Both, Pitot and PIV data, were used to extract the skin friction velocity indirectly. Three different approaches were applied and compared to analytical and numerical data. First, a fitting approach was used based on the incompressible law- of-the-**wall**. Furthermore, the high resolution of PIV velocity data enabled an approach which approximated the velocity gradient close to the **wall**. Finally, an integral approach was used which utilized profiles of both measurement sections and the corresponding loss of momentum. All approaches agreed for both experimental techniques with the analytical and numerical predictions within their corresponding uncer- tainties. Based on Monte Carlo analysis, the fitting approach resulted in the lowest uncertainties and was therefore cho- sen to enable analysis of the velocity profiles in inner and outer scaling according to AGARD suggestions (Fernholz and Finley 1980 ). With the van Driest transformation, the compressible velocity profiles generally collapsed with the incompressible law-of-the-**wall**. Despite that, higher veloc- ities were determined in the buffer **layer** region, possibly driven by artificially higher velocities due to slip. In outer scaling, the data collapsed in the range of validity with the corresponding theories. Both, outer scaling and shape fac- tor, were biased in case of the Pitot profiles due to the lack of resolution close to the **wall**. Nevertheless, outer scaling parameters, as well as the skin friction velocities, could be extracted from the Pitot data.

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This paper presents the results of the **experiments** performed in the **hypersonic** wind tunnel H2K in the framework of the ESA technology research project “Laminar to Turbulent Transition in **Hypersonic** Flows”. The investigations include the free **boundary** **layer** transition on a flat plate as well as the influence of a shock wave **boundary** **layer** interaction on the transition. The **experiments** were performed at **Mach** 6.0 at three di ff erent unit Reynolds numbers and with a translational displacement of the shock generator. Be- sides the optical methods schlieren photography and infrared thermography several high-speed intrusive sensors were used. Heat flux measurements were carried out using coaxial thermocouples, thin film gauges and an atomic **layer** thermo pile. Kulite and PCB sensors were used for pressure measurements. This paper concentrates on the heat flux measurements and includes just a glance on the pressure measurements.

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Numerical and experimental studies have demonstrated that modal growth of planar Mack modes is responsible for laminar-turbulent transition on sharp cones at **hypersonic** speeds. However, the physical mechanisms that lead to transition onset upstream of the entropy-**layer** swallowing location over sufficiently blunt geometries are not well understood as yet. Modal amplification is too weak or nonexistent to initiate transition at moderate-to-large bluntness values. Nonmodal analysis shows that, with increasing nose bluntness, both planar and oblique traveling disturbances that peak within the entropy **layer** experience appreciable energy am- plification. However, because of the relatively weak signature of the nonmodal traveling dis- turbances within the **boundary**-**layer** region, the route to transition onset subsequent to the nonmodal growth remains unclear. Thus, nonlinear parabolized stability equations (NPSE) and direct numerical simulations (DNS) have been used to investigate the potential transition mechanisms over a 7-degree blunt cone that was tested in the AFRL **Mach**-**6** high-Reynolds- number facility. Computations are performed to separately follow the nonlinear development of two classes of inflow disturbances, namely, a pair of oblique traveling waves with equal but opposite angles with respect to the mean flow direction and a planar traveling wave. Results in both cases show an excellent agreement between the NPSE and DNS predictions, establishing that the NPSE is an accurate and efficient technique for predicting the nonlinear development for these particular nonmodal traveling disturbances. Computations reveal that the oblique mode interactions lead to the generation of stationary streaks inside the **boundary** **layer** that, in turn, facilitate the growth of a subharmonic sinuous disturbance. For relatively modest amplitudes of the inflow disturbance, the oblique-mode breakdown can lead to transition at the measured location of transition onset during the experiment. On the other hand, the nonlinear development of a planar traveling wave leads to the formation of inclined structures just above the **boundary**-**layer** edge and these structures are strongly reminiscent of the transitional events observed during blunt cone **experiments** by using schlieren flow visualizations.

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The basic structure of the second-mode disturbances; namely, that they are two- dimensional oscillations primarily in density rather than velocity, has motivated the implementation of optical-based measurement techniques (see Laurence et al. 2012). Recently, VanDercreek (2010) applied focused schlieren in combination with a photomultiplier tube to study the second-mode instability on a 7-degree straight cone at **Mach** 10 in AEDC’s Tunnel 9. He observed photomultiplier signal frequencies consistent with those measured with PCB® pressure sensors embedded in the model surface. Laurence et al. (2012) have also recently obtained time-resolved schlieren visualizations to determine the structural and propagation characteristics of second-mode instability waves within a **hypersonic** **boundary** **layer**. Almost all other previous **hypersonic** stability **experiments** – including those of Chokani in the M6QT at NASA Langley – have used single-point, hot-wire anemometry. The attendant limited frequency response, which is typically O(400 kHz), has hampered efforts to identify potentially higher harmonics and provide a more complete picture of the second-mode disturbance evolution process.

