Flow in a viscous jet escaping through a supersonic nozzle into a semi-infinite ambient space

The problem of an axisymmetric gas flow in a supersonic nozzle and in the jet escaping from the nozzle to a quiescent gas is solved within the framework of Navier-Stokes equations. The calculated pressure distribution is compared with that measured in the jet by a Pitot tube. The influence of the jet pressure ratio, Reynolds number, and half-angle of the supersonic part of the nozzle on nozzle flow and jet flow parameters is studied. It is shown that the distributions of gas-dynamic parameters at the nozzle exit are nonuniform, which affects the jet flow. The flow pattern for an overexpanded jet shows that jet formation begins inside the nozzle because of boundary-layer displacement from the nozzle walls. This result cannot be obtained with the inviscid formulation of the problem.     

Flow of a conducting gas jet beyond the nozzle outlet of an electromagnetic accelerator

A solution is given for the problem of the motion of a conducting gas beyond the outlet of an accelerator. The form of the jet is found as well as the distribution of all jet parameters. The problem is solved assuming that the flow is plane, that there are no Hall currents, and that the velocity increase in the jet is small compared with the magnitude of the velocity at the exit of the accelerator channel.     

The stick-slip problem for a round jet

Summary The stick-slip problem for a round jet studied in Part I gives a good approximation for the swell of a low speed jet when the surface tension is large but it fails when the surface tension is small. In this paper a new stick-slip problem (II) is defined and solved using matched eigenfunction expansions. The new problem reduces to that solved in Part I when the surface tension is large and gives good results in the case of zero and small surface tension.With 18 figures     

Mathematical simulation of unsteady flow past a wing with jets

The various approximate approaches to the investigation of the unsteady aerodynamic characteristics of an airfoil with jet flap [1–3] are applicable only for an airfoil, low jet intensity, and low oscillation frequencies. In the present paper, the method of discrete vortices [4] is generalized to the case of unsteady flow past a wing with jets and arbitrary shape in plan. The problem is solved in the linear formulation; the conditions used are standard: no flow through the wing and jet, finite velocities at the trailing edges where there is no jet, and also a dynamical condition on the jet. The wing and jet are assumed to be thin and the medium inviscid and incompressible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–144, May–June, 1982.     

Symmetric shapes of contact of a jet with the surface of a heavy liquid

The plane linearized problem of oblique impingement of a weightless jet of an ideal incompressible fluid on the surface of a heavy fluid is considered. Flows are sought with symmetric forms of the contact region. Mathematically we arrive at the problem of the eigenvalues and eigenfunctions of an integral equation; solving this problem we obtain various contact forms. The fundamental result for the infinitesimally thin jet of finite intensity is derived by passing to the limit, yielding a result analagous with the forms of free vibrations of a string. Some results are presented for the problem under consideration in the nonlinear formulation.The two-dimensional problem on (vertical) impingement of a jet on a liquid was solved by Olmstead and Raynor [1]. Some results for oblique impingement of a sufficiently thin, slightly curved jet are presented by Frolov [2], Information on other studies, primarily experimental, is presented in [3].This problem is related to the model of a jet curtain of an air-cushion vehicle; in this regard we note the study of Stepanov [4] in which, in particular, a result is obtained for an infinitesimally thin jet curtain.     

Thermal multipoles for a jet in ambient spathermal multipoles for a jet in ambient space

A general solution of the thermal problem for a non-self-similar axisymmetric jet is determined on the basis of the multiple approach developed for problems of non-self-similar jets in ambient space [1, 2], and several problems of convective heat-transfer in simply- or doubly-connected domains are solved. The advantage of expanding the solution of the convective heat conduction equation in eigenfunctions of the problem is demonstrated. As an illustration, the solutions for a thermal dipole and quadrupole and for a jet flow in a heated tube are presented. The corresponding solutions are also obtained for a turbulent jet in ambient space. The most favorable heat-exchange regime for a jet in a heated tube is predicted on the basis of the particular behavior of the eigenfunctions of the thermal problem.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–46, January–February, 1996.     

Stability of a viscous liquid microjet in DC and AC electric fields

The problem of the stability of a liquid electrolyte jet under the action of a tangential electric field is considered. The radii of these jets, usually observable in experiments, vary from nanoscales to microscales. In this study, we consider microjets with the characteristic thickness of the double ion layer near the interface much less than the jet radius. The stability problem is analytically solved with account for the presence of this small parameter. The assumption on the electric neutrality of the jet as a whole leads to an explicit expression for the surface electric charge induced by the external field. The solution of the hydrodynamic problem in the external domain closes the solution and gives the dependence of the disturbance growth rate on the wavenumber. The cases of DC and AC electric fields are qualitatively compared. The distinctive features of jet stabilization by an AC high-frequency electric field are discussed.     

