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![Structure of the flow in the first "barrel" of a sonic underexpanded jet: (a) the flow diagram, according to [1-8]; (b) the flow diagram, according to [9-13]; (c) a flow diagram illustrating the barrelshock formation mechanism, according to [2-5,8]; (d) a flow diagram illustrating the barrel-shock formation mechanism, according to [10].](publication/361992981/figure/fig1/AS:1182556565315584@1658954864123/Structure-of-the-flow-in-the-first-barrel-of-a-sonic-underexpanded-jet-a-the-flow.png)
Structure of the flow in the first "barrel" of a sonic underexpanded jet: (a) the flow diagram, according to [1-8]; (b) the flow diagram, according to [9-13]; (c) a flow diagram illustrating the barrelshock formation mechanism, according to [2-5,8]; (d) a flow diagram illustrating the barrel-shock formation mechanism, according to [10].
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Using the example of studying the supersonic underexpanded jet initial section, the issue of interpreting the experimental visualization data and Pitot pressure measurement data using the results of numerical calculations (2d RANS k-ω SST) is discussed. It is shown that the gradient S-shaped feature of the gas-dynamic structure near the nozzle exit...
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... example, in [1][2][3][4][5][6][7][8], in the diagram of the initial section of an axisymmetric sonic underexpanded jet, it is shown that the barrel shock is formed directly at the nozzle exit. Figure 1a shows a flow diagram illustrating the flow structure in the first "barrel", according to those works. ...
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... the other hand, in [9][10][11][12][13], it was shown that the barrel shock forms at some distance from the nozzle exit. Figure 1b shows such a flow diagram. Here, the character I denotes the point of origin of the barrel shock. ...
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... to [2][3][4][5]10], the barrel shock forms when the characteristics of the fan of expansion waves originating at the nozzle edge (indicated as point N) undergo reflection from the concave external boundary of the jet flow in the form of a compression fan (Figure 1c). At the intersection of the reflected characteristics, there forms a barrel shock. ...
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... was noted that, in the flow patterns that were observed near the nozzle exit, the expansion fan gave rise to a high-gradient flow structure that was bound by the trailing edge of the fan. It should be noted that the diagram in Figure 1d differs from the diagram in Figure 1c that is shown in the same figure: for flow characteristics that emerge from the point NO to reach the opposite boundary of the jet flow, it is necessary that barrel shock is absent near the nozzle exit. ...
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... was noted that, in the flow patterns that were observed near the nozzle exit, the expansion fan gave rise to a high-gradient flow structure that was bound by the trailing edge of the fan. It should be noted that the diagram in Figure 1d differs from the diagram in Figure 1c that is shown in the same figure: for flow characteristics that emerge from the point NO to reach the opposite boundary of the jet flow, it is necessary that barrel shock is absent near the nozzle exit. ...
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... (b) (c) (d) Figure 1. Structure of the flow in the first "barrel" of a sonic underexpanded jet: (a) the flow diagram, according to [1][2][3][4][5][6][7][8]; (b) the flow diagram, according to [9][10][11][12][13]; (c) a flow diagram illustrating the barrel-shock formation mechanism, according to [2][3][4][5]8]; (d) a flow diagram illustrating the barrel-shock formation mechanism, according to [10]. ...
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... barrel shock, the reflected shock, and the Mach disk; as well as the outer boundary of the jet, or the mixing layer; and the contact discontinuity, or the slip line that emerge from the triple point of intersection of the shocks are distinctly seen. It can be noted here that in all these photographs, the observed thin dark line G, or the gradient flow feature, looks precisely like a barrel shock that reaches the nozzle edge, in the same way that it occurs in the diagram of Figure 1a. ...
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... barrel shock, the reflected shock, and the Mach disk; as well as the outer boundary of the jet, or the mixing layer; and the contact discontinuity, or the slip line that emerge from the triple point of intersection of the shocks are distinctly seen. It can be noted here that in all these photographs, the observed thin dark line G, or the gradient flow feature, looks precisely like a barrel shock that reaches the nozzle edge, in the same way that it occurs in the diagram of Figure 1a. ...
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... photograph in Figure 2c also provides a good illustration of the physical mechanism of formation of the barrel shock that is shown in the diagrams of Figure 1, with the flow characteristics being very weak nozzle shocks extending from the inner surface of the nozzle. The main difference between the photograph and the diagram of Figure 1c is that here, the characteristics do not emerge from the region N; instead, they emerge from the region that is located at the opposite edge NO of the nozzle, in the same way it is shown in Figure 1d. ...
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... photograph in Figure 2c also provides a good illustration of the physical mechanism of formation of the barrel shock that is shown in the diagrams of Figure 1, with the flow characteristics being very weak nozzle shocks extending from the inner surface of the nozzle. The main difference between the photograph and the diagram of Figure 1c is that here, the characteristics do not emerge from the region N; instead, they emerge from the region that is located at the opposite edge NO of the nozzle, in the same way it is shown in Figure 1d. Moreover, in the photograph of Figure 2d one can notice longitudinal stripes, interpreted as longitudinal vortices that are formed in the mixing layer of the jet due to Taylor-Goertler instability [6]. Figure 2. Visualization of the flow in an underexpanded jet ejected out of a sonic convergent nozzle with Ma = 1.0 at flow regimes with n = 3.8 (a) and n = 8.2 (b); and out of a supersonic nozzle with Ma = 2.0 at flow regimes with n = 2 (c) and n = 160 (d). ...
