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(Mach rings) [ ] - stationary repeating wave formations in a supersonic jet of gases emanating from the nozzles of turbojet, ramjet and rocket engines. Mach disks become visible when fuel burns outside the engine. In a turbojet engine this is possible when the afterburner is turned on.

Education mechanism

Mach disks are formed in a supersonic jet of outgoing gases, the pressure of which at the nozzle exit is slightly higher or lower than atmospheric pressure. At the exit from the nozzle, atmospheric pressure expands/compresses the under-expanded/over-expanded gas stream, which leads to a change in the direction of movement of the outer layers of gas from axial to radial. A change in the direction of a supersonic gas flow occurs on oblique shock waves. Where the direction of gas flow again becomes parallel to the central line of flow, the first direct shock wave is located. A jet of gases passing through a direct compression shock heats up and ignites unburned fuel, making the first Mach disk visible. The luminous area may be disk or diamond shaped. The distance from the nozzle exit to the first Mach disk can be approximately determined by the following formula:

x = 0.67 D 0 P 0 P 1 (\displaystyle x=0.67D_(0)(\sqrt (\frac (P_(0))(P_(1))))),

where D 0 is the nozzle exit diameter,

P 0 - flow pressure at the nozzle exit,

When passing through a direct compression shock in the Mach disk, the gas pressure can become higher than atmospheric pressure. The expansion process then repeats with the final formation of the next Mach disk. This periodic compression/expansion process would be endless if not for the effect of gas viscosity on damping pressure fluctuations.

A supersonic jet has a periodic structure consisting of repeating barrel-shaped cells. If the jet non-design, which is defined as the ratio of the pressure at the exit of the supersonic nozzle to the pressure in the environment, differs significantly from unity, then direct shock waves, called Mach disks, become clearly visible in the shock wave structure of the jet. The Mach disk has significant dimensions only in the first barrel of the jet and sometimes in the second. However, its presence strongly influences the downstream geometry of the jet. Failures in developing methods for calculating jets, as a rule, are largely associated with the inability to find the position of the Mach disk. On the other hand, the flow in the vicinity of the Mach disk is characterized by large pressure gradients and strong viscous-inviscid interaction. In rocket engine jets in regions beyond the Mach disks, combustion and dissociation reactions occur, which leads to a significant increase in temperature, pressure and radiant flux. Despite the practical importance of the problem, a complete theory of the formation of a Mach disk in a supersonic jet is still missing. Below we present the necessary information about triple configurations of shock waves, a description of the “stationary Mach configuration” model, as well as a rationale for its application to the problem of calculating the Mach disk in a supersonic ideal gas jet.

triple point.

triple shock wave configuration

stationary Mach configuration

irregular reflection of jump

regular reflection of the jump

Mach leg

Mach disk

1. Gas dynamics of supersonic non-isobaric jets / V.S. Avduevsky, E.A. Ashratov, A.V. Ivanov, U.G. Pirumov. - M.: Mechanical Engineering, 1989. - 320 p.

2. Belyaev N.M., Karteshkin V.A. Study of the parameters of a sonic underexpanded jet of cold gas. - Dnepropetrovsk: DSU, 1982. - 14 p.

3. Bulat P.V., Zasukhin O.N., Uskov V.N. Formation of a jet during a smooth launch of a Laval nozzle // Gas dynamics and heat transfer. Vol. 10. Gas flows in channels and jets. - St. Petersburg: SPU Publishing House, 1993. - P. 1-22.

4. Melnikov D.A. Reflection of shock waves from the axis of symmetry // Mechanics and mechanical engineering. - 1962. - No. 3. Ed. Academy of Sciences of the USSR.

5. Interference of stationary gas-dynamic discontinuities / V.N. Uskov and others - Novosibirsk: VO "Science", 1995. - 180 p.

6. Uskov V.N. Interference of stationary gas-dynamic discontinuities. Supersonic gas jets. - Novosibirsk: Science, 1983. - P. 82-96.

7. Abbett M.J., Mach Disk in Underexpanded Exhaust Plumes // AIAA Journal. - 1971. - Vol.9, March. - R. 512-514.

8. Dash S.M. Seiner J.M., Wolf D.E. Analysis of Turbulent underexpanded Jets. Part. 1: Parabolized Navier Stokes Model, SCIPVIS // AIAA J. - 1985. - vol. 23, 23, April. - R. 505-514.

9. Dash S.M. Seiner J.M., Wolf D.E. Analysis of Turbulent underexpanded Jets. Part. 2: Parabolized Navier Stokes Model, SCIPVIS // AIAA J. - 1985. - vol. 23, 23, May.

10. Dash S.M. Thorpe R.D. Shock - Capturing Model of One- and Two-Phase Supersonic Exhaust Flow // AIAA J. - July 1981. - vol. 19. - R. 842-851.

11. Dash S.M., Sinha N. Noninteractive Cross - Flow integration Procedure for the Pressure - Split Analysis of two Dimensional, Subsonic Mixin Problems // AIAA J. - 1985. - vol. 23, Jan. - R. 183-185.

12. Dash S.M., Sinha N., York B.J. Implicit/Explicit Analysis of Interactive Phenomena in Supersonic Chemically - Reaching Mixing and Boundary Layer Problems // AIAA paper 8517, 17 July 1985.

13. Dash S.M., Wolf D.E. Interactiv Phenomena in Supersonic Jet Mixin Problems, Part. 1. - AIAA J. - May 1984. - R. 905-913.

14. Dash S.M., Wolf D.E., Pergament H.S. A Chock-Capturing Model for Two - Phase, Chemically reaching Flow in Rocket Nozzles and Diffusers, - AIAA R. 85-0.

15. Jungowski W.M. On flow in suddelargement of a duct. Fluid dynamic. - 1969. - vol. 4. - R. 231-241.

Supersonic jet (Fig. 1) In the general case, the outflow from the nozzle of an aircraft moving at a certain speed is a set of shock waves, surfaces of tangential velocity discontinuities and smooth flow regions. The presence of bottom rarefaction in region 1, compression waves 3, 7 arising as a result of the interaction of the jet with the supersonic co-flow 2, mixing layers 4, 9, 10 formed at tangential discontinuities lead to the formation of a complex shock wave structure (SWS) of the jet. It consists of rarefaction waves 4, 6 and shock waves. The incident shock 5 is always reflected from the axis with the formation of a triple configuration of shock waves or, as they also say, a triple point. The direct shock at the triple point is called a Mach disk or Mach disk, and shock 8 is called a reflected shock.

