Supersonic Core Length Research Articles

Effect of wall length on an interacting supersonic rectangular jet

PurposeThis study aims to study the interaction effects between a rectangular supersonic jet with a flat wall computationally using wall length as a parameter. The purpose of this study is to investigate the effect of change in wall length on supersonic core length (SCL) reduction, jet deflection and jet decay behavior.Design/methodology/approachThe design Mach number and aspect ratio at the rectangular exit were 1.8 and 2, respectively. To study the wall length effects on jet-wall interactions, wall length (Lw) was varied as 0.5Dh, 1Dh, 2Dh, 4Dh and 8Dh, where Dh was the hydraulic diameter of the nozzle exit. The flat wall with the matching width of the rectangular exit section of a supersonic nozzle was placed at the nozzle exit such that the supersonic jet grazed past the wall. The studies were carried out at over-expansion [nozzle pressure ratio (NPR) = 4], near optimum expansion (NPR = 6) and under-expansion (NPR = 8) levels.FindingsResults indicated that significant reduction in wall-bounded SCL was noticed in the range of 0.5Dh ≤ Lw ≤ 1Dh for both over-expansion and under-expansion conditions. At Lw ≥ 4Dh, SCL got enhanced at NPR = 4 and 6 but had a negligible effect at NPR = 8.Practical implicationsThrust vector control, noise reduction and easy take-off for high-speed aircraft.Originality/valueThe effect of change in flat wall length on interaction characteristics of a rectangular supersonic jet was not studied before in terms of SCL reduction and jet decay behavior.

Effect of increasing bypass ratio on supersonic co-flowing jet with finite lip thickness

The article presents the investigation on the effect of increasing bypass ratio on a supersonic co-flowing jet with finite lip thickness for a jet exit Mach number of 2.0. Co-flowing jets of differing bypass ratios (BR = ms/mp, where ms and mp are the mass flow rate of secondary and primary jets, respectively) 3.69, 9.0, and 16.0 were employed to explore the impact of high bypass secondary jets on the primary jet. A single-jet BR 0 is used for comparison. The supersonic core lengths of the single jet and the co-flow jet for BR 3.69, BR 9.0, and BR 16.0 were metrics for quantifying the mixing. The surrounding jet enhances the wake dominance in the nozzle lip, and the supersonic core length shortens. High bypass co-flowing jets are extremely efficient at shortening the supersonic core length compared to the low bypass counterpart, and hence, the jet mixing increases. The radial Mach number profiles quantitatively represent different zones in the co-flowing jet. The variation of these zones with bypass ratios highlights the dynamic interaction between the primary and secondary jets. The physical reason for apparent jet mixing and flow categories has been discussed based on considerations about changes in the flow field and shock structure.

An Investigation on Uncontrolled and Vortex-Generator Controlled Supersonic Jets

The present study is carried out with a motivation to investigate the axisymmetric supersonic jet both experimentally and computationally. An open jet facility was utilized to carry out the experiments, and the results were compared with computational simulations employing the K-omega SST turbulence model using ANSYS software. It is important to note that, the computational validation has been done incorporating the Rayleigh Pitot formula to match the centerline pressure for the uncontrolled jet, which has not been found in any other validation studies according to the authors’ understanding. Besides, the experimental study is extended with a focus on evaluating the impact of Vortex Generators (VGs) on Mach 1.6 supersonic jets. The aim was to enhance jet mixing, a critical factor for improving engine performance. Various nozzle geometry modifications were explored in the past, but VGs emerged as the most effective method for optimizing jet mixing efficiency. The investigation revealed a substantial decrement in the supersonic jet core length when VGs were introduced at the nozzle exit, especially under favorable pressure gradients. This reduction in the supersonic core emphasized the role of VGs in enhancing mixing efficiency. The study also confirmed that VGs significantly distort wave patterns within the supersonic core, crucial for improved jet mixing. This research signifies the importance of VGs in augmenting the mixing of Mach 1.6 jets, offering the potential for improved jet performance and reduced noise emissions in the aerospace industry.

