CN104361195A - Three-dimensional flow thermal coupling modeling method for cement grate cooler - Google Patents

Abstract

The invention discloses a three-dimensional flow thermal coupling modeling method for a cement grate cooler. The modeling method takes a cement clinker layer in the grate cooler as a porous medium, applies a mechanics of fluid through porous media theory for modeling, and comprises the following steps: building a three-dimensional flow thermal coupling physical model of the cement grate cooler according to the cooling condition of the clinker in the grate cooler; building a three-dimensional flow thermal coupling mathematical model of the grate cooler according to the physical model, the law of mass conservation, the law of conservation of momentum and the law of conservation of energy. The modeling method has the benefits that the factors of grate speed, supplied wind velocity, side wall heat dissipation, feeding temperature, clinker particle diameter, and the like are considered; the three-dimensional temperature distribution of the clinker can be calculated conveniently and accurately; different cooling strategies are simulated by adjusting the working condition parameters, so as to obtain an optimal strategy enabling the grate cooler to work efficiently and reasonably, improve the heat recovery efficiency of the grate cooler, and achieve the purposes of energy conservation and emission reduction; the modeling method is the optimal clinker cooling strategy applied to confirm that the discharging temperature of the grate cooler is relatively low, and the recovery wind warm is relatively high.

Description

A kind of three-dimensional flow thermal coupling modeling method for cement grate-cooler

Technical field

The present invention relates to cement clinker burning system modeling technique field, be specifically related to a kind of three-dimensional flow thermal coupling modeling method for cement grate-cooler.

Technical background

China is manufacture of cement and consumes big country, and annual production reaches 24.1 hundred million tons, and close to 50% of world's cement output, the proportion that cement made in China is equipped in international cement trade reaches more than 1/3.What require low carbonization along with various countries improves constantly, and the energy consumption in manufacture of cement, pollution and energy recovery problem become the focus that global cement industry is paid close attention to gradually.Cement producing line is mainly divided into grinding and burns till two Iarge-scale system, and in firing system, the cooling procedure of cement clinker is an important step of carrying out energy recovery and decreasing pollution dust emission, and grate-cooler has been the key equipment of clinker cooling and heat recovery.

Grate-cooler is a kind of solid and gas contact device of function admirable, contacting efficiency between clinker particles and refrigerating gas is improved greatly, enhance the heat-transfer effect in clinker layer, its Main Function is that the high temperature chamotte drawn off cement rotary kiln by grate plate is carried, cooled and heat recovery.The conveying of grog is carried out by the reciprocating of grate plate, in course of conveying, be blown into cooling-air vertically upward by grate plate bottom blower fan cool high temperature chamotte, cooling-air diffusion and grog in the bed of material carry out heat interchange, after heat interchange, its heat of air part enters in rotary kiln Sum decomposition stove with the form of Secondary Air and tertiary air and re-uses, and another part lingering remnants of past customs enters afterheat generating system.Now in cement production process, incomplete to energy recovery working mechanism research in grate-cooler, cannot be optimized the operation of grate-cooler, cause current cooling effectiveness and waste heat recovery rate all lower.Therefore, deeply carry out the research of clinker cooling heat transfer mechanism, to increase grog in grate-cooler heat exchanger effectiveness, improve heat recovery rate and reduce dust emission there is important theory significance and practical value.

At present improvement to grate-cooler physical construction, the research of grate-cooler control method and the Modeling Research of grate-cooler are comprised to the research of cement grate-cooler.To the improvement in grate-cooler physical construction, a kind of grate-cooler of Wang Lijun, China Patent No.: CN201110337865.3, provides " a kind of with the grate-cooler of grate cooler module composition ", can change longitudinal length or transverse width to adapt to the production line of different output; " a kind of grate-cooler cooling system and the grate-cooler thereof " of Gao Yuzong, China Patent No.: CN200920109193.9, this application case does not affect by the duty of indivedual blower fan, and can ensure continually provides cooling-air.To in the control method research of grate-cooler, there is China Patent No.: CN200910193434.7, denomination of invention is " grate-cooler exhausting temperature-controlled process and device for cement afterheat generation system ", this application case is controlled the rotating speed of the aperture of the lingering remnants of past customs air-valve in grate-cooler, one section of main biography rotating shaft, the rotating speed of two sections of main biography rotating shafts by controller, thus reduce the fluctuation of grate-cooler UTILIZATION OF VESIDUAL HEAT IN exhausting temperature, ensure that exhausting temperature maintains higher level; China Patent No.: " a kind of control system of grate-cooler " that CN201110428990.5, Liu Rongjin propose, it comprises control one section of grate, two sections of grates and three sections of grates respectively.Data identification modeling and modelling by mechanism are divided into the Modeling Research of grate-cooler, data identification modeling is that grate-cooler is considered as "black box" system, by obtaining the good model with data fitting to data analysis identification, if China Patent No. is CN200810011325.4, " intelligent control method of clinker grid type cooling machine cooling procedure " patented claim that Qiao Jinghui proposes, establishes the grate-cooler model of case-based reasioning; Also have China Patent No. to be " a kind of control method of cement clinker grate cooler " patented claim that CN201310277878.5, Yu Haibin propose, set up the tight form dynamical linearization model of clinker cooling process, by comb downforce, comb speed is controlled; In " the grate cooler Clinker Flow modeling based on fuzzy neural network " that " Chinese journal of scientific instrument " S2 phase in 2005 publishes, Li Haibin establishes the grate-cooler model based on fuzzy neural network; In " application of Dynamic matrix control in clinker cooling system " that " Chinese cement " 05 periodical in 2007 carries, Wang Xiaohong establishes the grate-cooler model based on grey Prediction Control.Without the need to understanding heat transfer mechanism in grate-cooler for its advantage of these models, modeling process is simple, but because grate-cooler system process is complicated, relation factor is more, adopt data modeling just to be set up by the data of a few variable, make institute's established model cannot react the course of work of grate-cooler accurately.Therefore for the object improving clinker cooling efficiency, heat recovery efficiency, optimizing operation, the mechanism model of grate-cooler need be set up, to carry out deep understanding and transparent assurance to clinker cooling mechanism in grate-cooler.

