Numerical Simulation of Supersonic Intake Using
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24TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES NUMERICAL SIMULATION OF SUPERSONIC INTAKE USING STRUCTURED-UNSTRUCTURED ZONAL APPROACH Masahiro Kanazaki*, Hitoshi Fujiwara*, Yasushi Ito**, Takeshi Fujita†, Shigeru Obayashi‡, Kazuhiro Nakahashi† *Institute of Space Technology and Aeronautics, Japan Aerospace Exploration Agency, Japan. ** Dept. of Mechanical Engineering, University of Alabama, USA. †Department of Aeronautics and Space Engineering, Tohoku University, Japan. ‡Institute of Fluid Science, Tohoku University, Japan. Keywords: Engine/Airframe Integration, Supersonic Intake, CFD, Zonal Approach Abstract pressure distortion, its performance should be predicted not only with the nacelle-only Numerical simulation method for the prediction configuration but also with the engine/airframe of supersonic intake performance is discussed. configuration with changing mass flow ratio To perform a practical simulation, it is inside the nacelle to simulate an actual engine. necessary to consider not only the nacelle-only In this study, intake performances are configuration but also the engine/airframe evaluated by pressure recovery and distortion configuration. In this study, the unstructured index. The pressure recovery indicates the mesh, known to have advantages with regard to efficiency of the engine operation and the adaptation to complex geometry, was generated uniformity of the pressure distribution at the end around aircraft geometry and Euler equation of the intake. They are defined as: was solved. To obtain higher numerical accuracy for the shock wave/boundary layer (Pressure recovery) (%) = 100 × p0out/p0 (1) interaction, which appears at the inlet, the (Distortion index) (%) = structured Navier-Stokes solver was applied to 100 × (p0max,out- p0min,out )/p0 (2) solve flows inside the flow-through nacelle. These regions were coupled with using the where, p0 is the total pressure of the mainstream, unstructured-structured zonal approach. The p0out is the average value of the total pressure at nacelle-only configuration and the the end of the diffuser. p0max,out and p0min,out are engine/airframe configuration were calculated the maximum pressure and the minimum using this method and the effects of the airframe pressure at the end of the diffuser, respectively. existence on supersonic intake performance Wind tunnel tests performed by NAL (Fig. were investigated. 1) measured the pressure recovery to invest the stability range. This test indicated that the stability range of the engine/airframe 1 Introduction configuration was decreased by about 5% as A next generation supersonic experimental compared with the nacelle-only configuration as aircraft with propulsion systems (National shown in Fig. 2. It revealed that the supersonic EXperimental Supersonic Transport: NEXST2) intake performance was affected by the airframe is currently under development at the Japan existence. To study the cause of the difference, Aerospace Exploration Agency (JAXA: the the simulation of the nacelle-only configuration former National Aerospace Laboratory of Japan and engine/airframe configuration were (NAL)) [1]. In such studies, the engine/airframe preformed and calculative results were integration problem [2] should be considered. compared. Due to the strong interactions among wing, To predict intake performance correctly, fuselage, and engine nacelle [3, 4], in the design the shock interaction to the boundary layer and of a highly efficient supersonic intake that can the separation at the intake ramp should be achieve higher pressure recovery and less calculated by a high order scheme. In previous 1 KANAZAKI, M., FUJIWARA, H., ITO, Y., FUJITA, T., OBAYASHI, S. AND NAKAHASHI, K. study [5], Navier-Stokes simulation with the low Reynolds number k-ε turbulent model using the structured grid method was applied to the nacelle-only configuration and it showed a high degree of numerical accuracy. On the other Intake hand, it is difficult to apply the structured grid method to complex geometry, such as the engine/airframe configuration. Therefore, the unstructured grid method is often used to adapt such complex geometry [3, 6]. However, the unstructured grid method has difficulties in Fig. 1 Wind tunnel model 02 for scaled obtaining a high degree of accuracy near the supersonic experimental aircraft and intake boundary layer. The hybrid prismatic/tetrahedral model. unstructured grid method for viscous flow was Sub-critical operation range nacelle-only proposed [7], but the structured grid method still 100 engine/airframe has advantages when applied to simple 98 96 geometry, such as inside the flow through a 94 nacelle with a high-order scheme using the 92 turbulent model [8]. 