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FIELD OF APPLICATION
The present invention relates to a method of measuring wall shear stress inside a blast furnace hearth. In particular it relates to evaluating the liquid velocity in an experimental set up and calculating therefrom the wall shear stress for different coke oven configurations of a blast furnace.
BACKGROUND OF THE INVENTION
The liquid velocity is generally measured to know the flow fields by which the factors affected by the flow can be known and quantified. The liquid velocity measurement is particularly difficult in areas i.e. porous media, where direct flow visualization is very difficult or where numerical simulation hardly renders tangible information with regard to the flow behavior. Although there is a technique such as particle image velocimetry (PIV) available for velocity measurement, it is, however, limiting to a single phase flow only.

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Many works can be found on the blast furnace fluid flow where the flow phenomenon has been addressed to understand the behavior of the hearth and also the chemical erosion that could take place in the hearth. Valts arid Dash and Dash et al have done extensive study on flow induced wall shear stress and found optimum tap hole length and tap hole angle which can produce minimum stress on the wall of the furnace. However, before proceeding to the work it is more important to validate the computational fluid dynamics (CFD) model with experimental measurements, which is the key objective of this part of the work. Furthermore, most of the authors have tried to validate their model with external variables like thermocouple temperatures because this is the only variable which can be measured from outside and can be compared with. But measuring velocity at any location inside the hearth is not possible in a working furnace but possible in a water model, which can be compared with numerical computations. Yoshikawa and Szekely investigated the recirculatory flow induced by natural convection and its effect on dissolution of carbonaceous refractories into the melt. They considered the situation where the taphole was plugged and assumed the hearth to be coke free, which is an unrealistic situation. A three-dimensional model developed by Shibata and co-workers was used to simulate the hearth flow for different deadman positions. However, the model was lacking the quantitative validation and emphasis on the flow induced stress distribution on the wall.
Because of limitations either in measurement technique or in simulation, the need to develop a new technique for velocity measurement inside the experimental set up of blast furnace hearth was felt.

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SUMMARY OF THE INVENTION
The main object of the present invention is to measure the velocity inside a blast furnace hearth by measuring liquid velocity in an experimental setup and validate the same with a mathematical model, which can further be used to generate the wall shear stress for various coke bed configurations.
This and other objects of the present invention can be achieved by using electric resistance sensors in an experimental set up, Liquid velocity measurement through electric resistance sensors is used in a scaled down water model of the system. This technique can also be used with porous medium and with multiphase flow. It has been used in the present invention in a 1:10 scaled down water model of a blast furnace hearth and then validated by mathematical modelling.
It can be very useful for validation purpose. For example, it is very difficult to know the velocity profile of the liquid in some processes operated at high pressure and temperature. Therefore, the numerical simulation of such processes without its validation renders little value.
For the purpose of the present invention the travelling time of tracer injection of potassium chloride is determined between two subsequent sensors based on their electric conductivity. The present invention uses 24 fixed electric resistance sensors placed at different places inside the hearth for the measurement of the average liquid velocity between two consecutive sensors, thus obtaining the velocity profile for different coke bed configurations and tapping rates. The invention also proposes a new methodology for the measurement of local fluid velocity inside the hearth (for water model). The comparison between the experiment and the computation was found to be very much reasonable.

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Thus the present invention provides a method of measuring wall shear stress inside a blast furnace hearth comprising the steps of: evaluating the liquid velocity in an experimental set up by using a plurality of electric resistance sensors; validating said liquid velocity with a mathematical model in a processor; and calculating therefrom wall shear stress for various coke-bed configurations of said blast furnace.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The invention can now be explained with reference to the Figures of the drawing, where
Figure 1 shows a schematic of 1:10 scaled down model of a blast furnace hearth.
Figure 2 shows coke-bed configurations
conical: 2a sitting model, 2b water model
Spherical: 2c floating, 2d water model

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Horizontal: 2e H = 0.04 m, 2f water model
Cylindrical: 2g non-uniform, 2h water model
Figure 3 shows positions of sensor placed at tap-hole level in the experimental set up
Figure 4 shows comparison of residence time distribution (RTD) curve at the exit of tap hole and at various points at the tap hole level in the hearth between experiment and computation
Figure 4a no coke-bed inside the hearth
Figure 4b fully packed hearth with e = 0.5
Figure 5 shows comparison of travelling time of tracer in the hearth between experiment and the CFD model.

