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.     

横向紊动射流的数值与实验研究进展

横向紊动射流作为流体运动的一种重要类型,广泛存在于如: 燃气轮机气膜冷却、锅炉燃烧室等的燃烧控制, V/STOL(垂直或短距离起落)飞机、废气排放的控制等工程实际应用中.由于射流的存在,增加了流场的复杂性,流场中同时存在射流剪切层涡、马蹄形涡系、反向旋涡对和尾迹涡等4种涡系结构,这对流体力学理论研究具有重要意义.长期以来,研究人员从理论分析、实验测量和数值模拟方面对横向紊动射流进行了大量的研究工作,目前已经认识了流场中的许多流动特性和流动机理.从数值模拟和实验研究两个方面,比较并分析了国内外横向紊动射流研究的现状和研究结果,评述了不同湍流模型以及不同的实验测量方法对横向紊动射流的预测能力,讨论了存在的问题并对该领域的研究方向进行了展望.      

Direct Numerical Simulation of a Square Jet Ejected Transversely into an Accelerating, Laminar Main Flow

A numerical simulation of a square jet ejected transversely into a laminar boundary-layer flow was performed at a jet-to-main-flow velocity ratio of 9.78 and jet Reynolds number of 6330. The jet consisted of a single pulse with a duration equal to the time required for the jet fluid to travel 173 jet widths. A strongly-favourable streamwise pressure gradient was applied to the boundary layer and produced a freestream acceleration that is above the typical threshold required for relaminarization. The results of the simulation illustrate the effect of the favourable streamwise pressure gradient on the flowfield created by the transverse jet. Notably, the horseshoe vortex system created upwind of the jet remains steady in time and does not induce noticeable fluctuations in the jet flow. The upwind and downwind shear layers of the jet roll-up through a Kelvin–Helmholtz-like instability into discrete shear-layer vortices. Jet vorticity in the upwind and downwind shear layers accumulates near the corners of the jet and produces two sets of vortex pairs, the former of which couple with the shear-layer vortices to produce large, counter-rotating vortices in the freestream, while the latter are unstable and periodically produce hairpin vortices in the main-flow boundary layer and elongated vortices in the freestream behind the jet. The departure of the jet flowfield from the vortical structures typically observed in transverse jets illustrates the substantive effect of the favourable streamwise pressure gradient on the flowfield created by the jet.     

The effect of streamwise vortices on the turbulence structure of a separating boundary layer

A high Reynolds number flat plate turbulent boundary layer is investigated in a wind-tunnel experiment. The flow is subjected to an adverse pressure gradient which is strong enough to generate a weak separation bubble. This experimental study attempts to shed some new light on separation control by means of streamwise vortices with emphasize on the change in the boundary layer turbulence structure. In the present case, counter-rotating and initially non-equidistant streamwise vortices become and remain equidistant and confined within the boundary layer, contradictory to the prediction by inviscid theory. The viscous diffusion cause the vortices to grow, the swirling velocity component to decrease and the boundary layer to develop towards a two-dimensional state. At the position of the eliminated separation bubble the following changes in the turbulence structure were observed. The anisotropy state in the near-wall region is unchanged, which indicates that it is determined by the presence of the wall rather than the large scale vortices. However, the turbulence in the outer part of the boundary layer becomes overall more isotropic due to an increased wall-normal mixing and a significantly decreased production of streamwise fluctuations. The turbulent kinetic energy is decreased as a consequence of the latter. Despite the complete change in mean flow, the spatial turbulence structure and the anisotropy state, the process of transfer of turbulent kinetic energy to the spanwise fluctuating component seems to be unchanged. Local regions of anisotropy are strongly connected to maxima in the turbulent production. For example, at spanwise positions in between those of symmetry, the spanwise gradient of the streamwise velocity cause significant production of turbulent fluctuations. Transport of turbulence in the spanwise direction occurs in the same direction as the rotation of the vortices.     

In-hole and mainflow velocity measurements of low-momentum jets in crossflow emanating from short holes

Discrete hole film cooling utilizes jet-in-crossflow geometry where the jet is supplied through a short hole which may be pitched relative to the main flow. Typically, the velocity ratio is near one. Under these conditions, the mean flow structure of the jet/mainstream interaction may be strongly affected by the characteristics of the flow within the hole. Magnetic resonance velocimetry (MRV) is used to measure the 3-dimensional mean velocity field for various jets in crossflow with short holes of varied inclination angles and blowing ratios typically of gas turbine applications. Novel measurements of the flow within inclined feed holes are captured using MRV. Secondary flows within the hole are found to be strongly dependent on the inclination of the hole. The traditional counter-rotating vortex pair is observed in the mainstream, as well as high levels of wall-normal vorticity. The 3D vorticity field is used to modify traditional jet-in-crossflow vortex ring theory to apply to low-momentum jets which remain attached to the ejection surface.     

