3.1.1 Aerodynamic force and moment measurement

The experiments were carried out at various free-stream Mach numbers in the range of 0.7 to 1.2. The result showed that the lift force coefficient varies linearly in the range of angle-of-attack tested, for Mach numbers less than 0.7 and more than 1. A sudden loss of lift or a break in the lift curve was observed in the Mach number range of 0.7 to 1.0. The present results (Model blockage = 0.36%) were compared with the reported experimental data on the AGARD-B configuration (Model blockage = 0.056%) [Reference Lombardi, Morelli and Haghiri38] at selected Mach numbers. Figure 4 (a) through (c) show the variation of coefficient of pitching moment (C $_{PM}$ ) with the lift coefficient (C $_{L}$ ) for $M_{\infty}$ = 0.8, 0.9 and 1.0, respectively. The coefficient of pitching moment and the lift showed a good agreement with the results reported by Lombardi et al. [Reference Lombardi, Morelli and Haghiri38]. It is also interesting to note that the breaks in the coefficients observed in the present results were evident in the results reported by Lombardi et al. [Reference Lombardi, Morelli and Haghiri38]. Figure 4(d) shows the variation of zero lift drag (C $_{d0}$ ) with Mach number and the comparison of the experimental data obtained from various wind tunnels. The results available in the literature were obtained on a 0.01% blockage model in AEDC tunnel [Reference Milillo30], 0.2% and 0.5% blockage model in CALSPAN and ONERA tunnel [Reference Valk and Van der Zwaan32], respectively, while the blockage of the test model used in the present study was 0.36%. In general, the zero lift drag showed a scatter over the range of transonic Mach number tested. The present results generally lie in the data band obtained from the literature at Mach numbers between 0.7 to 1.05, but the present results were close to the upper boundary of the data band beyond Mach number of 1.05. The scatter in the zero lift drag values might be due to several factors viz. test section wall configurations, open area ratios, sting support, model blockage etc., which influence the accuracy of the measurements. However, investigation of this aspect was not in the scope of the present study.

Figure 4.

Comparison of the present data with the literature (blockage of the model for present tests = 0.36%, Lombardi et al. [Reference Lombardi, Morelli and Haghiri38] = 0.056%, AEDC[Reference Milillo30] = 0.01%, CALSPAN[Reference Valk and Van der Zwaan32] = 0.2% and ONERA[Reference Valk and Van der Zwaan32] = 0.5%).

Since the breaks were evident in the present results and the literature in the Mach number range of 0.7 to 1.0, a detailed investigation was carried out at ${M_\infty }$ = 0.85. A typical variation of important aerodynamic coefficients such as lift force coefficient (C $_L$ ), pitching moment coefficient (C $_{PM}$ ), and drag force coefficient (C $_d$ ) with angle-of-attack ( $\alpha $ ) obtained at ${M_\infty }$ = 0.85 is shown in Fig. 5 (a) through (c). All the aerodynamic coefficients shown, varied linearly at the lower angle of attack. However, a sudden change or ‘break’ in the aerodynamic quantity was observed at around $\alpha $ = 13.2°. A zoomed view of the data near the break is shown in the inset for clarity. The loss in the lift near the break was significant and resulted in a corresponding sudden nose-up pitching moment (Fig. 5 (b)) and a sudden change in the coefficient of drag force (Fig. 5 (c)). The angle-of-attack where such a break was observed is termed as the critical angle-of-attack in the subsequent discussions. The critical angle-of-attack and corresponding change in important aerodynamic coefficients across it for the test model obtained at various free-stream Mach numbers are tabulated in Table 3.

Figure 5.

Variation of various aerodynamic coefficients with the angle-of-attack ( $\alpha$ ) at $M_{\infty} = 0.85$ .

Table 3.

