Convergent Section Research Articles

Numerical study on infrared radiation intensity and suppression methods of nozzle considering multi-component effects

Improving the accuracy of infrared intensity calculation in exhaust system and expanding infrared suppression methods are of great significance for enhancing aircraft stealth performanc. In this paper, the infrared radiation (IR) intensity (3–5 µm) of nozzle considering the influence of turbine and afterburner are numerically studied. Initially, the flow field characteristics are computed using commercial software, followed by ray tracing simulations using the reverse Monte Carlo method (RMCM) and transmission calculations using the multi-scale multi-group wideband k distribution model (MSMGWB). The wall emissivity is determined experimentally. This paper quantitatively analyzes the difference between infrared intensity obtained through traditional computational methods and that of the actual model, revealing the impact of low-emissivity coating and turbine cooling on the infrared intensity of the integrated model. It emphasizes the suppression effects and physical mechanisms of the heat shield flanging structure on the infrared characteristics of the integrated model. The results indicate significant differences between infrared intensity derived from traditional computational methods and that from actual models. The influence of the afterburner and turbine infrared characteristics must be considered in infrared numerical studies. When the computation model is a standalone nozzle, the infrared intensity can increase by up to 541.78 % and decrease by a maximum of 14.02 % compared to the integrated model compose of the turbine, afterburner, and nozzle. For the model composed of nozzle and afterburner, the infrared intensity can decrease by up to 10.5 % under non-swirl flow condition, without any increase observed. Compared with turbine wall, changing the emissivity of afterburner wall has more significant effect on infrared suppression of integrated calculation model. Reducing the emissivity of all afterburner walls from 0.7 to 0.1 significantly reduces the infrared characteristics in the range of 0° to 12.5°, while increasing it in the range of 12.5° to 45°. Applying a low-emissivity coating only to the high-temperature walls of the afterburner can inhibit the increase in emitted radiation on the wall, thereby eliminating the increase in infrared intensity mentioned above and reducing the infrared intensity by up to 39.14 %. Compared to low-emissivity coating technology for turbine, implementing cooling measures on turbine blades can effectively reduce the infrared intensity of the integrated model, achieving a maximum reduction of 19.7 % when the blade temperature is lowered by 240 K. Adding flanging structure to the heat shield in the convergent section alters the flow field structure near the nozzle walls, lowering wall temperature and thereby suppressing the infrared characteristics of the integrated model between 10° and 80°. This results in a maximum reduction in infrared intensity of 14.75 % with negligible impact on thrust coefficients. This is the angle range where afterburner low emissivity coatings and turbine cooling cannot achieve infrared suppression. This is of great significance for infrared stealth in large angle range. Combined with the above effective infrared suppression measures, the infrared intensity can be reduced by up to 49.42 %.

The impacts of structural parameters on performance and energy loss of the supersonic separator: A sensitivity analysis

The supersonic separator uses pressure energy to achieve highly efficient carbon capture and water vapor separation from the natural gas mixture. Structural parameters are crucial in determining both separation performance and pressure energy loss of the supersonic separator. However, a comprehensive understanding of how them influence flow behaviors and performance is hindered by their coupling effects and the limitations of numerical methods. This study introduces Euler-Lagrange-Euler model to predict separation performance and pressure energy loss of supersonic dehydration process with varying structural parameters. The results show that the expansion ratio of the divergent section, length of the convergent section, inlet radius of the inner body, and throat radius of the inner body significantly impact separation performance and pressure energy loss. Especially the first parameter, the swirl strength and centrifugal acceleration decay to 0.044 and 2.41 × 104 m s−2 as it increases. At the same time, the droplet removal rate significantly improves, but the separation performance does not increase indefinitely due to the shock waves. The dehydration efficiency first increases to 95.09 % at Er= 1.5 and then decreases; the dew point depression also expands to 25.28 K and then drops, and the corresponding pressure loss rises to 0.47 and then falls.

