Effect of local wall temperature on hypersonic boundary layer stability and transition

Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is complicated when the wall temperature distribution is nonuniform, and researchers have experimentally found that local wall cooling may delay the onset of transition. We attempt to clarify the physical mechanisms whereby the local wall temperature affects the transition and the stability of a hypersonic boundary layer. A numerical investigation of the disturbance evolution in a Mach-6 sharp cone boundary layer with local wall heating or cooling is conducted. Direct numerical simulation(DNS) is performed for the single-frequency and broadband disturbance evolution caused by random forcing. We vary the local wall temperature and the location of heating/cooling, and then use the eNmethod to estimate the transition onset. Our results show that local wall cooling amplifies high-frequency unstable waves while stabilizing low-frequency unstable waves, with local heating amplifying all unstable waves locally. The disturbance amplitude and second-mode peak frequency obtained by DNS agree well with the previous experimental results. Local cooling/heating has a dual effect on the stability of the hypersonic boundary layer. For local cooling, while it effectively inhibits the growth of the low-frequency unstable waves that dominate the transition downstream, it also further destabilizes the downstream flow. In addition, while upstream cooling can delay the transition, excessive cooling may promote it;local heating always slightly promotes the transition.Finally, recommendations are given for practical engineering applications based on the present results.

The effects of variable specific heat on the stability of hypersonic boundary layer on a flat plate

The gas temperature within hypersonic boundary layer flow is so high that the specific heat of gas is no longer a constant but relates to temperature. How variable specific heat influences on boundary layer flow stability is worth researching. The effect of the variable specific heat on the stability of hypersonic boundary layer flows is studied and compared with the case of constant specific heat based on the linear stability theory. It is found that the variable specific heat indeed has some effects on the neutral curves of both the first-mode and the second-mode waves and on the maximum rate of growth also. Therefore, the relationship between specific heat and temperature should be considered in the study of the stability of the boundary layer.

Receptivity of hypersonic boundary layer due to fast-slow acoustics interaction

The objective of receptivity is to investigate the mechanisms by which external disturbances generate unsta- ble waves. In hypersonic boundary layers, a new receptivity process is revealed, which is that fast and slow acoustics through nonlinear interaction can excite the second mode near the lower-branch of the second mode. They can generate a sum-frequency disturbance though nonlinear interaction, which can excite the second mode. This receptivity process is generated by the nonlinear interaction and the nonparal- lel nature of the boundary layer. The receptivity coefficient is sensitive to the wavenumber difference between the sumfrequency disturbance and the lower-branch second mode. When the wavenumber difference is zero, the receptivity coefficient is maximum. The receptivity coefficient decreases with the increase of the wavenumber difference. It is also found that the evolution of the sum-frequency disturbance grows linearly in the beginning. It indicates that the forced term generated by the sum-frequency disturbance resonates with the second mode.

Improved nonlinear parabolized stability equations approach for hypersonic boundary layers

The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPSEs will occur when disturbances imposed at the inlet no longer play a leading role or when the nonlinear effect becomes very strong.Two major improvements are proposed here to deal with the divergence of the NPSEs.First,all disturbances are divided into two types:dominant waves and non-dominant waves.Disturbances imposed at the inlet or playing a leading role are defined as dominant waves,with all others being defined as non-dominant waves.Second,the streamwise wavenumbers of the non-dominant waves are obtained using the phase-locked method,while those of the dominant waves are obtained using an iterative method.Two reference wavenumbers are introduced in the phase-locked method,and methods for calculating them for different numbers of dominant waves are discussed.Direct numerical simulation(DNS)is performed to verify and validate the predictions of the improved NPSEs in a hypersonic boundary layer on an isothermal swept blunt plate.The results from the improved NPSEs approach are in good agreement with those of DNS,whereas the traditional NPSEs approach is subject to divergence,indicating that the improved NPSEs approach exhibits greater robustness.

