Lateral Shock Waves Research Articles

Shock wave configuration in a transonic flow through a mid-section of a last stage turbine blade cascade equipped with a part-span connector

This paper deals with the study of a flow field and namely the configuration of shock waves in a blade cascade equipped with a part-span connector called tie-boss. The cascade consists of prismatic blades formed from the mid-section of a very long last-stage blade of a steam turbine. The study is based on numerical simulations of the flow through a cascade that was previously tested in a wind tunnel. Commercial software Ansys CFX was used for the simulations and Ansys ICEM for the mesh generation. The computational domain contains non-homogenous mesh interfaces. The simulations showed that the presence of the tie-boss has a profound effect on the configuration of the shock waves. The blade exit shock waves are disturbed and new lateral shock waves are introduced into the flow.

Free-surface undulation and velocity turbulence in shallow undular hydraulic jumps

Undular hydraulic jumps and bores occur in coastal and estuarial regions at small approach Froude numbers and introduce non-uniform evolution of hydraulic properties in the flow direction, affecting the transport and deposition of sediment and other materials. This paper reports an experimental study of relatively wide undular hydraulic jumps generated in a 1.4-m-wide flume, characterized by inflow aspect ratio less than 0.06 and no lateral shockwave crossing at the first standing wave crest. General free-surface shape observations were conducted for a range of Froude numbers between 1.5 and 2.9 and Reynolds numbers between 2.5 × 104 and 1.2 × 105, while detailed free-surface and velocity measurements were performed at longitudinal and transverse cross-sections using acoustic displacement meters (ADMs) and an acoustic Doppler velocimeter (ADV), at five Froude numbers from 1.5 to 1.9. The results highlight complicated relationship of the three-dimensional free-surface characteristics with the variation of Froude number, which exhibits different features at the first two waves and at other sequent waves. The velocity data highlighted unique features of turbulent velocity redistribution at the first wave, including the distributions of turbulence intensity and Reynolds shear stresses. Particular focus on the formation of a “quiet water” zone below the upward-deflected mainstream flow was reported, with presence of instantaneous reversing velocities above the channel bed. The flow pattern analysis was facilitated with mean vorticity characterization. The results reflect that the evolution of undular hydraulic jump with increasing Froude number is a process of gradual turbulence localization towards the first standing wave, and the transition to a breaking hydraulic jump is achieved by the formation of a surface roller at the steepened jump front overwhelming the “resistance” of the bottom “quiet water” zone and forcing a change in the main flow path.

Hydraulic Jump: A Brief History and Research Challenges

This paper presents a brief history of the hydraulic jump and a literature review on hydraulic jumps’ experimental and numerical studies. Leonardo da Vinci noticed this phenomenon early on, but it was only later studied by Bidone in 1820. Since the beginning of the 20th century, the hydraulic jump has received a lot of attention following the development of energy dissipater designs and stilling basins. The late 1920s and early 1930s saw many experimental studies researching the surface roller profile and energy dissipation. The study of internal flow features started in the late 1950s. Starting in the 70s, it was believed that the flow of a jump must be analyzed in its actual configuration of air–water mixture, an aspect that cannot be overlooked. Several experimental studies in the late 1980s and 1990s highlighted the existence of oscillating phenomena under specific flow conditions and particularly, a cyclic variation of jump types over long-lasting experiments. The early 2000s saw many experimental studies researching the complex structure of the separated region in very large channels downstream of the lateral shockwaves. Whereas most of the experiments provide measurements at a point or on a plane, the complete flow field supplied by CFD simulations enables us to have a deeper understanding of the dynamics of coherent structures that are responsible for free-surface fluctuations and aeration in hydraulic jumps. Therefore, in recent years, the computational fluid dynamics (CFD) method, through turbulence models, has become a useful tool to study this complex environmental fluid mechanic problem.

