Discharge of a supersonic jet from a nozzle with an inclined rim

The main results of a numerical study of the effect of the angle of the rim of a nozzle on the shape of the jet boundary and of the free shock and on the distribution of parameters in a three-dimensional underexpanded jet are presented. A noncentered second-order difference scheme is used to solve the gasdynamic equations for an inviscid perfect gas. Conditions are established for which the three-dimensional jet is observed to coincide partially in the radial planes and the corresponding planes of axisymmetric jets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–110, July–August, 1977.In conclusion, the authors thank G. I. Petrov and his colleagues for detailed discussion of the results of the investigation reported here.     

Convection experiments in an inclined narrow cavity

The liquid flow behaviour in a small vertical gap with a heated and a cooled sidewall was studied experimentally in a former work as far as heat and mass transfer are concerned [Heiland et al. in Heat Mass Transf 43:863–870, 2007]. Following this, the study of thermal convection in a narrow cavity with variable inclination angle has been performed with liquid crystal techniques. Velocity and temperature fields of the flow have been measured. The results show that the strongest convection intensity arises in a vertical cavity.     

Turbulent transport in an inclined jet in crossflow

The present study experimentally investigates a turbulent jet in crossflow relevant to film cooling applications. The jet is inclined at 30°, and its mean velocity is the same as the crossflow. Magnetic resonance imaging is used to obtain the full three-dimensional velocity and concentration fields, whereas Reynolds stresses are obtained along selected planes by Particle Image Velocimetry. The critical role of the counter-rotating vortex pair in the mixing process is apparent from both velocity and concentration fields. The jet entrainment is not significantly higher than in an axisymmetric jet without crossflow, because the proximity of the wall inhibits the turbulent transport. Reynolds shear stresses correlate with velocity and concentration gradients, consistent with the fundamental assumptions of simple turbulence models. However the eddy viscosity is strongly anisotropic and non-homogeneous, being especially low along the leeward side of the jet close to injection. Turbulent diffusion acts to decouple mean velocity and concentration fields, as demonstrated by the drop in concentration flux within the streamtube issued from the hole. Volume-averaged turbulent diffusivity is calculated using a mass–flux balance across the streamtube emanating from the jet hole, and it is found to vary slowly in the streamwise direction. The data are compared with Reynolds-Averaged Navier–Stokes simulations with standard k − ε closure and an optimal turbulent Schmidt number. The computations underestimate the strength of the counter-rotating vortex pair, due to an overestimated eddy viscosity. On the other hand the entrainment is increasingly underpredicted downstream of injection. To capture the correct macroscopic trends, eddy viscosity and eddy diffusivity should vary spatially in different ways. Therefore a constant turbulent Schmidt number formulation is inadequate for this flow.     

Heat transfer from a flat surface to an inclined impinging jet

An experimental study was carried out to investigate the effect of the inclination jet on convection heat transfer to horizontal flat plate. Local heat transfer determined as a function is of three parameters including inclination angle of the air jet relative to the plate in range of 90° ≤ θ ≤ 45°, jet-to-plate spacing in range of 2 ≤ L/D ≤ 8 and Reynolds number in range of 1,500 ≤ Re ≤ 30,000. The results show that the maximum heat transfer point moves towards the uphill side of the plate and the maximum heat transfer decreases as the inclination angle decreases. The correlations were conducted to predict maximum and local Nusselt number as a function of Re, θ, L/D, and x/D for a specific three regions.     

Investigation of the stability of a heavy fluid film in a hot heat-conducting gas jet on an inclined phase-transition surface

The stability of the flow of a heavy viscous fluid film flowing along the inclined phase-transition surface is examined. In contrast to [1] wherein it was assumed that a constant temperature is maintained on the free surface, it is assumed here that the fluid film is on the boundary with a gas jet which has finite specific heat and heat conduction. In this connection, the stability criteria differ substantially from [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–18, July–August, 1974.     

Free convection of a liquid binary mixture in an inclined rectangular cavity

A study is made of the influence of an inclination on the distribution of concentrations produced by thermal diffusion in a cavity of rectangular section. It is shown that even a very weak convective motion produced in the cavity in the case of heating from above leads to significant perturbations of the concentration field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 176–179, July–August, 1979.We thank G. Z. Gershuni, Yu. K. Bratukhin, and V. I. Chernatynskii for discussing the results and for helpful comments.     

Flow transitions of a low-Prandtl-number fluid in an inclined 3D cavity

We present a numerical and theoretical investigation on the natural convection of a low Prandtl number fluid (Pr=0.025) in 2D and 3D side-heated enclosures tilted α=80° with respect to the vertical position. The choice of this inclination angle comes from a previous linear stability analysis of the basic (plane-parallel) flow that predicts the same critical Ra for longitudinal oscillatory and stationary transversal modes. In both the 2D and 3D enclosures the first transition gradually leads to a transversal stationary centered shear roll. In the 2D geometry the flow becomes time-dependent and multicellular (3 rolls) at the onset of a Hopf bifurcation, followed by subsequent period-doubling. On the other hand, in the 3D enclosure, the onset of oscillations is due to a fully three-dimensional standing wave composed of three counter-rotating longitudinal rolls. The further evolution of the 3D flow qualitatively agrees with previous experiments (J. Crystal Growth, 102 (1990) pp. 54–68): a quasiperiodic flow followed by a frequency locked state. The main contribution of this work is the analysis of the flow structure underlying the secondary frequency: a transversal wave composed of two shear rolls that coexist with the three longitudinal cells. This is the first numerical work that explicitly illustrates this scenario which was suggested at the onset of the biperiodic regime in many of the previous experiments.     