Analysis of mixing enhancement ability of bypass dual throat nozzle with single/multi-tabs

Bypass dual throat nozzle (BDTN) represents an innovative fluidic thrust vectoring nozzle capable of adjusting thrust vectoring angles through self-adaptive flow control. This study explores the BDTN-single/multi-tabs configurations, ensuring that the nozzle’s outlet projected area remains constant while introducing one or more pairs of tabs coplanar with the convergent section of the cavity. This design accounts for aerodynamic performance, thrust vectoring capabilities, and mixing abilities of the BDTN. Through theoretical analysis, design implementation, numerical simulations, and wind tunnel experiments, findings reveal that, in the case of BDTN-single-tab configuration, an increase in tab angle (α) leads to heightened streamwise vortex intensity at the nozzle outlet, reduced high-temperature core area, and enhanced jet centerline velocity and temperature attenuation rate. BDTN-single-tab achieves up to a 90% reduction in centerline-temperature/velocity decay rate, implying stronger mixing enhancement with higher tab angles. Compared to α = 10° BDTN-single-tab, the area of the high-temperature core area decays by 75%. For the BDTN-multi-tab configuration, an increase in the number of tabs results in increased thrust coefficient and vectoring angle, alongside diminished streamwise vortex strength at the nozzle outlet, and a more complex streamwise vortex structure. However, the jet’s centerline velocity and temperature decay rate decreased as a consequence.

Optimization of Process Parameters for Flow Nozzle with Different Geometry using Computational Fluid Dynamics Method

A nozzle is a tubular structure designed to facilitate the flow of hot gases. Rocket nozzle designs typically consist of a stationary convergent section and a stationary divergent section. The term "CD" is an abbreviation for "convergent-divergent" and is used to refer to this specific nozzle type. Upgrades are being made to nozzles and other engine components in order to enhance performance and optimise thrust delivery. Application-specific improvements will be made to rocket nozzles and other current combustion expansion systems. An instance of such progress is the implementation of the bell and twin bell nozzle. This study conducted a comparative analysis of two kinds of nozzles, namely bell and conical, at different Mach speeds to ascertain which one yields the most optimal flow. Subsequently, the flow parameters were modelled with computational fluid dynamics (CFD). Ensuring optimal pressure thrust integral throughout the supersonic zone of the nozzle surface while taking the base pressure into account was the aim of the problem formulation. The research focused on irrotational flow, taking into consideration the impacts of boundary layers.

Investigation on mixing characteristics of rotating detonation combustor with convergent inlet

Mixing characteristics play an important role on the operational process of rotating detonation combustor (RDC). In this paper, a series of numerical calculations were conducted to analyze the influence of injection diameter, injection position, reactant mass flow rate, and equivalence ratio on mixing characteristics. Mixing performance parameters and total pressure loss in combustor dome and ignition zone were analyzed in detail. The findings indicated that all four injection conditions had significant influence on mixing characteristics, among which injection position was the most significant factor. When injection position was in convergent section, the mixing characteristics were better than those in ignition section. Reducing the fuel diameter gradually improved mixing characteristics, but also increased total pressure loss. The change of reactant mass flow rate had a minimal effect on mixing characteristics. As equivalence ratio decreased, mixing characteristics decreased and total pressure loss decreased. In addition, the comparative analysis also showed that penetration depth of hydrogen had an impact on flow field disturbance and distribution of return region, which led to the difference in mixing characteristics. When hydrogen was injected into the convergent structure section where air flow velocity did not reach sonic speed and was in acceleration phase, total pressure loss would be effectively reduced in combustor dome.

Experimental and numerical investigation on thermochemical erosion and mechanical erosion of carbon-based nozzles in hybrid rocket motors

In order to enhance energy characteristics of propellants in hybrid rocket motors, aluminum particles are added into the solid fuel. However, these particles may lead to nozzle mechanical erosion, which significantly affects the motor performance. This paper intends to study thermochemical and mechanical erosion mechanism of carbon-based nozzles in hybrid rocket motors with aluminum metallized fuel. A firing test is performed, and 95 % hydrogen peroxide and hydroxyl‑terminated polybutadiene based fuel with aluminum particles are utilized. Experimental results show that many metal particles are ejected from the nozzle, and aluminum oxide deposits heavily on the nozzle inner surface. A method of numerical calculation coupled with two-phase flow, combustion of aluminum metallized fuel, thermochemical ablation reactions, and mechanical erosion is established. The errors of combustion chamber pressure and throat erosion rate between numerical calculation and test results are 0.53 % and 7.76 %, respectively. Simulation results indicate that with the increase of aluminum content, nozzle wall pressure gradually increases, while the mass fraction of H2O, CO2, OH, and O declines. The nozzle wall temperature and thermochemical erosion rate raise first and then reduce as aluminum content increases. The mechanical erosion is mainly distributed in the convergent section, and it raises with the increase of aluminum content. When aluminum content is up to 38 %, the maximum mechanical and thermochemical erosion rates are 0.09185 mm/s and 0.0976 mm/s, respectively. This reveals that effects of mechanical erosion on hybrid rocket nozzles should be carefully considered and evaluated under conditions of high aluminum content.