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... photograph in Figure 2c also provides a good illustration of the physical mechanism of formation of the barrel shock that is shown in the diagrams of Figure 1, with the flow characteristics being very weak nozzle shocks extending from the inner surface of the nozzle. The main difference between the photograph and the diagram of Figure 1c is that here, the characteristics do not emerge from the region N; instead, they emerge from the region that is located at the opposite edge NO of the nozzle, in the same way it is shown in Figure 1d. Moreover, in the photograph of Figure 2d one can notice longitudinal stripes, interpreted as longitudinal vortices that are formed in the mixing layer of the jet due to Taylor-Goertler instability [6]. Figure 2. Visualization of the flow in an underexpanded jet ejected out of a sonic convergent nozzle with Ma = 1.0 at flow regimes with n = 3.8 (a) and n = 8.2 (b); and out of a supersonic nozzle with Ma = 2.0 at flow regimes with n = 2 (c) and n = 160 (d). ...
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... photograph in Figure 2c also provides a good illustration of the physical mechanism of formation of the barrel shock that is shown in the diagrams of Figure 1, with the flow characteristics being very weak nozzle shocks extending from the inner surface of the nozzle. The main difference between the photograph and the diagram of Figure 1c is that here, the characteristics do not emerge from the region N; instead, they emerge from the region that is located at the opposite edge NO of the nozzle, in the same way it is shown in Figure 1d. ...
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... photograph in Figure 2c also provides a good illustration of the physical mechanism of formation of the barrel shock that is shown in the diagrams of Figure 1, with the flow characteristics being very weak nozzle shocks extending from the inner surface of the nozzle. The main difference between the photograph and the diagram of Figure 1c is that here, the characteristics do not emerge from the region N; instead, they emerge from the region that is located at the opposite edge NO of the nozzle, in the same way it is shown in Figure 1d. Moreover, in the photograph of Figure 2d one can notice longitudinal stripes, interpreted as longitudinal vortices that are formed in the mixing layer of the jet due to Taylor-Goertler instability [6]. ...
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... photograph in Figure 2c also provides a good illustration of the physical mechanism of formation of the barrel shock that is shown in the diagrams of Figure 1, with the flow characteristics being very weak nozzle shocks extending from the inner surface of the nozzle. The main difference between the photograph and the diagram of Figure 1c is that here, the characteristics do not emerge from the region N; instead, they emerge from the region that is located at the opposite edge NO of the nozzle, in the same way it is shown in Figure 1d. Moreover, in the photograph of Figure 2d one can notice longitudinal stripes, interpreted as longitudinal vortices that are formed in the mixing layer of the jet due to Taylor-Goertler instability [6]. ...
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... feature looks like a barrel shock that has already formed directly near the nozzle exit. At the same time, the numerical visualization is more consistent with the diagram of Figure 1d, where the fan trailing edge is observed near the nozzle exit, and only later a barrel shock forms. This difference needs to be clarified. ...
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... feature looks like a barrel shock that has already formed directly near the nozzle exit. At the same time, the numerical visualization is more consistent with the diagram of Figure 1d, where the fan trailing edge is observed near the nozzle exit, and only later a barrel shock forms. This difference needs to be clarified. ...
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... example, it is assumed that the cause of the curvature may be an effect similar to that which is observed in the flow behind the aft cut of the cone [27,28]. The curvature of the shock near the nozzle exit is associated with the influence of the boundary layer on the inner wall of the nozzle, in which the fan of expansion waves near the point N(I), Figure 1c, is not centered. This interpretation does not contradict the interpretation of the sounding results (Figure 7) and requires further clarification. ...
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... circle marks the gradient feature G of the flow, whose position in space is shown in Figure 7. According to the diagram of Figure 1d, in Figure 6b-d this flow feature G can be interpreted as the trailing edge of the expansion fan, separating out the expansion fan from the compression fan. In Figure 7f, this feature corresponds to a barrel shock. ...
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... process of formation of the barrel shock can be traced, considering Figures 10 and 11. Figure 10a shows the distribution of Mach-number isolines in the region of the first jet barrel. ...
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... process of formation of the barrel shock can be traced, considering Figures 10 and 11. Figure 10a shows the distribution of Mach-number isolines in the region of the first jet barrel. The solid black lines show the characteristics in the supersonic flow region. ...
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... to the numerical calculation, the shock formation region (point I in the figure) is located at a distance from nozzle exit x/Ra~1.7. A closer examination of an instantaneous shadowgraph picture taken at 4-µs exposure (see Figure 10b) shows that the barrel shock becomes visible starting from distances x/Ra > 1.5. Three characteristic streamlines L1-L3 are shown in gray color. ...