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Figure 6 shows a schematic diagram of average velocity measurements.
Figure 7 shows validation of velocity profile on the
peripheral path between the experiment and
the CFD model (fully packed bed, voidage = 0.33).
Figure 8 shows validation of velocity profile between
experiment and the computation on the central path (conical sitting coke-bed with voidage = 0.33).
Figure 9 shows validation of velocity profile between experiment and the computation on the central path at the tap whole level (Horizontal coke-bed with voidage = 0.33).
Figure 10 shows variation of normalized wall shear stress with ? for
different coke-bed positions with a conical coke-bed in hearth.
Figure 11 shows maximum normalized stress on hearth wall at taphole level as a function of taphole length for conical coke bed.

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DETAILED DESCRIPTION
Figure 1 shows a shematic diagram of 1:10 scaled down water model of a blast furnace hearth, in the X-Y plane. To simulate the coke-particles inside the blast furnace hearth, spherical polystyrene balls can be used in water model. Water was simulated as a liquid metal. All other arrangements are shown in Figure 1. The experimental procedure is presented in the subsequent section.
Figures 2a to 2h show the coke bed shapes and configurations used in the experiment. Four different kinds of coke-bed configurations, namely conical (Figures 2a, 2b), spherical (Figures 2c, 2d), horizontal (Figures 2e, 2f) and cylindrical (Figures 2g, 2h), were considered , depending on bottom shape of the coke-bed. For each shape, two coke-bed positions, namely, sitting and floating, were considered. A sitting coke bed means where the coke bed is really sitting on the heath bottom and a floating coke bed means the coke bed is floating in the hearth with some bottom clearance. In the present experiment the minimum bottom clearance was varied from 0.03 to 0.07m for horizontal, conical and spherical coke beds. The rest of the zone in the hearth is modeled as a coke-free zone, although strictly speaking it is not purely coke free in a practical operating furnace. The objective of the problem is to compute the local fluid velocity at any level in the hearth by injecting a tracer and monitoring its peak intensity at two positions by two probes and hence computing the velocity and compare that with the mathematical model.

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Mathematical Formulation and Assumptions
In order to formulate the governing equations for this case, a number of assumptions have been employed. It is assumed that the level of the molten metal remains constant while drainage is taking place through the taphole. This happens at the onset of drainage and continues for some time, and then the level gradually decreases. During this period the stresses on the wall will be at their maximum. When the level falls off, the velocity near the taphole also decreases, resulting in a decrease in the stresses on the wall. To simulate the maximum stresses, a steady state situation of drainage is assumed because this represents the worst case in practice. The taphole is represented as a hollow enclosure, with no coke inside it. Chemical reactions and heat transfer are not considered, as the objective is to analyse the flow-induced stresses on the wall. It is believed that the resulting distortion in flow field owing to this approximation will have a negligible effect on the computations of the stresses on the wall, because the scale of velocities in the entire hearth is small in magnitude. Also for this reason, a laminar solution is assumed for the flow field although there may be little turbulence present at the tap hole due to high velocity, but this volume is negligible compared to the entire volume of the hearth.

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The flow field in the coke-free zone inside the hearth of the blast furnace was computed by Navier-Strokes equations, and in the coke packed porous zone by Ergun equation. Equation for dispersion of tracer in the hearth was solved to capture the variation of tracer concentration in the hearth as well as to validate the CFD model with the physical (water) model.
Governing Equations
The governing equations were solved for the scaled down model. Based on below mentioned equations, the velocity and the stress at the wall were calculated. The experimental velocity was then taken as a measure to validate the calculated velocity. Thus once the velocity profile is validated, the computed stresses at the wall would be assumed correct. The results thus obtained by scaled down model can be made applicable to the actual process by scaling up.
Continuity:

Momentumequation:
where

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The source term Si represents the flow parameters due to the presence of the coke packed zone in the hearth. This means the flow solution will automatically adapt to the Ergun equation when it is computing for the coke packed zone and the Navier-Stokes equation will be automatically adopted in the coke free zone.
Where,

ShearStress on Blast Furnace Wall (tw)
Tracer Dispersion

Boundary Conditions
1. Upper Boundary: Inlet boundary condition was specified at the top of the hearth (Y = 0.05 m; see Fig. 1), where it was specified that water entered the hearth with a specific velocity, which was computed from the water flow rate of 10 liter per minute in to the hearth.

