Investigation of the microstructure a turbulent jet in a wake

The study of the characteristics of the turbulence in the boundary layer and in free jets is one of the most important problems of the aerodynamics of viscous fluids. The accumulation of information on the pulsation characteristics of jet flows and the establishment of the corresponding governing laws may serve to verify the basic hypotheses of the semiempirical theories of turbulence, and also for the development of more advanced computational methods. In many cases the measurement of the pulsation characteristics of turbulent jets is of practical interest.The studies made up till now [1–5] of the microstructure of turbulent flow in the primary region of submerged axisymmetric jets have made it possible to obtain several interesting results. In particular, in addition to the average velocity profiles, hot-wire anemometric equipment has been used to measure the normal and tangential Reynolds stresses and also the intermittency factor in cross sections of the jet, the distribution of the intensity of the longitudinal and lateral velocity pulsations along the axis, the correlation coefficients and the corresponding integral turbulence scales, etc. These measurements have made it possible to draw several important conclusions on the mechanism of turbulent exchange, on the order of the terms omitted in the equation of motion, and on the semiempirical theories of turbulence [6–9].The common deficiency of the studies mentioned above is that near the boundary of a submerged jet, where the average velocity is practically equal to zero, the intensity of the pulsations is so great that it makes the reliability of the results obtained by means of the hotwire anemometer questionable. In this connection Townsend [6] indicated the advisability of studying the microstructure of a turbulent jet issuing into a low-velocity ambient flow.The present study had as its objective the investigation of the microstructure of the primary region of an axisymmetric jet in a wake flow over quite a broad range of the flow ratio parameter m=u/u₀;here u₀ is the average velocity at the nozzle exit, u is the velocity of the ambient stream. For various values of the parameter m in the primary region of the jet measurements were made of the profiles of the three components of the pulsation velocity and the Reynolds shear stresses, and also the values of the average velocity and two components of the pulsation velocity at a large number of points on the jet axis. The measured profiles of the Reynolds shear stresses were compared with the corresponding profiles calculated on the basis of the boundary layer equations from the experimentally determined average velocity profiles. For two values of the parameter m, in one of the sections of the jet measurements were made of the correlation coefficients of the longitudinal components of the pulsation velocity and the variation across the jet of the integral turbulence scale was determined.The results obtained give an idea of the influence of the parameter m on the characteristics of the turbulent jet in an ambient stream.     

The critical jet flow regime

The critical jet flow regime is investigated on the basis of the equations for the Reynolds stresses, the boundary layer equations and the elements of the theory of thermal explosion. The results of calculating the transition Reynolds numbers for plane and axisymmetric jets and for wake flows are compared with the theoretical values obtained by other methods and with the data of experimental research.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–15, May–June, 1990.     

Calculation of the initial segment and the stabilized flow segment in two-dimensional separation-free diffusers

The aerodynamic characteristics of a series of plane diffusere with straight walls are calculated for a broad range of divergence angles, Reynolds numbers, and the parameter which characterizes the initial flow nonuniformity.The fluid is assumed to be incompressible. The calculations are made for the case in which the boundary layer is fully turbulent, i. e., there is no laminar flow segment near the entrance section.The calculation of separation-free flow in diffuser channels is based on the use of boundary layer theory [1]. It has now become possible to carry out large-scale calculations for diffusers whose geometric and aerodynamic parameters vary over rather wide limits. This is the result both of the use of computers and of the fact that the modern approximate methods for calculating the turbulent boundary layer have been reduced to comparatively simple interpolation formulas [2].Usually, in the calculation of diffusers we examine only the initial flow segment, within the limits of which the boundary layers which form on the walls do not come together, i. e., there is a potential core. The laws governing diffuser flow in the absence of the potential core have been studied relatively little; the only known solutions are those of [3], which are valid at a very great distance from the entrance section.In this study we examine three characteristic flow zones: the initial segment, extending from the entrance section to the section at which the boundary layers come together; the stabilized-flow zone with closed boundary layers comprised of two characteristic segments-the transitional segment extending from the plane where the boundary layers join to the beginning of the radial flow segment; and, finally, the radial (self-similar) flow segment, characterized by constancy of all the dimensionless boundary layer characteristics along the flow. It is obvious that this division into characteristic zones is arbitrary: a consequence of the adopted flow idealization is a break in the curves expressing the aerodynamic characteristics as a function of the axial coordinate at the junction of the initial segment and the stabilized-flow segment. It is well known that a similar phenomenon occurs in the calculation of free turbulent jets based on arbitrary division of the jet into two segments-initial and primary segments [4].The computer calculation of the initial segments was performed by A. N. Smol'yaninova, and the stabilized-flow segments were calculated by I. N. Podol'nyi.     

