The engineering computation of turbulent flows is mainly based on turbulence modeling,however,accurate aerothermal computation of hypersonic turbulent boundary layers is still a not well-solved problem. Aerothermal computation for turbulent boundary layers on a supersonic or hypersonic blunt cone with small bluntness is done firstly by using both direct numerical simulation and BL model,and seven different cases are investigated. Then the results obtained by the two methods are compared,and the reason causing the differences is found to be the incorrect assumption in the turbulence modeling that the ratio between eddy heat conductivity and eddy viscosity is constant throughout the whole boundary layer. Based on certain theoretical arguments,a method of modifying the expression of eddy heat conductivity in the region surrounding the peak location of the turbulent kinetic energy is proposed,which is verified to be effective,at least for the seven cases investigated.
DONG Ming & ZHOU Heng Department of Mechanics,Tianjin University,Tianjin 300072,China
The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N factor is an empirical factor.In this paper the reliability of this key assumption in the improved eN method is checked by results of transition prediction by using the Parabolized Stability Equations(PSE).Transition locations of an incompressible boundary layer and a hypersonic boundary layer at Mach number 6 on a flat plate are predicted by both the improved eN method and the PSE method.Results from both methods agree fairly well with each other,implying that the transition criterion proposed in the improved eN method is reliable.
SU CaiHong1,2 1 Department of Mechanics,Tianjin University,Tianjin 300072,China
The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice.The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow.Two types of disturbances are imposed at the entrance,i.e.,identical amplitude and wavepacket disturbances,along the spanwise direction in the incompressible boundary layers.The disturbances of identical amplitude are consisted of one two-dimensional(2D) wave and two three-dimensional(3D) waves.The parabolized stability equation(PSE) is used to research the evolution of disturbances and to predict the transition position.The results are compared with those obtained by the numerical simulation.The results show that the PSE method can investigate the evolution of disturbances and predict the transition position.At the same time,the calculation speed is much faster than that of the numerical simulation.
The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al.using direct numerical simulation(DNS).It was found that certain small-scale 3-D disturbances amplified rapidly.These disturbances exhibit the characteristics of second modes,and the most amplified components have a welldefined spanwise wavelength,indicating a clear selectivity of the amplification.In the case of a cone,the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification.In order to ascertain which of these two effects are essential,in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance(wavepacket) in a flat-plate boundary layer.A similar amplification of small-scale disturbances was observed,suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow,even though the latter does alter the spanwise distribution of the disturbance.The rapid growth of 3-D waves may be attributed to the secondary instability mechanism.Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting(T-S) waves in an incompressible boundary layer.The results show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber.It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.
Transition prediction of the supersonic boundary layer on a cone with small angle of attack and Mach number 3.5 is investi-gated under the consideration of receptivity to slow acoustic waves, as the acoustic waves are the main environmental distur-bances in a conventional, i.e. non-quiet, wind tunnel. It is shown that the e-N method can still yield fairly satisfactory results incomparison with those obtained in wind tunnel experiments, provided that the boundary layer receptivity to slow acousticwaves is properly taken into account, including the dependence of the amplitude of disturbances on the frequency andstream-wise location. Neither the conventional e-N method nor the improved e-N method can yield correct result of transitionprediction, because the receptivity mechanisms considered there are not in accord with the real situation in the wind tunnel.
Turbulence modeling has played important roles in solving engineering problems. However, with the development of aero-space technology, turbulence modeling faces new challenges. How to further improve turbulence modeling for su-per/hypersonic flows is an urgent problem. Through analyzing a set of data resulting from DNS and experiments, it is foundthat some most popular models suffer from essential flaws, and can be hardly improved following the traditional mode ofthinking. On the contrary, the BL model, which is one of the simplest and widely-used models, can be further improved. In thispaper, through analyzing results from DNS data, the main cause of the inaccuracy in applying the BL model to supersonic andhypersonic turbulent boundary layers is found to have resulted from the mismatch between the location of the matching pointof the inner and outer layers of the BL model determined by the conventional way and those given by DNS. Improvement onthis point, as well as other improvements is proposed. Its effectiveness is verified through the comparison with DNS results.
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 eNmethod considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed. The results show that for the same oncoming flow condition and wall condition, the transition positions of hypersonic sharp wedge boundary layer move much nearer to the leading edge than those of the flat plate. The greater the oncoming flow Mach number, the closer the transition position to the leading edge.