Second mode unstable disturbance measurement of hypersonic boundary layer on cone by wavelet transform

Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel. Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface in the streamwise direction to investigate the development of the unstable disturbance. Wavelet transform is employed as a mathematical tool to obtain the multi-scale characteristics of fluctuating surfacethermal-flux both in the temporal and spectrum space. The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbance waveform from the fluctuating surface-thermal-flux signals.The generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique. The development of the unstable disturbance in the streamwise direction is assessed both in the temporal and spectrum space. Our study shows that the local unstable disturbance detection method based on wavelet transformation offers an alternative powerful tool in studying the hypersonic unstable mode of laminar-turbulent transition. It is demonstrated that, at hypersonic speeds, the dominant flow instability is the second mode, which governs the course of laminar-turbulent transition of sharp cone boundary layer.

Experimental study on surface arc plasma actuation-based hypersonic boundary layer transition flow control

Effective control of hypersonic transition is essential.In order to avoid affecting the structural proflle of the aircraft,as well as reducing power consumption and electromagnetic interference,a low-frequency surface arc plasma disturbance experiment to promote hypersonic transition was carried out in theΦ0.25 m double-throat Ludwieg tube wind tunnel at Huazhong University of Science and Technology.Contacting printed circuit board sensors and non-contact focused laser differential interferometry testing technology were used in combination.Experimental results showed that the low-frequency surface arc plasma actuation had obvious stimulation effects on the second-mode unstable wave and could promote boundary layer transition by changing the spectral characteristics of the second-mode unstable wave.At the same time,the plasma actuation could promote energy exchange between the second-mode unstable wave and other unstable waves.Finally,the corresponding control mechanism is discussed.

Response of a hypersonic blunt cone boundary layer to slow acoustic waves with assessment of various routes of receptivity

The hypersonic boundary-layer receptivity to slow acoustic waves is investigated for the Mach 6 flow over a 5-degree half-angle blunt cone with the nose radius of 5.08 mm. The plane acoustic wave interacts with the bow shock, and generates all types of disturbances behind the shock, which may take various routes to generate the boundarylayer unstable mode. In this paper, two routes of receptivity are investigated in detail.One is through the disturbance in the entropy layer. The other is through the slow acoustic wave transmitted downstream the bow shock, which can excite the boundary-layer mode due to the synchronization mechanism. The results show that, for a low frequency slow acoustic wave, the latter route plays a leading role. The entropy-layer instability wave is able to excite the first mode near the neutral point, but its receptivity efficiency is much lower.

Research Progress of hypersonic boundary layer transition control experiments

Hypersonic boundary layer transition is a hot yet challenging problem restricting the development and breakthrough of hypersonic aerodynamics.In recent years,despite great progress made by wind tunnel experiment,transition mechanism and transition prediction,only partial knowledge has been gained so far.In this paper,firstly,the specific scenarios of hypersonic boundary layer transition control are clarified.Secondly,the experimental research progress and mechanism of passive control and active control methods under different hypersonic transition control demands are summarized,with their advantages and disadvantages being analyzed separately.Plasma actuation is easy to produce controllable broadband aerodynamic actuation,which has potential in the field of boundary layer transition control.Hence,the following part of the paper focuses on plasma flow control.The feasibility of plasma actuation to control the hypersonic boundary layer transition is demonstrated and the research ideas are presented.Finally,hypersonic boundary layer transition control methods are summarized and the direction of future research is prospected.

Design and transition characteristics of a standard model for hypersonic boundary layer transition research

To understand fundamental problems in hypersonic laminar-turbulent boundary layer transition for three-dimensional complex vehicles,a new standard model with typical lifting-body features has been proposed,named as hypersonic transition research vehicle(HyTRV).The configuration of HyTRV is fully analytical,and details of the design process are discussed in this study.The transition characteristics for HyTRV are investigated using three combined methods,i.e.,theoretical analyses,numerical simulations,and wind tunnel experiments.Results show that the fully analytic parameterization design of HyTRV can satisfy the model simplification requirements from both numerical simulations and wind tunnel experiments.Meanwhile,the flow field of HyTRV reveals typical transition mechanisms in six relatively separated regions,including the streamwise vortex instability,crossflow instability,secondary instability,and attachment-line instability.Therefore,the proposed HyTRV model is valuable for fundamental researches in hypersonic boundary layer transition.

