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NASA NTRS2022

Combined Bluntness and Roughness Effects on Cones at Hypersonic Speeds

This computational study investigates the effects of discrete roughness elements on a blunt cone at zero degrees angle of attack in a Mach 6 flow. Motivation was provided by experiments conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number facility on a 7-degree half-angle cone with a roughness array located at 45 degrees from the apex on two nose tips of different blutness but equivalent roughness Reynolds number. Transition was only affected on the blunter cone, indicating that the transition onset is associated with the combined effects of bluntness and roughness. The present study investigates the 15.24 mm nose radius, 420 azimuthal wavenumber case via Navier-Stokes computations of the laminar base flow and instability analysis. Plane-marching parabolized stability equations (PSE) and inflow-resolvent analysis based on the three-dimensional, harmonic linearized Navier-Stokes equations (HLNSE) are used to calculate the amplification of disturbances along the roughness wake as well as over the roughness nearfield. Results show that the roughness shape can have a great impact on the characteristics of the most amplified wake instabilities. For the experimental configuration with cubic roughness elements of 15 μ m height, the flow is marginally unstable. For prismatic elements of 20 μ m height, the PSE predicts a logarithmic disturbance amplification ratio of N = 5.6 along its wake, but this ratio increases to N = 9.6 when the amplification over the roughness and separation regions is included in the inflow-resolvent analysis.

Boundary-layer transition↗

NASA NTRS2022

Hypersonic Boundary-Layer Instabilities over Ogive-Cylinder Models

Computational investigations of an ogive-cylinder geometry with varying nosetips at zero degrees angle of attack are presented. The model geometry and conditions are selected to match experiments conducted in the Air Force Research Laboratory (AFRL) Mach 6 Ludwieg Tube. Five nosetips of interest were selected for the computational studies herein: two sharp ogives, two blunt ogives, and one hemispherical nosetip. Computations are performed at a freestream Reynolds number of 7.01 × 10 6 m -1 . Each sharp and blunt tip ogives had a 14 and 28 degree version for the tip angles. A cylindrical section follows the nosetip, resulting in a meter long model such as in the experiments. The laminar flow solutions are analyzed. The boundary-layer-edge properties and the velocity and temperature profiles are compared across streamwise locations aft of the ogive-cylinder junction. The blunt nosetips induce an entropy layer that envelopes the boundary-layer profiles. Modal stability analysis identifies most amplified frequencies corresponding to Mack’s second modes that agree with experimental results for the sharp tips. Similar to the experimental measurements based on wall-mounted pressure sensors, no unstable modes are found for the blunt models. Nonmodal analysis revealed a broadband set of disturbances present for the blunter tips, in agreement with experimental observations. Flow perturbation contours of most amplified planar and oblique disturbances are shown to qualitatively match wind tunnel Schlieren images, with a switch from rope-like to elongated structures, i.e., from high frequency Mack’s second modes to low frequency Mack’s first modes, as the nosetip angle is increased for the sharp tip, and from boundary-layer to entropy-layer disturbances as the bluntness is increased.

Boundary layer transition↗

NASA NTRS2021

Boundary Layer Instabilities Over a Cone-Cylinder-Flare Model at Mach 6

Computations are performed to investigate the boundary-layer instabilities over a sharp cone-cylinder-flare model at zero degrees angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The geometry consists of a nominally sharp 5-degree half-angle cone, followed by a cylindrical segment and then a 10-degree flare. An axisymmetric separation bubble is generated as a result of the laminar shock/boundary-layer interaction in the cylinder-flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundarylayer edge and the reattachment shock. The predicted heat flux distribution is also in agreement with the measured values downstream of the reattachment location. The analysis of convective and global instabilities is performed for flare half angles equal to 8, 10, and 12 degrees and nosetip radii equal to 0.1, 1, and 5 mm. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations (PSE) and the harmonic linearized Navier-Stokes equations (HLNSE). The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves are compared with the measured spectra at the various locations of the PCB and Kulite sensors. The comparison shows that the computational analysis captures the distinct lobes within the disturbance amplification spectra measured in the experiments, but some differences in amplification characteristics are noted at low frequencies. Overall, the oblique disturbances are found to be more amplified than the planar disturbances. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 degrees. The unstable global mode for the experimental configuration of a 10 degrees flare and a sharp nosetip cone corresponds to a stationary three-dimensional disturbance that is concentrated in the recirculation region and achieves its maximum growth rate for an azimuthal wavenumber of 5.