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2. Tap hole exit: Outflow boundary condition was applied at the tap hole exit, which forces the inlet mass to be equal to the outflow mass at the tap hole exit. It must be mentioned here that if one tries to put pressure outlet condition at the tap exit then the solution may not coverage for such a situation where the tap hole exit area is very small compared to the inlet area of the hearth. In fact in the actual experiment the tap hole exit was connected to a pump, which was sucking the fluid from the hearth, so an outlet boundary condition is more appropriate than a pressure boundary condition in such a situation.
3. Side and bottom wall surface: The bottom of the hearth and the sidewall of the hearth were given a wall boundary condition of zero velocity. For the tracer the walls were treated as impervious, so the flux was assumed to be zero on the wall.
Solution Procedure
The set of governing equations (1) (2) and (5) were discretized using the finite volume technique in a computational domain and solved with the help of above boundary conditions. Second order upwind scheme was used for discretization of convective term in the governing equations to provide better accuracy but for the tracer dispersion equation power law scheme was used. The algebraic multi grid solver of FLUENT software solved the differential equations now converted to algebraic equations. SIMPLE (semi-implicit method for the pressure-linked equations) algorithm proposed by Patankar was used to resolve the pressure-

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velocity coupling in the momentum equation. The SIMPLE algorithm imposes indirectly the principle of mass continuity via the solution of pressure-correction equation. Unstructured grids were used in the computational domain. Momentum equation was first solved for the steady state to get the velocity field. The shear stresses on the wall were computed using equation (4) and then the tracer dispersion equation (5) was solved for unsteady state along with the momentum to get the residence time distribution (RTD) curve. It is to be noted that a steady field obtained from momentum equation can no longer be used to get the tracer dispersion because the flow of the tracer itself is much higher locally compared to the flow being induced by the top sprinkler in the hearth. So both the tracer and momentum equations are to be solved simultaneously for obtaining the tracer dispersion inside the hearth. A validation of RTD with the experiments will be presented in the next section of model validation. The density and viscosity of iron was kept constant at 6800 kg/m3 and 0.00715 kg/ms respectively, throughout the computational domain. The solution procedure was assumed to have converged when the whole field normalized residuals for all variables (vx, vy, vz, C and P) fell below 1e-3.271053 cells uniformly discretized the computational domain in an unstructured manner. The grid density was kept higher near the taphole region, as the change of velocity is expected to be very high in this region.

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Experimental Condition and Procedure
It is essential that dynamic similarity be obtained between the flows in the physical model and in the actual process. To ensure the similarity, the below mentioned dimensionless numbers values must fall in a close range. In the present invention this is assured by considering 3 dimensionless numbers. The Froude number is modified by Niu et al. Galilei and Reynolds numbers by Fukutake et al. The dimensionless numbers are given as:

Where u, dp, f, g, e, p, µ are superficial velocity, particle diameter, sphericity of particle, gravitational acceleration, voidage of bed, density and viscosity of liquid, respectively.
Table 1 shows a comparison of the dimensionless numbers defined by eqs. (6) to (8) between the physical model and those estimated in the blast furnace. Table 2 shows the major variables influencing the flow conditions in the hearth and a comparison of the flow and geometrical parameters between the actual G blast furnace and the scaled down model.

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Table-1 Comparison of various dimensionless numbers between the actual blast furnace and the experimental setup.

Dimensionless number
Blast furnace
Physical model
Reynolds number
3.42
1.75-5.28*
Froude number
5.00 X 104
2.038 X 10"5 - 7.00 X 10"5
Galilei number
2.33 X 108
1.22 X 106 - 9.24 X 106
* Corresponding to drain rates 0.005-0.015 m3/min, respectively
Table-2 Variables considered in the physical model corresponding to that of the actual blast furnace.

