Fig. 1. Field of the Mach number and streamlines (cruise, М = 0.8)

Transcription

1 ICMAR 2014 SHAPE OPTIMIZATION OF THE ENGINE NACELLE USING RANS A.A. Savelyev, N.A Zlenko, S.V. Mikhaylov Central Aerohydrodynamic Institute (TsAGI) , Zhukovsky, Moscow Region, Russian Federation Introduction The environmental requirements for up-to-date aircraft entail the usage of high-bypass turbofan (bypass ratio, BPR 8), the characteristic feature of which is separate outflow jets from the core nozzle and fan nozzle. One of the main features of the turbofan with separate jets is a small length of the nacelle cowl that is usually no more than one and a half the midsection diameter. For this reason, the interference of the air inlet and nozzle significantly affects the aerodynamic characteristics of the nacelle. According to the monograph [1] more than 25 geometric parameters affect the aerodynamic characteristics of the high-bypass turbofan nacelle therefore the aerodynamic design of this type of engine nacelles is an extremely complex task, requiring the selection of optimal geometrical parameters both the inlet and nozzle. An algorithm for optimal aerodynamic design of the high-bypass turbofan nozzle is set forth in [2]. This algorithm allows us to find a solution under conditions when the quality of the designed product evaluated according to several competing criteria (multicriterion optimization). Generalization of the approach to the case of real turbofan nozzle with structural constraints described in [3]. Efficiency of the methodology is demonstrated on the example of optimizing the shape of the nozzle with a bypass ratio of ~ 10. In this paper, we consider the problem of choosing optimal aerodynamic contours of isolated turbofan nacelle as a whole. Shape optimization problem is solved in a rigorous formulation, considering the number of typical structural and gas-dynamic restrictions on the allowable variation range of the control geometrical parameters typical for such engines. Problem statement Typical flow around isolated nacelle at cruising flight Mach number M 0. 8 is shown in Fig. 1. Except Mach number, the figure shows streamlines and contours with M 1. 0 marked supersonic zones. Fig. 1. Field of the Mach number and streamlines (cruise, М = 0.8) It should be noted the following features of the flow around the nacelle characteristic of highbypass turbofan. Near the leading edge of the inlet cowl at the cruise, you may experience the supersonic zone and, consequently, the shock wave (see. Fig. 1). Shock-wave intensity significantly affects external nacelle drag and hence effective thrust. Properties of the supersonic zone depends not only on the shape of the inlet lip, but also on the diameter and position of the midsection. In the aerodynamic design, it is expedient to choose values of the control geometrical parameters so as to minimize the intensity of shock waves on the upper surface of the nacelle, and in the limiting case to exclude the possibility of a supersonic zone. At the same time, the shape of the inlet lip is one of the parameters, which determine the nature of the flow in the intake channel at take-off. For example, bad choice of control geometrical parameters can lead to the separation of the flow in the inner inlet duct and unacceptable increase of the inhomogeneity level in the inlet flow. This is A.A. Savelyev, N.A. Zlenko, S.V. Mikhaylov, 2014

2 Section 3: Gas Dynamics of Internal and External Flows clearly seen in Fig. 2, which presents the streamlines and the field of Mach numbers corresponding to take-off regime ( ) for one of the intermediate geometry models. M 0 Fig. 2. Field of the Mach number and streamlines (take-off, М = 0) Nacelle design is pronounced compromise, due to the need to ensure stable and effective operation of the cruise engine in all flight regimes. In such situation, the choice of decisive criterion (objective function) has a definite difficulty because different objective functions has optimum in different zones of control parameter and control parameters often have an opposite influence on these functions. For example, an increase of the inlet lip thickness favorably affects the degree of inhomogeneity of the inlet flow (especially in crosswind presence), but it increases the external drag at cruising flight. In this paper, a cruising effective thrust of the engine is proposed as a decisive criterion for optimal design of the isolated nacelle. The basis for this choice is the fact that the projected engine focused on the family of modern long-haul aircrafts for which the cruising flight mode is the most time-consuming. It is supposed that the optimum of the selected objective function is defined taking into account all necessary constructive and gas-dynamic constraints. Practically, the problem of optimal aerodynamic design of the isolated nacelle reduced to conditional one-criterion optimization of the selected objective function. The calculation of the objective function value and verification of compliance with specified restrictions are carried out with the help of numerical simulation of viscous flow around the nacelle for each set of control parameters and flight regime. Parametric nacelle model Task decomposition. One of the most significant stages of the optimization, which largely determines the complexity of the problem, is to choose a set of control parameters. It is worth breaking the task into stages because of complexity of the optimization problem with a large number of parameters. Taking into account the symmetry of the nozzle concerned and the negligibility of the nozzle impact on the inlet flow, we propose the following task decomposition: axisymmetric optimization; three-dimensional optimization. Inlet control geometric parameters. Fig. 3 shows the main geometric parameters influencing the aerodynamic properties of the inlet. 2

