Abstract
This study experimentally investigates the effects of nose-tip bluntness on boundary-layer transition over a \(7^\circ\) half-angle cone at Mach 6.76, using the Seoul National University Hypersonic Shock Tunnel. Transition characteristics were examined through high-speed schlieren visualization, surface heat flux measurements, and high-frequency surface pressure measurements for varying nose-tip radii (0.1 mm, 1 mm, and 2 mm) and unit Reynolds numbers. Increasing nose-tip bluntness effectively delayed transition onset, as indicated by turbulent intermittency and heat flux distributions. Spectral proper orthogonal decomposition and pressure spectral analyses revealed distinct second-mode instabilities with frequency shifts to lower values as bluntness increased. Additionally, a low-frequency instability around 200 kHz was identified in the configuration with a 2 mm nose-tip radius, suggesting the presence of multiple instability modes. These observations highlight the influence of nose-tip bluntness on hypersonic boundary-layer stability and emphasize the necessity for comprehensive consideration of multiple instability modes in hypersonic vehicle design.
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Introduction
Boundary-layer transition in hypersonic flows is a critical factor influencing the thermal and structural design of high-speed vehicles, primarily due to the significant rise in aerodynamic heating and skin friction that occurs as the boundary layer transitions to turbulence1,2. The inability to accurately predict the transition location often results in excessively conservative thermal protection systems and unreliable vehicle performance. For slender, sharp-nosed bodies, the transition mechanism is relatively well understood and is predominantly governed by the amplification of Mack or second-mode instability—a high-frequency, two-dimensional acoustic disturbance confined within the boundary layer3,4. In contrast, the introduction of blunt nose-tips has been found to significantly alter the underlying mechanisms of boundary-layer transition, with these mechanisms remaining less well understood compared to those associated with sharp-nosed configurations5,6.
Early experimental studies demonstrated that increasing the nose-tip radius delays the onset of turbulent transition5,7. Blunt nose-tips produce highly curved bow shocks, resulting in an expanded entropy layer that suppresses second-mode instabilities and subsequently delays transition8,9. However, when the bluntness exceeds a certain critical threshold, the transition location unexpectedly shifts upstream, indicating a transition reversal5. This behavior challenges the predictive capabilities of linear stability theory (LST), which fails to account for transition at the observed low N-factors in highly blunt configurations10,11. Subsequent numerical analyses have confirmed that second-mode instabilities alone are insufficient to trigger transition under these conditions, motivating the exploration of alternative mechanisms such as entropy-layer instabilities and non-modal transient growth12,13,14.
Recent high-speed schlieren imaging and surface pressure measurements have revealed the emergence of elongated or wisp-like structures above the boundary layer in moderately to highly blunt cones. These structures are characterized by non-modal growth and broad frequency content, distinguishing them from the well-defined, rope-like second-mode waves typical of sharp configurations. Notably, these elongated structures extend beyond the boundary-layer edge, indicating a fundamentally different instability mechanism6,15,16. Their presence implies that non-modal disturbances or off-wall instabilities may play a substantial role in triggering boundary-layer transition in blunt geometries, representing a mechanism that is not fully accounted for by traditional modal stability analyses.