Influence of viscous boundary layer on initiation zone structure of two-dimensional oblique detonation wave

The influence of the viscous boundary layer on the oblique detonation wave structure has been simulated and analyzed by solving the two-dimensional Navier–Stokes equations containing the hydrogen/air elementary reaction model. It is found that the effect of the viscous boundary layer can be neglected in the smooth transition initiation structure, but not in the abrupt transition initiation structure. The interaction of the lateral shock wave and the viscous boundary layer results in the formation of a high-temperature recirculation zone near the wall of the initiation zone, a novel structure that does not appear in inviscid formulations. Within this structure, the chemical reaction is triggered to occur in advance, eventually leading to the equilibrium initiation position relocating upstream compared with the inviscid case. Nevertheless, the viscous boundary layer has a limited impact on the main flow region downstream of the oblique detonation. The shock wave structures and pressure distributions at various Mach numbers are obtained computationally and analyzed in detail.

Steep Bedload‐Laden Flows: Near Critical?

Steep gravel‐bed rivers sometimes experience floods that dramatically rework river bed structure and topography. Hazard assessments and paleo‐event reconstructions require better knowledge of such phenomena. This paper explores morphodynamic evolution of steep channels carrying bedload‐laden flows, using a generic Froude‐scaled model. Bedload‐laden floods were introduced in a narrow flume and spread into a 5 times wider unconfined area with a 0.1 steep slope (m/m). Image analysis enabled measurements taken at an unprecedented level of accuracy on unconfined flows laden with bedload. A flow reconstruction procedure was used to compute depth, Froude (Fr) and Shields (τ*) numbers on millions of pixels based on a friction law and measurements of surface velocity, slope, and roughness. Despite the steep slope, Froude numbers proved to be mostly subcritical in all but the regions experiencing the most active sediment transport. Competent flows, identified by the transport stage higher than unity ( ), were near critical and seldom had Fr> 1.3–1.5. This demonstrates that, providing that bed width and structure can adjust, hydraulic features such as standing waves, hydraulic jumps, and lateral shock waves dissipate energy very efficiently in addition to adjusting channel features. These competent flows also tend to rework channels to approach the energy minimum of near‐critical flows. This hypothesis was postulated by Gordon Grant (1997, https://doi.org/10.1029/96WR03134, Wat. Resour. Res. 33(2):349‐358) but demonstrated here for the first time at this scale. Considering near‐critical flows during discharges high enough to be clearly competent in laterally unconfined reaches seems reasonable as a first approximation in steep channels.

Undular hydraulic jump formation and energy loss in a flow through emergent vegetation of varying thickness and density

Floods resulting from extreme events like tsunamis may inundate widespread inland areas, but vegetation can act as a natural buffer zone to reduce the inundation area and dissipate the energy of flowing water. This paper summarizes a series of laboratory experiments in which the energy loss through emergent vegetation in a steady subcritical flow was investigated. The energy loss was determined against vegetation of variable thickness (dn, where d = diameter of cylinder, n = number of cylinders in a stream-wise direction per unit of cross-stream width), density (G/d, where G = spacing of each cylinder in cross-stream direction, d = diameter of cylinder), and initial Froude number. On the upstream side of vegetation, the backwater rise increased by increasing both vegetation thickness and density. Contrarily, on the downstream side a breaking undular jump with a lateral shock wave was observed for a dense vegetation arrangement (G/d = 0.25), whereas a non-breaking undular jump with and without air bubbles was identified for intermediate (G/d = 1.09) and sparse (G/d = 2.13) vegetation conditions, respectively. Under these conditions, the maximum energy reduction due to a jump reached 6.4% for dense vegetation, and was reduced to 1.7% and 1.4% for intermediate and sparse vegetations, respectively. Hence, denser vegetation offers larger resistance, thus causes significant energy loss.