Numerical investigation of axisymmetric flows in the wake of blunt bodies in a supersonic stream of viscous gas

The axisymmetric flow in the near wake of spherically blunted cones exposed to a supersonic stream of viscous perfect heat-conducting gas is numerically investigated on the basis of the complete Navier-Stokes equations. The free-stream Mach numbers considered M = 2.3 and 4 were such that the gas can be assumed to be perfect, and the Reynolds numbers such that for these Mach numbers the flow in the wake is laminar but close to laminar-turbulent transition [1–4]. The flow structure in the near wake is described in detail and the effect of the Mach and Reynolds numbers on the base pressure, the total drag and the wake geometry is investigated. The results of calculating the flow in the wake of spherically blunted cones are compared with the experimental data [4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 42–47, July–August, 1988.     

Influence of the initial conditions on axisymmetric jets in a parallel flow

An experimental investigation was made of the initial-section flow of axisymmetric helium, air, and freon-12 jets in a parallel air flow for two different velocity profiles at the nozzle exit near the boundary of the jet. In one case, the velocity profile was determined by boundary layers on the nozzle walls; in the other case, it was produced artificially by means of a honeycomb of tubes of variable length. Measurements were made of the profiles of the mean and the pulsation velocity and the temperature. The flow was also photographed. The investigations showed that, depending on the initial conditions, the intensity of mixing of the jets in the initial section at Reynolds numbers Re 10⁴ (calculated using the jet diameter) can change from the level determined by molecular diffusion to the level characteristic of developed turbulent flow. The flow structure in the annular mixing layer also depends strongly on the initial conditions. The observed ordered structures in the mixing layer are related to a section of development of perturbations near the nozzle. The ordered structures are strongly influenced by the effect on the jet of acoustic vibrations from an external source. When the initial velocity profile is produced by the honeycomb, the transition to developed turbulence may be due to the development of long-wavelength perturbations or to the development of small-scale turbulence generated by the flow over the end of the honeycomb.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 18–24, July–August, 1980.We thank V. M. levlev and K. I. Artamonov for assistance and for discussing the work.     

Effect of a dispersed component on the nature of heat exchange during flow of a heterogeneous-jet around a barrier

Flow in a turbulent nonisothermal heterogeneous jet is characterized by considerable velocity [1, 2] and temperature disequilibrium [3] (u_s u and T_s T, where u_s, T_s and u, T are velocity and temperature of dispersed and gas components). As was shown in [4], an impurity is not passive, and it leads to suppression of jet turbulence (a result of interphase exchange by pulse and heat). Nonetheless, during reaction of a heterogeneous jet with a barrier orientated along the normal to the running flow, a significant increase is observed in heat emission characteristics in the vicinity of the point of deceleration [5] (for a single-phase jet an increase in heat exchange is typical with an increase in the intensity of turbulence [6]). The intensity of the change in heat emission in this case is a result of velocity and temperature disequilibrium for flow in jets, and it depends on a number of factors (temperature, concentration, phase condition of the dispersed impurity, etc.) and on the nature of the reaction of the dispersed component with the barrier surface [7]. There are numerous experimental data devoted to this. Apart from work in [5, 7], attention is drawn to [8] where an increase is also noted in the heat flow (by a factor of 1.4) at the deceleration point for a plane cylindrical end and a hemisphere. The aim of the present work is a study of the effect of a dispersed component on heat exchange with jet flow around a barrier.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 63–68, November–December, 1986.     

