Profiling the Supersonic Part of a Plug Nozzle with a Nonuniform Transonic Flow

The effect of transonic flow nonuniformity on the profiling of optimal plug nozzles is studied in the inviscid gas approximation. Sonic and supersonic regions providing maximum thrust for given nozzle dimensions and a given outer pressure are designed for given subsonic contours and calculated nonuniform transonic flows. As in the case of uniform flow on a cylindrical sonic surface, the initial regions of the designed contours satisfy the condition that in these regions the flow Mach number is unity or near-unity. In all the examples calculated, the optimal plug nozzles produce a greater thrust than the optimal axisymmetric and annular nozzles with a near-axial flow for the same lengths and the same gas flow rates through the nozzle. It is established that contouring without regard for transonic flow nonuniformity can result in considerable thrust losses. However, these losses are due only to a decrease in the flow rate, while the specific thrust may even increase slightly.     

Effect of the Streamwise Component of the Vorticity Formed in a Turbulent Jet Source on the Acoustic Characteristics of the Jet

The results of an experimental study of the effects of different nozzle heads on turbulent jet noise are analyzed. A configuration of four cylindrical heads, tabbed heads, and chevron nozzles are considered and the decreases in the acoustic-mechanical efficiency of the jet (acoustic power reduction) for jets exposed to different modes of action are compared.It is shown that the effects of tabbed and cylindrical heads, as well as of chevrons, share a common property which is associated with the occurrence of vorticity in the jet source and can be described on the basis of a unified criterion characterizing the action on both the jet flow structure and the jet noise.     

Analysis of the thrust characteristics of jet nozzles designed by various methods

A comparative numerical analysis of the thrust characteristics of axisymmetric jet nozzles designed by various methods is carried out. “Extremal“ nozzles designed by variational methods in the absence/presence of internal shocks (I), so-called “truncated“ nozzles with a uniform characteristic (II), and nozzles designed by the method of conjugate circular arcs (III) are considered. A comparison is carried out for both perfect and real gases (in the latter case the boundary layer gas viscosity is taken into account). It is shown that extremal nozzles are the most efficient, while truncated nozzles are somewhat less so. The thrust characteristics of nozzles designed by the method of conjugate circular arcs for both inviscid and viscous flow are inferior to those of extremal nozzles by 0.7–1%. Moscow, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 2000. The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-00891).     

Flow structure at the initial section of a supersonic jet exhausting from a nozzle with chevrons

The spatial structure of the flow in a supersonic underexpanded jet exhausting from a convergent nozzle with vortex generators (chevrons) at the exit is experimentally studied. Exhaustion of a supersonic underexpanded jet from a nozzle with chevrons at the nozzle exit is numerically simulated with the use of the Fluent commercial software package. The experimental and numerical data are demonstrated to be in reasonable agreement. The influence of chevrons on the process of gas mixing is estimated.     

Mixing of high speed coaxial jets

In this study, five different supersonic nozzles – conical, elliptical, tabbed, radially lobed and two-dimensional lobed – are compared experimentally for their mixing performance. With the background of studies by various groups conducted on the above nozzles, the present paper aims to provide an experimental comparison of their respective mixing performances with that of a conventional conical nozzle under identical operating conditions. The mixing of the supersonic stream coming from such nozzles with a coaxial sonic stream is investigated. The investigation is performed non-intrusively, using digital image processing of planar Mie-scattering images of the flow field. The results of these investigations reveal the superiority of mixing performance of the two-dimensional lobed nozzle over conventional circular and other non-conventional nozzles. Received: 15 July 1999/Accepted: 3 July 2000     

Influence of nozzle profile on the characteristics of a gas-dynamic laser

The results are given of numerical profiling and analysis of the influence of nozzle shape and the gas-dynamic parameters on the characteristics of gas-dynamic lasers. Investigation of the two-dimensional nonequilbrium flow in a family of similar nozzles and nozzles with different angles of inclination of the contracting part show that it is expedient to choose a shape of the subsonic part that ensures a straight sonic line. Relationships between the geometrical parameters of the subsonic and transonic part of the nozzle are recommended which ensure separationless flow and a shape of the sonic surface that is nearly flat. A parametric investigation was made of the supersonic section of two classes of planar gas-dynamic laser nozzles constructed on the basis of uniform and symmetric characteristics at the exit. The parametric investigations of the influence of the degree of expansion, the total pressure and the temperature, and also the gas composition show that the smallest losses of useful vibrational energy in the cavity are achieved for nozzles constructed on the basis of uniform characteristics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 163–167, November–December, 1982.     