It should be noted that as the incident shock approaches the axis of symmetry, its curvature TOσ tends to infinity, because TO σ ~y-1, therefore, conditions for the formation of a Mach disk in an off-design jet are always created. This fact corresponds to what is known from the works of D.A. Melnikov. (1962) the position about the impossibility of regular reflection of the shock wave from the axis of symmetry, which is also indicated conditions of dynamic compatibility(UDS) at shock waves. On the axis of symmetry, the conditions must be satisfied that the angle of inclination of the velocity vector and the curvature of the streamline behind the reflected shock are equal to zero, but at y= 0 this is impossible.

Rice. 1. Supersonic flow around the bottom of an aircraft: 1 - bottom area; 2 - cocurrent flow; 3 - tail jump; 4 - current dividing line; 5 - hanging jump; 6 - subsonic region of the mixing layer; 7 - compression waves and closing shock; 8 - reflected shock; 9 - mixing region behind the Mach disk; 10 - mixing layer at the jet boundary

Models of Mach disk formation - history of study

Let us dwell in more detail on the question of the position of the Mach disk in the jet. The Mach disk has noticeable dimensions only in the first barrel and sometimes in the second. However, its presence strongly influences the downstream geometry of the jet.

Failures in developing methods for calculating jets, as a rule, are largely associated with the inability to find the position of the Mach disk. A detailed analysis of this issue was carried out in, where various hypotheses of the transition from regular reflection of the shock wave from the axis to irregular (Mach) reflection available in the literature are discussed. The most famous of them is the so-called Abbett procedure, often mentioned in the famous works of Dash, devoted to the construction of a method for calculating the engine flame of a solid propellant tactical missile, as well as various assumptions about the value of pressure behind the reflected shock at the triple point. We will not consider the latter, because... Today it is already known that they are not applicable in the general case.

Abbet's procedure establishes some analogy between the Mach disk in the jet and the launch shock wave (PSW) that occurs when the Laval nozzle is launched. It was initially assumed that in the minimum cross section of the flow behind the Mach disk the pressure is equal to atmospheric pressure. Later it turned out that this assumption is approximately satisfied only in strongly underexpanded jets, in which a turbulent section begins immediately after the first barrel. In jets of small miscalculation, Abbet's hypothesis leads to too large errors.

Abbett's hypothesis was modernized by Dash, who assumed that in the critical section behind the Mach disk the “flow throat” condition is satisfied, i.e. the flow speed becomes equal to the local speed of sound. If you specify the position of the triple point on the falling shock, then the initial conditions for calculating the flow limited by the Mach disk and the tangential discontinuity are determined. Considering this flow to be one-dimensional, one can perform the calculation in the same way as in a Laval nozzle. If, as a result of the calculation, in the minimum section of the flow behind the Mach disk the speed is equal to the local speed of sound, then in the Abbett-Dash procedure it is assumed that the position of the Mach disk in the jet is chosen correctly.

Among other models, the experimentally described criterion is well confirmed, according to which the formation of a Mach disk occurs when the intensity of the incident shock reaches the value J = J 0 corresponding stationary Mach configuration(SMK) . Such configurations of shock waves have been studied in detail in connection with the problem of the reflection of a shock wave from a solid wall.
The J 0 criterion is indirectly substantiated by solving the first-order problem of triple configurations of shock waves (shocks). If at each point of a hanging shock (falling on the axis of symmetry) a formal calculation is made of the triple configuration of shock waves, then at intensities J< J 0 the outgoing tangential discontinuity τ has positive curvature. At the jump point, where J = J 0, the curvature τ becomes negative, which corresponds to the established empirical ideas about the shape of the tangential discontinuity.

Brief information from the theory of triple shock configurations

A triple configuration (TC) of shock waves (shocks) is a shock wave structure consisting of three fronts of shock waves σ intersecting on a certain line and the surface of a tangential discontinuity τ emanating from this line (Fig. 2), σ 1 is called an incoming shock, σ 2 - outgoing, σ With - main shock wave.

Rice. 2. Triple shock wave configuration

Triple configurations occur during irregular reflection of a shock from a solid surface and from the axis of symmetry in axisymmetric flows, in some problems about the interaction of counter shocks, as well as during the interaction of overtaking shocks. The concept of a TC was first introduced in the problem of a shock wave impinging on a wedge. As it propagates along the wedge, the intensity of the oncoming wave increases, and its surface becomes curved, remaining perpendicular to the surface of the wedge. Starting from a certain moment, the shock wave branches with the formation Mach's legs.

Later, the stationary case of reflection of a shock from a solid wall was studied. When the intensity of the shock incident on the wall is low, it is reflected from the wall in a regular manner (Fig. 3). Starting from a certain intensity, the reflected shock can no longer turn the flow so that the velocity vector behind it is parallel to the wall, because The limiting angle of flow reversal at a shock, calculated from the Mach number behind the first shock, is less than the angle of inclination of the velocity vector to the surface wall behind the first shock. Then the reflection occurs irregularly with the formation of SMC. In contrast to the non-stationary case, the intensity of the Mach leg is equal to the maximum J m (M).

Triple configurations are convenient to study on the plane of shock polars lnJ-β , nicknamed for their characteristic appearance heart-shaped curves. A detailed analysis of heart-shaped curves, singular points, and regions of existence of TCs is given in. According to the classification, triple configurations TK-1, TK-2 and TK-3 are distinguished.

Rice. 3. Regular (left) and irregular (right) reflection of the shock from the wall: σ With - Mach leg

Triple configurations TK-1 arise from the interaction of oncoming shock waves of different directions, for example, in supersonic internal compression air intakes. TK-1 corresponds to the point of intersection of the left branches of the polars (Fig. 4). As the intensity of the incoming shock 1 increases, the intersection point moves towards the top of the main polar until it reaches it, at which point the SMC corresponds.

TK-1 can only exist at Mach numbers M > M T

At lower Mach numbers the polars do not intersect. At Mach number equal to M T, after the shock, the maximum static pressure is reached at a given adiabatic index γ (for air γ = 1.4). Triple configurations TK-2 occur when the shock wave is irregularly reflected from the wall. The difference from TK-1 is that in TK-2 the direction of flow deflection at the main shock (Mach foot) changes to the opposite (Fig. 5). As the intensity of the jump increases J 1 main shock 4 is bent. When shock 1 is reflected from the wall, the Mach leg is bent, approaching the wall orthogonally.