Ice-water convection in an inclined rectangular cavity filled with a porous medium

This paper reports on the results of a numerical study on the equilibrium state of the convection of water in the presence of ice in an inclined rectangular cavity filled with a porous medium. One side of the cavity is maintained at a temperature higher than the fusion temperature while the opposite side is cooled to a temperature lower than the fusion temperature. The two remaining sides are insulated. Results are analysed in terms of the density inversion parameter, the tilt angle, and the cooling temperature. It appears that the phenomenon of density inversion plays an important role in the equilibrium of an ice-water system when the heating temperature is below 20°. In a vertical cavity, the density inversion causes the formation of two counterrotating vortices leading to a water volume which is wider at the bottom than at the top. When the cavity is inclined, there exist two branches of solutions which exhibit the bottom heating and the side heating characteristics, respectively (the Bénard and side heating branches). Due to the inversion of density, the solution on the Bénard branch may fail to converge to a steady state at small tilt angles and exhibits an oscillating behavior. On the side heating branch, a maximum heat transfer rate is obtained at a tilt angle of about 70° but the water volume was found to depend very weakly on the inclination of the cavity. Under the effect of subcooling, the interplay between conduction in the solid phase and convection in the liquid leads to an equilibrium ice-water interface which is most distorted at some intermediate cooling temperature.     

Elliptic cavity in a three-dimensional anisotropic body with inclined strata deformed by line loads and dislocations

Summary Analytical solutions are proposed for the stress and displacement fields in a quasi three-dimensional elastic anisotropic body containing an elliptic cavity or rigid inclusion. The directions of the principal elastic axes are allowed to be inclined arbitrarily with respect to the axes of the elliptic cavity. As an application, expressions for the stress intensity factors are formulated when the cavity reduces to a colinear crack.     

Frequency response of a synthetic jet cavity

A synthetic jet results from periodic oscillations of a diaphragm in a cavity. We present the results of a detailed experimental investigation wherein the effect of excitation frequency on the synthetic jet flow is studied for cavities of different depths and for orifices of different diameters. The exit velocity averaged over an excitation cycle indicates a lower and an upper bound on the frequency for the formation of a jet, and shows resonance at two frequencies. The resonant frequencies have been identified as being close to the diaphragm and the Helmholtz frequencies, with the former being more important in the present set of experiments. We discuss approaches to manipulate these frequencies from the point of view of cavity design. Interestingly, the input power is found to be at a minimum at the diaphragm frequency. Our measurements over a relatively large parameter domain suggest that the turbulence intensity in the near field is independent of the cavity depth and excitation frequency, but depends on the orifice diameter. These results are expected to be useful for designing synthetic jet cavity.     

Calculation of a supersonic gas jet exhausting into vacuum from a nozzle with an inclined exit

A study is made of the problem of supersonic exhausting of ideal gas into vacuum from a conical nozzle with inclined exit. The solution is sought in a region including part of the flow where the projection of the velocity vector of the gas onto the nozzle axis can be less than the local velocity of sound and take negative values.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–186, May–June, 1982.     

Density distribution in a supersonic jet exhausting into vacuum from a nozzle with an inclined exit

Fairly effective methods have been developed to calculate axisymmetric jets of an inviscid perfect gas exhausting into vacuum, and approximations have also been obtained for the density field in such jets at large distances from the nozzle exit (see, for example, [1—3] and the bibliography in them). If the plane of the exit of the nozzle is not perpendicular to its axis, the flow in the jet is three dimensional. In a number of cases one can take into account the influence of the inclined exit with sufficient accuracy by a correction in the density distribution. An expression for such correction is given in the present paper. It is obtained on the basis of earlier calculations of the author [4], in which flow from a source was specified at the nozzle exit.     

Turbulent jet impinging a cylindrical hot cavity

The possibility of improving the heat transfer is investigated numerically using finite volume method. The Reynolds number increase has a minor effect on flow structure but generates a systematic rise of Nusselt Number. The maximum heat exchange occurs when the cavity bottom is located at the potential core end. The main heat exchange occurs on the cavity bottom for every case. The stagnation Nusselt number is correlated according some problem parameters.     

