Jet Mach Number Research Articles

Pressure fluctuations due to ‘trapped waves’ in the initial region of compressible jets

An experimental study is conducted on unsteady pressure fluctuations occurring near the nozzle exit and just outside the shear layer of compressible jets. These fluctuations are related to ‘trapped waves’ within the jet's potential core, as investigated and reported recently by other researchers. Round nozzles of three different diameters and rectangular nozzles of various aspect ratios are studied. The fluctuations manifest as a series of peaks in the spectra of the fluctuating pressure. Usually the first peak at the lowest frequency (fundamental) has the highest amplitude and the amplitude decreases progressively for successive peaks at higher frequencies. These ‘trapped wave spectral peaks’ are found to occur with all jets at high subsonic conditions and persist into the supersonic regime. Their characteristics and variations with axial and radial distances, jet Mach number and aspect ratio of the nozzle are documented. For round nozzles, the frequency of the fundamental is found to be independent of the jet's exit boundary layer characteristics and scales with the nozzle diameter. On a Strouhal number (based on diameter) versus jet Mach number plot it is represented by a unique curve. Relative to the fundamental the frequencies of the successive peaks are found to bear the ratios of 5/3, 7/3, 9/3 and so on, at a given Mach number. For rectangular nozzles, the number of peaks observed on the major axis is found to be greater than that observed on the minor axis by a factor approximately equal to the nozzle's aspect ratio; the fundamental is the same on either edge. For all nozzles the onset of screech tones appears as a continuation of the evolution of these peaks; it is as if one of these peaks abruptly increases in amplitude and turns into a screech tone as the jet Mach number is increased.

Effectiveness of Reaction Control System in Hypersonic Rarefied Reactive Flow

The present study completes the simulation of a Terminal High Altitude Area Defense–like missile’s lateral jet flowfield at a rarefied high-altitude atmosphere using the in-house parallel direct simulation Monte Carlo–quantum kinetic method. For the simulation conditions, the flight speed and the flight altitude are set as 20 Ma and 80 km, with the real gas effect and rarefied gas effect considered. The influence of different impact factors, including angle of attack, angle of sideslip, jet pressure ratio, and jet Mach number, are investigated. The normal force coefficient and amplification factors are taken as indicators to evaluate the control performance. It is found that the gain effect of lateral jet interaction will drop when increasing angle of sideslip, jet pressure ratio, and jet Mach number, whereas the normal force coefficient of the missile will rise when raising jet pressure ratio and jet Mach number.

An experimental investigation into model-scale installed jet–pylon–wing noise

A model-scale experimental investigation of an installed jet–pylon–wing configuration was conducted at the University of Southampton, with the scope to study the effect a pylon has on noise generation and to clarify its impact on the fluctuating wall-pressure load. The set-up consisted of two single-stream nozzles, a baseline axisymmetric annular nozzle and a partially blocked annular pylon nozzle. The nozzles were tested first isolated and then installed next to a NACA4415 aerofoil ‘wing’ at a single nozzle–wing position. The jet Mach number was varied between $0.5 \leq M_{{j}} \leq 0.8$ and measurements were performed both under static and in-flight ambient flow conditions up to ${M_{{f}} = 0.2}$ . The jet flow-field qualification was carried out using a single-velocity-component hot-wire anemometer probe. The pressure field on the wing surface was investigated using two miniature wall-pressure transducers that were flush-mounted in the streamwise and spanwise directions within the pressure side of the wing. A linear ‘flyover’ microphone array was used to record the noise radiated to the far field. The unsteady pressure data were analysed in both time and frequency domains using multi-variate statistics, highlighting a far-field noise reduction provided by the presence of the pylon only in the installed case. Furthermore, the wake field generated behind the pylon is seen to significantly modify the wall-pressure fluctuations, particularly at streamwise locations close to the pylon trailing edge.

Supersonic jet noise source distributions.