Rice. 4. Triple configuration TK-1

Rice. 5. Triple configuration TK-2

Triple configurations TK-3 arise from the interaction of overtaking shock waves of the same direction. Their study is of great practical importance for the design of supersonic external compression air intakes. Triple shock configurations and Mach disks in the jet

Let us dwell in more detail on the triple configurations of TK-2, since they are directly related to the problem of calculating the Mach Disk in a supersonic jet. The triple configurations TK-1 and TK-2 are separated by a stationary Mach configuration, which corresponds to the case when the secondary shock polar intersects the main polar at its apex. In the SMC (Fig. 6), the main shock wave (4) is direct. Characteristic intensity J 0 is obtained from solving the cubic equation corresponding to the intersection of the polars at the vertex of the main polar (Fig. 6).

z 0 = J 0 ,

Rice. 6. Stationary Mach Configuration (SMC)　

At some characteristic Mach number M OR. in the SMC, the polar corresponding to the incoming shock 1 intersects the top of the main polar at the point of limiting rotation angle 4 (Fig. 7).

This implies a transcendental equation for a special number M 0R:

Odds A i have the same meaning as in the previous equation.

At Mach numbers lower M OR, polar intersects with the ordinate axis inside the main polar and intensity is often taken as a criterion for the transition to irregular reflection J R, which corresponds to the contact of the polar with the ordinate axis (Fig. 8), which allows us to find the value of this intensity from the solution of the following equation:　

Rice. 7. Special configuration corresponding to MOR

This criterion did not receive experimental confirmation in the stationary case.

Testing the SMC hypothesis for the case of Mach disk formation in a jet

In order to correctly verify the compliance of the calculation method with experimental data, it is necessary to reduce in the experiment the influence of viscous effects that distort the flow pattern in the vicinity of the nozzle edge to a minimum. This can be achieved in an installation in which the jet flows from a sound nozzle with a bottom screen. Inside such a nozzle the boundary layer is small, and there is no ejection flow at its edge.

Rice. 8. TC corresponding to J = JR, M< МOR

A similar experiment was carried out at Dnepropetrovsk University. In Fig. Figures 9 and 10 show the removal dependencies L from the nozzle exit characteristic sections of the jet, as well as the diameter value D the corresponding element of the first barrel of the jet from the self-similar parameter, obtained by calculation using the method of characteristics.

Rice. 9. Comparison of the removal of the main sections of the first barrel of the underexpanded jet, obtained by calculation, with experimental data:
L b - distance from the nozzle exit to the point of intersection of the reflected shock with the jet boundary; L BC - distance from the nozzle exit to the section with the maximum diameter of the hanging shock; L M is the distance from the nozzle exit to the section with the maximum diameter of the jet boundary; L DM - distance from the nozzle exit to the flywheel disk

Rice. 10. Comparison of the results of calculating the diameter of the main elements of the first barrel of the jet with experiment: D ВС - maximum diameter of the hanging shock; D M - maximum diameter of the jet boundary; D DM - diameter of the Mach disk

The triple point on the hanging shock was chosen in the section in which the intensity of the hanging shock was equal to J 0. Not only qualitative but also satisfactory quantitative agreement with experiment is observed.

Conclusion

It is shown that the model of a stationary Mach configuration makes it possible to well predict the position of Mach disks in a supersonic jet. When calculating, placing the Mach disk at the point of the hanging shock, at which its intensity J = J 0, you can determine the diameter of the Mach Disk and its distance from the nozzle exit. The calculation results showed good agreement with experiment. The above arguments can only serve as indirect evidence of the model; its theoretical justification and the results of a full computational and experimental study are beyond the scope of this work and will be considered separately.

Reviewers:

Baranov I.V., Doctor of Technical Sciences, Professor, Deputy Director of the Institute of Refrigeration and Biotechnology, St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg;

Pelenko V.V., Doctor of Technical Sciences, Professor, Deputy Director for Academic Affairs of the Institute of Refrigeration and Biotechnology, St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg.

The work was received by the editor on July 20, 2012.

Bibliographic link

Uskov V.N., Bulat P.V., Prodan N.V. HISTORY OF STUDYING THE IRREGULAR REFLECTION OF A COMPRESSION JUMP FROM THE AXIS OF SYMMETRY OF A SUPERSONIC JET WITH THE FORMATION OF A MAX DISC // Fundamental Research. – 2012. – No. 9-2. – P. 414-420;
URL: http://fundamental-research.ru/ru/article/view?id=30239 (date of access: 07/29/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"

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Health-improving and professionally applied effectiveness of physical education and mass work in the SPTU dormitory (using the example of construction)

M.: PROMEDIA

Therefore, the mandatory set of simulators for a bricklayer, for example, included the “Health Disc”, for a plumber-gas welder

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magnetic disk media.<...>Users and even programmers often say: “Disk A:”, “Disk B:”, etc.<...>from a disk, for example, to a screen, to another disk, or to a printer.<...>For this purpose, the teacher prepared disks for each workplace (on each disk Mikron with text<...>The list of names of files stored on a disk is called a disk directory.

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No. 5 [Thermophysics and aeromechanics, 2015]

The flow behind the reflected shock is supersonic, and behind the Mach disk is subsonic.<...> <...>Mach disk at rA = 0.35 and rA = 0.26.<...>subsonic flow zones behind the Mach disk.<...>Mach disk at rA = 0.35 and rA = 0.26.

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The results of numerical simulation of the inflow of an underexpanded pulsed gas-dispersed jet with a high concentration of particles onto a rigid obstacle unlimited in the transverse direction are presented. The characteristic features of such interaction have been studied, in particular, the “anomalous” formation of the shock-wave structure of a two-phase flow at subsonic speed along the carrier gas and the development of self-oscillations

Some differences, for example the calculated size of the Mach disk, are larger than what is observed experimentally (Fig.<...>In this case, the Mach 1 disk for the case of the initial bulk concentration of particles (Fig. 4) consists of two parts<...>This is due to the vortex motion of mixture 2, which is adjacent to the Mach disk near the axis of symmetry.<...>In the second option - behind the Mach disk x ′′ = 6.<...>Then the two-phase medium runs into the obstacle with the formation of a Mach 4 disk.

A method for correcting PIV data to reconstruct gas velocity from particle velocity in supersonic underexpanded jets is considered. The method is based on estimating the rate delay of tracers using their rate relaxation parameter as a correction to PIV data in the Newtonian approximation of interfacial interaction. It is shown that the parameter of velocity relaxation of tracers in flows with velocity jumps can be determined from the original PIV data. The correction with the found phase velocity relaxation parameter showed good accuracy.