Boundary layer transition↗

NASA NTRS2021

Hypersonic Boundary-Layer Instabilities over Ogive-Cylinder Models

Computational investigations of an ogive-cylinder geometry with varying nosetips at zero degrees angle of attack are presented. The model geometry and conditions are selected to match experiments conducted in the Air Force Research Laboratory (AFRL) Mach 6 Ludwieg Tube. Five nosetips of interest were selected for the computational studies herein: two sharp ogives, two blunt ogives, and one hemispherical nosetip. Computations are performed at a freestream Reynolds number of 7.01 × 10 6 m -1 . Each sharp and blunt tip ogives had a 14 and 28 degree version for the tip angles. A cylindrical section follows the nosetip, resulting in a meter long model such as in the experiments. The laminar flow solutions are analyzed. The boundary-layer-edge properties and the velocity and temperature profiles are compared across streamwise locations aft of the ogive-cylinder junction. The blunt nosetips induce an entropy layer that envelopes the boundary-layer profiles. Modal stability analysis identifies most amplified frequencies corresponding to Mack’s second modes that agree with experimental results for the sharp tips. Similar to the experimental measurements based on wall-mounted pressure sensors, no unstable modes are found for the blunt models. Nonmodal analysis revealed a broadband set of disturbances present for the blunter tips, in agreement with experimental observations. Flow perturbation contours of most amplified planar and oblique disturbances are shown to qualitatively match wind tunnel Schlieren images, with a switch from rope-like to elongated structures, i.e., from high frequency Mack’s second modes to low frequency Mack’s first modes, as the nosetip angle is increased for the sharp tip, and from boundary-layer to entropy-layer disturbances as the bluntness is increased.

Boundary layer transition↗

NASA NTRS2019

Nonmodal Growth of TravelingWaves on Blunt Cones at Hypersonic Speeds

The existing database of transition measurements in hypersonic ground facilities has established that, as the nosetip bluntness is increased, the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream. However, this trend is reversed at sufficiently large values of the nose Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nose-tip bluntness. Because modal amplification is too weak to initiate transition at moderate-to-large bluntness values, nonmodal growth has been investigated as the potential basis for a physics-based model for the frustum transition. The present analysis investigates the nonmodal growth of traveling disturbances initiated within the nose-tip vicinity that peak within the entropy layer. Results show that, with increasing nose bluntness, both planar and oblique traveling disturbances experience appreciable energy amplification up to successively higher frequencies. For moderately blunt cones, the initial nonmmodal growth is followed by a partial decay that is more than overcome by an eventual, modal growth as Mack-mode waves. For larger bluntness values, the Mack-mode waves are not amplified anywhere upstream of the experimentally measured transition location, but the traveling modes still undergo a significant amount of nonmodal growth. This finding does not provide a definitive link between optimal growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition in the absence of sufficient Mack-mode amplification implies a double peak in disturbance amplification and the appearance of transitional events above the boundary-layer edge.

Hypersonic speed↗

NASA NTRS2018

Nosetip Bluntness Effects on Transition at Hypersonic Speeds: Experimental and Numerical Analysis

The existing database of transition measurements in hypersonic ground facilities has established that the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream as the nosetip bluntness is increased with respect to a sharp cone. However, this trend is reversed at sufficiently large values of the nosetip Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nosetip bluntness. This transition reversal phenomenon, which cannot be explained on the basis of linear stability theory, was the focus of a collaborative investigation under the NATO STO group AVT-240 on Hypersonic Boundary-Layer Transition Prediction. The current paper provides an overview of that effort, which included wind tunnel measurements in three different facilities and theoretical analysis related to modal and nonmodal amplification of boundary layer disturbances. Because neither first and second-mode waves nor entropy-layer instabilities are found to be substantially amplified to initiate transition at large bluntness values, transient (i.e., nonmodal) disturbance growth has been investigated as the potential basis for a physics based model for the transition reversal phenomenon. Results of the transient growth analysis indicate that stationary disturbances that are initiated within the nosetip or in the vicinity of the juncture between the nosetip and the frustum can undergo relatively significant nonmodal amplification and that the maximum energy gain increases nonlinearly with the nose radius of the cone. This finding does not provide a definitive link between transient growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition during the reversal regime was highly sensitive to wall roughness, and furthermore, was dominated by disturbances that originated near the nosetip. Furthermore, the present analysis shows significant nonmodal growth of traveling disturbances that peak within the entropy layer and could also play a role in the transition reversal phenomenon.

