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Transverse rectangular microgrooves with local machining flaw are investigated using direct numerical simulations from the viewpoint of suppressing the second-mode instability in a Mach 6 hypersonic boundary layer. Two types of machining flaw are modeled for the local deformation of microgrooves, i.e., chamfered and protruded ones. The effect of locally deformed microgrooves on the boundary-layer stability is studied by superposing the second-mode disturbance to the base flow of the boundary layer. The investigated unstable second mode is 400 kHz, and the microgrooves are installed in its synchronous region. The results show that compression and expansion waves are generated on the surface of the deformed microgrooves, and microscale separation bubbles are formed at the rear edge of the deformed microgrooves. With the increase of local deformation height of microgrooves, the suppression effect of the second-mode disturbance gradually increases. As the deformation height reaches 0.09 mm, the amplitude inhibition rate of locally deformed microgrooves on the second-mode disturbance reaches 44.7%, compared to that of the regular one.

To improve robustness and efficiency of automatic transition prediction in aerodynamic design, a reduced model of linear stability analysis is usually adopted, such as eN-envelope or eN-database me...

To understand fundamental problems in hypersonic laminar-turbulent boundary layer transition for three-dimensional complex vehicles, a new standard model with typical lifting-body features has been proposed, named as hypersonic transition research vehicle (HyTRV). The configuration of HyTRV is fully analytical, and details of the design process are discussed in this study. The transition characteristics for HyTRV are investigated using three combined methods, i.e., theoretical analyses, numerical simulations, and wind tunnel experiments. Results show that the fully analytic parameterization design of HyTRV can satisfy the model simplification requirements from both numerical simulations and wind tunnel experiments. Meanwhile, the flow field of HyTRV reveals typical transition mechanisms in six relatively separated regions, including the streamwise vortex instability, crossflow instability, secondary instability, and attachment-line instability. Therefore, the proposed HyTRV model is valuable for fundamental researches in hypersonic boundary layer transition. A new standard model with typical lifting-body features for boundary layer transition research has been proposed. Results of three combined analysis methods show that the flow field of HyTRV reveals typical transition mechanisms in six relatively separated regions, including the streamwise vortex instability, crossflow instability, secondary instability, attachment-line instability. Therefore, the proposed HyTRV model is valuable for fundamental researches in hypersonic boundary layer transition.

A set of several exact coherent states in plane Couette flow is computed under spanwise wall oscillation control, with a range of wall oscillation amplitudes and periods $({A_w}, T)$ . It is found that the wall oscillation generally stabilises the upper branch of the equilibrium solutions and achieves the corresponding drag reduction, while it influences modestly the lower branch. The stabilisation effect is found to increase with the oscillation amplitude with an optimal time period around ${T^{+}} \approx 100$ . The exact coherent states reproduce some key dynamical behaviours of streaks observed in previous studies, while exhibiting the rich coherent structure dynamics that cannot be extracted from a phase average of turbulent states. Visualisation of state portraits shows that the size of the state space supporting turbulent solution is reduced by the spanwise wall oscillation, and the upper-branch equilibrium solutions become less repelling, with many of their unstable manifolds being stabilised. This change of the state space dynamics leads to a significant reduction in lifetime of turbulence. Finally, the main stabilisation mechanism of the exact coherent states is found to be the suppression of the lift-up effect of streaks, explaining why previous linear analyses have been so successful for turbulence stabilisation modelling and the resulting drag reduction.

Görtler vortex-induced hypersonic boundary layer transition controlled by grooves is investigated using direct numerical simulations and spatial bi-global stability analysis. In the simulations, Görtler vortices are excited by wall steady blowing and suction with spanwise wavelengths of 3 mm. It is found that when the wall is covered with grooves, the Görtler streaks keep more regular even at the end of the model. In addition, the skin friction coefficient is reduced efficiently. Furthermore, the wall-normal and spanwise velocity shear are both reduced, suppressing growths of secondary instabilities. In conclusion, grooves can delay Görtler vortex-induced transition by modifying the Görtler streaks structure and instability, which would shed light on hypersonic boundary layer transition control.