Effects of the particle residence time and the spray droplet size on the particle removal efficiencies in a wet scrubber

A new type of scrubbing system equipped with air-atomized spray nozzles, full cone type spray nozzles and the maze shape channels has been developed and the mass transfer mechanism to remove sub-micron particles is analyzed. There is a minimal time duration for the mixture of air and sprayed water droplets should remain in the scrubbing zone for the sub-micron particles and hydrogen fluoride (HF) gas to diffuse and be captured by water droplets. The grown water droplets enter the maze shape channels which have sharp corners and bends to eliminate the water droplets by collision with the walls. As a result of applying the developed design methodology, the sub-micron particle removal efficiencies of the scrubber are found to be above 99% for the particles of 0.5–1 μm, 96% for those of 0.3–0.5 μm, and 86% for those smaller than 0.3 μm in diameter under the optimum operating condition.     

Studies on freejets from nozzles for high-speed mixing applications

In this study four different supersonic nozzles – circular, elliptical, tabbed, and radially lobed nozzles are compared experimentally for their freejet mixing performance. With the background of studies by various groups conducted on elliptical, tabbed, and radially lobed nozzles, the present paper aims at a comparative experimental study to compare their mixing performance with that of a conventional circular nozzle under identical operating conditions. The investigation is performed non-intrusively, using digital image processing of the planar Mie scattering images of the flow field. The results of these investigations reveal the superiority of the mixing performance of the lobed nozzles over conventional circular and other non-conventional nozzles. Received: 29 July 1998/Accepted: 5 November 1999     

Investigation of flows in hypersonic nozzles in the framework of simplified Navier-Stokes equations

Simplified Navier-Stokes equations have found application as an alternative to the complete Navier-Stokes equations for the simulation of viscous gas flows in regions of large dimensions, when there is a predominant direction of the flow [1–4]. In the present paper, flows in wind tunnel nozzles are investigated on the basis of this model. Flows in conical and profiled axisymmetric hypersonic nozzles are calculated in a wide range of Mach and Reynolds numbers. Good agreement with the experiment is obtained. The important role of viscous-inviscid interaction in nozzles for large hypersonic Mach numbers is shown. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–26, November–December, 1986. The representation of the nature of flows in hypersonic nozzles given here arose as a result of repeated discussions of the results of the calculations with my colleagues: V. N. Vetlutskii, V. L. Ganimedov, G. P. Klemenkov, Yu. G. Korobeinikov, and V. I. Pinchukov, for which the author is deeply grateful to them.     

Analysis of optimum asymmetric plane nozzles with allowance for the moment characteristics

Some properties of the flow in asymmetric plane nozzles producing the maximum moment about a given point [1] are investigated. The maximum moment conditions, which follow from an analysis of the second variation, are obtained. A numerical analysis is carried out for nozzles with a relatively short lower wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 103–108, July–August, 1988.The author wishes to thank A. N. Kraiko for discussing the results and for his valuable advice, and V. P. Tenetov and N. A. Vodyanov for participating in the development and refinement of the programs for designing optimum asymmetric nozzles.     

Specific impulse losses due to friction and dispersion in a gas-film cooled liquid rocket engine nozzle

