A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations

Peijian Lv; Defu Lin; Li Mo

doi:10.3390/app122010194

Lv, Peijian;Lin, Defu;Mo, Li

2022-10-11 00:00:00

applied sciences Article A Power Based Analysis for a Transonic Transport Aircraft Conﬁguration through 3D RANS Simulations Peijian Lv , Defu Lin and Li Mo * School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100811, China * Correspondence: levin_mott@163.com; Tel.: +86-13911436237 Abstract: This paper presents a power-based analysis through 3D Reynolds-averaged Navier–Stokes simulations for a typical transonic transport aircraft resented by the DLR-F6 model. Two conﬁgura- tions were employed in CFD simulations. The original F6 model geometry was deﬁned as the wing body conﬁguration, and a wake-ﬁlling actuator disc was added to the F6 model to establish the BLI conﬁguration. This study proposes a segregated 3D computational domain in RANS simulations to track the change in power terms in the ﬂow ﬁeld so that the power conversion process can be studied and visualized. For the wing body conﬁguration, the power-based analysis illustrated the power conversion process, showing that about 35% of the total power input remains in the form of the mechanical power of aircraft wake at the outlet plane. For the BLI conﬁguration, 22% of the total power input was left in the form of the mechanical power of downstream ﬂow mixed with the wake and jet at the outlet plane. This study elaborates on the error of the mechanical power imbalance, showing that the convergence in aircraft drag does not necessarily lead to a small error in 3D RANS simulations. The high value of power imbalance error is associated with the wing. Keywords: power-based analysis; power imbalance error; 3D RANS simulation Citation: Lv, P.; Lin, D.; Mo, L. A 1. Introduction Power Based Analysis for a Transonic Transport Aircraft Conﬁguration Boundary layer ingestion (BLI) has been studied as a promising technology that through 3D RANS Simulations. Appl. utilizes favorable airframe propulsion integration to reduce aircraft fuel consumption. Sci. 2022, 12, 10194. https://doi.org/ BLI has been adopted by novel aircraft concepts, such as Boeing blended wing body 10.3390/app122010194 aircraft [1], silent aircraft [2], MIT D8 aircraft [3,4], the “propulsive fuselage” concept [5], H2020 CENTERLINE aircraft [6], and NASA STARC-ABL aircraft [7,8]. The beneﬁts due Academic Editor: Rosario Pecora to BLI range from 3% to 10% for these aircraft concepts. The ﬂow mechanisms of power Received: 5 September 2022 saving due to BLI were recognized and explained by Betz [9] in the early days. The ﬂow Accepted: 7 October 2022 mechanisms of BLI have become clear since the introduction of power-based methods, Published: 11 October 2022 which enabled the quantitative study of the actual power consumptions of aircraft using BLI. Drela [10] introduced a power balance method to evaluate mechanical power in the Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in ﬂow ﬁeld, showing that the power consumption associated with the aircraft wake and published maps and institutional afﬁl- jet is eliminated by BLI, as shown in Figure 1. Arntz et al. [11,12] established an exergy- iations. based method to include thermal power in the study of BLI. Lv et al. [13,14] utilized a mechanical power analysis to show that a BLI propulsor utilizes the power of the ingested boundary layer ﬂow as input power and reduces the wasted power in the downstream ﬂow. These power-based methods are different from a traditional method that breaks down Copyright: © 2022 by the authors. the aerodynamic force imposed on aircraft surfaces [15]. Power-based methods evaluate Licensee MDPI, Basel, Switzerland. the power in the ﬂow ﬁeld around the aircraft so that the actual power consumption of the This article is an open access article aircraft is calculated without ambiguity [16]. distributed under the terms and Recent efforts were made to inspect the potential beneﬁts of BLI in detailed aircraft conditions of the Creative Commons design. Computational ﬂuid dynamics (CFD) simulation has been widely used as a tool Attribution (CC BY) license (https:// to design aircraft shapes. Power-based methods are adopted to access the power terms creativecommons.org/licenses/by/ in the ﬂow ﬁeld in the postprocessing of simulations. Elmiligui et al. [17] performed an 4.0/). Appl. Sci. 2022, 12, 10194. https://doi.org/10.3390/app122010194 https://www.mdpi.com/journal/applsci Appl. Sci. 2022, 12, x FOR PEER REVIEW 2 of 23 Recent efforts were made to inspect the potential benefits of BLI in detailed aircraft design. Computational fluid dynamics (CFD) simulation has been widely used as a tool Appl. Sci. 2022, 12, 10194 2 of 22 to design aircraft shapes. Power‐based methods are adopted to access the power terms in the flow field in the postprocessing of simulations. Elmiligui et al. [17] performed an analysis of axisymmetric fuselage–propulsor configurations to evaluate the power sav‐ analysis of axisymmetric fuselage–propulsor conﬁgurations to evaluate the power savings ings due to BLI. Sanders and Laskaridis [18] employed Reynolds‐averaged Navier– Stok due es to (RAN BLI.S) Sanders simulation and s to Laskaridis study the [pot 18]eemployed ntial benefit Reynolds-averaged of BLI with a 2D ax Navie isymmet r–Stokes ric fus (RANS) elage geo simulations metry. Bask toaran study etthe al. potential [19] performed beneﬁt 2D of BLI CFD with sim au2D lations axisymmetric to optimize fuselage the geometry. Baskaran et al. [19] performed 2D CFD simulations to optimize the shape of an shape of an axisymmetric fuselage using BLI in transonic flight conditions. Besides the axisymmetric fuselage using BLI in transonic ﬂight conditions. Besides the aforementioned aforementioned studies using 2D simulations, 3D flow simulations are employed in the studies using 2D simulations, 3D ﬂow simulations are employed in the study of BLI. study of BLI. Blumenthal et al. [20] presented a study to optimize fuselage geometry Blumenthal et al. [20] presented a study to optimize fuselage geometry based on a common based on a common 3D research model to evaluate the benefit of BLI. Kenway and Kiris 3D research model to evaluate the beneﬁt of BLI. Kenway and Kiris [21] addressed the [21] addressed the flow distortion issue of BLI by optimizing fuselage geometry through ﬂow distortion issue of BLI by optimizing fuselage geometry through 3D RANS simulation. 3D RANS simulation. Gray et al. [22] employed 3D RANS analysis to perform the opti‐ Gray et al. [22] employed 3D RANS analysis to perform the optimization of a coupled mization of a coupled aeropropulsive aircraft model with BLI. aeropropulsive aircraft model with BLI. Figure 1. Boundary layer ingestion beneﬁts of reducing the mechanical energy of the downstream Figure 1. Boundary layer ingestion benefits of reducing the mechanical energy of the downstream wake and jet (adapted from reference [3]). wake and jet (adapted from reference [3]). Previous works using power-based methods combined with CFD simulations were Previous works using power‐based methods combined with CFD simulations were based on a well-deﬁned control volume so that the power terms of the entire ﬂow ﬁeld could based on a well‐defined control volume so that the power terms of the entire flow field be evaluated [17–20]. Nevertheless, the simplicity of control volume was not capable of could be evaluated [17–20]. Nevertheless, the simplicity of control volume was not capa‐ studying the detailed process of power conversion in these previous works. This limitation ble of studying the detailed process of power conversion in these previous works. This prevents the investigation of how aircraft components inﬂuence the power conversion limitation prevents the investigation of how aircraft components influence the power process. This incapability suggests further development of power-based analysis. To deal conversion process. This incapability suggests further development of power‐based with this issue, this study introduces a segregated 3D computational domain aiming to trace analysis. To deal with this issue, this study introduces a segregated 3D computational the changing process of power terms in the ﬂow ﬁeld over a typical transonic transport domain aiming to trace the changing process of power terms in the flow field over a aircraft. With this improved power-based analysis, to the knowledge of the authors, this is typical transonic transport aircraft. With this improved power‐based analysis, to the the ﬁrst time that the detailed process of power conversion in a 3D simulated ﬂow ﬁeld knowledge of the authors, this is the first time that the detailed process of power con‐ over an aircraft has been examined and visualized. version in a 3D simulated flow field over an aircraft has been examined and visualized. Based on the aforementioned framework, this research makes efforts to examine the Based on the aforementioned framework, this research makes efforts to examine the power conversion process in the ﬂow ﬁeld over a transonic transport aircraft through power conversion process in the flow field over a transonic transport aircraft through 3D 3D compressible RANS simulations as an extension of the previous work of studying compressible RANS simulations as an extension of the previous work of studying power power conversion in 2D incompressible ﬂow ﬁelds [23]. The well-known DLR-F6 model conversion in 2D incompressible flow fields [23]. The well‐known DLR‐F6 model was was selected as the baseline conﬁguration to study the power conversion process in the selected as the baseline configuration to study the power conversion process in the flow ﬂow ﬁeld over a typical aircraft airframe [24–27]. The BLI conﬁguration was established field over a typical aircraft airframe [24–27]. The BLI configuration was established by by combining the F6 model with a tail-mounted wake-ﬁlling actuator disc model. This combining the F6 model with a tail‐mounted wake‐filling actuator disc model. This wake-ﬁlling actuator disc model mimics an ideal BLI propulsor to re-energize the ingested wake‐filling actuator disc model mimics an ideal BLI propulsor to re‐energize the in‐ boundary layer ﬂow into the state of free stream so that the mechanical energy of the gested boundary layer flow into the state of free stream so that the mechanical energy of downstream wake and jet is kept to a minimum. To evaluate how well mechanical con- the downstream wake and jet is kept to a minimum. To evaluate how well mechanical servation is satisﬁed in simulations, this study introduced a power imbalance error study. Possible impact factors inﬂuencing the power imbalance error were examined. The power conversion process of the baseline wing body conﬁguration and BLI conﬁguration were analyzed and are discussed. This study is organized as follows: Section 2 introduces the method of power-based analysis used in the 3D simulations and the segregated computational domain of aircraft. Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 23 conservation is satisfied in simulations, this study introduced a power imbalance error study. Possible impact factors influencing the power imbalance error were examined. The power conversion process of the baseline wing body configuration and BLI config‐ uration were analyzed and are discussed. This study is organized as follows: Section 2 introduces the method of power‐based analysis used in the 3D simulations and the segregated computational domain of air‐ Appl. Sci. 2022, 12, 10194 3 of 22 craft. Section 3 presents the simulation results, and the power imbalance error of 3D RANS simulations is analyzed. The power conversion process of the aircraft is presented and discussed. Conclusions are provided in Section 4. Section 3 presents the simulation results, and the power imbalance error of 3D RANS simulations is analyzed. The power conversion process of the aircraft is presented and 2. Methodology discussed. Conclusions are provided in Section 4. 2.1. Power‐Based Analysis in 3D RANS Simulations 2. Methodology Computational fluid dynamics simulations obtain the flow field so that the conti‐ 2.1. Power-Based Analysis in 3D RANS Simulations nuity, momentum, and energy equations are satisfied. On the other hand, the mechanical energy equation is different from the energy equation. The former is obtained by multi‐ Computational ﬂuid dynamics simulations obtain the ﬂow ﬁeld so that the continuity, plying momentum, the momeand ntum ener equation gy equati with ons ve arelosatisﬁed. city [28], On while the the other lathand, ter is re the late mechanical d to the first ener gy law equation of thermo isddif yna fer mi ent cs. frTh om e diagr the ener am gy in equation. Figure 2 il The lustrat former es the is re obtained lation bet bywmultiplying een the conservation the momentum s of mequation echanical with enervelocity gy (mechanic [28], while al enthe ergy latter /Navis ierr– elated Stokesto moment the ﬁrstum law of thermodynamics. The diagram in Figure 2 illustrates the relation between the conservations equation) and energy (Navier–Stokes energy equation). Power‐based analysis utilizes the integra of mechanical l form of the ener kigy netic (mechani energycal equa ener tion. gy/Navier As a re–Stokes sult, numeric momentum al simu equation) lations provide and ener gy (Navier–Stokes energy equation). Power-based analysis utilizes the integral form of the sufficient and necessary conditions for power‐based analysis due to the conservation of kinetic energy equation. As a result, numerical simulations provide sufﬁcient and necessary momentum. conditions for power-based analysis due to the conservation of momentum. Figure 2. The diagram of the conservation of mechanical energy and total energy [23]. Figure 2. The diagram of the conservation of mechanical energy and total energy [23]. In power-based analysis, the integral mechanical energy equation can be simpliﬁed as In power‐based analysis, the integral mechanical energy equation can be simplified Equation (1). This equation establishes the equilibrium of mechanical power by using three as Equation (1). This equation establishes the equilibrium of mechanical power by using terms, namely power inputs; outputs; and an error, e. The power inputs and outputs are three terms, namely power inputs; outputs; and an error, e. The power inputs and out‐ introduced in the following paragraphs. The error, e, is elaborated in detail in the section puts are introduced in the following paragraphs. The error, e, is elaborated in detail in the on power imbalance error. section on power imbalance error. P = P + e (1) in out P P 𝑒 (1) Figure 3 depicts a control volume of a simpliﬁed transport aircraft that is bounded by an inlet, an outlet, a cylindrical far-ﬁeld boundary, and the aircraft surface. A survey Figure 3 depicts a control volume of a simplified transport aircraft that is bounded plane is introduced as an internal plane perpendicular to the ﬂow direction. The aircraft by an inlet, an outlet, a cylindrical far‐field boundary, and the aircraft surface. A survey surface consists of a fuselage, wing, and propulsor. These aircraft components can be plane is introduced as an internal plane perpendicular to the flow direction. The aircraft categorized into two groups: the fuselage and wing are power-consuming components, while the propulsor is the power-adding component. The power terms associated with the aircraft components and control volume are listed in Table 1. For the entire control volume, the total power input is the summation of the wake energy inﬂow (rate), E ; drag power, w,in DV ; and shaft power (mechanical power addition), P , as expressed by Equation (2). The ¥ s total power output is the summation of the wake energy outﬂow (rate), E ; thrust power, w,out TV ; and viscous dissipation rate, F, as given in Equation (3). The individual power terms are elaborated in the following paragraphs. The power balance equation of the entire Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 of 23 surface consists of a fuselage, wing, and propulsor. These aircraft components can be categorized into two groups: the fuselage and wing are power‐consuming components, while the propulsor is the power‐adding component. The power terms associated with the aircraft components and control volume are listed in Table 1. For the entire control Appl. Sci. 2022, 12, 10194 4 of 22 volume, the total power input is the summation of the wake energy inflow (rate), Ew,in; drag power, DV∞; and shaft power (mechanical power addition), Ps, as expressed by Equation (2). The total power output is the summation of the wake energy outflow (rate), control volume can be established by combining these power terms and the error, e, as given Ew,out; in thru Equation st powe(1). r, TV∞; and viscous dissipation rate, Φ, as given in Equation (3). The individual power terms are elaborated ˙in the following paragraphs. The power balance P = E + DV P (2) in w,in ¥+ S equation of the entire control volume can be established by combining these power terms P = E + TV + F (3) out w,out ¥ and the error, e, as given in Equation (1). Figure 3. Control volume of a simplified aircraft with a BLI propulsor. Figure 3. Control volume of a simpliﬁed aircraft with a BLI propulsor. Table 1. Power terms in the control volume of an aircraft. Table 1. Power terms in the control volume of an aircraft. Control Volume Wing/Body Propulsor Control Volume Wing/Body Propulsor Input term DV∞ PS ˙ Ew,in Input term E DV PS w,in Output term E , F - TV w,out ¥ Output term ‐ TV∞ Ew,out, Φ The power term of the wake energy ﬂow rate, E , refers to the mechanical energy P E DV P (2) passing through a plane. For the inlet plane, it corresponds to the mechanical energy inﬂow, E . Its value is simply zero for the free stream incoming ﬂow, V , but it has a w,in P E TV Φ ¥ (3) ﬁnite value for a possible headwind or backwind entering the control volume. For the out The power term of the wake energy flow rate, Ew, refers to the mechanical energy plane, E , it is the mechanical energy of the aircraft wake and jet that ﬂows out of the w, out passing through a plane. For the inlet plane, it corresponds to the mechanical energy in‐ control volume. For an internal survey plane (SP), the surface integral of E evaluates the mechanical energy of the ﬂow through the plane. On the other hand, depending on the flow, Ew,in. Its value is simply zero for the free stream incoming flow, V∞, but it has a fi‐ ˙ ˙ physical property, E can be broken down into the kinetic energy ﬂow rate, KE , and the w w nite value for a possible headwind or backwind entering the control volume. For the out pressure power, E , as shown in Equation (4). The former refers to the kinetic energy of plane, Ew,out, it is the mechanical energy of the aircraft wake and jet that flows out of the the ﬂow, as given in Equation (5). The latter is the pressure work, which might transform ˙ ˙ control volume. For an internal survey plane (SP), the surface integral of Ew evaluates isentropically into KE , as expressed by Equation (6). It is noted that E is zero for the free w w the mechanical energy of the flow through the plane. On the other hand, depending on stream, and the magnitude of E is based on the state of the free stream ﬂow. For the entire ˙ ˙ control volume, the inﬂow and outﬂow terms (E and E ) are listed in Table 1. w, w,out in ˙ ˙ ˙ E = KE + E (4) w w p x x 1 1 2 2 ˙ ˙ ˙ KE = E + E = u (u V ) dS + u v + w dS (5) w a v ¥ 2 2 SP SP Appl. Sci. 2022, 12, 10194 5 of 22 E = (p p )(u V )dS (6) p ¥ SP The drag force, D, is exerted on the surface of the aircraft components of the body, wing, empennage, etc. Regarding the conversion of mechanical power, the drag power, DV , is the input power of an aircraft. It corresponds to the power of an ideal force dragging the aircraft in a ﬂow ﬁeld. This power is obtained by simply multiplying D by V . It is straightforward that the propulsive system converts shaft power, P , into thrust power, TV . Therefore, P is an input term, while thrust power, TV , is an output term. In ¥ s ¥ this study, P is the mechanical power addition that enters the control volume through the boundary of the propulsor surface. For a simpliﬁed propulsor of actuator disc model only changing the axial ﬂow, the expression of P is given in Equation (7). The output power term thrust power, TV , is obtained by multiplying thrust, T, by V . ¥ ¥ { { P = (p p ) udS = Dp udS (7) prop prop Viscous dissipation, F, is an output term of the control volume. F exists in the viscous region (boundary layer and wake) where the velocity gradient exists. This term uses the volume integral of a domain. The integrand of F contains nine components. According to the physical property, it can be broken down into laminar, turbulent, and bulk viscous dissipation, as expressed by Equation (8). The expressions of the three components are given in Equations (9)–(11). The turbulent viscosity, , is introduced to access the tur turbulent dissipation, F , by applying the Boussinesq assumption. It is noted that F is a tur sink term in the mechanical energy equation. F = F + F + F (8) tur lam bulk " # 2 2 2 ¶v ¶u ¶w ¶v ¶u ¶w F = + + + + + dV (9) lam lam ¶x ¶y ¶y ¶z ¶z ¶x CV " # y 2 2 2 ¶v ¶u ¶w ¶v ¶u ¶w F = + + + + + dV (10) tur tur ¶x ¶y ¶y ¶z ¶z ¶x CV " # 2 2 2 ¶u ¶v ¶w F = ( + ) 2 + 2 + 2 dV (11) bulk lam tur ¶x ¶y ¶z CV 2.2. Model Geometry and Flight Conditions This study employs the DLR-F6 model, which has been extensively studied through numerical simulations and wind tunnel experiments. The results of these studies have been documented in detail [24,25,27,29]. The DLR-F6 was selected in this study as a well- established reference to examine the power-based analysis in the 3D ﬂow ﬁeld. The original DLR-F6 geometry is called the wing body conﬁguration in the following discussions. This study establishes a BLI conﬁguration by adding an actuator disc model to the wing body conﬁguration, aiming to ingest the boundary layer ﬂow developed over the body surface. This actuator disc is 100 mm in diameter (67% of body diameter), located at the aft fuselage with the axial location of 1181 mm (0.99% of the body length), as shown in Figure 4. The speciﬁcations of the wing body conﬁguration and the BLI conﬁguration are listed in Table 2. For this DLR-F6 geometry, the test ﬂight condition was subsonic with the Mach number of 0.75, and the ﬂow conditions were kept the same as in the reference studies. The key parameters of the test conditions are listed in Table 3. Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 23 been documented in detail [24,25,27,29]. The DLR‐F6 was selected in this study as a well‐established reference to examine the power‐based analysis in the 3D flow field. The original DLR‐F6 geometry is called the wing body configuration in the following discus‐ sions. This study establishes a BLI configuration by adding an actuator disc model to the wing body configuration, aiming to ingest the boundary layer flow developed over the body surface. This actuator disc is 100 mm in diameter (67% of body diameter), located at the aft fuselage with the axial location of 1181 mm (0.99% of the body length), as shown in Figure 4. The specifications of the wing body configuration and the BLI con‐ figuration are listed in Table 2. For this DLR‐F6 geometry, the test flight condition was subsonic with the Mach number of 0.75, and the flow conditions were kept the same as in the reference studies. The key parameters of the test conditions are listed in Table 3. Appl. Sci. 2022, 12, 10194 6 of 22 Figure 4. The geometry of the DLR-F6 wing body conﬁguration and the BLI conﬁguration (half model). Figure 4. The geometry of the DLR‐F6 wing body configuration and the BLI configuration (half model). Table 2. Speciﬁcations of DLR-F6 geometry (body wing and BLI conﬁgurations). Table 2. Specifications of DLR‐F6 geometry (body wing and BLI configurations). Parameters Value Mean aerodynamic chord 141.2 mm Parameters Value Projected half span 585.6 mm Half-model reference area, S 72,700.0 mm ref Mean aerodynamic chord 141.2 mm Fuselage diameter 148.4mm Projected half span 585.6 mm The diameter of the actuator disc 100 mm X location of the actuator disc (from fuselage nose) 1181 mm Half‐model reference area, Sref 72,700.0 mm Fuselage diameter 148.4mm Table 3. Test condition of DLR-F6 model. The diameter of the actuator disc 100 mm X location Parameters of the actuator disc (from fuselage nose) Value 1181 mm Mach number 0.75 Air model Perfect gas Table 3. Test condition of DLR‐F6 model. Temp 18 C Free stream velocity, V 260.4 m/s Parameters Value Mach number 0.75 2.3. Segregated Computational Domain and Simulation Conditions Air model Perfect gas The computation domain is the key in power-based analysis. The domain includes the Temp 18 °C half model of DLR-F6 to reduce computational resources. The model locates at the center part of this domain, and it is encompassed by external boundaries, including an inlet, a Free stream velocity, V∞ 260.4 m/s symmetry plane, a cylinder boundary, and an outlet plane, as depicted in Figure 5. The ex- ternal boundary, as the far-ﬁeld boundary, is sufﬁciently large. According to reference [24], the far-ﬁeld boundary is about 100 times the mean aerodynamic chord (MAC) away from the aircraft. The radius of the cylinder boundary is about 100 times the MAC, and the length of the domain is 130 times the MAC. This computational domain was used in the two cases of the wing body conﬁguration and the BLI conﬁguration so that the inﬂuences of the mesh were eliminated when com- paring the simulation results of the two cases. The switch between the two conﬁgurations could be realized by changing the boundary condition of the actuator disc plane: the plane was set as an internal plane for the wing body conﬁguration and it could be changed into a pressure jump plane for the BLI conﬁguration. As for the surfaces of wing and body, the boundary condition was set as the wall. Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 23 2.3. Segregated Computational Domain and Simulation Conditions The computation domain is the key in power‐based analysis. The domain includes the half model of DLR‐F6 to reduce computational resources. The model locates at the center part of this domain, and it is encompassed by external boundaries, including an inlet, a symmetry plane, a cylinder boundary, and an outlet plane, as depicted in Figure 5. The external boundary, as the far‐field boundary, is sufficiently large. According to reference [24], the far‐field boundary is about 100 times the mean aerodynamic chord (MAC) away from the aircraft. The radius of the cylinder boundary is about 100 times Appl. Sci. 2022, 12, 10194 7 of 22 the MAC, and the length of the domain is 130 times the MAC. Inlet symmetry plane aircraft Outlet Figure Figure 5. 5. Bou Boundaries ndaries of of computation computation domain. domain. A key feature of this power-based analysis is the segregation of the computational This computational domain was used in the two cases of the wing body configura‐ domain. By dividing the entire domain into individual subdomains, the power terms for tion and the BLI configuration so that the influences of the mesh were eliminated when each subdomain can be evaluated and the change in power terms is tracked [23]. Moreover, comparing the simulation results of the two cases. The switch between the two configu‐ the division of the domain can be associated with the geometry of aircraft components. The rations could be realized by changing the boundary condition of the actuator disc plane: mechanical power conversion of an individual component could be examined, enabling the plane was set as an internal plane for the wing body configuration and it could be us to study the impacts of a speciﬁc aircraft component. As for the entire aircraft, the big changed into a pressure jump plane for the BLI configuration. As for the surfaces of picture of power conversion was established by combining the power conversions of the subdomains. This study deﬁnes 13 internal survey planes that segregated the computational wing and body, the boundary condition was set as the wall. domain into 14 subdomains. These subdomains correspond to the components of wing, A key feature of this power‐based analysis is the segregation of the computational body, and propulsor, as illustrated in Figure 6. domain. By dividing the entire domain into individual subdomains, the power terms for To obtain the 3D ﬂow ﬁeld of the DLR-F6 model, this study employed ANSYS Fluent each subdomain can be evaluated and the change in power terms is tracked [23]. More‐ software to perform 3D compressible RANS simulations. The spatial discretization of over, the division of the domain can be associated with the geometry of aircraft compo‐ simulations employed the second-order upwind and the third-order MUSCL methods. nents. The mechanical power conversion of an individual component could be exam‐ This study used the SIMPLE scheme for the pressure–velocity coupling. As for turbulent ined, enabling us to study the impacts of a specific aircraft component. As for the entire ﬂow, three models were employed, namely the S-A model, the standard k-" model, and aircraft, the big picture of power conversion was established by combining the power Mentor ’s k-! SST model [30]. conversions of the subdomains. This study defines 13 internal survey planes that segre‐ Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 23 gated the computational domain into 14 subdomains. These subdomains correspond to Appl. Sci. 2022, 12, 10194 8 of 22 the components of wing, body, and propulsor, as illustrated in Figure 6. Survey planes Figure 6. Computational domains segregated by 13 survey planes. Figure 6. Computational domains segregated by 13 survey planes. Meshes were generated through ICEMCFD software, trying to follow the guidelines To obtain the 3D flow field of the DLR‐F6 model, this study employed ANSYS Flu‐ for mesh construction of the AIAA drag prediction workshop committee [24]. Unstruc- ent software to perform 3D compressible RANS simulations. The spatial discretization of tured mesh and multiblock structured mesh were generated in different densities: coarse, simulations employed the second‐order upwind and the third‐order MUSCL methods. medium, and ﬁne. The sizes of these meshes are listed in Table 4. The unstructured mesh This consisted study of us prismatic ed the SIand MPL tetrahedral E scheme elements. for the pressure Boundary –velocity layers coup wereling captur . As ed for by turbulent using flow, 25 layers three of mo prismat dels icwere elements, employed, as shown name inlFigur y the eS7‐A . The model, multiblock the stastr nda uctur rd k ed‐ε mesh model, uti- and lized O-type topology in the boundary layer region, as shown in Figure 8. For the medium Mentor’s k‐ω SST model [30]. density mesh, the thickness of the ﬁrst-layer prism was 0.001 m, while the thickness of the Meshes were generated through ICEMCFD software, trying to follow the guidelines ﬁrst layer was 0.0006 mm (Y + approximate equals 1) for the ﬁne mesh. The growth rate for mesh construction of the AIAA drag prediction workshop committee [24]. Unstruc‐ was 1.20 in the boundary layer region. tured mesh and multiblock structured mesh were generated in different densities: coarse, medium, and fine. The sizes of these meshes are listed in Table 4. The unstructured Table 4. Mesh size (cells). mesh consisted of prismatic and tetrahedral elements. Boundary layers were captured by using 25 layers of prismatic elements, as shown in Figure 7. The multiblock struc‐ Density Cell Number tured mesh utilized O‐type topology in the boundary layer region, as shown in Figure 8. Coarse 3.1 million For the medium density mesh, the thickness of the first‐layer prism was 0.001 m, while Unstructured mesh Medium 4.1 million Fine 7.8 million the thickness of the first layer was 0.0006 mm (Y + approximate equals 1) for the fine mesh. The growth rate was 1.20 in the boundary layer region. Medium 5.1 million Multiblock structured mesh Fine 8.4 million Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 23 Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 23 Table 4. Mesh size (cells). Table 4. Mesh size (cells). Density Cell Number Density Cell Number Coarse 3.1 million Coarse 3.1 million Unstructured mesh Medium 4.1 million Unstructured mesh Medium 4.1 million Fine 7.8 million Fine 7.8 million Appl. Sci. 2022, 12, 10194 9 of 22 Medium 5.1 million Medium 5.1 million Multiblock structured mesh Fine 8.4 million Multiblock structured mesh Fine 8.4 million Figure Figure 7. 7. Un Unstr stru uctur ctured ed mes mesh h ((top top left left:: gen general eral vi view ew of of me mesh; sh; top top right: right: prism prism mes mesh h ov over er body body Figure 7. Unstructured mesh (top left: general view of mesh; top right: prism mesh over body su surface; rface; bottom: bottom: gl global obal view view of of mes mesh). h). surface; bottom: global view of mesh). Figure 8. Cont. Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 23 Appl. Sci. 2022, 12, 10194 10 of 22 Figure 8. Multiblock structured mesh (top left: block topology; top right: general view of mesh; Figure 8. Multiblock structured mesh (top left: block topology; top right: general view of mesh; middle: global view of mesh; bottom: body and wing). middle: global view of mesh; bottom: body and wing). 2.4. Definition of Power Imbalance Error 2.4. Deﬁnition of Power Imbalance Error Power‐based analysis is based on the conservation of mechanical energy. This study Power-based analysis is based on the conservation of mechanical energy. This study elaborates on the power imbalance error, e, as given in Equation (12). e is the difference elaborates on the power imbalance error, e, as given in Equation (12). e is the difference between the power input and the power output of a domain. This provides a figure to between the power input and the power output of a domain. This provides a ﬁgure describe how well the mechanical conservation is satisfied in this domain. In CFD simu‐ to describe how well the mechanical conservation is satisﬁed in this domain. In CFD lations, the error of mechanical power imbalance can be attributed to numerical errors, simulations, the error of mechanical power imbalance can be attributed to numerical which can be further broken down into modeling error, discretization error, and con‐ errors, which can be further broken down into modeling error, discretization error, and vergence error. In principle, numerical errors lead to the imperfection of momentum convergence error. In principle, numerical errors lead to the imperfection of momentum conservation, causing an imbalance in mechanical power. conservation, causing an imbalance in mechanical power. 𝑒 P P (12) e = P P (12) in out For the entire computational domain, the power imbalance error is denoted by edo‐ For the entire computational domain, the power imbalance error is denoted by e . domain main. The value is obtained by subtracting the Pout from Pin of the entire domain. The input The value is obtained by subtracting the P from P of the entire domain. The input and out in and output terms are listed in Table 1. Once these power terms are assessed, the value of output terms are listed in Table 1. Once these power terms are assessed, the value of e domain edomain can be evaluated according to Equation (13). It is noted that the shaft power, Ps, can be evaluated according to Equation (13). It is noted that the shaft power, P , and thrust and thrust power, TV∞, are zero for the wing body configuration. For convenience pur‐ power, TV , are zero for the wing body conﬁguration. For convenience purposes, the poses, the relative error is used in the following discussions. Errors are normalized with relative error is used in the following discussions. Errors are normalized with a reference a reference power, Pref. This study uses the total power input of the entire domain as Pref: power, P . This study uses the total power input of the entire domain as P : DV for the ref ref ¥ DV∞ for the wing body configuration and Ps for BLI configuration. wing body conﬁguration and P for BLI conﬁguration. s Appl. Sci. 2022, 12, 10194 11 of 22 ˙ ˙ P + DV + +E E TV ? s ¥ w,in w,out ¥ e = (13) domian ref ˙ ˙ P + DV + E E TV ? s ¥ w,in w,out ¥ e = (14) sub ref subdomain e = e (15) domain å sub The entire computational domain contains 14 segregated subdomains. Mechanical energy conservation is satisﬁed for these subdomains. Therefore, it is feasible to evaluate the error of subdomains (denoted by e ) once all the input and output terms of the sub individual subdomains are obtained, as given in Equation (14). In principle, the power imbalance error of the entire computational domain, e , equals to the summation of the domain error of all of the subdomains, e , as expressed by Equation (15). sub 3. Results and Discussion This section presents the simulation results and elaborates on the power-based analysis. The power imbalance error is analyzed, and suggestions for performing the power-based analysis are provided accordingly. The power conversion processes for the two cases of the wing body conﬁguration and the BLI conﬁguration are presented and discussed. The aerodynamic forces imposed on the aircraft surface are inspected for validation purposes. The coefﬁcients of lift and drag for the wing body conﬁguration are assessed, and the results of different meshes are presented in Figure 9. In addition, the experiment results of the reference study are plotted as the solid line in the same ﬁgure [27]. The dash lines denote the envelope with 3% deviation in the drag coefﬁcient of the experiment data. Appl. Sci. 2022, 12, x FOR PEER REVIEWSimulation results obtained in this study are on the right side of the plot of the experiment 12 of 23 data, within the 3% deviation envelope. This indicates that the drag coefﬁcients obtained in the simulations were higher than those of the experiment, but the difference was less than 3%. The simulation results suggest a convergence in the aircraft drag. This validation establishes a baseline for the following discussions of the power-based analysis. Figure 9. Coefﬁcients of lift and drag for the wing body conﬁguration. Figure 9. Coefficients of lift and drag for the wing body configuration. 3.1. The Analysis of Power Imbalance Error Power imbalance error indicates how well mechanical energy conservation is satis‐ fied in a computational domain. This section discusses the error in the 3D flow field of the DLR‐F6 wing body configuration. Efforts were made to reduce this error in simula‐ tions. 3.1.1. Mesh Size Study and Subdomain Error Study This section presents the power imbalance error of the entire computational do‐ main. In the first place, all the power input and output terms listed in Table 1 were evaluated. For the wing body configuration, the only power input term is the drag pow‐ er, DV∞, while the output terms are the wake power at the outlet plane, Ew,out, and the viscous dissipation, Φ. Once the 3D flow field was obtained through numerical simula‐ tions, these power terms were evaluated according to their expressions, as given in Sec‐ tion 2.1. The power imbalance error of the entire computational domain, edomain, was as‐ sessed according to Equation (13). The input power, DV∞, is used as the reference power to calculate the relative error of edomain. A mesh size study is presented in Table 5. It shows that the relative differences in drag coefficient (with respect to the experiment result) were less than 3%. The aircraft drag was independent of the mesh size and its value agreed well with the experimental results. On the other hand, the value of edomain ranged from 36.4% to 66.3%. Even though edomain tended to decrease as mesh size increased, the errors obtained in the presented 3D simulation were much higher than the 4% value obtained in the previous incompressible 2D simulations [23]. In general, the error in 3D flow simulation was far from a satisfac‐ tory level. It is critical to identify the main courses of the high value of edomain. Appl. Sci. 2022, 12, 10194 12 of 22 3.1. The Analysis of Power Imbalance Error Power imbalance error indicates how well mechanical energy conservation is satisﬁed in a computational domain. This section discusses the error in the 3D ﬂow ﬁeld of the DLR-F6 wing body conﬁguration. Efforts were made to reduce this error in simulations. 3.1.1. Mesh Size Study and Subdomain Error Study This section presents the power imbalance error of the entire computational domain. In the ﬁrst place, all the power input and output terms listed in Table 1 were evaluated. For the wing body conﬁguration, the only power input term is the drag power, DV , while the output terms are the wake power at the outlet plane, E , and the viscous w,out dissipation, F. Once the 3D ﬂow ﬁeld was obtained through numerical simulations, these power terms were evaluated according to their expressions, as given in Section 2.1. The power imbalance error of the entire computational domain, e , was assessed according domain to Equation (13). The input power, DV , is used as the reference power to calculate the relative error of e . domain A mesh size study is presented in Table 5. It shows that the relative differences in drag coefﬁcient (with respect to the experiment result) were less than 3%. The aircraft drag was independent of the mesh size and its value agreed well with the experimental results. On the other hand, the value of e ranged from 36.4% to 66.3%. Even though domain e tended to decrease as mesh size increased, the errors obtained in the presented 3D domain simulation were much higher than the 4% value obtained in the previous incompressible 2D simulations [23]. In general, the error in 3D ﬂow simulation was far from a satisfactory level. It is critical to identify the main courses of the high value of e . domain Table 5. Mesh size study presented by the drag coefﬁcient and the power imbalance error of the computational domain. Mesh Cell Number C (Relative Difference) e D domain Experiment [24] - 0.0295 - Unstructured coarse 3.3 million 0.0299 (1.5%) 66.3% Unstructured medium 4.1 million 0.0299 (1.5%) 43.0% Unstructured ﬁne 7.8 million 0.0289 (1.9%) 38.5% Structured medium 5.1 million 0.0303 (2.7%) 37.5% Structured ﬁne 8.4 million 0.0298 (1.0) 36.4% To ﬁnd the major sources of power imbalance error, e , this section introduces a domain so-called subdomain error study. As introduced in Section 2.4, it is possible to inspect the power imbalance for an individual subdomain. In this study, all the power terms listed in Table 1 were assessed for the individual subdomains. With these inputs, the errors of the power imbalance for the individual subdomains, e , were computed according to sub Equation (14). For demonstration purposes, the results of the unstructured medium mesh are presented. The errors were plotted at the corresponding X location of the survey planes, as shown in Figure 10. The suberror denotes the error of an individual subdomain, while the bulk-error is deﬁned as the accumulation of the suberrors from the ﬁrst subdomain to the subdomain at the X location. This bulk error depicts how the error increases along the X axis. It is noted that the bulk error at the outlet plane simply equals e . domain This subdomain error study clearly showed that the error in the subdomain of the wing (denoted by e ) made the major contribution to e . The e value was 26.8%, wing domian wing while e was 43.0%. The contributions of the other subdomains were signiﬁcantly low: domain The suberror for the frontal body was less than 5%. The suberror in the downstream region was less than 0.5%. The error associated with the wing, e , was mainly responsible for wing the high errors of e . This study suggests that efforts should be made to reduce the domain suberror associated with the wing, e . wing Appl. Sci. 2022, 12, x FOR PEER REVIEW 13 of 23 Table 5. Mesh size study presented by the drag coefficient and the power imbalance error of the computational domain. Mesh Cell Number CD (Relative Difference) edomain Experiment [24] ‐ 0.0295 ‐ Unstructured coarse 3.3 million 0.0299 (1.5%) 66.3% Unstructured medium 4.1 million 0.0299 (1.5%) 43.0% Unstructured fine 7.8 million 0.0289 (−1.9%) 38.5% Structured medium 5.1 million 0.0303 (2.7%) 37.5% Structured fine 8.4 million 0.0298 (1.0) 36.4% To find the major sources of power imbalance error, edomain, this section introduces a so‐called subdomain error study. As introduced in Section 2.4, it is possible to inspect the power imbalance for an individual subdomain. In this study, all the power terms listed in Table 1 were assessed for the individual subdomains. With these inputs, the er‐ rors of the power imbalance for the individual subdomains, esub, were computed accord‐ ing to Equation (14). For demonstration purposes, the results of the unstructured me‐ dium mesh are presented. The errors were plotted at the corresponding X location of the survey planes, as shown in Figure 10. The suberror denotes the error of an individual subdomain, while the bulk‐error is defined as the accumulation of the suberrors from the first subdomain to the subdomain at the X location. This bulk error depicts how the error increases along the X axis. It is noted that the bulk error at the outlet plane simply Appl. Sci. 2022, 12, 10194 13 of 22 equals edomain. Figure 10. Subdomain error study of wing body conﬁguration (unstructured medium mesh). Figure 10. Subdomain error study of wing body configuration (unstructured medium mesh). Appl. Sci. 2022, 12, x FOR PEER REVIEW 14 of 23 3.1.2. Impact Factors of Power Imbalance Error This subdomain error study clearly showed that the error in the subdomain of the This section presents possible impact factors to reduce e . The inﬂuences of the domain wing (denoted by ewing) made the major contribution to edomian. The ewing value was 26.8%, mesh type, discretization scheme, and turbulence model are examined. Considering that the while error edo as maso in wa ciast ed 43 .0% wit.h The the contribution wing, ewing, ma s ofkes the the ot hma er jsubdomains or contribution were to signific edomain, the antly sub low ‐ : the error associated with the wing, e , makes the major contribution to e , the wing domain domain The suber of thror e wing for the is hi fron ghta ligh l body ted. was less than 5%. The suberror in the downstream re‐ subdomain of the wing is highlighted. gion As wa instrod lessuce than d in 0.5 Sec %. tTh ione 2. error 3, bot ashso stru ciated ctur wit edh mesh the wing, and un ewinstruc g, was tured main mesh ly responsi were ‐ As introduced in Section 2.3, both structured mesh and unstructured mesh were ble for the high errors of edomain. This study suggests that efforts should be made to reduce generated. The mesh sizes of the two were close: 4.1 million for the unstructured medi‐ generated. The mesh sizes of the two were close: 4.1 million for the unstructured medium um the mesh suberror and assoc 5.1 mi iate llion d with for the the wi stn rugct , eu win red g. medium mesh. It was straightforward to mesh and 5.1 million for the structured medium mesh. It was straightforward to perform perform the subdomain error study with their simulation results, as presented in Figure the subdomain error study with their simulation results, as presented in Figure 11. It 3.1.2. Impact Factors of Power Imbalance Error 11. It showed the same error contributions for the two types of mesh: high‐value error showed the same error contributions for the two types of mesh: high-value error existed in existed in the subdomain of the wing, which was mainly responsible for the high values This section presents possible impact factors to reduce edomain. The influences of the the subdomain of the wing, which was mainly responsible for the high values of e . The domain of edomain. The structured mesh indeed reduced the error in the wake region (less than mesh type, discretization scheme, and turbulence model are examined. Considering that structured mesh indeed reduced the error in the wake region (less than 1%). Nevertheless, 1%). Nevertheless, the error associated with the wing, ewing (35.4%), was higher than that the error associated with the wing, e (35.4%), was higher than that of the unstructured wing of the unstructured mesh (26.8%). The errors of edomain and ewing are summarized in Table 6. mesh (26.8%). The errors of e and e are summarized in Table 6. Even if the domain wing Even if the structured mesh obtained relatively low values of edomain, it did not offer a structured mesh obtained relatively low values of e , it did not offer a better result in domai better result in terms of ewing, the major error source. This study adopts the unstructured terms of e , the major error source. This study adopts the unstructured medium mesh as wing medium mesh as the reference mesh in the following discussions. the reference mesh in the following discussions. Figure 11. Subdomain error study for unstructured mesh (red lines) and multiblock structured mesh Figure 11. Subdomain error study for unstructured mesh (red lines) and multiblock structured (blue lines). mesh (blue lines). Table 6. Power imbalance error for unstructured mesh and multiblock structured mesh. Mesh Type edomain ewing Unstructured mesh 43.0% 26.8% Multiblock structured mesh 36.4% 25.6% In CFD simulations, discretization methods interpolate conservative independent variables. On the other hand, interpolation causes discretization error as an important source of numerical errors. This study tested two methods for comparison: the sec‐ ond‐order upwind and the third‐order MUSCL methods. The former method is widely used, and the latter method provides higher‐order precision. A first‐order discretization method is not discussed due to the low order precision. A subdomain error study was performed to check the impact of the discretization methods on the reference mesh. The results are listed in Table 7. The results showed that the reduction in ewing due to the third‐order MUSCL method was about 4.5%. Furthermore, the high‐order discretization method reduced ewing without increasing the error of other subdomains. Therefore, the high‐order discretization method is suggested for power‐based analysis. Table 7. Power imbalance error for the discretization methods. Discretization Methods edomain ewing Second‐order upwind 43.0% 26.8% Third‐order MUSCL 38.5% 22.3% Appl. Sci. 2022, 12, 10194 14 of 22 Table 6. Power imbalance error for unstructured mesh and multiblock structured mesh. Mesh Type e e domain wing Unstructured mesh 43.0% 26.8% Multiblock structured mesh 36.4% 25.6% In CFD simulations, discretization methods interpolate conservative independent variables. On the other hand, interpolation causes discretization error as an important source of numerical errors. This study tested two methods for comparison: the second- order upwind and the third-order MUSCL methods. The former method is widely used, and the latter method provides higher-order precision. A ﬁrst-order discretization method is not discussed due to the low order precision. A subdomain error study was performed to check the impact of the discretization methods on the reference mesh. The results are listed in Table 7. The results showed that the reduction in e due to the third-order MUSCL wing method was about 4.5%. Furthermore, the high-order discretization method reduced e wing without increasing the error of other subdomains. Therefore, the high-order discretization method is suggested for power-based analysis. Table 7. Power imbalance error for the discretization methods. Discretization Methods e e domain wing Second-order upwind 43.0% 26.8% Third-order MUSCL 38.5% 22.3% A turbulent model introduces complexity to simulations, and the impact of turbulent models was examined. This study examined three typical models: the S-A model, the standard k-" model, and the k-! SST model. The simulations employed the same reference mesh (unstructured medium mesh) and third-order MUSCL method discretization to eliminate the effects of the other impact factors. The results of the subdomain error study are listed in Table 8. It showed that the absolute value of e ranged from 38.5% to 40.9%. domain The two-equation k-! SST model led to the minimum level of power imbalance error. Table 8. Power imbalance error for three turbulent models. Turbulent Model e e domain wing S-A model 40.8% 23.0% standard k-" model 40.9% 22.3% k-! SST model 38.5% 22.3% As discussed in Section 3.1.1, the mesh size study showed that an increase in mesh size tended to decrease e . It might be beneﬁcial to increase the mesh density in the domain subdomain of the wing. Based on the reference mesh (Unstructured medium mesh), the mesh density was increased universally over the wing surface. The total mesh size was increased accordingly from 4.1 million to about 8.0 million. This reﬁnement of the mesh led to the reduction in e from 38.5% to 36.6%, while e was reduced from 22.3% to domain wing 22.0%. The increase in the mesh density of the wing reduced the power imbalance error by 2% at the cost of the doubled mesh size. Compared with the results of the unstructured ﬁne mesh (8.2 million), the universal increase in mesh density over the wing surface did not provide an extra beneﬁt. A more efﬁcient way to increase the mesh density was examined through the mesh adaptation technique. Based on the reference mesh, the mesh density was increased in the regions with the high gradient of wake power, E , After mesh adaptation, the total cell number increased from 4 million to about 8 million. The results showed that the e was domain reduced from 38.5% to 34.1% and e was reduced from 22.3% to 17.6%. The mesh density wing Appl. Sci. 2022, 12, 10194 15 of 22 was mainly increased in the outer region of the boundary layer of the wing surface and in the vicinity of the trailing edge. This effort led to a notable improvement compared with the results of the unstructured ﬁne mesh. The mesh adaptation obtained the best result for e (34.1%) in this study. domain In summary, the study of impact factors showed that a multiblock structured mesh obtained less total power imbalance error than the unstructured mesh, especially in the wake region. The high-order discretization method was beneﬁcial in reducing the error. The impact of the turbulent model was marginal. Increasing the mesh density in the outer region of the wing boundary layer could reduce the power imbalance error. In the best scenario, e was 34.1% and e was 17.6% for the wing body conﬁguration. These domain wing results are used in the following discussions. 