<...> <...> <...> <...>

The problem of initiating and stabilizing the detonation combustion of a hydrogen-air mixture entering an axisymmetric channel with a central body of finite length in a flow with a Mach number M0 = 5 ÷ 9 is solved. It is numerically shown that the presence of a central body both in the convergent-divergent nozzle and in the expanding channel ensures stabilization of detonation combustion of a stoichiometric hydrogen-air mixture at free-stream Mach numbers M0 > 7. A comparison was made of various channel configurations depending on the amount of thrust resulting from detonation combustion of a stoichiometric hydrogen-air mixture

of the central body, when a high-speed supersonic flow flows into it, a disk is formed near the axis of symmetry<...>hydrogen-air mixture was obtained for a nozzle with an internal cylinder, the presence of which prevents the formation of a disk<...>Thus, in an axisymmetric convergent-divergent nozzle without a central body, a disk is formed in the flow<...>the flow of the flammable mixture begins to interact with the central body as if behind the point of disk formation<...>Mach and in front of it (Fig. 4).

The results of a study of the inflow of a supersonic underexpanded air jet onto a porous metal barrier of finite thickness, the front plane of which is perpendicular to the axis of the jet, and the side surface is impenetrable to the gas flow, are presented. To determine the effect of porosity on the gas-dynamic characteristics of the interaction of a jet with an obstacle, the case of a non-porous obstacle of the same diameter was also considered.

The Mach number in the outlet section is Ma = 1.72, the degree of non-design of the jet outflow is n = 2.1.<...>A porous barrier in the shape of a disk with a diameter dp = 100 mm and a thickness ∆lp = 20 mm was inserted into a metal<...>Supersonic underexpanded jet interacting with a porous barrier: a - minimum distance between the disk<...>The amplitude of the Mach disk oscillations along the jet axis is 0.15da.<...>T. 56, N-◦ 3 corresponded to a rotation of the flow by an angle equal to 90◦, while the Mach disk was at a relative

No. 1 [Thermophysics and aeromechanics, 2018]

Founders of the journal: Siberian Branch of the Russian Academy of Sciences Institute of Thermophysics named after. S.S. Kutateladze SB RAS Institute of Theoretical and Applied Mechanics named after. S.A. Khristianovich SB RAS The main scientific topics of the journal are: - hydrogas dynamics - heat and mass transfer - turbulence - means and methods of aero- and thermophysical experiments - physics of low-temperature plasma - physical and technical problems of energy

However, with an increase in flight speeds above M = 4, the dimensions of the Mach disk decrease significantly and the frontal<...>At moderate supersonic free-stream Mach numbers, the Mach disk has a certain finite transverse<...>The dimensions of the Mach disk decrease significantly with increasing free-stream Mach number.<...>Mach, and then subsequent systems of funnel-shaped shock waves with Mach disks are formed.<...>must correspond to the presence of Mach disks (with subsonic flow speed directly behind them).

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Numerical modeling of the flow formed during transverse injection of a jet into a supersonic flow through a slotted nozzle was carried out at different pressure values in the injected jet and the main flow. For calculations on grids with different resolutions, the Spalart-Almaras turbulence model, the realizable k–ε model, the k–ω model, and the SST model are used. Based on a comparison of calculated and experimental data on the pressure distribution on the wall, the length of the recirculation region and the depth of penetration of the jet into a supersonic flow, conclusions were drawn about the accuracy of the calculation results using various turbulence models and the applicability of these models in solving similar problems.

Mach and shock wave caused by re-compression of the flow.<...> <...>injection, and the depth of penetration of the jet into the main flow H, which is determined by the position of the upper edge of the disk<...>Maha.<...>Mach 5.

A computational and theoretical study of the features of the flow of supersonic high-enthalpy flows in narrow cylindrical channels was carried out. The mathematical model is based on solving the complete nonstationary system of Navier-Stokes equations in an axisymmetric formulation. Calculations were performed for laminar and turbulent flow regimes using various turbulence models. The influence of the geometric parameters of the channel on the flow characteristics is analyzed. The features of the distribution of the Mach number along the radius of the flow in various sections of the channel are considered. It is shown that, depending on the conditions, braking of varying intensity occurs up to the formation of a subsonic flow zone of considerable length in the channel.

has several maxima, which corresponds, in our opinion, to the formation of additional jumps behind the disk<...>Mach during braking of a supersonic flow).<...>supersonic flows in narrow cylindrical channels 15 such as, for example, the mentioned additional shocks behind the disk<...>Mach can be identified more clearly.<...>supersonic flows in narrow cylindrical channels 17 in the k−ε model, a displacement of the first disk is observed

The work numerically simulates supersonic air flow in a flat channel with transverse injection of a turbulent hydrogen jet through a slot on the bottom wall. An algorithm is proposed for solving the Favre-averaged Navier–Stokes equations for the flow of a perfect multicomponent gas based on the WENO scheme. The main attention is paid to the interaction of the shock wave structure with the boundary layers on the lower and upper walls of the channel under conditions of internal turbulent flow, namely, a detailed study of flow structures was carried out, separation and mixing were studied depending on the width of the jet slit. It has been established that in addition to the known shock wave structures that arise during the interaction of the oncoming flow with a transverse jet and during the interaction of the leading shock wave with boundary layers near the walls, an additional system of shock waves and flow separation is formed on the lower wall at some distance from the jet downstream. A comparison with experimental data was carried out.

The Mach disk is clearly visible in the isobar 4 graphs.<...>the size of the slit leads to an expansion of the barrel-shaped structure in the jet and, as a consequence, to an increase in the disk<...>Mach (Fig. 4a and 4b).<...>However, in the case of the maximum gap size (h3) (Fig. 4c), the Mach disk decreases, since the separation zone<...>Mach, which demonstrates the distribution of the local Mach number (2 2M ,u w c= + here c  local speed

<...> <...> <...>

A three-dimensional supersonic turbulent flow with symmetrical perpendicular injection of round jets from the channel walls is numerically simulated. Using an algorithm built on the basis of the ENO scheme, the original Favre-averaged Navier-Stokes equations, closed using the (k–ω) turbulence model, are solved. For values of the off-design parameter 3 6 n 6 50, the mechanism of formation of vortex structures during the interaction of a jet with an oncoming flow is studied. It has been experimentally established that for n > 10, as a result of the mixing of the jet and the incoming high-speed flow, a pair of vortices appears and additional separation occurs near the wall behind the jet. It is shown that the results of calculating the pressure distribution on the wall in front of the jet in the symmetry plane are in satisfactory agreement with the experimental data.

