Slender Cone Research Articles

Relaminarization effects in hypersonic flow on a three-dimensional expansion–compression geometry

This experimental work explores the flow field around a three-dimensional expansion–compression geometry on a slender cone at Mach 8 using high-frequency pressure sensors, high-frame-rate schlieren, temperature-sensitive paint, shear-stress measurements and oil-flow visualizations. The $7^\circ$ cone geometry has a hyperbolic slice which acts as an expansion corner and suppresses the disturbances present in the upstream boundary layer. Downstream of the cone-slice corner, high-frequency boundary-layer disturbances attenuate in all cases. Under laminar conditions, second-mode instabilities from the cone diminish and lower-frequency second-mode waves develop on the slice at a frequency commensurate with the increased boundary layer thickness. For fully turbulent cases, the boundary layer over the slice shows evidence of a two-layered nature with a turbulent outer region and a near-wall region with strong attenuation of high-frequency disturbances and reappearance of lower-frequency instability waves. When a downstream compression ramp is added to the slice, the expanded boundary layer shows enhanced susceptibility to separation such that separation is observed at a $10^{\circ }$ deflection, which is smaller than expected for turbulent conditions. For a $30^{\circ }$ ramp, boundary-layer separation occurs further upstream where the heat flux contours show a decrease in heating that is characteristic of a transitional separation. These results demonstrate the effect of relaminarization caused by an upstream expansion on a subsequent shock-wave/boundary-layer interaction.

Direct numerical simulation of slender cones with variable nose bluntness based on graphics processing unit computation

Direct numerical simulation with up to 10×109 scale grid points based on graphics processing unit computation is carried out to investigate the bluntness effect on the hypersonic boundary-layer transition over a slender cone with zero angle of attack at Mach 6. Four cases with the nose radii of 1, 10, 20, and 40 mm are conducted, and the corresponding Reynolds number based on the nose radius varies from 1.0×104 to 4.0×105. Random disturbances with a broad spectrum of frequencies and a wide range of azimuthal wavenumbers were applied to the wall to simulate disturbances caused by wall roughness. The numerical results show that as the nose tip radius increases, the transition position gradually moves downstream with increased transition region. For the case with a nose radius of 1 mm, the flow transition and entropy swallowing occur almost simultaneously, while for other cases, the transition takes place earlier than the entropy swallowing. In consequence, the disturbance amplitude upstream of the transition in the 1 mm case is much larger than that of other cases. To further study the mechanism of the transition, the frequency spectrum analysis is carried out. It is found that all cases exhibit two characteristic frequencies within the transition region, i.e., the high frequency and extremely low frequency. Owing to the influence of the entropy layer, the characteristic high frequency of the 1 mm case is significantly higher than that of other cases. With the increase in the nose radius, the characteristic frequency of the high frequency decreases gradually.

Rotating disks and cones a centennial of von Kármán’s 1921 paper

It is now more than 100 years since the work of von Kármán (1921) on the boundary-layer flow over a rotating disk was published in the first volume of Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM, Vol. 1(4), pp 233-252). Recently, there has been a large amount of work undertaken addressing the instability and transition of the boundary-layer flows over rotating disks and cones using theoretical, numerical and experimental techniques. Here we will discuss some different methods to analyze experimental data that can give insight into the instability and transition to turbulence of boundary-layer flows over rotating slender and broad cones (including the disk). At first, we discuss the pdf-method (probability density function) that allows a simple way to determine regions of instability growth, transition and fully developed turbulence. Secondly, we look at various ways to use spectral information to investigate the boundary layers giving a deeper understanding of the transition process. Finally, a method to determine the most probable flow structure leading up to fully developed turbulence is discussed. We envisage that some of these methods can be useful in analyzing instability and transition also in other flow cases.

Hypersonic Boundary-Layer Disturbances on a Cooled, Slender Cone at Mach 6

This paper presents an experimental study of the effect of wall cooling on the boundary-layer structures of a sharp-nosed, 5° half-angle cone in Mach 6 flow. An experimental methodology was developed that allowed quantitative measurements of second-mode disturbance growth over a range of wall-temperature ratios from without modifying the freestream disturbance environment. The cooling system comprised probe cooling, liquid nitrogen injection, and thermal insulation. The model temperature was monitored before each run, with thermocouples mounted at the base and nosetip piece agreeing within 3.3 K. Calibrated schlieren provided global and time-resolved measurements of the boundary-layer features at a freestream unit Reynolds number of . An increase in wall-cooling level was associated with a shrinking of the boundary layer and a lowering of wavepacket structure angle at the wall. Despite some outlying results, an overall trend of increasing disturbance frequency with decreasing surface temperature was observed; additionally, cooling increased the spectral amplitude and growth rate of second-mode disturbances, pushing the point of saturation upstream.

