Researchers performing the wind tunnel experimental studies of wing nacelle for the configurations show the importance of wind tunnel testing. Experimental wind tunnel testing is crucial in the comprehension of intricate aerodynamic processes, particularly in high and UHBR engines. Important conclusions are shock-induced separation and buffet on the lower surface of the wing caused by nacelle mounting, ¹² with buffet peaks at a Strouhal number of approximately 0.4. Thrust reduction by spinning fan blades demonstrated a small decrease in landing distances, ¹³ and chine design with Kriging models enhanced lift performance. ¹⁴ Special wind tunnel rigs imaged windmilling phenomena and boundary layer separation via schlieren and infrared imaging. ¹⁵ Utilizing imaging techniques in the experiments indicated drag savings ranging from 5 to 19% through optimized lip shapes and blowing ratios. ¹⁶ Surface treatments such as superhydrophobic films minimized water retention but ice accretion was still geometry dependent. ¹⁷ Engine power settings had a direct impact on lift and pressure distribution at low speeds, ¹⁸ and CFD verification campaigns substantiated primary flow phenomena in HWB configurations. ¹⁹ Dynamics of separation and wake influences were examined under crosswinds and windmilling conditions using clean and vaned nacelle models, ^{20, 21} while PIV measurements recorded detailed chine-induced vortices. ^{22, 23} Research on aircraft engine bypass geometry ^{24, 25} and separation hysteresis ²⁶ further highlighted the vulnerability of nacelle performance to design and flow conditions.

Numerical studies on wing nacelle aerodynamics have fast progressed due to the use of CFD, optimization algorithms, and machine learning tools. The typical workflow starts with generating geometry, creating meshes, and performing RANS-based CFD simulations to gather flow-field data. This data is processed and used to train DNNs, which provide faster and accurate predictions of aerodynamic performance. The new approach cuts CPU time by a hefty margin. ²⁷ Designers still prefer sleek, compact nacelles and typically rely on CST for quick curves. Fang et al. ²⁸ showed that a RANS-CFD-based loop delivers drag and Mach estimates within a few counts. A crosswind-aware intake, run with fan-intake coupling and surrogate-based optimization, slashed DC60 distortion by 29%. That gain beat rivals that tackled only the intake. ²⁹ Tests on ultra-high bypass nacelles proved mounting position matters, with peak net thrust near x/c = -0.1. ³⁰ A multi-objective sweep of scarfed and drooped designs, fed by Kriging and an evolutionary routine, balanced drag, noise, and weight. ³¹ Finally, NLF holding roughly 30% chordwise laminarity trimmed overall drag by 13.3%. ³² Inverse pressure gradient designs allowed for shock-free, stable flow even under off-design conditions. ³³ Meanwhile, ASBRO strategies improved robustness and cut computational costs by nearly 60%. ³⁴ Additional studies investigated icing effects using 3D simulation methods, ³⁵ the aeroelastic response of powered engine mounts ³⁶ and reducing aerodynamic interference through NURBS-based free-form deformation combined with PSO. ³⁷ Body-force models provided useful tools for predicting inlet distortion without needing detailed fan geometry. ³⁸ Ground vortex dynamics under crosswinds were experimentally mapped in four unsteady phases, revealing their significant effect on inlet flow. ³⁹ Finally, high-incidence lip separation, which is a major source of distortion, was accurately modeled using ANSYS CFX. ⁴⁰ Powered intakes were shown to reduce flow distortion, improving stability and performance. ⁴¹

Fine-tuning wing-nacelle setups in the transonic zone calls for a careful trade-off among gains, run time, and design handle-ability. To speedup things, newer studies mix quick-look surrogates, machine-learning tricks, and flexible shape templates. Researchers ^{42, 43} show solid results using feed-forward nets to forecast drag and flow, cutting CPU time by almost 75% while keeping errors near 2.8% and hitting 98% on class tasks. Research ⁴³ pairs that with a CNN and Sobel edge map to sharpen shock-wave spotting. Research ⁴⁴ leans on a GAN loop and beats the old toolbox, turning out cleaner pressure fields and sleeker nacelle outlines. Research ⁴⁵ merge CST batched with a genetic code and Kriging to tune non-axisymmetric bodies inside RANS. Meanwhile, studies like ^{46, 47} run Gaussian Processes on a joint Pareto map, trading lift, drag, and noise via scarf angle, and trim the variable list upfront. NSGA-II optimization in ⁴⁸ and advanced response surfaces in ⁴⁹ enhance convergence and precision for gradient-sensitive objectives. ANN-based surrogate models in ⁵⁰ and multi-fidelity ANN/Euler-RANS frameworks in ⁵¹ achieve up to 92% computational saving while resolving intricate flow features. Off-design robustness including windmilling is explored in ⁵² with regression/classification models. Optimization of the combustion chamber in ⁵³ employs a POD-Hierarchical-Kriging approach with RMS errors less than 0.2% and good Pareto trade-offs. Parametric geometry tools in ⁵⁴ illustrate CST's value for quick production of feasible nacelle designs. POD-based 3D inlet optimization under high-angle conditions in ⁵⁵ captures realistic constraints. Finally, ⁵⁶ combines Euler/Navier–Stokes solvers with inverse design techniques to reduce installation effects for complicated aircraft configurations.