Two-way coupled CFD-DEM model of a pre-mixed abrasive water jet and its application to the investigation of abrasive motion characteristics

This paper uses the weight function to modify the particle volume fraction algorithm. The VOF model is modified by adding the particle phase volume fraction and momentum source to the control equation, the semi-resolved VOF-DEM model is established, and PTV experiment is used to verify the model. Based on this model, the flow and distribution characteristics of the abrasive are obtained: 1) The water-abrasive flow near the outlet of the convergent section of the nozzle has a significantly dense two-phase flow characteristic, and the collision between particles dominates particle flow. 2) The particles at the nozzle outlet are distributed in the radial direction of “n”, and with the increase of the stand-off distance of the jet, the particle phase volume transitions from “n” to “m” distribution. The research on the flow characteristics of particles can provide a basis for the nozzle design of pre-mixed abrasive water jets.

Numerical Analysis of Convergent-Divergent Angles and Operating Conditions Impact on Rocket Nozzle Performance Parameters

Comprehensive numerical analysis was conducted to elucidate the exhaust performance of rocket engine nozzles. The study focused on unravelling the intricate relationship between convergence and divergence angles and their impact on the exhaust performance parameters, including velocity coefficient (cv), angularity coefficient (Ca), and gross thrust coefficient (Cfg). In contrast to conventional studies that focus mainly on the divergent section, this research delved into both convergent and divergent aspects of nozzle geometry. For the convergent section, a range of angles from 20° to 45° was systematically examined. For the divergent section, a wide spectrum of angles was explored, ranging from small (10°-13°), medium (14°-19°) and large (20°-25°) divergent angles. Further, we venture beyond geometry, investigating the influence of nozzle pressure ratio (NPR) on these key metrics. Realisable 𝑘𝑘−𝜀𝜀, enhanced wall traitement was used to simulate nozzle flow. The study identified the optimal convergent angle at 37.5°. The 15° diverging angle provides good overall performance, while the 23° angle strikes the ideal compromise: maximizing thrust and efficiency while minimizing weight and maintaining optimal performance.

The Ability of Convergent–Divergent Diffusers for Wind Turbines to Exploit Yawed Flows on Moderate-to-High-Slope Hills

Small-to-medium-sized wind turbines operate with wind speeds that are often modest, and it is therefore essential to exploit all possible means to concentrate the wind and thus increase the power extracted. The advantage that can be achieved by positioning the turbine on hilly reliefs, which act as natural diffusers, is well known, and some recent studies can be found on the effects of the characteristics of hilly terrain on the turbine performance. The literature shows numerous investigations on the behavior of ducted wind turbines, i.e., equipped with a diffuser. But so far, there is a lack of studies on the flow acceleration effects achievable by combining natural relief and a diffuser together. In this study, we analyze the performance of a 50 kW ducted turbine positioned on the top of hills of various shapes and slopes, with the aim of identifying the geometric characteristics of the diffuser most suitable for maximizing power extraction. The results show that a symmetrical convergent–divergent diffuser is well suited to exploit winds skewed by the slope of the hill, and therefore characterized by significant vertical velocity components. Due to its important convergent section, the diffuser is able to convey and realign the flow in the direction of the turbine axis. However, the thrust on the diffuser and therefore on the entire system increases dramatically, as does the turbulence released downwind.

Effect of Convergent Angle on different Flow Parameters of a Convergent-Divergent Nozzle

Nozzle is defined as a device which is being used to convert the pressure energy into the kinetic energy. It basically controls the mass flow rate, pressure and velocity of the fluid stream. Consisting of three sections convergent, throat and divergent section, this device basically converts subsonic flow into supersonic flow. An extensive study have been conducted by the authors in the past about the divergent angle effect on flow parameters of a C-D (Convergent-Divergent) nozzle. In this paper, detailed study have been done to find the most optimum value of convergent angle of a C-D nozzle for the best flow parameters. Convergent angles under consideration are 15°, 20°, 25°, 30° and 35°.