A family of new solutions on the wall jet

The fluid flow problem within the wall jet created by fluid hitting on a solid surface at the right angle is solved based on the homotopy analysis method (HAM). A new family of solutions for jet with injection/suction which has been overlooked so far are obtained. Numerical evidence seems to suggest that these solutions decay algebraically far away from the wall.     

Computations for a jet impinging obliquely on a flat surface

A SIMPLE-C algorithm and Jones-Launder k-ε two-equation turbulence model are used to simulate a two-dimensional jet impinging obliquely on a flat surface. Both the continuity and momentum equations for the unsteady state are cast into suitable finite difference equations. The pressure, velocity, turbulent kinetic energy and turbulent energy dissipation rate distributions are solved and show good agreement with various experimental data. The calculations show that the flow field structure of the jet impinging obliquely on a flat surface is strongly affected by the oblique impingement angle. The maximum pressure zone of the obliquely impinging jet flow field moves towards the left as the oblique impingement angle is decreased.     

Optimization of energy supply in an electropulse water jet for the discharge-time-mean outflow velocity

The variational problem of optimizing the energy supplied to the discharge channel of a pulsed water jet in order to maximize the mean jet outflow velocity is considered. The problem is solved in the gasdynamic formulation using the general method of indefinite Lagrange multipliers. The optimality conditions are derived by considering the smeared flow. Both the direct and conjugate problems are solved by the shock-capturing method. An example of the calculation is presented. Donetsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 104–110, January–February, 1997. This research was carried out under the program of the International Research Fund, grant No. U9600.     

An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows

In this paper, an incompressible smoothed particle hydrodynamics (SPH) method is presented to solve unsteady free-surface flows. Both Newtonian and viscoelastic fluids are considered. In the case of viscoelastic fluids, both the Maxwell and Oldroyd-B models are investigated. The proposed SPH method uses a Poisson pressure equation to satisfy the incompressibility constraints. The solution algorithm is an explicit predictor-corrector scheme and employs an adaptive smoothing length based on density variations. To alleviate the numerical difficulties encountered when fluid is highly stretched, an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material. Two challenging test cases, the impacting drop and the jet buckling problems, are solved to demonstrate the capability of the proposed scheme in handling viscoelastic flows with complex free surfaces. The jet buckling test case was solved for a wide range of Weissenberg numbers. It was shown that in all cases the method is stable and fairly accurate and agrees well with the available data.     

气流作用下同轴带电射流的不稳定性研究

通过对气体驱动同轴电流动聚焦的实验模型进行简化,开展了电场力和惯性力共同作用下同轴带电射流的不稳定性理论研究.在流动为无黏、不可压缩、无旋的假设下,建立了三层流体带电射流物理模型并得到了扰动在时间域内发展演化的解析形式色散关系,利用正则模方法求解色散方程发现了流动的不稳定模态,进而分析了主要控制参数对不稳定模态的影响.结果表明,在参考状态下轴对称模态的最不稳定增长率最大,因此轴对称扰动控制整个流场.外层气流速度越高,气体惯性力越大,射流的界面越容易失稳.内外层液-液同轴射流之间的速度差越大,射流越不稳定.表面张力对射流不稳定性起到促进作用.轴向电场对射流不稳定性具有双重影响:当加载电场强度较小时,射流不稳定性被抑制;当施加电压大于某一临界值时,轴向电场会促进射流失稳.临界电压的大小与界面上自由电荷密度和射流表面扰动发展关系密切.这些结果与已有的实验现象吻合,能够对实验的过程控制提供理论指导.     

The spatial modulation of a forced triangular jet

An investigation of the possibility of controlling the evolution of jets into the far field is presented. Driven by practical concerns the study examined a highly turbulent jet flow. To enhance controllability of the flow evolution the virtues of non-circular nozzles and active flow excitation were combined. The study examined an air jet, Re _de =8000, average turbulence intensity 1.8%, issuing into stagnant room air out of a triangular nozzle, which had piezoceramic actuators mounted on the flat sides. The evolution of the jet flow field was examined over the range of 0X/D30.Small amplitude, single mode, excitation with frequency as the varying parameter was found to be ineffective for controlling the far field evolution. In contrast, excitation of the jet with non-integer and counter propagating azimuthal modes yielded marked changes in the jet streamwise evolution. The most notable changes in the far field were the transition of the cross section from round to elliptical, increased jet cross sectional area based on half centerline velocity contour, asymmetric threedimensional flow, and an increase in the entrainment rate. The entrainment of ambient air by the jet increased slightly more than twofold for non-integer and counter propagating azimuthal modes, compared with the unexcited jet, and only a 50% increase in the entrainment for single, integer, mode excitation.While excitation of the jet with modes m=0 and 1 resulted in symmetric evolution of the jet in the x-y-t space, excitation at non-integer and counter propagating modes resulted in time-dependent asymmetric motion. The near field induced jet column motion is controlling the far-field evolution of the examined jet.The authors would like to thank Dr. S. Ragab for useful discussions, and Dr. R. Kriz for access to the Scientific Visualization Laboratories, both from the ESM department at Va. Tech. The opportunities to discuss the research with Dr. M. G. Mungal from Stanford University are highly appreciated     

