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The three-dimensional flow on a plate with a V-shaped blunt leading edge (VsBLEP) is investigated numerically and experimentally at a freestream Mach number 6. A complex saddle-shaped shock front is observed on this VsBLEP under the interactions between the detached shock (DS) induced by the swept blunt leading edge and the bow shock (BS) induced by the crotch. It is demonstrated that a new type of spatial transition exists on this saddle-shaped shock front, which involves the transition of shock interactions (i.e., DS and BS) from the same family upstream of the crotch to opposite families downstream of the crotch. Moreover, this transition is quantitatively identified according to the shock-induced spanwise velocity along the inflection line between DS and BS, which is of great importance because it affects the crossflow significantly. The inward crossflow induced by the swept blunt leading edge is enhanced in the region where the DS and BS are from the same family, and the shear layers generated in this region converge gradually to the spanwise symmetry plane, which results in the formation of a streamwise counter-rotating vortex pair (CVP). In the region where the DS and BS turn to opposite families, the inward crossflow is eliminated, and a five-shock structure is identified downstream of the crotch. The CVP remains close to the spanwise symmetry plane as it trails downstream, showing a far-reaching influence on the flowfield. This study indicates that the V-shaped blunt leading edge affects the downstream flow significantly and therefore should be examined carefully in practical applications, such as in the design of an inlet cowl lip.The three-dimensional flow on a plate with a V-shaped blunt leading edge (VsBLEP) is investigated numerically and experimentally at a freestream Mach number 6. A complex saddle-shaped shock front is observed on this VsBLEP under the interactions between the detached shock (DS) induced by the swept blunt leading edge and the bow shock (BS) induced by the crotch. It is demonstrated that a new type of spatial transition exists on this saddle-shaped shock front, which involves the transition of shock interactions (i.e., DS and BS) from the same family upstream of the crotch to opposite families downstream of the crotch. Moreover, this transition is quantitatively identified according to the shock-induced spanwise velocity along the inflection line between DS and BS, which is of great importance because it affects the crossflow significantly. The inward crossflow induced by the swept blunt leading edge is enhanced in the region where the DS and BS are from the same family, and the shear layers generated in thi...

Shock oscillations on a series of V-shaped blunt leading edges with R/r (i.e., the crotch rounding radius R to the leading edge radius r) ranging from 0 to 9 are experimentally investigated at Mach 6. A combination of high-speed schlieren and image processing technologies is used to capture the flow features during the shock oscillations. The observed primary shock structures are categorized as regular reflection (type A), Mach reflection (type B), and regular reflection from the same family (type C). It is revealed that the competition of the two opposite jets near the stagnation point and the breathing-like motion of the flow at the crotch region cause severe oscillations for types B and C. These oscillations are classified into four patterns with the increase of R/r: global swing, mixing of swing and arch-recover, global arch-recover, and local arch-recover. Correspondingly, the coherent structure of the oscillations gradually changes from an antisymmetric one to a symmetrical one. The transitions of t...

The unsteady dynamics of shock interactions on the crotch of two typical V-shaped blunt leading edges have been investigated numerically and experimentally with a freestream Mach number 6 for different ratios (R), defined as the rounding radius at the crotch to the blunt radius at the leading edge. The primary flow features observed in the shock tunnel experiments are reproduced by the large-eddy simulations. The time-averaged flow structures in the crotch are clearly shown as counterrotating vortices originating from the collision of jets near the stagnation point. These jets and vortices undergo unsteady motions coupled with the dynamics of shock interactions. Of great interest, two typical global oscillations, i.e., swing oscillation and arch-recover oscillation corresponding to the two values of R, are identified. The coherent structures of the oscillations are analyzed using the proper orthogonal decomposition technique. It is demonstrated that the swing oscillation and arch-recover oscillation are characterized by an antisymmetric pattern and a symmetrical pattern, respectively. These two oscillations are also characterized by the energetic middle-frequency components of the broadband wall pressure spectra. Two feedback models are proposed for the prediction of such middle-frequency components. The results show that the swing oscillation causes much more severe pressure load, and the local impingement of the transmitted shock on the crotch is responsible for the peak value of the pressure fluctuation. This study illustrates that the geometry of R has a key impact on the unsteady shock interactions and, therefore, should be considered critically in practical applications, such as the cowl lip of a hypersonic inward-turning inlet.The unsteady dynamics of shock interactions on the crotch of two typical V-shaped blunt leading edges have been investigated numerically and experimentally with a freestream Mach number 6 for different ratios (R), defined as the rounding radius at the crotch to the blunt radius at the leading edge. The primary flow features observed in the shock tunnel experiments are reproduced by the large-eddy simulations. The time-averaged flow structures in the crotch are clearly shown as counterrotating vortices originating from the collision of jets near the stagnation point. These jets and vortices undergo unsteady motions coupled with the dynamics of shock interactions. Of great interest, two typical global oscillations, i.e., swing oscillation and arch-recover oscillation corresponding to the two values of R, are identified. The coherent structures of the oscillations are analyzed using the proper orthogonal decomposition technique. It is demonstrated that the swing oscillation and arch-recover oscillation are c...

