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.     

锥体效应对超音速湍流边界层统计特性的影响

通过直接数值模拟,计算了空间模式下,来流马赫数为2.5, 半锥角为$5^{\circ}$, 零攻角的绝热钝锥湍流边界层,研究了湍流的统计特性,并把结果与超音速平板湍流边界层和马赫数为6的高超音速钝锥湍流边界层的结果进行了比较,重点定量地考察了锥体效应对边界层湍流统计特性的影响. 研究发现,锥体效应对平均温度剖面以及压缩性的影响是显著的;而其它统计量,比如速度壁面律、雷诺应力的分布和湍动能各项的贡献等,受锥体效应的影响很小.      

Hypersonic boundary-layer transition on a flared cone

Transition on a flared cone with zero angle of attack was studied in our newly established Mach 6 quiet wind tunnel (M6QT) via wall pressure measurement and flow visualization. High-frequency pressure transducers were used to measure the second-mode waves’ amplitudes and frequencies. Using pulsed schlieren diagnostic and Rayleigh scattering technique, we got a clear evolution of the second-mode disturbances. The second-mode waves exist for a long distance, which means that the second-mode waves grow linearly in a large region. Strong Mach waves are radiated from the edge of the boundary layer. With further development, the second-mode waves reach their maximum magnitude and harmonics of the second-mode instability appear. Then the disturbances grow nonlinearly. The second modes become weak and merge with each other. Finally, the nonlinear interaction of disturbance leads to a relatively quiet zone, which further breaks down, resulting in the transition of the boundary layer. Our results show that transition is determined by the second mode. The quiet zone before the final breakdown is observed in flow visualization for the first time. Eventual transition requires the presence of a quiet zone generated by nonlinear interactions.     

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.     

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.     

Predicting crossflow induced transition with laminar kinetic energy transition model

The hypersonic laminar kinetic energy transition model is developed to be appropriate for crossflow induced boundary layer transition prediction. A crossflow timescale is constructed and incorporated in the k_T-k_L-ω transition model to reflect crossflow effect during three-dimensional boundary layer transition. The stream-wise vorticity is selected as the indicator of crossflow strength. Regarding the inviscid unstable characteristic of crossflow instability, the crossflow timescale is constructed by reference to the second mode timescale. To eliminate inappropriate development of the crossflow timescale where the effective length scale is large enough while the crossflow strength remains at a quite low level, a crossflow velocity limit function is proposed. The revised k_T-k_L-ω transition model has been applied to HIFiRE-5 and blunt cone with 1°angle of attack test cases. Results show good correspondence with the experimental data and DNS data, which demonstrates that the constructed crossflow timescale makes the revised transition model capable of reproducing crossflow induced transition behavior with a reasonable degree of accuracy.     

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.     

The hypersonic Mach number independence principle in the case of viscous flow

The hypersonic Mach number independence principle of Oswatitsch is important for hypersonic vehicle design. It explains why, above a certain flight Mach number (M _∞ ≈ 4−6, depending on the body shape), some aerodynamic properties become independent of the flight Mach number. For ground test facilities this means that it is sufficient for the Mach number in the test section to be high enough, that Mach number independence exists. However, the principle was derived for calorically perfect gas and inviscid flow only. In this paper a theoretical study for blunt bodies in the case of viscous flow is presented. We provide numerical results which give insight into how attached viscous flow behaves at high Mach numbers. The flow past an axisymmetric configuration is analysed by applying a coupled Euler/second-order boundary-layer method. Wall boundaries are treated by assuming an adiabatic or radiation-adiabatic wall for laminar flow. Calorically perfect or equilibrium air is accounted for. Lift, drag, and moment coefficients, and lift-to-drag ratios are given for several combinations of flight Mach number and altitude, i.e. Reynolds number. For blunt bodies considered here, which are pressure dominated, Mach number independence occurs for the adiabatic wall, but not for the radiation-adiabatic wall assumption.     