Investigation of slanted perforation diameter in tabs for supersonic jet control

PurposeThis study aims to investigate the effect of slanted perforation diameter in tabs for the control of Mach 1.4 underexpanded supersonic jet flow characteristics.Design/methodology/approachNumerical investigation was carried out for NPR 5 to analyze the effect of slanted perforation diameter in tabs to control the Mach 1.4 jet. Four sets of tabs with slanted circular perforation geometries (Φp = 1, 1.5, 2 and 2.5 mm) were considered in this study. The inclination angle of 20° (αP) with reference to the jet axis was maintained constant for all the four tabs considered.FindingsDetermined value indicates there is a 68%, 71%, 73% and 75% drop in supersonic core for the Φp = 1, 1.5, 2.0 and 2.5 mm, respectively. The results show that the tabs with 2.5 mm perforation diameter were found to be efficient in reducing the supersonic jet core in comparison with other tab cases. The reduction in supersonic core length is due to the extent of miniscule vortices exuviating from slanted small and large diameter perforation in the tabs.Practical implicationsThe concept of slanted perforation can be applied in scramjet combustion, which finds its best application in hypersonic vehicles and in noise suppression in fighter aircraft.Originality/valueSlanted perforation and circular shapes with different diameters have not been studied in the supersonic regime. Examining the effect of circular diameter in slanted perforation is an innovation in this research paper.

Influences of semi-circular, square, and triangular grooves on mixing behavior of an axisymmetric supersonic jet

The length of the supersonic jet ejected from the military aircraft must be reduced in order to decrease its heat signature and aeroacoustic noise and thereby to enhance its stealth capability. The reduction or manipulation of the supersonic core can be achieved through various passive control techniques. Considering this, the present study explores the mixing characteristics of supersonic jets with and without passive controls. Passive controls in the form of grooves configured at the exit of a Mach 1.73 convergent–divergent nozzle are investigated computationally. Particularly, the supersonic jet decay characteristics and flow development for a plain nozzle and a nozzle with semi-circular, square, and triangular grooves are presented. In addition, the study explores different turbulence models, namely, Spalart–Allmaras, realizable k-ε, std k-ω, shear stress transport (SST) k-ω, and SST transition. The realizable k-ε turbulence model is found to be the most effective one in capturing the supersonic jet structure. It is observed that the grooves produce large distortions in the jet structure, accompanied by significant mass entrainment and lateral spread. Interestingly, semi-circular grooves are proven to be most effective in all cases of expansion level than square and triangular grooves. For the semi-circular grooves, a maximum of 48.5% reduction in the supersonic core length of the correctly expanded jet at nozzle pressure ratio (NPR) of 5 is achieved. The reduction in the supersonic core length for semi-circular grooves is 31% for the overexpanded jet at NPR 4 and 29% for the underexpanded jet at NPR 7.

Shock-Structure Formation in Circular and Non-Circular Sonic Jets at Underexpanded Conditions

The generation of shock waves and their repercussions in high-speed vehicles are inevitable. Particularly, the hot plume from the aircraft exhaust ejecting at a high speed, as well as the emitted aeroacoustic noise, have several consequences. Besides, the occurrence of the supersonic core length and the emission of high screech noise are mostly due to the shock cells, prevailing in high-speed jets. Therefore, understanding the shock cell structures developed at the exit of aircraft or rocket nozzles is vital in improving mixing and thereby the noise characteristics. Essentially, non-circular nozzle shapes are well known for enhancing entrainment characteristics and mitigating the noise due to their differential spreading over the nozzle's perimeter. The current study examines the shock structures of circular, elliptic, and square jets at various sonic underexpansion levels. In this investigation, the nozzle geometries are considered to have the same exit area. The Nozzle Pressure Ratio (NPR) was adjusted to 3, 4, and 5 to achieve moderate and highly underexpansion conditions. The shadowgraph visualization method is used to study the development of shock cells from axisymmetric and asymmetric nozzles. It is interesting to observe that the incident and reflected shock structures exist only at moderate and high underexpansion levels. Besides, the elliptic and the square jets have distinctive flow patterns along their different axis planes. The intercepting shock appears on the elliptic jet in the minor axis rather than the major axis direction. The curvature of the intercepting shock wave was found to be greater for the elliptic jet than that for the circular jet. In addition, the square jet in the symmetry plane diverges from the jet centerline, but the jet in the diagonal direction converges. Moreover, the estimated shock cell lengths using shadowgraph images were compared to a theoretical model where the experimentally obtained results are in good agreement with the theoretical values.

