Effect of glow discharge on hypersonic flat plate boundary layer

Glow discharge is introduced as an artificial disturbance to investigate the evolution of first-and second-mode instabilities in a hypersonic flat plate boundary layer.Experiments are conducted in a Mach 6.5 quiet wind tunnel using Rayleigh scattering visualization and particle image velocimetry(PIV). Detailed analysis of the experimental observations is provided. It is found that the artificially introduced 17 kHz disturbance,which belongs to the first-mode frequency band, can effectively enhance first-mode waves.Moreover, it can enhance second-mode waves even more intensely. Possible mechanisms to explain this phenomenon are discussed.     

Transition control of Mach 6.5 hypersonic flat plate boundary layer

An artificial disturbance is introduced into the boundary layer over a flat plate to investigate the effect on the transition process in the Mach 6.5 wind tunnel at Peking University. A linear stability theory(LST) is utilized to predict the evolution of the eigenmodes, and the frequency of the artificial disturbance is chosen according to the LST results. The artificial disturbance is generated by glowing discharge on the surface of the plate close to the leading edge. The Rayleigh-scattering visualization and particle image velocimetry(PIV) measurements are performed. By comparing the experimental results with artificial disturbances with those under the natural condition(without artificial disturbances), the present paper shows that the second-mode instability waves are significantly stimulated by the artificial disturbances, and the boundary layer transition is effectively triggered.     

Linear evolution and interaction of disturbances in the boundary layers on impermeable and porous surfaces in the presence of heat transfer

The interaction of disturbances in the compressible boundary layers on both impermeable and porous surfaces is considered in the linear and nonlinear approximations (weakly-nonlinear stability theory) in the presence of surface cooling. The regimes of moderate (Mach number M = 2) and high (M = 5.35) supersonic velocities are considered. It is established that surface cooling leads a considerable change in the linear evolution of the disturbances, namely, the first-mode vortex disturbances are stabilized, whereas the second-mode acoustic disturbances are destabilized, the variation degree being determined by the temperature factor. A porous coating used for controlling flow regimes influences the stability in the opposite fashion. For vortex waves the nonlinear interactions in three-wave systems at M = 2 are considerably attenuated in the presence of cooling. It might be expected that the cooling of the surface can delay the laminar regime for M = 2 and accelerate transition to turbulence for M = 5.35.     

Spatial direct numerical simulation of high-speed boundary-layer flows Part II: Transition on a cone in Mach 8 flow

The laminar breakdown of the boundary-layer flow of an axisymmetric sharp cone in a Mach 8 flow is simulated by a synergistic approach that combines the parabolized stability equation (PSE) method and spatial direct numerical simulation (DNS). The transitional state is triggered by a symmetric pair of oblique second-mode disturbances whose nonlinear interactions generate strong streamwise vorticity, which leads in turn to severe spanwise variations in the flow and eventual laminar breakdown. The PSE method is used to compute the weakly and moderately nonlinear initial stages of the transition process and, thereby, to derive a harmonically rich inflow condition for the DNS. The strongly nonlinear and laminar-breakdown stages of transition are then computed by well-resolved DNS, with a highly accurate algorithm that exploits spectral collocation and high-order compact-difference methods. Evolution of the flow is presented in terms of modal energies, mean quantities (e.g., skin friction), Reynolds stresses, turbulent kinetic energy, and flow visualization. The numerical test case is an approximate computational analog of one of the few stability experiments performed for hypersonic boundary-layer flows. Comparisons and contrasts are drawn between the experimental and the computational results. Rope-like waves similar to those observed in schlieren images of high-speed transitional flows are also observed in the numerical experiment and are shown to be visual manifestations of second-mode instability waves.This research was supported under NASA Contracts NAS1-19831 and NAS1-20059 for the first and second authors, respectively.     

Nonlinear Instability in the Region of Laminar-Turbulent Transition in Supersonic Three-Dimensional Flow over a Flat Plate

Direct numerical simulation is applied to obtain laminar-turbulent transition in supersonic flow over a flat plate. It is shown that, due to the nonlinear instability, Tollmien–Schlichting waves generated in the boundary layer lead to the formation of oblique disturbances in the flow. These represent a combination of compression and expansion waves, whose intensities can be two orders higher than that of external harmonic disturbances. The patterns of the three-dimensional flow over the plate are presented and the structures of the turbulent flat-plate boundary layers are described for the freestream Mach numbers M = 2 and 4.     

Spatial direct numerical simulation of high-speed boundary-layer flows part I: Algorithmic considerations and validation

A highly accurate algorithm for the direct numerical simulation (DNS) of spatially evolving high-speed boundary-layer flows is described in detail and is carefully validated. To represent the evolution of instability waves faithfully, the fully explicit scheme relies on non-dissipative high-order compact-difference and spectral collocation methods. Several physical, mathematical, and practical issues relevant to the simulation of high-speed transitional flows are discussed. In particular, careful attention is paid to the implementation of inflow, outflow, and far-field boundary conditions. Four validation cases are presented, in which comparisons are made between DNS results and results obtained from either compressible linear stability theory or from the parabolized stability equation (PSE) method, the latter of which is valid for nonparallel flows and moderately nonlinear disturbance amplitudes. The first three test cases consider the propagation of two-dimensional second-mode disturbances in Mach 4.5 flat-plate boundary-layer flows. The final test case considers the evolution of a pair of oblique second-mode disturbances in a Mach 6.8 flow along a sharp cone. The agreement between the fundamentally different PSE and DNS approaches is remarkable for the test cases presented.     

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.     