Trajectories of charged solid particles in an air jet under the influence of an electrostatic field

Among modern coating techniques electrostatic powder spraying is one of the most attractive. In this method the plastic particles are charged by a high voltage electrode inside a coating gun. The charged particles are entrained by an air jet and directed towards the object to be coated, which is electrically grounded.In the present paper experimental trajectories of particles emerging from an electrostatic gun are determined. The equations of motion of particles in a jet are written in Lagrangean coordinates and solved numerically. Results are compared with the experimental data.     

Instability waves and low-frequency noise radiation in the subsonic chevron jet

Spatial instability waves associated with lowfrequency noise radiation at shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier–Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear,and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at downstream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.     

Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Direct numerical simulations of an axisymmetric jet with off-source volumetric heat addition are presented in this paper. The system solved here involves a three-way coupling between velocity, concentration and temperature. The computations are performed on a spherical coordinate system, and application of a traction free boundary condition at the lateral edges allows physical entrainment into the computational domain. The Reynolds and Richardson numbers based on local scales employed in the simulations are 1000 and 12 respectively. A strong effect of heat addition on the jet is apparent. Heating causes acceleration of the jet, and an increased dilution due to an increase in entrainment. Further, the streamwise velocity profile is distorted, and the cross-stream velocity is inward for all radial locations for the heated jet. Interestingly, the maximum temperature is realized off-axis and a short distance upstream of the exit of the heat injection zone (HIZ). The temperature width is intermediate between the scalar and velocity widths in the HIZ. Normalized rms of the concentration and temperature increases in the HIZ, whereas that of streamwise, cross-stream and tangential velocities increases rapidly after decreasing. Both mass flux and entrainment are larger for the heated jet as compared to their unheated counterparts. The buoyancy flux increases monotonically in the HIZ, and subsequently remains constant.     

Numerical study of spatial supersonic flow of a perfect gas with transverse injection of jets

Three-dimensional supersonic turbulent flow in the presence of symmetric transverse injection of round jets through slots in the walls is studied numerically. The simulation is based on Favre averaged Navier-Stokes equations solved using the Beam-Warming method. The influence of the ratio of the pressure in the jet to that in the flow (pressure ratio) on the spatial interaction of the injected jet with the oncoming flow is studied. Experimental pressure distributions on the wall near the jet approximated by curvilinear closed ellipses are reproduced numerically. The mechanism of the formation of two symmetric vortices in the mixing layer between the jet and the oncoming flow is studied. The results of the calculations are found to be in satisfactory agreement with the experimental dependence of the length of the separation zone on the pressure ratio of the jet to the flow.     

Stability of a viscous liquid jet in a high-frequency alternating electric field

The stability of a liquid electrolyte placed in a tangential electric field oscillating harmonically at high frequency is considered assuming that the liquid is viscous and Newtonian. It is shown that, if the Peclet number calculated from the thickness of the Debye layer is small, the problem can be solved separately for the electrodynamic part of the problem in the Debye layer and for the hydrodynamic part of the problem in the jet. The linear stability of the trivial solution of the problem is investigated. A dispersion relation is derived and used to study the effect of the amplitude and frequency of electric field oscillations on the stability of the jet. It is shown that the presence of the external oscillating field has a stabilizing effect on the jet. The basic stability regimes as functions of the control parameters of the problem and bifurcation changes in the regimes are investigated.     

Jet Outflow from a Small Hole in a Plane

On the basis of the method of matched asymptotic expansions, the problem of the outflow of a nonswirling axisymmetric laminar jet from a hole in a plane is solved for large Reynolds numbers. Since directly matching the leading terms of the asymptotic expansions for the axial boundary layer and the main flow region is impossible, the problem is solved by introducing an intermediate region. In the axial region the solution is the Schlichting solution [1] for an axisymmetric jet in the boundary-layer approximation, in the intermediate region the solution is found analytically, and in the main flow region the problem is reduced to that of viscous flow induced by a sink line in the presence of a transverse wall [2].