The change in the aerodynamic coefficients across the critical angle-of-attack for the AGARD-B model in the transonic regime

The critical angle-of-attack for various free-stream Mach numbers obtained from the present study were compared with the experimental data from the closed-circuit wind tunnel [Reference Lombardi, Morelli and Haghiri38]. Further, the experimental data available on a 65° swept delta-wing planform alone (without a fuselage) [Reference Elsenaar and Hoeijmakers7,Reference Erickson8] and computational data [Reference Longo12] available on the 60° swept delta-wing planform alone (without a fuselage) is superimposed and presented in Fig. 6. The present data agreed well at at M $_\infty $ = 0.8 and 0.9 with the data from the closed-circuit wind tunnel [38]. The computational data [12] available on a 60° swept pure delta-wing planform (without a fuselage) showed a significantly higher value of critical angle-of-attack at M $_\infty $ = 0.8. This shows that the presence of a fuselage reduces the critical angle-of-attack and the observation was consistent with the work reported by Ericsson [Reference Ericsson28].

Figure 6.

Variation of the critical angle-of-attack with free-stream Mach number.

Although the break was observed in the Mach number range of 0.7 to 1.0, a detailed investigation was carried out at the free-stream Mach number of 0.85 and the subsequent discussion is pertinent to the free-stream Mach number of 0.85, unless stated otherwise.

3.1.2 Flow visualisation

In order to investigate the anomaly in the aerodynamic coefficients near the critical angle-of-attack in detail, the surface oil flow visualisation and the shadowgraph were employed at 1 $^{\circ}$ before and after the critical angle-of-attack and the images obtained on leeward side of wing are shown in Fig. 7 (a) and (b), respectively. The left panel and the right panel of Fig. 7 show the results obtained at approximately 1 $^{\circ}$ before and after the critical angle-of-attack, respectively.

The surface flow features (Fig. 7(a)) obtained showed that the primary separation line (S $_1$ ) was at the sharp leading edge irrespective of the angle of attack. The flow features captured at $\alpha $ = 12.25° showed that the slopes of the primary attachment line (A $_1$ ) and the secondary separation line (S $_2$ ) remained constant. These flow features clearly indicate that the vortex was attached to the wing till the trailing edge. The surface streamlines approached the secondary separation line (S $_2$ ) at a glancing angle indicating that the primary vortex separates without the shock [8]. However, as the angle of attack was increased to $\alpha $ = 14.3°, a sharp change in the slope of secondary separation line (S $_2$ ) and an inboard movement of the secondary separation line (S $_2$ ) was observed at ${X_C}/{X_{RC}}$ $ \approx $ 0.66. Further, a significant reduction in the axially attached flow (AA) at $\alpha $ = 14.3° was observed as compared to $\alpha $ = 12.25°. The surface streamlines approached the secondary separation line (S $_2$ ) at a sharp angle indicating that the primary vortex separation was shock-induced [Reference Erickson8]. The footprint of a cross-flow shock wave (S $_C$ ) is highlighted due to the accumulation of oil particles as seen in the image corresponding to $\alpha $ = 14.3°. The secondary attachment line (A $_2$ ) showed an insignificant change with the change in angle-of-attack. The shadowgraph visualisation carried out at an identical angles of attack and M $_\infty $ = 0.85, is shown in Fig. 7(b). The wing root chord is shown in the shadowgraph, however it may be noted that the thickness of the wing is not to the scale and exaggerated for the clarity. The shadowgraph images show a system of curved normal shocks on the leeward side of the wing when the angle-of-attack is increased from 12.25° to 14.3° i.e. when the VB occurs.

Figure 7.

Visualisation at $M_{\infty}$ = 0.85 near the critical angle-of-attack.

The shadowgraph images show a two-dimensional, integrated (through line-of-sight) picture of a three-dimensional shock structure. Two disturbances, each at the mid chord of wing and just before trailing edge, are therefore seen in the shadowgraph image. The first and the second disturbance seen at each location correspond to the location of the shock front on the fuselage and to the end of the curved shock spanning over the wing, respectively. For the first disturbance corresponding to the shock present in the mid chord of the wing, the shock foot was traced to the location ${X_C}/{X_{RC}}$ $ \approx $ 0.51 on the fuselage centreline. The second disturbance observed, corresponding to the shock present at the mid chord of the wing, yields the location of the shock foot at ${X_C}/{X_{RC}}$ $ \approx $ 0.58 on the leeward wing. A similar exercise, carried out for the disturbance observed for the shock near the trailing edge of the wing, locates the shock foot at ${X_C}/{X_{RC}}$ $ \approx $ 0.91 on fuselage and for the second disturbance at the $X/D$ of 7 or ${X_C}/{X_{RC}}$ $ \approx $ 0.96 on the wing. The shape and the location of these shocks will be discussed in detail later in section 3.1.5. The separated flow behind the trailing edge observed at angle-of-attack of 14.3 $^{\circ}$ is significantly turbulent.

