Modeling of a Becker-System Coke Oven
Abstract Generated abstract
This paper describes the construction and testing of an approximate physical model of a Becker-system coke oven heating system, based on thermal and hydraulic observations from the Kuznetsk Metallurgical Plant. It develops the modeling rationale from mechanical similarity, emphasizing buoyancy, pressure, viscosity, density variation, heat transfer, and diffusion as factors governing gas motion in regenerators, vertical flues, and sole channels. The model study indicates that ascending gas flow is distributed unevenly, with stronger streams in the middle regenerator cells and vertical flues, while the descending flow is partly equalized by the horizontal collecting channel. Calculations and observations suggest that the sole channel strongly affects flow uniformity and should be designed with nonuniform grate openings rather than the existing arrangement, which tends to send stronger gas streams toward the oven middle.
Full Text
N. N. Norkin.
Modeling of a Becker-System Coke Oven.
I. Introduction.
The modeling of a Becker-system coke oven, carried out in the laboratory of the Department of Apparatus of the Tomsk Industrial Institute, had as its aim:
1) To study on the model the hydrodynamics of the coke oven, both qualitatively and quantitatively.
2) To give a technical characterization of the coupled system of individual flues and regenerators of the “Becker” coke oven, revealing its structural features. The materials underlying the design and construction of the model were the data of a thermal and hydraulic survey conducted in August–September 1935 on the ovens of the coke shop of the Kuznetsk Metallurgical Plant under the direction of the author.
Work on modeling in the TII laboratory is being conducted for the first time. Therefore some omissions and inaccuracies are inevitable; we would be extremely grateful to persons interested in this matter for comments on questions of modeling coke ovens.
II. Theory of the Model of the Heating System of Becker Coke Ovens.
The physical phenomena that are the objects of study in modeling the coupled system of coke ovens are as follows:
1) The motion of gases in the ascending flow of the coke oven, occurring under the influence of the changing density of the gases and the lifting force arising in the direction of motion. The change in gas density and the occurrence of lifting force are due to different temperatures at different points along the height of the ascending flow.
2) The motion of gases in the descending flow of the coupled oven system, occurring under the influence of the rarefaction created by the chimney.
3) Heat exchange of the ascending and descending forced flows. Here it should immediately be pointed out that difficulties arise in modeling heat exchange in a free flow, namely: the free ascending flow in the regenerators has a predominantly convective character of heat exchange, but in the heating flues the predominant significance is the heat exchange by radiant emission in the process of fuel combustion, i.e., direct transfer is of predominant significance.
To reproduce heat exchange by radiation, it is necessary to model the combustion process.
The hydrodynamic content of the phenomenon occurring in the heating system of the oven can be described by the following equations: the phenomenon of gas motion is described by two equations—the equation of motion and the equation of continuity.
Equation of motion
\[ \rho \frac{D w_x}{d\tau} = g_x \rho - \frac{\partial p}{\partial x} + \mu \left[ \frac{\partial^2 w}{\partial x^2} + \frac{\partial^2 w_x}{\partial y^2} + \frac{\partial^2 w_x}{\partial z^2} \right] + \frac{1}{3}\mu \left[ \frac{\partial^2 w_x}{\partial x^2} + \frac{\partial^2 w_y}{\partial x \partial y} + \frac{\partial^2 w_z}{\partial x \partial z} \right], \tag{1} \]
Flow continuity equation
\[ \frac{D\rho}{d\tau}+\rho\frac{\partial w_x}{\partial x}=0 \qquad\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots (2) \]
In these equations \(\frac{Dw}{d\tau}\) and \(\frac{D\rho}{d\tau}\) are substantial derivatives of velocity with respect to time and of density with respect to time (in the terminology of Prof. A. A. Gukhman).
In the above equations the following notation has been introduced:
\(\rho\)—density of the gases \((\mathrm{kg\cdot sec}/\mathrm{m})\).
\(\tau\)—time \((\mathrm{sec})\).
\(w_x\)—component of velocity \((\mathrm{m}/\mathrm{sec})\).
\(\mu\)—viscosity \((\mathrm{kg\cdot sec}/\mathrm{m}^2)\).
The equation of motion shows that, during the motion of a fluid, an interaction is established among forces of four categories: the force of gravity \(g\), the force of external pressure \(p\), the force of internal friction, characterized by the coefficient of viscosity \(\mu\), and inertial (velocity) forces.
Under conditions of “pure” forced motion, occurring under the influence of forces external to the system under consideration, the influence of gravity may be neglected. Then the equation of “pure” forced motion takes the form
\[ \rho\frac{Dw_x}{d\tau} = -\frac{\partial p}{\partial x} +\mu\left[ \left( \frac{\partial^2 w_x}{\partial x^2} + \frac{\partial^2 w_x}{\partial y^2} + \frac{\partial^2 w_x}{\partial z^2} \right) + \frac{1}{3} \left( \frac{\partial^2 w_x}{\partial x^2} + \frac{\partial^2 w_y}{\partial x\,\partial y} + \frac{\partial^2 w_z}{\partial x\,\partial z} \right) \right] \qquad (3) \]
This equation shows the interaction of three categories of forces: forces of external pressure, forces of internal friction (viscosity), and inertial (velocity) forces.
However, the application of equation (3) to the case of coke-oven operation is impossible. The influence of the force of gravity, or more precisely of the buoyant force opposite to it, cannot be neglected. In fact, the pressure drop in the descending flow, with the total height of the heating system, counting from the crossover flue to the sole flue, being \(8\ \mathrm{m}\), and with a very large temperature difference at these points—\(1300^\circ\) and \(300^\circ\mathrm{C}\), respectively—is caused not only by purely mechanical resistances (the resistance of flues and regenerators), but also by overcoming the buoyant force directed opposite to the direction of flow motion. The motion of the ascending flow is caused exclusively by the influence of the buoyant force.