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Figure 5 shows that the unstable secondary disturbances are concentrated in two separate frequency ranges. The low-frequency lobes (with peak frequencies below approximately 100 kHz) correspond to traveling crossflow instability modulated by the weak stationary crossflow vortex. Accordingly, they are labeled as TC1 and TC2, respectively, where the numerical suffix identifies the index of the azimuthal harmonic corresponding to the stationary mode. Thus, the mode TC1 corresponds to secondary modes with an azimuthal wavenumber equal to the local fundamental wavenumber of the stationary vortex, whereas mode TC2 corresponds to a secondary mode with an azimuthal wavenumber equal to twice the fundamental wavenumber. In a similar manner, the two high-frequency lobes correspond to second mode (i.e., Mack mode) waves of the unperturbed **boundary** **layer** over the cone, and hence, have been labeled MM0 and MM1, respectively. The mode MM0 corresponds to axisymmetric Mack mode whereas mode MM1 corresponds to an oblique Mack mode with an azimuthal wavenumber equal to that of the stationary crossflow vortex. Because the growth rate of second mode disturbances decreases rapidly with the wave angle, only the fundamental harmonic is unstable in this case. Representative mode shapes for the above families of disturbances are shown in Figs. **6**(a) through **6**(d). Peak velocity fluctuations associated with the Mack modes are relatively close to the surface, whereas those associated with the traveling crossflow modes are concentrated further away inside the **boundary** **layer**. In the remaining part of this paper, we focus mainly on the high-frequency disturbances since they appear to be linked more closely with the observed onset of laminar breakdown in the Purdue **experiments** [21, 22].

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The second verification case is a sharp two-dimensional wedge with an angle of **6** degrees relative to the freestream in **Mach** 20 flow with a freestream unit Reynolds number of 9 × 10 5 per foot. The **wall** temperature is held constant with T w /T ad = 0 . 1, using the equilibrium adiabatic **wall** temperature for the finite-rate case. Consistent with the results in the literature, this is simulated as a flat plate with constant **boundary** **layer** edge conditions determined by the conditions after the shock calculated using Rankine-Hugoniot conditions. The post-shock edge **Mach** number is 12.5. Changes to the post-shock conditions due to changes to the gas model are not taken into account. Verification against results published by Chang et al. [3] are shown in Figure 3, showing the nonparallel N-factor calculated at a selection of frequencies. For the perfect gas, the current results show slightly higher peak N-factors and a smaller decaying rate past the peak. As will be shown later in Section B, supersonic modes emerge downstream of the peak second mode for this flow. Previous results appear to track the decaying second mode, while the present results capture the slowly decaying supersonic modes in the linear PSE solutions shown here. The small discrepancy in peak N-factor could be due to a slightly different Prandtl number and grids used in the **boundary** **layer** solutions. Despite these differences, the overall N-factor envelope seems to agree. Both chemical equilibrium and finite-rate results show good agreement with the reference results, with discrepancies in N-factor magnitude at some frequencies. These discrepancies may be due to differences in the mean flow set up and improved accuracy in discerning peak growth rates in the current work.

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Strong interactions of shock waves with **boundary** layers lead to flow separations and enhanced heat transfer rates. When the approaching **boundary** **layer** is **hypersonic** and transitional the problem is particularly challenging and more reliable data is required in order to assess changes in the flow and the surface heat transfer, and to develop simplified models. The present contribution compares results for transitional interactions on a flat plate at **Mach** **6** from three different experimental facilities using the same instrumented plate insert. The facilities consist of a Ludwieg tube (RWG), an open-jet wind tunnel (H2K) and a high-enthalpy free-piston-driven reflected shock tunnel (HEG). The experimental measurements include shadowgraph and infrared thermography as well as heat transfer and pressure sensors. Direct numerical simulations (DNS) are carried out to compare with selected experimental flow conditions. The combined approach allows an assessment of the effects of unit Reynolds number, disturbance amplitude, shock impingement location and **wall** cooling. Measures of intermittency are proposed based on **wall** heat flux, allowing the peak Stanton number in the reattachment regime to be mapped over a range of intermittency states of the approaching **boundary** **layer**, with higher overshoots found for transitional interactions compared with fully turbulent interactions. The transition process is found to develop from second (Mack) mode instabilities superimposed on streamwise streaks.