The sharp change in the slope of the secondary separation line ( ${S_2}$ ) observed on the mid-board indicates that the primary vortex grows in the size as a result of the VB due to a shock-vortex interaction [Reference Kandil, Kandil and Liu11,Reference Schiavetta, Boelens, Crippa, Cummings, Fritz and Badcock16]. As the primary vortex rolls up from the leading edge of the wing and interacts with a shock, it experiences an adverse pressure gradient, which induces a rapid deceleration in its axial motion [Reference Delery1]. The overall suction created on the aft portion of the leeward surface of wing is significantly reduced due to the VB, resulting in a sudden loss of the lift and a corresponding change in the pitching moment. Therefore, the break in aerodynamic coefficients observed in the force and moment data, is due to the VB. Table 3 indicates that despite the AGARD-B being a very simple delta wing-body geometry, it experiences a large variation in longitudinal aerodynamic coefficients at a moderately low angle-of-attack due to the VB at transonic Mach numbers.

3.1.3 Unsteady pressure measurements

The occurrence of VB on the leeward side of the wing can be associated not only with an increase in the magnitude of unsteady pressure fluctuations or buffet loads in the aft portion of the wing planform but also several unsteady phenomena, which exist in the flow over the delta wings like vortex breakdown oscillation, turbulence downstream of breakdown, helical mode instability, shear layer instabilities, vortex shedding, vortex core rotation, etc [Reference Menke, Yang and Gursul47]. Ideally, a separate study of an aero-elastic wind tunnel model is required to determine the magnitude of the buffet loads. However, localised information regarding the fluctuating flow obtained by analysing the unsteady pressure fluctuations on the aft portion of the wing at a few discrete locations can be an indicator to the magnitude of the buffet loads.

Figure 8 shows the effect of the angle-of-attack on the nondimensional pressure spectra at the inboard location of $Z/D$ = −0.863, located at ${X_C}/{X_{RC}}$ = 0.71. The unsteady pressure fluctuations were measured at the discrete angles of attack of 8°, 12° and 15°. The spectral analyses of the pressure fluctuations at an angle-of-attack of 8° showed a very low amplitude of the pressure fluctuations with no dominant frequency peak. However, the distinct peaks centered around ${S_t}$ of 0.142 and 0.172 were identified at the angles of attack of 12° and 15°, respectively. This frequency is associated with the oscillation of the vortex breakdown location and falls in the range which has been previously identified by Menke et al. [Reference Menke, Yang and Gursul47]. A second distinct peak was also evident at approximately ${S_t}$ = 3 at an angle-of-attack of 15°, and is likely to be associated with the helical mode instability and winding. A more detailed description of the spiral mode of breakdown is described by Lambourne and Bryer [Reference Lambourne and Bryer48]. The results clearly indicated that the dominant frequency associated with an oscillation of the vortex breakdown location ( ${S_t}$ = 0.172) becomes significant from an angle-of-attack of 12° onwards, however, the helical mode instability and winding are found to be present only at an angle-of-attack of 15°. This implies that the formation and an onset of helical mode instability associated with the spiral-type VB was present beyond the critical angle-of-attack.

Figure 8.

Effect of an angle-of-attack on the unsteady pressure fluctuations measured at $Z/D$ = −0.863 and $X_{C}/X_{RC}$ = 0.71.