An investigation of the operation of coke ovens, carried out by the author at the Kuznetsk Metallurgical Plant, showed that the pressure drop in the descending flow, equal to \(16\text{--}18\ \mathrm{mm}\) water column, is distributed almost equally between overcoming resistances and overcoming the opposing action of the buoyant force. In the sole flues of the ascending flow, despite the fact that gas and air are supplied at higher pressures, a rarefaction exists, since the entire pressure head of the gases is expended in overcoming resistances in the valves, and the further motion of the ascending flow takes place under the influence only of the buoyant force.
Consequently, the phenomenon being modeled must be described by equation (1), and not by (3).
The substantial derivative of any quantity \(\dfrac{Du}{d\tau}\) characterizes the change of this quantity with time for a body in motion.
In our case, the substantial derivative \(\dfrac{D w_x}{dt}\) characterizes the change of the velocity component with time for a fluid moving in space; therefore its value may be represented in the form
\[ \frac{D w_x}{dt}=\frac{\partial w_x}{\partial \tau}+w_x\frac{\partial w_x}{\partial x}. \]
Considering a flow that is stationary in time, which is the case under the operating conditions of the heating system of a coke oven during the time between reversals, we have
\[ \frac{D w_x}{dt}=w_x\frac{\partial w_x}{\partial x} \]
since \(\dfrac{\partial w_x}{\partial \tau}=0\).
Then the equation of forced motion of a flow stationary in time will have the form
\[ w_x\frac{\partial w_x}{\partial x} = g_x-\frac{1}{\rho}\cdot\frac{\partial p}{\partial x} + \frac{\mu}{\rho} \left[ \left( \frac{\partial^2 w_x}{\partial x^2} + \frac{\partial^2 w}{\partial y^2} + \frac{\partial^2 w_x}{\partial z^2} \right) + \frac{1}{3} \left( \frac{\partial^2 w_x}{\partial x^2} + \frac{\partial^2 w_y}{\partial x\,\partial y} + \frac{\partial^2 w_z}{\partial x\,\partial z} \right) \right]. \tag{4} \]
In equation (4) we shall express the acceleration of the force of gravity through the lifting force arising as a result of the difference in the specific weights of the cooled and hotter streams of the flow of combustion products:
lifting force \(g\rho_0-g\rho\),
its acceleration
\[ a=g\left(\frac{\rho_0-\rho}{\rho}\right)=\frac{\Delta\gamma}{\rho}. \]
Then equation (4) is rewritten in the form
\[ w_x\frac{\partial w_x}{\partial x} = -\frac{1}{\rho} \left( \Delta\gamma+\frac{\partial p}{\partial x} \right) + \frac{\mu}{\rho} \left[ \left( \frac{\partial^2 w_x}{\partial x^2} + \frac{\partial^2 w_x}{\partial y^2} + \frac{\partial^2 w_x}{\partial z^2} \right) + \frac{1}{3} \left( \frac{\partial^2 w_x}{\partial x^2} + \frac{\partial^2 w_y}{\partial x\,\partial y} + \frac{\partial^2 w_z}{\partial x\,\partial z} \right) \right]. \tag{5} \]
Thus, the hydrodynamic content of the phenomena occurring in the heating system is described by the equation of motion in the form of formula (5).
In the flow-continuity equation, the substantial derivative
\[ \frac{D\rho}{dt}=\frac{d\rho}{d\tau}+w_x\frac{\partial\rho}{\partial x} \]
Under stationary conditions \(\dfrac{\partial\rho}{\partial\tau}=0\), the continuity equation takes the form
\[ w_x\frac{\partial\rho}{\partial x}+\rho\frac{\partial w_x}{\partial x}=0. \]
Although there are no large pressure drops in the heating system, nevertheless one cannot neglect the change in density due to the change in the temperature of the flows.
The continuity equation expresses the principle of conservation of mass for the flow.
The thermal content of the phenomena occurring in the heating system of a coke oven consists in the following:
1) blast-furnace gas and air are heated by the checkerwork of the regenerators in an ascending flow. When heating with coke-oven gas, only the air is heated;
2) in the vertical flues, in the ascending flow, the combustion process takes place, during which heat is transferred by radiation to the oven walls (direct transfer);
3) the combustion products cool, giving up their heat in the vertical flues and regenerators in the descending flow.
These phenomena can be described by differential equations of the temperature field, heat transfer at heating surfaces, and the combustion process can be approximately described by the equations of diffusion of gases (gas and air).
The equation of the temperature field
\[ \frac{\partial t}{\partial \tau} + w \frac{\partial t}{\partial x} = a \left( \frac{\partial^2 t}{\partial x^2} + \frac{\partial^2 t}{\partial y^2} + \frac{\partial^2 t}{\partial z^2} \right) \tag{6} \]
This equation characterizes the connection between the change of temperature with time and the change of temperature in space for a moving medium.
The coefficient of proportionality \(a = \frac{\lambda}{c \cdot \gamma}\), called thermal diffusivity, characterizes the intensity of temperature propagation: with an increase in thermal conductivity, thermal diffusivity increases; with an increase in heat capacity and specific weight, thermal diffusivity decreases.
For a stationary process, which with a known approximation may be accepted for the heating system of coke ovens,
\[ \frac{\partial t}{d \tau} = 0 \]
and the equation of the temperature field acquires the meaning of a relation between the change of temperature in space and the velocity of motion.