Despite recent numerical and experimental progress, significant uncertainties remain regarding the mechanisms of disturbance growth and turbulent transition in hypersonic boundary layers over blunt cones. Discrepancy between experimental observations and predictions from LST persists, indicating that linear-modal frameworks alone do not capture the dominant non-modal amplification over blunt cones6,17,18. The underlying physical mechanism responsible for the elongated or wisp-like structures observed in moderately to highly blunt cases has not been conclusively identified16. Additionally, comprehensive instability measurements, particularly those utilizing high-speed imaging and detailed visualization techniques, are limited for blunt configurations. While prior studies have thoroughly examined second-mode instabilities in sharp cones, the detailed instability mechanisms for blunt geometries, especially in terms of real-time visualization and spectral analysis, remain less understood. To address these gaps, boundary-layer transition on a \(7^\circ\) half-angle cone with varying nose-tip bluntness at Mach 6.76 in a hypersonic shock tunnel are examined in this study, employing high-speed imaging and concurrent wall diagnostics to enhance measurement accuracy and visualization. This provides a synchronized, high-resolution dataset that links spatial and temporal instability features to the corresponding wall response. Time-resolved schlieren imaging and surface heat flux measurements are utilized to detect the transition onset along the cone surface. In addition, high-frequency pressure measurements and spectral analysis of boundary-layer instabilities, derived from schlieren visualizations, are performed to investigate the spatial and temporal evolution of instability structures across different bluntness configurations.
Experimental set-up
Facility
All experiments in this study were performed in the Seoul National University Hypersonic Shock Tunnel (SHyST) (Fig. 1). The SHyST is a conventional reflected shock tunnel equipped with a contoured hypersonic nozzle, enabling the reproduction of flight-relevant flow conditions within a short test duration. The driver and driven sections are 3 m and 8.2 m in length, respectively, and can generate reservoir gas with a total enthalpy of up to 3 MJ/kg. The primary diaphragm consists of a 5-mm-thick Al1050 sheet designed with optimized grooves to achieve a fully open, petal-shaped rupture, enhancing flow quality. A 100-\(\upmu\)m-thick Mylar film is used as a secondary diaphragm, positioned within a removable insert tube upstream of the nozzle. Three pressure transducers (PCB 113B22, PCB Piezotronics) are installed along the driven tube to measure the incident shock speed and reservoir pressure at high frequency. The PCB 113B22 series has a sensitivity of 0.145 mV/kPa. The hypersonic nozzle produces a freestream Mach number (\(M_\infty\)) of 6.76 and the test rhombus was experimentally and numerically investigated in previous work19, demonstrating an effective test-section diameter of 230 mm and pitot pressure root-mean-square fluctuations within 5% of the mean value. The measured pitot pressure fluctuation is comparable to the noise levels of conventional (noisy) wind tunnels (\(>1\%\)), which are much higher than those of quiet tunnels (\(<0.1\%\)) or actual flight (\(<0.05\%\))20,21. Because boundary-layer transition is highly sensitive to the freestream disturbance environment, it is essential to quantify the noise level for interpreting and comparing transition data. As freestream disturbance levels increase, the amplification factor N decreases and the instability spectrum can shift. In addition, elevated noise lowers the growth requirement for transition, modifies the dominant second-mode content, and drives the transition upstream22,23. The freestream disturbance environment and its impact on boundary-layer transition have been carefully examined by both experiments and computations in previous studies20,24,25,26.
Seoul National University Hypersonic Shock Tunnel (SHyST).
In this work, the unit Reynolds number (\(Re_{u,\infty }\)) was varied by changing the driver and driven gas state while achieving near-tailored condition to maximize steady test time. Fig. 2 presents the time history of near-tailored reservoir pressures for different experimental cases with multiple runs. Effective test times were approximately 3 ms for Cases 1–3 and 2 ms for Case 4; pressure fluctuations were within 3% in terms of standard deviation during the test time. A quasi-1D thermochemical equilibrium calculation code, ESTCN27, was used to obtain stagnation conditions and freestream flow properties from measured propagating shock speed and reservoir pressure in the driven section. Table 1 lists the nominal freestream conditions and nose-tip bluntness for each case. The estimated mean \(Re_{u,\infty }\) was consistent across repeated runs, with a standard deviation of 2%.
Time history of reservoir pressure (solid lines: \(Re_{u,\infty } = 7.02 \times 10^{6}\) \(\mathrm {m^{-1}}\), dotted lines: \(Re_{u,\infty } = 29.10\times 10^{6}\) \(\mathrm {m^{-1}}\)).