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The 31-Inch **Mach** 10 Air Tunnel is an electrically-heated blowdown facility located at NASA Langley Research Center in Hampton, Virginia, USA. The full details of this facility can be found in the paper by Micol, 2 a brief summary of which is provided here. The facility has a nominal **Mach** number of 10 and a 31-inch square test section and operates on electrically heated, compressed air. Large windows—transparent in the ultraviolet down to approximately 190 nm—form three walls (including top, side and bottom) of the test section, with the fourth **wall** formed by the model injection system. The top window allows the laser sheet to pass through the test section, while the side window allows for imaging of the flow region of interest. The model is attached at the rear to a sting, which is subsequently side-mounted to the fourth **wall**. Run durations for the **experiments** were typically one to two minutes. Two nominal facility stagnation pressures, P 0 , of 3.45 MPa (500 psia) and 4.98 MPa (720 psia) were investigated. The nominal stagnation temperature, T 0 , was 1000 K (1,800 Rankine). Based upon the stagnation conditions, the approximate freestream **Mach** number was 9.8, the approximate freestream velocity was 1400 m/s. The approximate freestream unit Reynolds numbers (Re ∞ ) for the 3.45 MPa and 4.98 MPa stagnation pressure conditions were 2.4x10 **6** m -1 and 3.3x10 **6** m -1 , respectively.

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The potential of realizable, stationary streaks undergoing nonmodal growth to stabilize a **hypersonic** **boundary**-**layer** flow and, subsequently, delay the laminar-turbulent transition onset, is studied via numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment, namely, a 7-degree half-angle cone with 2.5 mm nose radius, freestream **Mach** number of 5.30, freestream unit Reynolds number equal to 13.42 × 10 **6** m − 1 , and **wall**-to-adiabatic tempera- ture ratio of approximately 0.35 over most of the test article. This paper investigates flow modifications induced by **wall**-mounted vortex generators (VGs), followed by an analysis of the modal instability of the perturbed, streaky **boundary**-**layer** flow. Results are presented both for a single array of VGs that was designed on the basis of optimal growth theory and for a VG configuration involving two separate arrays with opposite orientations that ware designed to provide staged control of flow instabilities while simultaneously reducing the amplification of streak instabilities resulting from the control devices. Earlier research had shown that the onset of transition during the HIFiRE-1 flight experiment, which did not include any control devices, correlated with an amplification factor of N = 14.7 for the planar Mack modes. If one assumes that the transition N -factor is not affected by the introduction of the VGs, then the control configurations based on a single array of VGs and two separate arrays would result in a transition delay of 17% and 40%, respectively. These findings suggest a passive flow control strategy of using VGs to induce streaks that would delay transition in **hypersonic** **boundary** layers dominated by Mack-mode instabilities.

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The successful operation of scramjet combustors requires com- pression of **hypersonic** viscous ducted flows and avoidance of separation effects which may preclude steady flow. Separa- tion effects in scramjet inlets and combustors can be caused by shock wave/**boundary** **layer** interactions. The **hypersonic** tur- bulent flow **experiments** needed are inherently difficult to de- sign because of the high sensitivity of the macroscopic flow parameters which cause the turbulent flow processes. Hence computational fluid dynamics (CFD) is a useful tool for the de- sign and characterisation of models in **hypersonic** flows before model construction. One of the greatest challenges however is to ensure that the flow is being modeled accurately. In this paper, a commercial code has been used to model an experi- ment performed in a small reflected shock tunnel using a **Mach** 8.65 condition. The research being carried out in this facility is concerned with separation due to incident shock wave/turbulent **boundary** interactions in **hypersonic** ducted flows. The model is designed to produce two conical shocks which interact with a turbulent **boundary** **layer** and it is instrumented with pres- sure transducers and thin film heat transfer gauges. The mea- surements have allowed graphical representation of unseparated static **wall** pressure and heat flux prior to and after each **wall** in- teraction. The results of the simulations are in excellent agree- ment with the experimental data. The code has been applied to identify parameter boundaries in the design of a model of simi- lar scale that will produce separated flow.

