Planar Jet Flow Research Articles

Numerical Simulation of Self-Excited Oscillation of a Turbulent Jet Flowing into a Rectangular Cavity

The example of a plane jet flow into a rectangular cavity (“dead end”) is used in comparing the capabilities of different approaches to numerical simulation of self-oscillatory turbulent flows characterized by global quasi-periodic oscillation of all flow parameters. The calculations are performed for two flow modes, of which the first one is statistically steady according to the available experimental data, and the second one is self-oscillatory. In both cases, three approaches are used to describe the turbulence, namely, the method of large eddy simulation (LES) in combination with the subgrid model of Smagorinsky, and steady and unsteady Reynolds averaged Navier-Stokes equations (SRANS and URANS) with two well-known differential models of turbulence. In the case of the first flow mode, all three approaches produce qualitatively similar and quantitatively close results. In the case of the second (self-oscillatory) mode, a steady-state solution of Reynolds equations may only be obtained in half the domain using the symmetry boundary conditions; within the framework of the other two approaches, the solutions turn out to be unsteady-state. In so doing, their characteristics calculated using the LES and URANS methods differ significantly from each other; in the case of URANS, they further depend on the model of turbulence employed. The best results as regards the accuracy of prediction of the amplitude-frequency characteristics of self-oscillation are produced by the use of the LES and three-dimensional URANS methods. A similar inference may be made with respect to the mean flow parameters. From this standpoint, the worst results are those obtained from calculations involving the use of the symmetry boundary conditions on the geometric symmetry plane of the flow.

Numerical simulation of turbulent free surface flow with two‐equation k–ε eddy‐viscosity models

AbstractThis paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time‐averaged Navier–Stokes equations is achieved by using the two‐equation eddy‐viscosity model: the high‐Reynolds k–ε (standard) model, with a time scale proposed by Durbin; and a low‐Reynolds number form of the standard k–ε model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non‐linear terms, a second/third‐order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high‐Reynolds k–ε model yields favourable predictions both of the zero‐pressure‐gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low‐Reynolds number form of the k–ε model are somewhat unsatisfactory. Copyright © 2004 John Wiley & Sons, Ltd.

An investigation of the behaviour of planar jets using a time accurate fractional step scheme

The transition behaviour of planar jets has been the subject of extensive investigation, using both numerical and experimental approaches. It is well known that above a critical Reynolds number the jet will exhibit a sinusoidal, flapping, bifurcation. Numerical simulations of planar jet flow have been carried out using a time accurate fractional step Navier-Stokes solver defined on a non-staggered grid. Results have been obtained for a range of Reynolds numbers to investigate the bifurcation and stability characteristics of the flow and to obtain the critical Reynolds number for the onset of unsteadiness. This critical Reynolds number is found to be in good agreement with that obtained experimentally and for a non-parallel Bickley jet using a semi-analytic stability technique, whereas earlier parallel stability results considerably under-predict this value. The numerical method is described and results presented detailing the character and behaviour of the steady and bifurcated flow together with comparisons to previous investigations.

Studies on a cooling of high heat flux surface in fusion reactor by impinging planar jet flow

Divertor surface of a fusion reactor is exposed to strong surface heating by high flux charged particles. According to typical design of ITER, the heat flux on divertor surface becomes locally near 20 MW m −2. Then, it is necessary to establish a cooling method to cool such high heat flux surface. A cooling by a planar impinging jet has been proposed. However, in the application of the impinging jet cooling to flat heated surface, high CHF is obtained in the limited region near center. As apart from the region, CHF decreases abruptly with a distance from the center. To overcome this difficulty, we proposed that an impinging planar jet was applied to a concave heated wall where a flow induced centrifugal force acts effectively along the curved surface. In a previous paper, we investigated the CHF for a free planer jet on the concave surface. In this study, CHFs in a confined planar jet, were investigated as a function of distance from the center in the various subcooling, flow velocity and curvature of cooling surface and compared with the CHF in the free planar jet cooling. To investigate CHF in the abnormal condition like mild plasma disruption, CHFs in the transient power input were investigated and discussed in comparison with the steady state CHF. Finally application by both impinging planar jets to the divertor surface are discussed.

PDF Modeling Study of a Self-Similar Turbulent Plane Jet Flow.