flows behind the jet due to the formation of a low pressure zone; the appearance of a barrel-shaped structure and disk<...>Mach in a jet.<...>are formed in the mixing zone, a pair of vortices 9 is formed due to the interaction of the jet passing through the disk<...>Mach D, with high-speed free flow.<...>way: - in a jet u = 0, v = 0, T = 0.6, w = √ T M0 / M∞, P0 = nP∞, z = 0, x 2 + y2 6 R (M0 is the Mach number

The results of spectroscopy of the initial section of a supersonic plasma jet formed using a pulsed discharge in a capillary with an ablating wall made of carbon-containing polymer are presented. Features of the spatial distribution of electron density and intensity of spectral components are revealed, which, in particular, are caused by the high value of electron temperature in the “hot” central zone, exceeding the “normal” temperature, as well as the significant non-isobaricity of the initial section of the supersonic jet. The radiative properties of the high-temperature core of the jet (intensity and contour of the Balmer lines Hα and Hβ, relative intensities of the C II ion lines) recorded with high temporal (1-50 μs) and spatial (30-50 μm) resolution made it possible to establish the main patterns in the distributions of pressure and temperature in the vicinity of the central shock wave. Thanks to the presence of molecular components in the flow, which exhibit their radiative properties at the periphery of the jet, it was possible to obtain an idea of the plasma parameters in the zone of formation of “hanging” shock waves.

based on the results of optical flow imaging and by analyzing shock wave structures: Mach number<...>The temperature values determined in this way are Te ~ 2 eV in the vicinity of the Mach disk (z = 2.5<...>The pressure profile p(r) in the vicinity of the Mach disk, reconstructed using the above procedure, is qualitatively<...>The reconstructed pressure profile in the vicinity of the Mach disk is in qualitative and quantitative agreement with the results

No. 3 [Thermophysics and aeromechanics, 2018]

At moderate supersonic free-stream Mach numbers, the Mach disk has a finite transverse size<...>The dimensions of the Mach disk decrease significantly with increasing free-stream Mach number, and in the resulting<...>must correspond to the presence of Mach disks with a subsonic flow velocity directly behind them.<...>Mach pseudo-leap.<...>behind the second Mach disk (x = 3.93 m, x = 10.15), curve 5 ⎯ end of the separation zone of the boundary layer (x =

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The results of experimental studies and numerical modeling of self-oscillations in a supersonic radial jet flowing from a flat radial nozzle into a flooded space are presented. It is shown that bending vibrations develop in the jet, leading to its destruction. It has been established that feedback, which is carried out by sound waves in the gas surrounding the supersonic jet, plays a large role in the formation of self-oscillations.

limited by cylindrical surfaces with radii r1, r2, and a radial channel limited by two disks<...>The angle of inclination of the Mach waves relative to the jet axis is α ≈ 40◦.<...>In Fig. Figure 6 shows the distribution of the Mach number on the jet axis at different times.<...>Using these values, we find the convective Mach number of the jet Mc = 2M/(1+ c0/cj) ≈ 2.3.<...>In a given outflow mode, there is a regular interaction of shock waves on the jet axis without the formation of a disk

Experimental study of the influence of acoustic-vortex self-oscillations on the process of destruction of an underexpanded supersonic jet in a flooded space [Electronic resource] / Aleksandrov, Arefiev, Ilchenko // Thermophysics and Aeromechanics. - 2016. - No. 4. - P. 45-55. - Access mode: https://site/efd/434738

Intensifying the mixing of the gaseous working fluid supplied through jet nozzles with the environment is an important scientific and technical problem, the solution of which will improve the efficiency of the work process in energy and power plants. A relevant, but little-studied area is the generation of acoustic-vortex self-oscillations in jet nozzles, which can accelerate the decay of a supersonic jet and thereby improve mixing performance. The article presents the features of excitation of acoustic-vortex self-oscillations in jet nozzles; the main results of an experimental study of a model jet nozzle are presented, in the channel of which plates are installed that provide the excitation of acoustic-vortex self-oscillations; patterns of decay of an underexpanded supersonic jet in a flooded space were found for various flow regimes. The presented data show the possibility of effective use of jet nozzles with generated acoustic-vortex self-oscillations in relation to gaseous fuel supply systems. The results of the study can be used in the design of power plants for advanced aerospace equipment and technological devices.

Reflection of the shock wave from the jet axis leads to the formation of a Mach 7 disk.<...>The frequency of the acting force is determined by the formula: St M ,f c t= ⋅ ⋅ here M is the Mach number of the flow in the cavity<...>centered rarefaction wave, 4  jet boundary, 5  compression wave, 6  hanging shock wave, 7  disk<...>Mach, 8  reflected shock wave, 9  external mixing region.<...>In the experiments, the change in the Mach number in the cavity was regulated by changing the diameter d of the MSF nozzle.

No. 3 [Applied mechanics and technical physics, 2004]

shock waves 3, 4, 5; 7 - fan of rarefaction waves; b: 1 - nozzle; 2 - compression shock; 3 - Mach disk<...>Mach near the axis (r/Ra = 0÷0.15).<...>Free-stream Mach number M = 5.<...>Maha.<...>time may result in loss of information recorded on the disc.

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No. 5 [Physics of combustion and explosion, 2015]

The journal publishes articles with the results of original experimental and theoretical research in the following sections: combustion in gases and condensed media, detonation of condensed explosives, gases and heterogeneous systems, production of new materials by the method of self-propagating high-temperature synthesis, shock and detonation waves, high-speed impact, dynamic loading of materials and structures, welding explosion and detonation spraying

Mach 3, and the flow speed directly behind the Mach disk becomes subsonic.<...>The flow velocity in front of the Mach disk reaches values of V = 545 m/s according to PIVFig. 5.<...>Further behind the Mach disk, the speed drops abruptly to V = 190 m/s and U = 95 m/s (PIV and calculation, respectively<...>Even on a direct shock (Mach disk), thanks to averaging over a large number of instantaneous realizations, one can see<...>In Fig. 6 also shows that behind the Mach disk, after a sharp deceleration of the flow, the speed lag of particles

Preview: Physics of combustion and explosion No. 5 2015.pdf (0.1 Mb)

M.: Publishing house of MSTU im. N.E. Bauman

The principles of magnetic-inertial thermonuclear fusion and laser-plasma methods of generating fields during the implosion of a magnetized target are considered. The results of the work open up the possibility of creating new high-density plasma sources for their use in materials science experiments and for promising areas of energy. Such plasma systems can be used for diagnostics and testing of various materials. The Richtmyer-Meshkov instability in pulsed systems with inertial particle confinement has been studied.