3.2. Power Conversion of Wing Body Conﬁguration This section aims to illustrate the mechanical power conversion process of the wing body conﬁguration. All power terms listed in Table 1 in the ﬂow ﬁeld were assessed. For the wing body conﬁguration, the wake energy inﬂow (rate), E , for the entire computational w,in domain was zero due to the free stream ﬂow inﬂow. Shaft power, P , was not involved in Appl. Sci. 2022, 12, x FOR PEER REVIEW 16 of 23 this case. The only mechanical power input was the drag power, DV , and it was used as the reference power for the normalization of power terms in this case. The output power terms of the wing body conﬁguration include the wake energy ﬂow as shown in Figure 12. This figure visualizes the wake power passing through the air‐ ˙ ˙ (rate), E , and viscous dissipation, F. E was assessed at the survey planes and the outlet w w craft and in the downstream flow. Crossing ˙ the aircraft, the high‐intensity wake power plane. The integrand of the wake power, E , was visualized at the survey planes, as shown over the body surface is highlighted. This region was thicker than the boundary layer of in Figure 12. This ﬁgure visualizes the wake power passing through the aircraft and in the body, and it was associated with the wake of the wing root. The original design of the downstream ﬂow. Crossing the aircraft, the high-intensity wake power over the body the DLR‐F6 geometry suffers flow separation issues at the body–wing junction [29], as surface is highlighted. This region was thicker than the boundary layer of the body, and it was associated with the wake of the wing root. The original design of the DLR-F6 geometry shown on the bottom right of Figure 12. High‐intensity Ew was also observed in the vi‐ suffers ﬂow separation issues at the body–wing junction [29], as shown on the bottom right cinity of the wing tip, denoting the high wake power of the wing tip vortices. In the of Figure 12. High-intensity E was also observed in the vicinity of the wing tip, denoting downstream region, the intensity of the wake power gradually reduced, and the area of the high wake power of the wing tip vortices. In the downstream region, the intensity of high wake power separated into two parts: the one corresponding to the body wake and the wake power gradually reduced, and the area of high wake power separated into two the one for wing tip vortices. parts: the one corresponding to the body wake and the one for wing tip vortices. Figure 12. Contours of the E integrand around the wing body conﬁguration. w • Figure 12. Contours of the Ew integrand around the wing body configuration. Viscous dissipation, Φ, is the sink term of power. As elaborated in Section 2.1, it ex‐ ists in the viscous region (boundary layer and wake) where the velocity gradient exists. The top plot in Figure 13 illustrates the integrand of the viscous dissipation in the flow field. A high intensity of Φ was observed in the region over the airframe surface and in the downstream wake. In the downstream wake, the intensity of Φ in the body wake was higher than that of the wing wake. Compared with the wing wake, the body wake might be less stable, and its mechanical energy dissipated at a faster pace. This study visualized the change in power terms by placing their values at the cor‐ responding X coordinates, as shown at the bottom of Figure 13. This plot illustrates how the power conversion process occurred in the flow field: drag power, DV∞, was trans‐ ferred into wake power, Ew, as well as viscous dissipation, Φ. Appl. Sci. 2022, 12, 10194 16 of 22 Viscous dissipation, F, is the sink term of power. As elaborated in Section 2.1, it exists in the viscous region (boundary layer and wake) where the velocity gradient exists. The top plot in Figure 13 illustrates the integrand of the viscous dissipation in the ﬂow ﬁeld. A high intensity of F was observed in the region over the airframe surface and in the downstream Appl. Sci. 2022, 12, x FOR PEER REVIEW 17 of 23 wake. In the downstream wake, the intensity of F in the body wake was higher than that of the wing wake. Compared with the wing wake, the body wake might be less stable, and its mechanical energy dissipated at a faster pace. Figure 13. The intensity of viscous dissipation and the power conversion process of the wing body Figure 13. The intensity of viscous dissipation and the power conversion process of the wing body configuration. conﬁguration. This study visualized the change in power terms by placing their values at the corre- The wake power, Ew, increased quickly after the nose, reaching the peak value sponding X coordinates, as shown at the bottom of Figure 13. This plot illustrates how the (37% of the total power input) after the wing. After that, it dropped quickly after the tail power conversion process occurred in the ﬂow ﬁeld: drag power, DV was•transferred ¥, and decreased slowly downstream. The abrupt increase in Ew was the result of mechan‐ into wake power, E , as well as viscous dissipation, F. ical power accumulation due to the boundary layer, the separated flow in the body– The wake power, E , increased quickly after the nose, reaching the peak value (37% of the total power input) after the wing. After that, it dropped quickly after the tail and wing junction, and the wing tip vortices. The mild decrease in Ew downstream of the decreased slowly downstream. The abrupt increase in E was the result of mechanical fuselage corresponded to the dissipation of the aircraft wake. At the outlet plane, Ew power accumulation due to the boundary layer, the separated ﬂow in the body–wing remained 35% of the total power input, indicating a substantial amount of mechanical junction, and the wing tip vortices. The mild decrease in E downstream of the fuselage power in the aircraft wake, as shown in Figure 12. corresponded to the dissipation of the aircraft wake. At the outlet plane, E remained Viscous dissipation, Φ, remained almost zero before the aircraft nose, mildly in‐ 35% of the total power input, indicating a substantial amount of mechanical power in the creased along the frontal fuselage, and quickly increased through the wing region. In aircraft wake, as shown in Figure 12. general, it kept increasing from the nose to the tail. At the X locus of the tail, Φ took about 31% of the total power input, mainly corresponding to the mechanical power loss associated with the boundary layer of the aircraft surface, while in the downstream re‐ gion, the increase in Φ was less than 2%, indicating a relatively slow process of dissipa‐ tion in the downstream wake. It was noted that the power input was about 34.1% higher than the summation of the output power at the outlet plane. The difference was the error of the mechanical power imbalance, as discussed in Section 3.1. The error in this 3D Appl. Sci. 2022, 12, 10194 17 of 22 Viscous dissipation, F, remained almost zero before the aircraft nose, mildly increased along the frontal fuselage, and quickly increased through the wing region. In general, it kept increasing from the nose to the tail. At the X locus of the tail, F took about 31% of the total power input, mainly corresponding to the mechanical power loss associated with the boundary layer of the aircraft surface, while in the downstream region, the increase in F was less than 2%, indicating a relatively slow process of dissipation in the downstream wake. It was noted that the power input was about 34.1% higher than the summation of the output power at the outlet plane. The difference was the error of the mechanical power imbalance, as discussed in Section 3.1. The error in this 3D simulation was signiﬁcantly higher than the 4% value in the previous study of 2D turbulent ﬂow simulation [23]. 3.3. Power Conversion of Boundary Layer Ingestion Conﬁguration Various sources in the previous study on BLI showed that the value of power saving due to BLI is in the range of 3~10%. On the other hand, the error of mechanical power imbalance is about 30%. The precision of power-based analysis in 3D simulation is not adequate to study the power saving of BLI. This section limits the discussion to the aspect of the power conversion process of the aircraft using BLI. The BLI conﬁguration combines the wing body conﬁguration with a BLI propulsor. This study employed a wake-ﬁlling actuator disc model with a nonuniform pressure jump to mimic an ideal BLI propulsor [13,31]. This model re-energized the ingested boundary layer ﬂow into the state of free stream so that the mechanical energy of the downstream wake and jet was minimized. The actuator disc model utilized a UDF function, which increased the total pressure of the ingested ﬂow into a constant total pressure, P . In t,const this case the P value was 46,000 Pascal, higher than the free stream total pressure. t,const In this manner, the thrust, T, generated by the actuator disc model was higher than the airframe drag, D. The UDF function enabled a nonuniform pressure jump DP, which was simply equal to P -P . P refers to the total pressure of the upstream t,const t,upstream t,upstream ﬂow. The thrust of this actuator disc model, T, was obtained as the surface integral of DP over the disc plane, as given in Equation (16). The T value was 116 N, so the TV value of 30,232 watts was obtained. It was noted that TV was considered a power output term, while the actual power input of the propulsor was shaft power, P , which was evaluated using Equation (7). In this BLI case, the P value was 54,793 watts and was used as the reference value for normalizing the power terms. I I T = DPdS = P P dS (16) t,const t,upstream prop prop Figure 14 shows the total pressure distribution at the symmetry plane in the vicinity of the actuator disc model. The boundary layer of the body is denoted by the contours of low-valued total pressure over the body surface. It was noted that the boundary layer over the bottom surface was thicker than that over the top surface. This was attributed to the non-axisymmetric pressure diffusion of the aft body shape. The total pressure was not uniform in the region behind the actuator disc model. Therefore, the actuator disc model was not capable of reﬁlling the total pressure in an ideal manner. This could be attributed to the highly distorted ﬂow ingested by the actuator disc. This study suggests that the aft body should be axisymmetric to best utilize the BLI beneﬁt. Aircraft drag, D, is the drag force imposed on the wing and body surface. The drag coefﬁcient was 0.03290 in the BLI conﬁguration. That was about 8% higher than the value in the wing body conﬁguration. The increase in drag was due to the suction of the actuator disc model imposed on the aft body. The drag power, DV , is obtained by multiplying D by V as a power input of the ﬂow ﬁeld. ¥ Appl. Sci. 2022, 12, x FOR PEER REVIEW 18 of 23 simulation was significantly higher than the 4% value in the previous study of 2D tur‐ bulent flow simulation [23]. 