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Figure 4.15 compares the **wall** static pressure on the 91-**6** model. The calculations compare very well with the experimental data. The small differences between the experiment and calculation possibly arise from model misalignment. The predicted surface temperature distribution for the 91-**6** model is compared with the experimental measurements in Figure 4.16. The rise in the measured temperature at x=12˝ for the adiabatic **wall** is due to the transitional nature of the **boundary** **layer**. Upstream of this location, the predictions and experiment are in very good agreement, within 3% of each other. A discrepancy between the experiment and cooled **wall** computations exists upstream of x=**6**˝. The computational results are obtained for a constant **wall** temperature. However, the tip of the thin-walled cone model is not cooled. Therefore, a temperature gradient exists between the relatively hot tip and the cooler thin **wall** downstream of the leading edge region. Uniform temperature is not achieved until x=7˝. In the range of 7≤x≤12˝, the calculated and experimental results agree within 1%. The

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The damping effect from the presence of CO 2 in the **boundary** **layer** is well doc- umented by numerous wind tunnel **experiments** in the California Institute of Tech- nology’s Graduate Aeronautical Laboratory at the California Institute of Technology (GALCIT) piston-free T5 wind tunnel. High enthalpy wind tunnel testing was con- ducted by Germain and Hornung [25] and Adam and Hornung [7] in which a sharp, 5 degree half angle cone was used. These **experiments** were the first to look at transition at high **Mach** numbers but not in a cold flow facility. Since cold flow facilities achieve high **Mach** numbers by lowering the speed of sound, the kinetic energy remains too low to look at kinetic effects on the molecules in the flow. Using freestream gases of air, N 2 and CO 2 , this testing showed that as enthalpy increased so did transition Reynolds number and it was noted that all the testing done with CO2 yielded a slightly higher Reynolds number than the other gases [25]. Adam noted that while there seemed to be little correlation with enthalpy when comparing Re tr , when com- pared to a reference temperature (Equation 2.6), the transition Reynolds number for flows with CO 2 showed a significant increase[7]. Figures 2.6 and 2.7 shows these re- sults. It was determined from these studies that CO 2 showed the greatest absorption when the freestream enthalpy was between 3 and 11 M J kg . Above this value, the energy of the flow as high enough to cause most of the CO2 to dissociate.

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For part of the rectangular-trip tunnel run, the laser sheet was placed on the model centerline and the angle of attack of the model was swept from 20º to 0°. This allowed virtually continuous visualization of the growth of the **boundary** **layer** relative to the height of the trip. A total of 57 frames of data were acquired during this sweep. Figure **6** shows every 8 th frame from this sequence. At the steepest flat plate angle of 20º, the **boundary** **layer** is thinner than the trip and flow is primarily diverted around the trip as shown in Fig. 5. As the angle of the plate decreases from 20º, the **boundary** **layer** in front of the trip, identified by the presence of NO, thickens. Eventually, the **boundary** **layer** grows to be thicker than the trip and wisps of NO are observed to pass over the trip. At still shallower angles, the **boundary** **layer** flows continuously over the center of the trip. Finally, at the lowest angle of attack, the flow passes directly over, engulfing the trip, while maintaining laminar flow. Curiously, all the images obtained on this angle of attack sweep appeared to show laminar-like behavior. Had the laser sheet been placed 5 mm to one side or the other of the centerline, turbulent images would probably have been observed at the higher flat plate angles, as evidenced by Fig.5. Note that the placement of the images relative to the rendered model may not be perfect during ViDI processing, so the absence of PLIF immediately in front of the trip should not necessarily be interpreted as a shock wave.

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such, this near-**wall** position is used only to support trends observed higher in the **boundary** **layer**. In Fig. 6.16, the normalized streamwise spectra at the nearest position to the **wall** (y + = 35) show a large “bulge” at a scale of 0.25δ – 0.3δ (250 – 300 viscous units), with negligible energy content at longer wavelengths, suggesting that the turbulent energy is confined to a relatively narrow range of scales. Note that this scale is several times smaller than the “inner peak” discovered by Hutchins & Marusic (2007b) at y + = 15, which they attributed to the near-**wall** turbulence regeneration cycle. Moving higher in the **boundary** **layer** to y + = 60, the local maximum has decreased in magnitude, as energy is transferred to longer wavelengths. However, this reduction may simply be due to the elevated uncertainty at y + = 35. Above this height, the “bulge” visible in the near-**wall** layers is now barely discernible, and has shifted to a slightly shorter wavelength of 0.2δ (~ 200 viscous units). Beyond y + = 200, the spectra are almost completely dominated by long-wavelength scales, extending beyond the FOV. Referring back to the inner-scaled velocity shown in Fig. 6.2, y + = 200 is near the upper edge of the logarithmic region for this flowfield, suggesting that the motions associated with the short wavelengths are relatively benign in the wake region. Also, note that the maximum energy content is located at wavelengths longer than the FOV for all distances from the **wall**, excepting the heights y + = 35 and 60, which reside within the buffer **layer**.