Test model and data acquisition
A 500 mm, \(7^\circ\) half-angle cone with removable nose-tips was used as a test model. The test model was manufactured using Al6065, while the nose-tip was made of stainless steel to take advantage of its higher wear resistance relative to aluminum. As shown in Fig. 3, three nose-tips of different radii (\(R_N\)) were chosen (0.1 mm, 1 mm, and 2 mm) to investigate the nose-tip bluntness effects on hypersonic boundary-layer transition. Due to limitations of the facility and model size, the present work focuses on the sharp-to-moderately-blunt regime. Although transition reversal is the primary question for highly blunt cones, instability growth and wave structures can still be captured at moderate bluntness6,16,28. The tip bluntness was defined as the ratio of the tip radius to the base radius of the cone. The measured tip radii were 0.096 mm, 1.009 mm, and 2.003 mm, each measured tip radius carrying a common uncertainty of \(\pm 0.005~\textrm{mm}\). The surface roughness of both the cone and the nose-tip was \(R_{a}=3.2~\mu \textrm{m}\). The tip–to–cone junction was flush within \(\pm 0.05~\textrm{mm}\). The test model has 5 pressure transducers (PCB 132B38, PCB Piezotronics) and 4 coaxial thermocouples (E type, Medtherm) in a single streamwise array at the uppermost of the cone surface between x = 250 and 430 mm. The PCB 132B38 series has a measurement range of 345 kPa and a sensitivity of 20.3 mV/kPa. These pressure transducers have been used in previous works6,29 for measurements of boundary-layer instabilities due to their high frequency response. The coordinate system defined and the location of each station is shown in Fig. 4 and Table 2. The model was installed in the test section at nominal zero angle-of-attack, with the misalignment controlled to within \(\pm 0.5^{\circ }\).
The pressure sensors were powered by a multi-channel signal conditioner (PCB 483C05, PCB Piezotronics), and the signals from coaxial thermocouples were amplified using a custom-built voltage amplifier. All signals were sampled at 2.5 MHz using a high-speed data acquisition device (PCIe-6376, National Instrument). Pressure signals were band-pass filtered within a frequency range of 11 kHz to 1 MHz, while thermocouple voltages were only low-pass filtered at 1 MHz prior to analysis. In particular, due to the small temperature variations on the surface of the test model, the voltage signals from the thermocouples were subsequently processed using a moving average to improve the low signal-to-noise ratio. The measured output voltages were converted to pressure values using the calibration factor supplied by the manufacturer.
Nose-tip configurations with varying radii.
\(7^\circ\) half-angle cone instrumented with pressure and temperature sensors.
Schlieren visualization
A Z-type schlieren setup was used as an optical diagnostic method. Two concave mirrors with a focal length of 2,540 mm were used to collimate the beam through the test section and then refocus the beam to a focal point where a horizontal knife-edge was positioned to partially block the converging light, thereby enhancing the visualization of density gradients normal to the surface. A high-speed camera (TMX 6410, Phantom) equipped with a lens with a focal length of 200 mm and a 2\(\times\) teleconverter was used. To clearly capture the unsteady behavior of instabilities within the boundary layer, images were recorded at a resolution of 1,280 \(\times\) 32 pixels covering a narrow horizontal field of view measuring 150 mm in length and 3.75 mm in height. The frame rate was set to 1,500,000 frames per second with an exposure time of 0.095 \(\upmu\)s. To extend the coverage beyond the 150 mm field of view of the camera, schlieren images were captured with overlapping regions under identical experimental conditions for each case. A schematic of the overlapping schlieren windows overlaid with sensor locations on the test model is shown in Fig. 4. The exact ranges of each field of view, referenced to the coordinate system defined in this study, are listed in Table 3.