Experimental studies highlight the value of wind tunnel testing to understand complex phenomena like shock-induced separation, buffet, and windmilling. Techniques such as schlieren imaging, infrared thermography, and PIV showed chine vortices, boundary layer behaviour, and drag patterns. Optimized nacelle lips and active blowing achieved drag reductions of up to 19%. ¹⁶ Engine power settings and surface treatments influenced lift and icing behaviour. Studies on crosswind and bypass flow noted how sensitive nacelle design is to mounting and flow conditions. Numerical research has advanced with RANS-based CFD and data-driven models. Machine learning, deep neural networks, and surrogate-based optimization greatly reduced computation time while maintaining precise aerodynamic predictions. Parametric sweeps looked at intake distortion, mounting effects, and laminar-flow designs, with some setups achieving over 13.3% drag reduction. ³² Shape optimization with tools like CST, NURBS deformation, and inverse design further improved performance across drag, noise, and weight trade-offs. Ground vortex and icing simulations made intake behaviour under tough conditions more realistic. A theoretical approach combined AI-driven models with flexible geometry control for quick and solid optimization. Neural networks, GANs, and Gaussian processes predicted complex flow features with little error and computational effort. Multi-objective optimization frameworks using genetic algorithms and Kriging supported balanced trade-offs. Multi-fidelity approaches brought together CFD and surrogate models for efficient exploration of the design space.

Table 1 presents a qualitative analysis of data from experimental, numerical, and theoretical studies focusing on nacelle aerodynamics under various flow conditions. Key model configurations, flow parameters, and control factors are listed to support aerodynamic evaluation of the aircraft nacelle. The experimental quantitative analysis explores aerodynamic behaviour using physical testing of nacelles, hybrid wings, and airfoil models, focusing on parameters like Reynolds number, Mach number, and AoA. The numerical quantitative analysis highlights CFD simulations with models such as DLR, RAE2822, and NACA airfoils incorporating advanced turbulence modeling and surrogate optimization to evaluate aerodynamic performance. The theoretical literature focus is on analysing different parameters and predicting outcomes using simpler models, Kriging surfaces, and Pareto optimization, which provide important information about how airflow behaves in perfect conditions.

After completing the systematic literature review of experimental, numerical, and theoretical research studies, it is observed that aerodynamic flow parameters need to be improved using different numerical techniques. Transonic flow typically ranges between Mach 0.8 and 1.3, but recent studies have only focused on the Mach number up to 0.85. Currently, no much literature explores flow parameters at Mach 1.3 for transport aircraft nacelle, and there are very few experimental studies involving transport aircraft nacelle with this Mach range. A limited research has been identified at transonic flow regime especially from Mach 0.8 to 1.3. The numerical studies on transport aircraft nacelle usually includes one or two turbulence models and address one or two aerodynamic parameters such as pressure, temperature, density, Mach distribution, velocity distribution, or turbulence. Therefore, this research includes the study of flow characteristics of a 3D nacelle using various numerical techniques, including different turbulence models, boundary condition variations, grid independence tests, etc. In this research the cone-core assembly was added to the nacelle and aerodynamic analysis is performed by varying the cone-core angle.

The objectives of the research are: •

To analyse the aerodynamic flow characteristics of a CRM nacelle and validate the results with available findings.

3.1.1 Nacelle baseline modeling

For the CFD analysis, the nacelle model was taken from the NASA 6 ^th drag prediction workshop. ⁵⁹ The nacelle model was converted from a sheet body into a solid body using the ANSYS 2023 R2 Spaceclaim tool. The continuity and integrity of the model were cross-checked to prevent issues during the CFD analysis.

The major parts of the nacelle are shown in Figure 3 and the geometry specifications of the nacelle is shown in Table 2. The total length of the nacelle is 6 m, the inlet diameter of the nacelle is 3.2 m, and the exhaust diameter of the nacelle is found to be 2.7 m. Additionally, a cylindrical far field was created, and the dimensions of both the nacelle and far fields are shown in Figure 2 and Figure 4. The detailed engine specifications ⁶⁰ of the CRM nacelle are shown in the Table 2.