3 ICMAR 2014 Fig. 3. Axisymmetric inlet parameterization Fig. 3 uses following designations: d0 inlet diameter; dth throat diameter; К lip thickness coefficient: K = (d0/dth - 1)*100%; den diameter of engine entrance; Lin inlet length; Lth distance between leading edge and throat; dif diffuser entering angle; k1 inner surface coefficient; k2 outer surface coefficient; dm midsection diameter; Lm distance between leading edge and midsection. Among parameters listed above the following are selected as control in the present work: dth, К, Lth, k1, k2, dm, and Lm. The engine entrance diameter den is constant and the inlet length Lin is equal to Lin /den = Nozzle control geometric parameters. Method of specifying the nozzle geometry used for optimization calculations in this paper is illustrated in Fig. 4. Variable elements of the mathematical model is denoted by dashed line in the figure. As a control geometric parameters were selected: diameter (dm) and location (Lm) of the nacelle midsection, which determine the location of the point М with coordinates (ХМ, YM); external taper angle of the cold nozzle ( e); location of the cooling air slot on the surface of the engine core relative to the hot nozzle exit (Lsl); taper angle of the central body ( cb). Internal taper angle of the cold nozzle is dependent geometrical parameter generatrices of the nozzle are taken fixed (solid line in the figure). i f e. Other A.A. Savelyev, N.A. Zlenko, S.V. Mikhaylov, 2014

4 Section 3: Gas Dynamics of Internal and External Flows Fig. 4. Nozzle parameterization Midsection. One of the main goals of the axisymmetric stage of the design is to choose the diameter of the middle dm and its position Lm. It should be understood that parameters dm and Lm influence not only on the characteristics of the nozzle, but also on the characteristics of the intake. In particular, the increase in the diameter of a middle section may positively affect the flow around the inlet, but negatively on the flow around the nozzle. The compromise solution can be found only modeling the entire nacelle. In this regard, despite the seeming partition of the nacelle into inlet and nozzle, in this paper we consider the entire axisymmetric model of the nacelle. Region of feasibility. Necessary and important step in the constrained optimization problem is to set limit values or each control parameter. Limit values are specified as a set of constraints of the first kind with the help of the system of inequalities: x (min) i i (max) i x x, i 1 N (min) (max) Values xi and x i are determined based on the experience of designing the input and output devices of high-bypass turbofan and surely taking constructive constraints into account. Automatic modification of geometry and calculation grid After creating a parametrized mathematical model of engine nacelle, it is necessary to organize an automatic modification of geometry and calculation grid, according to control geometrical parameters of model. This process includes two stages: modification of geometrical model in CAD system and automatic regeneration of calculation grid using grid-generator on basis of modified geometrical model. Geometry creation. Process automation is performed using macros. A macro#1 is written during the initial creation of the geometry in CAD system. Then, automatic modification of EN shape is performed using this macro. The macro text includes all geometrical model sizes and each size is a value of definite variable declared in macro. As a result of macro running, a file with geometrical model with given values of control geometrical parameters appears. Grid creation. A structured multi-block 3D calculation grid is used in the calculation of flow field around the engine nacelle. First, the computational domain is divided into rectangular blocks. When selecting the block structure it is necessary to consider all the features of the geometric model (fan and core nozzles, cooling air slot, edges, fan spinner, etc), and to add external buffer blocks to minimize the influence of the boundaries of the computational domain (Fig. 5). On the buffer blocks interface with main domain it is used boundary condition «connect», allowing to join surfaces with unmatched grids [4]. par, 4