The purpose of this work is to examine the noise source distributions of shock-containing supersonic jets at various pressure ratios corresponding to fully expanded Mach numbers ranging from 1.0 to 1.4 in intervals of 0.2 for various nozzle exit diameters. Source location measurements using a phased array (beamforming), farfield jet noise measurements, and schlieren flow visualization are presented. It is found that supersonic noise source distributions are more complex than those of subsonic jets. The source distributions for supersonic jets can be divided into three different Strouhal regions. At low Strouhal numbers ( fD/U≤0.3), the noise source distributions appear very similar to those of a subsonic jet, as reported in open literature. This Strouhal region is dominated by jet-mixing noise associated with small-scale turbulence mixing. At high Strouhal numbers ( fD/U≥1.0), the noise source distributions are comprised of several repetitive sources at various discrete downstream jet locations that produce noise at all frequencies. The locations of these sources roughly correspond to the shock cells in the jet, and thus, vary with jet Mach number. Another region exists at Strouhal numbers between these two regions ( 0.3<fD/U<1.0) for which the precise location of the sources as a function of Strouhal number was determined to be ambiguous due to a limitation of the phased array used. This region roughly corresponds to the frequencies of noise where jet-mixing noise and shock noise are of similar levels. The spacing of the shock sources in this region are smaller than the beam width of the array measuring them. Their locations can no longer can be separately recorded; and instead, they are averaged together and their centroid location is plotted.

Scaling law for shock-cell length and its correlation with shock-associated noise of circular and elliptic supersonic free jets

A supersonic core length Lc and an average shock-cell length Ls¯ are experimentally investigated for the acoustic properties of supersonic jets. Following Kumar and Rathakrishnan [“Scaling law for supersonic core length in circular and elliptic free jets,” Phys. Fluids 33(5), 051707 (2021)], a proper scale for the average shock-cell length Ls¯ of circular and elliptic supersonic free jets is found as Ls*¯AR0.2e−0.15γMj2, where Ls*¯ is the average shock-cell length normalized by nozzle throat diameter Dth, AR is the nozzle aspect ratio, γ is the specific heat ratio, and Mj is the ideally expanded jet Mach number. The scaling law developed for Ls*¯ exhibits a close similarity with the scaling law for supersonic core length Lc*AR0.5e−0.11γMj2, where Lc* is the nozzle throat diameter normalized supersonic core length. The scaling laws Ls*¯AR0.2e−0.15γMj2 and Lc*AR0.5e−0.11γMj2 are valid across a wide range of parameters, such as γ from 1.28 to 1.6, the nozzle design Mach number Md from 1 to 2, AR from 1 to 6, and Mj corresponds to the absence of Mach reflection. Discussion conducted on the scaling laws provides important insight into the choice of AR. Furthermore, the relationship between Lc* and Ls*¯ with the intensity of shock-associated noise is also discussed; hence, new correlation functions are developed for Lc* and Ls*¯ that provide an analogous measure of the shock-associated noise.

Single Expansion Ramp Nozzles: Impact of Ramp Length on Flow and Acoustics

This paper investigates the effect of external expansion ramps on supersonic flow emitted from high-aspect-ratio rectangular nozzles with a focus on additional sources of noise due to ramps as well as their effectiveness as noise reduction devices. Schlieren videos showed that the extended ramps stabilized the jet, reduced spreading, and elongated the shock cell systems. Far-field acoustics revealed that the most severe noise penalties arose from the impingement of the shear layer on the ramps and the expansion of the jet at the trailing edge of the ramp. For transonic jets, which contain only broadband sources of noise, noise due to ramps was louder than turbulence mixing noise. The penalty increased with the ramp length. On the contrary, the ramps were effective at reducing noise at higher jet Mach numbers, where the shock-associated components of noise were strong and turbulence mixing noise dominated jet scraping noise. The extent of reduction was dependent on the relative length between the ramp and the jet potential core. A ramp approximately as long as, but no longer than, the potential core minimizes peak mixing noise, shock-associated noise, and noise arising from the interaction between flow and the ramp.