Variable
Blast furnace
Physical model
hearth diameter (m)
9.2
0.92
tap-hole diameter (mm)
60
6
diameter of the coke (mm)
30
3-25
sphericity of coke
0.5
1.0
porosity of bed
0.3
0.3-1.0
density of iron (kg/m3)
6800
1000
viscosity of iron (kg/ms)
6.0 x 10 3
1.0 x 10-3
tapping of iron (m3/min)
0.735
0.005 - 0.015
superficial velocity (m/s)
1.4 X 10-4
(1.25 - 35) x 10-4
Tap hole angle (?)
10
10

-16-The magnitude of the Reynolds number is close to unity, which indicates that, the effect of inertial and visous forces are quite similar. Because the Froude number represents the relationship between inertial and gravitational forces and the Galilei number the relationship between inertial and gravitational forces to viscous forces, it is evident that the gravitational force governs the flow behavior in the hearth. Although values of, e.g., the Froude number in the model are not quite the same magnitude as in the blast furnace, it is evident that the gravitational force is also dominant in the water model.
The experimental set up is shown in Figure 1. The model is filled up with the polystyrene balls, which simulate the coke particles. Desirable casting rate is achieved by the placement of a pump at the exit. Steady state is maintained with the help of distributor. Flow rate distribution is kept uniform. Experimental procedure includes the filling of a model by water and once steady state is attained, a tracer solution of say 80 ml of saturated KCI solution, is injected at desired location. Tracer addition causes the conductivity of water to change, which is detected by sensors located below taphole level inside the hearth as shown in Figure 3. Three sensors are located on each peripheral path P-1, P-2, P-3 and P-4 as depicted in Figure 3. Rest of the sensors are located on the central path. The conductivity signal is then converted into digital mV by multiplexer and conductivity meter and finally recorded in the computer. To ensure exact timing a master remote switch (known as multiplexer) was built into the system so that conductivity from all sensors could be recorded at the same time. Although this method prolonged the setting-up work and complicated the measuring effort, the measurements were accurate and reproducible. It was extremely difficult to obtain the concentration data on peripheral path P-1 and P-2. So the data on peripheral path P-3 and P-4 have been shown. The calculation of velocity from conductivity data (concentration vs. time data) is shown under section on Validation of Velocity Profile from RTD.

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Validation by RTD
Figure 4a shows the RTD curve for the tracer measured at the tap hole exit in a coke free hearth and a comparison with the computation can also be seen from the same figure. It can be seen from the figure that the computation shows a little delay in the appearance of the tracer the tap hole exit but it shows the same peak in the tracer concentration curve as that of the experiment. The diffusion constant for the tracer is assumed from literature in the mathematical model and not experimentally determined. Moreover, the addition of tracer into the model is done at a point through a cylindrical rod and in the mathematical model we try to maintain the same amount of flow over the same time period of addition but certainly the local velocity pattern near the tip of addition cannot be reproduced in the mathematical model exactly as is happening in the experiment. So this may be the reason why the mathematical model predicts a little delay in the dispersion curve. Figure 4b shows the tracer response at the positions marked 2, 3 and 4 on path P-4 (in Figure 3) and a comparison with the mathematical prediction can also be seen from the same figure. Leaving aside point 2 the matching of the tracer response with the other two points seem to be quite reasonable. At point 2 the mathematical prediction shows a delay of about 10 sec in the appearance of the tracer otherwise the shape of the curve and the peak matches well with the experimental prediction.

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Validation of Flow Pattern by Travelling Time Measurement
The flow pattern of the molten iron is dependent on the packed structure of the coke-bed, because the molten iron dripped from the cohesive zone passes through voids in the coke-bed. Especially, the coke-free space is regarded as the important factor in determining the flow of the molten iron. In order to investigate the effect of the coke free space on the flow pattern, the travelling time of the tracer (from any point on the central line to the tap hole) was measured in a horizontal coke bed having a bottom free space of 0.04m and also in a fully packed bed. In order to validate the CFD model, the tracer (KCI) was injected also in the CFD model in the same manner as it was injected in the water model. A good agreement was found in the travelling time data between the water model and the CFD model, as can be seen from Figure 5. Travelling time of the tracer can be thought of as how much time the tracer takes to reach at the tap hole exit starting from the time of its injection at a desired location. Here the dimensionless travelling time is defined as the ratio of travelling time to the mean residence time of the system (which is, defined as, the ratio of the volume of the hearth to the volumetric flow rate into the hearth). When the dimensionless distance, X/D, is 0.2 this means the point of tracer injection is done very close to the tap hole, when X / D is 1 this means the tracer is injected just opposite to the tap hole. (Here the distance X is measured from the tap hole on the central path towards the opposite side of the tap hole). So it is quite natural that the travelling time of the tracer will be higher if it is injected away from the tap hole (X/D is away from 0). When the hearth is having a cylindrical coke bed with a bottom free space of 0.04m in height and if the point of tracer injection is such that its X/D value is more 0.5 then the travelling time for such points is less than that for a fully packed bed.

