Shape Design Optimization of Embedded Engine ...

Shape Design Optimization of Embedded Engine Inlets for N2B Hybrid Wing-Body Configuration Hyoungjin Kim* Science Applications International Corporation, Cleveland, OH 44135 and Meng-Sing Liou† NASA Glenn Research Center, Cleveland, OH 44135

ABSTRACT The N2B hybrid wing-body aircraft with embedded engines was conceptually designed to meet environmental and performance goals for the N+2 generation transport set by the Subsonic Fixed Wing project of NASA Fundamental Aeronautics Program. In the present study, flow simulations are conducted around the N2B configuration by a Reynolds-averaged Navier-Stokes flow solver using unstructured meshes. Boundary conditions at fan faces and engine exhaust planes are provided by the Numerical Propulsion System Simulation (NPSS) thermodynamic engine cycle model. The flow simulations reveal challenging design issues arising from the integration of boundary-layer-ingestion offset inlets with the wing-body airframe. Adjoint-based optimal designs of the inlet shape are then carried out to minimize the airframe drag force and flow distortion at fan faces. Design surfaces are parameterized by Non-Uniform Rational B-Spline (NURBS), and the cowl lip geometry is modified by a spring analogy approach. By the drag minimization design, a massive flow separation on the cowl surfaces is almost removed, and the strength of a shock wave unintended in the original design is now remarkably reduced. For the distortion minimization design, the diffuser bottom and side walls are reshaped to minimize flow distortion at fan faces. This minimization results in a 12.5 % reduction in distortion.

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Nomenclature ADP

= Aerodynamic Design Point

AIP

= Aerodynamic Interface Plane

AOA

= Angle of Attack

BLI

= Boundary Layer Ingestion

BPR

= Bypass Ratio

CL,CD, CT = Aircraft lift, drag and thrust coefficients Cp

= Pressure coefficient

HWB

= Hybrid Wing-body aircraft

ISA

= International Standard Atmosphere

M

= Mach number = Mass flow rate

NPSS

= Numerical Propulsion System Simulation

OML

= Outer Mold Line

OPR

= Overall Pressure Ratio

Pt, Tt

= Total pressure, total temperature

SFC

= Specific Fuel Consumption

SFW

= Subsonic Fixed Wing

SLS

= Sea Level Static

TOC

= Top of Climb

u, v

= parametric space coordinates

x, y, z

= Cartesian coordinates



= Mass-weighted average total pressure recovery at fan face

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I.

Introduction

The hybrid wing-body (HWB) aircraft, a configuration proposed by Northrop during 1946 and chronicled by Liebeck [1], is an alternative design concept to the conventional tube-and-wing aircraft. The fuselage and wings are integrated into a flying wing to yield a better aerodynamic efficiency than the tube-and-wing configuration. Also, the wide airframe body of the HWB is beneficial for shielding downward-propagating noise from engines installed above the aircraft. The Boeing Company conducted a conceptual design study of HWB configurations satisfying N+2 goals of NASA Subsonic Fixed Wing project [2] under a contract sponsored by NASA’s Fundamental Aeronautics Program [3]. As a starting point, the nonproprietary “Silent Aircraft” SAX-40 [4,5] configuration was chosen. Two HWB configurations were considered in the study: one is the N2A model employing conventional podded engines and the other is the N2B model, which adopts embedded engines and boundary layer ingestion (BLI) offset inlets. The SAX-40, N2A, and N2B configurations are illustrated in Fig. 1. Figure 2 shows the embedded engine adopted in N2B having three fans and variable area thrust vectoring/reversing nozzles in each nacelle. Compared to the conventional pylon-mounted engines, the embedded engines with BLI offset inlets allow reduced ram drag, wetted area, structural weight, and noise. Disadvantages of the embedded engines are higher flow distortion and reduced pressure recovery at engine faces due to the BLI offset inlet. Applications of design optimization methodologies for reducing distortion and improving total pressure recovery in the aerodynamic interface plane (AIP) in a BLI inlet have been carried out in several studies [6,8,9,10]. Allan et al. [6], using the design-of-experiments method and computational fluid dynamics (CFD) solutions, determined the size of a single-row flat vortex vanes. They reported an 80% reduction in DPCPavg, a circumferential distortion descriptor [7] and a decrease in recovery by more than 0.6% point at the AIP of the inlet A model. Lee and Liou [8] applied an adjoint-based shape design optimization to the inlet A model to modify the bottom surface near the inlet throat. The resulting design shape appears like a successive alternation of lateral bumps and grooves. They

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obtained not only a 52.5% reduction in the circumferential distortion but also a 3.3% increment in the total pressure recovery at AIP. Carter et al. [9] applied a knowledge-based inverse design method to a HWB configuration with a flow-through nacelle. Wing upper surface near the inlet entrance was redesigned to give better flow characteristics. Rodriguez [10] conducted a CFD-based design optimization study for BLI inlet shape design on a three-engine HWB configuration utilizing a complex variable method for calculation of objective function gradients. High-fidelity CFD-based analysis and design is essential for accurate performance evaluation and improvement of propulsion-airframe integration of HWB configurations with embedded engines like N2B. In the present study, flow simulations of the N2B configuration is conducted to understand effects of propulsion–airframe integration on the flow field around the vehicle and the embedded engine. Then an adjoint-based optimal inlet shape design study is performed to improve aerodynamic and propulsive performances. The remainder of this paper is organized as follows. In Section II, the N2B configuration is reviewed and response surfaces for thermodynamic cycle models of the embedded engine are generated for boundary conditions. In Section III, methodologies for the flow simulation and optimal shape design are explained, including the flow solver, mesh generation, boundary conditions, sensitivity analysis, and design parameterization. Simulation results for the N2B aircraft are presented in Section IV. Optimal shape design results are shown in Section V. Summary and conclusions athen follows in Section VI.

II. N2B Hybrid Wing-body Aircraft A. N2B Specification [3] N2B was suggested by Boeing as a cargo freighter aircraft and conceptually designed to have a 477,400 lbm maximum take-off gross weight (MTOGW), a 103,000 lbm payload and a 6,000 nm range. The cruise Mach number is 0.80 and initial cruise altitude is 31,000 ft. The time to climb 31,000 ft is 0.29 hr. The span length is 213 ft, and the reference area is 9246 ft2. It has three propulsion units, each of which has three fans in side-by-side flow passages and the center one houses a core engine.

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B. Engine Model The tri-fan embedded turbofan engine concept was based on the GRANTA engine of SAX-40 aircraft [4]. A conceptual design of the embedded engine was conducted at NASA Glenn Research Center for an expected 2020 technology level [11]. Each engine has a gas generator (core engine) that drives an inline fan and two additional outboard fans through a mechanical transmission system. The aerodynamic design point (ADP) is Mach number 0.8 at an altitude of 31,000ft. The required thrust per engine at ADP is 10,000 lb at ISA+0°F The design fan pressure ratio is 1.50 at ADP. All fans have the same diameter and rotate at the same speed. The design bypass ratio (BPR) of the core engine is 3.1 and overall effective BPR of the tri-fan engine is 11.3 at ADP. The fan face Mach number is 0.674. The fan efficiency was assumed to be degraded by one percent point because of the inlet flow distortion. The engine thermodynamic cycle was designed using the NPSS (Numerical Propulsion System Simulation) program [12,13] in the study of Ref. [11]. Some details of the N2B embedded engine cycle information are given in Table 1. Total pressure recovery values at engine fan faces at the ADP condition are estimated by Boeing from the mass averaged total pressure recovery of the inlet capture flow at the inlet highlight using Reynolds-averaged Navier-Stokes (RANS) flow analysis results for a clean wing configuration. A usage of fixed vane vortex generators is supposed to mitigate inlet distortion, and inlet diffuser loss was assumed to be 0.6% [3]. The recovery values are 0.96705 for side fans and bypass flow for the center passage, and 1.0 for core flow of the center passage assuming that uncontaminated flow is fed into the core engine, while the boundary layer flow is ingested into the two side fans and the bypass flow of the central passage. The engine thermodynamic cycle design is then conducted based on the recovery values at the ADP condition. In the present CFD simulations of the N2B configuration, the embedded turbofan engines are replaced with an NPSS engine model as illustrated in Fig. 3. Total pressure recoveries at engine fan faces are calculated by CFD and provided to the NPSS model and engine boundary conditions required by CFD simulations are obtained from the NPSS model as shown in Fig. 3(c).