Scaling law for supersonic core length in circular and elliptic free jets

We present here the experiments demonstrating the scaling law for supersonic core length in circular and elliptic free jets. A proper scale for the supersonic core length of free jets is found as Lc*AR e−0.11γMj2, where Lc* is the core length normalized by nozzle throat diameter Dth, AR is the aspect ratio of the elliptic nozzle, γ is the specific heats ratio, and Mj is the ideally expanded jet Mach number. The scaling law developed for supersonic core length shows a close dependence with nozzle expansion ratio pe/pa and agrees well with the results reported in open literature, including the data reported for γ = 1.28–1.67. In spite of their uniqueness, the present results refer to circular and elliptic jets only. Thus, other similar studies on rectangular and square jets for a wide range of parameters are needed for a full comprehension of the universality of the scaling law for non-circular jets.

Fluid Dynamics of a Bistable Diverter Under Ultrasonic Excitation—Part I: Performance Characteristic

Abstract This paper investigates an ultrasonically driven bistable fluidic diverter at inlet nozzle Mach numbers of up to Mn = 0.3 and operating pressure ratios of up to Pr = 1.1. Part I examines the switching characteristics with respect to nondimensional parameters of excitation amplitude, frequency, required energy, switching time and inlet total pressure. It is shown that to promote switching at turbulent jet Mach numbers of up to Mn = 0.3 it is necessary to excite a jet preferred mode of St = 0.45 which differs from previously reported laminar jet operation of the similar device. For the reference case the switching time amounts to 1.2 ms suggesting oscillation frequencies of up to 500 Hz. Part II is a combined experimental and numerical study that examines the triggered instability modes in the free shear layer using large eddy simulations (LES) and visualizes the flow field using Particle Image Velocimetry (PIV).

The near-field aerodynamic characteristics of hot high-speed jets

Abstract

Effect of tab parameters on the near-field mixing characteristics of a Mach 1.5 elliptic jet

The effect of delta-tabs with its apex leaning downstream on the jet mixing characteristics of a Mach 1.5 elliptic jet of aspect ratio (AR) 3.37 is reported in this paper. The delta-tabs were placed along the minor and major axes of the elliptic nozzle, referred to as tab configuration C1 and C2, respectively. For each tab configuration, four different orientation angles varying from θ= 90∘ to 150∘ were studied, where θ= 90∘ is the tab positioned normal to the nozzle exit and θ= 150∘ is the tab oriented in the downstream direction at the nozzle exit. The tab effects on jet manipulation were investigated via shadowgraph visualization, and the mean Pitot pressure was measured along the jet centerline and along the orthogonal planes of the jet. The non-dimensonalized supersonic core length Lc*, average shock-cell spacing Ls¯*, and the axis-switching location xas* were examined in detail to understand the jet characteristics of the natural and manipulated jets. The mixing capability of the manipulated jets quantified based on the reduction in supersonic core length ΔLc* depends strongly on the ideally expanded jet Mach number Mj, tab configuration (C1 and C2), and θ. As such, the ΔLc* for the manipulated jet at θ= 135∘ is the largest, revealing the optimal tab orientation for jet mixing enhancement, as also observed for the circular jet [Zaman et al., “Control of an axisymmetric jet using vortex generators,” Phys. Fluids 6(2), 778–793 (1994)]. The relationship between ΔLc* and ΔLs* is presented to understand the correlation between the jet mixing and noise characteristics of the manipulated jet. Discussion is conducted based on the dependence of ΔLc* and ΔLs* with θ, which provides useful insight into the jet flow physics. With suitable placement of tabs C1 and C2, the axis switching could be either stopped or augmented. The superior mixing characteristics of an elliptic jet relative to a circular jet, which were found in previous works on the supersonic over-expanded jet [Kumar and Rathakrishnan, “Characteristics of a supersonic elliptic jet,” Aeronaut. J. 120(1225), 495 (2016)] prevail in the supersonic jet under-expanded jet as well.