5 ICMAR 2014 Fig. 5. Block structure of the main grid (background Mach number) After generating the calculation grid for one geometrical model, the grid is modified for another geometrical model by associating nodes and edges of each block of old (basic) grid to control points and curves of the new geometry. For that, a modified geometry in IGES format is imported, then association is performed and new 3D grid is generated. All these actions are written in the macro#2 that is the main tool for automatic modification of calculation grid. For automation of process above of geometrical model and calculation grid modification, a control module generated on basis of high-level programming language Python [5] is used. As entrance parameters, the module uses all necessary parameters of the new geometrical model, modifies both macros is it is necessary and runs them in series. Automatic generation of geometry and calculation grid provides both essential acceleration of preparing the initial data for numerical calculations and entirely excludes a possibility of accidental errors that inevitably arise in mass manual developing the grids. Methodology of field and integral characteristics calculation Solver. For calculation of the flow around the engine nacelle, a code EWT ZEUS [6; 7] is used. Difference scheme is written in finite-volume form. The basis of calculation methodology for convective fluxes is a scheme MUSCL of the second approximation order in space [8; 9; 10]. Diffusive fluxes are calculated using central differences. Therefore, the scheme has second approximation order in space. The code ZEUS gives a possibility to obtain a stationary solution using a linearized implicit scheme [11]. The implicit scheme is written in delta-form [12] and has the first approximation order in time. In the current work, Reynolds equation system closed by SST turbulence model [13] is solved. Stationary solution is obtained using implicit scheme. Boundary and initial conditions. Main flow parameters are given and non-reflecting boundary condition is formulated at the outer boundary of calculation domain. A boundary condition of heatinsulated no-slipping wall is given at solid surfaces. Total pressure and total temperature corresponded to engine work regime are given at the entrance of each nozzle contour, static pressure at the engine entrance is taken as constant. Pressure value is corrected during the calculation so as to provide the balance of air consumption through the throat and inlet. Integral characteristics. Methods of determining the internal and external integral characteristics of the separate-flow nozzle corresponds to the procedure described in [1]. External aerodynamic loads are calculated by y integrating the pressure and friction forces on the relevant solid surfaces. Effective thrust is calculated as the sum of the aerodynamic loads on the solid surfaces plus the difference between the input and output momentums. A.A. Savelyev, N.A. Zlenko, S.V. Mikhaylov, 2014

6 Section 3: Gas Dynamics of Internal and External Flows Choosing optimal values of control geometrical parameters Optimal designing is performed on basis of numerical parametrical calculations of viscid gas flow around engine nacelle. In space of control parameters, the process of approaching to optimal value of objective function is defined using an algorithm of extremum search that is known as coordinate descent method [14]. One of its advantages is evidence of its convergence process. The same important property of the method is possibility to grade objective function calculation inaccuracies that are consequences of both non-stationary phenomena and grid dependence of used numerical method. At the first stage of the work parametric calculations of the flow around an axisymmetric nacelle carried out. Their goal is to preselect the form of intake that ensures steady flow for both outside and inside of the inlet at cruising and takeoff flight conditions, as well as satisfaction of the throat-loading restriction: λth λmax. In addition, it is assumed that chosen variant should be better than the base one, which has been designed in traditional way according to recommendations [1]. Based on parametric calculations, during which throat diameter dth, lip thickness coefficient K and outer surface coefficient k2were varied, was selected intake, meet the requirements at this stage. Fig. 6 8 show fields of Mach number and streamlines calculated for the chosen variant of the inlet at various flight regimes. Fig. 6. Field of the Mach number and streamlines for chosen geometry (cruise, М = 0.8) Fig. 7. Field of the Mach number and streamlines for chosen geometry (take-off #1, М = 0.0) 6

7 ICMAR 2014 Fig. 8. Field of the Mach number and streamlines for chosen geometry (take-off #2 М = 0.24) Fig. 6 8 show that designed inlet ensures steady flow at all three flight regimes. At that, in comparison to the base variant of inlet, the effective thrust at cruising flight increased by 0.6 %, the external drag reduced by 0.4 %, the maximum Mach number at the external surface of the inlet reduced from 1.22 to Fig. 9 shows the dependence of the relative effective thrust ( 0 / eff P eff P, where 0 P eff the effective thrust of the base variant) upon the shape of the upper part of the cowl, which is determined by the control parameter k2. Fig. 9. Relative effective thrust dependency upon the control parameter k 2 Variation in the maximum Mach number on the upper surface of the inlet cowl and external drag with the control parameter k2 are shown in Fig. 10 and 11, respectively. A.A. Savelyev, N.A. Zlenko, S.V. Mikhaylov, 2014

8 Section 3: Gas Dynamics of Internal and External Flows Fig. 10. The maximum Mach number on the upper surface dependency upon the control parameter k 2 Fig. 11. External drag dependency upon the control parameter k 2 As mentioned above, the control geometry parameters for nozzle within the framework of current problem statement are position of the cooling air slot Lsl, taper angles of cold nozzle and cone e and cb as well as position and diameter of the nacelle midsection Lm, dm. The next series of parametric calculations was aimed at determining the optimal form of a bypass nozzle, i.e. choice of parameter values, which provide the maximum effective thrust subject to accomplishment of all restrictions. As before, the main tool to search for a conditional extremum of the objective function is a well-proven method of descent. For instance, Fig. 12 shows the dependence of the relative effective thrust on the taper angle of the central body. Fig. 12. Relative effective thrust dependency upon the taper angle of the central body The sharp decline in the effective thrust at angles θcb greater than 27 is explained by the appearance of flow separation on the cone. This is clearly seen from a comparison of Fig. 13 and 14, where the results of calculations for nozzles corresponding to the values θcb=25 and θcb=30 are given. 8