3.1.4 Steady pressure measurement using PSP technique

In order to get a detailed surface steady pressure distribution on the leeward side of the wing post the VB, tests using pressure sensitive paint (PSP) were carried out on the test model at ${M_\infty }$ = 0.85 and $\alpha $ = 15°. The PSP results were compared with the results obtained at few discrete locations using an electronically scanned pressure scanner (ESP). Fig. 9 shows the surface contour plots of coefficient of pressure ( ${C_P}$ ) and superimposed 2D plots of the spanwise variation of coefficient of pressure ( ${C_P}$ ) at the several stream-wise ( ${X_C}$ / ${X_{RC}}$ ) locations. A good agreement between the results obtained using PSP and ESP was observed at all the ${X_C}$ / ${X_{RC}}$ locations which is of the order of 0.02 in ${C_P}$ .

Figure 9.

Comparison of $C_{P}$ contours measured using PSP and $C_{P}$ measured at discrete locations using ESP obtained on baseline configuration at $M_{\infty}$ = 0.85, $\alpha$ = 15 $^{\circ}$ .

The surface contour plot of ${C_P}$ obtained using the PSP shows that the leading edge vortex creates a considerable suction in the upstream portion of the wing till about ${X_C}$ / ${X_{RC}}$ = 0.5. The 2D plots at ${X_C}$ / ${X_{RC}}$ = 0.2, 0.3 and 0.4 clearly show the primary and secondary peaks in ${C_P}$ which are due to the primary and secondary vortices. However, the surface pressure coefficient contours show an abrupt vortex breakdown downstream of ${X_C}$ / ${X_{RC}}$ $ \approx $ 0.5. It is clear that the vortex system is coherent and strong upstream, however, the vortices disappear quite abruptly in the downstream. The span-wise variation of ${C_P}$ at ${X_C}$ / ${X_{RC}}$ = 0.7 and 0.95 is much flatter indicating the absence of primary and secondary vortices in the aft portion of the wing resulting in a loss of suction. It is also interesting to note that the breakdown of secondary vortex occurs slightly upstream of the primary vortex for this test case. The surface contour plot of ${C_P}$ also indicates that the major loss in suction occurs in the inboard region of the wing near the trailing edge.

3.1.5 Flow topology based on the experimental investigation

Based on the spanwise pressure distribution obtained through the PSP and the experimental flow visualisation, the shock location was determined and a schematic of the flow topology is shown in Fig. 10. The topology shows that a single shock is observed at around ${X_C}/{X_{RC}}$ = 0.7 on the fuselage centreline prior to the vortex breakdown ( $\alpha $ = 12.25°). However, the existence of two spanwise shocks and a cross-flow shock was evident after the vortex breakdown i.e at $\alpha $ = 14.3°. Though, the first spanwise shock and the cross-flow shock are located in the vicinity over the wing, it is difficult to comment if the cross flow shock and the first spanwise shock are interconnected. The first shock moves upstream ( ${X_C}/{X_{RC}}$ $ \approx $ 0.5 on fuselage centreline) with an increase in the angle of attack and interacts with the oncoming vortices near the midspan. As seen from the surface flow visualization, there is a reduction in the axially attached flow beyond the critical angle of attack which might be due to an increase in the size of the vortex after bursting. The burst vortex eventually creates a constricted flow passage for the axially attached flow downstream of the first shock ( ${X_C}/{X_{RC}}$ $ \approx $ 0.5 on fuselage centreline) and allows the flow to expand further which is terminated by an another shock at ${X_C}/{X_{RC}}$ $ \approx $ 0.9 on the fuselage centreline to match the flow conditions at the trailing edge. The flow topology constructed, clearly indicates the presence of a system of shocks, a shock-induced vortex breakdown and a bulging of the primary vortex as the angle-of-attack is increased beyond the critical angle of attack.

Figure 10.

Schematic of the flow topology before and after the vortex breakdown (VB) at M $_\infty$ = 0.85.

3.2.1 Steady pressure distribution using PSP technique

Figure 11 shows the effect of control jet injection location on the surface contour plot of ${C_P}$ and compares it with the baseline case. The jet locations are marked in each of the contour plot for clarity. A single sonic jet, each on starboard and port wing was injected from the same stream wise location ( ${X_C}$ / ${X_{RC}}$ ), and the air was drawn from the common source where the required stagnation pressure was held constant during each experiment. The stagnation pressure of the sonic jet for all these cases shown in Fig. 11, was chosen such that the momentum coefficient ( $J$ ) was 1.38 and corresponding coefficient of blowing (C $_\mu $ ) obtained was 0.000062. The justification for the selection of momentum coefficient ( $J$ ) of 1.38 is discussed in section 3.2.4.