Summary of the invention

For the blank that the three-dimensional modelling by mechanism technology of cement grate-cooler exists, the object of the present invention is to provide a kind of three-dimensional flow thermal coupling modeling method for cement grate-cooler, set up the three-dimensional flow thermal coupling model of cement grate-cooler, the Temperature Distribution of clinker layer and refrigerating gas can be calculated accurately according to known floor data, thus adjust cooling strategy according to this model, grate-cooler is run more effectively and rationally.

In order to the technical matters solving above-mentioned existence realizes goal of the invention, the present invention is achieved by the following technical solutions:

For a three-dimensional flow thermal coupling modeling method for cement grate-cooler, its content comprises the steps:

Clinker cooling procedural abstraction in grate-cooler is the stream strategy physical model of three-dimensional porous medium by step 1;

Step 2, set up the three-dimensional porous medium stream strategy mathematical model of cement grate-cooler according to built physical model, mathematical model comprises: seepage field system of equations, temperature field system of equations, boundary condition;

First the seepage field system of equations of described grate-cooler mathematical model is set up:

A, set up the three-dimensional continuity equation of grate-cooler mathematical model according to physical model, law of conservation of mass:

$\frac{\∂\left({\mathrm{\ρ}}_g\mathrm{\φ}\right)}{\∂t}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gx}}\right)}{\∂x}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gy}}\right)}{\∂y}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gz}}\right)}{\∂z}=0,$

In formula: ρ _gfor the cooling-air density in clinker layer, φ is clinker layer porosity, v _gx, v _gy, v _gzbe respectively the actual flow speed of cooling-air in clinker layer on x, y, z direction;

B, set up the three-momentum conservation equation of grate-cooler mathematical model according to physical model, Darcy's law:

$V_x=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂x},$

$V_y=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂y},$

$V_z=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂z},$

In formula: V _x, V _y, V _zwei the percolation flow velocity of cooling-air in clinker layer on x, y, z direction, δ inertia turbulent flow correction factor, K is the permeability of clinker layer, μ _gfor the aerodynamic force viscosity of cooling-air, P is the gaseous tension in clinker layer, wherein:

Clinker layer permeability:

$K=\frac{{0.23\mathrm{\φ}}^3}{{1.571}^2}{d}^2,$

Aerodynamic force viscosity:

${\mathrm{\μ}}_g=1.72\×{10}^{-5}\left(\frac{273+114}{T_g+114}\right){\left(\frac{T_g}{273}\right)}^{3/2};$

C, for compressible seepage flow, for make system of equations close, set up refrigerating gas state equation to reflect relation between state variable:

${\mathrm{\ρ}}_g=\frac{\mathrm{PM}}{z_g{\mathrm{RT}}_g},$

In formula: M is air molecule amount, R is gas law constant, z _gfor Gas Compression Factor;

Step 3, adopts Local Thermal Non-equilibrium theoretical, namely regarding two kinds of different continuous mediums respectively as piling up clinker particles and fluid, setting up the temperature field system of equations of grate-cooler mathematical model:

A, three-dimensional gas energy equation:

$\begin{array}{c}{\mathrm{\φ\ρ}}_g{C}_g\frac{{\∂T}_g}{\∂t}+{\mathrm{\φ\ρ}}_g{C}_g{v}_{\mathrm{gx}}\frac{{\∂T}_g}{\∂x}+\mathrm{\φ}{\mathrm{\ρ}}_g{C}_g{v}_{\mathrm{gy}}\frac{{\∂T}_g}{\∂y}+{\mathrm{\φ\ρ}}_g{C}_g{v}_{\mathrm{gz}}\frac{{\∂T}_g}{\∂z}\\ =({\mathrm{\φ\λ}}_g+{\mathrm{\λ}}_d)(\frac{{\∂}^2{T}_g}{{\∂x}^2}+\frac{{\∂}^2{T}_g}{{\∂y}^2}+\frac{{\∂}^2{T}_g}{{\∂z}^2})+\mathrm{S\α}(T_s-T_g)\end{array},$

B, three-dimensional grog energy equation:

$(1-\mathrm{\φ}){\mathrm{\ρ}}_s{C}_s\frac{{\∂T}_s}{\∂t}+(1-\mathrm{\φ}){\mathrm{\ρ}}_s{C}_s{v}_{\mathrm{sx}}\frac{{\∂T}_s}{\∂x}=(1-\mathrm{\φ}){\mathrm{\λ}}_s(\frac{{\∂}^2{T}_s}{{\∂x}^2}+\frac{{\∂}^2{T}_s}{{\∂y}^2}+\frac{{\∂}^2{T}_s}{{\∂z}^2})-\mathrm{S\α}(T_s-T_g),$

In formula: C _g, C _sfor gas and agglomerate ratio thermal capacitance, T _g, T _sfor the temperature of gas and grog, λ _g, λ _sfor gas and grog coefficient of heat conductivity, λ _dfor thermal dispersion coefficient of heat conductivity, S is the specific surface area of piling up clinker particles, and α is gas-solid integrated heat transfer coefficient, wherein:

Refrigerating gas specific heat is: $C_g=955+0.143\×T_g+3.85\×{10}^{-5}\×T_g^2+2.10\×{10}^{-10}\×T_g^3+1.20\×{10}^{-13}\×T_g^4,$

