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.     

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.     

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.     

Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

For direct numerical simulation (DNS) of turbulent boundary layers, gen- eration of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.     

Effect of the cone nose bluntness and the ultrasonically absorptive coating on transition in a hypersonic boundary layer

The effect of an ultrasonically-absorptive coating on laminar-turbulent transition on cones with different nose bluntnesses is experimentally investigated. The experiments were performed with a cone with the semi-vertex angle of 7° set at zero incidence in the Mach 8 flow for three Reynolds numbers. A material with a chaotic micropore structure was used as the ultrasonically-absorptive coating. One side of the model, along its generator, was coated with the porous material, while the second represented a rigid surface. The laminar-turbulent transition location was determined from the results of heat flux distribution measurements. The heat flux fluctuations were also measured on the model surface. It was found that the laminar region length increased with an increase in the bluntness radius. The ultrasonically-absorptive coating with a chaotic microstructure effectively stabilizes the boundary layer for all bluntness radii considered, increasing the laminar region length by 30 to 85%.     

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 disturbanceThe 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 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.     

Large injection rates on unsteady compressible boundary layer flow over cones at angles of attack

Summary Three-dimensional unsteady laminar boundary layer near the planes of symmetry of sharp cones at angles of attack subject to large rates of injection is obtained numerically by using an implicit finite difference scheme in combination with the quasi-linearization technique. Several model gases are considered with Mach numbers, wall-to-total-enthalpy ratios, and cross-flow parameters spanning the ranges of main engineering interest. A detailed study has been made of the solutions in the symmetry plane, in order to increase the understanding of the problem. Various cases are considered, when the free-stream velocity and the surface mass transfer (injection) vary arbitrarily with time. The effects of viscous dissipation and the cross-flow parameter have also been discussed.This research has been partially supported by the Research and Development Centre for Iron and Steel, Steel Authority of India Ltd. The constructive comments of Professor G. Nath and Professor A. K. Lahiri are sincerely appreciated.     

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     

Effect of the boundary layer on the base pressure in a two-dimensional flow with a Mach number M = 5

New data on the base pressure in a two-dimensional ow with a Mach number M = 5 are obtained for a wide range of variation of the normalized boundary-layer thickness in the flow-separation cross section. The test results are compared with Tanner’s theory, and a conclusion is made that this numerical model has to be corrected. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 23–28, May–June, 2005.     

Laminar-turbulent transition in the boundary layer on cones in a hypersonic flow at high Reynolds numbers per meter

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M _∞ = 12–14 and pressures in the settling chamber P₀ = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re _1e = (53–200) · 10⁶ m ⁻¹. The transition occurs at Reynolds numbers Re _tr = (2.3–5.7) · 10⁶. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 76–83, May–June, 2007.     

Three-dimensional boundary layer and vortex wake over a cone at high angle of attack: study of asymmetries

An experimental investigation of the flow over a one at a large angle of attack is reported. First, the study was focused on the wall shear stress measurement, including the localization of the separation. Secondly, the mean flow field in the whole wake of the cone was measured, as well as the velocity fluctuations. Results indicate that the separation and the fluctuations are asymmetrical in a certain way, whereas the mean flow field is approximately symmetrical. Finally, the different parts of the flow can be easily determined using vorticity calculations.List of symbols C vortex core - D diffusion coefficient for the polarographic solution - D cone diameter for the rotation plane of the electrochemical probes - D separation point - F function F (sin ) = (K ₁-K ₂)/(K ₁+K ₂) - G function G(sin ) = (K ₁+K ₂)/(K ₁+K ₂)( = 90dg) - g bidimensional gain of the electrochemical probe (constant for each probe) - K ₁, K ₂ mass transfer coefficients for differential probes - Re _x Reynolds number based on the X length, and relative to the forward upstream velocity - wall velocity gradient vector - S wall velocity gradient modulus - S enclosing saddle point - S _x azimuthal component of the wall velocity gradient (perpendicular to a generator) - S _z longitudinal component of the wall velocity gradient (along a generator) - U mean value of the forward upstream velocity - U _i component number i of the velocity vector in the (X, Y, Z) coordinates - X, Y, Z cone cartesian coordinates - non-dimensional cone cartesian coordinates (relative to D) Greek symbols incidence (part 1) angle between the wall velocity gradient and the neutral axis of the electrochemical probe (except part 1) - _r relative incidence /0 _c - velocity circulation - wavelength of the laser beam - kinematic viscosity - azimuthal angle - _c cone semi-apex angle     

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.     

Numerical modeling of perturbation propagation in a supersonic boundary layer

The growth of two-dimensional disturbances generated in a supersonic (M = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the second-mode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 33–44. Original Russian Text Copyright © 2004 by Egorov, Sudakov, Fedorov.     

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.     

Study of laminar boundary layer separation on a cone at an angle of attack

Experimental data are obtained on the position of the line of separation as a function of angle of attack, cone apex angle, and flow Mach number.     

STUDY OF MECHANISM OF BREAKDOWN IN LAMINARTURBULENT TRANSITION OF SUPERSONIC BOUNDARY LAYER ON FLAT PLATE

Spatial mode direct numerical simulation has been applied to study the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that, during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbance, when they became larger, leads to remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.     

Traveling disturbance appearing in boundary layer transition in a Yawed cylinder

Boundary layers that develop over a body in fluid flow are in most cases three-dimensional owing to the spin, yaw, or surface curvature of the body. Therefore, the study of three-dimensional (3D) boundary-layer transition is essential to work in practical aerodynamics. The present investigation is concerned with the problem of 3D boundary layers over a yawed body. A yawed cylinder model that represents the leading edge portion of a swept wing and the mechanism of crossflow instability are investigated in detail using hot-wire velocimetry and a flow visualization technique. As a result, traveling disturbances having frequencies f₁ and f₂, which differ by about one order of magnitude, are detected in the transition region. The phase velocities and directions of travel of those disturbances are measured. Results for the low-frequency disturbance f₁ show qualitative coincidence with results numerically predicted for a crossflow unsteady disturbance. Nameley, F₁ travels nearly spanwise to the yawed cylinder and very close to the cylinder wall. The results for the high-frequency disturbance f₂ good agreement with the existing experimental results. The ₂ disturbance is found to be the high-frequency inflectional secondary instability that appears in 3D boundary layer transition in general. A two-stage transition process, where stationary crossflow vortices appear as the primary instability and a traveling inflectional disturbance is generated as a secondary instability, was observed. Secondary instability seems to play a major role in turbulent transition.