Experimental study of bluntness effects on hypersonic boundary-layer transition over a slender cone using surface mounted pressure sensors

In this work, we studied the bluntness effect on the hypersonic boundary-layer transition over a slender cone at Mach 6 with interchangeable tips in a noisy Ludwieg tube tunnel before the so-called “transition reversal” phenomenon occurs. The evolution of instability waves is characterized using surface flush-mounted pressure sensors deployed along the streamwise direction within unit Reynolds number from 4E+ 6/m ≤ Reunit ≤ 10E+ 6/m, and the bluntness of the cone nose ranges from 0.1 mm to 5 mm. Power spectral density (PSD) of pressure fluctuation indicates that small nose bluntness (ReR ≤ 2000) has little influence on the evolution of instability waves along the hypersonic boundary-layer, whereas with a moderate nose size (2000 ≤ ReR ≤ 5000), the hypersonic boundary layer transition is delayed monotonically as the nose radius increases before the boundary-layer turns into fully laminar without instability waves. The delaying effect can be attributed to the increased entropy-layer swallowing distance with a large tip radius. Instability wave characterization reveals that the second mode instability wave plays a dominant role before the transition reversal happens. The quadratic phase locking of second mode instabilities can be identified by bispectral analysis, and it attenuates as the nose tip radius increases.

Assimilation of wall-pressure measurements in high-speed flow over a cone

A nonlinear ensemble-variational data assimilation is performed in order to estimate the unknown flow field over a slender cone at Mach 6, from isolated wall-pressure measurements. The cost functional accounts for discrepancies in wall-pressure spectra and total intensity between the experiment and the prediction using direct numerical simulations, as well as our relative confidence in the measurements and the estimated state. We demonstrate the robustness of the predicted flow by direct propagation of posterior statistics. The approach provides a unique first look at the flow beyond the sensor data, and rigorously accounts for the role of nonlinearity, unlike previous efforts that adopted ad hoc inflow syntheses. Away from the wall, two- and three-dimensional assimilated states both show rope-like structures, qualitatively similar to independent schlieren visualizations. Despite this resemblance, and even though the planar second modes are the most unstable upstream, three-dimensional waves must be included in the assimilation in order to accurately reproduce the wall-pressure measurements recorded in the AFRL Ludwieg Tube facility. The results highlight the importance of three-dimensionality of the field and of the base-state distortion on the instability waves in this experiment, and motivate future measurements that probe the three-dimensional nature of the flow field.

A symmetry-based length model for characterizing the hypersonic boundary layer transition on a slender cone at moderate incidence

The hypersonic boundary layer (HBL) transition on a slender cone at moderate incidence is studied via a symmetry-based length model: the SED-SL model. The SED-SL specifies an analytic stress length function (which defines the eddy viscosity) describing a physically sound two-dimensional multi-regime structure of transitional boundary layer. Previous studies showed accurate predictions, especially on the drag coefficient, by the SED-SL for airfoil flows at different subsonic Mach numbers, Reynolds numbers and angles of attack. Here, the SED-SL is extended to compute the hypersonic heat transfer on a 7 ∘ half-angle straight cone at Mach numbers 6 and 7 and angles of attack from 0 ∘ to 6 ∘. It is shown that a proper setting of the multi-regime structure with three parameters (i.e. a transition center, an after-transition near-wall eddy length, and a transition width quantifying transition overshoot) yields an accurate description of the surface heat fluxes measured in wind tunnels. Uniformly good agreements between simulations and measurements are obtained from windward to leeward side of the cone, implying the validity of the multi-regime description of the transition independent of instability mechanisms. It is concluded that a unified description for the HBL transition of cone is found, and might offer a basis for developing a new transition model that is simultaneously of computational simplicity, sound physics and greater accuracy.