Interaction of a turbulent jet and a cocurrent confined incompressible flow

The effects induced in a coaxial circular channel flow by an axisymmetric turbulent jet are investigated for various values of the velocity and radius ratios 0.16m<1 and 2.5f30.9. The problem is solved by means of an e-L model of turbulence [1, 2]. The calculation scheme differs from the usual one for boundary layers, jets and wakes in that the pressure p is assumed to be unknown and is determined by assigning the boundary conditions for the radial velocity component and the transverse gradient of the longitudinal velocity component on both boundaries. On the basis of the calculations and the experimental data of [3, 4] generalized relations are obtained. These make it possible to estimate the turbulence characteristics of an axisymmetric jet in a confined cocurrent flow when the pressure is variable along the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 14–19, September–October, 1986.In conclusion, the author wishes to thank G. S. Glushko for constructive discussion of the results and useful advice.     

“Lateral” interaction of a supersonic underexpanded ideal-gas jet with surfaces of different shape

A numerical investigation is made of the interaction of an underexpanded jet of an inviscid and nonheat-conducting gas issuing from an axisymmetric conical nozzle with plane, cylindrical, and spherical surfaces. It is assumed that the flow turning angle for flow about a barrier is smaller than the critical angle, and subsonic regions are absent in the flow field studied. The effect of the characteristic parameters (Mach number at the nozzle exit, jet underexpansion) on the flow pattern and jet forces is analyzed. The results of numerical calculations are compared to the results of approximate theories and experimental data. A theoretical solution of the problem of the effect of a supersonic jet on a surface of given shape, even in the approximation of an inviscid, nonheat-conducting gas, is quite difficult. A reason for this is that the flow region contains shock waves interacting with each other, contact discontinuities, and zones of mixed sub-and supersonic flow. As far as is known to the authors, the results obtained for three-dimensional problems for the interaction of supersonic jets with each other or with barriers are primarily experimental (for example, [1–6]). A numerical analysis of the interaction of axisymmetric ideal-gas jets was carried out in [7–10]. In [7] a three-dimensional form of the method of characteristics was used to calculate the initial interaction region for two supersonic cylindrical jets (with Mach number M=10) intersecting at an angle of 60. The interaction of several jets has been considered in [8, 9], where the solution was obtained according to the Lax—Wendroff method without elimination of the discontinuity lines of flow parameters. In [10] the lateral interaction of axisymmetric supersonic jets with each other and with a plate is investigated by means of a straight-through calculationTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–8, November–December, 1974.The authors thank A. N. Kraiko for useful discussions of the results, and A. L. Isakov and É. N. Gasparyan for kindly providing the experimental data.     

Interaction of a turbulent wake with the outer flow

The integral methods of boundary-layer theory are used to examine the interaction of a turbulent wake with the outer flow for the example of planar flow.In contrast with the known Crocco-Lees theory [1], the turbulent layer in the gas is described with the aid of an appropriate family of velocity profiles rather than by means of a Dorodnitsyn-type transformation of the incompressible turbulent layer. The selection of the simplest among the possible systems of first order interaction equations is justified; this system reduces to a single differential equation and an estimate is given of the influence of the arbitrariness in the equation selection on the final results.The hydrodynamic meaning of the singular and nonsingular integral curves and the singular point of the interaction equation is clarified on the basis of an examination of the interaction of compression and rarefaction waves in the outer supersonic stream with the wake. The effect of blowing (suction) and the initial boundary layer on the base pressure and the supersonic interaction flow as a whole is examined on the basis of the integral conditions for the splicing of the interaction flow with the isobaric mixing flow behind the corner. It is shown that, with proper selection of the single constant in the turbulent viscosity formula, the computational results are in satisfactory agreement with experiment.In conclusion, the authors wish to thank G. G. Chernyi for helpful discussions of the study, and L. V. Kapranova and Z. A. Donskova for assistance in the calculations.     