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In the flow simulation, the engine fan face is treated as a subsonic exit boundary condition with a specified target mass flow rate, which is matched by adjusting a uniform static back pressure. Also, the engine exhaust planes are treated as subsonic inflow boundary conditions with specified total conditions and mass flow rates. To perform the coupling of the NPSS model with the flow solver, one could link the NPSS code with the CFD flow solver to accomplish exchanging of data resulting from both codes. An alternative approach is to build an algebraic response surface model for the engine cycle and insert it into the flow solver, as done in our previous work [14]. In the present study, we again employ the response surface approach for its ease and simplicity in achieving the coupling without compromising accuracy, as evident in what follows. Engine parameters required for the present flow simulations are the mass flow rate total pressure

and the total temperature

model are the total pressure recoveries

, the

at the engine exit of each flow passage. Input variables to the NPSS at fan faces. Since the corrected mass flow rate includes the recovery value

at each fan face, it is the same and constant for the three passages, in the amount of 667.18 lb/s at the full power top of climb (TOC) condition. Therefore, only Pt and Tt need to be defined by the response surfaces. There are three input variables:

for passages 1 (center passage), 2, and 3 (two side passages), respectively. Treating the total

pressure recoveries at the AIP as independent variables,, the total temperature and pressure at the engine exit are expected to be dependent on them; hence they are expressed in general as

Pt _ exit1  f P1 1 ,2 ,3 , Tt _ exit1  fT 1 1 ,2 ,3  Pt _ exit 2  f P 2 1 ,2 ,3 , Tt _ exit 2  fT 2 1 ,2 ,3 

(1)

Pt _ exit 3  f P3 1 ,2 ,3 , Tt _ exit 3  fT 3 1 ,2 ,3  Sensitivities of engine parameters are calculated by finite differencing of off-design NPSS simulation results at the TOC condition for one percent point variation in the recovery at a fan face. Figure 4 shows only the significant results of the sensitivity study; other sensitivity terms not shown in Fig. 4 are all zero. The results of the sensitivity study can be summarized as follows: 1)

is affected significantly by the recovery of its own passage only.

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2)

of the central passage is negligibly affected by the recovery of the central passage.

3)

f the central passage are affected by recoveries of side passages because the turbine of the core engine needs to adjust in response to the fans which are affected by a change in recovery. However, the amount of sensitivity is negligible.

4) The recovery of the central passage has no effects on

or

of side passages.

Based on the results of the sensitivity study, the number of response surface models can be reduced from six to two; , and each model is a function of only the recovery of its own passage.

Pt _ exit1  f P1 1 , Tt _ exit1  const1 Pt _ exit 2  f P 2,3 2 , Tt _ exit 2  const2,3

(2)

Pt _ exit 3  f P 2,3 3 , Tt _ exit 3  const2,3 where

and

are set as 701 and 503 °R, respectively, according to the NPSS results.

Data points of the response surface models at off-design conditions can be generated by running the NPSS engine model at TOC for different inlet recovery values. Then, a least squares curve fit produces algebraic response surface models for

of three passages, as shown in Fig. 5; these simple and accurate models from the NPSS runs

will provide the boundary condition for the CFD calculations.

III. Methodologies A. Flow Solver A finite-volume unstructured-grid Navier-Stokes solver [14] is used in the current flow simulations. The compressible RANS equations are discretized by the cell-vertex finite volume method. Control volumes are non-overlapping dual cells constructed around each node. Each edge connecting two nodes is associated with an area vector of the control surface, at which flow fluxes are computed. For a second order accuracy, a linear reconstruction of

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the primitive gas dynamic variables inside the control volume is used in conjunction with a limiter. Several approximate Riemann solvers, including HLLEW [15] and AUSM+-up [16] are available for computing inviscid fluxes. In the present study, the HLLEW flux was used. Turbulence effects are considered by using Menter’s two equations Shear Stress Transport (SST) model [17,18]. For the time integration, the lower-upper symmetric Gauss Seidel (LU-SGS) implicit method is adopted [19]. Parallel processing is achieved by domain decomposition of the computational mesh and Message-Passing Interface (MPI). A validation study of the flow solver on a relevant BLI offset inlet is presented in the Appendix.

B. Computational Mesh Generation Computational mesh is generated by using MEGG3D (mixed element grid generation in 3D) code [20, 21]. A triangular surface mesh is generated directly on the Stereolithography data, which can be exported from a computer-aided design model. A hybrid volume mesh is then made by using advancing front/layer methods. Layers of prismatic cells are generated near viscous walls, tetrahedral cells in the remaining computational domain, and pyramid cells in between when necessary. Figure 6 (a) displays the surface mesh used for the N2B model. As mentioned earlier for Fig. 2 (b), the N2B aircraft has variable-area thrust-vectoring nozzles, which inevitably contain moving parts contacting each other or have very small gaps in between. The complex geometry of the movable devices was simplified into clean exhaust nozzles as shown in Fig. 6 (b). If the thrust vectoring function needs to be simulated, the simplified surface geometry can be deformed for that purpose. The total number of computational mesh points for the half model of the N2B configuration is about 13.3 million, and the first nodes off the viscous walls are clustered to the wall so that y+ values at the first nodes are less than 2. Required computational wall-clock time to get converged solutions starting from freestream conditions for the N2B configuration was about three hours on 516 processors at Westmere nodes of the NAS Pleiades supercomputer. For the clean wing HWB configuration analyzed for comparison purposes with the N2B configuration, the total number of mesh points is about six million, and the same wall clustering was applied as the N2B case. The required computational

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cost for the clean wing HWB is about one-third of that of the N2B configuration on the same supercomputer.