Hypersonic Turbulent Flow Reynolds-Averaged Navier–Stokes Simulations with Roughness and Blowing Effects

Thermal protection systems experience severe thermal load during atmospheric reentry of hypersonic vehicles. Inherent to the ablation process, roughness and blowing effects may appear, affecting the performance of the heat shield. The modeling and the simulation of these effects in the hypersonic regime are challenging and rarely compared to experimental data. In this paper, Reynolds-averaged Navier–Stokes simulations of hypersonic turbulent boundary layers with roughness and blowing wall conditions are performed on Holden’s experimental configurations (“Studies of Surface Roughness and Blowing Effects on Hypersonic Turbulent Boundary Layers over Slender Cones,” 27th Aerospace Sciences Meeting, AIAA Paper 1989-0458, 1989). Using the shear stress transport model. Four experimental configurations, characterized by different levels of turbulence compressibility, are considered. A detailed discussion is proposed about the behavior of equivalent sand grain corrections and blowing corrections in combination with turbulence compressibility corrections. The predictions of skin-friction coefficients and Stanton numbers are in good agreement with Holden’s experimental data. These results show that the combination of the Zeman compressibility correction and roughness/blowing wall corrections is promising for the simulation of hypersonic boundary layers over rough walls with blowing.

Effects of AoA on tangential three-dimensional film cooling of a slender cone

A supersonic annular supersonic nozzle was used to protect a slender cone from aerodynamic heating at angle of attack (AoA). Experiments were carried out in a Mach 6 wind tunnel. Temperature-sensitive paint (TSP) was used to measure surface temperature change of the cone body; nanoparticle-based planar laser scattering (NPLS) was used to visualize the flow field; oil flow was utilized to monitor surface flow of the cone. Results showed that cooling film can obviously decrease surface heating load in present cases; the coolant layer was able cover a relatively long distance along the model's surface than most other cooling solutions. AoA caused obvious transverse flow on the surface, and it produced much difference heating load between different sides of the cone body. Although the cooling film can mitigate the transverse flow, the windward side was still the hardest part to cool.

Characterization of instability mechanisms on sharp and blunt slender cones at Mach 6

Experiments are performed to investigate the effect of nose-tip bluntness on the instability mechanisms leading to boundary-layer transition on a $7^{\circ }$ half-angle cone in a Mach-6 free stream. The development of disturbances is characterized using a combination of high-speed calibrated schlieren images and pressure measurements, and the data are compared with results computed using the parabolized stability equations. The approximately 414 mm long cone model is equipped with an interchangeable nose tip ranging from sharp to 5.08 mm in radius. For nose tips with a radius $R_{N}<2.54\ {\rm mm}$ , second-mode instability waves are the dominant mechanism leading to transition. Time-averaged frequency spectra computed from the calibrated schlieren visualizations and pressure measurements are used to compute the second-mode most-amplified frequencies and integrated amplification rates ( $N$ factors). Good agreement is observed between the measurements and computations in the linear-growth regime for the sharp-nose configuration at each free-stream condition. Additionally, a bispectral analysis identifies quadratic phase locking of frequency content responsible for the growth of higher harmonics. For nose tips of $R_{N}\geqslant 2.54\ {\rm mm}$ , the schlieren visualization region is upstream of the entropy-layer swallowing length, and second-mode waves are no longer visible within the boundary layer; instead, elongated, steeply inclined features believed to be associated with non-modal instability mechanisms develop between the entropy-layer and boundary-layer edges. Simultaneously acquired surface pressure measurements reveal high-frequency pressure oscillations similar to second-mode instability waves associated with the trailing edge of these non-modal features.

Differential Regulation of Neurite Outgrowth and Growth Cone Morphology by 3D Fibronectin and Fibronectin-Collagen Extracellular Matrices.