Velocity measurements in a confined swirl driven recirculating flow

Laser-doppler measurements of the three components of mean velocity and their intensities have been made in an axisymmetric swirling isothermal turbulent combustion chamber flow. Swirl is generated by a gas-turbine aerodynamic swirler and the flow is representative of that found in the primary zone of many practical combustors. Two configurations were studied. In the first the fuel injector was removed and a central core jet entered the chamber via the resulting circular hole in the centre of the swirler. In the second case the injector was retained but a circular baffle was located at the exit plane: this latter device being necessary to prevent an inflow — not present for combusting flow — arising at the exit plane. The velocity data is sufficiently detailed to aid the testing and further development of methods for calculating combustion chamber flows.     

Special characteristics of the propagation of three-dimensional viscous jets

Numerical investigations were made of the propagation, in a supersonic wake, of uncalculated jets, flowing out of nozzles of square and rectangular cross section, and of lumped jets, made up of from two to nine individual jets; the special characteristics of their flow were investigated in the initial, transitional, and main sections. Specifically, for lumped jets, the possibility of replacing them by a single axisymmetric jet, equivalent in mass-flow rate, is discussed. To calculate a three-dimensional unexpanded supersonic jet, flowing out into a wake, in [1] it was proposed to use a numerical method for solving a simplified system of Navier-Stokes equations for steady-state flow, and numerical investigations were made of the three-dimensional interaction of four jets in a supersonic wake, at small distances from the outlet cross section of the nozzle, i.e., mainly in the initial sections of the jets, where the mixing layers along the boundaries of the jets are still not closed. Here the method of [1] is used to study the special characteristics of three-dimensional viscous jets at large distances from the outlet cross section of the nozzle in the region of the main section, where the mixing layers have come together and a single three-dimensional jet has been formed. The system of equations, the boundary conditions, the numerical method, the system of coordinates, and the nomenclature used are the same as in [1].     

Bifurcation and transition to turbulence in the gap between rotating and stationary parallel disks

The flow in the gap between rotating and stationary parallel disks is an attractive object for studying the transition characteristics in three-dimensional internal flows. Firstly, in this case a large region of the basic motion is satisfactorily described by a self-similar solution to the Navier-Stokes equations [1]; secondly, as the parameter = h²/v ( is the. angular velocity of rotation of one of the disks and h is the gap width) varies, there is an evolution of the basic motion, so that it is easy to produce different types of initial and subsequent instabilities. The basic steady regime for axially symmetric flow has been studied by many authors (see [1, 2]). Questions of the transition in the gap between disks have been considered [3, 4]. This paper presents a methodology and the results of experimental investigations for different types of initial and subsequent instabilities in the gap between disks enclosed by a cylindrical cover. It was found that as a result of the loss of stability of the basic regime one of two steady vortex regimes is developed depending on the value of the relative gap width. The subsequent stages of soft excitation of the turbulent regime are described and the corresponding boundaries established. It is shown that in very narrow gaps the excitation of turbulence has a hard nature of the type realized in Couette flow. The stability limit for a laminarized boundary layer on a rotating disk and the boundary for complete turbulence of the layer were determined for relatively wide gaps. A comparison was made with known data for an unenclosed rotating disk.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 28–36, September–October, 1984.     