Numerical simulation and experiment of a bypass dual throat nozzle with tab modification

Bypass dual throat nozzle (BDTN) is a new kind of fluidic thrust vectoring nozzle that can provide thrust vectoring by controlling self-adaptive flow. In this paper, BDTN-tab is proposed to improve the mixing ability of the nozzle. It is defined as a new kind of BDTN with an outlet modified by a pair of tabs. Under the premise of ensuring the nozzle outlet projected area remains unchanged, the pair of tabs coplanar with the convergent section of the cavity is designed to be. This design takes aerodynamic performance, thrust vectoring performance and mixing ability into account. Conclusions can be drawn through theoretical analysis, design, numerical simulation and wind tunnel experiments: The BDTN-tab can produce a thrust vectoring angle by opening the bypass valve, which can reach an extreme angle of 32°. As the tab angle increases, the thrust coefficient and thrust vectoring angle of the nozzle decrease. However, the vortex intensity at the nozzle outlet increases and can enhance the mixing between primary flow and external flow.

Analysis of energy loss in the helical hedge flow channel of fruit tree root emitter

This paper proposes the design of a helical hedge flow channel with a high energy loss, which shows promising potential for application in fruit tree root emitters. The aim is to investigate the relationship between the energy loss form in the channel and its influencing factors. The hydraulic performance testing method is employed to analyze the factors that affect energy loss. The main influencing factors are determined using the response surface methodology (RSM) for experimental design. Based on the obtained experimental results, the energy loss form and influencing factors are analyzed, and a prediction model for the energy loss coefficient (ξ) is established. The results indicate that the ξ exhibits a decreasing trend with an increase in the diversion angle (α), a trend of first increasing and then decreasing with an increase in the channel width (b), and an increasing trend with an increase in the number of channel units (n). The effects of the straight section length (l1), convergence section length (l2), and bend radius (r) on the ξ can be neglected. The ranking of the geometric parameters' influence on the ξ is as follows: n > b > α > l1 > r > l2. The experimental results reveal that the ξ ranges from 19.2 to 234.3. Furthermore, the head loss along the flow channel constitutes merely 0.06–0.47% of the local head loss, The main form of energy loss in the spiral counter flow channel is local head loss. There is a significant linear relationship between α, b, n and the ξ, The established prediction model (R2 = 0.9691) can accurately predict the ξ of the channel.

Numerical prediction of the two-phase flow and radiation effects on the thermal environment and ablation of solid rocket nozzle

The effects of two-phase flow and radiative heat transfer have a significant impact on the internal thermal environment and thermochemical ablation process in aluminized solid rocket motor (SRM). However, these two effects were not revealed systematically in previous studies. In this paper, a multiscale methodology combined radiative properties of molten alumina particles at microscale calculated by Mie theory and the two-phase flow and radiative heat transfer at macroscale calculated by Eulerian-Lagrangian method coupling with discrete ordinate method is constructed within aluminized SRM. The convection and radiation are coupled with the chemical kinetics to predict the thermochemical ablation and thermal environment. The influence of two-phase fluid flow and thermal radiation on the internal thermal environment and thermochemical ablation of a SRM nozzle is analyzed quantitatively. Comparisons are made among the methodologies that models the alumina particles as gas species, considers the effect of two-phase flow and considers the effects of two-phase flow and radiative heat transfer. The results show that the erosion rate and total heat flux at the inner wall in the convergent section increase noticeably when considering the effect of two-phase flow. Meanwhile, the erosion rate in the divergent section also increases and the thermal environment is dependent on the particle size and aluminum content. Radiative heat transfer considerably enhances the total heat flux, especially in the convergent section. On the contrary, its impact on the erosion rate is very small except for the inner wall with very low temperature.