The extracellular matrix (ECM) plays a critical role in development, homeostasis, and regeneration of tissue structures and functions. Cell interactions with the ECM are dynamic and cells respond to ECM remodeling by changes in morphology and motility. During nerve regeneration, the ECM facilitates neurite outgrowth and guides axons with target specificity. Decellularized ECMs retain structural, biochemical, and biomechanical cues of native ECM and have the potential to replace damaged matrix to support cell activities during tissue repair. To determine the ECM components that contribute to nerve regeneration, we analyzed neuron-ECM interactions on two types of decellularized ECM. One matrix was composed primarily of fibronectin (FN) fibrils, and the other FN-rich ECM also contained significant numbers of type I collagen (COL I) fibrils. Using primary neurons dissociated from superior cervical ganglion (SCG) explants, we found that neurites were extended on both matrices without a significant difference in average neurite length after 24h. The most distinctive features of neurites on the FN matrix were numerous short actin-filled protrusions and longer branches extending from neurite shafts. Very few protrusions and branches were detected on FN-COL matrix. Growth cone morphologies also differed with mostly filopodial growth cones on FN matrix whereas on FN-COL matrix, equivalent numbers of filopodial and slender growth cones were formed. Our work provides new information about how changes in major components of the ECM during tissue repair modulate neuron and growth cone morphologies and helps to define the contributions of neuron-ECM interactions to nerve development and regeneration.

In-place operculum demonstrates that the Middle Cambrian Protowenella is a hyolith and not a mollusc

Protowenella is an early–middle Cambrian, isostrophically coiled, calcareous microfossil originally described from the middle Cambrian (Miaolingian) of Australia; it has been referred previously to the molluscan classes Monoplacophora, Helcionelloida or Gastropoda. A unique specimen from the Henson Gletscher Formation (Miaolingian Series, Wuliuan Stage) of North Greenland has a bilaterally symmetrical operculum preserved in place within the shell aperture. Paired cardinal processes and clavicles on the inner side of the operculum indicate that Protowenella was a hyolith morphologically close to the orthothecid Conotheca. Protowenella is transferred from Mollusca to Hyolitha, Order Orthothecida, Family Protowenellidae nov., representing a novel morphological departure from the generally slender cones of other hyoliths. John S. Peel [ john.peel@pal.uu.se ], Department of Earth Sciences (Palaeobiology), Uppsala University, Villavägen 16, SE-75236, Uppsala, Sweden.

On the stability of boundary-layer flow over a rotating cone in an enforced axial free stream

Studies into the boundary-layer stability of rotating cones in an axial free stream have considered both cases of broad-angled cones and slender-angled ones. This distinction is made due to the findings that the dominant instability in the quiescent-fluid case results from different physical mechanisms for broad and slender cones. These investigations made use of an Orr-Sommerfeld-type analysis derived from the assumption of a small perturbation to a similarity-type solution for the mean fluid flow around the cone. In this work, we investigate the efficacy of a combination of sophisticated numerical techniques to find the basic flow, using ideas both from automatic differentiation and spectral collocation methods, to maximise the accuracy of the obtained solution. We inspect the solutions obtained for the Orr-Sommerfeld system in this setting and compare them to the results from previous studies.

Supersonic mode in a low-enthalpy hypersonic flow over a cone and wave packet interference

A computational fluid dynamics study is conducted in which acoustic-like waves are observed emanating from the boundary layer of a Mach 8 slender blunt cone with a relatively low freestream enthalpy and a warm wall. The acoustic-like wave emissions are qualitatively similar to those attributed to the supersonic mode. However, the supersonic mode responsible for such emissions is often found in high-enthalpy flows with highly cooled walls, making its appearance here unexpected. Linear stability analysis on the steady-state solution reveals an unstable mode S (Mack's second mode) with a subsonic phase velocity and a stable mode F whose mode F- branch takes on a supersonic phase velocity. It is thought that the stable supersonic mode F- is responsible for the acoustic-like wave emissions. Unsteady simulations are carried out using blowing-suction actuators at two different surface locations. The analysis of the temporal data and spectral data using Fourier decomposition reveals constructive/destructive interference occurring between a primary wave packet and a satellite wave packet in the vicinity of the acoustic-like wave emissions. The constructive/destructive interference between the wave packets also appears to have a damping effect on individual frequency growth in both unsteady simulations. Based on this study's results and analysis, it is concluded that a supersonic discrete mode is not limited to high-enthalpy, cold wall flows and that it does appear in low-enthalpy, warm-wall flows; however, the mode is stable.

