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).     

Free and confined jets at low Reynolds numbers

Free jets, and jets with tubular confinements, are investigated in the jet Reynolds number regime 80 Re_j 1000 being of interest for micro-jet pumps, among other applications. For issuing the jets, conventional (single-hole) nozzles as well as dual-hole nozzles of a particular design are used. Both flow visualization and LDA measurement indicate that, in agreement with previous findings, the jets issuing from conventional nozzles remain laminar up to large distances from the orifice. Thus there is but little entrainment of ambient fluid, and the performance of conventional nozzles in micro-jet pumps is rather poor. The dual-hole nozzles, on the other hand, are found to enforce transition to turbulent flow near the orifices. As a result, the entrainment rate is considerably increased, and the performance of jet pumps is improved when the dual-hole nozzles are applied. The experimental data are found to be in fair agreement with predictions based on mass and momentum balances.     

Temperature impact on the turbulence generated by the interaction of twin inline inclined jets in crossflow

Consideration is given to the interaction of twin tandem jets with an oncoming uniform crossflow. A variable temperature is assumed for the emitted jets while the crossflow is maintained constant, equivalent to the ambient temperature. Both jet nozzles are elliptic, as initially inclined with an angle of 60°, placed three diameters apart in line with the crossflow and discharge a nonreactive fume. The handled configuration is numerically simulated in the present work, by means of the finite volume method together with a non uniform grid system. The model is first validated with reference to available experimental data, in the simple isothermal case of air jets in air crossflow. It is then upgraded by considering a nonreactive fume discharged at a variable temperature. The upgraded model turbulence is described by means of the Reynolds Stress Model second order turbulent closure model. The present work is to our knowledge pioneering in the introduction of this particular model is such a configuration and its introduction proved to be highly valuable since is described satisfyingly the turbulent behavior of the resulting flowfield. This behavior is, precisely, specified in terms of shear stress components whose evolutions, explored along the different directions of the domain, showed a more pronounced vertical mixing, and gave rise to more significant vortices in most characterizing zones: near the injection plane as well as within the discharging nozzles.     

Electrostatic interaction of free EHD jets

Three spray systems with multiple nozzles arranged linearly, of different geometrical configurations were tested experimentally: (1) spray nozzles without induction electrodes facing a distant plate, (2) spray nozzles with two parallel bar induction electrodes, and (3) spray nozzles with individual ring induction electrodes. The systems were set to operate at the precession mode of spraying. In all the systems, except that of individual induction electrodes, the precession mode of spraying was first set at peripheral nozzles, and next, for higher voltages, at central nozzles. In the system with ring induction electrodes, the precession mode of spraying was generated for all nozzles at the same voltage level. The size and charge distributions of the droplets were measured for each spray system. The charge distribution of the droplets was measured with a ring induction probe, and it was compared with the charge distribution determined numerically from the size distribution of the droplets, based on the Rayleigh limit formula. It was shown that both these distributions correlate quite well. Free droplets suspended and moving irregularly within the centre of the charged spray plume were observed in the system with individual rings.     

Calculating the Thrust Characteristics of Nozzles from Their Outlet Cross-Section Parameters

Within the framework of boundary-layer theory, simple formulas are presented for finding the viscous loss from the gas parameters in the nozzle outlet cross-section. The analysis is performed for ordinary Laval nozzles and spike nozzles. It is found that for nozzles with large expansion ratios the viscous loss is almost independent of the outlet cross-section parameters and is determined only by the parameter values on the nozzle contour. The effect of the longitudinal nozzle curvature on this loss is investigated. It is shown that the viscous losses calculated from the nozzle outlet parameters and by integrating along the nozzle contour with account for the longitudinal curvature fully coincide.     

Experimental studies of a steam jet refrigeration cycle: Effect of the primary nozzle geometries to system performance

This paper describes an experimental investigation of a steam jet refrigeration. A 1 kW cooling capacity experimental refrigerator was constructed and tested. The system was tested with various operating temperatures and various primary nozzles. The boiler saturation temperature ranked from 110 to 150 °C. The evaporator temperature was fixed at 7.5 °C. Eight primary nozzles with difference geometries were used. Six nozzles have throat diameters ranked from 1.4 to 2.6 mm with exit Mach number of 4.0. Two remained nozzles have equal throat diameter of 1.4 mm but difference exit Mach number, 3.0 and 5.5. The experimental results show that the geometry of the primary nozzle has strong effects to the ejector performance and therefore the system COP.     

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     

Studies on freejets from radially lobed nozzles

The freejet characteristics of radially lobed nozzles were studied experimentally. Schlieren photographs of the freejets revealed that the lobes of the nozzles gave rise to alternate expansion-compression regions. For two of the lobed nozzles the potential core was reduced by a factor of three relative to the conical nozzle tested. The jet spread and the shear layer thickness of the lobed nozzles were considerably higher than those for the conical nozzle. The jet width and the shear layer thickness were higher in the major plane; however, the shear layer growth rate was higher in the minor plane of the lobed nozzles. Jet axial thrust measurements revealed a thrust loss of 14% for two of the lobed nozzles tested.     

Comparison of the efficiencies of spike and combined annular nozzles

The comparative efficiency of two layouts of self-adjusted annular nozzles operating over a wide flight altitude range is studied. One of the layouts is presented by the so-called spike nozzles (plane or antisymmetric, with a central body) having the property of self-adjustment when operating in different regions of the flight trajectory. The possibility of locating an annular plug nozzle or a conventional round nozzle in the base region of an axisymmetric spike is considered as a possible means for reducing its base losses. Two layouts of annular self-adjusted nozzles (in combination with internal nozzles or without them) are optimized for the mean thrust in operation in the launch and altitude flight regimes using the “classical” and “genetic” approaches. It is shown that optimal annular spike nozzles in combination with internal nozzles do not provide considerable advantages in the thrust compared with purely spiked optimal configurations. At the same time, an effective optimization of spike nozzles with account for the contribution made by the base thrust can ensure a comparatively low level of the losses.     