3.1.2 Nacelle and farfield meshing

After creating a nacelle model, the nacelle and farfield model were imported to create mesh. The ANSYS meshing module was used to mesh the model. Before meshing, an additional body of influence was created, as shown in Figure 5, which acts like a refined far field. A general unstructured tetrahedral mesh was chosen with a higher y ⁺ value, and a 15-boundary layer was created around the nacelle surface. The global mesh size was fixed to 15m with high smoothness and a 1.2 growth rate. Th pre-inflation algorithm and a 5 ^° curvature angle resulted in a minimum orthogonal quality of 0.1 and a maximum skewness of 0.9. The mesh size for the nacelle cowl and fan faces was generated using uniform face sizing of 0.1m, while the nacelle lip region was refined with face sizing ranging from 0.045m to 0.085m. The mesh over a nacelle and farfield surfaces can be seen from the Figure 5 and the detailed mesh settings of CRM nacelle are given in the Table 3.

A cylindrical farfield allows a linear transition of mesh elements from coarse at the boundary to finer near the wing surface. It reduces the distortion and ensures symmetry, which helps in handling the boundary conditions. Additionally, a dome-shaped far field improves the convergence and accuracy of the CFD analysis.

3.1.3 Numerical modeling

The Fluent software solves the following Navier-Stokes equations, composed of continuity equation and momentum equations as given below (1) – (5). ⁶¹ Continuity equation : ∂u ∂x + ∂v ∂y + ∂w ∂z = 0 (1) X − Momentum equation : ρ Du Dt = − ∂p ∂ x + μ ( ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 + ∂ 2 u ∂ z 2 ) + ρ . f x (2) Y − Momentum equation : ρ Dv Dt = − ∂p ∂ y + μ ( ∂ 2 v ∂ x 2 + ∂ 2 v ∂ y 2 + ∂ 2 v ∂ z 2 ) + ρ . f y (3) Z − Momentum equation : ρ Dw Dt = − ∂p ∂ z + μ ( ∂ 2 w ∂ x 2 + ∂ 2 w ∂ y 2 + ∂ 2 w ∂ z 2 ) + ρ . f z (4) Reynolds equation : R e = ρ . v . L μ (5)

The Reynolds number is a unitless parameter that determines the nature of fluid motion, indicating whether the fluid exhibits laminar or turbulent behaviour. Equation (5) gives the expression for the Reynolds number, where ρ denotes fluid density (kg/m ³), V is velocity (m/s), and μ refers to the dynamic viscosity of the fluid (kg/ms).

3.1.4 Boundary conditions for the wing analysis

The CFD setup has a cylindrical farfield with pressure-far-field boundary conditions, a symmetry plane, and a no-slip wall on the aircraft surface. Figure 6 and Table 4 the represents detailed boundary conditions are used in the aerodynamic analysis of the nacelle. Before establishing the boundary conditions, the International Standard Atmosphere (ISA) table ⁶² was used to determine the following important atmospheric parameters, such as temperature (218.81 K), density (0.3796 kg/m ³), and pressure (23842 Pa) of air at 35,000 ft altitude. ⁵⁷

The total pressure for the analysis was calculated by using the Equation 6. ⁶³ Similarly, the total temperature at the inlet of the engine was calculated using the Equation 7. ⁶³ By solving both Equation 1 and Equation 2, total pressure and temperature of 38238 Pa and 250K are obtained. P ∞ = p ∞ ( 1 + γ − 1 2 M 2 ) γ − 1 γ (6) T ∞ = t ∞ ( 1 + γ − 1 2 M 2 ) (7)

Where P _∞ is the total pressure in P _a, p _∞ is the static pressure in P _a, M is the Mach number, γ is the specific heat ratio, T _∞ is the total temperature in K, and t _∞ is the static temperature in K. In the boundary condition, the gauge pressure is applied at the fan inlet; to calculate the gauge pressure, Equation 8 ⁵⁷ is used. By solving the corresponding equation, a gauge pressure of 14396.238 Pa is obtained. P gauge = ( PR × P ∞ ) − p ∞ (8)

Where P _gauge is the gauge pressure at the inlet and PR is the blowing pressure ratio.

Additionally, the SST k-epsilon model accurately captures the boundary layer effects and shock separations in transonic flows. The material property for the air was selected as the ideal gas with Sutherland viscosity, allowing the solver to accurately calculate the density of the air based on pressure and temperature input.