Conclusions The proposed method and program for calculating the compressible turbulent boundary layer in rocket engine nozzles with gas film cooling make it possible to determine the specific impulse losses due to friction, the heat fluxes and other characteristics of the flow. The calculations are based on the numerical solution of the equations of gas dynamics in the boundary layer approximation using a three-parameter differential turbulence model.The calculations for nozzles without film cooling showed that the contours occupying a narrow interval between the families of contours with uniform and variational characteristics have the minimum impulse losses due to friction and dispersion. In contrast to the known results, the loss minimum is displaced relative to nozzles with a variational characteristic (Rao nozzles) towards truncated nozzles with a uniform characteristic.The dependence of the maximum heat transfer to the wall in the critical throat section of the nozzle on the rate of flow of fuel into the film has been determined for nozzles with film cooling. It is shown that as the film flow rate increases, the friction losses decrease, and the minimum of the impulse losses due to friction and dispersion is shifted towards the contours with a variational characteristic, which have the minimum dispersion losses. The total impulse losses, which take into account the change in the fuel component ratio in the flow core due to the diversion of part of the fuel into the film, increase with increase in the film flow rate.The results of our numerical investigation of the effect of the contour shape and film flow rate indicate that the contour with a variational characteristic, which has near-minimum specific impulse losses due to friction and dispersion, should be used as the optimum contour for LRE nozzles.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 82–93, May–June, 1993.deceased.The authors wish to thank their colleagues at the Énergomash NPO L. P. Vereshchak and L. K. Danilyuk for assisting with the calculations, the participants in G. A. Lyubimov's seminar for discussing the results obtained, and D. A. Mel'nikov, U. G. Pirumov, and A. A. Sergienko for valuable advice.     

Drag force on quasi-axisymmetric scramjets at various flight Mach numbers: theory and experiment

The net axial force on a non-fuelled quasi-axisymmetric scramjet model designed for operation at Mach 6 was measured in the T4 Stalker tube at The University of Queensland using a single-component stress wave force balance. The design used was a variant of a model that was tested previously at Mach 6. The new model was equipped with a modified thrust nozzle that was designed to improve the performance of the nozzle. Tests were performed to measure the drag force on the model for Mach 6, Mach 8 and Mach 10 shock tunnel nozzles for a range of flow conditions. The nozzle-supply enthalpy was varied from 3 to 10 MJ/kg and the nozzle-supply pressure from 35 to 45 MPa. For the test model, the drag coefficient increased with increasing nozzle-supply enthalpy. The test results are compared with a force prediction method based on simple hypersonic theories and three-dimensional CFD. The test results are in good agreement with the predictions over the wide range of conditions tested. The re-designed model has a more efficient nozzle but this comes at the expense of increased drag associated with the modifications required for the cowl. The results indicate that this type of vehicle design is not likely to be suitable for flight above Mach 8.

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Investigation of the flow structure in nozzles with a throat section of constant height

The results of a theoretical and experimental investigation of the flow structure in plane nozzles with a throat section of constant height are presented. The effect of longitudinal and transverse deviations in the nozzle geometry on the transonic and supersonic flow parameters is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 160–166, November–December, 1990.     

Experimental investigation of flow in nozzles of gas-dynamic lasers

To produce an active medium in a gas-dynamic laser, it is necessary to ensure rapid and deep cooling of a mixture of gases (usually CO₂-N₂-H₂O). For this, one uses, as a rule, flat supersonic nozzles with a corner point that are designed for obtaining a flow with Mach number M=4.5–6. The requirements on their dimensions and profile are determined by the kinetics of the relaxation processes in the expanding gas stream and the need to obtain at the exit a sufficiently uniform field of the gas-dynamic parameters. Because of the complexity of making nozzles, one frequently uses simplified shapes, which generate shock waves in the resonator cavity. This increases the divergence of the laser beam and reduces the population inversion of the vibrational levels of the CO₂ molecule [1] because of the growth of the temperature and the density behind shock waves. Therefore, for the correct interpretation of the results of measurements of the gain of a weak signal and correct comparison with calculations, it is necessary to make a combined study of the inversion properties of the flow and the aerodynamics of the flow. In the present work, we have investigated the flow structure in a number of small flat nozzles. Data on measurements of in a gas-dynamic laser using these nozzles are given in [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 178–182, September–October, 1980.     

Investigation of supersonic flows in conical nozzles

The article gives the results of an investigation of flows in supersonic axisymmetric conical nozzles with the presence of shock waves in the flow. The method of straight-through calculation [1] and the method of small perturbations [2] are used. An investigation is made of the effect of various geometric parameters and of the adiabatic index on the flow of a gas in conical nozzles. A comparison is made with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 101–107, May–June, 1974.In conclusion, the authors thank N. V. Drozdov for his participation in carrying out the calculations.     