3.3. Power Conversion of Boundary Layer Ingestion Configuration Various sources in the previous study on BLI showed that the value of power sav‐ ing due to BLI is in the range of 3~10%. On the other hand, the error of mechanical pow‐ er imbalance is about 30%. The precision of power‐based analysis in 3D simulation is not adequate to study the power saving of BLI. This section limits the discussion to the as‐ pect of the power conversion process of the aircraft using BLI. The BLI configuration combines the wing body configuration with a BLI propulsor. This study employed a wake‐filling actuator disc model with a nonuniform pressure jump to mimic an ideal BLI propulsor [13,31]. This model re‐energized the ingested boundary layer flow into the state of free stream so that the mechanical energy of the downstream wake and jet was minimized. The actuator disc model utilized a UDF func‐ tion, which increased the total pressure of the ingested flow into a constant total pres‐ sure, Pt,const. In this case the Pt,const value was 46,000 Pascal, higher than the free stream total pressure. In this manner, the thrust, T, generated by the actuator disc model was higher than the airframe drag, D. The UDF function enabled a nonuniform pressure jump ΔP, which was simply equal to Pt,const‐Pt,upstream. Pt,upstream refers to the total pressure of the upstream flow. The thrust of this actuator disc model, T, was obtained as the sur‐ face integral of ΔP over the disc plane, as given in Equation (16). The T value was 116 N, so the TV∞ value of 30,232 watts was obtained. It was noted that TV∞ was considered a power output term, while the actual power input of the propulsor was shaft power, Ps, which was evaluated using Equation (7). In this BLI case, the Ps value was 54,793 watts and was used as the reference value for normalizing the power terms. T ∮ ∆PdS ∮ P P dS (16) , , Figure 14 shows the total pressure distribution at the symmetry plane in the vicinity of the actuator disc model. The boundary layer of the body is denoted by the contours of low‐valued total pressure over the body surface. It was noted that the boundary layer over the bottom surface was thicker than that over the top surface. This was attributed to the non‐axisymmetric pressure diffusion of the aft body shape. The total pressure was not uniform in the region behind the actuator disc model. Therefore, the actuator disc model was not capable of refilling the total pressure in an ideal manner. This could be Appl. Sci. 2022, 12, 10194 18 of 22 attributed to the highly distorted flow ingested by the actuator disc. This study suggests that the aft body should be axisymmetric to best utilize the BLI benefit. Appl. Sci. 2022, 12, x FOR PEER REVIEW 19 of 23 Figure 14. Total pressure contours in the vicinity of the wake‐filling actuator disc model. Aircraft drag, D, is the drag force imposed on the wing and body surface. The drag coefficient was 0.03290 in the BLI configuration. That was about 8% higher than the val‐ ue in the wing body configuration. The increase in drag was due to the suction of the actuator disc model imposed on the aft body. The drag power, DV∞, is obtained by mul‐ tiplying D by V∞ as a power input of the flow field. Figure 14. Total pressure contours in the vicinity of the wake-ﬁlling actuator disc model. As discussed, the wake energy flow, Ew, was assessed as the surface integral over As discussed, the wake energy ﬂow, E , was assessed as the surface integral over the survey planes and the outlet plane. Thew integrand of Ew is illustrated in Figure 15. the survey planes and the outlet plane. The integrand of E is illustrated in Figure 15. Compared with the pattern in the case of the wing body configuration. The pattern in Compared with the pattern in the case of the wing body conﬁguration. The pattern in the BLI case is similar: the wake power accumulated as the flow passed through the air‐ the BLI case is similar: the wake power accumulated as the ﬂow passed through the craft and gradually reduced in the downstream region. Compared with the wing body aircraft and gradually reduced in the downstream region. Compared with the wing body configuration, a notable difference for the BLI configuration was the high intensity of Ew conﬁguration, a notable difference for the BLI conﬁguration was the high intensity of E in the downstream flow of the actuator disc. The downstream wake power was in‐ in the downstream ﬂow of the actuator disc. The downstream wake power was increased creased rather than decreased in this configuration. This was associated with the exces‐ rather than decreased in this conﬁguration. This was associated with the excessive high- sive high‐momentum addition of the actuator disc: the thrust not only balanced the momentum addition of the actuator disc: the thrust not only balanced the body drag but body drag but also overcame the wing drag. also overcame the wing drag. Figure 15. Contours of Ew integrand around the BLI conﬁguration. Figure 15. Contours of Ew integrand around the BLI configuration. The top picture of Figure 16 illustrates the intensity of F in the ﬂow ﬁeld. The high The top picture of Figure 16 illustrates the intensity of Φ in the flow field. The high intensity of F is highlighted around the airframe surface and in the aircraft’s downstream intensity of Φ is highlighted around the airframe surface and in the aircraft’s down‐ stream region. Once all of the power inputs and outputs terms in the flow field were calculated, they were normalized and plotted at the corresponding X coordinates, as shown in Figure 16. This figure illustrates the power conversion process of the BLI con‐ figuration with a propulsor. It shares a similar pattern to that of the wing body configu‐ ration. Appl. Sci. 2022, 12, 10194 19 of 22 region. Once all of the power inputs and outputs terms in the ﬂow ﬁeld were calcu- Appl. Sci. 2022, 12, x FOR PEER REVIEW 20 of 23 lated, they were normalized and plotted at the corresponding X coordinates, as shown in Figure 16. This ﬁgure illustrates the power conversion process of the BLI conﬁguration with a propulsor. It shares a similar pattern to that of the wing body conﬁguration. Figure 16. The intensFigure ity of v i16 sco. uThe s di sintensity sipation a of nd vi thsc e p ou ow s edi rssipat converio sin o nand pro cthe ess pow of theer B Lconver I confision gura tprocess ion. of the BLI con‐ figuration. The bottom plot in Figure 16 illustrates the power conversion process of the BLI conﬁguration. The shaft power, P , as the only power input in the ﬂow ﬁeld, was implanted The bottom s plot in Figure 16 illustrates the power conversion process of the BLI in the ﬂow ﬁeld by the propulsor. P was converted into viscous dissipation, F, and wake configuration. The s shaft power, Ps, as the only power input in the flow field, was im‐ power at the outlet plane, E , as well as the net force power, NV . w,out ¥ planted in the flow field by the propulsor. Ps was converted into viscous dissipation, Φ, The viscous dissipation, F, increased along the stream and shared a similar pattern and wake power at the outlet plane, Ew,out, as well as the net force power, NV∞. as in the wing body conﬁguration. It increased quickly over the aircraft surface, taking The viscous dissipation, Φ, increased along the stream and shared a similar pattern about 28% of the total power input at the body tail. Then, F increased by 5% in the as in the wing body configuration. It increased quickly over the aircraft surface, taking downstream region. Besides the viscous dissipation of the aircraft wake, the increase in F about 28% of the total power input at the body tail. Then, Φ increased by 5% in the in the downstream region was associated with the dissipation of the jet behind the actuator downstream region. Besides the viscous dissipation of the aircraft wake, the increase in disc model. Φ in the downstream region was associated with the dissipation of the jet behind the The wake power, E , increases across the airframe and decreases in the downstream actuator disc model. reﬂow. At the outlet, E took 22% of the total input power. This indicated a notable amount The wake power, Ew, increases across the airframe and decreases in the down‐ of mechanical power in the downstream ﬂow mixed with the jet and wake. This study shows the limitations of a single wake-ﬁlling actuator disc model: It can reﬁll the body stream reflow. At the outlet, Ew took 22% of the total input power. This indicated a no‐ wake, but it is not able to reduce the wing wake. On the other hand, the momentum excess table amount of mechanical power in the downstream flow mixed with the jet and wake. of the actuator disc model was required to balance the momentum deﬁcit of the wing. This study shows the limitations of a single wake‐filling actuator disc model: It can refill the body wake, but it is not able to reduce the wing wake. On the other hand, the mo‐ mentum excess of the actuator disc model was required to balance the momentum defi‐ cit of the wing. Therefore, the actuator disc model in this BLI configuration was not ca‐ pable of reducing the downstream mechanical power to zero. Appl. Sci. 2022, 12, 10194 20 of 22 Appl. Sci. 2022, 12, x FOR PEER REVIEW 21 of 23 Therefore, the actuator disc model in this BLI conﬁguration was not capable of reducing For the BLI configuration, the thrust power, TV∞, and drag power, DV∞, mutually the downstream mechanical power to zero. cancelled each other, leaving a finite value (10% of the total input power) of the net force For the BLI conﬁguration, the thrust power, TV , and drag power, DV , mutually ¥ ¥ power, NV∞, as a power output term. NV∞ was used to accelerate the aircraft. This was cancelled each other, leaving a ﬁnite value (10% of the total input power) of the net force different from the wing body configuration, in which NV∞ was zero to maintain the power, NV , as a power output term. NV was used to accelerate the aircraft. This ¥ ¥ thrust/drag equilibrium. In the plot of power conversion, the total power input, Ps, was was different from the wing body conﬁguration, in which NV was zero to maintain the not identical to the summation of the outputs in the flow field. The difference was about thrust/drag equilibrium. In the plot of power conversion, the total power input, P , was not 35% identical , denotin togthe thesummation power imba of lance the outputs error forin the the BLI ﬂow case. ﬁeld. The difference was about 35%, denoting A subdom theain power error imbalance study was err performed or for the BLI to process case. the simulation results of the A subdomain error study was performed to process the simulation results of the BLI BLI configuration, as presented in Figure 17. It was clear that the error associated with conﬁguration, the wing wasas 19pr .3%, esented which in was Figur sign e 17 ificantly . It was higher clear that than the the err erro orrs associated from the ot with her the sub‐ wing domain wass, 19.3%, whilewhich the error was of signiﬁcantly the BLI prop higher ulsorthan wasthe 8.2%. err ors This fr om stud the y shows other subdomains, that the error while the error of the BLI propulsor was 8.2%. This study shows that the error associated associated with the wing as well as the propulsor was mainly responsible for the high with the wing as well as the propulsor was mainly responsible for the high values of power values of power imbalance error. The error of the mechanical power imbalance was imbalance error. The error of the mechanical power imbalance was larger than the typical larger than the typical values of power saving due to BLI. So far, the precision of pow‐ values of power saving due to BLI. So far, the precision of power-based analysis in 3D er‐based analysis in 3D simulation is not adequate to analyze the power saving of BLI. simulation is not adequate to analyze the power saving of BLI. This poses challenges for This poses challenges for future work. future work. Figure 17. Subdomain error study of BLI configuration. Figure 17. Subdomain error study of BLI conﬁguration. 