This study presents a turbulence probability density function (pdf) equation model to solve a self-similar turbulent plane jet flow. The approximate moment method is also applied to solve this pdf equation. The calculated mean velocity, turbulent energy and Reynolds stress agree well with the available experimental data, indicating that the pdf equation model and the moment method can quantitatively describe the statistics of free turbulence. Additionally, the turbulence energy balance and shearstress balance are calculated. According to these calculations the pdf methods are more highly promising than conventional turbulence models in terms of revealing turbulence structure. The applicability of the simple theories of turbulence is also discussed.

The study of self-sustained oscillating plane jet flow impinging upon a small cylinder

Experimental studies of a plane jet impinging upon a small circular cylinder are conducted by hot-wire measurements. The cylinder is located on the jet centerline within the potential-core region. The jet–cylinder interactions on the instability shear layer frequency, the cylinder wake shedding frequency, and the induced self-sustained oscillation phenomenon are carefully investigated. Test data indicate that the self-sustained flow oscillation is mainly generated by the resonant effect of the flow between the jet exit and the cylinder. Its resonant frequency is found to vary linearly and exhibits jump-stage pattern as a function of the distance between the jet exit and the cylinder. The feedback mechanism and the hydrodynamic instability theorem are proposed to predict correctly the frequency jump position, wave number and the convection speed of the self-sustained oscillating flow for different jet exit velocities.

131 自由液面の自励振動を伴う2次元噴流の画像計測

This paper describes the results of PIV measurement of two-dimensional plane jet flow with self-induced sloshing, which are obtained by means of the so-called spatiotemporal derivative method. The research group for PIV measurement in Visualization Society in Japan has suggested this experiment for evaluating the performance of the analysis method. The results show the typical unsteady flow field owing to self-induced sloshing. PIV is a powerful tool for this experiment.

Dynamic characteristics analysis of forcing jet by Karhunen-Loeve transformation

The snapshot method is introduced to approximate the coherent structures of planar forcing jet flow. The numerical simulation of flow field is simulated by discrete vortex method. With snapshot method we could treat the data efficiently and approximate coherent structures inhered in the planer jet flow. By forcing the jet at a sufficient amplitude and at a well-chosen frequency, the paring can be controlled in the region of the jet. Finally we expressed the underlying coherent structures of planar jet flow in the minimum number of modes by Karhunen-Loeve transformation in order to understand jet flow and to make the information storage and management in computers easier.

A finite volume method for the solution of the extrudate swell problem on unstructured triangular meshes

The extrudate swell phenomenon is analysed by solving, simultaneously, the Navier‐Stokes equations along with the continuity equation by means of a finite volume method. In this work, the planar jet flows of incompressible viscous Newtonian and power‐law fluids for Reynolds numbers as high as 75 are simulated. The method uses the velocity components and pressure as the primitive variables and employs an unstructured triangular grid and triangular or polygonal control volume for each separate variable. The numerical results show good agreement with previously reported experimental and numerical results. Shear thickening results in an increase in swelling ratio, while the introduction of surface tension results in a describes in swelling ratio.

A finite difference analysis of the extrudate swell problem

AbstractThe extrudate swell phenomenon of a purely viscous fluid is analysed by solving simultaneously the Cauchy momentum equations along with the continuity equation by means of a finite difference method. The circular and planar jet flows of Newtonian and power‐law fluids are simulated using a control volume finite difference method suggested by Patankar called SIMPLER (semi‐implicit method for pressure‐linked equations). This method uses the velocity components and pressure as the primitive variables and employs a staggered grid and control volume for each separate variable. The numerical results show good agreement with the analytical solution of the axisymmetric stick‐slip problem and exhibit a Newtonian swelling ratio of 13.2% or 19.2% for a capillary or slit die respectively in accordance with previously reported experimental and numerical results. Shear thinning results in a decrease in swelling ratio, as does the introduction of gravity and surface tension.