Grog specific heat is: $C_s=699+0.318\×T_s-6.23\×{10}^{-5}\×T_s^2-1.37\×{10}^{-10}\×T_s^3-5.13\×{10}^{-14}\×T_s^4,$

Measurement of Gas Thermal Conductivity is:

${\mathrm{\λ}}_g=0.0244{\left(\frac{T_g}{273}\right)}^{0.759},$

Grog coefficient of heat conductivity is:

λ _s＝0.244[1+0.00063(T _s-273)]，

The calculating formula of thermal dispersion coefficient of heat conductivity is:

${\mathrm{\λ}}_d=0.04{\mathrm{\ρ}}_g{C}_g{\mathrm{dv}}_g\frac{(1-\mathrm{\φ})}{\mathrm{\φ}},$

In formula: d is clinker particles diameter, ν _gfor kinematic viscosity;

The specific surface area of piling up clinker particles can be expressed as:

$S=\frac{S(1-\mathrm{\φ})}{d},$

Gas-solid integrated heat transfer coefficient is:

$\mathrm{\α}=\frac{1}{\frac{d}{{\mathrm{\λ}}_g\mathrm{Nu}}+\frac{\mathrm{\θd}}{{2\mathrm{\λ}}_s}},$

In formula: θ is particle shape compensation coefficient, Nu is nusselt number;

Nusselt number Nu is:

$\mathrm{Nu}=2+1.8{\mathrm{Re}}^{\frac{1}{2}}{\mathrm{Pr}}^{\frac{1}{3}},$

In formula: Pr is Prandtl number, Re is Reynolds number;

Step 4, set up the boundary condition of grate-cooler mathematical model:

A, grate-cooler feeding mouth place, the pan feeding temperature of grog is T _sin, the boundary condition namely during x=0 is:

$\begin{array}{ccc}{-\mathrm{\λ}}_g\frac{{\∂T}_g}{\∂x}=h(T_g-T_{\sin })& T_s=T_{\sin }& \frac{\∂P}{\∂x}=0;\end{array}$

B, grate-cooler discharge outlet, ambient temperature is T _g0, gas temperature gradient is the difference of boundary gas temperature and environment temperature, and grog extraneous air carries out convection heat transfer, and L is grate-cooler length, and the boundary condition namely during x=L is:

$\begin{array}{ccc}\frac{{\∂T}_g}{\∂x}=T_g-T_{g0}& {-\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂x}=h(T_s-T_{g0})& \frac{\∂P}{\∂x}=0;\end{array}$

Bottom c, the bed of material, cooling-air is with pressure P _in, temperature T _g0be blown into, the air that grog and bottom are blown into carries out convection heat transfer, and the boundary condition namely during y=0 is:

$\begin{array}{ccc}{T}_g=T_{g0}& {-\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂y}=h(T_s-T_{g0})& P=P_{\mathrm{in}};\end{array}$

D, bed of material top, grate-cooler cavity gaseous tension P _out, the heat flow density that gas and grog dispel the heat to external world is respectively as q _g, q _s, H is thickness of feed layer, and the boundary condition namely during y=H is:

$\begin{array}{ccc}{-\mathrm{\λ}}_g\frac{{\∂T}_g}{\∂y}=q_g& {-\mathrm{\λ}}_s\frac{\∂T_s}{\∂y}=q_s& P=P_{\mathrm{out}};\end{array}$

E, grate-cooler inner walls material are mainly refractory brick, outer wall materials is steel plate, gas and refractory brick are convection heat transfer, grog and refractory brick are conduction heat transfer, refractory brick and steel plate are conduction heat transfer, steel plate and extraneous heat exchange comprise heat transfer free convection and radiation heat transfer, and when bed of material both sides and z=0 and z=L, the boundary condition outwards dispelled the heat by grate-cooler housing is:

$\begin{array}{cc}{-\mathrm{\φ\λ}}_g\frac{{\∂T}_g}{\∂z}-(1-\mathrm{\φ}){\mathrm{\λ}}_s\frac{\∂T_s}{\∂z}=\frac{\frac{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}{T}_g+\frac{(1-\mathrm{\φ})}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}{T}_s-T_{g0}}{\frac{R_{\mathrm{br}}}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}+\frac{{\mathrm{\δ}}_{\mathrm{br}}}{{\mathrm{\λ}}_{\mathrm{br}}}+R_{\mathrm{st}}+\frac{{\mathrm{\δ}}_{\mathrm{st}}}{{\mathrm{\λ}}_{\mathrm{st}}}+\frac{1}{h_{\mathrm{sg}}+h_r}}& \frac{\∂P}{\∂z}=0\end{array}$

In formula: T _g0for environment temperature, R _brfor the thermal contact resistance of grog and refractory brick, R _stfor the thermal contact resistance of refractory brick and steel plate, δ _brfor refractory brick thickness, δ _stfor steel plate thickness, λ _brfor refractory brick coefficient of heat conductivity, λ _stfor steel plate coefficient of heat conductivity;

The heat transfer coefficient of air and refractory brick inwall is:

$h_{\mathrm{gbr}}=\frac{{\mathrm{\λ}}_g{\mathrm{Nu}}_{\mathrm{gbr}}}{d}$

In formula: ${\mathrm{Nu}}_{\mathrm{gbr}}=\frac{8.02}{{(1+A^{5/4})}^{9/5}{A}^{9/4}}{(1-\mathrm{\φ})}^{1/5}{\mathrm{Re}}^{1/5},$ A＝0.478(1-φ) ^4/5Re ^1/5；

The NATURAL CONVECTION COEFFICIENT OF HEAT of steel plate outer wall and air:

$h_{\mathrm{sg}}=\frac{{\mathrm{\λ}}_g{\mathrm{Nu}}_{\mathrm{sg}}}{H}$

In formula: Nu _sg=0.59Gr ^1/4pr ^1/4, grashof number Δ T=T _s-T _g0, α _vfor the cubic expansion coefficient;

Steel plate radiological equivalent heat transfer coefficient:

$h_r=\mathrm{\ϵ\σ}\frac{{\left(\frac{T_{\mathrm{st}}}{100}\right)}^4-{\left(\frac{T_{g0}}{100}\right)}^4}{T_{\mathrm{st}}-T_{g0}}$

In formula: ε is steel plate blackness, σ is blackbody radiation constant, Τ _stfor steel billet temperature.