Boundary layer transition over a lifting body of 1.6 m length at $2^\circ$ angle of attack has been simulated at Mach 6 and a unit Reynolds number $1.0 \times 10^7$ m$^{-1}$. The model geometry is the same as the Hypersonic Transition Research Vehicle designed by the China Aerodynamics Research and Development Center. Four distinct transitional regions are identified, i.e. windward vortex region, shoulder vortex region, windward cross-flow region and shoulder cross-flow region. Multi-dimensional linear stability analyses by solving the two-dimensional eigenvalue problem (spatial BiGlobal approach) and the plane-marching parabolized stability equations (PSE3D approach) are further carried out to uncover the dominant instabilities in the last three regions as well as the shoulder attachment-line region. The shoulder vortex is conducive to both inner and outer modes of shear-layer instability, of which the latter most likely trigger the vortex breakdown. A novel method is presented to substantially reduce the computational cost of BiGlobal and PSE3D in resolving the cross-flow instabilities in cross-flow regions. The peak frequencies of cross-flow modes lie between 15 and 45 kHz. Whereas oblique second Mack modes are marginally unstable in the windward cross-flow region, they could be strong enough to compete with the cross-flow modes in the shoulder cross-flow region. In the shoulder attachment-line region, there exists only one unstable mode of Mack instability, differing from previous studies that show a hierarchy of modes in the context of symmetrical attachment-line flows. Results of the numerical simulation and multi-dimensional stability analyses are compared when possible, showing a fair agreement between the two approaches and highlighting the necessity of considering non-parallel effects.

A velocity-temperature coupled control method is proposed for turbulence drag reduction of supersonic boundary layers. Direct numerical simulations indicate that heated wall blowing achieves the best drag reduction, whereas cooled wall blowing leads to a drag increase. The reduction of mean viscous shear stress is mainly responsible for the drag reduction mechanism, though there is a substantial increase in Reynolds stresses. Nevertheless, the control efficiency of heated wall blowing is low due to high energy consumption, but further investigation is needed.

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: A first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.

Direct numerical simulations of a spatially developing Ma 2.25 supersonic turbulent boundary layer with streamwise-striped wall blowing (SSB) are performed for the purpose of turbulence drag reduction. The SSB is designed to blow through long and straight slots in the flow direction. The slots are equally distributed in spanwise direction, with different stripe spacing and width. Blowing amplitudes of 0.1% and 0.2% are investigated. For comparison, uniform blowing (UB) of 0.1% is also simulated. It is found that in spite of weak control amplitudes, 7.4% and 14.5% drag reduction can be achieved in the case of 6SSB 0.1% and 6SSB 0.2%, respectively. Similar to UB, the boundary layer displacement thickness is thickened by SSB, with a thicker viscous sub-layer and a logarithmic zone which moving away from the wall. Turbulence intensities and turbulent coherent structures are enhanced, although the streamwise scales of the latter are attenuated. Turbulent kinetic energy analysis presents that both the production and dissipation are increased in the near wall. Compressible Renard-Deck decomposition of C f shows that it is the spatially growth term that mainly responsible for the turbulence drag reduction.

Growing evidences show that the Symmetrical Conservative Metric Method (SCMM) is essential in preserving freestream conservation and orders of accuracy for high-order finite difference schemes to simulate flows with complex geometries. In this paper, a new family of Hybrid cell-edge and cell-node Dissipative Compact Schemes (HDCSs) has been developed for geometry-complex flows by fulfilling the SCMM as well as by introducing dissipation according to the concept adopted in the construction of the high-order Dissipative Compact Schemes (DCSs). The resolution and dissipation properties of HDCSs are investigated by the Fourier analysis, and the stability property of HDCSs is also investigated by asymptotic stability analysis and amplification factor analysis. HDCSs are validated by computing several benchmark test cases. The vortex convection test case demonstrates that the orders of accuracy of the HDCSs are preserved unless the GCL is satisfied. Although high resolution of HDCSs is observed in the test of acoustic wave scattering of multiple cylinders, the solutions can be contaminated if the GCL is not satisfied. Moreover, the numerical solutions of flow past a high lift trapezoidal wing demonstrate the promising ability of the newly developed HDCSs in solving complex flow problems.

Boundary-layer transition (BLT) is one of the key problems in developing hypersonic aircrafts. Major aerospace countries all over the world have been heavily supporting relevant researches, and the project funding keeps increasing in recent years. In this paper, wind tunnel experiments, numerical simulations and theoretical analysis are combined to study some hot issues in this area, which include effects of unit Reynolds number, angle of attack and nose bluntness, nonlinear interactions during breakdown, secondary instability of crossflow vortices, etc. Some of our views on understanding hypersonic BLT are summarized. The wind tunnel tests are conducted in the Φ1 m hypersonic wind tunnel of China Aerodynamics Research and Development Center, and the relation between transition location and different unit Reynolds numbers, angles of attack and nose bluntness is obtained. It is well known that hypersonic BLT undergoes an important phenomenon called “nose-bluntness inversal”, but a worldwide accepted reasonable explanation for this phenomenon is still missing. To investigate the “nose-bluntness reversal”, we suggest to consider the influence of front shock waves because free-stream disturbances are changed by shock waves. Meanwhile, we should also consider the following two aspects: blunt-nose receptivity and entropy-layer effect. Some premiliary but encouraging results are presented on these two aspects via direct numerical simulations (DNS) and stablity analysis. During the late stage of transition, a “quiet zone” may appear when the second mode waves reach large amplitude, and this is followed by low-frequency modes. DNS and the dynamic mode decomposition are applied to study this problem. The results indicate that the relation between the second modes and the low-frequency modes is possibly mode transformation. In the end of this paper, a newly discovered secondary unstable mode of saturated crossflow vortices is introduced. This mode has the same level of growth rate as Z mode, but is related to the wall-normal shear stress, thus it is named Y mode.

Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study. High resolution has been achieved by Dissipative Compact Schemes (DCS), however, according to the recent research, applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law (GCL) is not satisfied, and this may cause numerical instability. To cope with this problem, a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme (HDCS) has been formulated. The formulation of the HDCS contains two steps. First, a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL, and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables. The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry, while the DCS may suffer numerical instabilities. Moreover, high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.

Weighted Compact Nonlinear Schemes (WCNSs) possess the merits of high-order accuracy, high resolution, and high endurance in low quality grids. In order to implement WCNS on patched grids, high-order interpolations are generally needed for the purpose of ensuring overall high-order accuracy. However, high-order linear interpolations are susceptible to numerical oscillations in the vicinity of discontinuities and large gradient regions. In order to prevent this kind of oscillations, a new weighted interpolation is developed following the idea of Deng and Zhang (J Comput Phys, 2000). The new interpolation contains three fourth-order sub-interpolations which are weighted together according their smoothness. The weights are designed in such a way that in smooth regions they could approach to the optimal weights to achieve sixth-order accuracy, whereas in regions near discontinuities, the weights of the stencils which contain discontinuities are assigned to be nearly zero. The fifth-order WCNS is combined with the new weighted interpolation to solve flow problems on patched grids. Several benchmark problems, including shock waves, vortex, and shock/vortex interaction, are simulated to test the method. The results indicate that the new interpolation has similar performance with the sixth-order Lagrange interpolation in smooth regions, and is superior to the Lagrange interpolation in preventing interpolation oscillations in the vicinity of discontinuities.

A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods. Despite the rapid development of high-order algorithms in CFD, the applications of high-order and high accurate methods on complex configurations are still limited. One of the main reasons which hinder the widely applications of these methods is the complexity of grids. Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex. In order to implement high-order finite difference schemes on complex multi-block grids, the geometric conservation law and block-interface conditions are discussed. A conservative metric method is applied to calculate the grid derivatives, and a characteristic-based interface condition is employed to fulfil high-order multi-block computing. The fifth-order WCNS-E-5 proposed by Deng is applied to simulate flows with complex grids, including a double-delta wing, a transonic airplane configuration, and a hypersonic X-38 configuration. The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.

The Spalart-Allmaras (S-A) turbulence model, the shear-stress transport (SST) turbulence model and their compressibility corrections are revaluated for hypersonic compression corner flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme (WCNS-E-5) is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression corners at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris' and Shur's compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris' modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.

Hypersonic boundary-layer transition (BLT) is affected by multifarious factors, some of which cannot be simulated in ground wind tunnels, which makes the BLT data of wind tunnel experiments are usually different to that of flight experiments. In order to convert BLT data from wind tunnels to real flight cases, and to improve BLT prediction accuracy, a blunt cone model with zero angle-of-attack and 7° semi-cone angle is selected to contrastive analysis the boundary-layer stability and transition between wind tunnels and flights by using linear stability theory and eN method, based on the data set of our MF-1 flight test and hypersonic wind tunnel experiments, as well as an abroad flight test and wind tunnel experiments. The results show that the difference of stability and transition between wind tunnels and flights is essential. The wall temperature ratio in flights is smaller than that in wind tunnels, which leads to the second mode frequency in flight tests are greater than that of wind tunnel experiments. Two empirical formulas are developed to compute the most unstable frequency of the second mode. These formulas are shown suitable for both flight conditions and wind tunnel conditions. It is also shown that the N value ( N T) at the start of BLT is greatly affected by the nose Reynolds number. The larger the nose Reynolds number, the smaller the N T value. When the nose-tip bluntness is large enough, the BLT occurs even without boundary-layer mode instability. The front bow shock waves of blunt bodies will induce entropy layers, and the bluntness will affect the location (swallow point) where the entropy layers merge into the boundary layers. The relative location of transition point and swallow point is shown in good correlation with the N T, and the trend is similar for both wind tunnels and flights. A correlation between the transition-swallow relative location and the N T is developed by the least square method. This correlation is expected to conveniently predict hypersonic BLT of similar conditions.