Direct Numerical Simulation of Hypersonic Boundary-Layer Flow on a Flared Cone

The forced transition of the boundary layer on an axisymmetric flared cone in Mach 6 flow is simulated by the method of spatial direct numerical simulation (DNS). The full effects of the flared afterbody are incorporated into the governing equations and boundary conditions; these effects include nonzero streamwise surface curvature, adverse streamwise pressure gradient, and decreasing boundary-layer edge Mach number. Transition is precipitated by periodic forcing at the computational inflow boundary with perturbations derived from parabolized stability equation (PSE) methodology and based, in part, on frequency spectra available from physical experiments. Significant qualitative differences are shown to exist between the present results and those obtained previously for a cone without afterbody flare. In both cases, the primary instability is of second-mode type; however, frequencies are much higher for the flared cone because of the decrease in boundary-layer thickness in the flared region. Moreover, Goertler modes, which are linearly stable for the straight cone, are unstable in regions of concave body flare. Reynolds stresses, which peak near the critical layer for the straight cone, exhibit peaks close to the wall for the flared cone. The cumulative effect appears to be that transition onset is shifted upstream for the flared cone. However, the length of the transition zone may possibly be greater because of the seemingly more gradual nature of the transition process on the flared cone. Received 20 March 1997 and accepted 21 May 1997     

Study of effect of a smooth hump on hypersonic boundary layer instability

Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier–Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.     

Effect of wall conditions on DDT in hydrogen–oxygen mixtures

Detonation in ducts is usually studied assuming adiabatic walls because of the high kinetic energy due to the incoming flow being supersonic. In the present work, numerical simulations of deflagration-to-detonation transition (DDT) using a detailed chemical reaction model are performed under adiabatic and isothermal boundary conditions in a tube with no-slip walls. The results show a local explosion driving DDT, which occurs near the tube wall in the case of an adiabatic wall, but close to the flame front in the case of an isothermal wall. Furthermore, to examine the effects of a turbulent boundary layer, a simulation using the Baldwin–Lomax turbulence model is carried out. In the case of the isothermal wall, there is again a local explosion near the tube wall, which leads to detonation. In summary, the present study confirms that the boundary conditions affect the transition to detonation and that the boundary layer is a key component of DDT.     

Shock tunnel study of spiked aerodynamic bodies flying at hypersonic Mach numbers

A three-component accelerometer balance system is used to study the drag reduction effect of an aerodisc on large angle blunt cones flying at hypersonic Mach numbers. Measurements in a hypersonic shock tunnel at a freestream Mach number of 5.75 indicate more than 50% reduction in the drag coefficient for a 120° apex angle blunt cone with a forward facing aerospike having a flat faced aerodisc at moderate angles of attack. Enhancement of drag has been observed for higher angles of attack due to the impingement of the flow separation shock on the windward side of the cone. The flowfields around the large angle blunt cone with aerospike assembly flying at hypersonic Mach numbers are also simulated numerically using a commercial CFD code. The pressure and density levels on the model surface, which is under the aerodynamic shadow of the flat disc tipped spike, are found very low and a drag reduction of 64.34% has been deduced numerically.     

Experimental demonstration of a new concept of drag reduction and thermal protection for hypersonic vehicles

A new idea of drag reduction and thermal protection for hypersonic vehicles is proposed based on the combination of a physical spike and lateral jets for shockreconstruction. The spike recasts the bow shock in front of a blunt body into a conical shock, and the lateral jets work to protect the spike tip from overheating and to push the conical shock away from the blunt body when a pitching angle exists during flight. Experiments are conducted in a hypersonic wind tunnel at a nominal Mach number of 6. It is demonstrated that the shock/shock interaction on the blunt body is avoided due to injection and the peak pressure at the reattachment point is reduced by 70% under a 4° attack angle.     

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.     