Multi-particle models of molecular diffusion for Lagrangian simulation coupled with LES for passive scalar mixing in compressible turbulence

Lagrangian simulation coupled with large eddy simulation (LES) is studied for turbulent scalar mixing in compressible flows, where Lagrangian simulation solves advection-diffusion equations with computational particles. In Lagrangian simulation, a molecular diffusion term needs to be modeled with a so-called mixing model, which also requires modeling the dissipation rate of scalar fluctuations. The present study extends a particle-based subgrid-scale model for the scalar dissipation rate to compressible flows, and its validity in compressible turbulence is examined with direct numerical simulation databases of a temporally evolving turbulent planar jet with a jet Mach number of 0.6 or 1.6. A priori test confirms that the model can well predict the mean scalar dissipation rate in the subsonic and supersonic turbulent jets. The model hardly depends on the spatial distribution of the particles when the number of particles used in the model is about 12. However, the scalar dissipation rate tends to be overestimated by the model in regions with large dilatation fluctuations although such regions with strong compressibility effects occupy only a small part of the flow. Lagrangian simulation coupled with LES of the turbulent jet is also performed with the scalar dissipation model combined with the mixing volume model. Lagrangian simulation with these models effectively predicts passive scalar statistics, such as averages, rms fluctuations, and turbulent fluxes, in the turbulent jet with both subsonic and supersonic jet velocities. The scalar dissipation model well predicts the coarse-grained scalar dissipation rate in Lagrangian simulation. The present results confirm that the mixing volume model combined with the particle-based model of the scalar dissipation rate is useful in Lagrangian simulation coupled with LES, which is a promising approach for simulating high-speed turbulent reacting flows as reaction terms appear in Lagrangian simulation in a closed form.

Experimental investigation on mixing characteristics of high speed co-flow jets by using tabbed chevron nozzle

Abstract The present study investigates the effect of chevron with tab (Tabbed chevron) fixed at the exit of the co-flowing primary nozzle on the mixing characteristics in subsonic and sonic jets. The experiment was conducted for the jet Mach number 0.6 and 0.8. The centerline Mach number decay was calculated for all these jet Mach numbers for the co-flow baseline nozzle, nozzle with chevrons and tabbed chevron (primary flow) nozzle respectively. It was found that tabbed chevron was effective in reducing the potential core length by 88.23% as compared to the chevron nozzle with baseline nozzle. The radial profile also shows that the mixing enhancement by tabbed chevron is better than chevron nozzle.

Experimental investigation on mixing characteristics of high speed co-flow jets by using tabbed chevron nozzle

Abstract The present study investigates the effect of chevron with tab (Tabbed chevron) fixed at the exit of the co-flowing primary nozzle on the mixing characteristics in subsonic and sonic jets. The experiment was conducted for the jet Mach number 0.6 and 0.8. The centerline Mach number decay was calculated for all these jet Mach numbers for the co-flow baseline nozzle, nozzle with chevrons and tabbed chevron (primary flow) nozzle respectively. It was found that tabbed chevron was effective in reducing the potential core length by 88.23% as compared to the chevron nozzle with baseline nozzle. The radial profile also shows that the mixing enhancement by tabbed chevron is better than chevron nozzle.

Hydrogen fueled detonation ramjet: Conceptual design and test fires at Mach 1.5 and 2.0

The conceptual design of a hydrogen-fueled detonation ramjet (DR) of a new type for a cruising flight speed of Mach 2 at sea level is developed using multivariant three-dimensional (3D) numerical simulations of the operation process. The possibility of arranging the continuous-detonation (rotating or longitudinally pulsating) combustion of hydrogen in an expanding annular combustor of the DR is proved for the first time. 3D numerical simulations of the operation process in the DR for flight conditions with a Mach number M ranging from 1.1 to 2.7 are performed. The calculated effective thrust of such a DR is shown to become positive at M = 1.3, i.e., the startup Mach number for such a DR can be lower than M = 2.0, which is typical for ramjets operating on continuous-deflagration combustion. A DR demonstrator is designed and manufactured. Its test fires are performed in a pulsed wind tunnel (WT) at free air jet Mach numbers M = 2.0 and M = 1.5. The most important result of test fires is the experimental proof of the possibility of arranging stable continuous-detonation combustion of hydrogen in the DR of the developed design at both Mach numbers.

