2.1 Solver setting and boundary conditions

The Fluent module of ANSYS is used for 2D, transient, incompressible viscous analysis of the flow field around the configurations under study. A pressure-based solver was used with SST-kw selected as a turbulence model. The jet width acts as an inlet for the entire domain, whereas the domain boundary acts as a wind inlet and outlet according to the requirement. Both the inlets were modelled as velocity inlets to simulate jet flow and the incoming free stream. The outlet was modelled as a pressure outlet with zero-gauge pressure, and the aerofoils surfaces as no-slip walls. All the cases were simulated for various wind and jet velocities to capture the true effect of geometric variation. The domain and boundary conditions are annotated in Fig. 4 and Table 2. The selected domain inlet velocities of 10 and 20 m/s and wing chords of 8 inches correspond to Reynolds number (Re) of 1.37 × 10⁵ and 2.72 × 10⁵, respectively. A velocity ratio (bladeless fanjet velocity/freestream velocity) was kept as 2 for the present computational work owing to experimental capability limitation. Generally, the jet ratio $\left( {{V_J}/{V_\infty }} \right)\;$ must be greater than the ratio of local velocity at the maximum thickness of baseline wing to free stream $\left( {{V_{0.25c}}/{V_\infty }} \right)$ to ensure inducement and entrainment of the surrounding flow in the presence of free stream conditions.

Table 2.

Boundary conditions (BC) for the computational setup

Table 2 Long description

The table outlines boundary conditions for a computational setup, focusing on geometric features, applied boundary conditions, values of those conditions, and remarks. The first column lists geometric features such as jet inlet, domain inlet, domain outlet, fanjet surface, and baseline wing. The second column specifies the type of boundary condition applied, including velocity inlet, pressure outlet, and wall. The third column provides the values of these boundary conditions, ranging from 0 to 40 meters per second for velocity inlets and zero gauge pressure for the pressure outlet. The fourth column offers remarks, such as the step size for the jet inlet and the jet ratio for the domain inlet. Notable trends include the use of velocity inlets for both jet and domain inlets and the consistent application of no-slip conditions for walls.

Note: A jet ratio of 2 is higher than the local velocity ratio $\left( {{V_{0.25c}}/{V_\infty }} \right)$ for the computational cases.

Figure 4.

Computational domain, boundary conditions and domain meshing. Fanjet and bladeless fan have been used interchangeably in this work.

Figure 4 Long description

The diagram illustrates a computational domain for a bladeless fan. It features a velocity inlet at the top, a velocity inlet for the jet in the middle, and a pressure outlet on the right side. The wall, labeled as the baseline plus fanjet airfoil, is depicted with a curved shape. The diagram includes detailed views of the fanjet and the surrounding mesh structure. Arrows indicate the direction of airflow, and the overall structure shows the interaction between the jet and the surrounding air, demonstrating the principles of inducement and entrainment.

Figure 5.

Mesh independence study. The selection parameters are C _l and C _d at Re of 2.74× 10⁵. A mesh size of 0.987 m was selected with a % difference of 1.6 and 1.65% for C _l and Cd, respectively.

Figure 5 Long description

A line graph showing mesh independence study with C l and C d at Re of 2.74 105. The x axis represents mesh size in millions ranging from 0.4 to 1.2. The left y axis represents C l values ranging from 0.52 to 0.68. The right y axis represents C d values ranging from 0.012 to 0.018. The black line with square markers represents C l values at 5 degrees angle of attack, while the blue line with square markers represents C d values at 5 degrees angle of attack. The selected mesh size is 0.987 million, marked with red boxes on both lines. All values are approximated.

2.2 Mesh independence

A mesh independence study was conducted using drag and lift as a reference parameter. Only free-stream wind was simulated with no input from the bladeless fanjet. Meshing was done using the ANSYS Mesh module, and cases were simulated in the ANSYS Fluent module. Based on the drag and lift values computed from the test cases, a mesh size of 0.978 m was selected for further analysis. The domain mesh is presented in Fig. 4 and mesh independence study in Fig. 5.

2.3 Validation

Considering the complexity of the problem and non-availability of scientific investigations for this specific integrated domain, the authors exercised careful judgement and due diligence in selecting an appropriate validation strategy. Multiple cases with varying configurations were employed for validation, including bladeless fan and selected baseline aerofoil experimental and computational studies reported by various researchers. The summary of the validation process is presented in Table 3.

Table 3.

Summary of the validation work carried out for 2D and 3D cases

Table 3 Long description

The table presents a summary of the validation work conducted for 2D and 3D cases. It consists of four columns: Type of validation, Validation against, Validation parameter, and Remarks. The table has six rows, each detailing different validation scenarios. Row 1: Computational analysis of 2D bladeless fan, Experimental data by Li et al., Peak velocity value and velocity profile 15 centimeters downstream of jet inlet, Adopted from author's previous work, still valid for present work as computational settings are same. Row 2: Computational analysis of 3D bladeless fan, Computational data by Ravi et al., Ratio of outlet/inlet volume flow rate captured at 3-hydraulic diameter downstream of fan LE. Row 3: Computational analysis of aerofoil (NACA-0012), Published aerofoil data, Lift and drag with varying angles of attacks, Results shown in section III. A. Row 4: Computational analysis of NACA-0012 Wing (AR 3), Computational data by Shahrooz et al., Lift and drag with varying angles of attacks, Results shown in section V. A. Row 5: Computational analysis of 2D bladeless fan, Data generated for annular jets by Rehab et al. and Ball et al., Flow field similarities, Adopted from author's previous work and summary presented at section II. C.

Figure 6.

Validation study for 2D cases. Velocity profile downstream of bladeless fan was captured and compared against the experimental data captured by Li et al. [Reference Li, Deng and Lai40].

Figure 6 Long description

The image contains multiple graphs and diagrams related to a validation study for 2D cases. The top left section shows two shapes with annotations indicating validation against experimental data from Li et al. and published airfoil data for NACA 0012. The top right section features a line graph comparing the coefficient of lift and drag against the angle of attack for both bladeless fan (BW) and airfoil data. The bottom left section displays a diagram of the computational domain with dimensions and boundary conditions for the bladeless fan. The bottom right section presents a line graph comparing vertical distance against velocity, with data from present computational fluid dynamics (CFD) work and experimental data.

As the present work is the continuation of the author’s previous work [Reference Mehmood, Shahzad, Qadri, Salamat, Shams and Masud13] with the same 2D computational setup to analyse bladeless fan over baseline wing, therefore the validation process adopted for the bladeless fan holds good for present study as well. An overview of the validation is presented here for reference. The validation was carried out against the experimental work conducted by Li et al. [Reference Li, Deng and Lai40]. Based on the geometric parameters of Li et al. [Reference Li, Deng and Lai40], a 2D axis-symmetry case was modelled and meshed in an ANSYS environment. The simulations were conducted using a pressure-based solver with SST-kw as the turbulence model. As per the experimental setup [Reference Li, Deng and Lai40], the velocity profile at 15 cm downstream of the jet inlet from the validation work was compared with the experimental results. The velocity profile was successfully captured with peak velocity differing by a maximum of 3.9%, thus successful validation for the computational setup was achieved (Fig. 6). For further details on validation studies, readers are referred to authors’ previous study [Reference Mehmood, Shahzad, Qadri, Salamat, Shams and Masud13].

Figure 7.

Lift and drag coefficients of baseline wing (a) comparison with published aerofoil data [41]; (b) comparison at different Re (BLW-1 and BLW-2).

Figure 7 Long description

The line graph consists of two subplots labeled (a) and (b). Subplot (a) compares the lift and drag coefficients of a baseline wing with published airfoil data. The x-axis represents the angle of attack in degrees, ranging from negative 2 to 16 degrees. The y-axis on the left represents the coefficient of lift, ranging from 0 to 1.2, and the y-axis on the right represents the coefficient of drag, ranging from 0 to 0.6. The data series include BWL coefficient of lift, airfoil coefficient of lift, BWL coefficient of drag, and airfoil coefficient of drag. Subplot (b) compares the lift and drag coefficients at different Reynolds numbers, labeled as Re 2 and Re 1. The x-axis represents the angle of attack in degrees, ranging from negative 2 to 16 degrees. The y-axis on the left represents the coefficient of lift, ranging from 0 to 1.2, and the y-axis on the right represents the coefficient of drag, ranging from 0 to 0.6. The data series include coefficient of lift at Re 2, coefficient of lift at Re 1, coefficient of drag at Re 2, and coefficient of drag at Re 1. All values are approximated.

3.1 Baseline wing configuration

The baseline wing was analysed to set the reference for bladeless fan configurations. The test case was simulated at Re of 2.74 × 10⁵ and 1.37 × 10⁵ for a range of AoA until the stall angle to determine lift and drag coefficients. As per Fig. 7, the stall angle and maximum lift coefficient are consistent with the aerofoil data. Similarly, the drag profile is also consistent with the aerofoil data set, thus further validating the authenticity of the simulations. As the Re decreased, the overall lift decreased and drag increased; again, the trends are consistent with the established theoretical trends. The BLW-1 and BLW-2 correspond to Re₁ (1.37 × 10⁵) and Re₂ (2.74 × 10⁵), respectively. Pressure plots were presented at 0°, 5° and 10° to support the variation in lift and drag (Fig. 8).

Table 4.

Bladeless fan/fanjet configurations (FC), its dimensional parameters, and operating conditions

Table 4 Long description

The table presents a comparison of bladeless fan configurations, their dimensional parameters, and operating conditions. It consists of ten rows and six columns. The columns are labeled as S no, Configuration, Bladeless fan location, Freestream, Jet speed, and Re. The Bladeless fan location is further divided into X and H. The Freestream column lists the velocity in meters per second, and the Jet speed column lists the velocity in meters per second. The Re column lists the Reynolds number. The table includes configurations such as BLF-1, FC-1, FC-3, FC-5, FC-7, BLF-2, FC-2, FC-4, FC-6, and FC-8, with varying dimensions and operating conditions.

Different bladeless fan configurations were tested under the same solver settings with different jet speeds. The geometric details of the configurations tested are presented in Table 4. The cases for Re₁ are represented by odd number configurations and Re₂ with even numbers.

Figure 8.

Pressure plots at various angles of attack (a) 0°, (b) 5° (c) 10°. There is no variation of ΔP (difference in pressure of lower and upper surface of the aerofoil) at 0°; thus the lift is zero for both configurations. As the angle is increased, the ΔP increases more for Re₂ as compared to Re₁; therefore, more lift for BLW-2 as compared to BLW-1.

Figure 8 Long description

The line graph displays pressure plots at various angles of attack: (a) 0 degrees, (b) 5 degrees, and (c) 10 degrees. The x-axis represents the chord length in meters, ranging from 0 to 0.20 meters. The y-axis represents the pressure in Pascals, with different scales for each subplot: (a) ranging from -150 to 250 Pascals, (b) ranging from -500 to 300 Pascals, and (c) ranging from -1200 to 400 Pascals. Two data series are plotted: BLW-1 represented by black squares and BLW-2 represented by red triangles. At 0 degrees angle of attack, there is no variation in pressure difference between the lower and upper surfaces of the aerofoil, resulting in zero lift for both configurations. As the angle of attack increases to 5 and 10 degrees, the pressure difference increases more for BLW-2 compared to BLW-1, indicating more lift for BLW-2. All values are approximated.

3.2 Baseline fan configurations

The BLF, i.e. V _J = 0 m/s, are compared with the corresponding BLW and results are presented in Figs 9 and 10. The variation in the results is purely based on the geometry of the bladeless fanjet and its interaction with the wing itself as no blowing is carried out in the baseline thruster cases. It can be observed that at Re₁, the BLW1 is superior in performance to the BLF1 configuration, however, as the Re is increased (Re₂), the BLF2 becomes slightly better than the BLW2, especially in the post-stall region. The pressure plots captured for BLW1 and BLF1 at a 10° angle are presented in Fig. 11 for correlation with the trends.

Figure 9.

Comparison of BLW1 and BLF1 at Re₁ – (a) C _l (b) C _d .

Figure 9 Long description

The line graph consists of two subplots labeled (a) and (b). Subplot (a) shows the lift coefficient (C l) versus the angle of attack (AoA) in degrees for BLW1 and BLF1. BLW1 is represented by black squares, and BLF1 is represented by blue circles. The lift coefficient increases with the angle of attack, peaking around 10 degrees for both designs, then slightly decreases. Subplot (b) shows the drag coefficient (C d) versus the angle of attack (AoA) in degrees for BLW1 and BLF1. The drag coefficient remains relatively low and constant up to around 10 degrees, after which it increases sharply for both designs. All values are approximated.

At Re₁ (1.37 × 10⁵), a negligible difference was observed in the lift values till 5^° AoA; however, beyond 5^° the BLF1 showed degradation in the lift values till stalling AoA. The lift for the BLF1 configuration is the sum of the lift produced by the wing and bladeless fan. From the pressure profile captured at 10^°, it can be observed that the bladeless fan itself is generating negative lift due to low-pressure values at the pressure side of the aerofoil, thus making the overall lift much less as compared to BLW1. In the post-stall region, the BLF1 maintained its lift whereas the lift for BLW1 drastically reduced confirming the complete stall of the baseline wing. The streamline plots are captured in the post-stall region to establish the flow physics (Fig. 12). A strong formation and shedding of the vortex can be seen on BLW1, which degrades the overall lift generation capability of the wing, whereas a steady vortex system is formed on BLF1. The air flowing through the channel path between the wing and bladeless fanjet (BLF1) under a favourable pressure gradient suppresses the flow detachment from the leading edge of the baseline wing as observed in BLW1 and thus retains sufficient lift. The drag values for BLF1 are higher as compared to BLW1 in the pre-stall region and showed improvement over BLW1 in the post-stall region because of lesser pressure drag as compared to BLW1.

Figure 10.

Comparison of BLW2 and BLF2 at Re₂ – (a) C _l (b) C _d .

Figure 10 Long description

The image contains two line graphs side by side. The left graph (a) shows the lift coefficient (C l) versus the angle of attack (AoA) in degrees for BLW2 and BLF2. The right graph (b) shows the drag coefficient (C d) versus the angle of attack (AoA) in degrees for BLW2 and BLF2. Both graphs have data points marked with black squares for BLW2 and red circles for BLF2. In graph (a), the lift coefficient increases with the angle of attack, peaking around 10 degrees before decreasing. In graph (b), the drag coefficient remains relatively low and stable up to about 10 degrees, after which it increases sharply. The comparison indicates how the lift and drag coefficients vary with the angle of attack for the two different configurations.

Figure 11.

Pressure plots for BLW1 and BLF1 configurations at 10^o AoA. A clear pressure variation can be observed for the BLF1 configuration which degrades the lift as compared to the BLW1 configuration.

Figure 11 Long description

A heat map showing pressure variations for BLW1 and BLF1 configurations at 10 degrees angle of attack. The heat map consists of two panels, each representing a different configuration. The left panel shows the BLW1 configuration, while the right panel shows the BLF1 configuration. The color scale at the bottom ranges from -300 to 200, with blue indicating lower pressure and red indicating higher pressure. The BLF1 configuration exhibits a clear pressure variation, which degrades the lift compared to the BLW1 configuration. The heat map highlights regions of high and low pressure, with notable differences between the two configurations.

At Re₂ (2.74 × 10⁵), BLF2 is generating more lift as compared to BLW2. The difference is negligible in the pre-stall region (Fig. 13) and more pronounced in the post-stall region (Fig. 14). The drag showed similar behaviour, in the pre-stall region i.e. the values for BLF2 are higher than BLW2; however, noticeable improvement was observed in the post-stall region. In the post-stall region, strong vortex formation and shedding were observed on BLW2, whereas a stable vortex formation was observed on BLF2 (Fig. 14).

Figure 12.

Streamline plots at 15^° AoA (post-stall region) for (a) BLF1 and (b) BLW1.

Figure 12 Long description

A heat map showing streamline plots at 15 degrees angle of attack in the post-stall region for two different bladeless fan designs, BLF1 and BLW1. The heat map consists of two subplots labeled (a) and (b). Subplot (a) represents the streamline plot for BLF1, while subplot (b) represents the streamline plot for BLW1. The color scale at the bottom ranges from -500 to 200, with blue indicating lower values and red indicating higher values. The streamline plots show the flow patterns around the bladeless fan designs, with distinct vortices and flow separations visible. The plots highlight the differences in flow characteristics between the two designs in the post-stall region.

Figure 13.

Pressure profile of BLW2 and BLF2 (wing only) at 5^° AoA.

Figure 13 Long description

A line graph compares the pressure profiles of BLW2 and BLF2 at a 5-degree angle of attack. The x-axis represents the chord location in meters, ranging from 0 to 0.20 meters. The y-axis represents the pressure in Pascals, ranging from -800 to 400 Pascals. The graph includes two data lines: one for BLW2 represented by blue diamonds and another for BLF2-Wing represented by red triangles. The location where the fanjet modifies the pressure profile on the wing is indicated with an arrow. All values are approximated.

Figure 14.

Pressure and streamline plots for BLW2 (top) and BLF2 (bottom) configurations at 15^° AoA (post-stall region). The variation in aerodynamic forces (see Fig. 9) for both the cases is attributted to the difference in the vortex system formation and associated pressure profile.

Figure 14 Long description

A heat map displays pressure and streamline plots for two different configurations, labeled as BLW2 and BLF2, at a high angle of attack in the post-stall region. The heat map uses a color scale ranging from deep blue to dark red, indicating varying pressure values. The top section shows the BLW2 configuration, while the bottom section shows the BLF2 configuration. The color intensity represents the pressure distribution, with blue indicating lower pressure and red indicating higher pressure. Streamlines are overlaid to show the flow patterns around the configurations. Notable regions include areas of high and low pressure, as well as the formation of vortices. The overall trend shows significant differences in the vortex systems and associated pressure profiles between the two configurations, which contribute to variations in aerodynamic forces.

Figure 15.

Comparison of bladeless fanjet configurations with baseline wing at low Re (10 m/s freestream velocity) (a) lift coefficient; (b) drag coefficient.

Figure 15 Long description

The line graph compares bladeless fanjet configurations with a baseline wing at a low Reynolds number, specifically at a freestream velocity of 10 meters per second. The graph consists of two subplots: (a) lift coefficient and (b) drag coefficient, both plotted against the angle of attack (AoA) in degrees. In subplot (a), the lift coefficient (C_l) is plotted on the y-axis, ranging from 0 to 1, while the angle of attack (AoA) is plotted on the x-axis, ranging from 0 to 20 degrees. The data series include BLW1, FC1, FC3, FC5, and FC7, each represented by different symbols and line styles. In subplot (b), the drag coefficient (C_d) is plotted on the y-axis, ranging from 0 to 0.3, while the angle of attack (AoA) is plotted on the x-axis, ranging from 0 to 20 degrees. The same data series are represented here as well. The lift coefficient generally increases with the angle of attack up to a certain point, after which it starts to decrease. The drag coefficient increases with the angle of attack, with notable spikes at higher angles. All values are approximated.

3.3 Bladeless fanjet configurations

Different fan configurations were simulated as mentioned in Table 4 and the results were compared with corresponding BLW configurations. The lift and drag for all the configurations were calculated and presented in Figs 15 and 20.

1. 1. Low Free Stream Condition (Re ₁ = 1.37 × 10 ⁵ ). In the pre-stall region, negligible variation was observed at 0^° AoA for all cases. At 5^° AoA, fan configuration FC5 and FC7 performance was lower, whereas FC1 and FC3 were at par with the BLW1. At 10^° AoA, except FC3, all the fan configurations have low C _l values as compared to BLW1 (Fig. 15a). In the pre-stall region, all the bladeless fan configurations have higher drag coefficients as compared to BLW1. Detailed flow analysis was carried out to ascertain the reason for the underperformance of various bladeless fan configurations. Figure 16 compares the pressure distributions of FC3 and BLW1 at 5° and 10° AoA. The pressure distribution of FC3 is negligibly disturbed by the presence of active fan blowing at 20 m/s. Thus, FC3 has a comparable lift value with BLW1. Pressure distributions for FC5 and FC7 are presented in Fig. 17. The fan effectively modifies the pressure distribution in both cases. Strong suction is created in the case of FC5 due to lesser channel height. However, the stagnation pressure created at the leading edge of the bladeless fanjet also modifies the pressure distribution on the leading edge of the wing as can be observed in Fig. 18. The change in pressure (ΔP) for FC5 is smaller than the BLW1, coupled with the small lift produced by the fan, the overall lift of FC5 is lower than BLW1. At 10° AoA, the trend is similar for pressure distribution, ΔP is lower as compared to BLW1 and FC7, thus having lower lift among the configurations.

Figure 16.

Pressure distribution on the upper and lower surface of BLW1 and FC3 (wing only) at (a) 5° AoA; (b) 10° AoA.

Figure 16 Long description

Two line graphs compare the pressure distribution on the upper and lower surfaces of BLW1 and FC3 at two different angles of attack. The x-axis represents the chord location in meters, ranging from 0 to 0.2 meters. The y-axis represents the pressure in Pascals, ranging from -150 to 100 Pascals in graph (a) and from -300 to 100 Pascals in graph (b). The red line with diamond markers represents the FC3-Wing, while the blue line with square markers represents BLW1. In graph (a), at a 5-degree angle of attack, the pressure distribution shows a peak and trough pattern for both surfaces, with the FC3-Wing exhibiting slightly different pressure values compared to BLW1. In graph (b), at a 10-degree angle of attack, the pressure distribution follows a similar pattern but with more pronounced peaks and troughs, indicating higher pressure variations. All values are approximated.

Figure 17.

Pressure distribution on the upper and lower surface of BLW1 and (a) FC5 (wing only) at 5° AoA; (b) FC7 (wing only) at 5° AoA; (c) FC5 and FC7 (wing only) at 10° AoA.

Figure 17 Long description

The line graph presents the pressure distribution on the upper and lower surfaces of BLW1 and FC5 Wing at a 5-degree angle of attack. The x-axis represents the chord location in meters, ranging from 0 to 0.2 meters. The y-axis represents the pressure in Pascals, ranging from -150 to 100 Pascals. The graph includes two data lines: one for BLW1 represented by blue circles and a solid blue line, and another for FC5 Wing represented by red triangles and a solid red line. The pressure distribution shows significant variations, with notable peaks and troughs indicating areas of high and low pressure along the chord location. All values are approximated.

Bladeless fan also modifies the pressure distribution on FC7; however, the net ΔP for FC7 is lower than BLW1 and hence lower lift values. At 10^° AoA, the flow toward the trailing edge of the wing is detached from the surface of the wing. The fan located at the trailing edge of the wing becomes ineffective in creating lower pressures, thus the overall effect is much closer to BLW1. In the post-stall region, the lift for all the bladeless fan configurations is higher as compared to the baseline wing. The baseline wing stalls at 12^° AoA with a separated flow on most parts of the wing, but in cases of bladeless fan configurations, the flow is attached thus having a higher lift.

Drag for all the configurations in the pre-stall regions are higher than the baseline wing configuration. FC7 has the lowest drag among all the fan configurations mainly due to the similar pressure distribution as on the baseline wing. In the post-stall region, the drag values are lower for all configurations except FC7. The main reason behind lower drag is low-pressure drag due to the attached flow. A vortex shedding phenomenon was observed on the FC7, which resulted in high drag values (Fig. 19). The flow detached from the leading edge of the main wing and was further aggravated by the fan located near the trailing edge. Sinusoidal behaviour was observed in FC7 where flow kept on attaching and detaching with overall higher drag values.

1. 2. High Free Stream Conditions (Re ₂ = 2.74 × 10 ⁵ ). In the pre-stall region, negligible variation was observed at 0^° to 5^° AoA for all cases except FC8, which has lower lift values as compared to all other configurations including baseline BLW2 (Fig. 20). The pressure profiles for FC8 and BLW2 are presented in Fig. 21. It can be observed that ΔP is lower for the FC8 as compared to BLW2, but the negative lift created by the bladeless fanjet further reduces the overall lift for the FC8. At 10^o AoA, FC8 and FC6 have lower lift values and FC4 and FC2 have higher lift values as compared to BLW2. FC4 and FC6 pressure profiles are presented in Fig. 22. The ΔP for FC4 is better as compared to FC6 and comparable to BLW2. The overall pressure profile of FC4 with bladeless fanjet is better than BLW2 and that of FC6 is less than BLW2. In the post-stall region, the lift for all the bladeless fanjet configurations is higher as compared to the baseline wing with a maximum increase of 71%. The baseline wing stalls at 12^° AoA with separated flow on most parts of the wing, but in cases of bladeless fanjet configurations, the flow is attached thus having a higher lift. A 15^° stall angle (25% increment) was observed for fanjet configurations.

Figure 18.

Pressure distribution for FC7 (top), BLW1 (middle) and FC5 (bottom) configurations at 10^° AoA. The pressure variation on the baseline wing in the presence of fan can be observed.

Figure 18 Long description

A heat map displays the pressure distribution for three different configurations at a 10-degree angle of attack. The top section shows the pressure distribution for the FC7 configuration, the middle section for the BLW1 configuration, and the bottom section for the FC5 configuration. The color scale ranges from blue, indicating lower pressure, to red, indicating higher pressure. The heat map reveals variations in pressure across the wing surfaces, with notable differences between the configurations. The baseline wing's pressure variation in the presence of a fan is observable, highlighting areas of high and low pressure.

In the pre-stall region, drag values for all the configurations are higher than the BLW2 configuration (a minimum of 50% increment in zero-lift drag), however, in the post-stall region, values are lower than the baseline wing for all configurations mainly due to lesser pressure drag. A minimum of 39% reduction in drag at 15^° AoA was observed.

3.4 Selection of bladeless fanjet configuration for 3D experimental and computational analysis

1. 1. Aerodynamic Efficiency. The drag polar and C _l /C _d versus α (AOA) were plotted in Fig. 23 for all configurations. Based on the results, it was inferred that installation of a bladeless fanjet toward the trailing edge was not a viable option as post-stall drag increment was more for this configuration at low Re. For leading-edge configurations, FC3 provided better lift-to-drag (L/D) values at low Reand post-stall characteristics. At high Re, FC2 and FC4 have achieved higher efficiency than the rest of the configurations.

2. 2. Net Propulsive Force. As the bladeless fanjet is also going to produce thrust for the respective configurations, it was imperative to calculate the net propulsive force for the configurations. Although propulsion analysis was not part of the research scope, to select a feasible configuration, a sample net propulsive force analysis was carried out. In case the net propulsive force came out to be negative, the respective configuration under operating conditions would not be sustainable. The net propulsive force is defined as the thrust force minus the drag force of the configuration. To calculate, the net propulsive force in the forward direction i.e. along the x-axis, a control volume was drawn over the configuration, as shown in Fig. 24. The pressure is acting perpendicular to the control boundaries; therefore, the top and bottom pressure profiles were not included in the calculation as they will only contribute toward normal force. Momentum flux was considered for all the faces along the x-axis. Net propulsive force is then the summation of net momentum flux and pressure forces along the x-axis. For reference calculation, only cases with zero AoA were selected for comparison. The values for different configurations are presented in Table 5.

3. 3. Selection of Configuration. From the values, it can be observed that as the bladeless fanjet height increases at the leading edge, the net propulsive force increases due to increase in momentum flux at the rear. The trailing edge configuration failed to generate thrust, as the outlet momentum flux is less as compared to the inlet, mainly because of very little entrainment close to the wing configuration. Higher jet speed (V _J = 40 m/s) produces higher propulsive force and is preferred. Based on aerodynamics (Fig. 23) and propulsive analysis (Table 5), FC2 and FC4 have shown better results as compared to the rest of the configurations. Keeping in view the wingspan limitation for wind tunnel tests, FC2 (smaller radius as compared to FC4) was selected as a baseline geometry for further 3D computational and experimental analysis.

Figure 19.

Pressure and streamline plots for – FC7 (left) and BLW1 (right). A strong vortex formation can be seen in both cases. The bladeless fan located near the trailing edge further aggravates the detached flow, thus increasing the overall drag for the FC7.

Figure 19 Long description

A heat map showing pressure and streamline plots for FC7 and BLW1 with strong vortex formations. The left plot represents FC7, and the right plot represents BLW1. Both plots display a color scale ranging from -500 to 200 pascals, indicating static pressure. The streamlines show the flow of air around an object, with noticeable vortex formations in both cases. The bladeless fan located near the trailing edge in the FC7 plot aggravates the detached flow, increasing overall drag. The color intensity varies, with darker regions indicating lower pressure and lighter regions indicating higher pressure. The plots highlight the differences in flow characteristics and pressure distribution between the two configurations.

Figure 20.

Comparison of bladeless fanjet configurations with baseline wing at high reynolds (20 m/s freestream velocity); (a) lift coefficient; (b) drag coefficient.

Figure 20 Long description

The line graph consists of two subplots labeled (a) and (b). Subplot (a) shows the lift coefficient (C l) versus angle of attack (AoA) in degrees for five different configurations: FC-6, FC-4, FC-8, FC-2, and BLW2. Subplot (b) shows the drag coefficient (C d) versus angle of attack (AoA) in degrees for the same configurations. Each configuration is represented by a different colored line and marker: FC-6 with black squares, FC-4 with red circles, FC-8 with green triangles, FC-2 with blue inverted triangles, and BLW2 with gray diamonds. The lift coefficient increases with the angle of attack up to around 10 degrees and then decreases. The drag coefficient generally increases with the angle of attack. All values are approximated.

5.1 Baseline wing configuration (BLW)

The baseline wing was analysed at Re 2.74 × 10⁵ and aerodynamic coefficients were computed against various AoA and compared with available literature data [Reference Shahrooz and Abdulkareem42]. As per Fig. 27, the stall angle, maximum lift, and drag coefficient are consistent with the wing of small Aspect Ratio (AR) [Reference Shahrooz and Abdulkareem42], thus further validating the authenticity of the simulations. The stall angle for the baseline wing is approximately 32^°.

5.2 Single fan configuration (SFC)

In a single fan configuration, the fan is attached to the baseline wing at the centre of the wing as shown in Fig. 25(a). This bladeless fanjet configuration was tested under the same solver settings with different jet and wind speeds. The operating conditions for the configurations tested are presented in Table 8. The configurations are based on geometric and operating condition of the bladeless fan, e.g. a configuration of 1FW20J40 means single bladeless fanjet at 0 deg (1F), freestream velocity of 20 m/s (W20) and jet velocity of 40 m/s (J40). The C_L versus α plot of SFC is compared with BLW and presented in Fig. 28(a). It can be observed that the variation in C_L for SFC is small at angles less than 10^° AoA; however, at 10^° and above, there is a significant improvement in the lift in comparison with BLW (a maximum of 14% increase in the C_{L_max} at 30°). Below 10°, the effect of the bladeless fan on the wing is nullified by the bladeless fanjet itself by creating a negative lift (Fig. 28b). Due to the high-speed jet emanating at the pressure side of the bladeless fanjet aerofoil, the bladeless fanjet produces negative lift till 10^° AoA. The stall angle is the same for both the configurations; however, the bladeless fanjet configuration (1FW20J40) shows a gradual stall in comparison with baseline wing (a maximum of 22.5% increase in the C_L at 35° - post-stall region).

Table 8.

Operating conditions for single bladeless fanjet configurations

Table 8 Long description

The table presents operating conditions for single bladeless fanjet configurations, focusing on wind speed, jet speed, incidence angle, angle of attack, and Reynolds number. It consists of three rows and six columns. The columns are labeled as follows: Serial number, Configuration number, Wind speed in meters per second, Jet speed in meters per second, Incidence angle in degrees, Angle of Attack in degrees, and Reynolds number. Row 1: Serial number 1, Configuration number 1FW20J0, Wind speed 20 meters per second, Jet speed 0 meters per second, Incidence angle 0 degrees, Angle of Attack 0, 5, 10, 20, 30, 35 degrees, Reynolds number 2.74 times 10 to the power of 5. Row 2: Serial number 2, Configuration number 1FW20J40, Wind speed 20 meters per second, Jet speed 40 meters per second, Incidence angle 0 degrees, Angle of Attack 0, 5, 10, 20, 30, 35 degrees, Reynolds number 2.74 times 10 to the power of 5. Row 3: Serial number 3, Configuration number 1F5W20J40, Wind speed 20 meters per second, Jet speed 40 meters per second, Incidence angle 5 degrees, Angle of Attack 0, 5, 10, 20, 30, 35 degrees, Reynolds number 2.74 times 10 to the power of 5. The table highlights different configurations based on geometric and operating conditions of the bladeless fan, with variations in jet and wind speeds.

Figure 28.

Comparison of SFC and BLW: (a) C _L and C _D versus α; (b) comparison of C_L__Fan for SFC with jet ON (1FW20J40) and OFF (1FW20J0) condition.

Figure 28 Long description

A line graph comparing lift coefficient and drag coefficient versus angle of attack for different configurations. The x-axis represents the angle of attack in degrees, ranging from 0 to 40 degrees. The left y-axis represents the lift coefficient, ranging from 0 to 1. The right y-axis represents the drag coefficient, ranging from 0 to 0.6. The graph includes four data series: 1F, 1F with BLW, BLW, and BLW with 1F. Each series is represented by different symbols and line styles. The inset graph (b) compares the lift coefficient of the fan for two conditions: jet ON (1FW20J40) and jet OFF (1FW20J0). The inset graph's x-axis represents the angle of attack in degrees, ranging from 0 to 40 degrees, and the y-axis represents the lift coefficient of the fan, ranging from -0.02 to 0.03. All values are approximated.

Figure 29.

Comparison of fan with a preset incidence angle of 5° (IF-5 configuration): (a) C _L versus α for BLW, IF and IF-5; (b) exploded view; (c) L/D comparison.

Figure 29 Long description

The image contains three graphs comparing the performance of different fan configurations. Graph (a) is a line graph showing the lift coefficient (C_L) versus angle of attack (AoA) for three configurations: 1F, 1F-5, and BLW. The 1F configuration is represented by black squares, the 1F-5 configuration by red circles, and the BLW configuration by open triangles. The graph indicates that the lift coefficient increases with the angle of attack for all configurations, with the 1F-5 configuration showing the highest lift coefficient at higher angles. Graph (b) provides an exploded view of the lift coefficient versus angle of attack for angles between 0 and 5 degrees, highlighting the initial performance differences among the configurations. Graph (c) is a line graph comparing the lift-to-drag (L/D) ratio versus angle of attack for the same three configurations. The L/D ratio peaks around 10 degrees AoA for all configurations, with the BLW configuration showing a higher L/D ratio at angles greater than 10 degrees. The graphs collectively illustrate the performance advantages of the BLW configuration, particularly at higher angles of attack.

Figure 30.

Wind tunnel model for 1FW20J40 configuration.

Figure 30 Long description

The image shows a wind tunnel model designed for the 1FW20J40 configuration of a bladeless fan. The model features a smooth, curved surface that represents the Coanda profile, which is essential for directing airflow. The setup is mounted on a sturdy base, allowing for precise testing and analysis of aerodynamic performance. This model is used to study the flow dynamics of annular jets, which are crucial for the efficient operation of bladeless fans in various applications, including aerospace.

Figure 31.

Comparison of experimental and CFD results.

Figure 31 Long description

A line graph compares experimental and computational fluid dynamics results for lift and drag coefficients against angle of attack. The x-axis represents the angle of attack in degrees, ranging from 0 to 40 degrees. The left y-axis represents the lift coefficient, ranging from 0 to 1. The right y-axis represents the drag coefficient, ranging from 0 to 0.6. The graph includes four data lines: experimental lift coefficient, experimental drag coefficient, computational fluid dynamics lift coefficient, and computational fluid dynamics drag coefficient. The experimental lift coefficient is represented by black squares, the experimental drag coefficient by black open squares, the computational fluid dynamics lift coefficient by red triangles, and the computational fluid dynamics drag coefficient by red open triangles. All values are approximated.

Figure 32.

Comparison of TFC and DFC with SFC: (a) lift coefficient versus α; (b) drag coefficient versus α.

