Flow and acoustic features of a supersonic tapered nozzle

The acoustic and flow characteristics of a supersonic tapered jet were measured for free and shrouded flow configurations. Measurements were performed for a full range of pressure ratios including over- and underexpanded and design conditions. The supersonic tapered jet is issued from a converging-diverging nozzle with a 31 rectangular slotted throat and a conical diverging section leading to a circular exit. The jet was compared to circular and rectangular supersonic jets operating at identical conditions. The distinct feature of the jet is the absence of screech tones in the entire range of operation. Its near-field pressure fluctuations have a wide band spectrum in the entire range of measurements, for Mach numbers of 1 to 2.5, for over- and underexpanded conditions. The free jet's spreading rate is nearly constant and similar to the rectangular jet, and in a shroud, the pressure drop it is inducing is linearly proportional to the primary jet Mach number. This behavior persisted in high adverse pressure gradients at overexpanded conditions, and with nozzle divergence angles of up to 35°, no inside flow separation was observed.     

Density and compressibility effects in turbulent subsonic jets part 1: mean velocity field

The behavior of compressible jets originated from initially turbulent pipe flows issuing in still air has been investigated at three different subsonic Mach numbers, 0.3, 0.6 and 0.9. Helium, nitrogen and krypton gases were used to generate the jet flows and investigate the additional effects of density on the flow structure. Particle image velocimetry, high-frequency response pressure transducers and thermocouples were used to obtain velocity, Mach number and total temperature measurements inside the flow field. The jets were formed at the exit of an adiabatic compressible frictional turbulent pipe flow, which was developing toward its corresponding sonic conditions inside the pipe, and continued to expand within the first four diameters distance after it exited the pipe. Theoretical considerations based on flow self-similarity were used to obtain the decay of Mach number along the centerline of the jets for the first time. It was found that this decay depends on two contributions, one from the velocity field which is inversely proportional to the distance from the exit and one from the thermal field which is proportional to this distance. As a result, a small non-linearity in the variation of the inverse Mach number with downstream distance was found. The decay of the Mach number at the centerline of the axisymmetric jets increases by increasing the initial Mach number at the exit of the flow for all jets. The decay of mean velocity at the centerline of the jets is also higher at higher exit Mach numbers. However, the velocity non-dimensionalized by the exit velocity seems to decrease faster at low exit Mach numbers, suggesting a reduced mixing with increasing exit flow Mach numbers. Helium jets were found to have the largest spreading rate among the three different gas jets used in the present investigation, while krypton jets had the lowest spreading rate. The spreading rate of each gas decreases with increasing its kinetic energy relatively to its internal energy.     

UV-mediated coalescence and mixing of inkjet printed drops

In the present study, the characteristics of supersonic rectangular microjets are investigated experimentally using molecular tagging velocimetry. The jets are discharged from a convergent–divergent rectangular nozzle whose exit height is 500 μm. The jet Mach number is set to 2.0 for all tested jets, and the Reynolds number Re is altered from 154 to 5,560 by changing the stagnation pressure. The experimental results reveal that jet velocity decays principally due to abrupt jet spreading caused by jet instability for relatively high Reynolds numbers (Re > ~450). The results also reveal that the jet rapidly decelerates to a subsonic speed near the nozzle exit for a low Reynolds number (Re = 154), although the jet does not spread abruptly; i.e., a transition in velocity decay processes occurs as the Reynolds number decreases. A supersonic core length is estimated from the streamwise distribution of the centerline velocity, and the length is then normalized by the nozzle exit height and plotted against the Reynolds number. As a result, it is found that the normalized supersonic core length attains a maximum value at a certain Reynolds number near which the transition in the velocity decay process occurs.     