On the formation and sustenance of the compressible vortex rings in starting axisymmetric jets: A phenomenological approach

The present work numerically investigates the formation and sustenance of a primary vortex ring (PVR) and counter-rotating vortex rings (CRVRs) in laminar, axisymmetric, continuously blowing compressible jets. The effect of jet Reynolds number (Rej), jet Mach number (Mj), and pressure-ratio (pjpa) on these compressible vortex rings and their flow dynamics is explored. The core bow shock is formed in the inviscid core of the transonic/supersonic jets for sustaining the supersonic flow field in the PVR. The embedded shock (ES) and vortex-induced shock (VIS) are also found to sustain the evolving PVR in the supersonic jets. The effect of Mj and pjpa on the circulation and pinch-off of the PVR is also investigated. For over-expanded and perfectly expanded supersonic jets, Kelvin–Helmholtz vortices (KHVs) entrained into the PVR interact with the ES to cause a shock–vortex interaction, which results in the appearance of multiple VISs. It is established that the different events of interaction of KHV with the ES inside the PVR after the pinch-off are a manifestation of two factors: (i) the constraint imposed on the PVR by quasi-time-invariance of circulation around a material curve enclosing the PVR and (ii) the requirement of spatially cyclic property distribution inside the PVR. The shock-shear layer–vortex interaction in under-expanded jets is also investigated using vorticity analysis and oblique shock theory. For under-expanded jets, apart from the Mach-reflection timescale, the CRVR pattern formation is also governed by the initial strength of the slip-stream, which, in turn, is regulated by all three parameters, i.e., Rej, Mj, and pjpa.

Implicit large eddy simulation of passive scalar transfer in compressible planar jet

AbstractImplicit large eddy simulation (ILES) of passive scalar transfer in compressible turbulence is evaluated for subsonic and supersonic turbulent planar jets. The ILES used in this study relies on fully explicit numerical schemes for spatial and temporal discretization and low‐pass and shock‐capturing filters used as an implicit subgrid‐scale (SGS) model. The ILES results are compared with the direct numerical simulation (DNS) database of the same flows. The ILES results exhibit good agreements with the DNS for first‐ and second‐order statistics of velocity and passive scalar. The scalar transport by turbulent velocity fluctuations is well captured by the ILES. The temporal evolution of the jet strongly depends on the jet Mach number, where a higher Mach number results in the delay of jet development. The Mach number dependence of velocity and passive scalar fields is consistent between the ILES and DNS. The low‐pass filters used as the implicit SGS model contribute to the dissipation of turbulent kinetic energy and scalar variance. Under the present numerical conditions, the filters account for about 50% of the dissipation in a fully developed turbulent jet. The dissipation rate in the ILES, which is the sum of the grid‐scale and SGS dissipation rates, is very close to the dissipation rate in the DNS, and the amount of the SGS dissipation is well controlled by the low‐pass filters. The filters also dump numerical oscillations in the velocity field caused by strong pressure waves outside the supersonic jet at the high Mach number.

Investigation of acoustic propagation and source localization in a hot jet flow

A jet flow typically occurs in open-jet wind tunnels and turbofan engines, where there are velocity and temperature gradients between the source region and the outside environment. These gradients form a thermal shear layer that determines acoustic propagation and source localization. Moreover, they induce Kelvin–Helmholtz instabilities in numerical simulations. To stabilize simulations, a gradient-term suppression and filtering method is proposed and validated using time-domain linearized Euler equations. For sound propagation, the influences of the steep gradients of the velocity and temperature together with the spreading angle and source frequency are investigated through a self-similar shear layer with superposition of compressibility and heat. Those refraction influences strongly change the beamforming-related phase rather than the directivity-related amplitude. Next, the computed database is processed by delay-and-sum beamforming to localize the source position. In the beamforming part, refraction and amplitude corrections based on Amiet’s theory with an extension for temperature differences are numerically evaluated and later applied when analyzing the localization error. This localization error is basically proportional to the jet Mach number, temperature ratio, and source frequency and is inversely proportional to the spreading rate. Finally, the localization error is fitted as a linear function of the product of the jet Mach number and the Strouhal number.