Transition onset measurements
Boundary layer visualization
A time-resolved sequence of schlieren images of the boundary layer on the cone surface between x = 150 and 275 mm for Case 1 is presented in Fig. 5. The schlieren images were post-processed to enhance the visualization of wave structures and unsteady features within the high-speed boundary layer. The freestream flows from left to right, and the black rectangular mask represents the surface of the cone. Between \(\Delta t\) = 0 and 0.004 ms, a laminar boundary layer without significant disturbances is observed between x = 150 and 200 mm, while the breakdown and transition to turbulence begin near x = 210 mm. At \(\Delta t\) = 0.008 ms, small disturbances emerge from the initially quiet laminar boundary layer near x = 180 mm and subsequently grow into rope-like structures. These wave structures propagate downstream from their initial formation location and become clearly visible near x = 190 mm, indicating the presence of a second-mode wave packet. At \(\Delta t\) = 0.018 ms, fully developed turbulence is observed within the boundary layer around x = 250 mm, which also moves downstream along the surface of the test model. The development of rope-like structures and their subsequent breakdown into turbulence illustrate the nonlinear interactions of instabilities during the transition process and highlight the intermittent nature of the transitional boundary layer.
Time-resolved sequence of schlieren images for Case 1 (x = 150–275 mm).
Wall measurements along cone models (a) Turbulent intermittency (b) Time-averaged nondimensional heat flux.
A Canny edge detection method was employed to identify boundary-layer edges in the schlieren images, enabling the evaluation of whether the boundary layer was undergoing turbulent transition and the estimation of the transition onset location29,30. Pixels with local gradients exceeding a specified threshold were detected, and the maximum y-coordinates of the edges were identified at each streamwise location. These were then compared with the laminar boundary-layer edges, and if the detected edge was located above the laminar boundary layer, it was considered indicative of turbulence. The ratio of the presence of turbulent boundary layer over the test duration at a given location was subsequently calculated to determine the turbulent intermittency. Fig. 6 presents the turbulent intermittency calculated for each case. Due to the limited field of view, the images were captured with overlapping regions, resulting in the intermittency data in Fig. 6 also displaying overlapping regions with data points. In these regions, the turbulent intermittency shows good agreement across different experiments, indicating a reliable reproduction of freestream conditions. As the bluntness of the cone increases under the same unit Reynolds number, the onset of turbulent intermittency shifts further downstream. This observation suggests that increasing cone bluntness effectively delays the transition onset. The intermittency distribution for Case 4, conducted at a higher unit Reynolds number, is also presented for comparison. Notably, despite the significantly higher Reynolds number in Case 4 compared to Case 1, the transition onset occurs at a similar streamwise location, highlighting the substantial influence of cone bluntness in delaying boundary-layer transition.
Surface heat flux
Using coaxial thermocouples with a fast response time (\(\sim\)10 \(\upmu\)s), the surface temperatures were measured during the short test time. Through one-dimensional and semi-infinite body assumptions, the surface temperature was converted to the heat flux as follows31,32:
where \(\rho\), c, k are density, specific heat, and thermal conductivity coefficient of the thermocouple material, respectively. The calculated surface heat flux within the test time for each case is shown in Fig. 7. The initial overshoots of surface heat flux emerge on all cases starting from the thermocouple at the front (TC 1), which indicate the arrival of starting shock wave of the hypersonic nozzle. After the boundary layer sufficiently develops over the surface of the cone, the heat flux measured by each thermocouple reaches and maintains a certain level, during which large fluctuations are observed.
The onset of transition can be identified at the location where the measured heat flux deviates from the theoretical laminar prediction5. The surface heat flux was normalized into a Stanton number (\(C_H\)) to enable comparison with theoretical predictions and to identify the transition onset. Stanton number is defined as:
where the subscript, e, means the edge of the boundary layer. The edge conditions were estimated using Taylor-Maccoll equations33,34. The wall-temperature variations during the run are negligible due to short test duration. Therefore, a constant wall temperature of 300 K was used to compute the Stanton number. This leads to the wall-to-total temperature ratio (\(T_{w}/T_{0}\)) of 0.2, commonly regarded as a cold-wall condition9,26. The recovery temperature (\(T_r\)) can be estimated as follows:
where the recovery factor, r, was taken as 0.83 in this study35. The Stanton numbers for both the laminar and turbulent boundary layers were determined from semi-empirical relations1,35.