4. Conclusions and Recommendations 4. Conclusions and Recommendations A power-based analysis was performed to study the ﬂow ﬁeld over a transonic A power‐based analysis was performed to study the flow field over a transonic transport aircraft through 3D compressible Reynolds-averaged Navier–Stokes simulations. transport aircraft through 3D compressible Reynolds‐averaged Navier–Stokes simula‐ The error of mechanical power imbalance in the segregated computational domain was tions. The error of mechanical power imbalance in the segregated computational domain examined. The power conversion process of the wing body conﬁguration and the boundary was examined. The power conversion process of the wing body configuration and the layer ingestion conﬁguration were studied and presented. boundary layer ingestion configuration were studied and presented. Power-based analysis was capable of illustrating the process of power conversion Power‐based analysis was capable of illustrating the process of power conversion in in the 3D ﬂow ﬁeld, clearly visualizing the change in power associated with the aircraft the 3D flow field, clearly visualizing the change in power associated with the aircraft components. For the wing body conﬁguration, the input power, DV , was converted components. For the wing body configuration, the input power, DV∞, was converted in‐ into viscous dissipation and wake power at the outlet plane. Viscous dissipation mainly to viscous dissipation and wake power at the outlet plane. Viscous dissipation mainly occurred in the boundary layer over the aircraft surface, taking up 31% of the total power occurred in the boundary layer over the aircraft surface, taking up 31% of the total pow‐ input. The mechanical power of the aircraft wake took about 35% of the total power input er input. The mechanical power of the aircraft wake took about 35% of the total power at the outlet. For the BLI conﬁguration, the input power, P , provided by the actuator disc input at the outlet. For the BLI configuration, the input power, Ps, provided by the actu‐ model was converted into viscous dissipation and wake power at the outlet plane as well ator disc model was converted into viscous dissipation and wake power at the outlet as net force power. The viscous dissipation of the boundary layer over the aircraft surface plane as well as net force power. The viscous dissipation of the boundary layer over the was about 28% of the total power input. The wake power of the downstream ﬂow took aircraft surface was about 28% of the total power input. The wake power of the down‐ about 22% of the total power input at the outlet plane. About 10% of the total power input stream flow took about 22% of the total power input at the outlet plane. About 10% of was in the form of net force power that accelerated the aircraft. the total power input was in the form of net force power that accelerated the aircraft. Appl. Sci. 2022, 12, 10194 21 of 22 The simulation results showed that the power imbalance error of the entire computa- tional domain was 34.1% for the DLR-F6 wing body conﬁguration, even if the difference in the drag coefﬁcient was less than 3% compared to the experimental results. This study shows that the convergence in aircraft drag does not necessarily lead to a small power imbalance error. The error in 3D simulation is much higher than that in 2D simulations. The high power imbalance error is mainly associated with the wing. Efforts were made in this work to reduce the power imbalance error. High-order discretization methods and an increasing mesh density in the outer region of the wing boundary layer and in the vicinity of the trailing edge were beneﬁcial for reducing the error. However, the high value of error limits the precision of power-based analysis applied to 3D RANS simulations. Attempts to increase the mesh size to a higher order of magnitude were kept for future work due to limited computational resources in this study. Moreover, alternative simulation methods could be considered for power-based analysis in future work. Author Contributions: Conceptualization, writing—original draft preparation, P.L.; Resources, writing—review and D.L.; writing—review and editing, L.M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest. Abbreviations BLI Boundary Layer Ingestion CFD Computational Fluid Dynamics DLR Deutsches Zen-trum für Luft- und Raum-fahrt (German Aerospace Center) RANS Reynolds-Averaged Navier–Stokes MAC Mean Aerodynamic Chord References 1. Daggett, D.L.; Kawai, R.; Geiselhart, K.A. Blended Wing Body Systems Studies: Boundary Layer Ingestion Inlets with Active Flow Control; NTRS: Washington, DC, USA, 2003. 2. Plas, A.; Crichton, D.; Sargeant, M.; Hynes, T.; Greitzer, E.; Hall, C. Performance of a Boundary Layer Ingesting (BLI) Propulsion System. In Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit, Denver, CO, USA, 2–5 August 2011. 3. Hall, D.K.; Huang, A.C.; Uranga, A.; Greitzer, E.M.; Drela, M.; Sato, S. Boundary Layer Ingestion Propulsion Beneﬁt for Transport Aircraft. J. Propuls. Power 2017, 33, 1118–1129. [CrossRef] 4. Uranga, A.; Drela, M.; Greitzer, E.M.; Hall, D.K.; Titchener, N.A.; Lieu, M.K.; Siu, N.M.; Casses, C.; Huang, A.C.; Gatlin, G.M.; et al. Boundary Layer Ingestion Beneﬁt of the D8 Transport Aircraft. AIAA J. 2017, 55, 3693–3708. [CrossRef] 5. Bijewitz, J.; Seitz, A.; Isikveren, A.T.; Hornung, M. Progress in Optimizing the Propulsive Fuselage Aircraft Concept. J. Aircr. 2017, 54, 1979–1989. [CrossRef] 6. Seitz, A.; Habermann, A.L.; Peter, F.; Troeltsch, F.; Castillo Pardo, A.; Della Corte, B.; Van Sluis, M.; Goraj, Z.; Kowalski, M.; Zhao, X.; et al. Proof of Concept Study for Fuselage Boundary Layer Ingesting Propulsion. Aerospace 2021, 8, 16. [CrossRef] 7. Gray, J.S.; Mader, C.A.; Kenway, G.K.W.; Martins, J.R.R.A. Modeling Boundary Layer Ingestion Using a Coupled Aeropropulsive Analysis. J. Aircr. 2018, 55, 1191–1199. [CrossRef] 8. Yildirim, A.; Gray, J.S.; Mader, C.A.; Martins, J.R.R.A. Boundary-Layer Ingestion Beneﬁt for the STARC-ABL Concept. J. Aircr. 2022, 59, 896–911. [CrossRef] 9. Betz, A. Introduction to the Theory of Flow Machines; Pergamon Press: Oxford, UK, 1966; pp. 215–217. 10. Drela, M. Power Balance in Aerodynamic Flows. AIAA J. 2009, 47, 1761–1765. [CrossRef] 11. Arntz, A.; Atinault, O.; Merlen, A. Exergy-Based Formulation for Aircraft Aeropropulsive Performance Assessment: Theoretical Development. AIAA J. 2015, 53, 1627–1639. [CrossRef] 12. Arntz, A.; Atinault, O. Exergy-Based Performance Assessment of a Blended Wing–Body with Boundary-Layer Ingestion. AIAA J. 2015, 53, 3766–3776. [CrossRef] 13. Lv, P.; Rao, A.G.; Ragni, D.; Veldhuis, L. Performance Analysis of Wake and Boundary-Layer Ingestion for Aircraft Design. J. Aircr. 2016, 53, 1517–1526. [CrossRef] Appl. Sci. 2022, 12, 10194 22 of 22 14. Lv, P.; Ragni, D.; Hartuc, T.; Veldhuis, L.; Rao, A.G. Experimental Investigation of the Flow Mechanisms Associated with a Wake-Ingesting Propulsor. AIAA J. 2017, 55, 1332–1342. [CrossRef] 15. AIR4065A2012; Propeller/Propfan In-Flight Thrust Determination. SAE International: Warrendale, PA, USA, 2012. 16. Habermann, A.L.; Bijewitz, J.; Seitz, A.; Hornung, M. Performance bookkeeping for aircraft conﬁgurations with fuselage wake-ﬁlling propulsion integration. CEAS Aeronaut. J. 2020, 11, 529–551. [CrossRef] 17. Elmiligui, A.A.; Fredericks, W.J.; Guynn, M.D.; Campbell, R.L. Numerical Investigation of a Fuselage Boundary Layer Ingestion Propulsion Concept; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2013. 18. Sanders, D.S.; Laskaridis, P. Full-Aircraft Energy-Based Force Decomposition Applied to Boundary-Layer Ingestion. AIAA J. 2020, 58, 4357–4373. [CrossRef] 19. Baskaran, P.; Corte, B.D.; Sluis, M.V.; Rao, A.G. Aeropropulsive Performance Analysis of Axisymmetric Fuselage Bodies for Boundary-Layer Ingestion Applications. AIAA J. 2022, 60, 1592–1611. [CrossRef] 20. Blumenthal, B.T.; ElMiligui, A.A.; Geiselhart, K.A.; Campbell, R.L.; Maughmer, M.D.; Schmitz, S. Computational Investigation of a Boundary-Layer-Ingestion Propulsion System. J. Aircr. 2018, 55, 1141–1153. [CrossRef] [PubMed] 21. Kenway, G.K.; Kiris, C.C. Aerodynamic Shape Optimization of the STARC-ABL Concept for Minimal Inlet Distortion. In Proceedings of the AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimme, FL, USA, 8–12 January 2018. 22. Gray, J.S.; Mader, C.A.; Kenway, G.K.W.; Martins, J.R.R.A. Coupled Aeropropulsive Optimization of a Three-Dimensional Boundary-Layer Ingestion Propulsor Considering Inlet Distortion. J. Aircr. 2020, 57, 1014–1025. [CrossRef] 23. Lv, P.; Zhang, M.; Cao, F.; Lin, D.; Mo, L. 2D Numerical Study on the Flow Mechanisms of Boundary Layer Ingestion through Power-Based Analysis. Aerospace 2022, 9, 184. [CrossRef] 24. Laﬂin, K.; Brodersen, O.; Rakowitz, M.; Vassberg, J.; Wahls, R.; Morrison, J.; Tinoco, E.; Godard, J.-L. Summary of Data from the Second AIAA CFD Drag Prediction Workshop (Invited). In Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 5–8 January 2004. 25. May, G.; van der Weide, E.; Shankaran, S.; Jameson, A. Drag Prediction of the DLR-F6 Conﬁguration. In Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 5–8 January 2004. 26. Gatlin, G.; Rivers, M.; Goodliff, S.; Rudnik, R.; Sitzmann, M. Experimental Investigation of the DLR-F6 Transport Conﬁguration in the National Transonic Facility (Invited). In Proceedings of the 26th AIAA Applied Aerodynamics Conference, Honolulu, HI, USA, 18–21 August 2008. 27. Hemsch, M.; Morrison, J. Statistical Analysis of CFD Solutions from 2nd Drag Prediction Workshop (Invited). In Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 5–8 January 2004. 28. Sato, S. The Power Balance Method for Aerodynamic Performance Assessment. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2012. 29. Brodersen, O.P.; Rakowitz, M.; Amant, S.; Larrieu, P.; Destarac, D.; Suttcliffe, M. Airbus, ONERA, and DLR Results from the Second AIAA Drag Prediction Workshop. J. Aircr. 2005, 42, 932–940. [CrossRef] 30. Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994, 32, 1598–1605. [CrossRef] 31. Smith, L.H. Wake ingestion propulsion beneﬁt. J. Propuls. Power 1993, 9, 74–82. [CrossRef]

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A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations

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Applied Sciences – Multidisciplinary Digital Publishing Institute

Published: Oct 11, 2022

Keywords: power-based analysis; power imbalance error; 3D RANS simulation

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A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations

A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations

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A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations

A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations

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