There are still some challenges, such as grid quality, numerical stability, and boundary schemes, in the practical application of high-order finite difference schemes for complex configurations. This study presents some improved strategies that indicate potential engineering applications of high-order schemes. The formally fifth-order weighted compact nonlinear scheme developed by the authors is implemented on point-matched multiblock structured grids, which are generated over complex configurations to ensure the grid quality of each component block. The information transmission between neighboring blocks is carried out by new characteristic-based interface conditions that directly exchange the spatial derivatives on each side of an interface by means of a characteristic-based projection to keep the high-order accuracy and high resolution of a spatial difference scheme. The high-order scheme combined with the interface conditions is shown to be asymptotically stable. The engineering-oriented applications of the high-order strategy are demonstrated by solving several two- and three-dimensional problems with complex grid systems.

Co-rich, soft magnetic amorphous ribbons, with composition Co 68.25 Fe 4.5 Si 12.25 B 15 were prepared using a single roller melt-spinning technique. The effect of ac and dc Joule-heating annealing conditions on the GMI of these ribbons was investigated extensively. It was found that not only the current strength and annealing time, but also the cooling conditions, the geometry of the samples and the waveform of the annealing current affected the results significantly. The results of Joule-heating annealing were also found to be reversible under some conditions.

The results of the four drag prediction workshops (DPW) of AIAA indicate that the most current low-order CFD methods trend to given poor prediction for pitching moment of transonic aircraft configurations. The high-order weighted compact nonlinear scheme (WCNS) and algorithms for viscous terms as well as grid metrics are packaged together to establish a high-order code for complex geometries. The numerical results of the RAE2822 airfoil and the DLR-F6 wing-body configuration indicate that the accuracy for shock position and pitching moment may be improved by high-order methods. The American Institute of Aeronautics and Astronautics (AIAA) Applied Aerodynamics Committee have sponsored four drag prediction workshops (DPW) with the aim of assessing the state-of-the-art computational methods as practical aerodynamic tools for aerodynamic force and moment prediction of transonic aircraft configurations (http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw). Transonic flow occurs when there is mixed sub- and supersonic local flow in the same flowfield (typically with freestream Mach numbers from Ma = 0.6 or 0.7 to 1.2). The transonic flow regime provides the most efficient aircraft cruise performance, hence, most large commercial aircraft cruise in this regime [20]. However, transonic flow fields tend to be sensitive to small perturbations in flow conditions or to slight changes in geometrical characteristics, either of which can cause large variations in the flow field [20]. This complicates both computations and wind tunnel testing. As noted by Hafez [21], transonic aerodynamics is a rich field full of challenging problems for CFD, for example, the discretization process introduces errors, without controlling these errors, the results can be misleading. The four DPW show that current CFD codes may produce successful aerodynamic prediction for the transonic configurations. However, the results are somewhat scattered, especially for shock location, separation bubble, and drag as well as pitching moment. As the numerical methods of the four DPW are mainly low-order ones (less than 3th-order), the present invested the performance of high-order WCNS for complex transonic flows.

Tripping of boundary-layers from laminar to turbulent flow, which may be needed in specific practical applications, requires introducing high amplitude disturbances into the boundary layers without large drag penalties. As a possible improvement on fixed trip devices, a technique based on feedback instability is demonstrated in the present contribution for a Mach 1.5 boundary layer. The compressible Navier-Stokes equations are solved directly using a high-order (fifth-order in space and third-order in time) finite difference method. The geometries tested include wall-mounted rectangular blocks and off-surface cylinders. For a particular combination of an upstream cylinder and downstream block, a feedback loop is observed to provide more robust self-amplification of disturbances than a cylinder alone, whereas blocks by themselves only enhance a convective instability. A Fourier analysis and an impulse response simulation are used to confirm the presence of an acoustic feedback loop for the cylinder-block configuration. A parametric study of the size of the cylinder, the height, and the location of the rectangular block is also provided. It is observed that the feedback strength is not monotonically related to the height and location of the rectangular block.

In this paper, we present a method for extracting the magnetic parameters of soft magnetic Co-based alloy (Co 68.25 Fe 4.5 Si 12.25 B 15 ) in the high frequency regime (10MHz-2GHz). The magnetic sample (as-cast ribbon) is used as the conductor of a microstrip transmission line. The real and imaginary parts of series impedance (Z) of the line obtained from input impedance measurements, and a theoretical model based on the distributed parameters and the skin effect is used to extract the bulk transversal relative permeability. The effect of changing the applied external DC magnetic field is reported and the results show that the real parts of Z and propagation constant (γ) are very sensitive to the applied DC magnetic field. The model considers the geometrical contribution of the transmission line on the series impedance of the magnetic conductor (Co-based ribbon). In this work, we assume a real permeability, however the model can be readily used for extracting a complex transversal relative permeability (μ′ tr –jμ″ tr ).