9 ICMAR 2014 Fig. 13. Mach number field, θ cb=25 Fig. 14. Mach number field, θ cb=30 So, in comparison to base variant, the proposed nacelle provides: increase in the effective thrust by 1.2 %; reduction in maximum Mach number on the external surface of the inlet from 1.22 to 1.08; reduction in the nacelle overall length of 300 mm. Conclusion The methodology of optimization of the high-bypass turbofan nacelle is developed and approbated. The methodology is based on the numerical simulation of viscid gas flow around nacelle taking into account the working nozzle and inlet. Important feature of the developed methodology is to automate the stage of the geometry and grid generation. This approach enables to reduce the time of preparation of calculations by several orders and to eliminate random errors. The effectiveness of the proposed methodology is illustrated by solving the problem of optimal aerodynamic design of high-bypass turbofan nacelle (BPR ~ 10) subject to the large number of structural and aerodynamic constraints. Relative to the base variant, designed by traditional approach, the proposed nacelle provides more effective thrust and smaller overall dimensions. REFERENCES 1. Under red. G.S. Byushgens Aerodynamics and Flight Dynamics of Mainline Aircrafts, TsAGI publishing department PRC Avia-publishers, Moscow Beijing, 1995 (in Russian). A.A. Savelyev, N.A. Zlenko, S.V. Mikhaylov, 2014

10 Section 3: Gas Dynamics of Internal and External Flows 2. Zlenko N.A., Mikhaylov S.V., Shenkin A.V. Creation and Using the Simulation Model in Geometry Multicriterion Optimization of Jet Nozzles of High-Bypass Turbofans // Technics of Air Fleet Vol. 84, No. 2 (699). P (in Russian). 3. Zlenko N.A., Mikhaylov S.V., Savelyev A.A., Shenkin A.V. Optimal Design Methodology of of the High-Bypass Turbofan Nozzle // Proceedings of TsAGI No P (in Russian). 4. Bosnyakov S., Kursakov I., Lysenkov A., Matyash S., Mikhaylov S., Quest J., Vlasenko V. Computational Tools for Supporting the Testing of Civil Aircraft Configurations in Wind Tunnels // Progress in Aerospace Sciences No. 44. P Rossum G., Drake F.L.Jr. An Introduction to Python, Network Theory Ltd., Vlasenko V.V., Mikhaylov S.V. ZEUS Code for Calculation of Non-Stationary Flows in Framework of RANS and LES Approaches // Materials of XX school-seminar Aerodynamics of Aircrafts, P (in Russian). 7. Mikhaylov S.V. Program Based on Zonal Approach for the Calculation of Unsteady Viscous Turbulent Gas Flow around Complex Aerodynamic Shapes, Including High-Lift Wing (ZEUS) // Certificate of official registration of computer program (November 12, 2012). 8. Godunov S.K. Difference Method for Numerical Calculation of Discontinuous Solutions of Hydrodynamics // Sbornik: Mathematics Vol. 47 (89), No. 3. P (in Russian). 9. Kolgan V.P. Using Principle of Derivative Minimal Values in Creation of Finite-Difference Schemes for Calculation of Gasdynamics Discontinuous Solution // Scientific Notes of TsAGI Vol. 3, No. 6. P (in Russian). 10. van Leer B. Towards the Ultimate Conservative Difference Scheme. Part V: A Second-Order Sequel to Godunov's Method // Journal of Computational Physics Vol. 32, No Kazhan E.V. Increase of Explicit Godunov-Kolgan-Rodionov Scheme Stability by Introducing Implicit Smoother // Scientific Notes of TsAGI Vol. 43, No. 6, P (in Russian). 12. Ivanov M.Ya., Nigmatullin R.Z. Implicit Godunov Scheme of Extra Accuracy for Numerical Integration of Euler Equations // JCM and MPh Vol. 27, No. 11. P (in Russian). 13. Menter F.R. Improved Two-Equation k-omega Turbulence Models for Aerodynamic Flows // NASA TM Ravindran A., Reklaitis G.V., Ragsdell K.M. Engineering optimization: Methods and applications, John Wiley & Sons,