Figure 11.

Surface pressure contours obtained using PSP showing the effect of control jet injection and injection location on AGARD-B configuration at $M_{\infty}$ = 0.85, ${\alpha}$ = 15 $^{\circ}$ . ( $J$ = 1.38; C $_\mu$ = 0.000062).

The spanwise blowing (SWB) from ${X_C}$ / ${X_{RC}}$ location of 0.025, 0.06 and 0.1 (Fig. 11 (b), (c), (d)) show a significant improvement in the vortical structure when compared with the baseline case (Fig. 11 (a)). Interestingly, the sonic jet injection is energising the primary and secondary vortex and enhancing the coherence and the strength of the vortex system significantly. Additionally, a significant improvement in the suction is observed in the aft portion of the wing near the wing-fuselage junction. The SWB from ${X_C}$ / ${X_{RC}}$ location of 0.025, seems to be the most effective in strengthening the primary vortex such that the primary vortex breakdown is pushed downstream to ${X_C}$ / ${X_{RC}}\approx 0.7$ as against ${X_C}$ / ${X_{RC}}\approx 0.5$ in the baseline case. Similarly, the SWB from ${X_C}$ / ${X_{RC}}$ location of 0.025, energises the secondary vortex such that the secondary vortex breakdown is pushed downstream to ${X_C}$ / ${X_{RC}}\approx 0.55$ as against ${X_C}$ / ${X_{RC}}\approx 0.45$ in the baseline case. This might be due to the entrainment of the control jet fluid into the oncoming vortex which is eventually fed to the vortex core thus enhancing the axial velocity of the vortex core. The SWB from ${X_C}$ / ${X_{RC}}$ location of 0.06 and 0.1, however, is not able to push the vortex breakdown position downstream significantly as compared with the jet injected from ${X_C}$ / ${X_{RC}}$ location of 0.025. A plausible reason for the reduction in the effectiveness of the SWB from ${X_C}$ / ${X_{RC}}$ location of 0.06 and 0.1 could be a reduction in the entrainment of the control jet fluid due to the increase in the distance between the injection location and the vortex core.

In general, the SWB showed a considerable increase in the suction in the upstream part of the wing till ${X_C}$ / ${X_{RC}}\approx 0.5$ and in the aft portion of the wing near the wing-fuselage junction. SWB enhanced the coherence and the strength of the vortex system as compared to the baseline case.

Along the core or near core blowing (ACB) from ${X_C}$ / ${X_{RC}}$ = 0.2 and 0.3 location, did not show a significant improvement in the suction in the upstream part of the wing (till ${X_C}$ / ${X_{RC}}$ 0.5) as compared with the baseline case. ACB from ${X_C}$ / ${X_{RC}}$ = 0.2 indicated a marginal improvement in the suction in the inboard and the outboard region of the aft portion of the wing as compared with the baseline case (Fig. 11(e)).

In order to get more clarity of the benefits of SWB closest to the apex of the wing, the pressure distribution obtained using the PSP was extracted at several ${X_C}$ / ${X_{RC}}$ stations for the flow control case of spanwise blowing (SWB) from ${P_1}$ and compared with the baseline case as shown in Fig. 12. The control jet seems to be enhancing the suction significantly at all ${X_C}$ / ${X_{RC}}$ stations. It is also interesting to note that the spanwise location ( $Z/D$ ) where the peak in the ${C_P}$ occurred did not change significantly with the application of SWB indicating that the control jet injection does not alter the vortex core path significantly. Further, the pressure distribution indicated that the vortices were energised due to the control jet and seemed to be generating a higher suction from the apex of the wing till the trailing edge of the wing.

Figure 12.