Correlations of flow maldistribution parameters in an air cooled heat exchanger

The present paper provides correlations of flow maldistribution parameters in air‐cooled heat exchangers. The flow field in the inlet header was obtained through the numerical solution of the governing partial differential equations including the conservation equations of mass and momentum in addition to the equations of the turbulence model. The results were obtained for different number of nozzles of 2–4, different inlet flow velocities of 1–2.5m/s and different nozzle geometries in addition to incorporation of a second header. The results are presented in terms of mass flow rate distributions in the tubes of the heat exchanger and their standard deviations. The results indicate that the inlet flow velocity has insignificant influence on maldistribution while the nozzle geometry shape has a slight effect. Also, the results indicate that reducing the nozzle diameter results in an increase in the flow maldistribution. A 25% increase is obtained in the standard deviation as a result of decreasing the diameter by 25%. Increasing the number of nozzles has a significant influence on the maldistribution. A reduction of 62.5% in the standard deviation of the mass flow rate inside the tubes is achieved by increasing the number of nozzles from 2 to 4. The results indicate that incorporating a second header results in a significant reduction in the flow maldistribution. A 50% decrease in the standard deviation is achieved as a result of incorporation of a second header of seven holes. It is also found that the hole‐diameter distribution at the exit of the second header has a slight influence on the flow maldistribution. Correlations of the flow maldistribution in terms of the investigated parameters are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal supersonic nozzles with power-law generators

The problem of designing supersonic nozzles that provide maximum exhaust thrust is considered. An analytical solution is derived on the basis of a local analysis of the aerodynamic force distribution. It is shown that near-optimal thrust characteristics are realized by nozzles with a power-law dependence of the radius on the longitudinal coordinate with an exponent 2/3. The study is performed within the framework of the Euler model of an inviscid, non-heat-conducting gas.     

Mixed boundary-value problems of profiling of supersonic nozzles and channels

In the framework of the inverse method of numerical profiling of the supersonic part of nozzles and channels, two new mixed boundary-value problems of gas dynamics are formulated and solved with boundary conditions specified both along and across the flow. A modification of the grid-characteristic method with respect to layers formed by streamlines is constructed. The solution of the posed mixed problems makes it possible to profile a class of flat and axisymmetric nozzles and channels larger than the known class. Transition channels, which transform one expanding flow into another for which the flow at the exit is close to that from a source, are constructed Channel profiles are obtained with a bend in the generator that suppress shock waves on the wall. The results are presented of profiling of exit channels with contact discontinuity, and also channels that realize discontinuities in the exit sections, these being made isentropic by means of compression characteristics focused at the points of the discontinuity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 112–118, July–August, 1983.We thank U. G. Pirumov, M. Ya. Ivanov, and A. N. Kraiko for helpful discussions.     

Optimal Profiling of the Supersonic Part of a Plug Nozzle Contour

The problem of the optimal profiling of the supersonic part of a plug nozzle contour is solved within the framework of the ideal (inviscid and non-heat-conducting) gas model. The contours obtained provide a thrust maximum for given uniform sonic flow in the radial critical section of the nozzle, given constraints on the nozzle dimensions, and a given outer pressure (counterpressure). The initial sonic regions of the optimal contours are profiled on the basis of the condition that there the flow Mach number is unity. Varying the initial sonic region length makes it possible to construct nozzles of different sizes. The possibilities of the computational programs developed are demonstrated with reference to the example of plug nozzles, optimal when operated in a vacuum. It is shown that low thrust losses are obtained even for moderate nozzle dimensions. In the examples calculated, the optimal plug nozzles provide a greater thrust than the optimal axisymmetric and two-dimensional nozzles with an axial sonic flow for the same lengths and gas flow rates.     

Effect of Gas Non-Ideality on the Performance of Laval Nozzles with an Abrupt Constriction

The flows in Laval nozzles with a ero-length region of abrupt constriction and in nozzles with smooth entrance regions are studied on the basis of the Reynolds equations supplemented by a differential turbulence model. It is established that the viscosity effect does not lead to flow separation in the vicinity of the minimum section of optimal nozzles with an abrupt constriction. In all the examples calculated, the thrust of these nozzles is greater than that of nozzles with smooth a constriction and an optimally contoured supersonic part, the flow rate through the nozzle being larger when viscosity is taken into account than in the ideal (inviscid) case.