A two-dimensional contraction channel with a theoretically designed concave-oblique-convex wall profile is proposed to obtain a smooth planar-to-planar shock transition with shock intensity amplification that can easily overcome the limitations of a conventional shock tube. The concave segment of the wall profile, which is carefully determined based on shock dynamics theory, transforms the shock shape from an initial plane into a cylindrical arc. Then the level of shock enhancement is mainly contributed by the cylindrical shock convergence within the following oblique segment, after which the cylindrical shock is again "bent" back into a planar shape through the third section of the shock dynamically designed convex segment. A typical example is presented with a combination of experimental and numerical methods, where the shape of transmitted shock is almost planar and the post-shock flow has no obvious reflected waves. A quantitative investigation shows that the difference between the designed and experimental transmitted shock intensities is merely 1.4%. Thanks to its advantage that the wall profile design is insensitive to initial shock strength variations and high-temperature gas effects, this method exhibits attractive potential as an efficient approach to a certain, controllable, extreme condition of a strong shock wave with relatively uniform flow behind.

Saturated vapor pressure was calculated from the nucleation experimental data using the thermodynamically consistent nucleation theory in which the effect of real gas is considered. The cubic polynomial fit equations of saturation pressure for several substances were obtained based on the calculation. The results of the calculations were compared to those of thermodynamic equilibrium equation and the empirical equation and applied to the predictions of the classical nucleation theory. The results show that the saturation pressures estimated from the nucleation data agree fairly well with those of empirical equations for the substances investigated, and this indicates that the predictions from the classical nucleation theory are close to the experimental data.

A curved wedge with a specific shape is designed and manufactured to guarantee the wedge angle unvaried during the cylindrically converging shock moving along the wedge. Thus the variation of the wedge angle caused by the wedge will be eliminated in unsteady shock reflection. Different initial wedge angles are considered to observe regular reflection and Mach reflection. When Mach reflection occurs, it is found that direct Mach reflection is persisted over the wedge without wave pattern transitions, which differs from our previous work with varied wedge angles [Zhang et al. “Reflection of cylindrical converging shock wave over a plane wedge,” Phys. Fluids 28, 086101 (2016)]. Moreover, the Mach stem is nearly straight when the wedge angle is relatively large, and the trajectory of triple point can be well predicted by three-shock theory. It is believed that the straight Mach stem results from the coupling effect of the converging shock and the convexly curved wedge, which exert opposite effects on the Mach stem curvature. As the wedge angle reduces, the three-shock theory prediction deviates from the present results owing to the curved Mach stem. Stronger vortices are produced near the wall, which are caused by the interaction of two shear layers, and whether the stronger vortices will be generated near the wall depends on the reflection number of the shock wave over the tube wall and wedge. The length of disturbed shock front in the Mach reflection is found to increase nonlinearly due to the unsteady feature of the flow. The growth rate of length reduces as the shock converges because of the geometrical contraction effect. Further the lengths of the Mach stem and the disturbed shock front are compared, and the results show that although the difference exists between them, both of them show a similar variation tendency. Compared with our previous work with varied wedge angles, the variation of the wedge angle has great effects on the Mach stem length and wave pattern transitions. It is believed that the differences between the present study and the pseudo-steady shock reflection are mainly induced by the unsteady feature of the flow because the variation of the shock Mach number is limited and the wedge angle is constant.A curved wedge with a specific shape is designed and manufactured to guarantee the wedge angle unvaried during the cylindrically converging shock moving along the wedge. Thus the variation of the wedge angle caused by the wedge will be eliminated in unsteady shock reflection. Different initial wedge angles are considered to observe regular reflection and Mach reflection. When Mach reflection occurs, it is found that direct Mach reflection is persisted over the wedge without wave pattern transitions, which differs from our previous work with varied wedge angles [Zhang et al. “Reflection of cylindrical converging shock wave over a plane wedge,” Phys. Fluids 28, 086101 (2016)]. Moreover, the Mach stem is nearly straight when the wedge angle is relatively large, and the trajectory of triple point can be well predicted by three-shock theory. It is believed that the straight Mach stem results from the coupling effect of the converging shock and the convexly curved wedge, which exert opposite effects on the Mach...