LES of temporally evolving mixing layers by an eighth‐order filter scheme

An eighth‐order filter method for a wide range of compressible flow speeds (H. C. Yee and B. Sjogreen, Proceedings of ICOSAHOM09, June 22–26, 2009, Trondheim, Norway) is employed for large eddy simulations (LES) of temporally evolving mixing layers (TML) for different convective Mach numbers (M_c) and Reynolds numbers. The high‐order filter method is designed for accurate and efficient simulations of shock‐free compressible turbulence, turbulence with shocklets, and turbulence with strong shocks with minimum tuning of scheme parameters. The value of the M_c considered is for the TML range from the quasi‐incompressible regime to the highly compressible supersonic regime. The three main characteristics of compressible TML (the self‐similarity property, compressibility effects, and the presence of large‐scale structures with shocklets for high M_c) are considered for the LES study. The LES results that used the same scheme parameters for all studied cases agree well with experimental results and published direct numerical simulations (DNS). Published 2012. This article is a US Government work and is in the public domain in the USA.     

Wavy structures in compressible mixing layers

Semi-periodic structures namely inclined wavy structures(IWS) are experimentally observed in compressible mixing layers at two convective Mach numbers(Mc=0.11 and 0.47). Flow structures are visualized by the laserinduced planar laser Mie scattering(PLMS) technique. Two methods are developed to investigate the spatial distribution and geometry of IWS:(1) the dominant mode extraction(DME) method, to extract the dominant modes of IWS from the streamwise gray-level fluctuation, and(2) the phase tracking(PT) method, to identify the shape of IWS. The results suggest that pressure perturbations account for the formation of IWS in the initial mixing region and the joint efect of dilatation and coherent vortices enhances IWS in the welldeveloped region. The large transverse(cross-flow) scale of the IWS and their relation to coherent vortices(CV) indicate that the disturbance originated from CV in the mixing center propagates far into the free streams. The DME and the PT method are shown to be the efective tools to study the geometrical features of wavy structures in compressible shear flows.     

Measurements on supersonic free jets

Summary An experimental study of round supersonic air jets discharging into quiescent air is described. The initial stagnation enthalpy of the jets was equal to that of the atmosphere. Most of the experiments concerned a fully expanded jet with initial Mach number M _I =1.74. From the experimental results the turbulent Prandtl number and the turbulent coefficient of momentum transfer could be calculated in a large part of the mixing zone of the jets. A mixing parameter K has been introduced and calculated for the jets. The results of this investigation are compared with those obtained for low-speed jets.     

Near-field of coaxial jets with large density differences

 The paper describes an experimental investigation of coaxial jets with large density differences. Measurements by various techniques show that density effects on the flow dynamics are taken into account to first order by considering the specific outer to inner jet momentum flux ratio M and not separately the density and velocity ratios. A regime of recirculation occurs for M higher than a critical value (M _c ≈50). For a given value of M, however, the position of the recirculation bubble is slightly shifted in the upstream direction for density ratios much smaller than one. An unexpected result is obtained for an extremely low density ratio: the onset of recirculation occurs for a significantly higher value of M (100<M _c <140) for helium/SF₆ jets (density ratio : 0.028). Received: 1 October 1997 / Accepted: 8 March 1998     

Axisymmetric Coanda-assisted vectoring

An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach < 0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r − θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.     

Characteristics of counter-rotating vortex rings formed ahead of a compressible vortex ring

Characteristics of high Mach number compressible vortex ring generated at the open end of a short driver section shock tube is studied experimentally using high-speed laser sheet-based flow visualization. The formation mechanism and the evolution of counter rotating vortex ring (CRVR) formed ahead of the primary vortex ring are studied in details for shock Mach number (M) 1.7, with different driver section lengths. It has been observed that the strength of the embedded shock, which appears at high M, increases with time due to the flow expansion in the generating jet. Strength of the embedded shock also varies with radius; it is strong at smaller radii and weak at larger radii; hence, it creates a velocity gradient ahead of the embedded shock. At critical Mach number (M _c ≥ 1.6), this shear layer rolls up and forms a counter rotating vortex ring due to Biot-Savart induction of the vortex sheet. For larger driver section lengths, the embedded shock and the resultant shear layer persists for a longer time, resulting in the formation of multiple CRVRs due to Kelvin–Helmholtz type instability of the vortex sheet. CRVRs roll over the periphery of the primary vortex ring; they move upstream due to their self-induced velocity and induced velocity imparted by primary ring, and interact with the trailing jet. Formation of these vortices depends strongly upon the embedded shock strength and the length of the generating jet. Primary ring diameter increases rapidly during the formation and the evolution of CRVR due to induced velocity imparted on the primary ring by CRVR. Induced velocity of CRVR also affects the translational velocity of the primary ring considerably.     