field, i.e. at 0)B = , consisting of a group of lateral hanging shock waves (SW) and a central disk<...>Mach crossing the axis of symmetry.<...>Here, behind the central Mach disk (at subsequent moments of time) a vortex wake (toroidal<...>in this case, it is limited along the radial coordinate with a size of 1 cm.R ≤ In this spatial zone, the Mach number<...>structure, and the maximum temperature value in the jet is at the level of 3max 18 10 K,T ≈ ⋅ Mach number

No. 3 [Thermophysics and aeromechanics, 2017]

The diameter of this disk depends on the Mach number of the free-stream flow and the intensity of the incident shock.<...>In the case under consideration, the Mach disk practically does not appear as if it were falling on the axis of the initial shock<...>This is due to the high flow velocity when the initial Mach disk of small transverse size is formed<...>The Mach is larger and subsequent Mach disks are formed (Fig. 4b).<...>The area with separations and Mach disks gradually moves forward, and as a result, in front of the entrance cross-section

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No. 5 [Applied mechanics and technical physics, 2015]

The journal publishes original articles and custom reviews on the mechanics of liquid, gas, plasma, dynamics of multiphase media, physics and mechanics of explosive processes, electric discharge, shock waves, state and movement of matter at ultra-high parameters, thermal physics, mechanics of deformable solids, composite materials, methods diagnostics of gas-dynamic physical and chemical processes.

Mach in a jet.<...>The region of jet penetration into the main flow is limited by hanging shock waves and the Mach disk.<...>Maha.<...>Mach 5.<...>An experimental study of the lifting of a glass circular disk from the surface of water, the purpose of which was

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Parallel calculations in solving problems of aerohydrodynamics using the large particle method. manual for the course “Parallel Programming”

M.: Publishing house of MSTU im. N.E. Bauman

Problems of flow around bodies of various geometric shapes at different oncoming flow velocities (subsonic and supersonic) in plane and axisymmetric cases in the entire range of permeability: from no flow to free flow are considered. Descriptions of programs for calculating three-dimensional non-stationary problems taking into account the gravitational field (Rayleigh-Taylor instability problems) using the difference scheme of the large particle method on triangular, hexagonal and orthogonal computational grids are given. The textbook is accompanied by a CD containing the texts of 20 working programs in the algorithmic language FORTRAN, intended for solving problems of aerohydrodynamics using the KRUCHA-2 software.

Flow patterns: a - thin permeable body; b - disk with canopy-shell 2.<...>and P(30, 2) = 0.63 behind the disk near the axis of symmetry at time TC = 20.00.<...>and P(30, 2) = 0.78 behind the disk near the axis of symmetry at time TK = 20.00.<...>and P(30, 2) = 0.80 behind the disk near the axis of symmetry at time TK = 20.00.<...>and RO(30, 2) = 0.47 behind the disk near the axis of symmetry at time TC = 20.00.

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Teaching balances and turns in sports aerobics. allowance

Publishing house Siberian State University of Physical Culture

The training manual provides information about the technique of performing balances and turns, as well as the methodology for teaching these elements, taking into account the physical qualities and functional abilities necessary for successful training at the stage of initial training in sports gymnastics. The manual provides new information reflecting the methodology for teaching balances and turns in sports aerobics, based on the general biomechanical laws of their implementation, taking into account the requirements of the competition rules of this popular sport among young people.

Bent balance (vertical swing). 2. Studying the 180° rotation on the “health disk”. 3.<...>on the “health disk”, arms to the sides: 1–2 – push with the left and with a wave of the hands, turn the disk 360; 3–4 –<...>health”, left on the floor, arms to the sides: 1–2 – with a push of the left and a wave of the arms, turn the disk 360,<...>, left on the floor, arms to the sides: 1–2 – with a push of the left and a wave of the arms, turn on the disk 360, bending the left<...>floor, arms to the sides: 1–2 – with a push with the left and a wave of the arms, turn on the disk 360 with eyes closed;

Preview: Teaching balances and turns in sports aerobics. 2013 edition.pdf (0.3 Mb)

No. 5 [Applied mechanics and technical physics, 2001]

In this case, the internal diameter of the jet, determined from the diameter of the Mach disk, is almost 10 times larger<...>Mach, the flow around the element occurs without the Mach disk moving away.<...>Under these conditions, no significant change in the size of the jet behind the Mach disk occurs, and as an area<...>The jet area around the side holes can be taken to be the jet area at the level of the Mach disk.<...>For practical use with a Mach disk diameter 10 times the outflow hole diameter

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No. 2 [Applied mechanics and technical physics, 2010]

As well as a set of wheels and a fairing.<...>Top profiled disc, disc set, top of rotor fairing and top edge of guide<...>; N is the number of revolutions per minute of the classifier disks.<...>Mach, jet boundary.<...>Calculated distribution of Mach numbers at the exit of a multimode nozzle with different Mach numbers at the exit

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Thermogasdynamic calculation of centrifugal compressors, textbook. allowance

The calculation methodology is outlined and an algorithm for calculating the flow path of a centrifugal stationary compressor is presented. Examples of calculations of impellers, diffusers, return guide vanes, and outlet devices are given. The issues of optimization and selection of the compressor flow path are considered.

in section i; 111 awM w = – Mach number in section 1 at speed 1w; 222 acM c = – Mach number in the section<...>Mach number at peripheral speed (conventional Mach number) .612.0 28558.49695.030.1 83.25522 = ⋅⋅⋅ === nn<...>A closed-type wheel consists of a main disk 1, a covering disk 2 and blades 3 (Fig. 7.1).<...>The blades can be solidly milled together with the main disk, and the covering disk is soldered to them.<...>The blades are first welded to the main disk, and then the cover disk is soldered to the blades.

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Run! Jump! Throw! IAAF Official Athletics Training Guide: [teaching method. allowance]

M.: Man

The IAAF's Official Athletics Training Guide “Run! Jump! Throw!” is divided into three main sections, each covering one group of species, which forms the title of the section. The main sections begin with a very brief overview and basics of each species group. This includes the most important parts of the basic theory - general objectives, basic biomechanical principles and an overview of the structural phases - basic exercises, training tips and example games to help introduce the skills required to practice the activities included in this group. The running section also provides a brief overview of middle and long distance running training.

the leg swings in front of the body and straightens for contact (front swing), while the push<...>Copyright OJSC "CDB "BIBKOM" & LLC "Agency Kniga-Service" 182 DISC THROWING DISC THROWING V s i p o<...>swing back and ▲ active – forward.<...>NOTES: Do not grab the disc. ▲ Bend your legs as you roll the disc ▲ along the ground.<...>NOTES: Hold the disc at ▲ head level. Feel the release of the disc through your index finger.