A novel in-flight thrust modulation technique for SPRM: proof of concept

Thrust modulation (termination or reduction) is one of the most sophisticated topics in rocket motors. Thrust termination is employed when combustion must be terminated to ensure proper stage separation, to avoid motor explosion, to attain certain range, or for research purposes. While liquid and hybrid propellant rocket motors have the ability to extinguish thrust, thrust termination in solid propellant rocket motors (SPRMs) need the use of specialized technology. In-flight thrust termination of (SPRMs) can be achieved by sudden and sufficient increase in throat area. Increasing throat area causes high depressurization rate which consequently leads to extinguishing the rocket motor. In contrast, in-flight thrust reduction can be theoretically attained either by reducing chamber pressure to a new equilibrium level or by reducing the divergent section length. The objective of the present paper is to prove the concept of using Linear Shaped Charge (LSC) for thrust modulation; a technique novel to SPRM applications. Thrust termination concept is proved via a set of static firing tests on a standard test motor. In addition, a mathematical model is developed to predict the drop in thrust due to cutting the nozzle at any arbitrary location. The model is validated by comparing with published experiments for thrust termination and reduction. A parametric study is conducted based on model results. It is confirmed that by cutting the nozzle along its divergent section, thrust reduction less than 20% can be attained. Further reduction can be achieved by cutting the nozzle along its convergent section.

Analysis of the convergent section of a C-D nozzle and its influence on airflow performance using evolutionary strategies

The shape of a nozzle wall influences the phenomena associated with the behaviour of the fluid movement within the flow field mathematically described by the Navier—Stokes equations. This article studies different drawing techniques for the aerodynamic tracing of the wall contour searched by Vitoshinsky, Bell, Metha and Sivells. To the system of equations of the design models are added the math formulas that define Sauer’s method for redesigning the length of the converging section modifying simultaneously the contour sketches. The aim is to obtain a better distribution of the physical properties and to avoid excessive pressure in a limited space that could affect the internal structure of the wall. Numerical methods are used to visualize the features of the wave propagation, boundary layer separation and flow separation pattern to survey the appearance of the stream generated within the geometric profile of the wall and the ejected flow. A computational analysis is developed to make a comprehensive assessment of different chosen wall contours, including an optimized wall shape using genetic algorithms through a process to find maximum and minimum values of the cross-sectional area to change the wall layout. The selection carries out based on design parameters with variable area contraction ratio (from low to high) in the convergent section for being simulated in a boundary condition with a low-pressure ratio (NPR). Experimental data from Hunter's research are used for validation of the results for a J2-type aerospace nozzle operating at an NPR of 3.413.

Numerical investigation of wide continuous particle size distribution on the supersonic powder loading oxygen jet

Supersonic oxygen-powder jet injection has spanned wide range of operations in chemical engineering. However, the ubiquitous polydispersity of solid powder known to exert different flow behavior than the monodisperse counterpart has not been revealed. In this work, numerical simulation of the supersonic oxygen-powder jet injection via the Laval nozzle is performed under the Eulerian-Lagrangian framework to explore the impact of wide continuous size distribution of solid phase on the gas-solid hydrodynamics. Specifically, the gas phase is solved using the Eulerian method, while the particle motion is tracked under the Lagrangian framework. The numerical model is well validated with the experimental measurements. The results reveal that the blending of particles restricts the gas phase expansion, leading to the obvious reduction of gas velocity and increase of gas temperature. Additionally, a narrow particle size distribution (PSD) width corresponds to a higher proportion of large particles, inducing stronger vortices and hindering gas phase expansion. With regard to solid phase, the penetration ability of particles is significantly enhanced within the supersonic gas flow by accelerating the particle velocity to about 300 m/s. Furthermore, particles with wider PSD exhibit increased sensitivity to interphase interaction, particle-particle collisions and lift forces, resulting in higher velocities, lower temperatures along the axial direction and greater dispersion along the radial direction. Lastly, the interphase heat transfer mainly occurs in the convergent section, divergent section, and one nozzle length downstream from the nozzle exit. The findings obtained in this study offer valuable insights for industrial applications.

Numerical investigation on the bubble rising dynamics in ratchet channels filled with viscoelastic liquids

In this paper, we investigated the dynamics of a bubble rising inside ratchet channels filled with viscoelastic liquids by means of volume-of-fluid-based direct numerical simulations. The exponential Phan–Thien–Tanner constitutive model was used to describe the rheological behaviors of the nonlinear viscoelastic fluid. The effects of fluid elasticity [characterized by the relaxation time (λ)] and ratchet angle (θ) are mainly discussed in respect of bubble dynamics (e.g., rising velocity, flow field, and stress field, etc.). Our results found that the bubble rise velocity increases with fluid elasticity, and the average bubble velocity can be reduced up to 20% at low elasticity in ratchet channels. In addition, the periodic arrangement of the ratchet influences the distribution of the stress field, the vorticity component, and also the deformation of the entangled polymers in the flow. It was observed that the distributions of the stress field and the trace of the conformation tensor change significantly in a dense ratchet channel compared to a sparse one. Interestingly, the bubble velocity gradually increases after the bubble emerges from the convergent section, whereas it decreases on approaching the convergent section. The dynamical bubbles can be manipulated by the surrounding fluid viscoelasticity and ratchet channels, which will be useful in oil extraction and chemical process involving complex non-Newtonian fluids.