C. Boundary Conditions Free-stream conditions are the TOC flight conditions at Mach number of 0.8 and altitude of 35,000 ft, together with other details in Table 1. For the engine fan face boundary conditions, the density and velocity components from inside of the computational domain were extrapolated and a uniform static back pressure to match the target mass flow rate was imposed. The conventional uniform back pressure boundary condition for fan faces has been widely used for inlet-engine interaction problems [10, 14, 22]. For propulsion-airframe integration problems with highly distorted onset flows at fan faces, the assumption of uniformity of fan face static pressure may not be valid anymore. At a low recovery region on an AIP, the low momentum causes a larger local incidence angle for the fan blade section leading to a stronger suction effect by the fan, which mitigates the flow distortion. Therefore, the use of the uniform back pressure boundary condition is known to give conservative results in terms of the flow distortion at fan faces. A direct coupling of the inlet and full annulus fan blades in the computational domain would give a more realistic inlet fan interaction simulation, but it would require prohibitively large computational cost for shape design applications. As an alternative to the coupling with a full annulus fan blades simulation, the body force approach [23, 24] has been drawing attentions, The body force approach models rotor/stator blade row turning, loss and deviations using body force terms, which are integrated for a control volume around each blade row. The body force approach still requires more computational cost than the current uniform static back pressure approach because of the pre-analyses of single blade passages for body force model generation and increment of the mesh size as computational domains between fan faces and engine exhaust planes are included. However, application of the body force approach for more accurate inlet fan interaction would be beneficial, especially for BLI inlet diffuser flows. The uniform back pressure approach adopted in the present study paper is still valid for qualitative comparisons of inlet fan interaction problems when diffuser flow separation does not reach to the fan face [24]. More realistic simulation of the inlet fan interaction

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effects remains for future work. For the engine exhaust planes, the total pressure and total temperature are set and a static pressure is taken from downstream in the computational domain for subsonic inflow boundary conditions.

D. Distortion Indicators Flow distortion at fan faces can be quantified by calculating flow distortion indicators. In this study, two circumferential distortion indicators are selected and calculated; one indicator is DPCPavg [7], and the other is DC60 [25]. DPCPavg is the average SAE circumferential distortion indicator defined in the Aerospace Recommendation Practice 1420 standard [7]. (3) where i is the ring number on the AIP rake and Nrings is the total number of rings. The distortion intensity for ring i is defined as (4) where PAVi is the area-weighted average total pressure of ring i and PAVLOWi is the area-weighted average of the total pressure lower than PAVi. DC60 [25] is defined as (5) where PTavg is the mean total pressure at the AIP, PT60 is the mean total pressure on a 60° sector that has the lowest mean recovery, and qavg is the mean dynamic pressure calculated by (6) where

is the area-weighted average static pressure at the AIP. According to the SAE standard [7], a 40-probe rakes system is adopted having eight arms uniformly distributed

in the circumferential direction and five total-pressure probes on each arm in the radial direction. Since a much denser

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distribution of data is available from computed results, we employ 120 probes to provide a more precise description of distortion. These locations are defined by rotating the 40-probe rake by 15 and 30 degrees. In other words, two additional rakes of 10 probes are inserted between two neighboring rakes defined by the SAE standard.

E. Sensitivity Analysis Sensitivity analysis is one of the most important components to a gradient-based design optimization. The adjoint methods [26--30] allow an efficient calculation of gradients of an objective function, for a computational cost independent of the number of design variables. The present study adopts a discrete unstructured Navier-Strokes adjoint solver [29, 30] developed from the flow solver described above in Section III.A. The GMRES method [31] is iteratively used in the adjoint solver together with the LU-SGS procedure as a preconditioner. Parallel processing is also employed using domain decomposition of the computational mesh and MPI.

F. Geometry Parameterization NURBS (Non-Uniform Rational B-Spline) [32] is an industry standard for free-form shape representation in CAD. With the kth order surface representation, Ck-2 continuity is guaranteed. A NURBS surface with coordinates (x,y,z) can be represented in terms of basis functions and control points as

(7) where u and v are the parametric coordinates, Qi,j is the coordinate vector of a control point, Ni,k and Nj,l are blended basis functions of orders k and l in the u and v directions, respectively, and i,j is the weight of the control points. (m +1) and (n +1) are the numbers of control points in u and v directions, respectively. In the present study, i,j is treated as a constant and set as 1.0 for equal weights for control points, and k = l = 4 for a 4th order surface representation. The basis function N is defined as follows: (8)

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,

(9)

where ti are the knot values. For example, the knots are clustered in the v coordinate near the cowl lip surface, as shown in Fig. 7(a), and evenly distributed in the u coordinate. Design surfaces in the three-dimensional physical space are transformed into a two-dimensional parametric rectangular u-v space. The fixed boundary parameterization is conducted with a spring model in which each edge of the surface mesh is replaced with a tension spring, which has the spring coefficient inversely proportional to the edge length. Then minimization of the total energy of springs for the design surfaces, after imposing proper boundary conditions for u and v at each mesh nodes, results in smoothly distributed design surface nodes in the u-v space as shown in Fig. 7. The design surface in the u-v space is perturbed in the normal direction by moving control points of NURBS, then in turn this modification is transformed back to provide corresponding changes in the physical space. Figure 7(a) shows the design surface parameterization of cowl surfaces. The number of design parameters for the two cowl surfaces is 80. In Fig. 7(b), parameterization of design surfaces for the bottom and side walls of diffusers are illustrated. Vertical struts dividing flow passages for three fans are not designed. However, as the bottom surface is modified, the struts are deformed accordingly. The number of design parameters for the diffuser surfaces is also set to 80. For the cowl lip shape modification, the nacelle surfaces are deformed by a spring analogy and constrained to be sliding along the upper wing surface. All surface mesh patches under deformation are divided into two groups: primary and secondary deforming patches. The primary surface patches include cowl surfaces and the upper, bottom, and side walls of the diffuser; they are deformed by following the spring analogy, constrained with the cowl lip deformation as boundary conditions. Once the primary patches are deformed, the spring analogy is applied to the secondary patches, such as diffuser struts and the wing upper surface, in compliance with the deformation of primary patches. Since the wing upper surface shape is not altered, and the junction lines between the wing upper surface and nacelle is changed, the mesh points of the wing upper surface will be moved accordingly along the curved surface. This two-step deformation allows a smooth geometry modification especially around the surface junctions. Figure 8 shows an example of cowl lip shape modification. The height and width of the cowl lip are used as design parameters, resulting in

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four additional design parameters (two for each inlet) to the design variable set. The total number of design parameters is 164 (80 for cowl surfaces, 80 for diffuser surfaces and 4 for cowl lips). When the surface mesh is perturbed, volume mesh points are also moved, also according to the spring analogy, instead of a complete remeshing. Hence, the computational cost incurred for the grid modification is negligible.

.G. Overall Design Procedure Figure 9 illustrates the overall design procedure. First, a flow analysis is conducted for the current design configuration. Then an adjoint sensitivity analysis is performed based on the flow analysis results to determine a search direction. A step size along the search direction is selected by a line search method with the slope along the search direction. In the present study, a quadratic polynomial fitting is used for the line search. Then design variables are updated using the gradient information and step size. Design surfaces are then modified using the aforementioned design parameterization, and volume meshes are modified accordingly using the spring analogy. This loop is repeated until the design converges. For a gradient-based optimizer of the present unconstrained minimization problem, the conjugate gradient method [33] is employed.