Turbulence structure in non-equilibrium boundary layers with favorable and adverse pressure gradients

An experimental study was conducted to document the turbulence in boundary layers on smooth walls subject to a favorable pressure gradient followed by a zero pressure gradient recovery and an adverse pressure gradient. Two component velocity profiles were acquired along the spanwise centerline of the test section, and velocity fields were obtained at the same locations in streamwise wall-normal and streamwise–spanwise planes using PIV. The FPG was shown to reduce the turbulence in the outer part of the boundary layer, reducing the transport of this turbulence and the effect of sweeps toward the wall. This reduced the inclination angle of the large structures and increased their length scale, particularly in the streamwise and spanwise directions. Recovery from the FPG to a ZPG was rapid. The APG reduced the near wall shear, resulting in a reduced effect of ejections relative to sweeps. The APG had an opposite but smaller effect on the shape and size of structures compared to the FPG.     

The Flow Structure Produced by Pulsed-jet Vortex Generators in a Turbulent Boundary Layer in an Adverse Pressure Gradient

The effect of pulsed jet vortex generators on the structure of an adverse pressure gradient turbulent boundary layer flow was investigated. Two geometrically optimised vortex generator configurations were used, co-rotating and counter-rotating. The duty cycle and pulse frequency were both varied and measurements of the skin friction (using hot films) and flow structure (using stereo PIV) were performed downstream of the actuators. The augmentation of the mean wall shear stress was found to be dependent on the net mass flow injected by the actuators. A quasi steady flow structure was found to develop far downstream of the injection location for the highest pulse frequency tested. The actuator near field flow structure was observed to respond very quickly to variations in the jet exit velocity.     

Evolution of jets effusing from inclined holes into crossflow

The turbulent flow structure and vortex dynamics of a jet-in-a-crossflow (JICF) problem, which is related to gas turbine blade film cooling, is investigated using the particle-image velocimetry (PIV) technique. A cooling jet emanating from a pipe interacts with a turbulent flat plate boundary layer at a Reynolds number Re_∞ = 400,000. The streamwise inclination of the coolant jet is 30° and two velocity ratios (VR = 0.28, VR = 0.48) and two mass flux ratios (MR = 0.28, MR = 0.48) are considered. Jets of air and CO₂ are injected separately into a boundary layer to examine the effects of the density ratio between coolant and mainstream on the mixing behavior and consequently, the cooling efficiency. The results show a higher mass flux ratio to enlarge the size of the recirculation region leading to a more pronounced entrainment of hot outer fluid into the wake of the jet. Furthermore, the lateral spreading of the coolant is strongly increased at a higher density ratio. The results of the experimental measurements are used to validate numerical findings. This comparison shows an excellent agreement for mean velocity and higher moment velocity distributions.     

An experimental study into the effects of streamwise and spanwise acceleration in a turbulent boundary layer

We compare two turbulent boundary layers produced in a low-speed water channel experiment. Both are subjected to an identical streamwise pressure gradient generated via a lateral contraction of the channel, and an additional spanwise pressure gradient is imposed on one of the layers by curving the contraction walls. Despite a relatively high streamwise acceleration, hot-film probe measurements of the mean-velocity distributions show that the Reynolds number increases whilst the coefficient of friction decreases downstream. Visualization of the viscous layers using hydrogen bubbles reveal an increase in the non-dimensional streak spacing in response to the acceleration. Changes in statistical moments of the streamwise velocity near the wall suggest an increased dominance of high-velocity fluctuations. The near-wall streaks and velocity statistics have little sensitivity to the boundary layer three-dimensionality induced by the spanwise pressure gradient, with the boundary-layer crossflow velocity reaching 11 % that of the local freestream velocity.     