90 88 In this study, a structured grid-unstructured 86 Pressure Recovery(%) grid zonal approach was developed to predict 84 the supersonic intake performance of the 82 80 engine/airframe configuration. In this approach, 50 55 60 65 70 75 80 85 90 Mass Flow Ratio(%) the computational domain was decomposed into two sub-domains; inside the flow-through Fig. 2 Experimental results of pressure recovery nacelle from supersonic intake and outside the vs. nacelle mass flow ratio obtained by nacelle- aircraft integrated engine nacelle. For inside the only configuration and engine/airframe flow-through nacelle, a structured grid method configuration. [9] was used for highly accurate simulation of the boundary layer at the intake. For the outer flow around the aircraft, the unstructured grid 2 Structured-Unstructured Zonal Approach method [10] was applied to adapt the complex aircraft geometry. The Navier-Stokes code with 2.1 Structured Grid Navier-Stokes Solver the low Reynolds number k-ε turbulent model with Low Reynolds Number k-ε turbulent [11] was solved for the structured domain and model the Euler code [12] was solved for the unstructured domain assuming that the For accurate simulation of the shock wave and boundary layer effect is not strong for external the boundary layer interaction near the intake, flows around the aircraft. To exchange state the structured multi-block grid and the high variables between structured grid and order viscous flow solver were applied [5, 10]. unstructured grid domains, the structured- The computational domain was decomposed unstructured zonal approach [13] was developed into three sub-domains as shown in Fig. 3 and with the introduction of a one-mesh overlap 170×99×27 points for domain 1, 170×25×25 interface. To simulate actual flights, nacelle points for domain 2, and 105×65×46 points for mass flow ratios must be controlled. The throat domain 3, which is a cavity, and the Navier- was introduced to the flow-through nacelle of Stokes equation with the low Reynolds number the structured domain, and the nacelle mass k-ε turbulent model [11] was solved. The flow ratios can be controlled by changing the governing equation in the differential form is height of the throat. written as: 2 NUMERICAL SIMULATION OF SUPERSONIC INTAKE USING STRUCTURED-UNSTRUCTURED ZONAL APPROACH ∂Q 1 1 y + 3.45 = − F(Q)l − G(Q)l (3) f µ = 1− exp− 1+ ∂t xl Re 70 Rt T 2 2 + where Q=[ρ,ρu,ρv,ρw,e] is the vector of 2 Rt y f 2 = 1− exp− 1− exp− 9 6 5 conservative variables; ρ is the density; u, v, and (6) w are the Cartesian velocity components; and e ρk 2 R = is the total energy. The vectors F(Q) and G(Q) t µε represent the inviscid flux vector and viscous ρ k = 1.4, ρε = 1.3, flux vector. Cµ = 0.09, C1 = 1.4, C2 = 1.8 Spatial differences were evaluated by a third-order upwind biased Roe scheme [12, 13] with a TVD limiter of Chakravathy and Osher In this study, boundary conditions of k and ε are type [14]. For time advancement, a second- used as follows: order Runge-Kutta scheme was used. k = 0 To control nacelle mass flow ratios, the throat 2 ∂ k (7) was introduced to the flow-through nacelle of ε = 2ν the structured domain as shown in Fig. 3. The ∂y nacelle mass flow ratios are controlled by changing the area ratio of the throat as described 2.2 Unstructured Euler Solver in the previous chapter [3, 5]. For simulation of flow around the aircraft, the Low Reynolds number k-ε turbulent model unstructured grid method was applied to adapt Low Reynolds number k-ε turbulent model the complex geometry as shown in Fig. 4. In [11] can be written as: this study, it was assumed that the effect of the boundary layer around the outside of the aircraft ∂ ∂ µt ∂k ()ρk + ρkul − µ + = P − ρε t x x on the supersonic intake spaced from the lower ∂ ∂ l σ k ∂ l (4) 2 wing by a diverter was not particularly strong ∂ ∂ µt ∂ε ε ε ()ρε + ρεul − µ + = C1P − C2 f 2 ρ ∂t ∂x σ ∂x k k [15]. Therefore, the flowfield around the aircraft l ε l was calculated by the Euler equations written as: where ∂ QdV + F(Q)⋅ndS = 0 (8) 2 ∂t ∫Ω ∫∂Ω P = µ S − ρkD t 3 where Q=[ρ,ρu,ρv,ρw,e]T is the vector of ∂u ∂u ∂u 2 S = m + l m − D2 conservative variables; ρ is the density; u, v, and ∂x ∂x ∂x 3 l m l (5) w are the Cartesian velocity components; and e ∂u D = m is the total energy. The vectors F(Q) represent ∂x m the inviscid flux and n is the outward normal of ρk 2 µ = C f ∂Ω, which is the boundary of the control t µ µ ε volume Ω. Equations (8) were solved by a fµ, f2 are supplementary coefficients for wall finite-volume cell-vertex scheme. boundary and low Reynolds effect, respectively. The Harten-Lax-van_Leer-Einfeldt-Wada C1, C2, σk, σε are model coefficients, which (HLLEW) Riemann solver [16] was used for the many kind of models are proposed. In this study, numerical flux computations. A numerical Myong-Kasagi model is used.