The equation of heat transfer at the boundaries between the gas and the heating surfaces (the inner surfaces of the oven walls, the heating surfaces of the regenerators)
\[ \lambda \frac{\partial t}{\partial x} = \alpha \Delta t \tag{7} \]
This equation characterizes the connection between the specific heat flux and the temperature gradient at the heat-exchange surface. The heat-transfer coefficient \(\alpha\) acquires the meaning of a total heat-transfer coefficient both by means of radiation and by means of convection.
The combustion process proceeds in two stages: first, mutual diffusion of the fuel and air and, second, ignition accompanied by exothermic reactions.
The first stage—diffusion—can, with a known approximation, be described by the equation
\[ \frac{\partial c}{\partial \tau} + w \frac{\partial c}{\partial x} = D \frac{\partial^2 c}{\partial x^2} \tag{8} \]
Considering the diffusion process as established in time, we have
\[ \frac{\partial c}{\partial \tau}=0 . \]
and
\[ w \frac{\partial c}{\partial x}=D \frac{\partial^2 c}{\partial x^2} \]
This equation gives the dependence of the change in concentration \(C\) in the space of the moving gases.
The coefficient \(D\) is the diffusion coefficient, analogous to the coefficient of thermal conductivity.
In order to reproduce on a model phenomena similar to those occurring in an actual thermal installation (the prototype), it is necessary to observe the similarity conditions developed by the theory of similarity. For a model reflecting the actual phenomena in the prototype, the following conditions must be observed:
1) Geometric similarity. The dimensions of the individual elements of the model must be similar to the corresponding elements of the prototype. This means that the model differs geometrically from the prototype by a scale.
If for the prototype the linear dimensions are \(l_1, l_2 \ldots \ldots \ldots l_n\), then for the model they are respectively \(C_l l_1, C_l l_2 \ldots \ldots C_l l_n\), and the transformation multiplier of the linear dimensions \(C_l\) remains constant for all elements of the model
\[ C_l=\mathrm{const} \]
2) Time similarity—homochronicity. This means that the individual stages of the processes in the model are homogeneous in time with the corresponding stages in the prototype. The model differs from the prototype by the time scale. If for the prototype the duration of the stages of the processes is \(\tau_1, \tau_2 \ldots \ldots \tau_n\), then for the model the duration is respectively \(C_\tau \tau_1, C_\tau \tau_2 \ldots \ldots C_\tau \tau_n\), and the time transformation multiplier \(C_\tau\) remains constant for all stages of the processes in the model
\[ C_\tau=\mathrm{const} \]
It is obvious that in the case when \(C_\tau=1\), we shall have the case of synchronism, identity in time. In modeling synchronism is excluded owing to additional conditions.
It is also obvious that when modeling processes that have become established in time (stationarity of processes), the requirement of homochronicity falls away completely.
3) Similarity of fields of physical constants.
The phenomena occurring in the heating system of a coke oven are characterized by physical constants, and the absolute value of these constants in the developing processes does not remain constant, but changes. To reproduce similar phenomena in the model, it is necessary that the change in the physical constants of the substance used in the model be similar in corresponding parts of the model.
If for the prototype the constants have the values \(U_1, U_2 \ldots \ldots U_n\), then at corresponding points of the model \(C_u U_1, C_u U_2 \ldots \ldots C_u U_n\), and the transformation multiplier of the field of physical constants \(C_u\) remains constant.
Similarity of fields of physical constants also includes the requirement of similar change of vector quantities, for example, the velocity of flows at corresponding points.
The three similarity conditions given above are combined into one general concept—the conditions of uniqueness, which characterize the individuality, concret—
ness of phenomena. Consequently, the first requirement of the theory of similarity reduces to observance of the condition: in the model there must be a similar transformation of the conditions of uniqueness.
The second requirement of the theory of similarity consists in the fact that the choice of multipliers of similar transformations is restricted by the condition: for phenomena occurring in the prototype and in the model, the basic differential equations must be identical, and the similarity criteria at corresponding points must be one and the same, i.e.
\[ K = idem \]
Let us indicate a general method for compiling similarity criteria, applying the “rubber-band” rule. According to this rule, the transformation multipliers of quantities in the form of differential expressions are composed by striking out, “erasing,” the differential indices. As a result of such striking out, of such “erasing” of the differential operators, the differential equations take the form of reduced complexes. By term-by-term division of the entire expression of the algebraic sum of the reduced complexes by one of the terms, we obtain an algebraic sum of dimensionless reduced complexes, called similarity criteria (invariants). The number of similarity criteria (invariants) will be one less than the number of power complexes of the differential equation.
For the phenomena being modeled the similarity criteria will be the following (see Table No. 1).
Table I.
Criteria of similarity invariants for a model of the heating system of a coke oven.