(2804) Proposal to reject the name Ephedra major (Ephedraceae)

(2804) Proposal to reject the name <i>Ephedra major</i> (<i>Ephedraceae</i>)

Instability and transition in the boundary layer driven by a rotating slender cone

Abstract

Global stability analysis of axisymmetric boundary layer on a slender circular cone with the streamwise adverse pressure gradient

This paper presents a global stability analysis of the boundary layer developed on a slender circular cone. The base flow direction is towards the apex of a cone, and the pressure gradient is positive (adverse) in the flow direction. The decelerating base flow is non-parallel and non-similar. The increased semi-cone angle increases the adverse pressure gradient in the flow direction. For a given semi-cone angle, transverse curvature increases in the flow direction. However, increased semi-cone angle reduces transverse curvature at any streamwise location. The Reynolds number of the flow is defined based on the displacement thickness at the computational domain’s inlet. The radius of the cone reduces in the flow direction, which results in the increased transverse curvature. The governing stability equations are derived in the spherical coordinates and discretized using the Chebyshev Spectral collocation method. The discretized equations, along with homogeneous boundary conditions, form a general eigenvalue problem, and it is solved using Arnoldi’s iterative algorithm. The global temporal modes have been computed for small semi-cone angles α=2°, 4°, and 6°, azimuthal wave-numbers N=0, 1, 2, and 3 and Re=283, 416, and 610. Thus, the state of base flow is laminar at the inlet (line pq) of the domain pqrs. All the global modes computed within the range of parameters are found temporally stable. Further, the global modes are found less stable at higher semi-cone angles (α) due to the streamwise adverse pressure gradient. The effect of transverse curvature has been found significant at higher semi-cone angles. For a given Re and α, the global modes are found least stable for the helical mode N=1 and most stable for N=3. The eigenmodes’ two-dimensional spatial structure suggests that flow is spatially unstable as the disturbances grow in the streamwise direction.

Boundary layer instability over a rotating slender cone under non-axial inflow

Abstract

The convective instability of the boundary-layer flow over a rotating cone in and out of a uniform magnetic field

We present convective instability analyses of the boundary-layer flows originated over cones (with half-angle ψ≤90∘) rotating in an otherwise still conducting fluid. A uniform magnetic field (with magnetic strength parameter, m≥0) is acting normally on the surface of each cone. In the non-magnetic case of cones, comparison of present results with existing experimental and theoretical studies lead *to propose that onset of instabilities may be attributed to crossflow (type I) modes and streamline curvature (type II) modes for broad cones (with ψ≥40∘) and more slender cones (with ψ≤15∘), respectively. For slender cones with half-angle ψ in the vicinity of 25° the presented results validate the hypothesis of centrifugal (type III) modes ( discovered by Garrett et al. (2014)). In the magnetic case, increasing magnetic strength m∈(0,11] considerably delays the onset of instabilities (due to both type I and type II modes) over each rotating cone with fixed ψ. The stabilising influence of magnetism is in agreement with the meagrely available theoretical studies for magnetic rotating disk case ψ=90∘. In addition, our results lead to suggest that streamline curvature mode over each cone with fixed half-angle ψ become sensitive with increasing m. A minimum m0∈[0,11] exists for each fixed half-angle ψ0≤90∘ such that whenever m≥m0 the onset of instabilities (in the sense of minimum critical Reynolds numbers) over every cone with half-angle (ψ≤ψ0) are commenced by type II mode instead of type I mode whilst the aforementioned conjecture of stabilising effect of magnetism is not violated in the considered range of parameters. Under non-stationary vortices assumption with magnetism, we show that crossflow modes travelling at around 75% of the cone surface are likely to be selected in applications where smooth and frictionless surfaces are used. This finding is in complete agreement with the non-magnetic case of rotating cone in existing studies.

An improved local correlation-based intermittency transition model appropriate for high-speed flow heat transfer

An improved local correlation-based intermittency transition model is developed for high-speed flow heat transfer in this paper. Based on the intermittency transition model, two improvements have been proposed. One is introducing a new correlation of the momentum thickness Reynolds number for high-speed boundary layer into the transition onset function. In this new correlation, the free stream Mach number and the free stream Reynolds number are used to reflect the compressible effects. The other improvement is the modification of the intermittency factor transport equation to include physical information regarding the transition processes. Several test cases containing supersonic and hypersonic flat plates, a slender cone at different Reynolds numbers, the X-51A forebody, and the Hypersonic Inflatable Aerodynamic Decelerator are conducted to assess the applicability of the improved intermittency transition model. The numerical results show the ability of the improved model to describe the high-speed boundary layer transition processes. However, further research is needed to reproduce the overshoot phenomena and verify the capacity of the improved model on complex cases.