Geometric Optimisation of a Jet Pump

Transcription

1 Geometric Optimisation of a Jet Pump ASSIA HELALI, JEAN-LOUIS KUENY Laboratoire des Ecoulements Géophysiques et Industrielles Ecole Nationale Supérieure d Hydraulique et de Mécanique de Grenoble Institut National polytechnique de Grenoble BP 53 Grenoble 380 Cedex 9 France assia.helali@hmg.inpg.fr and Jean-Louis.Kueny@hmg.inpg.fr Abstract: The study presented in this paper deals with optimal design of swimming pool filtering system, namely jet pump. For this purpose, an optimisation tool EASY based on evolutionary algorithm is coupled with computational fluid dynamics software Fine/Turbo in order to evaluate the jet pump performances. The flow motion is governed by steady incompressible time averaged Navier-Stokes equations in the Cartesian coordinate system and the turbulence is parameterized by using K-ε model with wall functions. The optimization cycle is performed using flow solver for flow characteristics evaluation coupled with EAs and artificial neural networks (ANNs) in order to sought the minimum of the objective function This procedure is fully automatic (coupling geometry generation, NS, EAs and ANNs). The process ends when the number of generations predefined is reached. Our objective is to reduce pumping costs in term of electric energy by making some changes to the initial geometry shape. Key-words : Jet pump, Computational fluid dynamics, Optimal design, Evolutionary algorithms. 1 Introduction Jet pump has been widely used in various engineering and industrial applications. Examples include marine industry, oil energy and filtration system. Among of these practical applications, we refer to the faltering system of swimming pools. The process consists of pumping water from the pool through the filter system and returning it to the pool. This system is suitable for clean the dirty water with suspended solids. The recirculation system must operate hours a day to assure filtration and disinfection of the pool water. The source of the power used to re-circulate the water through the system is the jet-pump. Improving the jet-pump design is of crucial importance to reducing the amount of energy spent on pump operations and to save the money. Therefore, jet-pump optimization use to be a practical and highly effective method to reduce pumping costs by making some changes to the initial geometry. Depending on the number of variables and objectives considered, optimizing such jetpump problem may be very difficult, especially for large objectives and constraints. In the present investigation only one global objective is considered in which various targets and constraints are grouped in one function. The complete optimization of the jet pump has required the interaction between two kinds of numerical tools: the first concerns the flow computation based on CFD calculations which are assured by FINE/Turbo software already developed by Numeca International [1,,3]. The second tool consists of optimization software called EASY based on evolutionary algorithms and artificial neural networks. This later has been developed by NTUA (National Technical University of Athens), [, 5]). We have also developed various C++ programs in order to generate geometry, compute objective function and for results storage. The optimal jet-pump can be defined as a pump that optimizes particular objectives, while fulfilling system constraints. ISSN: Page 33 ISBN:

2 Problem configuration and motivations The fig. 1 presents the general jet pump geometry [6]. In this configuration, the water is aspired from the high pressure (HP) inlet using a propeller entrained by electric motor. The flow passes through the injector and entrains the water from the low pressure (LP) inlet via mixing process between both fluids. Further downstream a filtering process occurs when the global flow water containing possible suspended solids and impurities passes through a mesh bag located at the nozzle exit. To avoid pressure losses around the engine and in the injector, the flow is orientated by mean of several guide vanes. In such configuration, the both inlets HP and BP permit a deeper and a superficial cleaning respectively. The ultimate aim of the present work is to search geometry that, under specific operating conditions, provides the best performances in term of the jet pump efficiency. In order to achieve this goal, we first describe the objective to be reached and then we can decide which geometry part can be optimised. As mentioned above, the studied jet pump has two entries HP and LP. The first one is immersed in the water as well as the whole electrical device. That s why in this case of application we are limited to relatively small electrical power. This information is considered as first optimization constraint. Filtering the highest water quantity in shortest possible time constitute also our target. This represents a new objective which consists of sucking the most possible quantity of fluid from the two entries (HP and LP). Since, the fluid flow from HP inlet is driven by the motor; we aim to benefit from the HP kinetic energy to entrain at least the same quantity of fluid from the LP entry. The last constraint is then linked to the height of the LP free surface which must be around the value of m for the most favorable filtering operation. This value provides an equilibrium condition between the two circuits high and lower pressure. We have now an overview on the various targets and constraints linked to the optimization process. In the next section we present the geometry parameterization and the objective function formalism. Fig. 1: Jet pump system [6]. 3 Geometric parameterization The geometry of the jet pump is simple and almost axisymmetric, except of the low pressure LP inlet (Fig 1). In order to simplify the optimization study and to reduce the computational time cost, the LP inlet geometry has been adapted to be axisymmetric (Fig. ). The problem configuration can be then simplified to be two-dimensional axisymmetric instead of three-dimensional which minimizes the computational grid size. With this consideration, the computational time cost can be reduced significantly, since the optimization procedure requires several CFD calculations. Fig. : Simplification of the jet pump geometry [6]. ISSN: Page 3 ISBN:

3 Fig. 3: control points on jet pump geometry. Before initiating the optimal design process on the fully D axisymmetric jet pump geometry, we need to define the geometrical shape variations by specifying a series of parametric variables. Fig. 3, shows the control (parameterization) points on the jet pump geometry. These points can vary in streamwise and radial directions. Here the points determine the LP inlet are considered as fixes. Previous experimental studies carried out on the same jet pump geometry indicated that the global performances are insensitive to the modifications on the LP section [6]. The jet pump geometry definition and its corresponding mesh are generated automatically using the optimization variables provided stochastically by EASY. These variables data are first read by a script, once is executed by grid generator software IGG[], permits to create both the geometry and its corresponding mesh. Note that, optimization variables considered here include geometrical constraints and the mass flow rates on both inlets (HP and LP). These variables vary in only limited intervals of minimum and maximum values which are obtained by considering the grid feasibility as well as the flow physical mechanism in the jet pump. Fig. shows two types of geometry meshing: the first (Fig -a) is obtained when optimization variables are substituted by their maximum values and the second mesh is obtained using their minimum values. In this process the grid quality control is carried out simultaneously for each optimization variables. The generated is structured with 6 blocks and about 936 nodes. Fig. : Jet pump mesh.. Optimization procedure The optimization method used in this study based on coupling several numerical tools. For CFD calculations we used Fine/Turbo suite including grid generator (IGG), flow solver (EURANUS) and post processing software (CFVIEW) [3]. This package is coupled with the optimization code EASY. C++ program has been developed in order to impose correct initial conditions for each CFD simulation as well as the objective function evaluation. The optimization process can be described by the following steps (see also Fig. 5): Population: represents the geometry parameters, high pressure and low pressure flow rate. Whereby constraints can be imposed so that x [ x min,x max ]. The first population is chosen stochastically regarding to constraints imposed for each variable. Geometry: In this phase, the geometry definition program has used the optimisation variables to create a script. CFD: As first step, the script is executed by IGG in order to generate the grid mesh. After checking the grid quality, the flow solver is run and finally the results are treated in order to evaluate the objective function. Steady incompressible simulations are performed by mean of Euranus solver [1] using K-ε model with wall functions for turbulence modelling. 3 ISSN: Page 35 ISBN:

4 Optimization: the optimization is carried out using an Evolutionary Algorithm tool, namely Easy. Stopping criterion: The procedure ends when the number of generations predefined is reached. Fig. 5: Optimization process. Easy 1.3 optimization software, is considered as a generalization of the most frequently used EA variants (Genetic algorithms [7,8] and Evolution Strategies [9]). Moreover, Easy 1.3 offers the possibility of using ANNs as built-in surrogate evaluation models, in order to reduce the number of exact (CFD-based) evaluations required for the same solution quality [,5 ]. The notation symbols used for description of the optimization method are the standard ones used in Evolution Strategies. So ( μ, κ, λ ) denotes an EA with μ parents and λ offspring, where the maximum allowed life span for parent individuals is equal to κ generation. In this study the three numbers characterizing the Evolutionary Algorithms (EA) are selected such as ( μ = 7, κ =, λ = 1) and in order to accelerate the process of convergences, we used the artificial neural networks (ANNs), which reduce the number of evaluation tool calls. 5. Objective function In the present study only one objective function have been used, in which the whole of the objectives are integrated. This choice is mainly due to the availability of the computational means in multi-objectives. Below, we define each objective separately and the final objective function which we sought to minimize is just the algebraic sum of the following functions: Function 1 : F 1 = Qobj ( QHP + QLP ) / Qobj the minimum of this function can be obtained by maximizing the total flow rate; Function : F = QHP QLP / Qobj this function minimizes the difference between the HP and LP flow rates; Function 3: F3 = PElec Pellim / Pellim this function minimizes the difference between the electric power of the motor (P ellim ) and the hydraulic power (P Elec ) of the jet pump. This function is evaluated by considering the HP hydraulic power: Phyd = P HP Elec ηmoteur ηhp. The pump efficiency depends on both the flow rate and the specific speed: η HP = η HP (n q, Q HP ) With specific speed: QHP n q = n (n and nq [RPM] Q [m 3 /s].) 3 H The pump efficiency can be approximated by (more details can be found in [10]) : ηhp = [ ln( nq ) ln( 50) ] [ ln( Q ) ln( 0) ] HP Therefore the hydraulic power available at HP inlet can be written as: P hyd HP = P Elec [ ln( Q ) ln( 0) ] } HP η Motor { [ ln( n ) ln( 50) ] Function : F = Z / 0.03 the minimum of this function is reached when the height of the free LP surface (Z) equals to m. In previous studies this value was found to lead to the best skimming of the swimming pool surface and provides an equilibrium condition between the two circuits HP and LP [6]. q ISSN: Page 36 ISBN:

5 Finally, the global objective function consist of sub-functions summation and can be written as : Fobj = α i F i in which α i represent weighting factors Results and discussions In this section we present the main results obtained by the optimization process of the jet pump geometry. The flow motion is governed by steady incompressible time averaged Navier-Stokes equations in the Cartesian coordinate system. The turbulence has been parameterized by using K-ε model with wall functions. On the solid surface, the no-slip wall boundary conditions where used and static pressure at the domain exit. At both domain inlets a velocity value, corresponding to the desired flow rate, is specified. Fig.6 shows the convergence of the optimization process. This later has been stopped before achieving total convergence criterion since the minimized objective function value is achieved. The obtained results met very well with our objectives. Indeed, by performing some modifications on the jet pump geometry the filtered flow rate is considerably increased compared to what obtained with the initial geometry. The flow rate from LP inlet is found to be similar to that of HP inlet. Nevertheless, the visualization of velocity vectors in Fig. 7 highlighted the presence of small and large recirculation zones far and near the nozzle exit respectively. This is confirmed by the simulated streamlines on the same figure. The large recirculation at the exit of the nozzle is found to generate an important kinetic energy loss (not shown here). In order to solve this problem of recirculation and energy loss, we have decided to cut the nozzle before the recirculation zone and new optimization procedure have been conducted on this new geometry. Fig. 8 presents the new geometry to be optimized. Note that, only part colored in red is concerned by the optimization process. As expected, visualizations based on velocity vectors as well as simulated streamlines in Fig 9 show that the recirculation zone near the nozzle is considerably reduced with respect to the previous long geometry case. This can improve the jet pump performances in term of kinetic energy loss. The obtained results are very important and led to the maximum filtered water flow rate with a predefined electrical power by performing some low-cost modifications on the jet pump geometry design. OBJ_function_ Evaluations Fig. 6: Convergence of the optimization. Fig 7: Visualization of velocity vectors. 5 ISSN: Page 37 ISBN:

6 Fig 8: Geometry and grid of jet pump. Fig. 9: Visualization of velocity vectors on the short geometry. 7 Conclusions The present study deals with an optimal design process of jet pomp geometry. Our objective is to reduce pumping costs in term of electric energy by making some changes to the initial geometry shape. For this purpose, an optimisation tool EASY based on evolutionary algorithm is coupled with computational fluid dynamics software Fine/Turbo in order to evaluate the jet pump performances. The first obtained results met very well with our objectives. Indeed, by performing some modifications on the jet pump geometry the filtered flow rate is considerably increased compared to what obtained with the initial geometry at same operating conditions. Nevertheless, the flow analysis inside the device (nozzle) revealed the presence of large recirculation zone near the nozzle exit which can, under certain operating conditions, reduce considerably the jet pump performances. In order to solve this problem, we have decided to reduce the nozzle length by cutting it just before the zone of recirculation, and new optimization process has been conducted considering this new geometry. As expected, our results show that with this geometry of short nozzle, the recirculation zone is reduced in maximum. Despite this solution, the kinetic energy loss seems to persist in this system. Our suggestion in the future is to add a trumpet duct to the nozzle exit which may lead to a good homogenization of the flow. It is worth noting that in the present study we minimized only one objective function, which mainly includes four sub-functions. It is then crucial to carry out an optimization study with multi objectives function. Acknowledgements The authors wish to knowledge R. CALARD, F. DEBOOS, M. L. DEPAUX, M. FRINGANT and S. KOCH-MATHIAN for their kind collaboration. References: [1] Fine Turbo, User manual, Numeca international 003, Belgique. [] NUMECA, Igg-autogrid, 003. [3] NUMECA, Cfview, 003. [] K. C. Giannakoglou, A. P. Giotis and M. K. Karakasis. Low Cost Genetic Optimization Based on Inexact Pre Evaluations and the Sensitivity Analysis of Design Parameters, Journal of Inverse Problems in Engineering, Vol. 9, 389 1, 001. [5] K. C. Giannakoglou. Design of Optimal Aerodynamic Shapes using Stochastic Optimization Methods and Computational Intelligence, Progress in Aerospace Sciences, Vol. 38, 3 76, 00. [6] A. Helali, "Optimisation d'une turbine de type Kaplan", thèse de doctorat, INPG Grenoble, 006. [7] D.E. Goldberg. Genetic Algorithms in search, optimization & machine learning, Addison-Wesley, [8] Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs, nd edition, Springer-Verlag, 199. [9] Th. Bäck. Evolutionary Algorithms in Theory and Practice. Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford University Press, [10] W. Bohl, "Strömungs-Maschinen, Aufbau und Wirkunggsweise", Vogel Fachbuch- Kamprath-Reihe, Würzburg, ISSN: Page 38 ISBN: