Controlling spatio-temporal evolution of natural and excited square jets via inlet conditions

The paper presents numerical investigations of square jets in a wide range of Reynolds numbers with varying inlet turbulence characteristics. The research focuses on flow characteristics depending on inflow turbulent length/time scales and excitation frequencies in case of excited jets. It is found that the parameters of inlet turbulence affect the solutions qualitatively when the Reynolds number is sufficiently low. In these cases the impact of varying the turbulent time scale is considerably larger than changing the turbulent length scale. It was also observed that at sufficiently high Reynolds numbers the jets become quite independent of the inlet turbulence characteristics. This confirms findings of Xu et al. (Phys. Fluids, 2013) concerning weak/strong dependence of the jet evolution on inflow conditions. In case of excited jets the excitation frequencies play an important role and influence the jet behaviour most strongly at lower values of the Reynolds number. For some forcing frequencies a bifurcation occurs at sufficiently large forcing amplitudes. This phenomenon turned out to be independent of the assumed length and time scales of the turbulent fluctuations, both in terms of robustness as well as amplitude.     

Experimental investigation of the coherent structures in a spirally corrugated pipe

Previous numerical and theoretical results (Chen et al., 2019; Liu et al., 2018; Zhao et al., 2019) based on the optimization theory of convective heat transfer reveal that the optimized flow structures in a straight circular pipe enhancing convective heat transfer are multiple longitudinal vortices. This conclusion encourages us to find out whether such flow structures really exist in some enhanced heat transfer pipes by means of advanced experimental techniques. Therefore, a typical enhanced heat transfer pipe was selected, namely a spirally corrugated pipe, and stereoscopic particle image velocimetry (SPIV) was employed to measure its internal instantaneous flow field. Moreover, the proper orthogonal decomposition (POD) method was used to extract the large-scale coherent structures from the measured instantaneous velocity fields. Besides the spirally corrugated pipe, the fully developed turbulent flow in a straight pipe was also analyzed as benchmark of the enhanced heat transfer pipes. The results reveal that longitudinal whirling flow with multi-vortices is formed in both the fully developed turbulent flow field of the straight pipe and the spirally corrugated one. It is thus easy to explain the heat transfer enhancement mechanism of the above flow structures from the perspective of momentum transfer. The flow structures of the fully developed turbulent flow in a straight pipe are quite similar to the optimal flow pattern from the optimization theory. More specifically, multiple longitudinal vortices are spontaneously generated due to turbulence without external heat transfer enhancement techniques. Furthermore, the flow structures similar to multiple longitudinal vortices also exist in the spirally corrugated pipe, although these flow structures deviate from symmetric multiple vortices. Moreover, the flow structures in the spirally corrugated pipe are much more energetic than those in the fully developed turbulent flow in a straight pipe. This is probably the reason why a spirally corrugated pipe can enhance heat transfer compared with a straight circular pipe.     

Exact formula for the spreading width of jet flow velocity under the assumption of a radial adjusting coefficient

Recently, Lee et al. (Arch Appl Mech 81:397–402, 2011) proposed a new and very interesting formula to describe the velocity profile of a submerged jet flow by introducing a radial adjusting coefficient depending on the jet flow direction. Under some simplifying assumptions (granting convergence), the authors were able to express the spreading width of the jet flow analytically in terms of infinite series. In this short note, we show that such simplifying assumptions can be relaxed and exact solutions for the spreading width of the jet flow can be obtained: Such results are computationally more efficient and are able to better demonstrate the qualitative features of the solutions.     

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.     

Opposed round jets issuing into a small aspect ratio channel cross flow

Round jets (diameter D) discharging into a confined cross flow (dimension 3.16D × 21.05D) are investigated experimentally. Two configurations are considered: (1) a single jet (momentum flux ratio, J = 155) and (2) two opposed jets with two different momentum flux ratios (J = 60, and 155). A two-component laser-Doppler anemometer is used to make a detailed map of the normal stresses and mean velocities in the symmetry plane of the jets. In addition, smoke-wire and laser-sheet visualization are used to study the flow.

The rate of bending of the single confined jet is found to be higher than the rate of bending of an unconfined jet with the same momentum flux ratio. In the far field, the jet centerline velocity is observed to decay more slowly than the unconfined jet, indicating poor turbulent diffusion of linear momentum. Annular shear layer vortices are visualized on the upstream edge of the jet in the near field. In the far field, the flow visualization suggests that the jet loses its integrity and fragments into independent regions that are convected by the cross flow.

In the opposed jet configuration at the high momentum flux ratio (J = 155), the jets impinge in the center of the duct, and a pair of vortices is observed upstream of the impingement region. The flow visualization implies that the impingement vortices form quasi periodically and have a finite life span. In the impingement region, the jets are observed to penetrate alternately beyond the symmetry plane of the duct. In the two-jet configuration with J = 60, the jets do not impinge on each other owing to the higher rate of bending. Instead, the flow visualization indicates that the shear layers of the jets penetrate to the central region and periodically pinch off regions of the potential-like cross-flow fluid where they meet. The pinch-off regions of cross-flow fluid are convected by the turbulent flow for large distances, yet remain essentially unmixed.     

入口速度比对射流拟序结构的影响

为了深入了解湍流流动机理以及湍流拟序结构发现过程的影响因素，本文采用大涡模拟方法对不同入口射流伴流速度比的平面湍射流流动进行了数值模拟。采用分步投影法求解动量方程，亚格子项采用标准Smagorinsky亚格子模式模拟，压力泊松方程采用修正的循环消去法快速求解，空间方程采用二阶精度的差分格式，在时间方向上采用二阶精度的显式差分格式。模拟结果给出了平面射流中湍流拟序结构的瞬态发展演变过程，分析了入口速度比对射流拟序结构发展演化过程及宏观流场形态的影响。为进一步研究射流拟序结构及其在湍流流动中的作用提供了基础。     

Nonlinear stability of two-phase jets

The effect of solid particles on the flow stability and secondary regime branching in plane submerged jets is studied. The presence of the particles has an important influence on the macrostructure and microstructure of the jet flows, modifying the rate of turbulent momentum, heat and mass transfer [1,2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 50–55, May–June, 1985.The authors are grateful to V. N. Shtern for useful comments.     

The effect of roughness on separating flow over two-dimensional hills

Two new experimental data sets for turbulent flow over a steep, rough hill are presented. These include detailed laser Doppler anemometry measurements obtained at the separation and reattachment points and, in particular, within the reverse flow region on the lee side of the hill. These results allow the development of a new parametrization for rough wall boundary layers and validate the use of Stratford’s solution for a separating rough flow. The experiments were conducted in a water channel for two different Reynolds numbers. In the first set of rough wall experiments, the flow conditions and the hill shape are similar to those presented in Loureiro et al. (Exp. Fluids, 42:441–457, 2007a) for a smooth surface, leading to a much reduced separation region. In the second set of experiments, the Reynolds number is raised ten times. The region of separated flow is then observed to increase, but still to a length shorter than that recorded by Loureiro et al. (Exp. Fluids, 42:441–457, 2007a). Detailed data on mean velocity and turbulent quantities are presented. To quantify the wall shear stress, global optimization algorithms are used. The merit function is defined in terms of a local solution that is shown to reduce to the classical law of the wall far away from a separation point and to the expression of Stratford at a separation point. The flow structure at the separation point is also discussed.     

PIV study of large-scale flow organisation in slot jets

The paper reports on particle image velocimetry (PIV) measurements in turbulent slot jets bounded by two solid walls with the separation distance smaller than the jet width (5–40%). In the far-field such jets are known to manifest features of quasi-two dimensional, two component turbulence. Stereoscopic and tomographic PIV systems were used to analyse local flows. Proper orthogonal decomposition (POD) was applied to extract coherent modes of the velocity fluctuations. The measurements were performed both in the initial region close to the nozzle exit and in the far fields of the developed turbulent slot jets for Re ⩾ 10,000. A POD analysis in the initial region indicates a correlation between quasi-2D vortices rolled-up in the shear layer and local flows in cross-stream planes. While the near-field turbulence shows full 3D features, the wall-normal velocity fluctuations day out gradually due to strong wall-damping resulting in an almost two-component turbulence. On the other hand, the longitudinal vortex rolls take over to act as the main agents in wall-normal and spanwise mixing and momentum transfer. The quantitative analysis indicates that the jet meandering amplitude was aperiodically modulated when arrangement of the large-scale quasi-2D vortices changed between asymmetric and symmetric pattern relatively to the jet axis. The paper shows that the dynamics of turbulent slot jets are more complex than those of 2D, plane and rectangular 3D jets. In particular, the detected secondary longitudinal vortex filaments and meandering modulation is expected to be important for turbulent transport and mixing in slot jets. This issue requires further investigations.     

A phase averaged PIV study of circular and non-circular synthetic turbulent jets issuing from sharp edge orifices

An extensive experimental study using Particle Image Velocimetry (PIV) on synthetic jets issuing from different orifice shapes is reported. All data are phase and time averaged to derive mean velocity, half-velocity width and rms velocity profiles in the near field of the jet (0 < X/D < 7), at a Reynolds number around 10,000. Different non-circular orifice shapes as rectangular, square, elliptic and triangular are considered and results are compared to those of the circular orifice in order to investigate the effect of asymmetry on the turbulent flow field in view of mixing enhancement. The measurements are carried out on two orthogonal planes to capture three dimensional features of non-circular jets. Results show highest velocity decay rate for elongated orifices, especially the rectangular one, in comparison to the circular one, both in phase and time-averaged plots. Time averaged results show higher velocity decay rate of synthetic jets in comparison to those of continuous ones. It is also observed that, for X/D > 5, only profiles of circular and square jets become partially self-similar. For synthetic jets, higher turbulence content is measured for all orifice shapes at the centerline and close to the orifice exit in comparison to continuous jets.     

Direct numerical simulation of a turbulent plane Couette-Poiseuille flow with zero-mean shear

Direct numerical simulations of a turbulent Couette-Poiseuille flow with zero-mean-shear at the moving wall (SL-flow) is performed to examine flow features compared to those for a turbulent pure Poiseuille flow (P-flow). Profiles of the streamwise mean velocity, indicator function and ratio of production to dissipation show that the logarithmic region is significantly elongated for the SL-flow compared to that for the P-flow at a similar Reynolds number. In addition, the magnitudes of the Reynolds stresses are found to be larger in both inner and outer layers for the SL-flow than those for the P-flow. The spanwise spectra of the production term in the turbulent kinetic energy equation are examined to provide a structural basis for explaining the statistical behaviors. In addition, because the growth of the energy-containing motions extends to the outer layer further for the SL-flow due to the presence of a positive mean shear throughout the entire wall layer, the self-similar behavior of the energy balance between the production and transport terms with respect to the self-similar wavenumber is found far from the wall. We also find the increase in the number of uniform momentum zones in the SL-flow, revealing the hierarchical distribution of the energy-containing eddies which are composed of multiple uniform momentum zones. These coherent motions lead to the elongation of the logarithmic region for the SL-flow. Finally, investigation of the turbulent energy transfer process in a spectral domain for the SL-flow demonstrates importance of outer layer very-long structures, and these structures attribute to the energy transport process in an entire flow field.     

Evaluation of an algebraic model for laminar-to-turbulent transition on secondary flow loss in a low-pressure turbine cascade with an endwall

The predictive qualities of a recently developed algebraic intermittency model for laminar-to-turbulent transition are analysed for the flow through a linear cascade of low-pressure turbine blades with an endwall. Both steady RANS (Reynolds-averaged Navier–Stokes) and time-accurate RANS (URANS) simulations are performed. The results are compared with reference LES (Large Eddy Simulation) by Cui et al. (2017, Numerical investigation of secondary flows in a high-lift low pressure turbine, Int. J. of Heat and Fluid Flow, vol. 63) and results by the local correlation-based intermittency transport model (LCTM) by Menter et al. (2015, A one-equation local correlation-based transition model. Flow Turbul. Combust., vol. 95) for laminar and turbulent endwall boundary layers at the cascade entrance. Good agreement is obtained with the reference LES and with results by the LCTM for the evolution through the cascade of the mass-averaged total pressure loss coefficient and for profiles of pitchwise-averaged total pressure loss coefficient at the cascade exit.     

Scaling investigation of plasma-induced flows over curved and flat surfaces: Comparison to the wall jet

The present investigation deals with Dielectric Barrier Discharge (DBD) induced jets flowing over curved surfaces and studied in the framework of a circulation control application, carried out by acting near the rounded trailing-edge of an airfoil. These jets are characterized experimentally via Particle Image Velocimetry (PIV) in quiescent air conditions. The study assesses the evolution of these flows in terms of self-similarity of the mean flow and of its turbulent components. DBD wall jets evolution in the streaming direction is also analyzed through the rate of spread and the maximum velocity decay evolution as commonly done for fluidic wall jets, and also through several normalized quantities deriving from different length and velocity scales. A comparison with a canonical flow, such as the classical wall jet flowing over plane or curved surfaces, is made in order to find out the similarities and the discrepancies between these two flows. Results reveal that DBD wall jets and canonical fluidic wall jets show comparable properties in the diffusion zone. Compared to the plane DBD wall jet, centrifugal forces are responsible of the greater spread of curved DBD wall jets and are likely the source of instabilities leading to their transitional state. The momentum flux of the induced jet and the radius of curvature of the surface are two relevant scales for DBD induced flows developing over curved surfaces.     

The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet

The flow at the outer boundary of a submerged self-similar turbulent jet at Re=2᎒³ is investigated experimentally by means of combined particle image velocimetry (PIV) laser-induced fluorescence (LIF) measurements. The jet fluid contains a fluorescent dye so that the LIF data can be used to discriminate between the jet fluid and the ambient fluid. The axial velocity, Reynolds stress, and vorticity are determined relative to the jet boundary. The results are compared against the conventional profiles, and the results of a direct numerical simulation of the turbulent far-wake behind a flat plate. The results show a sharp transition between rotational and irrotational fluid at the fluid interface, and the existence of a layer of irrotational velocity fluctuations outside the turbulent region.     

Structural inclination angle of near-field scalar fluctuations in a turbulent boundary layer

Two-point concentration measurements are obtained in a meandering passive-scalar plume released at five different heights within the fully-turbulent region of a high-Reynolds number turbulent boundary layer (TBL). Mean statistics of two-point concentration measurements are found to agree very well with the single-point measurements previously reported in Talluru et al. (2017a). The two-point correlation results of concentration indicate strong coherence in the scalar field similar to the large-scale coherence observed in the streamwise velocity fluctuations in a TBL (Marusic and Heuer, 2007). Particularly, the isocontours in the two-dimensional correlation map of concentration fluctuations illustrate that the scalar structures are inclined at 30^∘ to the direction of the flow; such a trend is consistently observed for all the elevated plumes below z/δ ≤ 0.33. This observation of steeper inclination angle of scalar structures relative to the inclination angle of large-scale velocity fluctuations in a TBL is explained using the physical model put forth by Talluru et al. (2018). Most importantly, these results provide insights on the differences in the structural organisation of a passive scalar plume in the near- and the far-field regions.     

Convective-Region Top Front Propagation in a Uniform Medium under the Action of Point, Linear, and Plane Heat and Momentum Sources

A relation between the height of a convective front rising in an unstratified medium and the momentum and heat fluxes released on the substrate surface is proposed for point, linear, and uniform plane sources arbitrarily dependent on time. This relation makes it possible to determine the integral power of a plume on the basis of optical observations of the height of the propagating convective front. As particular solutions, three classes of self-similar regimes related with the heat and momentum sources, whose rate is a step-shaped, power-law, or exponential function of time, are obtained. A one-dimensional integral model of a rising convective jet is constructed. The classes of self-similar jets corresponding to power or exponential heat and momentum sources are described. It is shown that all self-similar jets corresponding to heat and momentum sources governed by a power law with a fairly large exponent are characterized by the same temperature and velocity profiles.     

Large eddy simulation of vertical turbulent jets under JONSWAP waves

The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the fil...     

Mass and momentum transport in the near field of swirling turbulent jets. Effect of swirl rate

Local transport of the flow momentum and scalar admixture in the near-field of turbulent swirling jets (Re = 5,000) has been investigated by using a combination of the particle image velocimetry and planar laser-induced fluorescence methods. Advection and turbulent and molecular diffusions are evaluated based on the measured distributions of the mean velocity and concentration and the Reynolds stresses and fluxes. As has been quantified from the data, the flow swirl intensifies the entrainment of the surrounding fluid and promotes mass and momentum exchange in the outer mixing layer. A superimposed swirl results in the appearance of a wake/recirculation region at the jet axis and, consequently, the formation of an inner shear layer. In contrast to the scalar admixture, the momentum exchange in the inner shear layer is found to be strongly intensified by the swirl. For the jet with the highest considered swirl rate, a substantial portion of the surrounding fluid is found to enter the unsteady central recirculation zone, where it mixes with the jet that is issued from the nozzle. The contribution of the coherent velocity fluctuations, which are induced by large-scale vortex structures, to the turbulent transport has been evaluated based on triple decomposition, which was based on proper orthogonal decomposition analysis of the velocity data sets. For the considered domain of the jet with the highest swirl rate and vortex breakdown, the contributions of detected helical vortex structures, inducing pressing vortex core, to the radial fluxes of the flow momentum and the scalar admixture are found to locally exceed 65% and 80%, respectively.     

水下欠膨胀高速气体射流的实验研究

采用实验途径研究了下水高速气体射流的动力学特性,研制了水下高速气体射流实验系统并发展了相应的测试手段。实验中,用插入式静压探针测量了射流轴线静压分布;用γ射线衰减法测量了径向空隙率分布,从而揭示了水下高速气体射流均压和掺混两个过程的基本规律。测量结果表明：水下高速气体射流在欠膨胀工况下运行时,近场将出现含有复杂波系结构的膨胀压缩区域,由于气水的掺混作用,水下欠膨胀气体射流均压化过程比空气中衰减得快。测量结果还表明,水下射流在近场区的混合层由气水两相占据,其流态从靠近气体侧的液滴流型过渡到靠近液体侧的气泡流型。