Design of Fluidic Injector for Supersonic Jet Manipulation

A Mach 2.0 round jet at design and off-design condition is experimentally manipulated using two steady radial injectors to investigate the effect of fluidic injection on jet mixing. A new scaling law for , the supersonic core length of manipulated supersonic free jets, is found as , where is normalized by the nozzle throat diameter , is the specific heats ratio, is the ideally expanded jet Mach number, is the momentum ratio of the individual injector jet to the main jet, and is the expansion ratio of the main jet. The discussion pertaining to the scaling law provides an important insight into the choice of diameter ratio for efficient jet manipulation, where and are the injector and nozzle exit diameters, respectively. Such insight can yield valuable information on the practical usability of fluidic injectors for the full-scale applications. It is also documented that fluidic injectors can provide an effective flow control mechanism for jet mixing applications in comparison to the elliptic jet.

Parametric study and scaling of Mach 1.5 jet manipulation using steady fluidic injection

We present the experimental investigation conducted to study the mixing characteristics of a Mach 1.5 jet manipulation using steady fluidic injection. Two important parameters are investigated, namely, the number of injectors, N, and the mass flow rate ratio of the injector jet to the main jet, Cm, along with the expansion ratio of the main jet, pe/pa, where pe and pa are the nozzle exit and atmospheric pressures, respectively. The jet mixing quantified as a measure of supersonic core length, Lc*, strongly depends on N, Cm, and pe/pa. Two distinct regions behind the jet manipulation are identified, and a physical reasoning based on pe/pa is presented using Pitot pressure measurements and Schlieren images. Empirical scaling analysis conducted on the experimental data for Lc* = f1(N, Cm, Ui/Uj, pe/pa) is reduced to Lc* = f2(MRNγMj2pe/pa), where MRN is the momentum ratio of the individual injector jet to the main jet, expressed as MRN = Cm,NUiUj and Cm,N = Cm/N. Here, U is the velocity, and suffixes “i” and “j” represent the injector and the main jet, respectively. Discussion conducted based on the scaling laws provides important insight into the optimal choice of injector diameter and the injection pressure ratio for practical utility.

Effect of flat wall length on decay and shock structure of a supersonic square wall jet

Experiments were conducted to find the effect of wall length on the decay behaviour and shock structure of a supersonic wall jet issuing from c-d nozzle of the square-shaped exit. A straight flat wall of width same as the side length of the square was attached to the lip of the nozzle such that the leading edge of the wall and the side of the square aligned properly which allowed the supersonic jet to graze past the flat wall. Experiments were conducted with five different wall lengths, that is, [Formula: see text] = 0.5, 1, 2, 4 and 8. Wall pressure measurements were made from leading edge to the trailing edge of the wall along its centreline. Schlieren flow visualization of the jet flow over the wall for the different wall lengths revealed the shock pattern and the effect of the wall length on the shock structure. The shock structure and jet deflection were significantly affected due to the presence of the wall. There was an upward jet deflection for [Formula: see text] up to [Formula: see text] whereas a downward jet deflection was observed for [Formula: see text]. Noticeable changes in the shock structure were observed for the wall lengths up to 2 D h. The wall length also significantly affected the jet decay characteristics and supersonic core length. Maximum enhancement in jet decay and maximum reduction in supersonic core length resulted when the wall length was [Formula: see text]. However, when the wall length was increased to [Formula: see text], there was a significant reduction in jet decay and a recovery of [Formula: see text]. Presence of wall always resulted a reduction in Lsc irrespective of wall length. The wall effect was to induce a more precipitous pressure drop closer to the nozzle exit, and a more gradual drop farther from it for [Formula: see text] > [Formula: see text].

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.