Spanwise variation of $C_{P}$ at various $X_{C}$ / $X_{RC}$ stations showing a comparison of SWB ( $J$ = 1.38; C $_\mu$ = 0.0001) from $P_{1}$ location ( $X_{C}$ / $X_{RC}$ = 0.025) with a baseline case at $M_{\infty}$ = 0.85, ${\alpha}$ = 15 $^{\circ}$ .

A close inspection of Fig. 11(e) and (f) revealed that ACB at ${X_C}$ / ${X_{RC}}$ = 0.2 and 0.3 created a higher suction in the upstream part of the starboard wing than that observed on the port wing. The spanwise location of the primary vortex core at ${X_C}$ / ${X_{RC}}$ = 0.2 and 0.3 is traced to $Z/D \approx $ 0.7 and 0.75, respectively, using the spanwise variation of ${C_P}$ plotted in Fig. 12 (a) and (b). It would be of interest to take a note of the fact that the spanwise location ( $Z/D$ ) of ${S_4}$ and ${S_5}$ was slightly inboard of the spanwise location of the primary vortex core as compared to the location of ${P_4}$ and ${P_5}$ (refer Table 1). Thus, the ACB from the inboard of the spanwise location of the primary vortex core seemed to be more effective in energising the vortices as compared to injecting right underneath or slightly outboard of the primary vortex core as it is done on the port wing.

3.2.2 Unsteady pressure measurements

As discussed earlier (refer section 3.1.3), the magnitude of unsteady pressure fluctuations can be a prime indicator for the occurrence of VB and it’s associated unsteady phenomena. The unsteady pressure fluctuations were measured for the control jet injection case and the results are compared with the baseline case. Figure 13 shows the nondimensional pressure spectra of the inboard ( $Z/D$ = −0.863) and outboard ( $Z/D$ = −1.136) kulite transducer i.e. ${K_3}$ and ${K_4}$ respectively, located at ${X_C}$ / ${X_{RC}}$ = 0.71, for the baseline and the control configuration. Figure 13 (a) and (b) show the spectra obtained at the inboard and the outboard, respectively for the baseline case and the control case when the jet is injected spanwise (SWB) ${S_1}$ i.e from ${X_C}$ / ${X_{RC}}$ = 0.025. The same is shown in Fig. 13 (c) and (d) for the baseline case and control case when jet is injected along the core (ACB) from ${S_5}$ i.e from ${X_C}$ / ${X_{RC}}$ = 0.3. The nondimensional pressure spectra analyses of the pressure fluctuations, identified three distinct frequencies. Out of these three frequencies, two were dominant frequencies, which appear to be centred around the dimensionless frequencies of ${S_t}$ = 0.172 and 0.29. The dominant frequency of ${S_t}$ = 0.172 is associated with the oscillation of the vortex breakdown location and falls in the range which has been previously identified by Menke et al. [Reference Menke, Yang and Gursul47]. The power of the frequency centred around ${S_t}$ = 0.29 was significantly lower compared with the first dominant frequency. The similar trend showing second peak having a very low energy in the spectra were reported by Menke et al. [Reference Menke, Yang and Gursul47], however, this frequency could not be associated with any unsteady phenomena that exist in the flow over delta wings.

Figure 13.

Spectra of nondimensional pressure fluctuations at $X_{C}$ / $X_{RC}$ = 0.71 showing the effect of the spanwise blowing (SWB) at $X_{C}$ / $X_{RC}$ = 0.025 i.e. at $S_{1}$ and along the core blowing (ACB) at $X_{C}$ / $X_{RC}$ = 0.3 i.e. at $S_{5}$ location on the AGARD-B configuration at $M_{\infty}$ = 0.85, ${\alpha}$ = 15 $^{\circ}$ .

A third distinct peak was also evident at approximately ${S_t}$ = 3 and is likely associated with the helical mode instability and winding, which was reported by Menke et al. [Reference Menke, Yang and Gursul47]. The helical mode instability, which occurs over the delta wings, is described as a helix of the rotating vortex core filament. The sense of this helix is found to be in the opposite direction to the vortex rotation upstream of breakdown. However, the whole structure also rotates, with the same sense as the vortex core. A detailed description of the spiral mode of breakdown can be found in Lambourne and Bryer [Reference Lambourne and Bryer48].