Figure 8 shows the normalized heat flux measurements with standard deviations for all cases. In Case 1 and 2, the mean Stanton number increases monotonically along the streamwise direction, indicating that the boundary layer is undergoing turbulent transition. Among the three cases conducted at identical unit Reynolds numbers, the sharp cone (Case 1) exhibits the highest heat flux across all measurement stations and the most rapid rise toward turbulent values. At x = 370 mm, the heat flux in Case 1 nearly approaches the level predicted for a fully turbulent boundary layer. In contrast, Case 2 does not reach turbulent levels within the measurement domain, with heat flux remaining between laminar and turbulent predictions. Case 3, with the largest nose-tip bluntness, maintains heat flux values close to laminar predictions throughout, suggesting a further downstream transition onset. An increase in standard deviation is observed where the heat flux departs from laminar levels and approaches turbulent values, reflecting intermittent nature of boundary-layer transition. This is consistent with the time-resolved schlieren images in Fig. 5, which show repeated formation and downstream propagation of turbulent wave packets. For direct comparison across runs with different freestream conditions (including Case 4), the time-averaged \(C_{H}\sqrt{Re_{x}}\) was computed where \(Re_x\) is the Reynolds number based on the streamwise position x; this normalization effectively collapses the heat flux data29,35. Fig. 6 shows these results together with the turbulent intermittency derived from schlieren images. The black dotted lines bound the interval from which heat flux data were obtained (\(x=250\)–370 mm). The intermittency and heat flux curves across all cases exhibit good agreement in overall trend and transition onset, supporting the intermittency calculations based on Canny edge detection employed in this study and suggesting that both schlieren visualization and heat flux measurements are effective for estimating the transition onset.
Time history of calculated surface heat flux (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4.
Due to the discrete placement and limited number of coaxial thermocouples, accurately determining the transition onset location based solely on heat flux measurements is challenging. Therefore, the transition onset was estimated using both the measured heat flux data and turbulent intermittency calculated from schlieren image sequences. Among the regions where turbulent wave packets begin to form and develop, the most upstream location was identified as the onset of laminar-to-turbulent transition, corresponding to the point where turbulent intermittency first increases. Fig. 9 shows the correlation between the nose-tip radius and the transition onset by plotting the transition Reynolds number (\(Re_{x_T}\)) against the Reynolds number based on the nose-tip radius (\(Re_{R_N}\)). Experimental results obtained in previous works5,9, as replotted on these axes in the literature11,36, are also included for comparison. The results for blunt cones in this study exhibits similar trends compared to those reported by previous works5,9 as shown in Fig. 9. Even the transition onset of the 0.1 mm nose-tip radius, which is conventionally considered a sharp cone, exhibits a good agreement with the correlation trend observed in the small bluntness regime (\(Re_{R_N}<\mathrm {10^5}\)). In this regime, the transition onset is delayed further downstream with increasing bluntness, consistent with findings from previous studies.
Measured Stanton numbers with laminar and turbulent predictions.
Transition Reynolds number as a function of the nose Reynolds number.
Instability measurements
Spectral proper orthogonal decomposition
Spectral proper orthogonal decomposition (SPOD) is a frequency-resolved modal decomposition technique that extracts orthogonal modes representing energetically dominant coherent structures in unsteady flows37. Each SPOD mode evolves coherently in both space and time, being perfectly correlated with itself across all times and uncorrelated with other modes. Owing to this property, SPOD has been shown effective in isolating physically meaningful structures, such as the rope-like patterns associated with second-mode instability28,38,39,40. In this study, the SPOD analysis was performed using the Welch’s method to estimate spectral densities by averaging over overlapping segments. A total of 1,000 schlieren image frames were used for each case, and the data were divided into segments with Hann windows of 128 samples and 50% overlap. With a frame rate of 1.5 MHz, the resulting frequency resolution in the mode energy spectra was 11.7 kHz. The length of schlieren frames used in each SPOD analysis correspond to approximately 0.7 ms within the test time.