Refraction of a cylindrical converging shock wave at an inclined air/helium interface is investigated. Experimentally, based on the shock dynamics theory, a special wall profile is designed to generate a perfectly cylindrical converging shock wave. A soap film technique is developed to form an inclined discontinuous air/helium interface, and high-speed schlieren photography is adopted to capture the flow. Numerical simulations are also performed to compare with the experimental counterparts and to show details of refraction. In this work, two initial incident angles (45° and 60°) are considered. As the incident shock converges inward, the shock intensity increases while the incident angle decreases, causing possible transitions among the wave patterns. For the case of 45°, an irregular refraction of free precursor refraction (FPR) first occurs and gradually transits into regular refraction, while for the case of 60°, various irregular refractions of twin von Neumann refraction (TNR), twin regular refracti...

The cylindrical converging shock reflection over a plane wedge is investigated experimentally and numerically in a specially designed shock tube which converts a planar shock into a cylindrical one. When the converging shock is moving along the wedge, both the shock strength and the incident angle are changing, which provides the possibility for the wave transition. The results show that both regular reflection (RR) and Mach reflection (MR) are found on the wedge with different initial incident angles. The wave transitions from direct Mach reflection (DiMR) to inverse Mach reflection (InMR) and further to transitioned regular reflection (TRR) are observed with appropriate initial incident angles. The instability development in the shear layer and strong vortices formation near the wall are evident, which are ascribed not only to the interaction of two shear layers but also to the shock impact and the shock converging effect. Because of the flow unsteadiness after the converging shock, the detachment criterion provides a good estimation for the RR → MR transition, but fails to predict the DiMR → InMR transition, and MR is found to persist slightly below the mechanical equilibrium condition. A hysteresis process is found in the MR → TRR transition and becomes more apparent as the increase of the initial incident angle due to the shock converging effect.

We developed a new device that is capable of top-view optical examination of the coalescence of liquid drops. The device exhibits great potential for visualization, particularly for the early stage of liquid bridge expansion, owing to the use of a high-speed shadowgraph technique. The fluid densities of the two approaching drops and that of the ambient fluid are carefully selected to be negligibly different, which allows the size of the generated drops to be unlimitedly large in principle. The unique system design allows the point of coalescence between two drops to serve as an undisturbed optical pathway through which to image the coalescence process. The proposed technique extended the dimensionless initial finite radius of the liquid bridge to 0.001, in contrast to 0.01 obtained for conventional optical measurements. An examination of the growth of the bridge radius for a water and oil-tetrachloroethylene system provided results similar to Paulsen's power laws of the inertially limited viscous and inertial regimes. Furthermore, a miniscule shift in the center of the liquid bridge was detected at the point of crossover between the two regimes, which can be scarcely distinguished with conventional side-view techniques.

A shock tube facility for generating a cylindrical converging shock wave is developed in this work. Based on the shock dynamics theory, a specific wall profile is designed for the test section of the shock tube to transfer a planar shock into a cylindrical one. The shock front in the converging part obtained from experiment presents a perfect circular shape, which proves the feasibility and reliability of the method. The time variations of the shock strength obtained from numerical simulation, experiment, and theoretical estimation show the desired converging effect in the shock tube test section. Particular emphasis is then placed on the problem of shock-interface interaction induced by cylindrical converging shock waves. For this purpose, membrane-less gas cylinder is adopted to form the interface between two different fluids while the laser sheet technique to visualize the flow field. The result shows that it is convenient to perform such experiments in this facility.

The evolution of a spherical gas interface under reshock conditions is experimentally studied using the high-speed schlieren photography with high time resolutions. A number of experimental sets of helium or SF6 bubble surrounded by air for seven different end wall distances have been performed. Distinct flow structures are observed due to the additional vorticity and wave configuration caused by the reshock. In the air/helium case, the deformation of the reshocked bubble is dependent on the development of the penetrating air jet along the symmetry axis of the bubble. In general, two separate vortex rings can be observed, i.e., one develops slowly, and the other approaches and eventually impinges on the shock tube end wall. In the air/SF6 case, two SF6 jets moving in opposite directions are generated and the oscillation of the interface is observed for small end wall distances, while small scale vortex morphologies on the gas interface are found for large end wall distances. The physical mechanisms of the...

A simple but effective technique is proposed to generate cylindrical converging shock waves. The shock dynamics is employed to design a curved wall profile of the test section in a shock tube. When a planar shock wave propagates forward along the curved wall, the disturbances produced by the curved wall would continuously propagate along the shock surface and bend the shock wave. As an example, the wall profile for an incident shock Mach number of M0=1.2 and a converging angle of 15° is tested numerically and experimentally. Both numerical and experimental results show a perfect circular shock front, which validates our method.