Modified flapping jet for increased jet spreading using synthetic jets

The present paper is an experimental investigation, using a PIV system, on modified rectangular jet flow co-flowing with a pair of synthetic jets placed symmetrically with respect to the geometric centerline of the main flow. The objective was to determine the optimal forcing conditions that would result in jet spreading beyond what would be obtained in a simple flapped jet. The main jet had an exit Re_h = 36,000, based on the slot height, h. The synthetic jets were operated in a periodic manner with a periodic momentum coefficient of about 3.3% and at a frequency of the main jet preferred mode. A short, wide angle diffuser of half angle of about 45° was attached to the main jet. Generally for the vectored jet, much of the flow features found here resembled those reported in the literature except that the deflection angle in this study increased with downstream distances inside the diffuser and then remained roughly unchanged thereafter. Larger jet spreading was achieved when the main jet was subjected to simultaneous actuation of the synthetic jets but the flow did not achieve the initial jet spreading that was observed in the vectored jet. Further jet spreading was achieved when the synthetic jets were alternately actuated in which each synthetic jet was actuated for a number of cycles before switching. This technique allowed the jet to flap across the flow between transverse positions larger than what would be obtained in a simple flip-flop jet. Under the present flow geometry and Reynolds number, it was found that when the ratio f_s/f_al, where f_s is the synthetic actuation frequency and f_al is the alternating frequency, was larger than 10, the mean streamwise velocity of the main jet had two peaks symmetrically placed with respect to the jet axis and the jet had the appearance of flowing into two streams each moving nearly parallel to the diffuser wall. For a value of f_s/f_al of about 10, the optimal value in this study, the desired flow properties were achieved in that, the mean velocity was nearly uniform with an increase in the jet width compared to the simultaneous actuations, and the jet flapping was more effective in redistributing and homogenizing the turbulent kinetic energy across the main jet.     

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.     

Investigation of a continuous adjoint-based optimization procedure for aeroacoustic control of plane jets

A control optimization technique using the continuous adjoint of the compressible Navier–Stokes equations is implemented for aeroacoustic optimization of plane jet flows. The purpose of the adjoint equations is to provide sensitivity information, which is afterwards used in a gradient-based minimization of a prescribed cost functional, designed to describe the far-field sound pressure level (SPL). The objective of the present paper is to demonstrate the ability to reduce the sound in the near far-field of plane jets. Furthermore, as the continuous adjoint approach can become inaccurate, due to inconsistencies between the continuous and the discretized system, the accuracy of the continuous adjoint approach is investigated. The considered cases exhibit a nozzle exit Reynolds number of Re_jet = ρu_jetD/μ = 2000 and a Mach number of M_jet = 0.9, performed using two-dimensional direct numerical simulation and three-dimensional large-eddy simulation, respectively. A comparison of the obtained gradient via adjoint and finite differences is presented and it is shown, that in order to obtain reliable gradient directions, the length of the optimization time needs to be restricted. Furthermore, a receding horizon optimization for the two-dimensional plane jet simulation is used to obtain a sound reduction over much longer time intervals. The influence of different formulations of the viscosity in the adjoint equations is finally investigated.     

