In recent years, computer-aided design technology has developed rapidly in the electronics, construction, textile, general machinery and other industries at home and abroad, and has developed a large number of practical software products. However, the development of CAD technology in the boiler industry, which is one of the machinery industries, is relatively simple. slow. The design of the boiler is an iterative process, and multiple design schemes must be optimized and compared to arrive at an optimal design. The current boiler design still uses traditional manual design. In order to improve the design quality of the product, shorten the design cycle of the product, and promote the development of CAD technology in the boiler industry, Zhejiang University Chemical Machinery Research Institute and Hangzhou, one of the national application demonstration points for CAD The boiler factory cooperated and developed the "CAD Application System of Hangzhou Boiler Factory", which was highly praised by experts.
Establishment of optimization model for boiler heating surface
The boiler is a complex thermal mechanical system, and the objective function of its optimized design cannot be clearly expressed by explicit functions. There are many factors affecting boiler design quality, such as fuel properties, furnace type selection, reasonable selection of furnace heat load, selection of various convective heating surface flue gas flow rates, and selection of smoke temperature in each section. Boiler design involves basic sciences such as combustion, heat transfer, fluid mechanics, and environmental science, as well as thermal calculation, calculation of smoke resistance, hydrodynamic calculation, strength calculation of pressure components, wall temperature calculation, etc. These factors must be considered when designing.
Obviously, the optimal boiler design model is to use economics as the objective function when the basic constraints are met. We know that when designing the boiler, the lower exhaust gas temperature is selected, the boiler efficiency is increased, the coal burning amount is decreased, and the running cost is lowered. On the other hand, the temperature of the heating surface of the boiler is lowered, the heating surface area is increased, and the boiler cost is increased. And the smoke resistance increases. According to the above analysis, the optimal model of the most economical boiler efficiency is obtained.
Objective function:
Where xi - the heating area of ​​the i-stage boiler, m2;
Yi——the production cost per unit area of ​​the heating surface of the i-stage boiler, yuan/m2;
M——the number of segments of the boiler heating surface.
Constraints: 1 to ensure stable, continuous combustion; 2 working fluid parameters meet the design requirements; 3 each section of smoke temperature, working temperature meets safety requirements, meet the strength test, wall temperature calculation, hydrodynamic calculation safety test to prevent heat Surface slagging; 4 the heating speed of the heating surface of each section shall not be greater than the maximum allowable speed of the heating surface; 5 exhaust smoke temperature shall be higher than the flue gas acid dew point; 6 tail heating surface shall be arranged in two stages to satisfy the best fitting condition; 7 heating surface geometry Dimensions meet process and layout requirements.
Optimization model solving strategy
The boiler optimization design model has both continuous variables and discrete variables, which is a mixed discrete programming problem. The existing mature engineering optimization methods are optimization methods for continuous variables. On the surface, the objective function of the above optimization model is a linear function. In essence, the above objective function is very complicated, and the area of ​​each heated surface is determined by boiler thermal calculation and smoke resistance calculation. The above constraint function is also very complex, involving wall temperature safety test (requires wall temperature calculation) and hydrodynamic calculation, etc., geometric dimensions are mixed variables (such as pipe diameter, row number, etc. are integer variables). In view of the characteristics of the boiler optimization model, we improved the traditional orthogonal test method to solve the problem of solving the boiler heating surface optimization model.
The orthogonal test method is to solve the optimization problem of mixed discrete variables by orthogonal table. In recent years, it has been widely used in optimization design in many fields, but the general orthogonal test method has certain limitations when used in complex boiler optimization models. Sex, mainly in the objective function and constraint function is more complex, and the feasible domain is non-continuous, often only get a local best advantage, and sometimes this point and the global best advantage sometimes far from each other, therefore, the original optimization model did The improvement is as follows.
2.1 Using the augmented objective function instead of the original objective function
According to the idea of ​​continuous variable penalty function, the penalty function is introduced to construct the augmented objective function.
Where: ri - the penalty factor;
f(x) - the objective function;
m - the number of constraints;
Gi(x) - constraint function;
Ui(gi) - unit step function.
In this way, by comparing the size of the augmented objective function to determine the iteration point, it is avoided that the ideal iteration point cannot be determined because the feasible point cannot be found after the iterative calculation, so that the iteration can proceed faster.
2.2 Different orthogonal tables for each round
When multiple rounds of calculations are used in orthogonal tests, if different orthogonal tables are used for each round, multiple local best points can be found, making it possible to find the global best or approximate global best.
Definition: n horizontal displacement.
Add all the horizontal numbers of a column of the orthogonal table to a natural number n (t is the horizontal number) not greater than t. If it is greater than t after the addition, then subtract t from it. We call this processing a alignment. This column of the table is n horizontally displaced. The so-called n-level displacement actually means that two different horizontal numbers in one column of the orthogonal table are sequentially exchanged, and a total of (t-1) horizontal replacements are performed. Therefore, n-level displacement of one or several columns of the orthogonal table belongs to the elementary transformation of the orthogonal table. The orthogonal table resulting from the n horizontal displacement should be an isomorphic table.
Theorem: If the basic column of the u column of the orthogonal table Ltu(tq) remains unchanged, and the remaining (qu) columns are n horizontal displacements, then:
(1) A t(qu) isotropic table can be constructed;
(2) Any two rows in the t(qu) isomorphism table are different;
(3) This t(qu) isotropic table is different from each other.