| Name of class of phenomena | Mathematical model of this class—differential equation | Applying the “rubber-band” rule, we obtain reduced complexes | Dividing one reduced complex by another, we obtain a dimensionless reduced complex—similarity criterion (invariant). | Dimension of the equation |
|---|---|---|---|---|
| Steady forced motion of a viscous fluid (gases) | \(w_x \dfrac{\partial w_x}{\partial x} = -\dfrac{\Delta \gamma}{\rho} + \dfrac{\partial p}{\partial x}\dfrac{1}{\rho} + \dfrac{\mu}{\rho}\left[\left(\dfrac{\partial^2 w_x}{\partial x^2}+\ldots\right)+\dfrac{1}{3}\left(\dfrac{\partial^2 w_x}{\partial x\,\partial x}+\ldots\right)\right]\) | \(P_1=\dfrac{w^2}{l}\) \(P_2=\dfrac{\Delta\gamma}{\rho}\) \(P_3=\dfrac{\Delta p}{l\rho}\) \(P_4=\dfrac{\mu}{\rho}\cdot\dfrac{w}{l^2}\) |
1) \(\dfrac{w^2}{l}:\dfrac{\mu}{\rho}\dfrac{w}{l^2}=\dfrac{w\rho l}{\mu}=Re\) 2) \(\dfrac{w^2}{l}:\dfrac{\Delta\gamma}{\rho}=\dfrac{w^2\rho}{\Delta\gamma l}=Fr\) 3) \(\dfrac{\Delta p}{\rho l}:\dfrac{w^2}{l}=\dfrac{\Delta p}{w^2\rho}=Eu\) 4) \(\dfrac{\Delta\gamma}{\rho}:\dfrac{\Delta p}{\rho l}=\dfrac{\Delta\gamma}{\Delta p}l=Ne\) |
\(\dfrac{m}{sec^2}\) |
| Steady temperature field in gases | \(w_x\dfrac{\partial t}{\partial x}=a\left(\dfrac{\partial^2 t}{\partial x^2}+\dfrac{\partial^2 t}{\partial y^2}+\dfrac{\partial t^2}{\partial z^2}\right)\) | \(P_1=\dfrac{wt}{l}\) \(P_2=a\dfrac{t}{l^2}\) |
\(\dfrac{wt}{l}:a\dfrac{t}{l^2}=\dfrac{wl}{a}=Pe\) | \(\dfrac{{}^{\circ}C}{sec}\) |
| Heat transfer at the heat-exchange surface | \(\lambda\dfrac{\partial t}{\partial x}=\alpha\Delta t\) | \(P_1=\lambda\dfrac{t}{l}\) \(P_2=\alpha t\) |
\(\alpha t:\lambda\dfrac{t}{l}=\dfrac{\alpha l}{\lambda}=Nu\) | \(\dfrac{Cal}{m^2\,hour}\) |
Note: Names of the criteria
Reynolds criterion \(= Re\)
Froude criterion \(= Fr\)
Euler criterion \(= Eu\)
Newton criterion \(= Ne\)
Péclet criterion \(= Pe\)
Nusselt criterion \(= Nu\)
III. Calculation of the Hydraulic Model of the Heating System of a Coke Oven
For the calculation of the hydraulic model of the coke oven, the average operating indices of Becker-system coke ovens at the Kuznetsk Metallurgical Plant, when fired with blast-furnace gas, were adopted as the initial data.
The average indices adopted for calculating the model:
- Oven throughput by charge: 17 tons/13 hours.
- Heat consumption for coking: 650 cal/kg.
- Calorific value of blast-furnace gas: 860 cal/m³.
- Second-by-second volume of blast-furnace gas for one half of a heating wall on the machine side: 0.167 m³/sec.
- Second-by-second volume of combustion air: 0.139 m³/sec.
The model was made on a scale of 1/10. The criteria of hydrodynamic similarity for the water and air models were determined from average temperature data at the most characteristic points of the specimen of the coke-oven heating system and for the working fluids in the model at a constant temperature of 20°C.
In the appended Table II are brought together the geometric dimensions of the specimen and the model, as well as the calculated quantities and similarity criteria for the air and water models under the condition of constant water and air flow rates in the models.
Table II.
| Name of quantities and dimension | Locations | Air flue, ascending | Air flue, descending | Gas flue, ascending | Gas flue, descending |
|---|---|---|---|---|---|
| Cross-sectional area, m² | Specimen | 0,1222 | 0,1222 | ||
| Cross-sectional area, m² | Air model | 0,001222 | 0,001222 | ||
| Cross-sectional area, m² | Water model | 0,001222 | 0,001222 | ||
| Second-by-second volume, \(V\), m³/sec | In the specimen | 0,139 | 0,2814 | 0,167 | 0,1407 |
| Temperature, °C | Specimen | 30 | 270 | 30 | 290 |
| Temperature, °C | Air model | 15 | 15 | 15 | 15 |
| Temperature, °C | Water model | 15 | 15 | 15 | 15 |
| Second-by-second volume at \(Re = idem\), \(t = const\) | Air model | 0,0144 | 0,018 | ||
| Second-by-second volume at \(Re = idem\), \(t = const\) | Water model | 0,00093 | 0,0012 | ||
| Actual velocity, \(w\), m/sec | Specimen | 1,24 | 1,48 | ||
| Actual velocity, \(w\), m/sec | Air model | 12,0 | 15,2 | ||
| Actual velocity, \(w\), m/sec | Water model | 0,78 | 0,98 | ||
| Reduced diameter | Specimen | 0,282 | 0,282 | ||
| Reduced diameter | Air model | 0,282 | 0,282 | ||
| Reduced diameter | Water model | 0,0282 | 0,0282 | ||