IV. Flow Simulation Results

The integrated airframe-nacelle configuration shows very complex flow features. Figure 10 (a) displays envelops of separation bubbles delineated by a negative u velocity component. Many separation bubbles are present around the nacelle: inside of inlet diffusers, on the cowl surfaces, and nacelle base regions. In all the color contours presented in this paper, the static and total pressure values are normalized by the frees-tream static and total pressures, respectively. Streamlines flowing into the engine faces are visualized in Fig. 10 (b), showing local yaw angles relative to the outboard inlet, resulting from the sweep of the wing-body configuration. This yaw angle to the inlet axis, also observed

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in Ref. [34], explains the asymmetric shape of the separation bubble on the cowl surface of the outboard inlet , as seen in Fig. 10 (a).The upper surface pressure contours for the N2B and clean wing HWB, which does not have any engine installed, are compared in Fig.11. The installation of embedded engine nacelles on the upper surface causes higher pressure in front of the inlets because of the pre-compression resulting from flow deceleration in the presence of nacelles. The lift coefficients CL of the clean HWB and N2B are 0.237 and 0.167, respectively, at the flow condition. In Ref. [34 ], CL of BLI configurations at a constant angle of attack (AOA) increased compared to a strut-mounted configuration because the precompression is more than compensated by the accelerated low pressure flow region on the cowl surface. In the N2B case this compensation does not happen or is too weak, because of the massive flow separation on the outer inlet cowl. Distributions of pressure coefficients at selected wing sections are displayed in Fig. 12. The y = 0.01 section shows N2B has an accelerated flow terminated with a strong shock wave on the cowl upper surface. The higher pressure in front of the inlet entrance is also evident in Figs. 12(a) and 12(c). Higher pressure on the upper wing surface is propagated to outboard sections such as y = 0.3 and y = 0.5 (Figs. 12(d) and (e)). The ingested boundary layer can be visualized by total pressure contours at the center section of each inlet, as shown in Fig. 13. The center inlet has a thicker boundary layer ingested into the diffuser than the side inlet, because of the longer distance form the airframe leading edge to the inlet entrance. Mach contours in Fig. 13 also show flow separation patterns on the upper surface of the nacelle. It is noted that there is a big difference in surface slopes in front of the offset inlet between the the center and outer inlets. In the symmetry plane of the center inlet, the upper wing surface at the inlet entrance is well aligned with the cowl surface. On the other hand, in the center plane of the outer inlet, the cowl leading edge has a large incidence angle to the incoming flow along the upper surface. This large AOA at the cowl lip causes a leading-edge separation on the cowl surface of the outer inlet. This difference in angles of attack of the center and outer inlets is a combined result of spanwise and streamwise variations of the wingbody geometry, together with their installed locations. To accommodate the geometrical variations and locations, care must be taken to ensure that the cowl lip angles of embedded engine nacelles align with local inflow directions, in order to reduce

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adverse effects. The boundary layer edges (defined as the location where the local total pressure is at 99% of the freestream value), of the N2B and clean wing configurations are compared in Fig. 14, showing a significant difference in both configurations, primarily resulting from the embedded engine. Boundary layer profiles obtained from CFD simulations of a clean wing configuration have been used for sizing the inlet capture area of BLI offset inlets and estimating the pressure recovery at fan faces of embedded engines [3, 35]. As seen in Fig. 14, as the flow on the upper surface of N2B approaches to the inlet, the boundary layer thickens more than the clean wing, because of the adverse pressure gradient developed in front of the inlet. Table 2 gives a quantitative comparison of the boundary layer thicknesses, which shows that the N2B has thicker boundary layers than the clean wing at inlet throat locations and the thickness increment gets larger for a thicker bounday layer. Longitudinal and cross-sectional views of total pressure contours in both center and outer inlets are shown in Fig. 15, clearly displaying differences in the thickness of ingested boundary layers in them. Also, it can be noted that at the entrance of the side inlet (x = 0.718), the boundary layer thickness has significant variations in the spanwise direction, becoming increasingly severe towards the AIP. A minimum recovery occurs at the corner between bottom and side walls in the diffuser. Compared in Fig. 16 are recoveries of the side inlet obtained for clean wing [3] and the present N2B analysis. AIP1 is the outermost fan face from the center fan face AIP5, also denoted in the bottom of Fig. 15. As mentioned in Section IIB, the recoveries estimated in Ref. [3] are based on clean wing analyses and used as input values to conceptual design of the engine. A single-valued recovery, of 0.9671 in this case, was obtained for both the side passages (AIP1 and AIP3) of the outer inlet from the clean wing results, using a mass-weighted averaging of the bypass and core recoveries at the design BPR of 3.1. The recoveries estimated on the basis of the clean wing results are in good agreement with the present N2B analysis for the outer inlet, although a much closer match occurs for AIP2. Clean wing results for recoveries of the center inlet are not available in Ref. [3]. For the present N2B simulations, the recoveries for the center inlet (AIP4 and AIP5) are about a couple of percent lower than the side inlet recoveries, resulting from a

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thicker boundary layer approaching the center inlet. Next, attention is turned to flow distortion described by two indicators, DPCPavg and DC60. The values of indicators for the five fan faces are presented in Fig. 17. It is noted that DPCPavg and DC60 have the smallest value in AIP2 because of a thinner onset boundary layer and lack of side wall effects. Also, AIP4 has a much larger DPCPavg value than AIP5 because of the side wall boundary layer. DC60 has a different trend for AIP4 and AIP5 from the DPCPavg. In Fig. 18, local Mach number contours in the symmetry plane are shown around the nozzle flow, which is choked at the throat. Under the nozzle, a sizable separation zone exists with very low local Mach number. The separated base region is expected to significantly increase the drag force. This suggests that care must be taken when installing an engine nacelle, requiring a reduction in the area of the base region for a better aerodynamic performance of the HWB. Separation bubbles in the base region will also be depicted in Fig. 19.

V. Optimal Inlet Shape Design

The optimal shape design in this study is conducted in two separate steps: the first step is a drag minimization to improve flow characteristics of the integrated airframe-nacelle by reducing flow separations and shock wave strengths and the second step is a distortion minimization taking the result of the first step as a starting point. Hereafter, the results of the drag minimization and distortion minimization will be referred to as Design 1 and Design 2, respectively. As an alternative to the sequential two-step design process, the two designs could have been combined into a single design, for instance, by using a weighted sum of the design objectives. The reason of adopting the two-step approach instead of the combined approach is that the amount of aerodynamic performance improvement by reducing the drag and increasing the lift is expected to be much larger by orders of magnitude than that by the distortion minimization. In other words, the design objective 1 is expected to have dominating impacts on the overall

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aerodynamic performance of the HWB configuration compared to the design objective 2. Design 2 can be meaningful when the outer cowl surfaces are well designed such that massive flow separations and strong shock waves are removed. In addition, Design 2 is expected to have negligible impacts on the drag force, which is verified later. Therefore, the sequential two-step approach is selected for the present design problems.

A. Design 1: Drag Minimization The design objective is to minimize the drag coefficient CD at a fixed AOA. The drag coefficient is calculated by surface integration of pressure and skin friction forces on wetted surfaces. The thrust coefficient appearing later in Eq. (8) is calculated by surface integration of pressure forces and momentum fluxes in the fan and engine exhaust planes. The objective function is defined as follows: ,

(6)

where the second term in the right-hand side is a penalty term that prevents the design from reducing the drag by simply reducing the lift force. The

term can be calculated by a sensitivity analysis or a finite differencing by a

perturbation of AOAs. A simple approximate way is to use the quadratic relation between CL and CD as follows [36]. , from which

=2K

, where

(7)

. By including the second term, minimization of F can be achieved

with a combination of reducing CD and increasing CL. As the design optimization process to minimize the drag force will impact the total pressure recovery at AIP, the engine performance will in turn be affected. Therefore, the effects of recovery on the engine thrust force should be included in the objective function because reduction in thrust can be considered equivalent to an increase of the drag. To accomplish this, the objective function is modified as follows: , where NAIP is the number of AIPs of the configuration and

i is the total pressure recovery at fan face i. CT in Eq.