Figure 10 presents the SPOD mode energy distribution as a function of frequency, obtained from schlieren images in Case 1 with sharp nose-tip. The streamwise domain analyzed corresponds to the region shown in Fig. 5, encompassing the laminar-to-turbulent transition process. At each frequency, the leading mode—defined as the mode with the highest spectral energy—is highlighted with a bold line. A distinct energy peak is observed near 680 kHz, accompanied by a broad plateau at lower frequencies. This indicates that the dominant instability peaks near 680 kHz, suggesting the presence of second-mode instability within the boundary layer. The corresponding spatial structures at 656.25 and 679.69 kHz are shown in Fig. 11, where characteristic rope-like features are observed. These wave structures begin to dissipate between x = 225 and 250 mm, coinciding with the turbulent transition region identified in Figs. 6 and 8, indicating the breakdown of second-mode instability into turbulence.
Similarly, for the experimental cases with blunt nose-tips (Case 2 and Case 3), the SPOD mode energy spectra and corresponding spatial mode structures are presented in Fig. 12–15. For each case, schlieren images were acquired over streamwise ranges selected to capture the evolution of the turbulent boundary layer. In the mode shape contours, red dotted lines indicate the estimated edge of the laminar boundary layer, as identified from the original schlieren images. In Case 2, a mode energy peak and rope-like structures are observed near 670 kHz within the region of x = 250–400 mm. These wave structures remain confined to the boundary layer, marked by the red dotted line in Fig. 13. However, the peak energy mode at 670 kHz vanishes from the spectrum in the downstream region of x = 370–520 mm, where the amplification of lower-frequency components becomes prominent. The corresponding SPOD modes display irregular structures without clear spatial patterns, suggesting that the boundary layer has reached a fully developed turbulent state.
The dominant energy modes for Case 3 with a 2 mm nose radius under identical freestream conditions are presented in Figs. 14 and 15. As shown in Fig. 14, a distinct energy peak appears near 620 kHz, corresponding to second-mode instability, consistent with observations in cases with smaller bluntness. Notably, as the bluntness increases, the frequency of the second-mode instability shifts to lower values, as evident in the energy spectra. In addition, a secondary energetic mode appears at a lower frequency around 200 kHz, which was absent in the cases with smaller bluntness. The mode shape at 199.22 kHz, depicted in Fig. 15, displays low-frequency wave structures with longer wavelengths compared to the second-mode waves, extending beyond the boundary-layer edge. The normalized propagation speeds (\(u_{prop}/u_{e}\)) were estimated from SPOD-derived coherent mode shapes by measuring the streamwise wavelength, yielding 1.02 at 199.22 kHz and 0.93 at 621.09 kHz. Comparable propagation speeds were reported by Kennedy et al.6 using schlieren images: the non-modal structure propagates at \(u_{prop}/u_{e}\) = 1.03, whereas the second-mode wave remains within \(u_{prop}/u_{e}\) = 0.94–0.97. Similar low-frequency instability over blunt cones have also been reported in prior study with pressure measurements41. In the downstream region of x = 370–520 mm, both energy peaks persist; however, the spectra gradually evolve into a saturated broadband distribution, indicative of a transitional boundary layer. From approximately x = 450 mm, the instability modes at the peak frequencies begin to dissipate and transition into irregular structures, suggesting the onset of turbulence, as illustrated in Fig. 15. These observations indicate that both second-mode and low-frequency instabilities coexist within the boundary layer over blunt cone.