| Kinematic viscosity, \(10^{-6}\delta\), m²/sec | Specimen | 15,9 | 41,1 | 15,0 | 42,6 |
| Kinematic viscosity, \(10^{-6}\delta\), m²/sec | Water model | 1,0 | 1,0 | 1,0 | 1,0 |
| Kinematic viscosity, \(10^{-6}\delta\), m²/sec | Air model | 15,5 | 15,5 | 15,5 | 15,5 |
| Reynolds, \(Re = \dfrac{wd}{\delta}\) | In the specimen | 22000 | 27560 | ||
| Reynolds, \(Re = \dfrac{wd}{\delta}\) | In the models at constant flow rate: air | 11400 | 22400 | ||
| Reynolds, \(Re = \dfrac{wd}{\delta}\) | In the models at constant flow rate: water | 16200 | 16200 |
| Average for air nozzle | Average for air nozzle | Average for gas nozzle | Average for gas nozzle | Entry into oblique flue of air regenerator | Entry into oblique flue of air regenerator | Entry into oblique flue of gas regenerator | Entry into oblique flue of gas regenerator |
|---|---|---|---|---|---|---|---|
| Asc. | Desc. | Asc. | Desc. | Asc. | Desc. | Asc. | Desc. |
| 0,535 | 0,700 | 0,0686 | 0,0078 | 0,0686 | 0,0078 | ||
| 0,00535 | 0,007 | 0,000686 | 0,000078 | 0,000686 | 0,000078 | ||
| 0,139 | 0,1407 | 0,167 | 0,1407 | 0,00995 | 0,01 | 0,0119 | 0,02 |
| 0,139 | 0,1407 | 0,167 | 0,1407 | 0,00995 | 0,01 | 0,0119 | 0,01 |
| 600 | 710 | 582 | 700 | 1100 | 1250 | 1065 | 1250 |
| 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |
| 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |
| 0,007 | — | 0,0088 | — | 0,00535 | — | 0,0068 | — |
| 0,00045 | — | 0,00056 | — | 0,00035 | — | 0,00043 | — |
| 0,805 | — | 0,72 | — | 0,71 | — | 0,83 | — |
| 1,3 | — | 1,25 | — | 0,56 | — | 0,71 | — |
| 0,085 | — | 0,081 | — | 0,036 | — | 0,045 | — |
| 0,222 | 0,274 | 0,259 | 0,0864 | 0,259 | 0,0864 | ||
| 0,022 | — | 0,0264 | 0,0259 | 0,00864 | 0,0259 | 0,00864 | |
| 95,0 | 113,0 | 87,0 | 111,0 | 197,0 | 215,5 | 182,5 | 415,5 |
| 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| 15,1 | 15,5 | 15,5 | 15,5 | 15,5 | 15,5 | 15,5 | 15,5 |
| 1880 | — | 2140 | — | 935 | — | 1180 | — |
| 4000 | — | 3620 | — | 3620 | — | 3620 | — |
| 2900 | — | 2640 | — | 2640 | — | 2640 | — |
| Heating channel, average | Heating channel, average | Regenerator | Regenerator | Collecting horizontal channel | Collecting horizontal channel | Crossover channel | Crossover channel |
|---|---|---|---|---|---|---|---|
| Asc. | Desc. | Asc. | Desc. | Asc. | Desc. | Asc. | Desc. |
| 0,1173 | 0,1173 | 0,03 | 0,03 | 0,43. 6,387 = 2,72 | 0,22. 0,33 = 0,0726 | ||
| 0,001173 | 0,001173 | 0,0003 | 0,0003 | 0,043. 0,6387 = 0,027 | 0,022. 0,033 = 0,0007 | ||
| 0,02 | 0,02 | 0,2 | 0,02 | 0,2814 | 0,2814 | 0,0938 | 0,0938 |
| 15,0 | 1300 | 1386 | 1350 | 1386 | 1350 | 1386 | 1350 |
| 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |
| 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |
| 0,01 | 0,0123 | 0,022 | 0,0118 | 0,0113 | 0,0113 | 0,011 | 0,01 |
| 0,00066 | 0,0079 | 0,00078 | 0,00074 | 0,00073 | 0,00073 | 0,0007 | 0,00068 |
| 1,285 | 0,965 | 4,44 | 4,18 | 0,617 | 0,60 | 7,85 | 7,7 |
| 0,61 | 0,75 | 2,9 | 2,82 | 0,42 | 0,4 | 5,25 | 5,0 |
| 0,04 | 0,048 | 0,185 | 0,18 | 0,027 | 0,025 | 0,33 | 0,32 |
| 0,340 | 0,340 | 0,15 | 0,15 | 0,804 | 0,264 | ||
| 0,034 | 0,0340 | 0,015 | 0,015 | 0,084 | 0,0264 | ||
| 336,0 | 227,0 | 238,9 | 230,0 | 238,9 | 230,0 | 238,9 | 230,0 |
| 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| 15,5 | 15,5 | 15,5 | 15,5 | 15,5 | 15,5 | 15,5 | 15,5 |
| 1 335 | 1650 | 2800 | 2720 | 2100 | 2080 | 8923 | 8500 |
| 2780 | 2780 | 4800 | 4800 | 3000 | 3000 | 3500 | 3500 |
| 1750 | 1750 | 3500 | 3500 | 2180 | 2180 | 2550 | 2550 |
Explanations to summary table II of the calculated quantities for the water and air model.
Designations adopted in the table:
\(F \, m^2\) — cross-sectional area.
\(V_0 \, m^3/\text{sec}\) — volume of gases flowing through the section, reduced to NTP.
\(t^\circ C\) — temperature of the flowing gases.
\(v_t = v_0 (1 + at) \, m^3/\text{sec}\) — volume of the flowing gases at their actual temperature.
$w$, m/sec — actual gas velocity
\[ w=\frac{V_t}{F}=\frac{V_0(1+\alpha t)}{F}. \]
$Re$ — Reynolds criterion
\[ Re=\frac{wd}{\delta} \]
where: $d$ is the equivalent diameter, calculated from the condition
\[ d=4r_{\text{hydr}}=4\frac{F}{\Pi} \]
where: $\Pi$ is the perimeter of the section.
$\delta$, m²/sec — coefficient of kinematic viscosity; the values were taken from the book by M. V. Kirpichev and M. A. Mikheev, Modeling of Thermal Devices.
The water flow rate for the model was determined from the following relations: for the prototype and the model the Reynolds criterion must be one and the same,
\[ Re=idem. \]
Consequently:
\[ Re=\frac{w'd'}{\delta'}=\frac{w''d''}{\delta''}=idem. \]
Hence the average discharge velocity of water or air in the model is
\[ w''=Re\frac{\delta''}{d''}\ \frac{m}{sec} \]
The average flow rate of water or air in the model is
\[ v=w''f''=Re\frac{\delta''}{d''}f''\ m^3/sec \]
The flow rate calculated in this way would have to be, for the water model, from $0.00035$ to $0.0012\ m^3/sec$ of water, and for the air model from $0.00535$ to $0.018\ m^3/sec$ of air. The non-constancy of the flow rate of water and air in different sections of the models is explained by three reasons:
1) Complete similarity of phenomena in the prototype and in the models can exist only when, in addition to the identity of criteria, for example $Re=idem$, it is necessary to observe constancy of the fields of physical constants.
In the present case it would have been necessary to observe
\[ \frac{\delta'}{\delta''}=const \]
in all corresponding sections of the prototype and the models.
Constancy of the fields of physical constants would practically have necessitated having working fluids (water, air) in different sections at different temperatures. If this condition were observed, the fluid flow rate would be constant. But for the models a working fluid of constant temperature was used, and consequently also of constant kinematic viscosity; therefore, equality of the criteria could not be observed.
The magnitude of the deviations of the Reynolds criteria from their equality is given in Table II. Thus, not complete but approximate similarity was reproduced.
2) Exact calculation of the criteria for the prototype is difficult, owing to the fact that an exact determination of the temperatures in the prototype by means of measurements and calculations could not be carried out. Thus, for example, temperature measurements in the regenerators of the oven were made at only two points: in the sole flue and in the under-sole space of the regenerators at a distance of 1–1.5 m from the outer wall of the regenerators. Measurements of the temperature of the flame jet also could not be made, and could only be calculated. If one bears in mind the approximate and even conditional nature of the calculation of the flame-jet temperature, it becomes clear that an exact calculation of the Reynolds criteria for the heating system of the ovens could not be made; this may also have been reflected in the considerable discrepancy between the volumetric flow rates of the modeling liquid in the different sections of the model.
3) As a result of the combustion of blast-furnace gas, the volume of the combustion products is not equal to the arithmetic sum of the volumes of the blast-furnace gas and air, but is equal to the stoichiometric sum of the reacting gases. Therefore, without reproducing the combustion process in the model, it is also impossible to obtain identity of the similarity criteria.
However, the absence of identity of the criteria and the failure to maintain constancy of the kinematic-viscosity fields is not an obstacle to attaining a certain degree of approximation of the modeled phenomena to the actual ones, owing to the stability and self-modeling character of flows of viscous liquids; for more detail, see Chapter 3 of the book by M. V. Kirpichev and M. A. Mikheev, Approximate Modeling.
Taking into account all that has been stated above, the water flow rate in the water model was taken as
\[ v_{\text{water}} = 0.0007\ \text{m}^3/\text{sec} \quad \text{or} \quad 2.52\ \text{m}^3/\text{hr}, \]
at a temperature of 10° C and with a coefficient of kinematic viscosity
\[ \delta_{\text{water}} = 1.10^{-6}\ \text{m}^2/\text{sec}. \]
The air flow rate in the air model was taken as
\[ v_{\text{air}} = 0.015\ \text{m}^3/\text{sec} \quad \text{or} \quad 54\ \text{m}^3/\text{hr} \]
at a temperature of 15° C with a coefficient of kinematic viscosity
\[ \delta_{\text{air}} = 15.5 \cdot 10^{-6}\ \text{m}^2/\text{sec}. \]
The model was made at 1/10 of full scale. The frame of the model was made of wood and lined inside with common white tinplate. The outer covering surfaces were made of thick mirror glass. Through the glass, therefore, the entire internal arrangement of the model heating system was visible. The regenerator checkerwork was made of wooden “bricks,” likewise with dimensions of 1/10 full scale. On the outer glass surfaces 16 nipples were installed, with taps for measuring pressure drops. The sealing of the nipples in the glass was accomplished with rubber gaskets. Plate stabilizers were arranged for introducing air (or water) into the model. In constructing the model, the appropriate instructions on the construction of models, set forth in the book by M. V. Kirpichev and M. A. Mikheev, Modeling of Thermal Devices, were taken as the basis.
A diagram of the construction of the model is shown in the accompanying drawing (Fig. 1). The general setup of the model during testing is shown in Fig. 2.
Air was supplied to the model by a centrifugal fan through a pressure equalizer (air receiver).
Measurements of pressure drops were made with a KS—08 micromanometer No. 1309.
For illustrative qualitative observations, the air driven through the model was saturated with HCl and NH₄OH vapors. As a result, the formed
$\mathrm{NH_4Cl}$ in the form of a fog was clearly visible through the outer glass surfaces, which made it possible to judge the nature of the distribution of gas flows.
IV. Results of testing the model and conclusions.
In testing the air model, the main objective was set—to determine the pressure drops in individual sections of the heating system of the coke-oven model and the nature of the distribution of gas flows at various points along the length of the regenerators in the vertical flues.
Fig. 1.
Table III gives the pressure drops obtained during testing of the air model when air was blown through the model. From the pressure drops obtained, the dynamic-similarity criteria—the Euler criteria—were calculated for the corresponding sections.
\[ Eu=\frac{\Delta P}{\rho w^2} \]
With complete similarity, the condition must be satisfied
\[ Eu = \mathrm{idem} \]
then it is possible to calculate the hydraulic resistances of similar sections of the prototype (the actual oven)
\[ \Delta P_{\text{prototype}} = Eu\,\rho_{\text{prot.}}\,w_{\text{prot.}}^{2}\ \text{mm water column}. \]
The calculated resistances for the prototype, given in Table III, when compared with literature data, show their close agreement with the actual resistances in the heating system of a coke oven. In analyzing the calculated resistances, one should treat their absolute value with caution, since an approximate but incomplete similarity was carried out; however, comparison of the resistances in individual sections of the heating system indicates that the greatest resistances are those of the flues and the crossover channels.