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(8) (8) is

the engine thrust coefficient, which is nondimensionalized by the free-stream dynamic pressure and reference area in the same way as the lift and drag coefficients. The

terms are calculated using the NPSS engine model by a

finite difference approximation. At the design flow condition with full powered engines,

=0.60×10-2 for the

central AIP and 0.39×10-2 for the side AIPs of the tri-fan engine, which means a 1% change in recovery at an AIP results in roughly a half (0.39~0.60) count variation in thrust force. The cowl surfaces and diffuser surfaces are designed with 164 parameters: 80 for outer cowl surfaces, 80 for diffuser surfaces, and 4 for cowl lip shape deformation. For Design 1, variation ranges of the design variables are not explicitly specified. To avoid non-realistically oscillatory surfaces being created by using many number of design variables, a smoothing process of the objective function gradient vector was applied. By conducting Design 1, CD was reduced by 45 counts, and CL was increased from 0.167 to 0.193, which is still lower than the clean wing CL of 0.237. Further increase in CL can be expected if the whole topology of the engine nacelle including the base region is changed in the shape design. Figure 19 compares separation bubbles and surface oil flows of the initial and Design 1 configurations. Most separation bubbles are removed on the cowl surfaces by Design 1. But a new separation bubble appears on the right hand side of side nacelle of Design 1, due to an increased yaw angle in the incoming flow. Side views of the separation bubbles in Fig. 19 (b) clearly show the change of separation bubble patterns before and after the design. Local Mach number contours are compared for the initial and Design 1 configurations in Fig. 20. The design shape has a larger cowl lip radius and thicker cowl than the initial shape. In the symmetric plane, flow is less accelerated along the cowl leading edge on the upper surface, and the shock strength is much weakened on the cowl. In the center plane of the side inlet, the separation bubble is eliminated and flow is more accelerated on the cowl surface as the local flow angle is more aligned with the cowl design. The cowl section shapes are directly compared in Fig. 21 for two constant-y sections. Distributions of pressure coefficients Cp at selected constant-y sections are shown in Fig. 22. The surface pressure distributions show all the flow features of the design configuration such as reduced shock strengths and lower overall

18

pressure on the cowl surfaces. Also, the steeper and higher flow acceleration on the lower surfaces of the cowl lip is the result of increased cowl lip radius and decreased local flow incidence angles. Total pressure contours of the initial N2B and Design 1 at fan faces are compared in Fig. 23, showing little difference between them.

B. Design 2: Distortion Minimization The result of the drag minimization is used as a baseline configuration for the distortion minimization at the same design condition as in the flow simulation and the drag minimization. The design objective is to minimize the sum of values of the circumferential distortion indicator DPCPavg for the three AIP’s of the side inlet (AIP1,2, and 3); the amount of geometric variation is restricted to be less than 10% of fan diameter. The design problem is mathematically stated as follows: Min Subject to

(9) < 10% of fan diameter

The design parameters are the perturbations of control points on the diffuser surfaces. The total number of design parameters is 52 for the side inlet only, and the center inlet is not changed in the current design case. Figure 24 compares diffuser surface shapes between Design 1 and Design 2. In Design 2, the side walls have become more curved and the bottom surfaces also got wavier than in the Design 1. A comparison of total pressure contours in Design 1 and Design 2 is depicted in Fig. 25. Noticeably, the low recovery region in AIP1 is smeared out and broken into two distinct regions in Design 2; the values of the lowest recovery get significantly increased as well. In the passage of AIP 3, the concentration of low recovery is lessened, especially in section x = 0.740. Figure 26 compares distortion indicators of the initial, Design 1, and Design 2 configurations. Although Design 1 has reduced the drag force remarkably, it has also increased distortion expressed in terms of both indicators. Through distortion minimization, the objective function, the sum of DPCPavg in AIP1, 2, and 3 together is reduced by 12.5%

19

compared with Design 1. The most improvement comes from AIP1, where DPCPavg is reduced by 23.9 %. DC60 shows a slightly different trend. DC60 is reduced in AIP1 and AIP2, but is increased in AIP3 of Design 2. AIP4 and AIP5 have no changes in distortion indicators by Design 2 because the distortion design is limited to the side inlet. Meanwhile, Design 2 causes very small drag increment, which was about 0.3 counts. As of now, however, it is very hard to make a quantitative comparison of a distortion reduction and drag increment. The trade-off study could be conducted as a future work when a quantitative relation between the fan face distortion and fan performance degradation is available. As shown in Fig. 27, Design 1resulted in slightly reduced recovery values from the initial N2B configuration for all the five AIPs, although it is very hard to tell from seeing the total pressure contours at AIPs in Fig. 21. And by Design 2, the recovery is reduced in AIP1, slightly increased in AIP2, and not changed in AIP3. AIP4 and AIP5 should have no changes because the center inlet is not modified by Design 2. Figure 28 compares the lift coefficients of the clean wing, initial N2B, Design 1 and design 2 configurations. As mentioned earlier, the initial N2B gives rise to a much lower lift force than the clean wing at the same AOA, and Design 1 has recovered a significant portion of the lost lift force by drag minimization. The lift of Design 2, which focuses on improving internal flow behavior, shows little difference from that of Design 1, as expected.

VI. Concluding Remarks High-fidelity flow simulations were conducted for the N2B hybrid wing-body configuration with a focus on the effects of aerodynamic performance by airframe-propulsion integration. Thermodynamic cycles of turbofan engines proposed for the N2B aircraft were represented by the NPSS engine models. The CFD results revealed complex flow characteristics resulting from the tightly integrated airframe-propulsion system, which are very hard to estimate accurately a priori; the results are a considerable departure from that of a clean wing without embedded engines. The simulation results show that strong shock waves and flow separations occurred on the cowl surface. The

20

pre-compression in front of the embedded engine inlet and the poor performance of the inlet cowl caused a lift deficit, significantly affecting the aircraft performance. Effects of local inflow angle, such as side angle or incidence angle to the inlet cowl, were significant and should be considered in a detailed shape design of the integrated airframe-propulsion system. The present flow simulation results on the hybrid wing-body configuration provide, to the authors’ knowledge, the first-ever detailed quantitative information about the N2B aircraft and other HWB configurations when embedded engines are considered. The present study also established an adjoint-based optimal shape design system for a BLI inlet in a HWB vehicle; the design system consists of utilizing NURBS patches for surface perturbations, a spring analogy for more drastic design changes like cowl lip shape variations, and efficient mesh modification. The current design system can be applied with various combinations of design parameters insofar as the amount of design change is relatively small and topology of surface patches is not changed. Otherwise, component-based Boolean operations followed by a re-generation of surface and volume meshes would be required. Shape optimization of the inlet of the N2B configuration was conducted in two steps. The first step was a drag minimization by reshaping the cowl surfaces, resulting in remarkably reduced shock wave strengths and flow separations. The second step was a distortion minimization at fan faces by modifying diffuser wall surfaces. The objective function, which is the sum of distortion index values DPCP, was reduced by 12.5% from that of an initial configuration. Future work will include varying densities of design parameters at various locations of design surfaces in the distortion minimization design.

Acknowledgements The authors are grateful for the support by the NASA’s Subsonic Fixed Wing Project of the Fundamental Aeronautics Program.