On the persistence of regular reflection

It is well accepted that the persistence of regular reflection of a shock wave off a wedge beyond the ideal theoretical prediction is due to viscous and thermal boundary layers induced behind the reflection point. Experiments have been done by reflecting two shock waves of equal strength off each other so that the plane of symmetry between them becomes an ideal inviscid and adiabatic reflection plane thereby experimentally mimicking the assumptions of the theory. There is one definitive experiment done at a wall angle of 40° using a bifurcated shock tube that indicates that the actual transition angle is the theoretical detachment condition. This paper extends these results to two cases near limiting conditions; one at a very low incidence shock Mach number and one at a wall angle very close to the theoretical transition limit. The first confirms the reasons for the von Neumann Paradox but cannot discriminate between sonic and detachment conditions, but is within about 0.5% of them, and the second shows transition much closer to the sonic than the detachment condition but with both within the experimental error bounds. In both cases, the results are notably different from transition conditions off a wedge and confirm the effects of transport properties being the cause of persistence of regular reflection.     

An experimental research on the instability of natural convection boundary layer around a vertical heated flat plate

Experimental results on the instability of the isothermal naturalconvection boundary layer around a vertical heated flat plate are presented. It is demonstrated that the characteristics of the instability wave in the outer layer is consistent with the calculation of Brewster & Gebhart. After an initial growth of its low frequency components at the downstream side of the turning point of the neutral curve (Gr≈120) its comparatively higher frequency components develop and become turbulent subsequently with a buoyancy subrange in its power spectra. Simultaneously, in the measurement at the inner layer near the wall a viscous instability signal the same as the Tollmien-Schlichting waves in ordinary boundary layer and its subharmonics in a much higher frequency domain is discovered and an inertial subrange can be observed in the spectra atGr≈378.6. The project supported by the National Natural Science Foundation of China (19572004)     

Flat-plate hypersonic boundary-layer ?ow instability and transition prediction considering air dissociation

The effects of air dissociation on ?at-plate hypersonic boundary-layer ?ow instability and transition prediction are studied. The air dissociation reactions are assumed to be in the chemical equilibrium. Based on the ?at-plate boundary layer, the ?ow stability is analyzed for the Mach numbers from 8 to 15. The results reveal that the consideration of air dissociation leads to a decrease in the unstable region of the ?rst-mode wave and an increase in the maximum growth rate of the second mode. High frequencies appear earlier in the third mode than in the perfect gas model, and the unstable region moves to a lower frequency region. When the Mach number increases, the second-mode wave dominates the transition process, and the third-mode wave has little effect on the transition. Moreover, when the Mach number increases from 8 to 12, the N-factor envelope becomes higher, and the transition is promoted. However, when the Mach number exceeds 12, the N-factor envelope becomes lower, and the transition is delayed. The N-factor envelope decreases gradually with the increase in the altitude or Mach number.     

Numerical simulation of boundary-layer transition at Mach two

The linear and early nonlinear stages of boundary-layer transition at free-stream Mach numberM ==2.0 are investigated by direct numerical simulation of the compressible Navier-Stokes equations. Results from simulations with a large computational box and small-amplitude random initial conditions are compared with linear stability theory. The growth rates of oblique waves are reproduced correctly. Two-dimensional waves show a growth that is modulated in time, indicating the presence of an extra unstable mode which moves supersonically relative to the free stream. Further simulations are conducted to investigate the nonlinear development of two- and three-dimensional disturbances The transition due to oblique disturbance waves is the most likely cause of transition at this Mach number, and is found to lead to the development of strong streamwise vortices.     

Continuous Mode Transition in High-speed Boundary-layers

Mode interaction is studied via direct numerical simulations of a Mach 4.5 boundary layer with discrete and continuous modes imposed at the inflow. An approximate decoupling procedure is developed to create separate vortical, acoustic and entropic continuous mode components. Oblique horizontal vorticity modes induce boundary layer disturbances that grow with downstream distance, similarly to their incompressible counterpart. One salient difference is that a low frequency vorticity mode, alone, is found to induce transition by spawning two-dimensional, unstable discrete modes. The discrete modes are non-linearly excited at high harmonics of the inlet perturbation. Adding a Mack second mode, in addition to the vorticity mode, causes even earlier transition, suggesting that, in supersonic flow, unstable discrete modes play a crucial role in breakdown of boundary-layer streaks.     

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%.