On the mechanism of the influence of medium density on the supersonic core length of an underexpanded jet

Exhaustion of a supersonic underexpanded air jet into air–helium and air–sulfur hexafluoride mixtures is studied experimentally. The air jet escapes from a convergent circular nozzle in the range of moderate Reynolds numbers covering the laminar and transitional regimes of the jet flow. The experiments are performed with “cold” and heated jets in a low-pressure jet setup, which allows the Reynolds number of the jet exhaustion from the nozzle, the jet pressure ratio, and the density of the gas surrounding the jet to be maintained independently. A Pitot tube is used to measure the supersonic core length of the air jet as a function of the density of the ambient medium whereto the jet exhausts. In addition, the spatial distributions of the amplitude–frequency characteristics of acoustic oscillations generated by the jet in the ambient space are measured by a moving sensor of pressure fluctuations. The effect of the ratio of the underexpanded air jet density to the ambient medium density on the supersonic core length is demonstrated. It is shown that the mechanism of influence of the ambient medium density is associated with a change in the conditions for the global instability of the underexpanded air jet and, in particular, the conditions for generation of the screech tone.

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.

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.

Influence of nozzle exit geometrical parameters on supersonic jet decay

Abstract Experiments and simulations were carried on C-D nozzles with four different exit geometry aspect ratios to investigate the impact of supersonic decay characteristics. Rectangular and elliptical exit geometries were considered for the study with various aspect ratios. Numerical simulations and Schlieren image study were studied and found the agreeable logical physics of decay and spread characteristics. The supersonic core decay was found to be of different length for different exit geometry aspect ratio, though the throat to exit area ratio was kept constant to maintain the same exit Mach number. The impact of nozzle exit aspect ratio geometry was responsible to enhance the mixing of primary flow with ambient air, without requiring a secondary method to increase the mixing characteristics. The higher aspect ratio resulted in better mixing when compared to lower aspect ratio exit geometry, which led to reduction in supersonic core length. The behavior of core length reduction gives the identical signature for both under-expanded and over-expanded cases. The results revealed that higher aspect ratio of the exit geometry produced smaller supersonic core length. The aspect ratio of cross section in divergent section of the nozzle was maintained constant from throat to exit to reduce flow losses.

Influence of nozzle exit geometrical parameters on supersonic jet decay

Abstract Experiments and simulations were carried on C-D nozzles with four different exit geometry aspect ratios to investigate the impact of supersonic decay characteristics. Rectangular and elliptical exit geometries were considered for the study with various aspect ratios. Numerical simulations and Schlieren image study were studied and found the agreeable logical physics of decay and spread characteristics. The supersonic core decay was found to be of different length for different exit geometry aspect ratio, though the throat to exit area ratio was kept constant to maintain the same exit Mach number. The impact of nozzle exit aspect ratio geometry was responsible to enhance the mixing of primary flow with ambient air, without requiring a secondary method to increase the mixing characteristics. The higher aspect ratio resulted in better mixing when compared to lower aspect ratio exit geometry, which led to reduction in supersonic core length. The behavior of core length reduction gives the identical signature for both under-expanded and over-expanded cases. The results revealed that higher aspect ratio of the exit geometry produced smaller supersonic core length. The aspect ratio of cross section in divergent section of the nozzle was maintained constant from throat to exit to reduce flow losses.

Modeling of supersonic jet behavior in the vacuum refining process

There are two problems to be solved in the numerical simulation of the top blown oxygen vacuum refining process. (1) The two-equation turbulence models underpredict the turbulence mixing shear process for high-temperature gradient jet flows. (2) The high compressibility of the jet in a low vacuum environment. In this study, the SST k-ω turbulence model is modified by the composite function of the compressibility factor and the total temperature gradient. Based on the experimental model of the Kotani vacuum jet, the modified turbulence model was used to simulate the supersonic jet behavior of oxygen lance at different ambient temperatures. The reliability of the model is verified by the semi-empirical formula of Ito and Muchi. The simulation results show that the entrainment rate is an important inducing factor. The potential core length and the supersonic core length at the temperature of 1800 K are 2.5 times and 2.0 times that at the temperature of 285 K, respectively. Besides, based on the ejection model established by Ricou and Spalding, the calculation formula of turbulence entrainment rate at different ambient temperatures is obtained. This research work will benefit greatly to the supersonic jet behavior in Vacuum Refining.