Heat and mass transfer in a system of plane turbulent jets with diffusion combustion

We consider turbulent motion of premixed chemically active gases in an infinite system of plane turbulent jets in the presence of diffusive combustion. The proposed calculation method permits determining the distribution of all the parameters in the mixing zone, including the longitudinal pressure. Numerical examples of the calculation of hydrogen combustion in air are presented.The study of heat and mass transfer in jet flows presents major difficulties at the present time. Therefore all the existing methods for calculating jet flows with heat and mass transfer and chemical processes [1–5] are based on an extension of the known semiempirical theories of free turbulence to the more complex cases of flow with chemical reactions. The present study is no exception in this sense; it covers an investigation of the motion in an infinite system of plane turbulent jets with diffusive combustion.     

Nichtisotherme ebene Freistrahlen unter Schwerkrafteinfluß

Higher-order boundary layer theory is used to study the behaviour of nonisothermal laminar and turbulent free jet flows. In addition to the Prandtl boundary layer equations, an equation is used to describe the equilibrium of forces normal to the flow direction. This equilibrium exists between the buoyancy forces caused by gravity and the centrifugal forces resulting from the curvature in the flow. The proper selection of reference values permits the characteristics of the jet flow to be expressed as universal functions in which only the initial jet orientation and the Prandtl number in the case of laminar flow are input parameters. When the volume flow is given in addition to the momentum and thermal energy, the characteristic parameter are the Archimedes number for turbulent flow and the modified Archimedes number for laminar flow. The jet flow is calculated using an integral method in which the eddy viscosity and the turbulent Prandtl number are given as functions of the local Archimedes number. Comparison of experimental data from the literature and from our laboratory on nonisothermal free jets with the theoretical results, show satisfactory agreement. The universal diagrams given in the paper are valid forall plane laminar (Pr=0.7) and turbulent nonisothermal jets.     

Experimental investigation of a three-dimensional viscous underexpanded jet

The three-dimensional interaction of jet issuing from two- and four-nozzle systems into ambient space or an outer flow has been investigated experimentally. The range of the important parameters include the following: pressure imbalance n=P_a=/P=10–1.5·10², Mach number at the nozzle exit M_a=3.15, Mach number of the outer flow M=0, 3.1, and 6, the flow is turbulent in the mixing layer (P_a and P are the static pressures at the nozzle exit and in the outer flow). It is shown that the interaction of the jets broadens a multinozzle jet considerably in the plane of interaction, which is a plane of symmetry and which passes through the axis of the system between neighboring nozzles. The cross-sectional shape of a four-nozzle jet is cross-like over the entire length of the initial segment of the jet. The width of the mixing layer in the plane of interaction is considerably larger than in the central plane, which passes through the axis of opposed nozzles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 21–26, September–October, 1974.     

The entrainment behavior of a turbulent axisymmetric jet in a viscous host fluid

Although turbulent jets have been studied extensively, one configuration that has not received much attention is the viscosity-stratified jet, wherein a turbulent jet of lower viscosity issues into a density-matched host liquid of higher viscosity. We present experimental data for scalar dispersion and two-dimensional velocity measurements in the axial plane of a turbulent axisymmetric jet with a Reynolds number (Re) of 2,000 issuing into a viscous host liquid at viscosity ratios (m) ranging from 1 to 55. The presence of a strong viscosity discontinuity across the jet edge results in a significant decrease in the scalar spread rate. We attribute this to the rapid reduction in turbulence intensity and the suppression of large engulfing eddies at the jet edge. The velocity profile, on the other hand, indicates that the velocity width and mass flux reduce with increasing m up to about 20, but then increase for higher values of m. This non-monotonic variation is explained by the growing influence of viscous stress for m>20. The scalar spread rate, the velocity spread rate, the centerline velocity decay rate, and the jet mass flux are all minimized for m20 for Re=2,000.