References

21

[1] Liebeck, R. H., “Design of the Blended Wing body Subsonic Transport,” Journal of Aircraft, Vol. 41, No. 1, 2004, pp.10-24. [2] NASA Research and Technology Program and Project Management Requirements, NASA Procedural Requirements 7120.9. Appendix J. Technology Readiness Levels (TRLs), February 05, 2008. [3] Kawai, R. and Brown, D., “Acoustic Prediction Methodology and Test Validation for an Efficient Low-Noise Hybrid Wing-body Subsonic Transport,” Phase I Final Report PWDM08-006A, NASA Contract Number NNL07AA54C, October, 2008. [4] Hileman, J. I, Spakovszky, Z. S., Drela, M., Sargeant, M. A., Jones, A., “Airframe Design for Silent Fuel-Efficient Aircraft,” Journal of Aircraft, vol.47, No.3, May-June 2010, pp. 956-969. See also AIAA Paper 2007-453, January 2007. [5] de la Rosa Blanca, E., Hall, C. A., and Crichton, D., “Challenges in the Silent Aircraft Engine Design,” AIAA Paper 2007-454, January 2007. [6] Allan, B. G., Owens, L. R., and Lin, J. C., "Optimal Design of Passive Flow Control for a Boundary-Layer-Ingesting Offset Inlet Using Design-of-Experiments," AIAA Paper 2006-1049, January 2006. [7] Gas Turbine Engine Inlet Flow Distortion, Society of Automotive Engineers, Rept. ARP-1420, March 1978. [8] Lee, B. J., Liou, M.-S., and Kim, C., "Optimizing a Boundary-Layer-Ingesting Offset Inlet by Discrete Adjoint Approach," AIAA Journal, Vol. 48, No.9, 2010, pp. 2008-2016. [9] Carter, M. B., Campbell, R. L., Pendergraft, O. C. Jr., Friedman, D. M., and Serrano, L. “Designing and Testing a Blended Wing-body with Boundary-Layer Ingestion Nacelles,” Journal of Aircraft, Vol. 43, No.5, 2006, pp. 1479-1489. [10] Rodriguez, D. L. "Multidisciplinary Optimization Method for Designing Boundary Layer Ingestion Inlets," Journal of Aircraft, Vol. 46, No.3, 2009, pp. 883-894. [11] Tong, M., Jones, S. M., Haller, W. J., and Handschuh, R. F., “Engine Conceptual Design Studies for a Hybrid Wing-body Aircraft," NASA/TM-2009-215680, November 2009. Appears also in Turbo Expo 2009, ASME, Orlando, FL, June 8-12, 2009. [12] “Numerical Propulsion System Simulation User Guide and Reference,” NASA-Industry Cooperative Effort, Software Release NPSS 1.5.0, May 7, 2002. [13] Litle, J. K., “Numerical Propulsion System Simulation: An Overview,” NASA/TM-2000-209915, NASA Glenn Research Center, Cleveland, OH, 2000.

22

[14] Kim, H., Kumano, T., Liou, M.-S., Povinelli, L. A., and Conners, T., “Numerical Propulsion Flow Simulation of Supersonic Inlet with Bypass Annular Duct,” Journal of Propulsion and Power, Vol.27, No.1, 2011. pp. 29-39. [15] Obayashi, S. and Guruswamy, G. P., “Convergence Acceleration of a Navier-Stokes Solver for Efficient Static Aeroelastic Computations,” AIAA Journal, Vol.33, No.6, 1995, pp. 1134-1141. [16] Liou, M.-S., “A sequel to AUSM, Part II: AUSM+-up for all speeds,” Journal of Computational Physics, Vol. 214, issue 1, 2006, pp.137-170. [17] Menter, F.R, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, Vol.32, No.8, 1994, pp.1598-1605. [18] Spalart, P. R. and Rumsey, C., “Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations,” AIAA Journal, Vol.45, No.10, 2007, pp. 2544-2553. [19] Sharov, D. and Nakahashi, K. “Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss-Seidel Computations,” AIAA Journal, Vol.36, No.3, 1998, pp.484–486. [20] Ito, Y. and Nakahashi, K., "Direct Surface Triangulation Using Stereolithography Data," AIAA Journal, Vol. 40, No. 3, 2002, pp. 490–496. [21] Ito, Y., Shih, A. M., Soni, B. K. and Nakahashi, K., "Multiple Marching Direction Approach to Generate High Quality Hybrid Meshes," AIAA Journal, Vol. 45, No. 1, 2007, pp. 162–167. [22] O’Brien, D. M. Jr., Calvert, M. E., Butler, S. L. “An Examination of Engine Effects on Helicopter Aeromechanics,” AHS Specialist’s Conference on Aeromechanics, San Francisco, CA, Jan. 23-25, 2008. [23] Hsiao, E., Naimi, M., Lewis, J. P., Dalbey, K., Gong, Y., Tan, C., “Actuator Duct Model of Turbomachinery Components for Powered-Nacelle Navier-Stokes Calculations,” Journal of Propulsion and Power, Vol.17, No.4, 2001, pp. 919-927. [24] Chima, R.V., “Rapid Calculations of Three-Dimensional Inlet/Fan Interaction,” NASA Fundamental Aeronautics 2007 Annual Meeting, Oct. 30 - Nov. 1, 2007, New Orleans, LA. [25] Hercock, R.G. and Williams, D. D., “Aerodynamic Response,” Paper 3, AGARD Lecture Series 72, 1974. [26] Jameson, A., “Aerodynamic Shape Optimization Using the Adjoint Method,” Lecture series, Von Karman Institute for Fluid

23

Dynamics, Feb. 2003. [27] Nielson, E. J., and Anderson, W. K., “Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations,” AIAA Journal, Vol.37, No. 11, 1999, pp. 1411-1419. [28] Mavriplis, D. J. “A Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes,” AIAA Journal, Vol. 45, No. 4, 2007, pp. 740-750. [29] Kim, H., Sasaki, D., Obayashi, S., and Nakahashi, K., "Aerodynamic Optimization of Supersonic Transport Wing Using Unstructured Adjoint Method," AIAA Journal, Vol. 39, No. 6, 2001, pp. 1011-1020. [30] Kim, H. and Nakahashi, K., “Unstructured Adjoint Method for Navier-Stokes Equations,” JSME International Journal Series B, Vol. 48, No.2, 2005, pp. 202-207. [31] Saad, Y. and Schultz, M. H., "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems", SIAM Journal on Scientific and Statistical Computing, Vol. 7, 1986, pp. 856-869. [32] Lepine, J., Guibault, F., Trepanier, J.-Y., Pepini, F., “Optimizaed Nonuniform Rational B-Spline Geometrical Representation for Aerodynamic Design of Wings, " AIAA Journal, Vol. 39, No.11, 2001, pp. 2033-2041. [33] Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design: With Applications, McGraw Hill, New York, 1984, pp. 88-89. [34] Kawai, R. T., Friedman, D. M., and Serrano, L. “Blended Wing-body (BWB) Boundary Layer Ingestion (BLI) Inlet Configuration and System Studies,” NASA CR-2006-214534, December 2006. [35] Felder, J. L., Kim, H. D., Brown, G. V., and Chu, J. “An Examination of the Effects of Blundary Layer Ingestion on Turboelectric Distributed Propulsion Systems,” AIAA 2011-0300, 49th AIAA Aerospace Science Meeting, January 2011, Orlando, FL. [36] Takenaka, K., Hatanaka K. and Nakahashi, K., "Efficient Aerodynamic Design of Complex Configurations by Patch-Surface Approach," Journal of Aircraft, Vol. 48, No.5, 2011, pp. 1473-1481. [37] Owens, L. R., Allan, B. G., and Gorton, S. A., " Boundary-Layer-Ingesting Inlet Flow Control," Journal of Aircraft, Vol. 45, No.4, 2008, pp. 1431-1440.