3D SPH modelling of hydraulic jump in a very large channel

The formation of different undular hydraulic jumps in a very large channel is investigated and reproduced using a weakly-compressible XSPH scheme which includes a mixing-length turbulence model. An analysis of the ability and of the limits of the SPH method to reproduce undular hydraulic jumps is preliminarily performed on reference two-dimensional cases. The numerical description of the three-dimensional jump in a very large channel, where the hydraulic-jump front is trapezoidal and the lateral shock waves induce a large recirculation region along the side walls, is compared with experiments in a laboratory flume on two undular jumps at upstream Froude number equal to 3.9 and 8.3. Acoustic Doppler velocity measurements were compared with SPH instantaneous and time-averaged flow fields in order to evaluate whether the numerical method could help in having a clearer understanding of both hydraulic-jump development and lateral shockwave formation. The predicted free-surface elevations and velocity profiles show a satisfactory agreement with measurements and most of the peculiar features of the flow, such as the trapezoidal shape of the wave front and the flow separations at the toe of the oblique shock wave along the side walls, are qualitatively and quantitatively reproduced.

Considerations on shock wave/boundary layer interaction in undular hydraulic jumps in horizontal channels with a very high aspect ratio

It can be seen in the literature that the fundamental factors governing oblique shock wave development, typically in very large channels with straight sidewalls, have not yet been completely understood and remain at the level of indicating its presence and formation. In this study, in addition to an analysis of various properties of hydraulic jump behaviour in very large channels, some aspects of boundary layer development and its detachment from the channel lateral sidewall are also investigated. At the detachment point of the lateral shock waves, it was noted that the displacement thickness experiences a significant increase; this is accompanied by a significantly reduced gradient normal to the channel sidewalls of the flow velocity as well as the occurrence of a strong, sudden adverse pressure gradient. An analysis of the flow velocity distribution and the background turbulence intensity of both the streamwise and spanwise velocity components was also carried out. Furthermore, it is argued that the supersonic flow separation analogy with a supercritical free surface flow can be applied to this case study and that the behaviour of the supercritical flow during separation can be interpreted by the free interaction theory typically used in aerodynamics.

Experimental study of recirculating flows generated by lateral shock waves in very large channels

Due to the lack of data on hydraulic-jump dynamics in very large channels, the present paper describes the main characteristics of the velocity field and turbulence in a large rectangular channel with a width of 4 m. Although a hydraulic jump is always treated as a wave that is transversal to the channel wall, in the case of this study it has a trapezoidal front shape, first starting from a point at the sidewalls and then developing downstream in an oblique manner, finally giving rise to a trapezoidal shape. The oblique wave front may be regarded as a lateral shockwave that arises from a perturbation at a certain point of the lateral wall and travels obliquely toward the centreline of the channel. The experimental work was carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). In addition to the hydraulic jump formation, a large recirculating flow zone starts to develop from the separating point of the lateral shock wave and a separate boundary layer occurs. Intensive measurements of the streamwise and spanwise flow velocity components along one-half width of the channel were taken using a bidimensional Acoustic Doppler Velocimeter (ADV). The water surface elevation was obtained by means of an ultrasonic profiler. Velocity vectors, transversal velocity profiles, turbulence intensities and Reynolds shear stresses were all investigated. The experimental results of the separated boundary layer were compared with numerical predictions and related work presented in literature and showed good agreement. The transversal velocity profiles indicated the presence of adverse pressure gradient zones and the law of the wall appears to govern the region around the separated boundary layer.

Analysis of the velocity field in a large rectangular channel with lateral shockwave

In this work the authors describe the main characteristics of the velocity field of hydraulic jumps in a very large channel where lateral shockwaves occur. Experiments were carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). Extensive flow velocity measurements were investigated in order to have a clearer understanding of both hydraulic jump development and lateral shockwave formation in a very large channel. Eight experiments were performed in a 4m wide rectangular channel; the experiments differed in the inlet Froude number F0 and the jump type. Seven tests were carried out with undular jumps and one with a roller jump. The flow velocity and the flow free surface measurements were taken using a two-dimensional Acoustic Doppler Velocimeter (ADV) and an ultrasonic profiler, respectively. The experimental results can be summarized as follow: (i) the formation of well developed lateral shockwaves similar to those of oblique jumps were observed; (ii) the comparison of the experimental and theoretical data shows that the classic shockwave theory is sufficiently confirmed in the analyzed range of Reynolds number, taking into account the experimental errors and the difference between the theoretical and experimental assumptions; (iii) the transversal flow velocity profiles in the recirculating zone show a good agreement with the numerical simulations presented in literature in the case of a separated turbulent boundary layer over a flat plate. This conclusion enables us to confirm the hypothesis that the lateral shockwaves in the channel are the result of a boundary layer which, as observed, forms on the channel sidewalls.