Turbulent plane jet with and without confining end walls

THE published data on turbulent plane jets show variations in both the mean and turbulence quantities that in most instances have been attributed to differences in experimental conditions. The major influencing factors are the inlet geometry and aspect ratio of the nozzle, the nature of the exit velocity profile and the associated magnitude of the turbulence intensity, the Reynolds number at the nole exit, and the state of the ambient environment.1'2 However, one fundamental difference among plane jet apparatus that is not well documented concerns the use of confining end walls and/or a wall section at the plane of exit. This paper describes the characteristics of a plane jet issuing from a wall with and without confining end walls. The objectives are to provide a perspective for the comparison of existing data under these conditions and to identify the relative merits of the two configurations for the design of future experiments. Contents The plane jet flow facility consists of a centrifugal blower that supplies air via a 1.0-m diffuser section to a 400 mm x 600 mm x 12.5 mm settling chamber, followed by a corner section containing 90-deg turning vanes, a second shorter settling chamber, and finally a 40:1 two-dimensional contraction (based on a cosine curve) that ends as a 600-mm long x 10-mm wide (D) slot. The design of the nozzle insures that the exit turbulence intensity is low [(u2)l/2/U0 = 0.008] and that the wall boundary layers at the exit will be laminar. The jet issues vertically from a horizontal wall section extending along the length of the slot and 1.1 m to each side and may be confined by removable vertical walls located at each end of the slot and extending 1.1 m to the sides and 1.85 m downstream, and vertical screens of open air ratio 0.8 spanning the ends of the vertical walls. The jet exit velocity U0 was 11.0 m/s for all of the test runs, and the Reynolds number based on U0 and the slot width D was 7230.3 Mean velocities were measured independently with a pitot tube (connected to an electronic micromanometer) and also simultaneously with a pitot tube and a normal hot-wire (HWA) separated by 5 mm in the spanwise (z) direction. In addition to near-field pitot tube measurements that confirmed the symmetry of the exit profile, detailed lateral velocity profiles were obtained in the far-field regions of the free and the confined jets to identify any structural differences and to determine the extent of two-dimension ality. The far-field profiles for the free jet show considerably more twisting and variability along the length of the slot than those of the confined jet. The walls of the confined jet achieved the expected effect of extending the region of two-dimension ality. For the streamwise region between x/D = 50 and 100, the standard deviation of the growth rates of the confined jet, based on

A finite element computation of turbulent boundary layer flows with an algebraic stress turbulence model

A finite element computational procedure for turbulent boundary layer flows and an algebraic stress turbulence model are presented. The finite element method is based on the semi-discrete Galerkin finite element method, the convergence nature of which has been reported previously. The algebraic stress turbulence model used in the present study can be characterized by the following three aspects: firstly, the eddy viscosity expression was derived from the Reynolds stress turbulence model; secondly, the turbulent kinetic energy dissipation rate equation was improved by including a production range time scale; and lastly, the diffusion coefficients for turbulence equations were adjusted so that the kinetic energy profile extends further into the free stream region which can be found in most of experimental data. Example problems considered include: a fully developed channel flow, a fully developed pipe flow, a flat plate boundary layer flow, a plane jet exhausting into a moving stream, a circular jet exhausting into a moving stream, and a wall jet flow. Computational results compared favorably with experimental data for most of the example problems considered. Significantly improved computational results were obtained for the plane jet flow and the wall jet flow, whereas rest of the computational results were comparable to those obtained by finite difference methods using the standard k- ϵ turbulence model.

Coherent Structures in the Similarity Region of Two-Dimensional Turbulent Jets

The strongest indication of an ordered structure in the similarity region of plane jet flows is the well documented (but controversial) apparent “flapping” behavior. Previously, the negative correlation between probes placed on opposite sides of the jet centerline has been attributed to the periodic displacement of the mean velocity profile centerline about its average position, i.e., a flapping motion. The present investigation is directed at evaluating the premise of an essentially two-dimensional von Karman vortex street as being responsible for the apparent “flapping” behavior.

Calculation of the interaction of planar jets of ideal gas with different Bernoulli constants

A numerical method is proposed for calculating stationary planar jet flows with unequal total heads in different jets in the case when the medium is ideal and compressible and the flow is subsonic, adiabatic, and irrotational in each individual jet. Features of the method are considered in the example of the calculation of the interaction of two free jets flowing along the sides of a wedge. The line separating the jets is the line of a shear discontinuity. The results of the calculations are given.

Two-dimensional free boundary layer in a stratified medium

Expressions for the fluctuation characteristics of shear flow in a stratified medium are obtained on the basis of the equations for the single-point second-order moments of the velocity and temperature fields and then closure of those equations by means of semiempirical hypotheses. The Prandtl equation, with the influence or Archimedean forces taken into account, is used to analyze plane jet flows and wake flows of a body, Numerical computations are carried out for a plane wake, and the results are compared with the experimental data.