Numerical Study of Characteristics of Underexpanded Supersonic Jet

Correlations for the supersonic jet characteristics, the mean shock cell length and the supersonic core length, have been obtained in terms of the jet parameters. The jet parameters considered in this study are the exit diameter of the nozzle (de), the design Mach number (Me), the nozzle pressure ratio (NPR) and the ratio of specific heats of the medium (γ). The parameters were varied as follows: exit diameters, from 0.5 to 25 mm; Mach number from 1 to 3; the NPR from 2.14 to 35. Initially, working fluid used is cold air and then effect of variation of γ is taken into consideration. The computational model has been validated and then used for all the numerical simulations. A quadratic fit for both characteristics has been obtained which is applicable to any supersonic jet. The correlations developed are valid within the respective ranges of the parameters stated above.

Passive control of coaxial jet with supersonic primary jet and sonic secondary jet

The mixing enhancement of a coaxial jet with a Mach 1.4 primary jet and sonic secondary jet, at different convective Mach numbers, is presented in this study. Rectangular tabs of aspect ratios (AR = h/w, where h and w are the tab height and width, respectively) 2.0 and 0.75 were employed to manipulate the primary and secondary jets, respectively. The primary jet (C0) and coaxial jet without control or manipulation (C1) are studied in order to decouple the effects of rectangular tabs on jet mixing. Four different tab configurations were studied, viz., tabs placed in the primary jet (C2), tabs placed in the secondary jet (C3), and tabs placed in both primary and secondary jets with the relative orientation between them of 0° (C4) and 90° (C5), to document the effect of tabs on mixing. The supersonic core length Lc* of the manipulated jet was used as a measure to quantify the mixing performance of the manipulated jet. The secondary flow reduces the growth rate of the primary shear layer and elongates the supersonic core length. This study reveals that the manipulated jet emulates the characteristic of a non-circular jet. Primary tabs are highly effective in reducing the supersonic core length of the coaxial jet than secondary tabs, and hence, the jet mixing increases. Two different flow categories of the manipulated jet have been identified. The physical reason behind the observed jet mixing and flow categories have been presented based on arguments related to changes in the flow field and shock structure.

Effect of Hydraulic Diameter on Potential Core Decay of Supersonic Jets

Various studies dealing with decay characteristics of circular and noncircular supersonic jets were conducted by previous researchers. But in these studies due emphasis was not given to the hydraulic diameter (Dh), shape factor (ζ) & the nozzle lip parameters which have significant impact on the characteristics of noncircular supersonic jet. In this study, it has been shown that these parameters played a significant role on supersonic core decay characteristics [2, 3, 6] of the jet. The scope of this study included supersonic core length (Lc), decay pattern, due to noncircular shaped nozzle. In the literature, the supersonic jet characterization and the related experimental correlation are available for optimum expansion conditions whereas for other expansion (under and over) conditions the experimental correlation is barely available. While investigating experimentally, new empirical relations were obtained which were the improved forms of earlier correlations for supersonic core length [4]. For experiments, six different types of nozzles (circular, hexagon, square, triangular, elliptical and rectangular) with the same exit to throat area ratio, convergent length and divergent length were used. The results obtained from the experimentally developed correlations were coherent with numerical results, experimental data and flow visualization.

Multi-Schlieren CT Measurements of Supersonic Microjets from Circular and Square Micro Nozzles

Instantaneous three-dimensional (3D) density distributions of a shock-cell structure of perfectly and imperfectly expanded supersonic microjets escaping into an ambient space are measured. For the 3D observation of supersonic microjets, non-scanning 3D computerized tomography (CT) technique using a 20-directional quantitative schlieren optical system with flashlight source is employed for simultaneous schlieren photography. The 3D density distributions data of the microjets are obtained by 3D-CT reconstruction of the projection’s images using maximum likelihood-expectation maximization. Axisymmetric convergent-divergent (Laval) circular and square micro nozzles with operating nozzle pressure ratio 5.0, 4.5, 4.0, 3.67, and 3.5 have been studied. This study examines perfectly expanded, overexpanded, and underexpanded supersonic microjets issued from micro nozzles with fully expanded jet Mach numbers Mj ranging from 1.47 - 1.71, where the design Mach number is Md = 1.5. A complex phenomenon for free square microjets called axis switching is clearly observed with two types “upright” and “diagonal” of “cross-shaped”. The initial axis-switching is 45° within the first shock-cell range. In addition, from the symmetry and diagonal views of square microjets for the first shock-cells, two different patterns of shock waves are viewed. The shock-cell spacing and supersonic core length for all nozzle pressure ratios are investigated and reported.