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Validation of Velocity Profile From RTD
It is possible to get concentration curve at each sensor location with the help of the multiplexer and conductivity meter. The travelling time corresponding to the peak in the concentration curve on the abscissa represents the time that a tracer has taken to travel from the point of injection to the sensor. In this way the travelling time between two sensors, e.g. points 1 and 2 in Figure 3, can also be measured by taking difference between the travelling times of two subsequent sensors, as depicted in Figure 6 provided that the locations of injections are the same. However, it is not so easy to locate the path that a tracer follows. But if the two sensors, of which the travelling times are known, are located very closely, it is then possible to measure the velocity between the two sensors. As can be seen from Figure 3, all sensors are located very closely, thus making it possible to calculate the average velocity between any two sensors. The average velocity is taken as the ratio of distance between two sensors (ds) and the difference of travelling time. Distance on the peripheral path P-3 and P-4 is the perimeter between two sensors.
Figure 7 shows the comparison of velocity distribution on the peripheral path P3 and P4 between the water model and that of the computation. As X/R increases from -1 to 1 one is travelling from the opposite side of the tap hole towards the tap hole. Here, the distance X is measured from the center of the hearth

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The velocity slowly increases from the opposite side of the tap hole towards the tap hole, which is logical to expect from both the models. Figure 8 shows the velocity distribution on the central path (a line connecting the opposite side of the tap hole to the tap hole through the center of the hearth) for a conical sitting dead man having s=0.33 and Figure 9 also shows the velocity distribution on the central path for a horizontal coke bed having a bottom clearance of .04m and .07m. In all these cases the comparison of velocity profile between the experiment and the mathematical model seems to be pretty reasonable.
Thus, the average velocity profile can be known with the help of physical model from RTD analysis. With the help of RTD analysis and average velocity measurement, it is seen that the CFD model of 'G' blast furnace hearth of Tata steel is in good agreement with the measured velocity profile. The CFD model was then applied to calculate the stresses on the hearth wall for the G blast furnace.
As the present invention emphasis on the liquid velocity measurement technique and there from the calculation of wall stresses, few results based on stress calculations and its importance are shown below. Figure 10 shows the normalized wall stresses for sitting and floating positions of a conical coke bed.

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It shows that sitting bed may cause more wear to the wall, however, the maximum stress for both coke-bed positions are same. The maximum stress values were then plotted for different taphole lengths, as shown in Figure 11. It was found that an optimum taphole length, at which the maximum wall stress is minimum, could be obtained in presence of coke-bed (for both sitting and floating), whereas maximum stress continues to decrease as the taphole length increase, in absence of coke-bed inside the hearth.
The normalized stress at the hearth wall is computed in the following way,

where Vavg is the average inlet velocity of liquid iron into the furnace, which is computed from daily production rate.

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Conclusions
The numerical solution of the mass conservation equation along with the momentum equation could generate a flow field inside the scaled down water model and with the help of the tracer dispersion equation it could be possible to determine the RTD curve for a scaled down model and a comparison with the experimental setup also could be made for the RTD curve which were seen to be in good agreement. It was possible to measure the travelling time between two sensors in the experimental setup by injecting a tracer at a desired location and hence the local average velocity between the two sensors could be determined because the distance between the two sensors is known a priori. The velocity thus found from the experiment could be compared with the numerical solution very well. Thus, the tracer injection can be used as an effective tool to measure the local fluid velocity in an experimental setup. It should, however, be ensured that the injection is made at sensor's tip for all sensors, otherwise it should be ensured that the time that a tracer has traveled from the location of the injection to the sensor's tip is excluded form travelling time. The present study presents a new methodology for the measurement of local velocity in scaled down water model of blast furnace hearth.

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References
1. Y. Tomita, H. Ookusu and M. Kawano: CAMP-ISD, 1, (1988), 79.
2. K. Shibata, Y. Kimura, S. Shimizu and S. Inaba: CAMP-ISD, 2, (1989), 92.
3. F. Yoshikawa and J. Szekely: Iron making Steelmaking, 8, (1981), 159.
4. A.K. Vats and S.K. Dash: Iron making Steelmaking, 27, (2000), 123.
5. S.K. Dash, D N Jha, Satish K Ajmani and Alka Upadhyaya, Ironmaking and Steelmaking International J. of Technological Advances, 31, No. 3, (2004), 207.
6. S.K. Dash, Ajmani, S.K. Ashok Kumar and Sandhu H.S., Ironmaking and steelmaking International J. of Technological Advances, 28, No. 2, (2001), 110.
7. S.V. Patankar and D.B. Apalding: Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, (1980).
8. Niu M, Akiyama T, Takahashi R, Yagi J: Testu-to hagane, 8, (1996), 13.
9. Fukutake T, Rajakumar V.: Trans ISD, 5 (1982), 355.
1.
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WE CLAIM:
1. A method of measuring wall shear stress inside a blast furnace hearth
comprising the steps of:
- evaluating the liquid velocity in an experimental set up by using a plurality of electric resistance sensors;
- validating said liquid velocity with a mathematical model in a processor; and
- calculating therefrom wall shear stress for various coke-bed configurations of said blast furnace.

2. The method as claimed in claim 1, wherein said experimental set up is a scaled down water model of a blast furnace hearth.
3. The method as claimed in claim 2, wherein for simulating coke particles, polysterene balls are used in said experimental set up.
4. The method as claimed in claim 2, wherein said water model is provided with a pump to achieve a desirable casting rate.
2.
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5. The method as claimed in claim 2, wherein a distributor is provided for maintaining a uniform distribution and steady state
6. The method as claimed in claim 5, wherein a tracer is added to water after the steady state is attained.
7. The method as claimed in claim 6, wherein said tracer is potassium chloride solution, about 80 ml of which is injected at a desired location.
8. The method as claimed in claim 1, wherein 24 fixed electric resistance sensors are placed inside the hearth at various places for measurement of average liquid velocity between two consecutive sensors.
9. The method as claimed in claim 8, wherein three sensors are located in each peripheral path and rest of the sensors are located in the central path.
10. A method of measuring wall shear stress inside a blast furnace hearth substantially as herein described and illustrated in the accompanying drawings.
Dated this 19th day of January 2007
The main object of the present invention is to measure the velocity inside a blast furnace hearth by measuring liquid velocity in an experimental setup and validate the same with a mathematical model, which can further be used to generate the wall shear stress for various coke bed configurations.
This and other objects of the present invention can be achieved by using electric resistance sensors in an experimental set up, Liquid velocity measurement through electric resistance sensors is used in a scaled down water model of the system. This technique can also be used with porous medium and with multiphase flow. It has been used in the present invention in a 1:10 scaled down water model of a blast furnace hearth and then validated by mathematical modelling.
It can be very useful for validation purpose. For example, it is very difficult to know the velocity profile of the liquid in some processes operated at high pressure and temperature. Therefore, the numerical simulation of such processes without its validation renders little value.
For the purpose of the present invention the travelling time of tracer injection of potassium chloride is determined between two subsequent sensors based on their electric conductivity. The present invention uses 24 fixed electric resistance sensors placed at different places inside the hearth for the measurement of the average liquid velocity between two consecutive sensors, thus obtaining the velocity profile for different coke bed configurations and tapping rates. The invention also proposes a new methodology for the measurement of local fluid velocity inside the hearth (for water model). The comparison between the experiment and the computation was found to be very much reasonable.
Thus the present invention provides a method of measuring wall shear stress inside a blast furnace hearth comprising the steps of: evaluating the liquid velocity in an experimental set up by using a plurality of electric resistance sensors; validating said liquid velocity with a mathematical model in a processor; and calculating therefrom wall shear stress for various coke-bed configurations of said blast furnace.