PLIF and PIV measurements of the self-preserving structure of steady round buoyant turbulent plumes in crossflow

Measurements of the mean concentration of source fluid and mean velocity fields were obtained for the first time in the self-preserving region of steady round buoyant turbulent plumes in uniform crossflows using Planar-Laser-Induced-Fluorescence (PLIF) and Particle-Image-Velocimetry (PIV), respectively. The experiments involved salt water sources injected into water/ethanol crossflows within a water channel. Matching the index of refraction of the source and ambient fluids was required in order to avoid image distortion and laser intensity nonuniformities. Further experimental methods and procedures are explained in detail. The self-preserving structure properties of the flow were correlated successfully based on the scaling analysis of [Fischer, H.B., List, E.J., Koh, R.C., Imberger, J., Brooks, N.H., 1979. Mixing in Inland and Coastal Waters, Academic Press, New York, pp. 315–389]. The resulting self-preserving structure consisted of two counter-rotating vortices having their axes nearly aligned with the crossflow direction that move away from the source in the streamwise (vertical) direction due to the action of buoyancy. This alignment, was a strong function of the source/crossflow velocity ratio, u₀/v_∞. Finally, the counter-rotating vortex system was responsible for substantial increases in the rate of mixing of the source fluid with the ambient fluid compared to axisymmetric round buoyant turbulent plumes in still environments, e.g., transverse dimensions in the presence of the self-preserving counter-rotating vortex system were 2–3 times larger than the transverse dimensions of self-preserving axisymmetric plumes at similar streamwise distances from the source.     

Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV

A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbulent kinetic energy can be accomplished. Parameters of the Q criterion and negative λ₂ techniques used for vortex identification can be evaluated in the mean flow field. Experimental data obtained for a circular turbulent jet issuing normal to a crossflow in a low speed wind tunnel for a jet-to-crossflow velocity ratio of 3.3 are presented to show the applicability of the proposed technique. The results reveal the presence of a secondary counter-rotating vortex pair (SCVP) which is located within the jet core and has a sense of rotation opposite to that of the primary one (PCVP). Consistency of the measurements is verified by the agreement of data obtained in two perpendicular planes. Accuracy of the data is discussed and algebraic relations for some measurement uncertainties are presented.     

Effect of an adverse pressure gradient on the streamwise Reynolds stress profile maxima in a turbulent boundary layer

It is widely accepted that in a turbulent boundary layer （TBL） with adverse pressure gradient （APG） an outer peak usually appears in the profile of streamwise Reynolds stress. However, the effect of APG on this outer peak is not clearly understood. In this paper, the effect of APG is analysed using the numerical and experimental results in the literature. Because the effect of upstream flow is inherent in the TBL, we first analyse this effect in TBLs with zero pressure gradient on flat plates. Under the individual effect of upstream flow, an outer peak already appears in the profile of streamwise Reynolds stress when the TBL continues developing in the streamwise direction. The APG accelerates the appearance of the outer peak, instead of being a trigger.     

The Effect of Pressure Gradient on Boundary Layer Receptivity

This paper presents numerical results for the receptivity of three laminar boundary layers with zero (ZPG), adverse (APG) and favourable (FPG) pressure gradients. Each boundary layer is subjected to a series of simple freestream waveforms which can be considered as constituent parts of either an isotropic or a non-isotropic turbulent freestream. Each freestream waveform has a single frequency in each spatial direction and is divided into two mutually perpendicular components. The first component has a zero spanwise velocity and hence lies in the streamwise normal plane whereas the second component lies in a plane which is perpendicular both to this plane and the spatial frequency vector. High boundary layer receptivities are only obtained for a minority of these waveforms and so only the resulting flow structures for these waveforms are considered in detail. The dominant flow structures are identified as either Tollmien Schlichting (T-S) waves or streaky structures. The streaky structures can be induced by both freestream components, but the response to the second component, which results in streamwise vortices in the freestream, is considerably stronger and occurs over a much larger streamwise frequency range. The boundary layer is only receptive to a relatively narrow band of spanwise wavelengths ranging from approximately one to four times the local boundary layer thickness. The APG leads to receptivities which are more than double those for the FPG case. The ratio of the freestream fluctuation streamwise wavelength to the distance from the plate leading edge is identified as an important influential parameter for receptivity leading to streaks. Significant T-S activity is only observed for APG, but is also detected for ZPG.     

Hybrid LES-RANS study of an effusion cooling array with circular holes

A multi-row effusion cooling configuration with scaled gas turbine combustor conditions is studied numerically, using a novel wall-proximity-based hybrid LES-RANS approach. The distribution of the coolant film is examined by surface adiabatic cooling effectiveness (ACE). Simulation results have shown that the accuracy of cooling effectiveness prediction is closely related to the resolution of turbulent flow structures involved in hot-cold flow mixing, especially those close to the plate surface. The formation of the coolant film in the streamwise direction is investigated. It is shown that the plate surface directly downstream the coolant holes are covered well by the coolant jets, while surface regions in between the two columns of the coolant holes could not be protected until the coolant film is developed sufficiently in the spanwise direction in the downstream region. More detailed study has also been carried out to study the time-averaged and time-dependent flow fields. The relation between the turbulent flow structures and coolant film distribution are also examined. The Kelvin–Helmholtz instability in the upper and lower coolant jet shear layer, is found to have the same frequency of around 8000 Hz, and is independent of the coolant hole position. Additionally, it is suggested by the spectral coherence analysis that those unsteady flow structures from the lower shear layer are closely related to the near wall flow temperature, and such effect is also independent of the coolant hole position.     

Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.     

Bypass transition receptivity modes

The prediction of bypass transition remains an important problem in many engineering applications. This is largely because there is no suitable theoretical model for bypass transition and predictions are made using empirical models. This paper presents numerical results for the receptivity of a zero pressure gradient boundary layer subjected to simple freestream waveforms which are the constituent parts of a turbulent flow field. Significant receptivities are only obtained for a minority of freestream waveforms and these lead to two types of flow structure in the boundary layer. The first type of flow structure is essentially two dimensional in nature and consists of two rows of counter-rotating spanwise vortices and is induced by freestream waves of large normal and spanwise wavelength and streamwise wavelengths approximately equal to the boundary layer thickness. The second type of flow structure are the streamwise streaks frequently observed in flow visualisation experiments. These streaks are induced by freestream waves of long streamwise and normal wavelength and spanwise wavelengths in the range of 14.5-46 θ (1.7-5.4δ). The freestream waves can be formed of velocity components in any direction, however the boundary layer is most receptive to fluctuations that lie in a plane perpendicular to the streamwise direction. The overall receptivity to a full spectrum of waves typical of freestream turbulence is considered and is shown to have similar characteristics to those from experiments.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Mean Flow and Turbulence Measurements in a Turbulent Free Cruciform Jet

The results of measurements of all three components of the mean velocity vector, the Reynolds normal and primary shear stresses and the mean static pressure in a turbulent free jet, issuing from a sharp-edged cruciform orifice, are presented in this paper. The measurements were made with an x-array hot-wire probe and a pitot-static tube in the near flow field of the jet. The Reynolds number, based upon the equivalent diameter of the orifice, was 1.70 × 10⁵. In addition to the quantities measured directly, the mean streamwise centreline velocity decay, the jet half-velocity widths, the jet spreading rate, the mean streamwise vorticity, the mass entrainment rate, the integral momentum flux and the one-dimensional energy spectra have been derived from the measured data. The results show that the mean streamwise centreline velocity decay rate of the cruciform jet is higher than that of a round jet issuing from an orifice with the same exit area as that of the cruciform orifice. The mean streamwise velocity field changed shape continuously from a cruciform close to the orifice exit plane to circular at 12 and half equivalent diameters downstream. The mean streamwise vorticity field, up to about three equivalent diameters downstream of the orifice exit plane, consists of four pairs of counter-rotating cells, which are aligned with the four edges in the centre of the cruciform orifice.     

Turbulence and transport of passive scalar in magnetohydrodynamic channel flows with different orientations of magnetic field

DNS of turbulent flow and passive scalar transport in a channel are conducted for the situation when the fluid is electrically conducting (for example, a liquid metal) and the flow is affected by an imposed magnetic field. The cases of wall-normal, spanwise, and streamwise orientation of the magnetic field are considered. As main results, we find that the magnetic fields, especially those in the wall-normal and spanwise directions, significantly reduce the turbulent scalar transport and modify the properties of the scalar distribution.     

Large-eddy Simulation of Film Cooling Flows with Variable Density Jets

The present paper investigates the impact of the velocity and density ratio on the turbulent mixing process in gas turbine blade film cooling. A cooling fluid is injected from an inclined pipe at α=30° into a turbulent boundary layer profile at a freestream Reynolds number of Re_∞ = 400,000. This jet-in-a-crossflow (JICF) problem is investigated using large-eddy simulations (LES). The governing equations comprise the Navier–Stokes equations plus additional transport equations for several species to simulate a non-reacting gas mixture. A variation of the density ratio is simulated by the heat-mass transfer analogy, i.e., gases of different density are effused into an air crossflow at a constant temperature. An efficient large-eddy simulation method for low subsonic flows based on an implicit dual time-stepping scheme combined with low Mach number preconditioning is applied. The numerical results and experimental velocity data measured using two-component particle-image velocimetry (PIV) are in excellent agreement. The results show the dynamics of the flow field in the vicinity of the jet hole, i.e., the recirculation region and the inclination of the shear layers, to be mainly determined by the velocity ratio. However, evaluating the cooling efficiency downstream of the jet hole the mass flux ratio proves to be the dominant similarity parameter, i.e., the density ratio between the fluids and the velocity ratio have to be considered.