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... should be noted here that, according to the calculated data, when crossing the feature G, the streamlines L1-L3 behave differently: the streamline L2 retains its direction, whereas the streamline L3 abruptly changes its direction, this circumstance indicating the absence of a shock near the nozzle exit and the presence a shock near the Mach disk. The CFD distributions of static pressure are shown in Figure 11. ...
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... (b) Figure 11. The passage of the streamlines through the region occupied by the compression waves: the distribution of pressure isolines in the regions of the first barrel (a) and the distribution of pressure along the streamlines (b). Figure 11a shows the isolines of the relative static pressure p/pe near the nozzle exit in the first barrel of the jet. ...
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... passage of the streamlines through the region occupied by the compression waves: the distribution of pressure isolines in the regions of the first barrel (a) and the distribution of pressure along the streamlines (b). Figure 11a shows the isolines of the relative static pressure p/pe near the nozzle exit in the first barrel of the jet. For the convenience of a flow analysis, the isolines in the interval of p/pe-values ranging from 0 to 1 (up to the pressure in the region of the stationary gas surrounding the jet) are shown. ...
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... to the numerical calculation, the shock formation region (point I in the figure) is located at a distance from nozzle exit x/R a ~1.7. A closer examination of an instantaneous shadowgraph picture taken at 4-µs exposure (see Figure 10b) shows that the barrel shock becomes visible starting from distances x/R a > 1.5. Three characteristic streamlines L 1 -L 3 are shown in gray color. ...
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... CFD distributions of static pressure are shown in Figure 11. Figure 11a shows the isolines of the relative static pressure p/p e near the nozzle exit in the first barrel of the jet. ...
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... CFD distributions of static pressure are shown in Figure 11. Figure 11a shows the isolines of the relative static pressure p/p e near the nozzle exit in the first barrel of the jet. For the convenience of a flow analysis, the isolines in the interval of p/p e -values ranging from 0 to 1 (up to the pressure in the region of the stationary gas surrounding the jet) are shown. ...
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... similar increase in the pressure along the streamline L 3 between the barrel and reflected shocks amounts to 0.2 to 0.5 of p/p e . The variation of pressure along these streamlines as a function of the distance to the nozzle exit is shown in Figure 11b. The main elements of the structure, such as the expansion and compression waves, and the barrel and reflected shocks, can be traced here. ...
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... results that are presented above allow us to conclude that the gradient flow nonuniformity G that is observed in the experimental photographs in the form of a solid line near the nozzle exit is a characteristic (called in [12] the fan trailing edge) separating out the rarefaction and compression regions, and at some distance from the nozzle exit this feature transforms into a barrel shock. The performed analysis well agrees with the diagram of Figure 1d. ...
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... reason for the S-bending of the gradient line G (like that in Figure 2) can be explained considering Figure 12, which shows the structure of an axisymmetric (upper half of the figure) and a flat two-dimensional (lower half of the figure) jet with M a = 1 and n = 2.64. The density isolines are shown here in gray, and the characteristics, in black. ...
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... the transverse size of the axisymmetric jet is much smaller than that of the plane jet. This is because, in a plane jet, the flow expands in an expansion fan (similarly to the Prandtl-Meyer flow), whereas in an axisymmetric jet, an additional expansion of the flow occurs due to the increase in its azimuthal size ( Figure 12 shows an explanatory diagram, located on the right). In this case, the pressure p e is attained earlier, causing a smaller transverse size (diameter) of the axisymmetric jet. ...
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... feature transforms into a barrel shock. The performed analysis well agrees with the diagram of Figure 1d. ...
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... reason for the S-bending of the gradient line G (like that in Figure 2) can be explained considering Figure 12, which shows the structure of an axisymmetric (upper half of the figure) and a flat two-dimensional (lower half of the figure) jet with Ma = 1 and n = 2.64. The density isolines are shown here in gray, and the characteristics, in black. ...
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... the transverse size of the axisymmetric jet is much smaller than that of the plane jet. This is because, in a plane jet, the flow expands in an expansion fan (similarly to the Prandtl-Meyer flow), whereas in an axisymmetric jet, an additional expansion of the flow occurs due to the increase in its azimuthal size ( Figure 12 shows an explanatory diagram, located on the right). In this case, the pressure pe is attained earlier, causing a smaller transverse size (diameter) of the axisymmetric jet. ...
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... This shock is incident into the axis of the flow, and its slope and intensity continuously increase as the shock approaches the axis. Thus, regular reflection from the axis of flow is not possible and the appearance of Mach shock configurations appears as shown in Figure 1.2 [15,16]. This non-desirable aerodynamics phenomenon results in the deterioration of the dynamic characteristics of the gas flow. ...
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This study investigates and discusses the performance of the thermal cutting process through the assessment of gas flow dynamics inside the kerf geometry. The flow dynamics of the highspeed gas passing through a nozzle during the process of thermal cutting play an important role in affecting the cutting performance. However, the gas flow dynamics are greatly influenced by the shape of the cut kerf, and the cut kerf geometry is affected by the varying operating conditions. This study is focused on understanding the effects of thermal cutting process parameters on the kerf geometry and the study of gas flow dynamics inside various kerf geometries through computational fluid dynamics (CFD) and the Schlieren method.
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