Effect of free convection on thermodiffusion in a liquid mixture filling an inclined rectangular cavity

The convective motion which develops in an inclined cavity upon heating from above determines to a significant degree the form of the concentration field produced by thermodiffusion. The interaction of convective and thermodiffusion fluxes at small thermal Grashof numbers Gr causes the appearance of longitudinal jumps in concentration. Increase in temperature difference intensifies convection and encourages reduction in concentration gradients. The dominant role of convection for fixed Gr is determined by the angle of inclination of the liquid layer [1, 2]. A significant feature of liquid solutions is their low diffusion coefficient and thus high Schmidt number. This fact does not permit use of results obtained for gas mixtures, and greatly complicates numerical simulations. In contrast to [2], the present study will investigate thermodiffusion separation in a cavity with impermeable boundaries.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 73–76, September–October, 1986.In conclusion, the authors thank G. Z. Gershun for evaluation of the results and helpful remarks.     

Heat transfer from an open-wedge cavity to a symmetrically impinging slot air jet

Heat transfer from an open-wedge cavity to a symmetrically impinging slot air jet is investigated at the present study. The effect of the cavity angle was mainly examined on the Nusselt number distribution. Based on the results, heat transfer was generally poor at the vicinity of the apex, rising to form a maximum at the impingement and then followed by a moderate decline at further distances. The region of maximum heat transfer on the surfaces shifted outward the cavity as the cavity angle was decreased. Also, average Nusselt number over an effective length of the surface remained almost constant and independent of the cavity angle for a specified jet Reynolds number and nozzle-to-apex spacing.     

An inclined rectangular jet in a turbulent boundary layer-vortex flow

A model test study was performed on streamwise vortices generated by a rectangular jet in an otherwise flat-plate turbulent boundary layer. The study was conducted in a low speed wind tunnel. The rectangular jet had a cross-section size of 28 mm by 5.5 mm. The oncoming boundary layer had a 99.5 percent thickness of 25 mm. The freestream speed of the oncoming flow was 20 m/s. Measurements were performed with a three-element LDA system. The effects of skew angle and streamwise development of vortex were investigated and the mean flow properties are presented. The study showed that the rectangular jet was able to produce a streamwise vortex of higher strength than that of a round jet, while at the same time keeping the same size and shape as that of a round jet. A 63% increase in the maximum vorticity was found. The 45^∘ skew angle was identified as the optimal skew angle for vortex production. Received: 24 June 1998/ Accepted: 21 May 1999     

矩形倾斜腔体中的两种对流斑图和分区

为了研究矩形倾斜腔体中普朗特数Pr=0.72的流体对流斑图和分区,本文基于流体力学方程组进行了数值模拟。在相对瑞利数r=6.0的情况下,观察了倾角θ=10°和θ=60°时对流斑图随着时间的发展,发现系统存在单圈型对流和多圈型对流两种斑图。流线随着倾角的变化说明:随着倾角增加,对流圈数逐渐减少,对流波长逐渐增加,对流波数减小;然后,随着对流圈数显著地减少,系统由多圈型对流过渡到单圈型对流。根据模拟计算结果,给出了多圈型对流过渡到单圈型对流的临界倾角θc随着相对瑞利数r变化的关系曲线。对流在θ-r平面上分为两个区域:θ<θc时系统是单圈型对流,θ>θc时系统是多圈型对流。对流最大振幅A和努塞尔数Nu随着倾角θ的变化曲线被临界倾角θc分成两段,它们有不同的变化规律。因此,临界倾角也可以由对流最大振幅A或努塞尔数Nu的变化曲线来确定。     

Control of a submerged jet in a thin rectangular cavity

An innovative method is presented for control of an oscillatory turbulent jet in a thin rectangular cavity with a thickness to width ratio of 0.16. Jet flow control is achieved by mass injection of a secondary jet into the region above the submerged primary jet nozzle exit and perpendicular to the primary nozzle axis. An experimental model, a 2-D and a 3-D computational fluid dynamics (CFD) model are used to investigate the flow characteristics under various secondary injection mass flow rates and injection positions. Two-dimensional laser Doppler anemometry (LDA) measurements are compared with results from the CFD models, which incorporate a standard k–ε turbulence model or a 2-D and 3-D realisable k–ε model. Experimental results show deflection angles up to 23.3° for 24.6% of relative secondary mass flow are possible. The key to high jet control sensitivity is found to be lateral jet momentum with the optimum injection position at 12% of cavity width (31.6% of the primary nozzle length) above the primary nozzle exit. CFD results also show that a standard k–ε turbulence closure with nonequilibrium wall functions provides the best predictions of the flow.     

Optimization of an inclined elliptic impinging jet with cross flow for enhancing heat transfer

This work presents a parametric study and optimization of a single impinging jet with cross flow to enhance heat transfer with two design variables. The fluid flow and heat transfer have been analyzed using three-dimensional compressible Reynolds-averaged Navier–Stokes equations with a uniform heat flux condition being applied to the impingement plate. The aspect ratio of the elliptic jet hole and the angle of inclination of the jet nozzle are chosen as the two design variables, and the area-averaged Nusselt number on a limited target plate is set as the objective function. The effects of the design variables on the heat transfer performance have been evaluated, and the objective function has been found to be more sensitive to the angle of inclination of the jet nozzle than to the aspect ratio of the elliptic jet hole. The optimization has been performed by using the radial basis neural network model. Through the optimization, the area-averaged Nusselt number increased by 7.89% compared to that under the reference geometry.