Table III
Pressure drops—resistances \(\Delta P\), mm water column, of individual sections of the model heating system.
| No. | Name of model section | Measured \(\Delta P\), mm water column | Euler criterion \(Eu = \dfrac{\Delta P}{w\rho^{2}}\) | Calculated for the prototype \(\Delta P\), mm water column |
|---|---|---|---|---|
| 1 | Resistance of the sole channel | 0.25 | 2.4 | 0.3 |
| 2 | Resistance of the regenerators | 0.15 | 0.25 | 0.015 |
| 3 | Resistance of the flues for the ascending flow | 2.4 | 4.00 | 3.2 |
| 4 | Resistance of the flues for the descending flow | 1.0 | 1.6 | 1.28 |
| 5 | Resistance of the vertical | 0.05 | 1.0 | 0.0027 |
| 6 | Resistance of the crossover channel | 0.55 | 0.085 | 0.12 |
| Total resistance of the heating system | 4.80 | — | 4.8577 |
Measurements of pressure drops at various points located at different distances from the inlet end of the model, but in the same horizontal planes, make it possible to obtain an idea of the distribution of gas flows horizontally in the heating system of the oven. Measurements of pressure drops horizontally were made opposite 3 and 11 verticals. The results are given in Table IV.
Table IV
Pressure drops between two points in one horizontal plane (opposite 3 and 11 verticals) in the air model
| No. | Name of model section | mm water column |
|---|---|---|
| 1 | Top of regenerators | +0.45 |
| 2 | Sole of verticals | +0.1 |
| 3 | Sole channel | +0.03 |
| 4 | Crossover channel | +0.02 |
Analyzing the results presented, the following conclusions may be drawn: first, the distribution of flows along the horizontal is nonuniform. More powerful flows pass through sections farther from the inlet end (from the damper) toward the middle of the oven; second, the nonuniformity of the flows in the regenerators is evened out as the air exits into the inclined flues, but is not completely eliminated. And only in the descending flow can one practically consider there to be an absence of pressure differences in the horizontal planes, and consequently a complete equalization of the flows. These conclusions may serve as certain factual material for establishing the mode of adjustment of the register openings and for designing sole channels. As is known, the cross section of the sole channels in operating ovens is identical along the entire length of the regenerator. The results obtained indicate the necessity of designing the sole channels narrowed toward the middle of the oven.
A vivid confirmation of what has been said about the nonuniformity of the air flows may be provided by the deposition of ammonium chloride on the glass opposite the inclined flues from the regenerators into the inclined flues. The experiment was carried out as follows: three inlets were made in the stabilizer at the inlet end of the model: air was blown through the main one, through one lateral inlet a pair of concentrated hydrochloric acid was introduced, and through the other lateral inlet a pair of ammonia was introduced. In the sole channel of the model, ammonium chloride was formed. The latter, in the form of a white dense fog, was driven through the model by a stream of air. From the density of the ammonium-chloride fog it was possible to judge the intensity and uniformity of the flows in the horizontal planes of the model. The greatest density of the fog was observed toward the middle of the oven and its discontinuity near the partition of the regenerator.
In Fig. No. 3, the deposition of ammonium chloride on the glass opposite the inclined flues of the descending flow is reproduced. From the character of the deposition one may judge the equalization of the descending flows.
A substantial influence on the operation of the regenerators of the ascending current is exerted—
Fig. 2.
the construction of the sole distributing channel. The uniformity of gas and air admission along the length of the regenerators depends on the distribution of the sole openings in the channel.
To determine the hydrodynamic operating conditions of the sole channel, let us use the Epure equation of pressures for a channel of constant cross-section with uniform distribution of gas along its length:
\[ -P=-P_0-\gamma\frac{w_0^2}{2g}\left[\left(\frac{x}{l}\right)^2+\frac{\lambda}{3}\cdot\frac{l}{d}\left(\frac{x}{l}\right)^3\right] \tag{9} \]
With the aid of this equation, for different values of \(x\), i.e., for different points in the sole channel, one can construct the curve of pressure variation along the length of the channel.
In accordance with the pressure curve calculated from equation (9), the dimensions of the live cross-section of the openings in the sole grate can be determined in order to ensure uniform distribution of gas and air to the regenerators along the length of the sole channel.
The determination of the cross-sectional area for different values of \(x\), with a known approximation, may be carried out by means of the equation
\[ f=\frac{v}{l\mu\sqrt{\frac{2g}{\gamma}}\sqrt{P_0+\gamma\left[\frac{w^2}{2g}\left(\frac{x}{l}\right)^2+\frac{\lambda}{3}\frac{l}{d}\left(\frac{x}{l}\right)^3\right]}} \tag{10} \]
The values of the individual quantities in equations (9) and (10) are as follows:
\(P_0\) — mm water column, pressure at the beginning of the sole channel;
\(\gamma\) — kg/m³, specific weight of the gas (or air);
\(w_0\) — m/sec, velocity of entry of the gas (or air) from the volute into the sole channel;
\(l\) — m, length of the sole channel;
\(d\) — m, hydraulic diameter of the sole channel;
\(\lambda\) — coefficient of friction;
\(x\) — m, distance from the beginning of the sole channel to any opening in the sole channel;
\(v\) — m³/sec, volume per second of gas (or air) entering the sole channel;
\(\mu\) — coefficient of discharge;
\(f\) — m²/m, area of the cross-section of the sole openings per one running meter of the sole channel, determined for different distances from the beginning of the sole channel.