The power spectral analysis showed a significant reduction in the magnitude of unsteady pressure fluctuations with the application of flow control as compared with the baseline case. The peak amplitude corresponding to a dominant frequency ( ${S_t}$ = 0.172) associated with the oscillation of the vortex breakdown location reduced significantly for the spanwise (SWB) and along the core blowing (ACB) case. This observation is an indication of the downstream movement of the vortex breakdown location. However, the distinct peak at ${S_t}$ = 3 having relatively lower energy content which was corresponding to the helical mode instability and winding, seemed to be affected insignificantly due to the control. ACB from ${X_C}$ / ${X_{RC}}$ = 0.3, however, showed a slightly broader frequency peak at ${S_t}$ = 3 when compared with the baseline case and seemed to moderately alter the helical mode instability.

The overall or cumulative coefficient of fluctuating pressure ( ${C_{Prms}}$ ) integrated over 0 to 40 kHz is tabulated in Table 4 for the baseline case and the flow control case. The ${C_{Prms}}$ value for the control case was compared with the baseline case and a significant reduction in overall coefficient of fluctuating pressure was observed. The reduction in overall unsteady pressure fluctuations at location ${X_C}$ / ${X_{RC}}$ = 0.71 and $Z/D = - 0.863$ i.e. inboard location due to SWB from ${X_C}$ / ${X_{RC}}$ = 0.025 (i.e ${S_1}$ location) and ACB from ${X_C}$ / ${X_{RC}}$ = 0.3 (i.e ${S_5}$ location) was about 8% and 20% respectively. The overall unsteady pressure levels at location ${X_C}$ / ${X_{RC}}$ = 0.71 and $Z/D = - 1.136$ i.e. outboard location due to SWB from ${X_C}$ / ${X_{RC}}$ = 0.025 (i.e ${S_1}$ location) increased marginally compared to baseline case however a reduction of 10% was observed due to ACB from ${X_C}$ / ${X_{RC}}$ = 0.3 (i.e ${S_5}$ location). The overall reduction in the ${C_{Prms}}$ measured at ${X_C}$ / ${X_{RC}}$ = 0.71 was better in case of ACB as compared to the SWB. The reduction in overall coefficient of fluctuating pressure measured at both the locations is higher in case of ACB as compared to SWB. This could be due to the proximity of location of unsteady pressure taps to the location of ACB as compared to the SWB location.

Table 4.

Experimental results showing effect of pneumatic flow control on overall or cumulative coefficient of unsteady pressure fluctuation ( $C_{Prms}$ ) in the range of 0 to 40 kHz at $X_{C}/X_{RC}$ = 0.71

3.2.3 Aerodynamic force and moment measurement

The PSP tests indicated a significant improvement in the suction on the leeward surface of the delta wing by employing a spanwise (SWB) and along the core blowing (ACB). Subsequently, force measurements were carried out on the test model with spanwise blowing (SWB) to capture the overall effect on the aerodynamic coefficients. The test model (baseline configuration) used for the force and moment measurement was suitably modified to accommodate the spanwise blowing (SWB) keeping the sting-balance combination identical. A circular control jet was issued spanwise, through a 0.5mm diameter hole located at ${X_C}$ / ${X_{RC}}$ = 0.025 i.e. from S $_1$ and P $_1$ location. The arrangement required for ‘along the core blowing (ACB)’ could not be accommodated due to the limited space in the force model.

The control jet was blown spanwise from ${X_C}$ / ${X_{RC}}$ = 0.025 location in an identical fashion as in case of the PSP tests. The angle-of-attack was varied in the range of −5° to 25° continuously at the rate of 2°/sec. The control jet was blown continuously over the entire angle-of-attack range keeping the jet stagnation pressure constant during the test. The jet stagnation pressure was measured using a GE UNIK^® 5,000 transducer of ± 1.72 bar range. The jet momentum coefficient ( $J$ ) of 1.38 was maintained for these tests which translated to a coefficient of blowing (C $_\mu $ ) of 0.0002.