24

[38] Allan, B. G. and Owens, L. R., "Numerical Modeling of Flow Control in a Boundary-Layer-Ingesting Offset Inlet Diffuser at Transonic Mach Numbers," AIAA 2006-0845, 44th AIAA Aerospace Science Meeting, January 2006, Reno, NV. [39] Johnson, B. C., Webster, R. S., and Sreenivas, K., "A Numerical Investigation of S-Duct Flows with Boundary-Layer Ingestion," AIAA 2010-0841, 48th AIAA Aerospace Science Meeting, January 2006, Orlando, FL.

APPENDIX: Validation of the Flow Solver for a Boundary Ingestion Offset Inlet Diffuser

For validation of the flow solver on configurations including BLI offset inlets, flow simulations are conducted for a flush-mounted offset inlet shown in Fig. A1, and the results are compared to the experimental data obtained by Owens et al. [37] in NASA Langley’s 0.3-Meter Transonic Cryogenic Tunnel, in which the inlet was flush mounted on the tunnel sidewall. Computational mesh for the BLI offset inlet is shown in Fig. A2. Outer boundaries are composed of inflow, side, top, and outlflow planes. The outer boundaries are set as free-stream boundary conditions. The side, top, and outflow planes respectively are 50 inches away from the inlet throat centroid. The viscous flat plate length ahead of the inlet is adjusted to match the experimental bondary layer thickness at the inlet. The total number of mesh points is about 10 million, and the first nodes off the viscous walls are clustered to the wall so that a maximum y+ value is less than 2. To ensure the numerical simulations are conducted at the same flow condition as in the wind tunnel testing of the BLI offset inlet, several parameters need to be matched: the free-stream Mach number, the Reynolds number, the boundary layer profile at the inlet, and the inlet mass flow rate. As mentioned earlier, the height of boundary layer is matched at a measurement location by adjusting the flat plate length ahead of the inlet. The inlet mass flow rate is controlled by varying a static back pressure at the AIP. The free-stream Mach number is 0.85 and the Reynolds number based on AIP diameter, ReD = 3.8×106, consistent with the experimental flow conditions in Ref. 17. Free-stream boundary conditions for turbulence valriables are set as

,

recommendations given in Ref. [18].

25

following

Because the flow field has an adverse pressure gradient as the flat plate boundary layer flow approaches the inlet entrance, just matching the boundary layer height does not necessarily mean the same boundary layer is ingested into the inlet. The amount of adverse pressure gradient due to the local flow conditions in the test section of the wind tunnel would affect more the detailed shape of the boundary layer profile ahead of the inlet. Figure A3 shows velocity profiles by the present numerical simulations and experimental results at the boundary layer rake location. The computaional velocity profile in a solid line has slightly higher verlocity in the bottom part of the boundary layer, which is consistent with other CFD analysis results in Ref. [38]. Lee et al. [9] compared boundary layer velocity profiles for ReD = 2.2×106 and 3.8×106; they found the lower Reynolds number (ReD = 2.2×106) gives a closer velocity profile to the experimental profile than the higher one and a better comparison of pressure distributions with the experimental data. Thus, it is conjectured that there is a direct correlation between the incoming boundary layer profile and the pressure distributions developed inside the duct. CFD simulations for the BLI offset inlet test case in literature often uses a lower Reynolds number than the experimental Reynolds number ReD = 3.8×106 to match the boundary layer velocity profile more closely to the experimental data (e.g., ReD = 2.2×106 in Ref. [38]). However, the use of a lower Reynolds number also results in significantly lower total pressure recoveries at AIP [9, 38]. In this study, instead of changing the Reynolds number, the static back pressure of the outflow boundary plane is adjusted to match the computational and experimental velocity profiles in the boundary layer as closely as possible. In the case of back pressure adjustment, the side and top boundary surfaces are treated as inviscid walls. Figure A3 confirms that a close agreement of the velocity profile can be obtained by adjusting the back pressure in the flow exterior to the nacelle while keeping the Reynolds number and Mach number in the experiment. It is reminded that the exterior outflow plane and AIP have different pressure settings. Figure A4 compares the inlet centerline pressures from the experimental and present CFD results. The CFD results include two sets of data without and with the back pressure adjustment for boundary layer profile matching, respectively denoted as CFD-1 and CFD-2 results. The pressure distribution without the back pressure correction deviates upward from the experimental data. Meanwhile the pressure with the back pressure adjustment gives a very

26

good agreement with the data for both upper and lower surfaces inside the inlet. The inlet mass flow rate was represented by the area ratio A0/Ac where A0 is the area in the free-stream flow that corresponds to the mass flow rate fed into the inlet: (A1) The inlet capture area, Ac, is defined by the inlet section area at the cowl highlight. As for an indicator for flow distortion at AIP, the SAE circumferential distortion descriptor, DPCPavg [8] is used to compare with results of experimental and other numerical studies in the literature. The inlet performance parameters obtained by the present flow simulations are compared with the experimental data in Table A1. The present results agree well with the experimental and other CFD results. Finally, contours of the local total pressure normalized by the free-stream value are compared for experimental and other CFD results. The present results are calculating the location of the minimum total pressure region slightly higher than other results. Other than that, the overall trend is well simulated by the present CFD code.

27

(a) SAX-40.

(b) N2A with podded engines.

(c) N2B with embedded engines. Fig. 1 HWB aircraft configurations [3].

(a) Tri-fan + core engine.

(b) Core engine + variable area thrust vectoring nozzle. Fig. 2. Multiple fan embedded turbofan engine for N2B [3].

(a) Replacement of the engine with an NPSS model.

Pressure recovery at AIP Flow Solver

NPSS model

AIP and engine exit boundary conditions (c) Coupling of the flow solver and the NPSS model. Fig. 3 Representation of the propulsion system by an NPSS model and its coupling with the CFD solution.

1.6

1.488

TPR1 1  1%

1.4

Sensitivity (%)

1.2 1.0

0.8 0.6 0.4

0.2

0.029

Pt_exit1

Tt_exit1

(a) When 1.2

Sensitivity (%)

Pt_exit2

Tt_exit2

is varied by 1% point.

TPR2 2  1%

1.0

0.000

0.000

0.0

1.112

0.8 0.6 0.4 0.2 0.091

0.008

0.0

Pt_exit1

0.000

Tt_exit1

(b) When

Pt_exit2

Tt_exit2

is varied by 1% point.

Fig. 4 Sensitivity of engine parameters with respect to changes in recovery at fan faces.

7.6 7.4

y = 9.8500x - 2.2620 R² = 1.0000

7.2

Pt_exit2,3 y = 7.8250x + 0.0047 R² = 1.0000

7.6

Pt_exit1 [psi]

Pt_exit1 [psi]

7.8

Pt_exit1

7 6.8

7.4

7.2 6.6

6.4 0.88

7 0.9

0.92

0.94 Recovery 1

0.96

0.98

1

0.88

0.9

0.92

0.94

0.96

0.98

1

Recovery 2,3

Fig. 5 Response surfaces for the NPSS engine model at the TOC maximum power condition with Mach 0.8 at 35,000 ft.

(a) Surface mesh for the symmetric half model.

(b) Near the nozzles. Fig. 6 Surface mesh for the N2B configuration.

Deformation by NURBS in u-v plane and mapped back to physical space

v

v

u

u

(a) Parameterization of cowl surfaces.

v

v

u

u

(b) Parameterization of diffuser bottom and side surfaces. Fig .7 u-v Parameterization of design surfaces.