The results of calculations of the Epure of pressures and of the cross-section of the openings are given in Table V; as the initial quantities for the calculations, the following were adopted:
\(P_0=1\) mm water column, which corresponds to the usual furnace operation with blast-furnace gas;
\[
\gamma=1.12\ \text{kg/m}^3
\]
for blast-furnace gas at \(t=40^\circ\mathrm{C}\);
\[ w_0=\frac{\text{volume per second of blast-furnace gas}}{\text{cross-section of the sole channel}} =\frac{0.167}{0.355\cdot0.216}\cdot\frac{(273+40)}{273} =2.5\ \text{m/sec}. \]
Here the volume per second of blast-furnace gas is taken from the calculation for half of the wall on the machine side.
\[
l=6454\ \text{mm}
\]
— length of the sole channel;
\[ d=4\frac{0.355\cdot0.216}{2(0.355+0.216)}=0.268\ \text{m}; \]
\[ \gamma \text{ according to Trinks}=0.038; \]
\[ v=0.167\left(\frac{273+40}{273}\right)=0.191\ \text{m}^3/\text{sec}; \]
\[ \mu = 0.62 \quad \text{(for sharp-edged openings);} \]
\[
\begin{aligned}
x_1 &= 0.45 \text{ m;}\\
x_2 &= 2.417 \text{ m;}\\
x_3 &= 5.23 \text{ m;}\\
x_4 &= 6.454 \text{ m.}
\end{aligned}
\]
Different values of \(x\), depending on the type and dimensions of the sections of the openings in the sole grate. (See Fig. No. 4).
Table V
of the calculated values of draft and areas of the sections of the sole grate under the condition of uniform distribution of blast-furnace gas along the length of the sole channel
| No. | Distance from the beginning of the sole channel \(x\), m | \(\dfrac{x}{l}\) | \(f\), m²/m | Draft in the sole channel opposite the opening \(P\), mm water column | \(f\), m²/m |
|---|---|---|---|---|---|
| — | 0.0 | — | — | −1.0 | — |
| 1–2 | 0.450 | 0.07 | 0.04 | −1.0018 | 0.0118 |
| 3–7 | 2.417 | 0.375 | 0.0175 | −1.057 | 0.0113 |
| 8–15 | 5.230 | 0.81 | 0.0255 | −1.2848 | 0.0105 |
| 16–18 | 6.454 | 1.0 | 0.04 | −1.3670 | 0.0101 |
NOTE: In the sole channels of the ovens there are three types of sole openings, 18 openings in all, of which:
5 openings, each with a section of \(0.076 \cdot 0.14 = 0.0106\ \text{m}^2\).
5 openings, each with a section of \(0.050 \cdot 0.14 = 0.007\ \text{m}^2\).
8 openings, each with a section of \(0.064 \cdot 0.14 = 0.00895\ \text{m}^2\).
The distribution of the sections is shown in Fig. No. 4.
Comparing \(f\), calculated with \(f\) from practical data, the following conclusions may be drawn:
a) According to the theory of distribution channels, toward the end of the sole channel the sections of the openings in the sole grate per 1 m of channel length must decrease, owing to the change in static pressure in the channel.
Fig. 4.
b) In actuality, the cross sections of the floor grate per 1 m increase toward the end of the channel.
c) In actuality, a uniform distribution of gases along the length of the floor channel is not achieved; more powerful gas streams go toward the end of the floor channel (toward the middle of the oven), which is caused by the increase in the grate cross sections per 1 m toward the end of the channel; confirmation of this is provided by the qualitative characteristics obtained in testing the air model.
V. Conclusion.
1) On the basis of the theory of mechanical similarity, an approximate modeling of the aerodynamics of the heating system of a coke oven has been carried out and investigated.
2) It has been established that the ascending gas stream is distributed nonuniformly along the length of the regenerators and vertical flues. The movement of the more powerful gas streams is established in the middle cells of the regenerators and the middle vertical flues.
3) The descending stream, owing to the continuous horizontal collecting channel, is equalized.
4) The floor channel, which substantially affects the uniformity of the gas streams, must be designed with a nonuniform cross section.
The work was carried out in the laboratory of the Department of Apparatus of the Tomsk Industrial Institute on a subject approved by the Main Administration of Educational Institutions of the People’s Commissariat of Heavy Industry. Students of the fifth year of the Chemical Faculty, comrades Antonov, Sinyakov, and Kozmina, took part in the design and fabrication of the model. The model was fabricated by the mechanic N. D. Velikzhanin. Laboratory assistant N. M. Nevzorov participated in the testing. The model is at present a teaching visual aid in the study of oven construction. The preliminary test results were reported by the author to the engineering and technical personnel of the coke shop of the Kuznetsk Metallurgical Plant in February 1937.
List of guiding literature on the theory and practice of modeling.
- A. A. Gukhman, “Physical Foundations of Heat Transfer.”
- M. V. Kirpichev, I. A. Mikheev, “Modeling of Thermal Devices.”
- P. M. Volkov, “Study on a Water Model of the Nature of Gas Motion in the Heating Chamber of Coke Ovens.”
- P. M. Volkov, “Study of the Operation of Rotary Furnaces on Models.”
- M. A. Kuzmin, “On the Methodology of Studying Gas Motion in Furnaces.”
- Problems of Gas Motion in Furnaces. Works of Stalproekt, edited by G. P. Ivantsov.