Experimental Investigation of Nozzle Exit Reflector Effect on Supersonic Jet

The present study describes an experimental work to investigate the effect of a nozzle exit reflector on a supersonic jet that is discharged from a convergent–divergent nozzle with a design Mach number of 2.0. An annular reflector is installed at the nozzle exit and its diameter is varied. A high-quality spark schlieren optical system is used to visualize detailed jet structures with and without the reflector. Impact pressure measurement using a pitot probe is also carried out to quantify the reflector’s effect on the supersonic jet which is in the range from an over-expanded to a moderately under-expanded state. The results obtained show that for over-expanded jets, the reflector substantially increases the jet spreading rate and reduces the supersonic length of the jet, compared with moderately under-expanded jets. The reflector’s effect appears more significant in imperfectly expanded jets that have strong shock cell structures, but is negligible in correctly expanded jet.     

Experimental investigation of a three-dimensional viscous underexpanded jet

The three-dimensional interaction of jet issuing from two- and four-nozzle systems into ambient space or an outer flow has been investigated experimentally. The range of the important parameters include the following: pressure imbalance n=P_a=/P=10–1.5·10², Mach number at the nozzle exit M_a=3.15, Mach number of the outer flow M=0, 3.1, and 6, the flow is turbulent in the mixing layer (P_a and P are the static pressures at the nozzle exit and in the outer flow). It is shown that the interaction of the jets broadens a multinozzle jet considerably in the plane of interaction, which is a plane of symmetry and which passes through the axis of the system between neighboring nozzles. The cross-sectional shape of a four-nozzle jet is cross-like over the entire length of the initial segment of the jet. The width of the mixing layer in the plane of interaction is considerably larger than in the central plane, which passes through the axis of opposed nozzles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 21–26, September–October, 1974.     

Convective-Absolute Transition of Non-Isothermal Compressible Shear Layer

The linear stability of inviscid compressible shear layers is studied. When the layer develops at the vicinity of a wall, the two parallel flows can have velocity of the same sign or of opposite sign. This situation is examined in order to obtain first hints on the stability of separated flows in the compressible regime. The shear layer is described by an hyperbolic tangent profile for the velocity component and the Crocco relation for the temperature profile. The gravity effects and the superficial tension are neglected. By examining the temporal growth rate at the saddle point in the wave number space, the flow is characterized as being either absolutely unstable or convectively unstable. This study principally shows the non-isothermal effect on the absolute-convective transition in compressible shear flow. Results are presented, showing the amount of the backflow necessary to have this type of transition for a range of primary flow Mach number M ₁ up to 3.0. The boundary of the absolute-convective transition is defined as a function of the velocity ratio, the temperature ratio and the Machnumber.     

Modelling of pressure–strain correlation in compressible turbulent flow

Previous studies carried out in the early 1990s conjectured that the main compressible effects could be associated with the dilatational effects of velocity fluctuation. Later, it was shown that the main compressibility effect came from the reduced pressure-strain term due to reduced pressure fluctuations. Although better understanding of the compressible turbulence is generally achieved with the increased DNS and experimental research effort, there are still some discrepancies among these recent findings. Analysis of the DNS and experimental data suggests that some of the discrepancies are apparent if the compressible effect is related to the turbulent Mach number, Mt. From the comparison of two classes of compressible flow, homogenous shear flow and inhomogeneous shear flow （mixing layer）, we found that the effect of compressibility on both classes of shear flow can be characterized in three categories corresponding to three regions of turbulent Mach numbers： the low-Mr, the moderate-Mr and high-Mr regions. In these three regions the effect of compressibility on the growth rate of the turbulent mixing layer thickness is rather different. A simple approach to the reduced pressure-strain effect may not necessarily reduce the mixing-layer growth rate, and may even cause an increase in the growth rate. The present work develops a new second-moment model for the compressible turbulence through the introduction of some blending functions of Mt to account for the compressibility effects on the flow. The model has been successfully applied to the compressible mixing layers.     