Figure 32 Long description

The image contains two line graphs. The first graph (a) plots the lift coefficient (C L) against the angle of attack (AoA) in degrees. The second graph (b) plots the drag coefficient (C D) against the angle of attack (AoA) in degrees. Each graph includes three data lines representing different fan configurations labeled as 1F, 2F, and 3F. In graph (a), the lift coefficient increases with the angle of attack for all configurations, with 3F showing the highest values, followed by 2F and 1F. In graph (b), the drag coefficient also increases with the angle of attack, with similar trends across the configurations. All values are approximated.

Figure 33.

Comparison of pressure profile of TFC with SFC and DFC at 10^° AoA.

Figure 33 Long description

The image contains six line graphs arranged in a two-by-three grid. Each graph compares the pressure coefficient (CP) along a location in feet (ft) for different configurations: TFC, SFC, and DFC at a 10-degree angle of attack. The x-axis represents the location in feet, ranging from 0 to 1.0 or 0.7, depending on the graph. The y-axis represents the pressure coefficient, ranging from -2.0 to 1.5. Each graph uses different colors and symbols to represent data series for 1F, 2F, and 3F configurations at varying conditions. The graphs show how the pressure coefficient varies along the location for each configuration, highlighting differences in pressure profiles. All values are approximated.

Figure 34.

Pressure contours of DFC at: (a) 3.5-inch; (b) mid-span; (c) 8.5-inch; (d) quarter-chord.

Figure 34 Long description

A heat map showing pressure contours of a DFC at different span positions. The heat map consists of four subplots labeled (a) through (d), each representing different span positions: 3.5-inch, mid-span, 8.5-inch, and quarter-chord. The color scale at the bottom ranges from blue to red, indicating varying pressure values. Blue represents lower pressure, while red indicates higher pressure. Each subplot shows the distribution of static pressure around an object, with distinct patterns and gradients visible. Subplot (a) shows a concentrated area of high pressure near the object, while subplot (d) displays a more spread-out pressure distribution. The heat map provides a visual representation of how pressure varies across different span positions of the DFC.

Figure 35.

Pressure contours for TFC at: (a) 2.5-inch; (b) 5.0-inch; (c) 7.5-inch; (d) quarter-chord at 10^°; (e) quarter-chord at 20^°; (f) quarter-chord at 35^°.

Figure 35 Long description

A heat map displays pressure contours for TFC at different positions. The map includes six subplots labeled (a) through (f), each representing different measurement points: 2.5-inch, 5.0-inch, 7.5-inch, quarter-chord at 10, quarter-chord at 20, and quarter-chord at 35. The color scale ranges from blue to red, indicating varying pressure levels. Higher pressure areas are marked in red, while lower pressure areas are in blue. Each subplot shows the distribution of pressure around a bladeless fan, with noticeable variations in pressure contours at different positions. The heat map provides a detailed visualization of how pressure changes across different points in the fan's operation.

The coefficient of drag is also compared, as shown in Fig. 28(a). The drag for SFC is slightly higher than BLW. The effect is more evident beyond the stalling angle (∼16% increase in drag at 35° - post-stall region). The reasons for higher drag are associated with interference drag created due to fan attachments and additional skin friction and pressure drag due to presence of bladeless fan.

To balance out the negative lift produced by the fan, a preset incidence angle of 5^° was given to the bladeless fan. With the increase in fan’s lift due to positive orientation, the overall lift of the configuration increased from the basic fan configuration by approx. 7% as presented in Fig. 29(a). The L/D ratio is also improved and even higher from BLW at an angle greater than 10° AoA.

5.3 Experimental verification of SFC

A baseline experimental model was fabricated with a single bladeless fanjet installed at the mid (Fig. 30). The dimensions were kept similar to the 1FW20J40 configuration (single bladeless fanjet, freestream 20 m/s, fanjet 40 m/s). The model was tested in the low-speed wind tunnel for the calculation of aerodynamic forces. A low-pressure compressor was connected to the model through a mass flow calibrator to ensure an average velocity of 40 m/s at the jet slit. The tunnel speed was set to 20 m/s for tests. The test readings after necessary tunnel corrections (refer to Appendix A) are presented in Fig. 31. A maximum error of 5% was recorded in the lift values and 12% in the drag values. The reason for the higher error in drag values is attributed to the experimental model fabrication tolerance and surface finish.

5.4 Double & triple bladeless fanjet configurations

In a double bladeless fanjet configuration, the fanjets are installed at 3.5 and 8.5 inches from the wing tip, as shown in Fig. 25(d). Similarly, in the triple fanjet configuration, the fanjets are installed at 3, 6 and 9 inches from the wing tip, as shown in Fig. 25(f).

The cases for dual fan configuration (DFC) and triple fan configuration (TFC) were simulated for the entire range of AoAs and the results were compared with SFC (Fig. 32). The results of TFC are better than SFC and DFC because of the resulting pressure profile developed on the wing by triple fanjets (Fig. 33). As can be observed in the chordwise and spanwise distribution, ΔP for TFC is more as compared to SFC and DFC (∼22% increase in lift for TFC over SFC). Figures 34 and 35 presents pressure contours at various chordwise and spanwise locations for DFC and TFC, respectively.

The TFC was compared with the BLW as shown in Fig. 36. Although the lift of TFC is much higher as compared to BLW (approx. 45% increase in lift), the overall L/D ratio is still lower than BLW in pre-stall condition mainly due to increment in skin friction and pressure drag due to presence of additional fan surfaces.