The nacelle surface area was taken from the reference paper, ⁵⁷ and the chord length of the wing was taken as the reference length. The report definition was defined to calculate C _d at the wing surface. In this analysis, implicit method with AUSM flux type scheme was utilized. Additionally, Second-order equation blending was selected using transonic solution steering, and the “Least square based cell” scheme was used to calculate all gradients. The solution convergence was monitored until the solution reached the convergence threshold of 10 ⁻⁶ (i.e. 0.000001). Hybrid initialization was used in the analysis because it combines all the initialization techniques to provide accurate and effective starting point for the simulation. Since the analysis is focused on transonic flow over a wing, it is essential to opt for hybrid initialization to achieve faster convergence and improved solution quality. After initialization, the solution was iterated for 1000 iterations and due to good mesh quality, the solution converged within 350 iterations. The convergence graph of the nacelle can be seen from Figure 7.

The results shown in the Figure 8 and Table 5 represent the grid independency test of a CRM nacelle at 0.85 Mach, 0 ^° AoA, and an altitude of 35,000 ft. From the table, the highest C _d observed is 0.00256 at 1.47 million cells with an error of 5.78%. The lowest C _d value is 0.00245, consistently observed at 1.64 million cells onwards with a reduced error of 1.24%. In the graph, the C _d shows a sharp drop as the cell count increases from 1.4 to 1.64 million; thereafter, the C _d stabilizes. The highlighted point at 1.64 million cells indicates the selected grid size for further simulation.

The CRM nacelle underwent a grid independency test with five different mesh sizes shown in the Figure 9. From a grid size of 1.64 million elements, a constant C _d of 0.00245 was observed. At 0.85 Mach and 0 ^° AoA, a high pressure of 38030.69 Pa appeared near the nacelle lip region. Intermediate pressure between 12039.975 Pa and 26891.816 Pa is observed over the nacelle cowl surface. The low pressure ranging from 894.189 Pa to 8335.731 Pa is observed at the nacelle exit where the velocity is maximum. The above contour results validate accurate prediction under the grid-independency test. The continuous pressure contours on the nacelle surfaces confirms that a 1.64 million mesh size is good enough to capture the key aerodynamic parameters.

The above Figure 10 represents the pressure contours of the halved nacelle. A maximum pressure of 14500 Pa is observed at the inlet fan face. The peak pressure is uniformly distributed over the fan surface, but at the inlet fan edges, an intermediate pressure is observed.

The above Figure 10 highlights pressure contours over the baseline nacelle surfaces. From the figure, a maximum pressure of 41417.2 Pa is observed at the nacelle lip and inlet fan surfaces. The peak pressure is much higher compared to the reference article because, in the baseline analysis, the full engine is used. Similarly, an intermediate pressure of 20920.07 Pa to 32632.719 Pa is observed on the cowl surface. Additionally, at the fan face the pressure ranges from 8327.015 Pa to 15752.936 Pa, and it is closer to the. ⁵⁷ Additionally, variation in the pressure values of baseline and reference model can be observed from the graph.

Six different turbulence models were evaluated for a CRM nacelle at 0.85 Mach using a fixed grid size of 1.64 million cells. The table and graph highlight the C _d values for six different turbulence models. The highest C _d was 0.00245 using the K-epsilon standard model with a validation error of 1.24%. The lowest C _d was 0.00231 from the Reynolds stress model, but this model has the highest error of 4.54%. The graph clearly shows minimal grid count variation while C _d varies among turbulence models. Figure 11 and Table 6 show that the K-epsilon model has the lowest validation error of 1.24%, and this model was selected for further analysis of the CRM nacelle.

Six different turbulence models were tested using 1.64 million mesh elements, and the k-epsilon model showed the lowest validation error of 1.24%. Compared to other turbulence models, the k-epsilon model provided more accurate results due to its robustness in predicting fully developed turbulent flows and its ability to handle high Reynolds number boundary layers in the nacelle. From the pressure contour shown in Figure 12, a high pressure of 38030.69 Pa is noticed at the nacelle lip region. Intermediate pressure between 12039.975 Pa and 26891.816 Pa appeared on the nacelle cowl surface. A low-pressure zone ranging from 894.189 Pa to 8335.731 Pa is observed near the rear exit portion, indicating flow expansion and pressure drop.

Figure 13 and Table 7 shows how the C _d varies with the different Mach numbers for a CRM nacelle simulated on a mesh with 1.64 million cells. The Mach number varies from 0.8 up to 1.3 under the transonic regime. The C _d is very low at subsonic speeds, starting at about 0.00165 at 0.8 Mach. As the Mach number increases towards transonic speed, the cd rises sharply, reaching a peak at 0.95 Mach and slightly dropping at 1 Mach. As the Mach number increases from 1.05 to 1.3, the C _d gradually decreases from 0.0127 to 0.0113. This trend reflects typical drag behaviour near the critical Mach number, where the drag rises sharply due to shock formation and then decreases slightly as the flow becomes fully supersonic.

The contour plot Figure 14 represent the complete flow analysis of the CRM nacelle at 0.8 Mach. In the velocity streamline the flow separation is observed at the nacelle lip, where the velocity reaches 375.969 m/s. The maximum velocity of 563.954 m/s appears at the nacelle exit region. An intermediate velocity between 56.395 m/s and 112.791 m/s is observed over the nacelle cowl surface. Additionally, air velocity between 250.646 m/s and 375.969 m/s is observed over the nacelle cowl. From pressure contours, the maximum pressure of 36148.5 Pa occurs at the nacelle lip due to stagnation. Intermediate pressures of 15013.665 Pa to 25581.08 Pa are seen over the cowl surface. On the diffuser, the pressure ranges from 7968.72 Pa to 11491.192 Pa. In density contours, the maximum value of 0.525 kg/m ³ appears at the nacelle lip, while intermediate densities from 0.274 kg/m ³ to 0.424 kg/m ³ are observed over the cowl surface. Temperature contours show a high temperature of 230.705K uniformly distributed along the nacelle cowl and lip region, while the fan face experiences the intermediate temperature of 199.159K. Kinetic energy contours reveal low values between 0 and 1431.48 m ²/s ² covering the entire nacelle rare.

The flow contours shown in Figure 15 illustrate the complete CRM nacelle aerodynamic behaviour at 0.85 Mach. In the velocity streamline contour, a flow separation is observed at the nacelle lip region at 379.589 m/s stagnation velocity. The maximum velocity of 569.383 m/s occurs at the nacelle exit. Intermediate velocities ranging from 189.794 m/s to 379.589 m/s are distributed along the nacelle cowl surface, and the intermediate velocity is experienced at the fan face. The pressure contour shows a peak value of 38030.699 Pa at the nacelle lip caused by stagnation. Over the cowl surface, an intermediate pressure ranges between 15752.936 Pa and 26891.816 Pa. The diffuser experiences a pressure ranging between 8327.015 Pa and 15752.936 Pa. In density contours, the highest density of 0.545 kg/m ³ is observed at the lip region, whereas intermediate densities range between 0.231 kg/m ³ and 0.388 kg/m ³ across the cowl surface. The temperature contour shows a high uniform temperature of 234K throughout the lip and cowl regions. The fan face experiences temperatures between 169.691K and 201.846 K. Additionally; the kinetic energy contours reveal low energy levels between 0 m ²/s ² and 1545.535 m ²/s ² across all the nacelle faces.

Figure 16 shows the flow contours of the CRM nacelle analysis at 0.9 Mach. Velocity streamlines indicate flow separation near the nacelle lip region, with local velocity reaching 382.18 m/s. The highest velocity is observed at the nacelle exit with a value of 573.27 m/s. An intermediate velocity between 254.787 m/s and 445.877 m/s is observed over the nacelle cowl surface, and the same velocity is also observed at the fan faces. The pressure contour shows a high pressure of 40106.301 Pa at the nacelle lip region caused by the stagnation effect. The intermediate pressure between 20532.842 Pa and 32276.918 Pa is observed on the cowl surface. The diffuser face has moderate pressure between 8788.765 Pa and 16618.148 Pa. In the density contour, a maximum density of 0.567 kg/m ³ is observed at the nacelle lip, while the cowl surface shows a density range between 0.186 kg/m ³ and 0.404 kg/m ³. The temperature contour shows a uniform high-temperature value of 221.332K over the lip and cowl surfaces. The fan face experiences a temperature range from 172.456K to 221.332K. The kinetic energy values remain low across the nacelle region, ranging from 0.001 m ²/s ² to 1520 m ²/s ².

Figure 17 shows all the flow contours of the nacelle analysis at 0.95 Mach. From the velocity streamlines, flow separation is observed near the nacelle lip region with a velocity reaching 386.511 m/s. The maximum velocity at the nacelle exit is 579.767 m/s. Over the cowl surface, an intermediate velocity between 257.674 m/s and 450.93 m/s is observed. The same intermediate velocity is observed at the fan faces. From the pressure contours, a maximum pressure of 42383.199 Pa is observed at the nacelle lip region. Over the cowl surface, intermediate pressure ranges between 21635.088 Pa and 29934.332 Pa. On the diffuser surface, the pressure value further reduces between 13335.841 Pa and 21635.088 Pa. The density contour shows a maximum density of 0.592 kg/m ³ near the nacelle lip region, while moderate density between 0.251 kg/m ³ and 0.421 kg/m ² is observed over the cowl surface. The temperature distribution is almost uniform with a value of 207.925K across the fan face, nacelle lip, and cowl regions. The kinetic energy contour indicates lower values ranging between 0.001 m ²/s ² and 1939.731 m ²/s ² across the nacelle faces.

Figure 18 presents the flow contours of the CRM nacelle at 1 Mach. Velocity streamlines indicate flow separation near the nacelle lip region, where the flow velocity reaches 406.556 m/s. The maximum velocity of 609.834 m/s is observed at the nacelle exit. Intermediate velocity ranging from 271.037 m/s to 406.556 m/s is observed over the cowl surface, and the same velocity is observed at the fan face. The pressure contours show a maximum pressure of 44881.102 Pa at the nacelle lip region caused by the flow stagnation. Intermediate pressure values ranging between 18213.582 Pa and 31547.344 Pa occur over the cowl surface. The diffuser faces experience a pressure between 9324 Pa and 18213.582 Pa. In the density contour, the highest density of 0.618 kg/m ³ is observed at the nacelle lip region. An intermediate density value from 0.254 kg/m ³ to 0.436 kg/m ³ is observed on the lip and cowl surface. The temperature contour shows a uniform high temperature of 225.253K across both the cowl and lips regions. At the fan face, the temperature ranges between 225.253K and 243.733K. The kinetic energy contour reveals that nacelle faces experience a low kinetic energy between 0 m ²/s ² and 2492.131 m ²/s ².

Figure 19 displays all the flow contours of the CRM nacelle analysis at 1.05 Mach. From the velocity streamline, flow separation is observed near the nacelle lip region with a velocity reaching 412.398 m/s. A maximum velocity of 618.597 m/s is observed at the nacelle exit regions. Over the cowl surface, intermediate velocities between 247.439 m/s and 433.018 m/s are observed. The fan face of the nacelle experiences a moderate flow velocity of 247.439 m/s. The pressure contour shows a maximum value of 47615.801 Pa at the nacelle lip due to stagnation. Pressure on the cowl moderately ranges between 19268.906 Pa and 33442.352 Pa, while the diffuser face experiences a pressure between 14544.423 Pa and 19268.906 Pa. Density contour shows a maximum density value of 0.646 kg/m ³ at the nacelle lip. Similarly, an intermediate density between 0.264 kg/m ² and 0.455 kg/m ³ is observed at the cowl and fan faces of the nacelle. Temperature contour shows a high temperature of 209.505 uniformly distributed over the nacelle cowl and lip areas. The fan faces record a temperature between 209.505K and 247.626K. Additionally, Kinetic energy values range from 0.001 m ²/s ² to 2507.291 m ²/s ² across all nacelle faces.

Figure 20 show all flow contours of the CRM nacelle at 1.1 Mach. Flow separation is visible near the nacelle lip, where velocity reaches 418.022 m/s. The highest velocity occurs at the nacelle exit, with a value of 627.033 m/s. Over the cowl surface, intermediate velocity ranges from 348.352 m/s to 487.692 m/s, and a moderate velocity of 250.813 m/s is observed at the fan face. From the pressure contour, a peak pressure of 50540.302 Pa is recorded at the nacelle lip due to stagnation. Intermediate pressures are distributed over the nacelle cowl surface, ranging from 20420.861 Pa to 35480.73 Pa. The diffuser faces experience a pressure between 10380.949 Pa and 15400.905 Pa. Density contours show a maximum density of 0.675 kg/m ³ at the nacelle lip, and an intermediate density ranging from 0.275 kg/m ³ to 0.475 kg/m ³ is observed over the cowl surface. Temperature contours indicate a nearly uniform high temperature of 271.378K across the nacelle cowl and lip region. At the fan face the temperature varies between 232.154K and 271.378K. The kinetic energy remains low over nacelle faces with values ranging from 0 m ²/s ² to 2579.031 m ²/s ².

The Figure 21 provides flow contours of the CRM nacelle at 1.15 Mach. From the velocity streamline it is observed that flow separation appears near the nacelle lip at 381.929 m/s. At the exit, velocity reaches a maximum value of 636.548 m/s, while the cowl region and fan face show moderate velocities ranging from 190.964 m/s to 445.584 m/s. Maximum pressure of 53719.699 Pa is observed at the nacelle lip due to the stagnation effect. Intermediate pressure on the cowl ranges from 21673.746 Pa to 37696.723 Pa. The diffuser pressure lies between 10991.761 Pa and 21673.746 Pa. The lip region shows a maximum density of 0.706 kg/m ³.

The cowl surface and fan faces have moderate density values ranging from 0.287kg/m ³ to 0.497kg/m ³. Temperature reaches 215.544K and it is distributed uniformly throughout the cowl surface. At the fan face, the temperature ranges from 215.544K to 276.291K. Additionally, the kinetic energy is low across all surfaces, ranging up to 2686.041 m ²/s ².