Direct numerical simulation of the transition to turbulence in a supersonic boundary layer on smooth and rough surfaces

Direct numerical simulations of instability development and transition to turbulence in a supersonic boundary layer on a flat plate are performed. The computations are carried out for moderate supersonic (free-stream Mach number M = 2) and hypersonic (M = 6) velocities. The boundary layer development is simulated, which includes the stages of linear growth of disturbances, their nonlinear interaction, stochastization, and turbulent flow formation. A laminar–turbulent transition initiated by distributed roughness of the plate surface at the Mach number M = 2 is also considered.     

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     

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.     

微槽-吸气组合控制平板边界层多模态稳定性研究

边界层转捩会使高超声速飞行器壁面摩阻和热流显著增加,因此在高超声速飞行器设计过程中往往占据重要地位.针对高超声速飞行器多模态转捩控制问题,提出了微槽道(1 mm)与边界层吸气的组合控制方法,并通过直接数值模拟和线性稳定性理论研究了Ma=4.5平板边界层的稳定性及组合控制效果.边界层在无控状态时,同时存在失稳的第一、二模态波,且二维第二模态波最不稳定;单纯施加微槽道控制时,边界层第二模态波会被抑制但第一模态波会被略微激发.对比而言,采用“微槽-吸气”组合控制后,不仅增强了对第二模态波的抑制效果,而且减弱了第一模态波的激发程度;同时随着吸气强度的增加,第二模态波不稳定区域明显收缩、频率显著增高,而第一模态波则变化不明显.相较于单纯的微槽道,吸气增强了“微槽吸收”与“声波散射”作用,因此中等吸气强度下该组合控制方法对第一和第二模态波的增长率分别实现了12.63%和28.02%的抑制效果.以上结果表明“微槽-吸气”组合控制手段具有适用宽频、布置区域灵活的优点,展现出了一定的多模态控制效果.     

超声速混合层中扰动增强混合实验

以基于纳米技术的平面激光散射(nano-based planar laser scattering, NPLS)流动显示技术定性研究了隔板扰动对超声速混合层($Mc=0.5$)的混合增强效果. 首先通过系列实验优化设计了扰动参数. 实验结果表明,超声速混合层对于从隔板引入的扰动非常敏感. 二维扰动的混合强化机制是提前混合层失稳位置,增厚混合层;而三维扰动的混合强化机制主要是通过诱导流向涡和展向运动,促进流动三维性质的发展. 总体而言,三维扰动的混合强化效果优于二维扰动. 由于是超声速混合层,隔板上的扰动片虽然很薄,但同样会引起激波的产生,是该方法中总压损失的主要原因.      

Three-wave interactions of disturbances in a hypersonic boundary layer on a porous surface

Interactions of disturbances in a hypersonic boundary layer on a porous surface are considered within the framework of the weakly nonlinear stability theory. Acoustic and vortex waves in resonant three-wave systems are found to interact in the weak redistribution mode, which leads to weak decay of the acoustic component and weak amplification of the vortex component. Three-dimensional vortex waves are demonstrated to interact more intensively than two-dimensional waves. The feature responsible for attenuation of nonlinearity is the presence of a porous coating on the surface, which absorbs acoustic disturbances and amplifies vortex disturbances at high Mach numbers. Vanishing of the pumping wave, which corresponds to a plane acoustic wave on a solid surface, is found to assist in increasing the length of the regions of linear growth of disturbances and the laminar flow regime. In this case, the low-frequency spectrum of vortex modes can be filled owing to nonlinear processes that occur in vortex triplets.     

A hybrid approach for nonlinear computational aeroacoustics predictions

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier–Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier–Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.     

Interaction between an unsteady pressure disturbance and a hypersonic boundary layer

The development of disturbances in a hypersonic boundary layer on a cooled surface is investigated in the case in which the characteristic velocity of disturbance propagation is small but greater than the flow velocity in the wall region of the three-layer disturbed zone with interaction. The nonlinear boundary value problem formulated involves a single similarity parameter that characterizes the contribution made by the main, on average either subsonic or supersonic, region of the boundary layer to the generation of the pressure disturbance. In the linear approximation, an analytical solution and an algebraic dispersion equation are derived. It is shown that only waves exponential in time and in the streamwise coordinate can propagate downstream when themain region of the undisturbed boundary layer is subsonic on average.     

Nonlinear Mechanisms of the Initial Stage of the Laminar–Turbulent Transition at Hypersonic Velocities

Weakly nonlinear development of waves in an axisymmetric hypersonic boundary layer is studied by the method of bispectral analysis. The type of nonlinear interaction that was not observed previously in such flows is found. The possibility of subharmonic resonance of the second mode at the nonlinear stage of transition is demonstrated. The previously discovered nonlinear generation of the harmonic of the fundamental wave of the second mode of disturbances is observed.     

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.     

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.     

Bispectral analysis of nonlinear processes in the hypersonic boundary layer on a porous cone surface

The results of the experimental investigation of the nonlinear stage of laminar-turbulent transition in the hypersonic boundary layer on porous and impermeable cone surfaces are presented. The bispectral analysis is applied to show that the porous surface suppresses the subharmonic resonance due to second mode disturbances. It is established that on the porous surface nonlinear processes develop more slowly than on the impermeable surface. This behavior indicates that the subharmonic resonance plays the role of a catalyzer in transferring energy from the mean flow to low-frequency disturbances in transition process, in much the same way as it occurs in a subsonic boundary layer.     

Tollmien-Schlichting wave generation by flow turbulence

The problem of freestream-turbulence-generated instability waves in the flat-plate boundary layer is solved on the basis of a nonlinear turbulence model admitting the deviation of the speed of propagation of vortex disturbances from the flow velocity. The solution obtained well describes the experimental dependence of the laminar-turbulent transition Reynolds number on the freestream turbulence degree.