Pump impeller automation options: mathematical and chemical
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Impeller is the core components of the pump, the main impact of work efficiency factors. Under certain conditions, hydraulic and gap losses can occur at the pump inlet and vanes if the impeller is not designed properly.
Such losses are estimated by many one-dimensional models; most notable models include Pfleiderer et al.1, Japikse et al.2,3, Tuzson4,5, Stepanoff6 and Neumann7. There are many other studies 8-12 that present some of the pump design procedures based more or less on these models.
The main limitation of these models is their analogy: the optimization process can not proceed with these models. Computational fluid dynamics (CFD) simulation technology to solve this problem. This technique calculates flow distribution using the Navier Stokes partial differential equation algorithm. The optimization process is still a critical process and it is difficult to automate it. Designers often have to first try and test, and then modify the geometry according to the results to improve the flow distribution, and repeat the experiment. This iterative process is repeated until the designer thinks the result of step i is ideal (in relation to the designer's own experience).
Figure 1: Data Points Distribution Grid Diagram
Some studies 13 also suggest that the role analysis of each geometric parameter should be based on multivariate analysis (principal component analysis). The authors repeated computational fluid dynamics simulations (CFDs) using different geometric parameters and studied the effects of each of these factors. These studies allow designers to analyze only a small number of geometric parameters, reducing the size of the manual optimization process, thereby reducing optimization time (number of iterations).
In recent years, this procedure has been greatly improved, thanks to the development of multi-objective optimization software. The software uses algorithms such as genetic algorithms and hill climbing, parallel structures, and Pareto frontiers to make common CFD software, typically design tools, run automatically. The optimizer can use CFD software to progressively improve the geometry of the impeller until the optimal geometry is obtained.
In recent years, some new optimization methods based on different concepts have been developed; Zangeneh16-18 is one of the typical representatives. This method is different from the past, or rather "reverse": first specify the blade load, and then use the 3D reverse design method to calculate the corresponding blade geometry. The optimizer can modify some of the parameters that determine blade loading, so the optimization process is easier than ever.
There are many difficulties with manual and automated optimization processes. Observations show that new knowledge emerging during record optimization is necessary. This problem is especially important to pump designers if the optimization process is a routine activity. Most well-designed impellers can be reused. So the question is: how to optimize the design process?
The main method is to use the experimental curve of the pump. These curves represent the pressure-flow rate relationship at a particular speed (Figure 2b). This set of curves is a surface in the three-dimensional space of pressure-flow-speed. The surface must be compared with the specific flow rate, head and speed required by the customer.
Mathematical fitting of surfaces
If we want to automate the selection process, it is necessary to fit the surface using mathematical models. This set of flow-speed-pressure points is modeled using the function p = f (Q, n).
There are many mathematical methods for fitting surface data points; neural networks 19, nurbs (non-uniform rational B-spline) and B-spline fitting 20 are just a few of them. We chose a revised version of one of the methods mentioned recently, because the surfaces are easy to copy and the calculations are very fast.
The method is based on the multi-level B-spline fit (MBA) algorithm proposed by Lee et al. 21; the surface is fitted using a uniform B-spline cubic function defined by its control grid Φ (see Fig. 1). See the detailed mathematical procedure in Box 1.
The second feature of this algorithm is multi-level. Given a grid, the fitting function can be calculated. The fitting function returns an error at the specified point xc, yc (flow rate and speed). Then we use a second, more refined grid (second level) that fits the difference between the previous error, and the estimate of the expected output and the function defined earlier. The function model is built from two fit values. As the number of fitting increases, the marginal error decreases, but the complexity of the same fitting function also increases.
The software implementation of the above method is shown in FIG. 2.
It must be emphasized that by changing the size (mxn) of the starting grid and the number of stages we get different results. Figure 3 shows, in particular, the course of the mean variance with progression and the resulting curve obtained by this algorithm.
The algorithm is particularly efficient because it can quickly output the desired result: Using a grid of about 40 points with m = n = 3 and a six-level calculus, the surface can be fully simulated in less than a second. The second advantage of this method is that the fitting error is very low. For example, the average error of a given point, taking pressure as an example, is below 10-5 bar.
Choose the process
After the surface modeling is complete, it is easy to choose the most suitable pump. The user gives the desired operating point; in particular, the flow and speed values ​​are input values ​​for the step i mathematical modeling of the pump using a multi-level B-spline fit (MBA) algorithm. The output value (pressure) is calculated by the mathematical function and compared with the expected pressure value; if the difference between the two is within the pump's specific limits, the pump is selected. If the situation is the opposite, the selection process needs to be improved: the neighboring values ​​of the specified speed and flow rate are checked and the software automatically determines if the pressure is within a certain specified range. The selection process will eventually give a clear list of possible pump impellers in a list (see Figure 4).
Conclusion: The difficulties in the design of pump impellers determine the need to re-use the knowledge gained in past projects. That is, it is necessary to use the performance curves of previously designed impellers, and the selection of new pumps also needs to be made from the surfaces of these impellers; therefore, mathematical modeling is necessary to automate the selection criteria. Once the selection process is complete, the designer can either select the recommended impeller (where it is done) or manually and automatically modify and optimize the impeller geometry recommended by the selection software. The optimization process will be fast because the initial geometry is very close to the expected value, so it takes just a few iterations to complete. Figure 1: Data Points Distribution Grid Diagram