Temperature effects on the noise source mechanisms in a realistic subsonic dual-stream jet

A detailed numerical investigation of temperature effects on both aerodynamics and acoustics of a dual-stream jet including a central plug is carried out. The geometry is representative of a realistic turbofan with a high by-pass-ratio (BPR) close to 9. Two take-off high-subsonic operating points are investigated numerically by compressible large-eddy simulation. For these two selected points, the secondary stream is exactly the same in terms of static temperature and velocity. Both jets have also the same primary velocity. The only difference lies in the static temperature of the primary jet. There is a ratio of two between the two jets considered in this study, namely Tj=400 K and Tj=800 K. More precisely, the primary jet temperature is reduced while keeping the acoustic Mach number constant, leading to an increase of the primary jet Mach number from Mj=0.65 in the heated case to Mj=0.89 in the cold case. Some experimental data are available for the hot jet while the cold jet is introduced for academic reasons. The heated jet compares reasonably well with the experimental data, taking into account the complexity of the geometry. Temperature effects have a limited impact on aerodynamic development and acoustic radiation. The influence of the core flow is found to be weak due to the high BPR considered and the radiated acoustic is mainly driven by the secondary flow. Further investigations are carried out in order to highlight the differences between the two cases. The acoustic production area are identified by the way of axial velocity skewness coefficient maps. Finally, a decrease of the primary stream temperature leads to the development of trapped acoustic waves inside the jet core. An increase of the overall sound spectrum level about 5 dB is thus observed in the upstream direction for the cold jet, in agreement with the vortex sheet theory.

Multiband RadioAstron space VLBI imaging of the jet in quasar S5 0836+710

Context. Detailed studies of relativistic jets in active galactic nuclei (AGN) require high-fidelity imaging at the highest possible resolution. This can be achieved using very long baseline interferometry (VLBI) at radio frequencies, combining worldwide (global) VLBI arrays of radio telescopes with a space-borne antenna on board a satellite. Aims. We present multiwavelength images made of the radio emission in the powerful quasar S5 0836+710, obtained using a global VLBI array and the antenna Spektr-R of the RadioAstron mission of the Russian Space Agency, with the goal of studying the internal structure and physics of the relativistic jet in this object. Methods. The RadioAstron observations at wavelengths of 18 cm, 6 cm, and 1.3 cm are part of the Key Science Program for imaging radio emission in strong AGN. The internal structure of the jet is studied by analyzing transverse intensity profiles and modeling the structural patterns developing in the flow. Results. The RadioAstron images reveal a wealth of structural detail in the jet of S5 0836+710 on angular scales ranging from 0.02 mas to 200 mas. Brightness temperatures in excess of 1013 K are measured in the jet, requiring Doppler factors of ≥100 for reconciling them with the inverse Compton limit. Several oscillatory patterns are identified in the ridge line of the jet and can be explained in terms of the Kelvin–Helmholtz (KH) instability. The oscillatory patterns are interpreted as the surface and body wavelengths of the helical mode of the KH instability. The interpretation provides estimates of the jet Mach number and of the ratio of the jet to the ambient density, which are found to be Mj ≈ 12 and η ≈ 0.33. The ratio of the jet to the ambient density should be conservatively considered an upper limit because its estimate relies on approximations.

Single and Multivariate Statistics of Jet-Induced Pressure Fluctuations over an Infinite Plate

Motivated by the problem of the installation effects of modern turbofan engines, we experimentally investigated the interaction between a compressible subsonic jet and a tangential flat plate. Measurements of wall pressure fluctuations were performed in a semi-anechoic environment addressing the effect of several governing parameters, such as the stream-wise and span-wise location, the jet Mach number and the radial distance of the plate surface from the jet axis. The statistical properties of the wall pressure signals were analyzed in terms of both power spectra and cross-correlations, with the latter providing the estimation of the phase speed. The analysis is also carried out in the time-frequency domain through the application of the wavelet transform to further characterize the dynamics of the wall pressure signatures.