SPOD mode energy spectra for Case 1 (x = 150–300 mm).
SPOD mode shapes for Case 1 (x = 150–300 mm).
SPOD mode energy spectra for Case 2 (a) x = 250–400 mm (b) x = 370–520 mm.
SPOD mode shapes for Case 2 (a) x = 250–400 mm (b) x = 370–520 mm.
SPOD mode energy spectra for Case 3 (a) x = 250–400 mm (b) x = 370–520 mm.
SPOD mode shapes for Case 3 (a) x = 250–400 mm (b) x = 370–520 mm.
Pressure spectra
The development of instabilities within the hypersonic boundary layer under varying bluntness configurations can also be analyzed through the frequency spectra of pressure fluctuations. The power spectral density (PSD) was computed from the PCB pressure signals using Welch’s method with Hann windows of length 128 and a 50% overlap between segments, allowing frequency resolution of 19.5 kHz. Each PSD calculation employed 3,000 pressure samples, which correspond to approximately 1 ms within the test time. Fig. 16 presents the PSDs along the sharp cone at \(Re_{u,\infty } = 7.02 \times 10^{6}\) \(\mathrm {m^{-1}}\), displaying broadband frequencies with nearly saturated values, indicating the early onset of turbulent transition. The second-mode band near 700 kHz is still discernible, but no narrow, well-separated peaks are observed. Given that the PCB transducers are positioned downstream of the onset of increasing turbulent intermittency near x = 220 mm and the region where the second-mode SPOD mode shape is identified, as shown in Figs. 6 and 11, it is expected that all pressure sensors would display broadband PSDs. Although the characteristic frequency peaks also appear outside the second-mode band between 100 and 350 kHz, they are not discriminated in SPOD mode energy spectra (see Fig. 10), indicating that these frequencies do not feature spatially coherent structures.
However, for Case 2 and 3 with blunt nose-tips, where the transition initiates along the surface where the pressure transducers are located, more distinct peak frequencies are observed compared to the sharp cone, as shown in Figs. 17 and 18. In Fig. 17, the pressure spectrum at PCB 2 displays a peak frequency at 680 kHz, consistent with the SPOD analysis for Case 2, which identifies a peak near 670 kHz. This transducer is located upstream of the region where turbulent intermittency starts to increase, suggesting the presence of second-mode instability. However, for the transducers positioned downstream of PCB 2, the high-frequency peaks associated with the second-mode instability become broader, indicating that turbulent transition is likely occurring within this region.
Figure 18 presents the PSDs for the blunt cone with a 2 mm nose-tip radius under the same unit Reynolds number. A peak frequency around 600 kHz is detected at PCB 2, and 550 kHz at PCB 3, corresponding to the peak frequencies identified in the SPOD analysis, further confirming the presence of second-mode waves. These high-frequency instabilities are more pronounced in Case 3 than in the other cases, attributed to the delayed transition. Furthermore, as the high-frequency instabilities propagate downstream, they undergo a downward shift in frequency accompanied by an increase in intensity. This behavior has been reported in previous studies29,42, reflecting a characteristic feature of second-mode instability as the boundary layer thickens downstream. In addition, with increasing nose-tip bluntness, the peak frequencies of the second-mode instability tend to shift toward lower values, along with a decrease in the overall PSD magnitude at the peak. Additional peaks near 200 kHz are observed at all PCB transducers in the PSDs for Case 3, which has the largest bluntness. These characteristic frequencies in pressure PSDs appeared in repeated runs for Case 3, as shown in Fig. 19. These peaks are also revealed in the SPOD mode energy presented in Fig. 14, indicating the presence of a low-frequency instability that is not observed in Cases 1 and 2.