Owing to adopting technique scheme, a kind of three-dimensional flow thermal coupling modeling method for cement grate-cooler provided by the invention, compared with prior art has such beneficial effect:

The cement clinker layer of grate-cooler is considered as the porous medium be made up of packed particle by the present invention, permeation fluid mechanics and thermal nonequilibrium theory is adopted to set up the three-dimensional flow thermal coupling model of grate-cooler, consider the factor such as grate speed, air feed wind speed, the heat radiation of limit wall, feeding temperature, grog particle diameter simultaneously, the three dimensional temperature distribution of grog can be calculated accurately, and simulate different cooling strategies by each duty parameter of adjustment, thus obtain the optimal strategy making efficient, the reasonable operation of grate-cooler, improve the heat recovery efficiency of grate-cooler, reach the object of energy-saving and emission-reduction.

The present invention is applied to determine that grate-cooler drop temperature is relatively low and reclaim the relatively high best clinker cooling strategy of wind-warm syndrome.Best cooling strategy described here is by under identical starting condition, simulate different cooling strategies, namely in cooling procedure, speed of combing is changed, the parameters such as each air compartment blast, recovery wind-warm syndrome when relatively adopting the different type of cooling to cool cement clinker and drop temperature, acquisition drop temperature is relatively low and reclaim the relatively high best clinker cooling strategy of wind-warm syndrome, thus improves the heat recovery efficiency of grate-cooler to greatest extent, reaches the object of energy-saving and emission-reduction.

Accompanying drawing explanation

Fig. 1 is the three-dimensional flow thermal coupling heat exchange physical model schematic diagram of grate-cooler;

Fig. 2 is grate-cooler clinker temperature distribution plan;

Fig. 3 is bed of material longitudinal profile gaseous tension, gas flow rate, gas and clinker temperature distribution plan under different air feed blast, v _s=0.008m/s, wherein (a) is pressure, and (b) is wind speed, and (c) is gas temperature, and (d) is clinker temperature;

Fig. 4 is different speed lower bed of material longitudinal profile gaseous tension, gas flow rate, gas and the clinker temperature distribution plan of combing of output one timing, P=5000Pa, wherein (a) is pressure, and (b) is wind speed, c () is gas temperature, (d) is clinker temperature;

Fig. 5 is different speed lower bed of material longitudinal profile gaseous tension, gas flow rate, gas and the clinker temperature distribution plan of combing of thickness of feed layer one timing, P=5000Pa, wherein (a) is pressure, and (b) is wind speed, c () is gas temperature, (d) is clinker temperature.

Embodiment

Below for the grate-cooler on general dry cement production line, and the present invention will be further described by reference to the accompanying drawings

A kind of three-dimensional flow thermal coupling modeling method for cement grate-cooler of the present invention, its content comprises the steps:

Step 1, by the stream strategy physical model of the three-dimensional porous medium that the clinker cooling procedural abstraction in grate-cooler is formed for such as Fig. 1 institute packed particle; High temperature chamotte particle enters grate by the left side of model, and slowly move right under grate plate promotes, period continues the Air flow be blown into by bottom, and finally flow out grate right-hand member, grog temperature under the effect of cooling-air reduces gradually; In figure, x is bed length direction, and y is thickness of bed layer direction, and z is bed Width.

Step 2, set up the three-dimensional porous medium stream strategy mathematical model of cement grate-cooler according to built physical model, mathematical model comprises: seepage field system of equations, temperature field system of equations, boundary condition;

First the seepage field system of equations of described grate-cooler mathematical model is set up:

A, set up the three-dimensional continuity equation of grate-cooler mathematical model according to physical model, law of conservation of mass:

$\frac{\∂\left({\mathrm{\ρ}}_g\mathrm{\φ}\right)}{\∂t}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gx}}\right)}{\∂x}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gy}}\right)}{\∂y}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gz}}\right)}{\∂z}=0,$

In formula: ρ _gfor the cooling-air density in clinker layer, φ is clinker layer porosity, v _gx, v _gy, v _gzbe respectively the actual flow speed of cooling-air in clinker layer on x, y, z direction;

B, set up the three-momentum conservation equation of grate-cooler mathematical model according to physical model, Darcy's law:

$V_x=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂x},$

$V_y=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂y},$

$V_z=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂z},$

In formula: V _x, V _y, V _zwei the percolation flow velocity of cooling-air in clinker layer on x, y, z direction, δ inertia turbulent flow correction factor, K is the permeability of clinker layer, μ _gfor the aerodynamic force viscosity of cooling-air, P is the gaseous tension in clinker layer, wherein:

Clinker layer permeability:

$K=\frac{{0.23\mathrm{\φ}}^3}{{1.571}^2}{d}^2,$

Aerodynamic force viscosity:

${\mathrm{\μ}}_g=1.72\×{10}^{-5}\left(\frac{273+114}{T_g+114}\right){\left(\frac{T_g}{273}\right)}^{3/2};$

C, for compressible seepage flow, for make system of equations close, set up refrigerating gas state equation to reflect relation between state variable:

${\mathrm{\ρ}}_g=\frac{\mathrm{PM}}{z_g{\mathrm{RT}}_g},$

In formula: M is air molecule amount, R is gas law constant, z _gfor Gas Compression Factor;

Step 3, adopts Local Thermal Non-equilibrium theoretical, namely regarding two kinds of different continuous mediums respectively as piling up clinker particles and fluid, setting up the temperature field system of equations of grate-cooler mathematical model:

A, three-dimensional gas energy equation:

$\begin{array}{c}{\mathrm{\φ\ρ}}_g{C}_g\frac{{\∂T}_g}{\∂t}+{\mathrm{\φ\ρ}}_g{C}_g{v}_{\mathrm{gx}}\frac{{\∂T}_g}{\∂x}+\mathrm{\φ}{\mathrm{\ρ}}_g{C}_g{v}_{\mathrm{gy}}\frac{{\∂T}_g}{\∂y}+{\mathrm{\φ\ρ}}_g{C}_g{v}_{\mathrm{gz}}\frac{{\∂T}_g}{\∂z}\\ =({\mathrm{\φ\λ}}_g+{\mathrm{\λ}}_d)(\frac{{\∂}^2{T}_g}{{\∂x}^2}+\frac{{\∂}^2{T}_g}{{\∂y}^2}+\frac{{\∂}^2{T}_g}{{\∂z}^2})+\mathrm{S\α}(T_s-T_g)\end{array},$

B, three-dimensional grog energy equation:

$(1-\mathrm{\φ}){\mathrm{\ρ}}_s{C}_s\frac{{\∂T}_s}{\∂t}+(1-\mathrm{\φ}){\mathrm{\ρ}}_s{C}_s{v}_{\mathrm{sx}}\frac{{\∂T}_s}{\∂x}=(1-\mathrm{\φ}){\mathrm{\λ}}_s(\frac{{\∂}^2{T}_s}{{\∂x}^2}+\frac{{\∂}^2{T}_s}{{\∂y}^2}+\frac{{\∂}^2{T}_s}{{\∂z}^2})-\mathrm{S\α}(T_s-T_g),$

In formula: C _g, C _sfor gas and agglomerate ratio thermal capacitance, T _g, T _sfor the temperature of gas and grog, λ _g, λ _sfor gas and grog coefficient of heat conductivity, λ _dfor thermal dispersion coefficient of heat conductivity, S is the specific surface area of piling up clinker particles, and α is gas-solid integrated heat transfer coefficient, wherein:

Refrigerating gas specific heat is: $C_g=955+0.143\×T_g+3.85\×{10}^{-5}\×T_g^2+2.10\×{10}^{-10}\×T_g^3+1.20\×{10}^{-13}\×T_g^4,$

Grog specific heat is: $C_s=699+0.318\×T_s-6.23\×{10}^{-5}\×T_s^2-1.37\×{10}^{-10}\×T_s^3-5.13\×{10}^{-14}\×T_s^4,$

Measurement of Gas Thermal Conductivity is:

${\mathrm{\λ}}_g=0.0244{\left(\frac{T_g}{273}\right)}^{0.759},$

Grog coefficient of heat conductivity is:

λ _s＝0.244[1+0.00063(T _s-273)]，

The calculating formula of thermal dispersion coefficient of heat conductivity is:

${\mathrm{\λ}}_d=0.04{\mathrm{\ρ}}_g{C}_g{\mathrm{dv}}_g\frac{(1-\mathrm{\φ})}{\mathrm{\φ}},$

In formula: d is clinker particles diameter, ν _gfor kinematic viscosity;

The specific surface area of piling up clinker particles can be expressed as:

$S=\frac{S(1-\mathrm{\φ})}{d},$

Gas-solid integrated heat transfer coefficient is:

$\mathrm{\α}=\frac{1}{\frac{d}{{\mathrm{\λ}}_g\mathrm{Nu}}+\frac{\mathrm{\θd}}{{2\mathrm{\λ}}_s}},$

In formula: θ is particle shape compensation coefficient, Nu is nusselt number;

Nusselt number Nu is:

$\mathrm{Nu}=2+1.8{\mathrm{Re}}^{\frac{1}{2}}{\mathrm{Pr}}^{\frac{1}{3}},$

In formula: Pr is Prandtl number, Re is Reynolds number;

Step 4, set up the boundary condition of grate-cooler mathematical model:

A, grate-cooler feeding mouth place, the pan feeding temperature of grog is T _sin, the boundary condition namely during x=0 is:

$\begin{array}{ccc}{-\mathrm{\λ}}_g\frac{{\∂T}_g}{\∂x}=h(T_g-T_{\sin })& T_s=T_{\sin }& \frac{\∂P}{\∂x}=0;\end{array}$

B, grate-cooler discharge outlet, ambient temperature is T _g0, gas temperature gradient is the difference of boundary gas temperature and environment temperature, and grog extraneous air carries out convection heat transfer, and L is grate-cooler length, and the boundary condition namely during x=L is:

$\begin{array}{ccc}\frac{{\∂T}_g}{\∂x}=T_g-T_{g0}& {-\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂x}=h(T_s-T_{g0})& \frac{\∂P}{\∂x}=0;\end{array}$

Bottom c, the bed of material, cooling-air is with pressure P _in, temperature T _g0be blown into, the air that grog and bottom are blown into carries out convection heat transfer, and the boundary condition namely during y=0 is:

$\begin{array}{ccc}{T}_g=T_{g0}& {-\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂y}=h(T_s-T_{g0})& P=P_{\mathrm{in}};\end{array}$

D, bed of material top, grate-cooler cavity gaseous tension P _out, the heat flow density that gas and grog dispel the heat to external world is respectively as q _g, q _s, the boundary condition namely during y=H is:

$\begin{array}{ccc}{-\mathrm{\λ}}_g\frac{{\∂T}_g}{\∂y}{=q}_g& {-\mathrm{\λ}}_s\frac{\∂T_s}{\∂y}=q_s& P=P_{\mathrm{out}};\end{array}$

E, grate-cooler inner walls material are mainly refractory brick, outer wall materials is steel plate, gas and refractory brick are convection heat transfer, grog and refractory brick are conduction heat transfer, refractory brick and steel plate are conduction heat transfer, steel plate and extraneous heat exchange comprise heat transfer free convection and radiation heat transfer, and when bed of material both sides and z=0 and z=L, the boundary condition outwards dispelled the heat by grate-cooler housing is:

$\begin{array}{cc}{-\mathrm{\φ\λ}}_g\frac{{\∂T}_g}{\∂z}-(1-\mathrm{\φ}){\mathrm{\λ}}_s\frac{\∂T_s}{\∂z}=\frac{\frac{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}{T}_g+\frac{(1-\mathrm{\φ})}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}{T}_s-T_{g0}}{\frac{R_{\mathrm{br}}}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}+\frac{{\mathrm{\δ}}_{\mathrm{br}}}{{\mathrm{\λ}}_{\mathrm{br}}}+R_{\mathrm{st}}+\frac{{\mathrm{\δ}}_{\mathrm{st}}}{{\mathrm{\λ}}_{\mathrm{st}}}+\frac{1}{h_{\mathrm{sg}}+h_r}}& \frac{\∂P}{\∂z}=0,\end{array}$

In formula: T _g0for environment temperature, R _brfor the thermal contact resistance of grog and refractory brick, R _stfor the thermal contact resistance of refractory brick and steel plate, δ _brfor refractory brick thickness, δ _stfor steel plate thickness, λ _brfor refractory brick coefficient of heat conductivity, λ _stfor steel plate coefficient of heat conductivity;

The heat transfer coefficient of air and refractory brick inwall is:

$h_{\mathrm{gbr}}=\frac{{\mathrm{\λ}}_g{\mathrm{Nu}}_{\mathrm{gbr}}}{d},$

In formula: ${\mathrm{Nu}}_{\mathrm{gbr}}=\frac{8.02}{{(1+A^{5/4})}^{9/5}{A}^{9/4}}{(1-\mathrm{\φ})}^{1/5}{\mathrm{Re}}^{1/5},$ A＝0.478(1-φ) ^4/5Re ^1/5；

The NATURAL CONVECTION COEFFICIENT OF HEAT of steel plate outer wall and air:

$h_{\mathrm{sg}}=\frac{{\mathrm{\λ}}_g{\mathrm{Nu}}_{\mathrm{sg}}}{H},$

In formula: Nu _sg=0.59Gr ^1/4pr ^1/4, grashof number Δ T=T _s-T _g0, α _vfor the cubic expansion coefficient;

Steel plate radiological equivalent heat transfer coefficient:

$h_r=\mathrm{\ϵ\σ}\frac{{\left(\frac{T_{\mathrm{st}}}{100}\right)}^4-{\left(\frac{T_{g0}}{100}\right)}^4}{T_{\mathrm{st}}-T_{g0}},$

In formula: ε is steel plate blackness, σ is blackbody radiation constant, Τ _stfor steel billet temperature.

Setting model design conditions are: grog and the gas temperature of material bed feed end are 1650K, the cooling-air be blown into bottom bed is 303K, supply wind pressure to be 5000Pa bottom the bed of material, particle moving speed is bed top pressure is standard atmospheric pressure, and particle moving speed is 0.008m/s ^-1, cooling captain 24m, wide 5m (due to symmetrical on Width, molded breadth is 0-2.5m), thickness of bed layer 0.7m.

Solve according to the three-dimensional flow thermal coupling model of above design conditions to built grate-cooler.

Figure 2 shows that the Temperature Distribution of grog on whole material bed, grog is reduced gradually to discharging opening temperature by charging aperture under the effect of cooling-air as seen from Figure 2, and bed front bottom end clinker temperature declines comparatively rapid, and in bed, rear end cooldown rate slows down gradually; Bed temperature is raised to top gradually by bottom.It is 376.1K that grate-cooler exit calculates gained bed of material head temperature, and drop temperature is about 368K in actual production, error is less, in the bed of material simultaneously emulating gained, profiling temperatures meets the scene temperature regularity of distribution, and therefore institute's established model can reflect the cooling procedure of cement clinker in grate-cooler.

Figure 3 shows that bed of material longitudinal profile gaseous tension, gas flow rate, gas and clinker temperature distribution plan under different air feed blast.As seen from Figure 3 along with the increase gas flow rate of pressure increases gradually, but the distribution trend of flow velocity is roughly the same, and clinker cooling speed is accelerated, and the temperature of grog and gas reduces gradually.

Different speed lower bed of material longitudinal profile gaseous tension, gas flow rate, gas and the clinker temperature distribution plan of combing when Figure 4 shows that output is constant, as shown in Figure 4 along with the increase thickness of feed layer of speed of combing reduces gradually, gas flow rate strengthens gradually; Bed of material top gas temperature declines very fast, and bottom gas temperature declines slower; Bed of material front end, middle part declines to the clinker temperature at top, and bottom the bed of material, the temperature of grog raises; Bed of material rear end, clinker temperature raises.

Different speed lower bed of material longitudinal profile gaseous tension, gas flow rate, gas and the clinker temperature distribution plan of combing when Figure 5 shows that thickness of feed layer is constant, speed of combing is increased as seen from Figure 5 when thickness of feed layer is certain, grate-cooler output increases thereupon, and gas flow rate reduces, and the temperature of gas and grog raises.