(a) Initial shape. (Arrows represent sample deformations in cowl lip height and width)

(b) Modified shape with reduced height and increased width.

(c) Overlapped view of initial and modified cowl surfaces. Fig. 8 An example of cowl lip shape deformation by a spring analogy approach.

Flow Analysis Sensitivity Analysis Selection of Search Direction Selection of step size (Line search) Determine new dv’s Mesh modification Flow Analysis No

Converged ? Yes End

Fig. 9. Overall shape design procedure.

(a) Separation bubble envelops around the BLI inlet nacelle.

(b) Visualization of surface oil flows around the side nacelle.

(c) Streamlines into the engine faces. Fig. 10. Visualization of flow patterns around N2B. Color contours represent the normalized static pressure.

Fig. 11. Comparison of upper surface pressure contours of N2B and clean wing HWB at Mach 0.8, altitude 35,000 ft., and AOA 3.5deg. (left: clean wing, right: N2B).

(a) y = 0.01.

(c) y = 0.167.

(b) y = 0.083.

(d) y = 0.300.

(e) y = 0.500. (f) y = 0.700. Fig. 12 Comparison of sectional pressure distributions between clean wing and N2B at Mach 0.8, altitude 35,000 ft., and AOA 3.5 deg.

(a) Normalized total pressure and Mach contours at symmetric plane.

(b) Normalized total pressure and Mach contours in the center plane of outboard inlet. Fig. 13. Total pressure and Mach contours at inlet center sections.

N2B Clean wing

OML of N2B OML of clean wing

(a) Symmetric plane.

N2B Clean wing

OML of N2B

OML of clean wing

(b) Center plane of outboard inlet. Fig. 14 Comparison of boundary layer edge lines for N2B and clean wing configurations.

(a) Locations of streamwise section cuts. (Left: outer inlet, right: center inlet)

Outer inlet

Center inlet

X=0.718

X=0.777

X=0.740

AIP1

AIP2

X=0.800

AIP3

AIP4

AIP5

(b) Total pressure contours Fig. 15 Normalized total pressure contours inside diffusers for initial N2B configuration.

0.99

Recovery

0.98 0.97 0.96 0.95 0.94

0.93 0.92

AIP1

AIP2

AIP3

AIP4

AIP5

Present simulation

0.9650

0.9758

0.9644

0.9401

0.9553

Boeing estimation

0.9671

0.9751

0.9671

N/A

N/A

Fig. 16 Total pressure recovery at AIPs (fan faces). #1 denotes the outermost fan and #5 the center fan.

0.50

0.10

DPCPavg

DC60

0.46 0.424

0.09 0.42 0.08

0.38

0.0752

0.0749

0.362 0.344

0.357

0.34 0.07

0.0666

0.30 0.0574

0.06

0.22

0.0489

0.05

0.257

0.26

0.18 0.14

0.04 AIP1

AIP2

AIP3

AIP4

AIP5

AIP1

AIP2

AIP3

AIP4

Fig. 17 Distortion indicator values at AIPs.

Fig. 18. Mach contours near nozzle exhaust in the symmetric plane.

AIP5

(a) Front-top view of separation bubble envelops.

(b) Side view of separation bubble envelops.

(c) Top view of surface oil flows. Fig. 19 Comparison of flow patterns around initial (left) and Design 1 (right) configurations.

(a) Symmetric plane.

(b) Center plane of outer inlet. Fig. 20 Mach contours for initial (left) and design (right) configurations.

Fig. 21 Comparison of cowl shapes in two constant-y sections.

(a) y = 0.01.

(b) y = 0.167. Fig. 22 Comparison of section pressure distributions between initial N2B and design configuration at Mach 0.8, altitude 35,000 ft., and AOA 3.5deg. (The right figures are zoomed windows of the left ones.)

(a) Initial N2B.

(b) Design 1. Fig.23 Normalized total pressure contours at AIPs.

(a) Design 1 (flow is from up to down).

(b) Design 2 (flow is from up to down).

(c) Section view of the bottom surfaces. Gold is Design 1 and blue is Design 2. (flow is from right to left.) Fig. 24 Comparison of design shape change of diffuser bottom and side walls for the side inlet.

AIP1

X=0.718

X=0.718

X=0.740

X=0.740

AIP2

AIP3

AIP1

AIP2

AIP3

(a) Design 1. (b) Design 2. Fig. 25 Comparison of normalized total pressure contours inside the diffuser of the side inlet for Design 1 and Design 2 configurations.

0.09

0.46

DPCPavg

DC60

0.42

0.08

0.38 0.34

0.07

0.30 0.06

0.26 0.22

0.05

0.18 0.04

0.14

AIP1

AIP2

AIP3

AIP4

AIP5

AIP1

AIP2

AIP3

AIP4

AIP5

Initial

0.0749

0.0489

0.0666

0.0752

0.0574

Initial

0.424

0.257

0.362

0.344

0.357

Design1

0.0857

0.0532

0.0741

0.0773

0.0594

Design1

0.399

0.289

0.394

0.347

0.375

Design2

0.0654

0.0514

0.0706

0.0773

0.0594

Design2

0.311

0.283

0.415

0.347

0.375

Fig. 26 Comparison of distortion indicators at AIP.

0.99

Recovery

0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91

AIP1

AIP2

AIP3

AIP4

AIP5

Initial

0.9650

0.9758

0.9644

0.9401

0.9553

Design1

0.9628

0.9724

0.9624

0.9368

0.9523

Design2

0.9583

0.9726

0.9624

0.9368

0.9523

Fig. 27 Comparison of recoveries at AIP

0.35 Clean wing

0.30

CL

N2B

0.25

Design 1

0.20

Design 2

0.15 0.10 0.05

0.00 1.0 -0.05

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

AOA (deg)

Fig. 28 Comparison of lift coefficients at the TOC condition

(a) Side and front views.

(b) CAD surface representation.

Fig. A1 BLI offset inlet configuration: Inlet A model [38].

(a) Surface mesh for the computational domain.

(c) Zoomed view near the inlet entrance. Fig. A2 Computational mesh.

1.0

EXP CFD-1 (w/o back pressure adjustment) CFD-2 (with back pressure adjustment)

Normal distance from tunnel wall, in.

0.9

0.8 0.7 0.6 0.5

0.4 0.3 0.2

U/Ue=0.99

0.1

0.0 0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

U / Ue

Fig. A3 Comparison of boundary layer profiles. Exp: M∞=0.843, ReD=3.3×106, CFD: M∞=0.850, ReD=3.8×106. CFD-1: present simulation results without back pressure adjustment. CFD-2: present simulation results with back pressure adjustment.

1

Exp, Top Exp, Bottom

0.9

CFD-1, Top CFD-1, Bottom

0.8

CFD-2, Top CFD-2, Bottom

Cp

0.7

0.6

0.5

0.4

0.3 -6

-4

-2

0

2

4

x, inches (Tunnel Coordinates)

Fig. A4 Comparison of inlet centerline pressure on the top and bottom of the BLI inlet. M∞=0.85, ReD = 3.8×106, Experimental data: wall correction. (See Fig. A3 for definitions of CFD-1 and CFD-2.)

(a) Experiment (ReD =3.8M) [38].

(c) Present CFD-1 (ReD =3.8M).

(b) CFD (ReD =2.2M) [39].

(d) Present CFD-2 (ReD =3.8M).

Fig. A5 Comparison of total pressure contours at AIP (M ∞=0.85). (See Fig. A3 for definitions of CFD-1 and CFD-2.)