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Methodology for developing strength in the process of physical education of students at a university. recommendations

This work introduces students to methods of developing strength abilities in physical education classes. The work discusses the basic and additional means that can be used in physical education classes to develop the strength abilities of students. This paper proposes control exercises to determine the level of development of strength abilities.

Bend forward with a half squat and swing your arms back, straighten with swing your arms forward and up<...>Breathing: swing your legs back, inhale, exhale forward. 7.<...>Breathing: swing your legs up, inhale, legs down, exhale. 8.<...>Breathing: in and. p. inhale, exhale. 37.<...>one leg, at the same time swing the hip of one leg.

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No. 3 [Thermophysics and aeromechanics, 2019]

Estimates from the data showed that for a water drop with d = 2.7 mm, the shock wave Mach numbers Ms = 1.3, 1.5<...>Mach 5 at NPR = 4 (Fig. 4a) and NPR = 6 (Fig. 4c).<...>Mach " in pure gas, and in the two-phase core of the jet it is an indirect sign of the existence of a "third<...>Mach in a supersonic underexpanded jet consisting only of gas.<...>Here M∞ is the Mach number, Re1 is the unit Reynolds number, T∞ is the free-stream temperature, p∞ is the pressure

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Athletics. Questions and answers methodological recommendations for students of the Faculty of Physical Culture of higher educational institutions

FSBEI HPE "ShGPU"

The methodological recommendations are compiled on the basis of the educational and methodological complex for the discipline “Athletics”, developed at the Department of Sports Disciplines of the State Educational Institution of Higher Professional Education “ShGPU”. The recommendations are intended for students of the physical education faculty of pedagogical universities, teachers and teachers of physical education.

Holding the disc.<...>Turns without a disc and with a disc at different speeds. 2.<...>Swing your leg while standing against the wall on a pushing leg. 2.<...>Coaches consider the straightening leg swing to be more effective.<...>Disk.

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No. 6 [Applied mechanics and technical physics, 2009]

In the works, overexpanded jets were considered, the Mach disk and subsonic zone were obtained by calculation<...>In the case of an underexpanded jet, a flow field with a vortex formed behind the Mach disk was obtained.<...>Since the flow in the nozzle was off-design, oblique shocks and a Mach disk were formed inside it, and<...>In front of the Mach disk, the gas accelerates to values of the Mach number on the axis M = 6.8; 4.4 corresponding to the values<...>Towards the calculation of a supersonic overexpanded jet of ideal gas in the presence of a Mach disk in the flow // Uchen

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Athletics: basic knowledge (in questions and answers) textbook. allowance

The textbook contains brief information on the history of the development of types of athletics, analysis of techniques and methods of teaching athletics exercises, organization and basic rules of judging competitions in the sport, which are presented in a form convenient for study and assimilation. Typical mistakes when performing athletics exercises and recommendations for correcting them are given.

copper or bronze disk.<...>In the long jump, the swing is performed with one arm up and forward; in the triple jump, the swing is performed with both<...>, disk - around the vertical.<...>Swing with a bent leg. The radius of the circle is 8–10 m. 2.<...>the swing was performed with the heel forward) 2.

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Initial motor training in sports aerobics. allowance

Publishing house Siberian State University of Physical Culture

The textbook is written on the basis of the requirements of the federal state educational standard of higher professional education, direction 034300.62 “Physical culture”, and the work program of the discipline “Theory and methodology of the chosen type of physical culture and sports activity”. The manual substantiates the structure of the types of initial training in sports aerobics, presents sets of special exercises in combination with training devices for initial motor training in sports aerobics, and outlines the main organizational forms of educational and extracurricular work.

right back within 40°; 2 swing right forward upward; 3 - right swing back; 4 swing right forward upward<...>health, 1_2 _ push (, with a left hand and a swing of the ARM, turn on the disc to the 3M’°’ left back to the BOTTOM; 3 -4 then with<...>“’m left and with a wave of the arms, turn on the disc to ZbO°S0GNUV left forward; 3 -4 the same; 5-8 the same 1, and left I<...>RUSHVST°R °Н1: 1 -2 with a left push and a wave of the arms, turn on the disc 36” with eyes closed; 3-4 the same<...>*stand on the right, on the health disk; 6 push - with a wave of the ARM, turn to the right 360 7

Preview: Initial motor training in sports aerobics.-2nd ed., revised. and additional 2013 edition.pdf (1.2 Mb)

Special exercises for teaching types of athletics. allowance

Sib. federal university

Contains a systematic presentation of methodological and practical material on athletics, necessary for students of higher educational institutions to master the profession of a coach-teacher, physical education teacher. Filmgrams and diagrams of techniques in the main types of athletics - running and walking, jumping and throwing - are presented with methodological recommendations for their development, as well as examples of basic introductory, imitation and special training exercises in the sections of preparation.

Swing your leg while standing sideways against the gymnastics wall.<...>Performing a swing without moving the body forward and up; simultaneously with the swing, the torso leans back<...>Jumping on one leg backwards: a) without swinging the left leg, b) with swinging the left leg, c) with stance<...>Simulation exercises for teaching discus throwing techniques Discus and hammer throwing are assigned to students<...>The mass of a male disk is 2 kg, a female disk is 1 kg.

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Calculation of crank presses, textbook. allowance

This manual outlines the procedure for performing calculations related to the design of the drive, parts and assemblies of crank presses. The diagrams and calculation dependencies necessary for this are presented. Complete reference material is provided. Intended for university students studying the disciplines: “Forging and stamping equipment”, “Calculation and design of forging and stamping equipment”.

Data for determining friction parameters and disk thicknesses 60 5.2.3.<...>Calculate the design length of the belts using the formula:     2 0.25 2 1.57 max shk max shk D D L D D     <...>   2 2 0.25 1.57 0.125max shk max shkL D D D D      .<...>, cm hd Thickness of the drive disk, cm h1 Number of inserts, pcs mв 5.2.3.<...>The thickness of the drive disk is 1 (0.11 0.0002) mh B n    . (5.17) 5.3.4.

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Rhythmic gymnastics at the university

Publishing and Printing Center of Voronezh State University

The educational and methodological manual was prepared at the Department of Physical Education and Sports of Voronezh State University.

I. p. – emphasis while standing on your knees: 1 – swing your right leg back; 2 – sitting on heels; 3 – left leg swing back<...>I. p. – emphasis while standing on your knees: 1 – swing your right leg back; 2 – swing the right leg to the right; 3 – count 1; 4<...>.; 3 – swing the leg forward; 4 – i. P.; 5 – leg back; 6 – i. P.; 7 – swing up; 8 – i. paragraph 36.<...>I. p. – the same: 1 – right swing forward; 2 – swing of the right to the left hand; 3 – right swing forward; 4 – i. P.<...>Walking in a disco manner. Slow walking. 26.