Claims (1)

1., for a three-dimensional flow thermal coupling modeling method for cement grate-cooler, it is characterized in that the method content comprises the steps:

Clinker cooling procedural abstraction in grate-cooler is the stream strategy physical model of three-dimensional porous medium by step 1;

Step 2, set up the three-dimensional porous medium stream strategy mathematical model of cement grate-cooler according to built physical model, mathematical model comprises: seepage field system of equations, temperature field system of equations, boundary condition;

First the seepage field system of equations of described grate-cooler mathematical model is set up:

A, set up the three-dimensional continuity equation of grate-cooler mathematical model according to physical model, law of conservation of mass:

$\frac{\∂\left({\mathrm{\ρ}}_g\mathrm{\φ}\right)}{\∂t}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gx}}\right)}{\∂x}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gy}}\right)}{\∂y}+\frac{\∂\left({\mathrm{\ρ}}_g{v}_{\mathrm{gz}}\right)}{\∂z}=0,$

In formula: ρ _gfor the cooling-air density in clinker layer, φ is clinker layer porosity, v _gx, v _gy, v _gzbe respectively the actual flow speed of cooling-air in clinker layer on x, y, z direction;

B, set up the three-momentum conservation equation of grate-cooler mathematical model according to physical model, Darcy's law:

$V_x=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂x},$

$V_y=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂y},$

$V_z=-\mathrm{\δ}\frac{K}{{\mathrm{\μ}}_g}\frac{\∂P}{\∂z},$

In formula: V _x, V _y, V _zwei the percolation flow velocity of cooling-air in clinker layer on x, y, z direction, δ inertia turbulent flow correction factor, K is the permeability of clinker layer, μ _gfor the aerodynamic force viscosity of cooling-air, P is the gaseous tension in clinker layer, wherein:

Clinker layer permeability:

$K=\frac{{0.23\mathrm{\φ}}^3}{{1.571}^2}{d}^2,$

Aerodynamic force viscosity:

${\mathrm{\μ}}_g=1.72\×{10}^{-5}\left(\frac{273+114}{T_g+114}\right){\left(\frac{T_g}{273}\right)}^{3/2};$

C, for compressible seepage flow, for make system of equations close, set up refrigerating gas state equation to reflect relation between state variable:

${\mathrm{\ρ}}_g=\frac{\mathrm{PM}}{z_g{\mathrm{RT}}_g},$

In formula: M is air molecule amount, R is gas law constant, z _gfor Gas Compression Factor;

Step 3, adopts Local Thermal Non-equilibrium theoretical, namely regarding two kinds of different continuous mediums respectively as piling up clinker particles and fluid, setting up the temperature field system of equations of grate-cooler mathematical model:

A, three-dimensional gas energy equation:

$\begin{array}{c}{\mathrm{\φ\ρ}}_g{C}_g\frac{{\∂T}_g}{\∂t}+{\mathrm{\φ\ρ}}_g{C}_g{v}_{\mathrm{gx}}\frac{{\∂T}_g}{\∂x}+\mathrm{\φ}{\mathrm{\ρ}}_g{C}_g{v}_{\mathrm{gy}}\frac{{\∂T}_g}{\∂y}+{\mathrm{\φ\ρ}}_g{C}_g{v}_{\mathrm{gz}}\frac{{\∂T}_g}{\∂z}\\ =({\mathrm{\φ\λ}}_g+{\mathrm{\λ}}_d)(\frac{{\∂}^2{T}_g}{{\∂x}^2}+\frac{{\∂}^2{T}_g}{{\∂y}^2}+\frac{{\∂}^2{T}_g}{{\∂z}^2})+\mathrm{S\α}(T_s-T_g)\end{array},$

B, three-dimensional grog energy equation:

$(1-\mathrm{\φ}){\mathrm{\ρ}}_s{C}_s\frac{{\∂T}_s}{\∂t}+(1-\mathrm{\φ}){\mathrm{\ρ}}_s{C}_s{v}_{\mathrm{sx}}\frac{{\∂T}_s}{\∂x}=(1-\mathrm{\φ}){\mathrm{\λ}}_s(\frac{{\∂}^2{T}_s}{{\∂x}^2}+\frac{{\∂}^2{T}_s}{{\∂y}^2}+\frac{{\∂}^2{T}_s}{{\∂z}^2})-\mathrm{S\α}(T_s-T_g),$

In formula: C _g, C _sfor gas and agglomerate ratio thermal capacitance, T _g, T _sfor the temperature of gas and grog, λ _g, λ _sfor gas and grog coefficient of heat conductivity, λ _dfor thermal dispersion coefficient of heat conductivity, S is the specific surface area of piling up clinker particles, and α is gas-solid integrated heat transfer coefficient, wherein:

Refrigerating gas specific heat is: $C_g=955+0.143\×T_g+3.85\×{10}^{-5}\×T_g^2+2.10\×{10}^{-10}\×T_g^3+1.20\×{10}^{-13}\×T_g^4,$

Grog specific heat is: $C_s=699+0.318\×T_s-6.23\×{10}^{-5}\×T_s^2-1.37\×{10}^{-10}\×T_s^3-5.13\×{10}^{-14}\×T_s^4,$

Measurement of Gas Thermal Conductivity is:

${\mathrm{\λ}}_g=0.0244{\left(\frac{T_g}{273}\right)}^{0.759},$

Grog coefficient of heat conductivity is:

λ _s＝0.244[1+0.00063(T _s-273)]，

The calculating formula of thermal dispersion coefficient of heat conductivity is:

${\mathrm{\λ}}_d=0.04{\mathrm{\ρ}}_g{C}_g{\mathrm{dv}}_g\frac{(1-\mathrm{\φ})}{\mathrm{\φ}},$

In formula: d is clinker particles diameter, ν _gfor kinematic viscosity;