Study of heat transfer in the separation zones formed in front of supersonic jets in a subsonic carrier flow

The heat transfer taking place between the gas and the surface of the plate in the zone of three-dimensional separation of the turbulent boundary layer in front of a set of supersonic jets injected perpendicularly to a subsonic carrier flow is considered. The aim of this investigation is to establish the main physical characteristics of heat transfer in the separation zones in front of jet obstacles and to obtain the distributions of the local heat-transfer coefficients and the temperature of the thermally insulating wall as functions of the parameters of the carrier flow and the injected jets. Analysis of the experimental results yields certain approximating relationships for the distribution of the local heat-transfer coefficients as functions of the Mach number of the carrier flow M, the Mach number of the jet M_j, the relative boundary-layer displacement thickness _s= _s ^* /d, and the degree of jet superheating T_ojT_o relative to the separation zones in front of supersonic jet obstacles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–72, July–August, 1975.     

Large eddy simulation of compressible round jets with coflow

Large eddy simulations of subsonic round jets are carried out using high order compact finite difference scheme and an explicit filtering based approximate deconvolution method. The jets have a Mach number of 0.9 and Reynolds number of $4.5\times {10}^5$ based on jet diameter and centerline velocity at inflow. Results obtained for the mean flow and turbulence intensities agree well with those in existing literature. We also study the effects of co-flow velocity ratio on the flow physics. Increase in potential core length and decrease in spreading rate of jet is observed in the presence of co-flow. The effects of co-flow velocity ratio on the axial Reynolds stress and turbulent kinetic energy budgets are also presented. It is observed that increasing co-flow velocity ratio leads to reduction in the turbulence intensities and near-field sound levels.     

Experimental investigation of jets from rectangular six-lobed and round orifices at very low Reynolds number

This article presents an experimental study conducted on a six-lobed rectangular jet at a very low Reynolds number of 800. The near-exit flow dynamics is compared to the reference counterpart circular jet with same initial conditions. Flow dynamics is analyzed using time-resolved flow-visualizations, hot-wire anemometry and laser Doppler velocimetry. In the round jet, flow motion is dominated by large primary Kelvin–Helmholtz (K–H) structures. In the six-lobed rectangular jet, the K–H vortices are very thin compared to the large secondary vortices generated by the high shear at the lobed nozzle lip. The inspection of mean-velocity profiles and streamwise evolutions of the spreading rates in the major and the minor planes of the lobed jet confirm the absence of the switching-over phenomenon not observed on flow images. The streamwise structures that develop in orifice troughs render the volumetric flow rate significantly higher than that of the reference circular jet. Comparison of the obtained results to available data of the literature of similar rectangular six-lobed jets investigated at very high Reynolds numbers reinforces the notion that the three-dimensional flowfields at very low and very high Reynolds numbers are similar if the geometry of the lobed nozzle is conserved. However, important variations in flow dynamics might occur if one or several geometric parameters of the lobed nozzle are modified.     

Mathematical modeling of jet interaction with a high-enthalpy flow in an expanding channel

Results of modeling the interaction of a plane supersonic jet with a supersonic turbulent high-enthalpy flow in a channel are reported. The problem is solved in a two-dimensional formulation at external flow Mach numbers M_∞ = 2.6 and 2.8 and at high values of the total temperature of the flow T ₀ = 1800–2000 K. The mathematical model includes full averaged Navier-Stokes equations supplemented with a two-equation turbulence model and an equation that describes the transportation of the injected substance. The computations are performed by using the ANSYS Fluent 12.1 software package. Verification of the computational technique is performed against available experimental results on transverse injection of nitrogen and helium jets. The computed and experimental results are demonstrated to agree well. For the examined problems, in addition to surface distributions of characteristics, fields of flow parameters are obtained, which allow one to reproduce specific features that can be hardly captured in experiments. Parametric studies show that an increase in the angle of inclination and the mass flow rate of the jet leads to an increase in the depth of jet penetration into the flow, but more intense separated flows and shock waves are observed in this case.