Figure 22 presents a detailed flow field analysis of the CRM nacelle operating at 1.2 Mach. From the velocity streamline contour, a flow separation is observed near the nacelle lip where the velocity reaches 429.099 m/s. The peak velocity of 643.649 m/s is observed at the nacelle exit region. Intermediate flow over the nacelle cowl surface ranges between 286.066 m/s and 500.616 m/s, whereas the fan face experiences a velocity between 193.095 m/s and 321.824 m/s. Pressure contour reveals a stagnation pressure of 57075 Pa at the nacelle due to incoming flow deceleration. Across the cowl surface, pressure values fall between 22999.947 Pa and 40037.473 Pa. Similarly, over the diffuser section, pressure reduces between 11641.597 Pa and 22999.947 Pa. Density contour shows a maximum density of 0.739 kg/m ³ at the nacelle lip region. Intermediate densities across the cowl surface range between 0.373 kg/m ³ and 0.519 kg/m ³. The temperature distribution is nearly uniform, showing a value of 219.072K across the nacelle lip and cowl surface. At the fan face, the temperature varies between 239.854K and 281.419K. The turbulent kinetic energy distribution remains low over the nacelle faces with a low value between 0 to 2798.591 m ²/s ².

Figure 23 shows all the flow contours of the CRM nacelle at 1.25 Mach. Velocity streamlines indicate flow separation near the nacelle lip region, with stagnation velocity reaching 433.983 m/s. A maximum velocity of 650.974 m/s is observed at the nacelle exit. Over the nacelle surface, the intermediate velocity ranges from 361.652 m/s to 506.313 m/s. Moderate pressure between 195.292 m/s and 260.39 m/s is observed at the nacelle fan face. From the pressure contour, a maximum pressure of 60669.801 Pa is observed at the nacelle lip due to stagnation. An intermediate pressure between 30465.691 Pa and 42547.336 Pa is observed over the cowl surface. Similarly, the fan face and diffuser section experience a moderate pressure between 18384.047 Pa and 36506.512 Pa. The density contour shows a maximum density of 0.772 kg/m ³ at the nacelle lip region. The cowl region shows a density between 0.389 kg/m ³ and 0.466 kg/m ³. The temperature contour indicates a nearly uniform temperature of 224.026K across the nacelle cowl and lip surface. The fan face experiences temperatures ranging from 224.026K to 289.008K. The turbulence kinetic energy remains low across all nacelle regions with values between 0 m ²/s ² and 2781.231 m ²/s ².

Figure 24 displays all the flow contours of the CRM nacelle analysis at 1.3 Mach. From the velocity streamline, flow separation is observed near the nacelle lip region with a velocity reaching 439.241 m/s. A maximum velocity of 658.862 m/s is observed at the nacelle exit regions. Over the cowl surface, intermediate velocities between 292.828 m/s and 512.448 m/s are observed. The fan face of the nacelle experiences a moderate flow velocity of 2263.545 m/s. From the pressure contour, a peak pressure of 64450.398 Pa is recorded at the nacelle lip due to stagnation. Intermediate pressures are distributed over the nacelle cowl surface, ranging from 32344.08 Pa to 45186.605 Pa.

The diffuser faces experience a pressure between 19501.553 Pa and 45186.605 Pa. In the density contour, a maximum density of 0.807 kg/m ³ is observed at the nacelle lip, while the cowl surface shows a density range between 0.0246 kg/m ³ and 0.0567 kg/m ³. The temperature contour shows a high uniform temperature of 229.786K throughout the lip and cowl regions. The fan face experiences temperatures between 229.786K and 274.503K. Additionally, the kinetic energy contours reveal low energy levels between 0 m ²/s ² and 3029.031 m ²/s ² across all the nacelle faces.

4.5.1 Nacelle cone core modeling

The nacelle core assembly, which encloses and safeguards the jet engine, plays a critical role in enhancing aerodynamic efficiency, minimizing noise emissions, and facilitating maintenance accessibility. The nacelle core assembly also integrates thrust reversers to improve braking and flight safety.

During nacelle optimization, a core cone was assembled in accordance with a reference design, ⁵⁸ and the baseline angle of the core cone was found to be 15.7 ^°. To investigate the transonic aerodynamics of the nacelle, the core-cone angle was uniformly increased from 15.7 ^° to 16.7 ^° in 0.5 ^° step increments and decreased down to 13.7 ^° in 0.5 ^° step decrements. The optimized nacelle was tested at 0.82 Mach to understand the nacelle's aerodynamic performance and efficiency. The cone angle variation and 3D model of the cone assembled nacelle are shown in Figure 25.