Flow Conditions of Undular Hydraulic Jumps in Horizontal Rectangular Channels

The flow conditions of undular jumps for fully developed inflow condition have been investigated systematically. If the inflow Froude number is larger than 1.2, an undular jump has lateral shock waves near the toe of the jump. For a narrow channel, the shock waves cross upstream of the first wave crest, and the flow conditions of undular jumps depend on the aspect ratio and the inflow Froude number. In contrast, for a wide channel the shock waves do not cross upstream of the first wave crest, and the flow conditions of undular jumps are independent of the aspect ratio. The flow conditions of undular jumps are classified by considering the cross position of the lateral shock waves and the inflow Froude number. Also, the hydraulic conditions for the formation of nonbreaking and breaking undular jumps are determined. The effect of the Reynolds number on undular-jump formations is discussed, and changes of the flow conditions with the Reynolds number are described.

A model for radio source expansion

We present a theoretical model for the propagation of extragalactic jets, taking into account the detailed expansion of the lobe surrounding the jet. Numerical simulations of hydrodynamic supersonic jets have been carried out and different features of the jet propagation not present in most analytical treatments are incorporated into the model. In particular, we describe the pressure gradient inside the lobes and point out its implications in face of the suggestions that the lateral shock wave would be responsible for the optical emission and the triggering of star formation in the neighborhood of compact radio sources. The numerical simulations are also used to test the validity of the model. This procedure is expected to improve our description of the jet propagation phenomenon.

階段状開水路流れにおける三次元波状跳水の内部構造

Characteristics of separated shear layer due to a backward facing step, newly developed boundary-layer after the reattachment point and an undular hydraulic jump have been investigated experimentally to clarify the turbulent flow structure and energy dissipation mechanism of stepped steep open chan el. Flow measurements were conducted byusing particle image velocimetry (PIV), a high-resolution camera with 15fps (frame per second) and hot film anemometry. In this paper, authors discussed the three-dimensional turbulent flow structure, dynamic pressure distribution and bed shear stress in the stepped open channel with the undular hydraulic jump, which was generated by interaction between lateral shock waves propagating from sidewall. The upstream Froude numbers were 1.42, the Reynolds number based on step height were about 12500.

Characteristics of Undular Hydraulic Jumps: Experiments and Analysis

The writers measured velocity, pressure and energy distributions, wavelengths, and wave amplitudes along undular jumps in a smooth rectangular channel 0.25 m wide. In each case the upstream flow was a fully developed shear flow. Analysis of the data shows that the jump has strong three-dimensional features and that the aspect ratio of the channel is an important parameter. Energy dissipation on the centerline is far from negligible and is largely constrained to the reach between the start of the lateral shock waves and the first wave crest of the jump, in which the boundary layer develops under a strong adverse pressure gradient. A Boussinesq-type solution of the free-surface profile, velocity, and energy and pressure distributions is developed and compared with the data. Limitations of the two-dimensional analysis are discussed.

Characteristics of Undular Hydraulic Jumps: Experimental Apparatus and Flow Patterns

In open channels, the transition from supercritical to subcritical flows is called a hydraulic jump. For low upstream Froude numbers, free-surface undulations develop downstream of the jump and the hydraulic jump is called an undular jump. New experiments on undular hydraulic jumps were performed in a rectangular channel in which the upstream flows were fully developed turbulent shear flows. In this paper, the main flow patterns are described. Visual and photographic observations indicate five types of undular jumps. One of the main flow characteristics is the presence of lateral shock waves for Froude numbers larger than 1.2. The results show that the disappearance of undular jump occurs for Froude numbers ranging from 1.5 to 2.9, and the wavelength and amplitude of free-surface undulations are functions of the upstream Froude number and the aspect ratio y c /W.