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No. 5 [Thermophysics and aeromechanics, 2016]

Mach number 10, altitude 90 km.<...>Maha.<...>Mach strong jet limited by the contact surface.<...>When the disk rotation speed increases on the cylinder axis, the axial component first slows down<...>With a further increase in disk rotation, this region with a reduced value of the axial velocity component

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No. 6 [Applied mechanics and technical physics, 2017]

Calculation and design of centrifugal compressor machines, textbook. allowance

Omsk State Technical University Publishing House

The 2nd edition of the textbook addresses issues of thermogasdynamic calculation, design and strength analysis of the elements of the flow path of centrifugal compressors; the thermogasdynamic design of the flow part using a calculation technique through dimensionless parameters is described; examples of performing thermogasdynamic and strength calculations are given.

The Mach number MW1 should have values MW1  0.55...0.65 (for axial radial rockets MW1  0.87).<...>To determine the Mach number in the “throat” section of the MW1G RK, you can use the technique developed<...>The speed Mach number at the outlet of the diffuser is 444 TRkСМС  . (1.119) Gas pressure, Pa:   .)1()1(<...>To the calculation of Mach numbers in the “throat” section of the blade diffuser array Equation (1.130) is nonlinear,<...>In this case, the conventional Mach numbers for the RC of section I turn out to be quite large MU = 0.88, and the Mach numbers according to

Preview: Calculation and design of centrifugal compressor machines A. D. Vanyashov, G. G. Kustikov, 2017. - 255 pp. pdf (0.9 Mb)

No. 3 [Applied mechanics and technical physics, 2011]

An important gas-dynamic characteristic of a supersonic jet is the position of the Mach disk - direct shock<...>The position of the Mach disk was determined by the formula lM = 0.67d∗ √ p0/pк, where lM is the distance to the Mach disk<...>These data made it possible to estimate the flow regimes in the jets and determine the position of the Mach disk at various<...>For measurements in the supersonic region of the jet (in front of the Mach disk), a point was chosen at a distance from the cutoff<...>nozzle equal to 8 mm, in the area behind the Mach disk - a point at a distance from the nozzle exit equal to 50 mm.

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No. 1 [Bulletin of Moscow State Technical University named after N.E. Bauman. Series "Mechanical Engineering", 2010]

M.: Publishing house of MSTU im. N.E. Bauman

Issues in the following areas are covered: mechanics of power structures for various purposes; energy problems; modern problems of technology; fundamental problems of mathematics, physics, continuum mechanics, etc.

At Mach numbers M > 3, it is necessary to switch to a direct-flow circuit.<...>Mach number fields in the central axial section during flight with zero angle of attack for Mach numbers M=6,8,10<...>The dependences of these characteristics on the Mach number and angle of attack were studied.<...>; μ - coefficient of friction between the block and disk 45

No. 3 [Proceedings of the Russian Academy of Sciences. Mechanics of fluid and gas, 2017]

Theoretical, computational and applied research in the field of aeromechanics, hydrodynamics, plasma dynamics, soil hydrodynamics, and biomechanics of continuous media is published. Particular attention is paid to new areas of research, such as the theory of multiphase flows and their applications, chemically reactive flows, flows of liquids and gases in electromagnetic fields, new hydrodynamic methods for increasing oil production, new approaches to describing turbulent flows, etc. The journal is peer-reviewed and included to the List of Higher Attestation Commissions.

front view, angle between the line of sight and the axis of the disk Θ = 0°; b – side view Θ = 90°; c – the disk is turned at an angle<...>Flat and axisymmetric configurations, streamlined with a maximum critical Mach number // Prikl. 1987<...>Optimization of the shape of symmetrical flat bodies in order to increase the critical Mach number // Uch. zap.<...>Mach number M1 of the total velocity of a homogeneous flow behind a plane shock wave attached to the front<...>the edge of the leeward console, or behind the centered rarefaction wave (symbols I); Mns – Mach number

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The National Training Methodological Center for Testing of Abrasive Materials, at the request of the editors of the KUZOV magazine, has begun a new series of tests. The center's research includes testing abrasives in P120 grit wheels, one of the most common gradations used in auto body work, on two types of surfaces - putty and putty-filled metal. The test involves abrasive wheels from fourteen series of different manufacturers - almost everyone who is present on the Russian market today, from leaders to little-known brands. All samples are tested under exactly the same conditions, on an identical surface, at the same humidity and temperature. Based on the results of two tests, the tested abrasive wheels were awarded points according to the system: 1 point for the minimum result and then in ascending order

During the test, the disc wore unevenly.<...>The NORTON A275 drive also worked stably.<...>OJSC "CDB "BIBKOM" & LLC "Agency Kniga-Service" BODY 201363 FIREWORK CENTER x 1 accrual max.<...>RADEX Gold 9 4 12 Skilled Red 10 3 12 NORTON A275 10 3 11 Siarun 11 2 8 Mirka Abranet 12 1 1 accrual max<...>Skilled Red 13 5 81 siarun 14 4 75 NORTON A275 15 3 53 Mirka Abranet 16 2 46 RADEX Gold 17 1 2 accrual max

No. 4 [Thermophysics and aeromechanics, 2014]

I installed VirtualBox on my Linux PC. I really wanted to use one of the LXFDVDs to install a Linux virtual system. But I get an error message that states that VirtualBox does not recognize the disk format. I think the reason is that the disc is a hybrid ISO file. Is it possible to create a standard ISO disk image for installing Linux in Virtual Box? If yes, how to do it?

I think the reason is that the disc is a hybrid ISO file.<...>This will allow you to select the physical disk you are using.<...>A good secure distribution like Tails, as long as you don't download it on newer systems<...>This is not a requirement of Windows 10, which also boots in older BIOS/MBR systems, but<...>and recording of si tags, then the quality of the copied files will be the same in all programs

Formations in a supersonic jet of gases emanating from the nozzles of turbojet, ramjet and rocket engines. Mach disks become visible when fuel burns outside the engine. In a turbojet engine this is possible when the afterburner is turned on.

Education mechanism

x = 0.67 D 0 P 0 P 1 (\displaystyle x=0.67D_(0)(\sqrt (\frac (P_(0))(P_(1))))),

where D 0 is the nozzle exit diameter,

P 0 - flow pressure at the nozzle exit,

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