4.5.2 Optimized nacelle grid indecency test

Figure 26 and Table 8 represent the grid independency test results of the optimized CRM nacelle model under specific flow conditions, where the AoA is 8 ^°, the altitude is 35000ft, and the Mach number is 0.82. The gauge pressure and total temperature are calculated using the isentropic relations corresponding to 0.82 Mach by ensuring realistic flight boundary conditions. Among the tested mesh sizes ranging from 2.3 to 2.9 million elements, the highest C _l error was 8.87%, observed at 2.3 million cells. Meanwhile, the lowest error recorded was 8.42%, consistently found at 2.55, 2.7, and 2.9 million cells. This confirms that beyond 2.55 million cells, further refinement yields negligible improvement in accuracy; therefore, this mesh size was selected for further analysis.

4.5.3 Different turbulence models for the optimized nacelle

The Table 9 and Figure 27 represent the performance of six different turbulence models tested at 0.82 Mach on the optimized CRM nacelle model. All simulations used a constant mesh size of 2.55 million elements, allowing a fair comparison of each turbulence model's C _l prediction and corresponding error percentage. Among the tested models, the Reynolds stress model produced the highest 0.01342 C _l value with a 13.81% error. The Spalart-Allmaras model predicted a C _l of 0.01099, yielding the lowest error of 8.42%, indicating superior agreement with the reference value. The K-epsilon and K-omega models showed moderate errors of 9.5% and 10.02%, respectively. Transition-based models, including SST and K-Kl, displayed higher deviation, with errors above 10%. Upon validation, the Spalart-Allmaras model produced a C _l value closer to the reference data and showed the least validation error of 8.42%; therefore, this turbulence model was selected for further nacelle core optimization.

4.5.4 Optimized nacelle results and discussions

Figure 28 and corresponding Table 10 represent the results of aerodynamics optimization for nacelle core assembly at the transonic speed of 0.82 Mach. The cone angle was varied from 13.7 ^° to 16.7 ^°at a fixed mesh size of 2.55 million elements. The C _l corresponding to each cone angle was determined using CFD simulations with the Spalart-Amara turbulence model.

The highest C _l value of 0.011035 was achieved at 1.37 ^°, indicating an optimal cone geometry for lift enhancement. At the 15.7 ^° baseline angle, the C _l was 0.01098, which was lower than the optimal case, indicating suboptimal efficiency. As the cone angle increased beyond 15.7 ^°, the C _l progressively decreased and reached a minimum C _l value of 0.01094 at 16.7 ^°. The results clearly demonstrate that a reduction in cone angle below the baseline enhanced the aerodynamic performance.

Figure 29 represents all flow contours of the optimized CRM nacelle at 0.82 Mach. From the velocity streamlines, flow separation is observed near the nacelle lip region with a local velocity of 270.716 m/s. Over the cowl surface, air velocities were distributed in the range of 270.716 m/s to 406.075 m/s, and a similar velocity is observed at the fan faces. A maximum velocity of 609.112 m/s is noted at the nacelle exit.

From the pressure contour it is observed that due to the stagnation effect, a maximum pressure of 36857.5 Pa is observed at the nacelle lip. An intermediate pressure between 20570.785 and 28714.143 Pa is observed over the cowl surface. At the diffuser region, the pressure values were found in the range of 8355.746 Pa to 20570.785 Pa. The density contour shows a maximum value of 0.536 kg/m ³ near the nacelle lip. Over the cowl surface, density ranges from 0.24 kg/m ³ to 0.358 kg/m ³.

At the diffuser and fan face areas, the density values are between 0.181 kg/m ³ and 0.24 kg/m ³. A nearly uniform temperature of 206.688K is observed over the cowl and lip surfaces. Temperature between 144.509K and 206.688K is observed at the fan face and diffuser surface. Similarly, the kinetic energy values range from 0 m ²/s ² to 8482.033 m ²/s ² over the entire nacelle surface.

In Figure 30, the optimized nacelle is compared with the baseline nacelle. The velocity streamlines of the CRM nacelle at a 15.7° base cone angle and a 13.7° optimized cone angle show a clear aerodynamic difference due to shape refinement. In the baseline case, flow separation occurs near the lip region with a velocity of 271.89 m/s. Similarly, at the nacelle exit, the streamline reaches a maximum value of 611.571 m/s. The internal flow fields show intermediate velocities between 203.857 m/s and 407.714 m/s, indicating non-uniform fan face inflow. From the streamline contour, it is observed that the optimized nacelle produces more attached streamlines compared to the baseline. The maximum velocity of the optimized is 609.114 m/s, which is slightly less compared to the baseline. Similarly, the intermediate velocity of the optimized nacelle ranges between 237.657 m/s and 406.971 m/s; this results in smoother and reduced flow distortion. The optimized CRM nacelle resulted in better pressure recovery, reduced drag, improved lift, and stable inflow conditions.