The effect of the spanwise blowing (SWB) on the longitudinal aerodynamic coefficients of the test model at a free-stream Mach number of 0.85 is shown in Fig. 14. The lift force coefficient curve (Fig. 14 (a)) shows that the SWB enhanced the lift force near the critical angle-of-attack while it smoothened the pitching moment curve (Fig. 14 (b)) near the critical angle-of-attack. Further, the coefficient of drag (Fig. 14 (c)) curve was smoothened near the critical angle-of-attack. In general, the SWB shifted the break occurring in baseline case by approximately 2° for all the aerodynamic coefficients.

Figure 14.

Effect of spanwise blowing (SWB) on aerodynamic coefficients of AGARD-B configuration at $M_{\infty}$ = 0.85.

The SWB was further evaluated for the free-stream Mach numbers of 0.8, 0.9 and 0.95, and the similar observations were made; however, detailed results are not presented here for brevity. The changes observed in the aerodynamic coefficients of the test model noted at a typical angle-of-attack post the critical angle-of-attack for a given free-stream Mach number, due to SWB are summarised in Table 5. The negative sign corresponds to a reduction while the positive sign indicate an increase in the aerodynamic coefficients. Overall an enhancement in lift ( $ {\approx}\ 6{-}9$ %) and lift to drag ratio ( $ {\approx}\ 4{-}9$ %) was observed depending up on the free-stream Mach number.

Table 5.

Experimental results showing effect of spanwise blowing (SWB) from $X_{C}$ / $X_{RC}$ = 0.025 on aerodynamic coefficients of AGARD-B configuration at various free-stream Mach numbers

3.2.4 Selection of optimum jet momentum coefficient (J)

The local static pressure on the test model where the control jet was injected (i.e. S $_1$ and P $_1$ location) is a function of the free-stream Mach number, angle-of-attack, angle of side slip etc. Hence, the selection of the coefficient of blowing (C $_\mu $ ) or momentum coefficient of the jet ( $J$ ) was an important parameter. In the present experiments, static pressure was measured at the blowing location (P $_1$ and S $_1$ ) for distinct angles of attack for ${M_\infty }$ = 0.85. In order to identify the effect of $J$ or C $_\mu $ on the effectiveness of spanwise blowing (SWB), a few experiments were carried out by systematically varying $J$ within the limitation of experimental setup. A comparison of various $J$ tested and the variation of static pressure at S $_1$ location is shown in Fig. 15. It is interesting to note that the $J$ = 1.38 condition corresponds to a sonic jet with a free-stream pressure-matched state at the exit, $J$ = 0.87 corresponds to a subsonic jet at the exit and $J$ = 2.34 and 3.56 correspond to an under-expanded jet at the exit.

The effect of $J$ on lift force coefficient is shown in Fig. 16. It can be observed that the SWB benefits in delaying the critical angle-of-attack were maximum for $J$ = 1.38 while SWB with $J$ = 0.87 and 2.34 did not deteriorate the performance significantly. However, the critical angle-of-attack advanced significantly as $J$ is increased to 3.56, thereby degrading the operational envelope significantly. Although, a jet with a higher momentum coefficient is highly underexpanded at the exit and is capable of adding a higher momentum to the flow, it is stiff and results in a blockage to the oncoming flow. Consequently, a highly underexpanded jet at the exit would probably disrupt the oncoming vortex and would eventually result in a loss in the effectiveness, especially since the blowing was very close to the apex of the wing. On the contrary, it was observed that the sonic jet with a roughly free-stream pressure-matched state at the exit and a lower jet momentum coefficient did not disrupt the growth of leading edge vortices drastically and added the momentum gently to the vortex core in order to postpone the VB.

Figure 15.

Comparison of variation of coefficient of static pressure ( $C_{P}$ ) at S $_1$ location with angle-of-attack and various momentum coefficient ( $J$ ) tested at $M_{\infty}$ = 0.85.

Figure 16.

Effect of momentum coefficient ( $J$ ) or coefficient of blowing ( $C_{\mu}$ ) for spanwise blowing (SWB) on lift force coefficients of AGARD-B configuration at $M_{\infty}$ = 0.85.