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.     

A numerical study of turbulent opposed impinging jets issuing from triangular nozzles with different geometries

In present research, two turbulent opposed impinging air jets issuing from triangular nozzles with fixed and variable exit velocity ratios and different nozzle-to-nozzle distances have been studied numerically and then compared with rectangular and circular nozzles. The finite volume method has been applied for solving mass and momentum equations. The turbulence model being used here is k-ε RNG. Distributions of pressure, turbulence, kinetic energy and its dissipation rate in various regions especially on the impingement regions have been obtained with high accuracy. Study of the nozzle geometries has shown the advantage of triangular nozzles over other geometries. First, the triangle’s base in nozzle geometry has an important role in our study case which, mixing two flows and regions with high turbulence intensity, directly depends on it. Second, our results show that circular and rectangular nozzles have less efficiency than triangular nozzles in mixing applications. Third and last, it was found that the radial jet being created by opposed jets has some similarities to free jets. In this investigation, air in standard atmospheric pressure has been applied as working fluid.     

Investigation into the effect of nozzle shape on the nozzle discharge coefficient and heat and mass transfer characteristics of impinging air jets

High velocity impinging air jets are commonly used for heating, cooling and drying, etc. because of the high heat and mass transfer coefficients which are developed in the impingement region. In order to provide data for the designers of industrial equipment, a variety of slot nozzles were tested to determine the effect on heat transfer of both nozzle shape and slot width. A large multi-nozzle rig was also used to measure average heat and mass transfer characteristics under arrays of both slot nozzles and circular holes. As a necessary preliminary to the heat transfer investigation, the discharge coefficients of the nozzles were measured. Then, the experimental results are compared with the simplified flow model. A good agreement was found between the theoretical and experimental results. From the tests, it was also found that the heat transfer results from differently shaped nozzles could be satisfactorily correlated provided that the effective slot width or hole diameter was used to characterize the nozzle shapes.     

Loss of Specific Impulse Due to Friction in Spike Nozzles

The class of nozzles with a central body, so-called spike nozzles, is considered for axisymmetric and plane central body geometries. A method of constructing the nozzle contour is outlined. The boundary layer is calculated using a three-parameter turbulence model and the loss of specific impulse due to friction in both spike nozzles and a Laval nozzle with the same expansion ratio are determined. A comparative analysis of the calculation results obtained, which makes it possible to determine the advantages and limitations of the nozzles considered, is carried out.     

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.     

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     

Limits of existence of shock-free extremal axisymmetric nozzles

A series of curves bounding the region of existence of shock-free extremal exhaust nozzles is constructed for various values of the specific heat ratio. Outside this region the extremal nozzles contain focused suspended shocks.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–177, March–April, 1991.     

Nozzle parameters affecting vortex tube energy separation performance

This experimental study reports the effect of nozzle parameters on the energy separation of the vortex tube. The results indicate that maximum energy separation is achieved with tangential nozzle orientation while the symmetry/asymmetry of nozzles has a minimal effect on the performance of the energy separation. For current selected conditions and parameters, the study shows that the optimum number of nozzles for maximum energy separation is around 4 nozzles.     

Supersonic Gas Flows in Radial Nozzles

Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.     

An experimental study on jets issuing from elliptic inclined nozzles

This paper reports on an experimental flow visualisation and digital particle image velocimetry investigation on forced jets exhausting from aspect ratio equal to three elliptic nozzles with exits inclined at 30° and 60°. Flow images show that shear layer instabilities and subsequent vortex roll-ups are formed parallel to the inclined nozzle exits at 30° incline and that rapid re-orientation of the vortex roll-ups occurs at 60° incline. Flow observations also show that strong axis-switching occurs in a non-inclined elliptic nozzle. However, 30° and 60° elliptic inclined nozzles produce significant distortions to and suppression of the axis-switching behaviour, respectively. As a result, flow stresses and turbulent kinetic energy distributions become increasingly asymmetric. Their coherency and magnitudes along the shorter nozzle lengths also vary significantly. This can be attributed to the dissimilar formations of vortex roll-ups and rib structures, as well as unequal mutual interactions between them as the incline-angle increases. Lastly, results also show that unlike circular inclined nozzles, elliptic inclined nozzles do not produce serpentine-shaped jet columns nor lead to significant lateral jet-spread at large incline-angles.     

Analysis of some supersonic nonsymmetric nozzles

Supersonic nonsymmetric plane nozzles, which are characterized mainly by centered compression and rarefaction waves, were constructed earlier in [1]. An intensive compression wave is undesirable in a number of cases, because of the possibility of boundary-layer detachment on the nozzle walls, for instance. Hence, some constraints on the pressure gradient, for example, the condition that the pressure does not grow at the walls, must be included in the formulation of the problem. The presence of this last condition distinguishes the results in [1] only by the fact that the centered compression waves in the nozzles are replaced by constant parameter sections. Considered below under identical conditions are nonsymmetric nozzles with compression waves, with constant parameter sections, and, also, known nozzles with a straight lower wall for comparison.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–156, May–June, 1976.The author is grateful to A. N. Kraiko for his interest and attention to the research and for useful discussions.