Mechanism of transition in a hypersonic sharp cone boundary layer with zero angle of attack

Firstly, the steady laminar flow field of a hypersonic sharp cone boundary layer with zero angle of attack was computed.Then,two groups of finite amplitude T-S wave disturbances were introduced at the entrance of the computational field,and the spatial mode transition process was studied by direct numerical simulation (DNS) method. The mechanism of the transition process was analyzed.It was found that the change of the stability characteristics of the mean flow profile was the key issue.Furthermore,the characteristics of evolution for the disturbances of different modes in the hypersonic sharp cone boundary layer were discussed.     

Stability analysis and transition prediction of hypersonic boundary layer over a blunt cone with small nose bluntness at zero angle of attack

Stability and transition prediction of hypersonic boundary layer on a blunt cone with small nose bluntness at zero angle of attack was investigated. The nose radius of the cone is 0.5 mm; the cone half-angle is 5°, and the Mach number of the oncoming flow is 6. The base flow of the blunt cone was obtained by direct numerical simulation. The linear stability theory was applied for the analysis of the first mode and the second mode unstable waves under both isothermal and adiabatic wall condition, and eN method was used for the prediction of transition location. The N factor was tentatively taken as 10, as no experimentally confirmed value was available. It is found that the wall temperature condition has a great effect on the transition location. For adiabatic wall, transition would take place more rearward than those for isothermal wall. And despite that for high Mach number flows, the maximum amplification rate of the second mode wave is far bigger than the maximum amplification rate of the first mode wave, the transition location of the boundary layer with adiabatic wall is controlled by the growth of first mode unstable waves. The methods employed in this paper are expected to be also applicable to the transition prediction for the three dimensional boundary layers on cones with angle of attack.     

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 boundary-layer 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.     

Laminar boundary layer separation at a fin-body junction in a hypersonic flow

Planar laser-induced fluorescence (PLIF) imaging was performed to visualize the fin bow shock, separation shock, viscous shear layer and recirculation region of the flowfield at the junction of a blunt fin and a flat plate. Making use of the temperature dependence of the PLIF technique, images were made sensitive to temperature to provide qualitative information on the flowfield. The PLIF technique was also used as the basis for a flow-tagging technique, making it possible to measure a velocity component and to demonstrate the reverse flow of the separated region. Flow visualisation of the plane of symmetry allowed determination of the point of boundary layer separation, the angle of the separation shock and the bow shock standoff distance. These parameters were compared with predictions made by computational fluid dynamic simulations of the flowfield. Good agreement between theory and experiment was achieved. Comparisons between theoretical and experimental velocity measurements showed good agreement. Received 17 October 2000 / Accepted 13 November 2000     

The unstable modes of natural convection boundary layer

The instability of natural convection boundary layer around a vertical heated flat plate is analyzed theoretically in this paper. The results illustrate that the “loop” in the neutral curve is not a real loop but a twist of the curve in the frequency-wave number-Grashof number space, and there is only one unstable mode at small Prandtl numbers. Specially, when the Prandtl number is large enough two unstable modes will be found in the “loop” region. Along the amplyfying surface intersection the two unstable modes have the same Grashof number, wave number and frequency but different amplifying rates. Their instability characteristics are analyzed and the criterion for determining the existence of the multi-unstable modes is also discussed.     

Effect of disturbances at inlet on hypersonic boundary layer transition on a blunt cone at small angle of attack

To investigate the effect of different disturbances in the upstream, we present numerical simulation of transition for a hypersonic boundary layer on a 5-degree half-angle blunt cone in a freestream with Mach number 6 at 1-degree angle of attack. Evolution of small disturbances is simulated to compare with the linear stability theory （LST）, indicating that LST can provide a good prediction on the growth rate of the disturbance. The effect of different disturbances on transition is investigated. Transition onset distributions along the azimuthal direction are obtained with two groups of disturbances of different frequencies. It shows that transition onset is relevant to frequencies and amplitudes of the disturbances at the inlet, and is decided by the amplitudes of most unstable waves at the inlet. According to the characteristics of environmental disturbances in most wind tunnels, we explain why transition occurs leeside-forward and windside-aft over a circular cone at an angle of attack. Moreover, the indentation phenomenon in the transition curve on the leeward is also revealed.     

Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer

A numerical algorithm and code are developed and applied to direct numerical simulation (DNS) of unsteady two-dimensional flow fields relevant to stability of the hypersonic boundary layer. An implicit second-order finite-volume technique is used for solving the compressible Navier–Stokes equations. Numerical simulation of disturbances generated by a periodic suction-blowing on a flat plate is performed at free-stream Mach number 6. For small forcing amplitudes, the second-mode growth rates predicted by DNS agree well with the growth rates resulted from the linear stability theory (LST) including nonparallel effects. This shows that numerical method allows for simulation of unstable processes despite its dissipative features. Calculations at large forcing amplitudes illustrate nonlinear dynamics of the disturbance flow field. DNS predicts a nonlinear saturation of fundamental harmonic and rapid growth of higher harmonics. These results are consistent with the experimental data of Stetson and Kimmel obtained on a sharp cone at the free-stream Mach number 8.     

Investigation of a hypersonic crossing shock wave/turbulent boundary layer interaction

A combined theoretical and experimental study is presented for the interaction between crossing shock waves generated by (10°, 10°) sharp fins and a flat plate turbulent boundary layer at Mach 8.3. The theoretical model is the full 3-D mean compressible Reynolds-averaged Navier-Stokes RANS) equations incorporating the algebraic turbulent eddy viscosity model of Baldwin and Lomax. A grid refinement study indicated that adequate resolution of the flowfield has been achieved. Computed results agree well with experiment for surface pressure and surface flow patterns and for pitot pressure and yaw angle profiles in the flowfield. The computations, however, significantly overpredict surface heat transfer. Analysis of the computed flowfield results indicates the formation of complex streamline and wave structures within the interaction region.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Experimental study of compressible boundary layer on a cone at angles of attack

Experimental study was conducted for boundarylayers on a sharp 5° half-angle cone of 400mm length at angles of attack. The model was tested in the T-326 hypersonic wind tunnel （ITAM） at freestream Mach number M = 5.95. Mean and fluctuation wall characteristics of the boundary layer are measured at 0°, 2°, 3° and 4° angles of attack for different stagnation pressures. Pulsation measurements are carried out by means of ALTP sensor. Pressure and temperature distributions along the model are obtained, and transition beginning and end locations have been found. Boundary layer stabilization with the increase of angle of attack and the decrease of stagnation pressure is observed. High frequency pulsations inherent to hypersonic boundary layer （second mode） have been detected.     

Development of slow disturbances in a hypersonic boundary layer

The mechanisms of development of slow time-dependent disturbances in the wall region of a hypersonic boundary layer are established and a diagram of the disturbed flow patterns is plotted; the corresponding nonlinear boundary value problem is formulated for each of these regimes. It is shown that the main factors that form the disturbed flow are the gas enthalpy near the body surface, the local viscous-inviscid interaction level, and the type, either subsonic or supersonic, of the boundary layer as a whole. Numerical and analytical solutions are obtained in the linear approximation. It is established that enhancement of the local viscous-inviscid interaction or an increased role for the main supersonic region of the boundary layer makes the disturbed flow by and large “supersonic”: the upstream propagation of the disturbances becomes weaker, while their downstream growth is amplified. Contrariwise, local viscous-inviscid interaction attenuation or an increased role for the main subsonic region of the boundary layer has the opposite effect. Surface cooling favors an increased effect of the main region of the boundary layer while heating favors an increased wall region effect. It is also found that in the regimes considered disturbances travel from the turbulent flow region downstream of the disturbed region under consideration counter to the oncoming flow, which may be of considerable significance in constructing the nonlinear stability theory.     

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.     

A theoretical mode for the instability of turbulent boundary layer over compliant surface

A theoretical model for the instability of turbulent boundary layer over compliant surfaces is described. The investigation of instability is carried out from a time-asymptotic space-time perspective that classifies instabilities as either convective or absolute. Results are compared against experimental observations of surface waves on elastic and viscoelastic compliant layers.     