Laboratory-Scale Low-Speed Water Tunnel: Comparison of Experimental Flow Visualization and Computer-Aided Simulation

This study aimed at developing the laboratory-scale low-speed water tunnel design by first evaluating the effect of varying the number of wide-angle diffuser vanes and then confirming flow visualization against object geometries tested by experiments and computer-aided simulation. The low-speed water tunnel design in this study consists of a wide-angle diffuser, a honeycomb, a convergent section, and a working section. To ascertain the laminar flow of water would act in the experiment, a prior simulation using 3, 6, and 12 vanes and without a vane was conducted. Some geometries, including tube, triangle, aerofoil, and car models have been tested and then compared to the experimental results. The results indicate that the twelve vanes diffuser is more effective in minimizing turbulent flow and producing a streamlined pattern in the water tunnel. Laminar flow with a Reynolds number of 2238 and flow velocity of 0.008 m/s was obtained in the working section. The flow visualization by experiment and computational fluid dynamics simulation was almost similar.

Numerical Investigation of the Cavitation Characteristics in Venturi Tubes: The Role of Converging and Diverging Sections

Cavitation is a typical physical process that has shown to be highly valuable in the wastewater treatment field. This study aims to investigate the effects of the converging and diverging sections of a Venturi tube on the cavitation flow field. Multiphase flows in tubes are presented using the mixture model and the standard k-ε model. And the Schnerr and Sauer cavitation model is employed to simulate the vapor–liquid phase transition process. Both grid independence and the numerical method’s feasibility were validated before the research. The results showed that the influence of the divergence section length on Venturi cavitation characteristics depends on the provided pressure conditions. As the pressure increases, shorter divergence sections result in more significant cavitation effects. The length of the convergence section displays various cavitation behaviors under different pressure situations. A small contraction section length can achieve better cavitation effects in high-pressure applications, whereas the opposite is true in low-pressure cases. Within the scope of this study, it was observed that the Venturi tube with a divergent section of 14 Lt and a convergent one of 2.4 Lt provided enhanced cavitation performance when subjected to inlet pressures ranging from 0.8 to 1.2 MPa. Our findings indicate that the selection of converging and diverging section lengths in Venturi tubes should consider the corresponding operational pressure conditions, which provides valuable guidance and engineering significance in the research and development of Venturi cavitation devices in hydraulic engineering.

Large-eddy simulations of flow and aeroacoustics of twin square jets including turbulence tripping

In this study, we investigate the flow and aeroacoustics of twin square (i.e., aspect ratio of 1.0) jets by implicit large-eddy simulations (LESs) under a nozzle pressure ratio of 3.0 and a temperature ratio of 1.0 conditions. A second-order central scheme coupled with a modified Jameson's artificial dissipation is used to resolve acoustics as well as to capture discontinuous solutions, e.g., shock waves. The flow boundary layer inside of the nozzle is tripped, using a small step in the convergent section of the nozzle. The time-averaged axial velocity and turbulent kinetic energy of LES with boundary layer tripping approaches better to particle image velocimetry experimental data than the LES without turbulence tripping case. A two-point space–time cross-correlation analysis suggests that the twin jets are screeching and are coupled to each other in a symmetrical flapping mode. Intense pressure fluctuations and standing waves are observed between the jets. Spectral proper orthogonal decomposition (SPOD) confirms the determined mode and the relevant wave propagation. The upstream propagating mode associated with the shock-cell structures is confined inside jets. Far-field noise obtained by solving Ffowcs Williams and Hawkings equation is in good agreement with the measured acoustic data. The symmetrical flapping mode of twin jets yields different levels of the screech tone depending on observation planes. The tonalities—the fundamental tone, second and third harmonics—appear clearly in the far-field, showing different contributions at angles corresponding to the directivities revealed by SPOD.