The Initiation, Development, and Decay of the Secondary Flow in a Bounded Jet

The secondary flow in a low aspect ratio incompressible turbulent bounded jet is described in terms of a near, middle, and far field in which the secondary motion is initiated, developed, and decayed, respectively. The initiation of the secondary flow is explained by the distortion of the planar vortex loops which bound the jet at the exit plane. In the region away from the bounding plates, the vortex loop distortion is similar to that found in rectangular free jets; however, the bounding plates cause an additional production of streamwise vorticity near the plates which has no counterpart in the free jet flow. Downstream of the jet core region, a large-scale secondary flow develops from this vorticity. Farther downstream the secondary flow decays; the resultant flow may be characterized as a combination of a plane jet and boundary layer flows. This explanation is supported by the vorticity and velocity data of this investigation. Velocity measurements of this study are sufficiently comprehensive to allow formulation and evaluation of several quantitative measures of the secondary flow strength. The average (over a transverse plane) momentum flux thickness, and the far field behavior show the secondary flow to be dynamically passive. Properly nondimensionalized transverse velocity profiles exhibit characteristic distortions from a basically “self-similar” shape from which the center of the secondary flow rotation can be determined. Integrals of the velocity data allow the inference of mass transport across planes parallel to the bounding plates.

Plane jet flows from slowly varying nozzles

The solution to the steady problem of an inviscid jet emerging from a symmetric nozzle of slowly varying profile is sought as an asymptotic series in the wall slope. The expansion of the solution in the region near the nozzle lip is singular at infinity, so that a matched expansion technique is evolved to solve the problem. To the order to which the solution is obtained in the present paper, the jet contraction ratio is shown to be the same as that from a nozzle formed by two inclined planes with inclination angle the same as the exit slope of the nozzle. Composite expansions are formed and used to check the consistency of expansion and matching procedures.

Planar jet flow of a radiating gas

Propagation of a laminar jet of a thermodynamically equilibrious “gray” gas is examined in the boundary layer theory approximation. The one-dimensional radiative energy transport is accounted for in the P 1 approximation of the spherical harmonic method. Numerical solution of the problem is made under additional simplifying assumptions for various values of the radiation parameters to illustrate the radiation effect. The method and the computational scheme used are applicable to the study of complex jet flows of a radiating gas.

The spread of a turbulent plane jet issuing into a parallel moving airstream

The results of an experimental investigation into the development of a turbulent plane jet issuing into a parallel moving airstream are described. On the basis of a simple dimensional argument, it is shown that the results for the spread of jets with different ratios of jet nozzle to free-stream velocity can be collapsed into a single universal curve provided the effective origins of the various sets of data can be shifted. Evidence is found of a change in structure of the jet from a self-preserving plane jet flow near the origin of the flow towards a selfpreserving wake type of flow far downstream from the origin. This change of structure is compared with a prediction based on a simple application of Town-send's large-eddy hypothesis. It is shown that the hypothesis does not account for the way in which the jet structure changes and possible reasons for this are briefly discussed. Finally, some comments are made on the usefulness of the various theories of jet spreading.

Two-dimensional flow at high subsonic speeds past wedges in channels with parallel walls

Investigations are made of the plane flow of an inviscid isentropic gas at high subsonic and sonic speeds past a finite wedge of small angle set at zero incidence in a channel with parallel walls. Hodograph methods are applied to the determination of the stream function, which, under the usual transonic approximation, is a solution of Tricomi's equation. In § 2 a brief summary is given of the derivation of the fundamental solution of this equation in terms of Bessel functions.Two models of the flow pattern are discussed. The model of Cole is examined in § 3 with the sonic line from the shoulder extending completely across the channel at right angles to the wall. In § 4 the Helliwell-Mackie model is taken in which there is a free stream breakaway at sonic velocity from the shoulder of the wedge and the velocity far downsteam may be either uniformly subsonic or sonic. Values are obtained for the drag coefficient in both cases and a high degree of both qualitative and quantitative agreement is found. On the basis of the free streamline theory explicit formulae are given relating, in terms of the channel width and upstream Mach number, the drag of the wedge in the channel to that of the same wedge in the free stream.Attention is drawn in § 5 to certain properties of plane jet flows that may be deduced from the investigation of the flow with free stream breakaway past a wedge in a channel.