Incipient separation in shock wave/boundary layer interactions as induced by sharp fin

The incipient separation induced by the shock wave/turbulent boundary layer interaction at the sharp fin is the subject of the present study. Existing theories for the prediction of incipient separation, such as those put forward by McCabe (1966) and Dou and Deng (1992), can thus far only predic the direction of surface streamline and tend to overpredict the incipient separation condition based on the Stanbrook’s criterion. In this paper, the incipient separation is first predicted with Dou and Deng (1992)’s theory and then compared with Lu and Settles’ (1990) experimental data. The physical mechanism of the incipient separation as induced by the shock wave/turbulent boundary layer interactions at sharp fin is explained via surface flow pattern analysis. Furthermore, the reason for the observed discrepancy between the predicted and experimental incipient separation conditions is clarified. It is found that when the wall-limiting streamlines behind the shock wave becomes aligned with one ray from the virtual origin as the strength of the shock wave increases, the incipient separation line is formed at which the wall-limiting streamline becomes perpendicular to the local pressure gradient. The formation of this incipient separation line is the beginning of the separation process. The effects of Reynolds number and Mach number on incipient separation are also discussed. Finally, a correlation for the correction of the incipient separation angle as predicted by the theory is also given.

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Prediction of hypersonic boundary layer transition on sharp wedge flow considering variable specific heat

When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge.     

Three-wave interactions between disturbances in the hypersonic boundary layer on impermeable and porous surfaces

The interaction between disturbances in the hypersonic boundary layer on impermeable and porous surfaces is considered within the framework of weakly-nonlinear stability theory. It is established that on the impermeable surface nonlinear interactions between different waves (acoustic and vortex) occur in the parametric resonance regime. The role of pumping wave is played by a plane acoustic wave. The nonlinear interactions take place over a wide frequency range and can lead to the packet growth of Tollmien-Schlichting waves. On the porous surface the analogous interactions are fairly weak and result in a slight decay of the acoustic mode and a slight amplification of the vortex mode. This leads to the dragging out of the laminar flow regime and the regions of linear disturbance growth. In this situation the low-frequency spectrum of the vortex modes may be filled on account of the nonlinear processes occurring in the three-wave systems between the vortex components.     

Analysis of nonlinear oscillations by wavelet transform: Lyapunov exponents

In this paper we give the definition of exponents which would look like Lyapunov exponents in the cases of non-smooth flows of differential equations or iterated maps, and carry back Lyapunov exponents in smooth cases. Here we test our definition by using some simple linear and nonlinear smooth examples.     

Investigation of intermittency measurement methods for transitional boundary layer flows

Three turbulent intermittency methods, namely the , TERA (turbulent energy recognition algorithm), and M-TERA (modified turbulent energy recognition algorithm) methods, for identifying the intermittent flow characteristics associated with boundary layer transition from laminar to turbulent were considered and compared. The data used were obtained from hot-wire measurements in transitional boundary layer flows on a concave surface with a 2-m radius of curvature and on a flat plate. Comparisons show that the and TERA methods are more sensitive to the choice of threshold constants than the M-TERA method. In terms of the intermittency distribution across the boundary layer, the values obtained by the and TERA methods are unrealistically high in the near-wall region, while those obtained by the M-TERA method are more realistic. In the outer boundary layer region and outside the boundary layer, the and M-TERA methods give reasonable intermittency values, whereas the TERA method produces unrealistically high values in the region outside the boundary layer. In addition, the M-TERA method provides a sharper definition of theend of transition.     

Evolution of a 2-D disturbance in a supersonic boundary layer and the generation of shocklets

Through direct numerical simulation, the evolution of a 2-D disturbance in a supersonic boundary layer has been investigated. At a chosen location, a small amplitude T-S wave was fed into the boundary layer to investigate its evolution. Characteristics of nonlinear evolution have been found. Two methods were applied for the detection of shocklets, and it was found that when the amplitude of the disturbance reached a certain value, shocklets would be generated, which should be taken into consideration when nonlinear theory of hydrodynamic stability for compressible flows is to be established.     

Multi-resolution analysis of wavelet transform on pressure fluctuations in an L-valve

A novel diagnostic method to characterize the flow patterns in an 80 mm-i.d. L-valve had been developed by using multi-resolution analysis (MRA) of wavelet transformation on the pressure fluctuation signals which were acquired from the standpipe and the horizontal part of L-valve. Parameters including the aeration rate, aeration positions, riser gas velocity and composition of binary particle mixture (194-μm and 937-μm sand particles) were used to investigate the relationship of performance of L-valve and its pressure fluctuations. By means of MRA, the original pressure fluctuations were divided into multi-scale signals. They were macro-scale, meso-scale and micro-scale successfully described the structures of gas–solid flow in the L-valve, such as the gas bubbles/slugs, dune-ripple flow, suspension particle flow, etc.