The specific surface area of piling up clinker particles can be expressed as:

$S=\frac{S(1-\mathrm{\φ})}{d},$

Gas-solid integrated heat transfer coefficient is:

$\mathrm{\α}=\frac{1}{\frac{d}{{\mathrm{\λ}}_g\mathrm{Nu}}+\frac{\mathrm{\θd}}{{2\mathrm{\λ}}_s}},$

In formula: θ is particle shape compensation coefficient, Nu is nusselt number,

Nusselt number Nu is:

$\mathrm{Nu}=2+1.8{\mathrm{Re}}^{\frac{1}{2}}{\mathrm{Pr}}^{\frac{1}{3}},$

In formula: Pr is Prandtl number, Re is Reynolds number;

Step 4, set up the boundary condition of grate-cooler mathematical model:

A, grate-cooler feeding mouth place, the pan feeding temperature of grog is T _sin, the boundary condition namely during x=0 is:

$\begin{array}{ccc}{-\mathrm{\λ}}_g\frac{{\∂T}_g}{\∂x}=h(T_g-T_{\sin })& T_s=T_{\sin }& \frac{\∂P}{\∂x}=0;\end{array}$

B, grate-cooler discharge outlet, ambient temperature is T _g0, gas temperature gradient is the difference of boundary gas temperature and environment temperature, and grog extraneous air carries out convection heat transfer, and L is grate-cooler length, and the boundary condition namely during x=L is:

$\begin{array}{ccc}\frac{{\∂T}_g}{\∂x}=T_g-T_{g0}& {-\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂x}=h(T_s-T_{g0})& \frac{\∂P}{\∂x}=0;\end{array}$

Bottom c, the bed of material, cooling-air is with pressure P _in, temperature T _g0be blown into, the air that grog and bottom are blown into carries out convection heat transfer, and the boundary condition namely during y=0 is:

$\begin{array}{ccc}{T}_g=T_{g0}& {-\mathrm{\λ}}_s\frac{{\∂T}_s}{\∂y}=h(T_s-T_{g0})& P=P_{\mathrm{in}};\end{array}$

D, bed of material top, grate-cooler cavity gaseous tension P _out, the heat flow density that gas and grog dispel the heat to external world is respectively q _g, q _s, H is thickness of feed layer, and the boundary condition namely during y=H is:

$\begin{array}{ccc}{-\mathrm{\λ}}_g\frac{{\∂T}_g}{\∂y}=q_g& {-\mathrm{\λ}}_s\frac{\∂T_s}{\∂y}=q_s& P=P_{\mathrm{out}};\end{array}$

E, grate-cooler inner walls material are mainly refractory brick, outer wall materials is steel plate, and gas and refractory brick are convection heat transfer, and grog and refractory brick are conduction heat transfer, refractory brick and steel plate are conduction heat transfer, and steel plate and extraneous heat exchange comprise heat transfer free convection and radiation heat transfer; When bed of material both sides and z=0 and z=L, the boundary condition outwards dispelled the heat by grate-cooler housing is:

$\begin{array}{cc}{-\mathrm{\φ\λ}}_g\frac{{\∂T}_g}{\∂z}-(1-\mathrm{\φ}){\mathrm{\λ}}_s\frac{\∂T_s}{\∂z}=\frac{\frac{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}{T}_g+\frac{(1-\mathrm{\φ})}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}{T}_s-T_{g0}}{\frac{R_{\mathrm{br}}}{{\mathrm{\φh}}_{\mathrm{gbr}}{R}_{\mathrm{br}}+(1-\mathrm{\φ})}+\frac{{\mathrm{\δ}}_{\mathrm{br}}}{{\mathrm{\λ}}_{\mathrm{br}}}+R_{\mathrm{st}}+\frac{{\mathrm{\δ}}_{\mathrm{st}}}{{\mathrm{\λ}}_{\mathrm{st}}}+\frac{1}{h_{\mathrm{sg}}+h_r}}& \frac{\∂P}{\∂z}=0,\end{array}$

In formula: T _g0for environment temperature, R _brfor the thermal contact resistance of grog and refractory brick, R _stfor the thermal contact resistance of refractory brick and steel plate, δ _brfor refractory brick thickness, δ _stfor steel plate thickness, λ _brfor refractory brick coefficient of heat conductivity, λ _stfor steel plate coefficient of heat conductivity;

The heat transfer coefficient of air and refractory brick inwall is:

$h_{\mathrm{gbr}}=\frac{{\mathrm{\λ}}_g{\mathrm{Nu}}_{\mathrm{gbr}}}{d},$

In formula: ${\mathrm{Nu}}_{\mathrm{gbr}}=\frac{8.02}{{(1+A^{5/4})}^{9/5}{A}^{9/4}}{(1-\mathrm{\φ})}^{1/5}{\mathrm{Re}}^{1/5},$ A＝0.478(1-φ) ^4/5Re ^1/5；

The NATURAL CONVECTION COEFFICIENT OF HEAT of steel plate outer wall and air

$h_{\mathrm{sg}}=\frac{{\mathrm{\λ}}_g{\mathrm{Nu}}_{\mathrm{sg}}}{H},$

In formula: Nu _sg=0.59Gr ^1/4pr ^1/4, grashof number Δ T=T _s-T _g0, α _vfor the cubic expansion coefficient;

Steel plate radiological equivalent heat transfer coefficient:

$h_r=\mathrm{\ϵ\σ}\frac{{\left(\frac{T_{\mathrm{st}}}{100}\right)}^4-{\left(\frac{T_{g0}}{100}\right)}^4}{T_{\mathrm{st}}-T_{g0}},$

In formula: ε is steel plate blackness, σ is blackbody radiation constant, Τ _stfor steel billet temperature.