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Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.List of symbols b _u velocity half-width of the jet - C _u, C _u,0 constants defining the velocity decay rate - D nozzle width - E _u one dimensional power spectrum of velocity fluctuations - f frequency - K _u, K _u,0 constants defining the jet spread rate - k wavenumber (2f/U) - L longitudinal integral scale - R ₁₁ correlation function - r separation distance - Re jet Reynolds number (U ₀ D/v) - St Strouhal number (fD/U ₀) - t time - U axial component of the mean velocity - U _m mean velocity on the jet axis - U ₀ mean velocity at the jet exit - u the rms of u - u fluctuating component of the axial velocity - V lateral component of the mean velocity - fluctuating component of the lateral velocity - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - v kinematic viscosity - time lag A version of this paper was presented as paper no. 86-0038 at the AIAA 24th Aerospace Sciences Meeting, Reno NV, USA, January 1986     

Numerical investigation of “lateral” interaction with an obstacle of an axisymmetric jet exhausting into vacuum

The problem of the interaction of a strongly underexpanded axisymmetric jet with an obstacle for which the normal to the surface makes an angle near /2 with the jet axis is rather laborious for numerical solution due to the high disequilibrium of the gas-dynamic parameters in the peripheral part of the jet and the three-dimensional nature of the flow in the interaction region. Therefore, the results at present available have mainly been obtained experimentally [1, 2]. Among the theoretical studies made in this direction, it is necessary to mention Ivanov and Nazarov's [3], which gives the results of numerical investigation of lateral interaction of a jet with obstacles of various shapes in the case of weakly underexpanded jets when the flow in the interaction region is everywhere supersonic. In the present paper, a study is made of the case when a jet exhausts into vacuum and in front of the obstacle there is a detached shock wave, behind which there is mixed subsonic and supersonic three-dimensional flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 49–54, November–December, 1982.We thank V. I. Uskov for assistance in the present work.     

The near field behavior of turbulent gas jets in a long confinement

The present investigation reports on the near field behavior of gas jets in a long confinement and points out the differences between this type of jet flow and those of free jets and jets in a short confinement.The jet, with a diameter of 8.73 mm, is aligned concentrically with a tube of 125 mm diameter; thus giving a confinement area ratio of 205. The arrangement forms part of the test section of an open-jet wind tunnel and this gives a confinement length-to-jet diameter ratio of 1,700. Experiments are carried out with carbon dioxide, air and helium/air jets at different jet velocities. Mean velocity and turbulence measurements are made of the jet near field using a one-color, one-component laser doppler velocimeter operating in the forward scatter mode. In addition, the turbulent shear field of an air jet is examined in more detail using hot-wire anemometers.In view of the long confinement, the presence of the jet is not being felt immediately at the tunnel exit. Consequently, the air column inside the tunnel is first compressed by the jet and then slowly pushed out of the tunnel. This behavior causes the jet to spread rapidly and to decay quickly. As a result, an equilibrium turbulence field is established in the first two diameters of the jet. This equilibrium field bears striking similarity to that found in self-preserving, turbulent free jets and jets in short confinement and is independent of jet fluid densities and velocities. In terms of these characteristics, the near field of jets in a long confinement is very different from that found in free jets and jets in short confinements.     

Interaction of a gas-droplet turbulent jet with a cocurrent high-velocity high-temperature gas flow

A mathematical model and a method for calculating a gas-droplet turbulent jet with allowance for velocity nonequilibrium and virtual mass of the condensed phase during turbulent fluctuations and also heat and mass transfer within the three-temperature scheme are developed. Methodical calculations are performed. The results of these calculations are in reasonable agreement with available experimental data. The structure of the gas-droplet jet in a cocurrent high-velocity high-temperature gas flow is studied by numerical methods. The ratio of intensities of heat and mass transfer between the phases and turbulent diffusion transfers of substances is found to be different at the initial, transitional, and basic segments of the jet. This difference is responsible for the nonmonotonic axial distribution of vapor density and the lines of the halved mass flow of the condensed phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 85–94, May–June, 2008.