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 shock wave and turbulent boundary layer interaction in a sharp cone/flare model

A direct numerical simulation of hypersonic Shock wave and Turbulent Boundary Layer Interaction(STBLI)at Mach 6.0 on a sharp 7.half-angle circular cone/flare configuration at zero angle of attack is performed.The flare angle is 34.and the momentum thickness Reynolds number based on the incoming turbulent boundary layer on the sharp circular cone is Re θ=2506.It is found that the mean flow is separated and the separation bubble occurring near the corner exhibits unsteadiness.The Reynolds analogy factor changes dramatically across the interaction,and varies between 1.06 and 1.27 in the downstream region,while the QP85 scaling factor has a nearly constant value of 0.5 across the interaction.The evolution of the reattached boundary layer is characterized in terms of the mean profiles,the Reynolds stress components,the anisotropy tensor and the turbulence kinetic energy.It is argued that the recovery is incomplete and the near-wall asymptotic behavior does not occur for the hypersonic interaction.In addition,mean skin friction decomposition in an axisymmetric turbulent boundary layer is carried out for the first time.Downstream of the interaction,the contributions of transverse curvature and body divergence are negligible,whereas the positive contribution associated with the turbulence kinetic energy production and the negative spatial-growth contribution are dominant.Based on scale decomposition,the positive contribution is further divided into terms with different spanwise length scales.The negative contribution is analyzed by comparing the convective term,the streamwise-heterogeneity term and the pressure gradient term.

A decomposition formula for the wall heat flux of a compressible boundary layer

Understanding the generation mechanism of the heat flux is essential for the design of hypersonic vehicles.We proposed a novel formula to decompose the heat flux coefficient into the contributions of different terms by integrating the conservative equation of the total energy.The reliability of the formula is well demonstrated by the direct numerical simulation results of a hypersonic transitional boundary layer.Through this formula,the exact process of the energy transport in the boundary layer can be explained and the dominant contributors to the heat flux can be explored,which are beneficial for the prediction of the heat and design of the thermal protection devices.

Accurately predicting hypersonic transitional flow on cone via a symmetry approach

A new algebraic transition model is proposed based on a Structural Ensemble Dynamics(SED)theory of wall turbulence,for accurately predicting the hypersonic flow heat transfer on cone.The model defines the eddy viscosity in terms of a two-dimensional multi-regime distribution of a Stress Length(SL)function,and hence is named as SED-SL.This paper presents clear evidence of precise predictions of transition onset location and peak heat flux of a wide range of hypersonic Transitional Boundary Layers(TrBL)around straight cone at zero incidence,to an unprecedented accuracy as validated by over 70 measurements for varying five crucial influential factors(Mach number,temperature ratio,cone half angle,nose Reynolds number and noise level).The results demonstrate the universality of the postulated multi-regime similarity structure,in characterizing not only the spatial non-uniform distribution of the eddy viscosity in hypersonic TrBL on cone,but also the dependence of the transition onset location on the five influential factors.The latter yields a novel correlation formula for transition center Reynolds number which takes similar functional form as the SL function within the symmetry approach.It is concluded that the SED-SL model simulates TrBL around cone with uniformly high accuracy,and then points out to an optimistic alternative way to construct hypersonic transition model.

On the mechanism by which nose bluntness suppresses second-mode instability

A physical mechanism by which nose bluntness suppresses second-mode instability is proposed.Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm,5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well.Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.

Effects of sweep angles on turbulent separation behaviors induced by blunt fin

An experimental study was conducted on turbulent separation behaviors induced by blunt fins with different sweep angles at Mach number 6.0.The Nano-particle based Planar Laser Scattering technique(NPLS)was applied to visualize the flowfield,complemented by pressure tests.Sweep angles of the fins were 10°,20°,...,60°,with the same leading edge diameter of 10 mm.Fine structures of the interference flowfield induced by blunt fins have been obtained,including the shock systems and vortexes.It was found that the features and shapes of the detached shock depended on sweep angle.When sweep angle<50°,the detached shock appeared as the form of trailing shock,and the supersonic jet with its reflection could be observed.The detached shock would be curved for the 50°and 60°fins and became a transmitted shock.The Scale-Invariant Feature Transform(SIFT)was successfully applied to obtain the velocity field from NPLS images,and the extent of the separated region was found to decrease with increasing sweep angle.No separation appeared as sweep angle>30°.Two peak values were detected on the centerline pressure distribution.The first peak did not rely on sweep angle,while the second peak value decreased with increasing sweep angle.