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The effect of **Mach** number on the growth of unstable disturbances in a **boundary** **layer** undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory 共LST兲. To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number 共based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow兲 and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations 共 PSE 兲 . At **Mach** 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At **Mach** 4.5 and **Mach** 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear **layer**. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher **Mach** number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wavenumbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at **Mach** 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes. © 2007 American Institute of Physics.

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L aminar-to-turbulent **boundary**-**layer** transition is of critical concern for the design of many **hypersonic** vehicles as it affects the heat transfer to the vehicle, the skin-friction drag, and the vehicle controllabil- ity. Although our understanding of the physical mechanisms that cause transition in **hypersonic** **boundary** layers has greatly improved over the past several decades, our current ability to predict when and where transition will occur on a given **hypersonic** configuration is still lacking. In the near term, improvements to our predictive methodologies will depend greatly on both computational methods and experimental mea- surements in ground-based facilities. Experimental measurements, with unsteady or dynamic sensors in particular, provide critical validation data for **boundary** **layer** stability and transition calculations and they allow us to identify the mode(s) of **boundary**-**layer** transition for a given **hypersonic** configuration. Unsteady measurements can also be used to evaluate various methods for **boundary** **layer** transition control.

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To gain deeper understanding of the controlling mechanism of the drag reduction and radical behavior of the grooved surfaces, the pressure drop readings for each surface and the flow rate are simultaneously recorded over 60’s. There are at least two groups of fluctuations that make up the **wall** pressure. This is according to the suggestion provided by the collective body of results [49-52]. The first group of pressure fluctuation signals is made up of large-scale disturbances that are of low-frequency. Such disturbances come from the surrounding portions of the **boundary** **layer** and goes up to within the unsteady potential flow. The large-scale disturbances remain consistently on course with the character of the interface of the potential flow which is outside the **boundary** **layer**. On the other hand, the second group of

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In the present study, the surface roughness effect on the turbulent shock **boundary** **layer** interaction flows in transonic circular bump geometry was investigated using computational techniques. The accuracy of different turbulence models in predicting the surface roughness effect on shock **boundary** **layer** interaction flows was investigated. It was found that the SST k- ω model, which uses the enhanced **wall** treatment, predicts the pressure fluctuation along the rough bump surface more accurately compared to the experimental results. As the **wall** roughness height increases the shock strength decreases. This is mainly due to the decrease in flow acceleration produced by the additional frictional effects. As a result of this the shock location moves upstream as the **wall** surface height value increases. The upstream influence length also increases with increase in surface roughness. The flow separation re attachment distance for **smooth** **wall** simulation shows higher value compared to rough **wall** simulations. This is mainly due to fact that the adverse pressure gradient required for the flow separation decreases with increase in surface roughness. The flow variations downstream to the shock front are propagated to a much higher distance for rough walls compared to **smooth** walls. The turbulent kinetic energy along the bumps surface increases with increase in surface roughness and this will increase the flow variation region downstream to the shock.

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The structure of **wall** pressure fluctuations beneath a turbulent **boundary** **layer** interacting with a normal shock wave is investigated through direct numerical simulation (DNS). In the zero- pressure-gradient (ZPG) region upstream of the interaction pressure statistics well compare with canonical **boundary** layers in terms of fluctuation intensities and frequency spectra. Across the interaction zone, the r.m.s. **wall** pressure fluctuations attain large values (in excess of ≈ 162 dB), with an increase of about 7 dB from the upstream level. The main eﬀect of the interaction on the frequency spectra is to enhance of the low-frequency Fourier modes, while inhibiting the high-frequency ones. Excellent collapse of frequency spectra is observed past the interaction zone when data are scaled with the local **boundary** **layer** units. In this region an extended ω − 7/3

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viii LIST OF FIGURES Number Title Page 1 Wind Tunnel-General View 68 2 Experimental Set- Up 69 3 Wavy Wall Models - Details of Construction 70 4 Wavy Wall Models 71 5 Shape of Wavy Wall [r]

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