 300 mm ⋅ 100 mm are measured by DPIV, followed by concentration measurements by PLIF. The mixing phenomena are closely related to the fundamental flow pattern. The experiments show that the mixing process is completed after five times of the mean residence time (θ ≈ 5). In the future, the results of such experiments will be used as validation criteria for accompanying CFD simulations.

ACKNOWLEDGMENT

The authors gratefully acknowledge the financial support (project PF 394/11-1) of the German Science Foundation (DFG).

LITERATURE REFERENCES

[1] HÜLSTRUNG, J.: PhD thesis, RWTH Aachen, 2006 [2] ODENTHAL; H.-J.: Habil. thesis, RWTH Aachen, 2004 [3] COOLEN, M.C.J., KIEFT, R.N., RINDT, C.C.M., VANSTEENHOVEN, A.A.,: Experiments in

Fluids 27 (1999) 5, p. 420-426 [4] DEUSCH, S., MERAVA, H., DARCOS, T., RYS, P.: Experiments in Fluid 29 (2000) 4, p. 388-

401 [5] MAYINGER, F., FELDMANN, O.: Optical measurements, Springer Verlag, Berlin, 2001 [6] MEYER, K.E., ÖZAN, O., LARSEN, P.S., GJELSTRUP, P., WESTERGAAR, C.: 10th Intern.

Symp. Appl. Lasertechn. Fluid Mech, 11.-13.07.2000, Lisboa, 18.5 [7] COWEN, E.A., CHANG, K.-A., LIAO, Q.: Experiments in Fluids 31 (2001) 1, p. 63-73 [8] HJERTAGER, L.K., HJERTAGER, B.H., DEEN, N.G., STOLBERG, T.: Canadian Journal of

Chemical Engineering 81 (2003) 6, p. 1149-1158 [9] PASTOR, J.V., LOPEZ, J.J., ENRIQUE, J.J.: Optics Express 10 (2002) 7, p. 309-323 [10] LEVENSPIEL, O.: Chemical reaction engineering, 3rd ed., Wiley/VCH, Weinheim, 1999 [11] SAHAI, Y., AHUJA, R.: Iron and steelmaking, 13 (1986) 5, p. 241-247 [12] HYOUNG, B., ISAC, M., GUTHRIE, R., THUBAUUJA, R.: steel research 76 (2005) 1,

pages53-58 [13] DANTEC DYNAMICS: Planar-LIF software for Flow Manager - Installation and Users Guide,

2002 [14] BÖLLING, R.: PhD thesis, RWTH-Aachen, 2003 [15] JAVUREK, M.: PhD thesis, TU Linz (A), 2006 [16] BÖLLING, R., ODENTHAL, H.-J., PFEIFER, H.: steel research, 76 (2005) 1, p. 71-80 [17] OHLER, C., ODENTHAL, H.-J., PFEIFER, H.: steel research 74 (2003) 11+12, p. 739-747 [18] ODENTHAL, H.-J., BÖLLING, R., KOITZSCH, R., PFEIFER, H.: 5th World Congress on

Comp. Mech., 07.-12.07.2002 Vienna (A), II-572 [19] ODENTHAL, H.-J., BÖLLING, R., PFEIFER, H.: steel research 74 (2003) 1, p. 44-55 [20] KOITZSCH, R., ODENTHAL, H.-J., PFEIFER, H.: 11. GALA Fachtagung - Lasermethoden in

der Strömungsmesstechnik, 9.-11.09.2003, Braunschweig, 24.1-24.8 [21] KOITZSCH, R.: PhD thesis, RWTH Aachen, 2007

simulation of steelgrade change in a water...

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