Freestream Mach Number↗

NASA NTRS2018

Nosetip Bluntness Effects on Transition at Hypersonic Speeds: Experimental and Numerical Analysis Under NATO STO AVT-240

The existing database of transition measurements in hypersonic ground facilities has established that the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream as the nosetip bluntness is increased with respect to a sharp cone. However, this trend is reversed at sufficiently large values of the nosetip Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nosetip bluntness. This transition reversal phenomenon, which cannot be explained on the basis of linear stability theory, was the focus of a collaborative investigation under the NATO STO group AVT-240 on Hypersonic Boundary-Layer Transition Prediction. The current paper provides an overview of that effort, which included wind tunnel measurements in three different facilities and theoretical analysis related to modal and nonmodal amplification of boundary layer disturbances. Because neither first and second-mode waves nor entropy-layer instabilities are found to be substantially amplified to initiate transition at large bluntness values, transient (i.e., nonmodal) disturbance growth has been investigated as the potential basis for a physics-based model for the transition reversal phenomenon. Results of the transient growth analysis indicate that disturbances that are initiated within the nosetip or in the vicinity of the juncture between the nosetip and the frustum can undergo relatively significant nonmodal amplification and that the maximum energy gain increases nonlinearly with the nose radius of the cone. This finding does not provide a definitive link between transient growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition during the reversal regime was highly sensitive to wall roughness, and furthermore, was dominated by disturbances that originated near the nosetip.

Numerical analysis↗

NASA NTRSDate not supplied

Separation and Transition on a CCF: Experimental Campaigns

Several experimental campaigns have been conducted across a number of Mach-6 facilities on the hypersonic flow around a CCF (CCF) geometry with a 5° half-angle cone and a 12° half-angle flare. These experiments were conducted as part of the NATO STO Research Task Group AVT-346, which is focused on predicting hypersonic boundary-layer transition on complex geometries. Two conventional wind tunnels (AFRL M6LT and ONERA R2Ch) and one quiet tunnel (Purdue BAM6QT) were used to test the same CCF geometry and to study the instabilities in both the boundary layer in the attached parts of the flow and the shear layer above the axisymmetric separation bubble near the cylinder-cone junction. Two nosetip radii (one nominally sharp and one blunt with a 5 mm radius) were tested. For the sharp nosetip case, there was a great deal of agreement between the measurements of both second-mode and shear-layer instabilities across the two conventional facilities. However, the measured spectra for the blunt nosetip case showed more significant differences between the two tunnels, potentially due to an alternate dominant instability mechanism coupled with the variations in the freestream noise spectra. The quiet facility resulted in a flow that remained laminar to much higher freestream unit Reynolds numbers, as well as in instability measurements that had more distinct spectral peaks for the sharp tip case and broadband rises for the blunt one. The instability mechanisms at play in the sharp quiet case were found to be the same as those in the conventional facilities.

Boundary Layer Transition↗

NASA NTRSDate not supplied

Separation and Transition on a Cone-Cylinder-Flare: Computational Investigations

Base flow computation and stability analysis were conducted for hypersonic flow over a cone-cylinder-flare (CCF) geometry for conditions that correspond to the experimental runs carried out in three wind tunnels. Owing to the presence of an attached boundary layer, a separation bubble induced by a shock-boundary layer interaction, and a reattachment region, the chosen flow configuration is physically rich. The complexity of this flowfield encompasses a combination of convective instabilities developing on the cone, global instabilities in the separation bubble, and shear-layer modes and streaks in the reattachment region. Thus, the selected CCF configuration provides the opportunity for a comprehensive comparison of the currently available methodologies for analyzing boundary layer instabilities. Various tools are used for the analysis, including global stability codes as well as convective instability analyses based on a local theory, a weakly non-parallel analysis, and tools that are applicable to strongly non-parallel flows. The paper presents a comparison of the convective instability characteristics based on different methodologies, such as linear stability theory (LST), the harmonic form of linearized Navier-Stokes equations (HLNSE), and resolvent analysis. The CCF configuration provided an effective framework for conducting a detailed cross-validation of this type, which had not yet been addressed in existing literature. This document is accompanied by a companion paper that is focused on the experimental aspects of the CCF configuration. Both papers are being presented in a dedicated session that highlights the research activities of the NATO STO Research Task Group AVT-346.

Boundary Layer Transition↗