The peak second-mode frequencies (f) extracted from the wall-pressure PSDs at each pressure sensor were collapsed using Stetson’s scaling5, as shown in Fig. 20. This enables direct comparison of instability data across nose-tip bluntness configurations. The dimensionless second-mode frequency (F) is defined as:
and the stability Reynolds number (R) is defined as:
where \(Re_x\) is the Reynolds number based on freestream unit Reynolds number and position x. In Fig. 20, the scaled second-mode frequency generally decreases with streamwise distance, consistent with previous works6,9. Under identical freestream conditions, the nose-tip with \(R_{N}=2\) mm yields systematically lower dimensionless frequencies along the cone than the tip with \(R_{N}=1\) mm. This frequency shift of dominant second-mode instability with increased nose-tip bluntness is corroborated by the SPOD analysis presented in the previous section. For Case 1, the early transition upstream of the PCB stations prevents clear identification of narrow-band second-mode peaks, causing the data to slightly deviate from the overall trend. In addition, the scaled frequencies in Case 1 are comparable to those in Case 2, due to the thickened boundary layer before turbulent transition, shifting the peak frequency to lower values.
Pressure spectra for Case 1 at each PCB transducer.
Pressure spectra for Case 2 at each PCB transducer.
Pressure spectra for Case 3 at each PCB transducer.
Pressure spectra for Case 3 at PCB 4 from repeated runs (Run 1–3).
Scaling of second-mode frequencies for different \(R_N\).
Conclusion
The effects of nose-tip bluntness on hypersonic boundary-layer transition were investigated using a \(7^\circ\) half-angle cone model in the SHyST facility. Time-resolved schlieren visualization, surface heat flux measurements, and high-frequency pressure measurements were utilized to characterize the boundary-layer transition and associated instabilities across varying nose-tip bluntness and unit Reynolds numbers.
The results demonstrated that increasing nose-tip bluntness delayed the transition onset by suppressing the amplification of second-mode instabilities. Turbulent intermittency analysis based on schlieren imaging revealed that a larger nose-tip radius shifted the transition location further downstream at a fixed unit Reynolds number. Surface heat flux measurements obtained using coaxial thermocouples provided transition onset locations consistent with the intermittency data. Additionally, dominant instability frequencies were determined through high-speed imaging and surface pressure measurements. SPOD and pressure spectral analyses highlighted distinct instability characteristics associated with cone bluntness. For the sharp cone configuration, a clear second-mode instability peak around 680 kHz was observed, accompanied by broadband pressure spectra indicative of an early turbulent transition. Blunt cones also displayed second-mode instability peaks, although at lower frequencies. Specifically, the 2 mm blunt cone case showed an additional low-frequency instability near 200 kHz, which was not present in sharper configurations, suggesting the coexistence of multiple instability mechanisms in blunt cones.
Comparison with previous studies confirmed the transition delay and frequency shifts with increased bluntness. The appearance of low-frequency instabilities indicates more complex instability mechanisms in blunt cone boundary layers, requiring further investigation. These findings highlight the need to account for multiple instability modes in hypersonic boundary-layer transition for blunt bodies.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Funding
This research was supported by the Challengeable Future Defense Technology Research and Development Program through the Agency For Defense Development (ADD) funded by the Defense Acquisition Program Administration (DAPA) in 2025 (No.915067201).
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J. Kim contributed to conceptualization, methodology, investigation, data curation, formal analysis, visualization, and writing—original draft. J. Nam contributed to conceptualization, methodology, investigation, data curation. J. Hur contributed to conceptualization, methodology, investigation, data curation. J. Kim contributed to conceptualization, methodology, investigation. B. J. Lee contributed to conceptualization, methodology, investigation, supervision, writing—review and editing, and funding acquisition.
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Kim, J., Nam, J., Hur, J. et al. Experimental study of nose-tip bluntness effects on hypersonic boundary-layer transition in a shock tunnel. Sci Rep 15, 38301 (2025). https://doi.org/10.1038/s41598-025-22323-5
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DOI: https://doi.org/10.1038/s41598-025-22323-5






