It is known from the above theorem that different orthogonal tables can be constructed by performing n horizontal displacements on the (qu) columns of the orthogonal table, so that each orthogonal iteration can use different orthogonal tables to find a different local optimum. . By continuously constructing the isomorphic table, many local advantages are obtained. When the number of local best points reaches a certain value or the local optimum value is within a predetermined range, it can be considered that a certain local maximum advantage has fallen around the global best advantage. This is the best local part we think is the best. The advantage, and then narrow the solution around it, that is, to perform 2 or 3 horizontal orthogonal table optimization centered on this point, it is possible to find the global best.
Optimized design of heated surface
3.1 System Design
In the traditional heating surface design process, it is necessary to apply dozens of formulas, consult a large number of curves and tables, consume a lot of time, can not be continuously calculated, and it is very difficult to achieve optimal design. Therefore, one of the main tasks in the design process is to complete the computer-aided design formula of the heated surface in the system design process, and to fit a large number of charts and curves with formulas.
3.2 Parameter optimization design
In the parameter optimization design process, the orthogonal design method is used for multiple rounds of tuning, and the minimum heating area under the initial conditions is taken as the evaluation index, and the direct optimal combination of each parameter is sought. Use L9 (34) orthogonal table. The center level of the first round of parameter optimization is directly taken from the calculation results of computer-aided design, and the upper and lower levels are appropriately expanded within a certain range. After each round of parameter optimization design, the next round of factor center level is a set of design conditions with the lowest value of the previous objective function. The first and third levels are appropriately expanded according to the upper and lower ranges of the center level, and the computer is tuned for multiple rounds until various factors. The range is less than 10.
3.3 Technology key
(1) Completing the computer-aided optimization design of the heated surface to directly and quickly investigate the influence of the change of the design variable on the objective function, and transform the uncalculated project into a computable project in the system design process.
(2) In the process of parameter design, the important surface of the heated surface is taken as the evaluation target. The method of orthogonal test design optimization is used to directly search the optimal solution to achieve optimal design.
Optimization design of air preheater for 220t/H pulverized coal fired boiler
In the convection heating surface of the boiler, the heat transfer surface of the tail, especially the air preheater, has less heat transfer, but the heat transfer area is much larger than the heat transfer area of ​​the superheater. Therefore, the design and layout of the heating surface of the tail is a relationship. An important economic issue to the boiler cost. Taking a 220t/H pulverized coal furnace as an example, the superheater system includes a ceiling superheater, a screen superheater, a high temperature convection superheater, a low temperature convection superheater, and a wall tube. The total area of ​​the superheater is 1700 m2, and the boiler has a total area of ​​1700 m2. The tail heating surface adopts a two-stage arrangement, and the total heat transfer area of ​​the two-stage air preheater is as high as 14,000 m2, which is eight times the total heat transfer area of ​​the superheater. The reason is that the convective heat transfer coefficient of the flue gas side and the air side of the air preheater is relatively low, so the heat transfer coefficient is quite low; in addition, the air preheater is in the lowest temperature part of the flue gas flow, and the heat transfer temperature is low. The pressure is also much smaller than the other heated surfaces. Therefore, the design and arrangement of the tail heating surface, especially the air preheater, is a major problem affecting the boiler cost.
The author used the augmented objective function method to carry out the specific design calculation of the air preheater of the 220t/H boiler. The minimum heat transfer area is used as the objective function of the optimized design. The partial calculation results of the high temperature air preheater are shown in Table 1.
Table 1 Optimization results of high temperature air preheater for 220t/H pulverized coal boiler dw(m) S1(m) S2(m) Z1 Z2 H(m2)
Original design 0.040 0.062 0.040 32 44 4800.30
Excellent 0.037 0.058 0.037 34 47 4507.54
0.039 0.061 0.039 32 43 4601.30
Set 0.040 0.060 0.040 32 43 4675.78
Count 0.041 0.062 0.041 31 43 4777.18
The author also optimized the design of the low temperature air preheater of the 220t/H boiler. The heat transfer area of ​​the original design is 9408m2, and the heat transfer area after optimization is only 7489.01m2, which can save 20.4% of heat transfer area.
5 Conclusions and prospects
5.1 Conclusion
(1) The computer-aided optimization design of the boiler has very important practical significance for the design and manufacturing department. It provides a scientific, simple and reliable calculation basis for the optimized combination of design parameters, and overcomes the traditional empirical or limited test results. Determine the blindness of the design parameters.
(2) The computer-aided design method is very effective in the process of boiler orthogonal optimization design. It not only completes the design task of the system, but also becomes the key to optimization. At the same time, after the optimal parameter combination is determined, the design of other parameters can be completed quickly. jobs.
(3) The optimal design model of the heating surface of the boiler is a constrained nonlinear hybrid discrete variable optimization model. It is very effective to use the improved orthogonal test method to solve the iterative solution. It can find the optimal solution directly and quickly, and obtain the objective function. Optimal design parameters at the best.
(4) In the design and calculation process of the boiler, the curve and the table can be fitted. In the process of optimizing the iteration, the iterative process is quickly completed by introducing the fitting formula.
5.2 Outlook
(1) The problem of optimal design of boiler heating surface is an important issue affecting economy and safety. Under the premise of ensuring safety, designing with the optimized method can achieve significant economic effects of reducing heat transfer area, saving metal consumption, and reducing the cost of the heated surface.
(2) When designing the economizer and air preheater, in addition to optimizing the structural parameters, the optimization method should be used to determine whether to use single-stage or two-stage layout, and how to perform optimal two-level layout. problem.
(3) When the rear heating surface is arranged in two stages, it is advantageous to reasonably distribute the heat absorption of the high and low temperature economizer and the high and low temperature air preheater, which is beneficial to reducing the cost of the entire heating surface of the tail and improving economy.
(4) The boiler is an organic thermal mechanical system. Establishing a boiler overall optimization model and overall optimization design is a major issue for us in the future.
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