Nozzle Pressure Ratio Research Articles

Experimental Characterization of Supersonic Diamond Jet Acoustics

Acoustic emissions from supersonic jets are of interest due to their deleterious effects on nearby personnel and structures. As development of both military and commercial supersonic aircraft continues to grow, it is essential to combat increasing noise pollution. Axisymmetric jets are highly prevalent where their aeroacoustic characteristics have been well-documented; in contrast, relatively few studies have examined non-axisymmetric jets. In the present study, aeroacoustics of supersonic jets produced by a diamond-shaped Mach 2 nozzle are explored across a large operational envelope under different pressure ratios ranging from highly overexpanded to moderately underexpanded. Measurements of the far-field acoustics in an anechoic environment were used to characterize the acoustic flowfield and contrast the distribution of energy in the spectral domain between the characteristic major and minor axes of the nozzle. Overall, the diamond jet exhibits a highly directional acoustic field with a distinct local minimum for sideline noise. Furthermore, screech behavior was only observed in a narrow, overexpanded flow regime; this is in contrast to the documented behavior of axisymmetric and rectangular jets. Over the conditions examined there is no indication of distinct staging. Additionally, there exists a nozzle pressure ratio threshold beyond which peak noise switches axes.

Evaluation of generalized k-ω turbulence model in strong separated flow estimation of thrust optimized parabolic nozzle

One of the frequently reported defects of RANS-based turbulence models is overestimation of turbulent kinetic energy production in high speed separated flow problems, which causes significant prediction errors. The correct estimation of such flow in thrust optimized parabolic nozzles extremely depends upon the accurate prediction of the onset of flow separation. In this paper, firstly, the significant error of conventional RANS-based turbulence models is shown to predict the onset of flow separation in this type of nozzles. Then, the prediction accuracy is improved through the modification of the essential parameters of the generalized k-ω (GEKO) turbulence model. It was found that modifying the separation and mixing parameters of the GEKO model to realize the turbulent kinetic energy production resulted in the accurate prediction of onset of flow separation at the extensive range of nozzle pressure ratios. Using this modified model with new coefficients reduced the error of about 30% of the k-ω-sst model in estimating the onset of flow separation. Also, the nozzle pressure value at which the transition from free shock separation (FSS) to restricted shock separation (RSS) occurs is well predicted by this approach. After strengthening the turbulence model, the flow physics has been investigated with increasing and decreasing nozzle chamber pressure. The length of the separation shock and reflected shock waves which impose the presence of FSS or RSS patterns and transitional phenomena are discussed. Our new findings show that unlike the transition from FSS to RSS, the inverse transition from RSS to FSS did not depend on the length of the separation and reflective shocks.

Parametrical Investigation of Transverse Injection in a Dual-Bell Nozzle During Altitude-Varying Conditions

The dual-bell nozzle (DBN) is a rocket nozzle concept that could provide a substantial payload gain. The present paper focuses on the impact of radial secondary injection on DBN behavior during its ascent and descent in the atmosphere. The influence of the secondary injection settling chamber (cavity) volume is discussed. The positive influence of the cavity volume on the DBN behavior during transition phases has been exposed, and its effects during retransition were shown to be negligible. The use of secondary injection allowed the transition nozzle pressure ratio to be increased by nearly 24%, and the lateral forces were reduced to less than 1% of the nozzle thrust. A first approach regarding secondary injection optimization is finally proposed.

Numerical investigation on expansion–deflection nozzle flow during an ascending–descending trajectory

The flow characteristics of an annular expansion–deflection (ED) nozzle are investigated numerically during an ascending–descending trajectory over a large nozzle pressure ratio span. The shock pattern evolution, nozzle operation mode transition, nozzle flow hysteresis, and thrust variation during this trajectory are examined, and the interactions between them are discussed. A new criterion for distinguishing the open and closed wake modes of the ED nozzle is proposed based on a perturbation front in combination with sonic lines. Using this criterion, an exact boundary between the open and closed wake modes can be readily drawn. The present study shows that the interaction between the shock pattern transition and nozzle operation mode transition is indirect. During the ascent, the open-to-closed wake mode transition lays the foundation of the downstream shock pattern variation. During the descent, however, the stretching of the dominating Mach stem delays the nozzle closed-to-open wake mode transition. The different flow mechanisms during the ascent and descent result in an overall hysteresis of nozzle operation mode transition. The nozzle thrust undergoes dropping-rising developments (the thrust troughs) in the ascent and descent. These thrust troughs are also found to be the results of two very different flow mechanisms, namely, the forward–backward movement of shock separation point on nozzle shroud and the pressure rise on pintle base after closed-to-open mode transition.

CFD Analysis of Over-Expanded Flow in Convergent Divergent Nozzles

The classical one-dimensional inviscid theory does not reveal the complex flow features in an over-expanded nozzle accurately. The code Fluent has been used to simulate the viscous fluid (air) flow passing through three different 2-D Convergent-Divergent (C-D) nozzles for nozzle pressure ratios (NPR) corresponding to over-expanded flow. The steady state RANS equation with five different turbulence models has been simulated for turbulence model study. Two different types of boundary layer grids: grid1 (y<sup>+</sup>=1) and grid 2 (y<sup>+</sup=50) have been simulated. Shear Stress Transport k-w (SSTKW) turbulence model with grid 1 has been chosen for turbulence modeling. Both inviscid and viscous flows have been simulated. The converged solutions captured asymmetric lambda shock in all the three nozzles at higher NPRs for viscous flows. It also predicted aftershock and flow separation depending upon NPR. The shock wave angle of the incident and reflected shock generally reduces with increase in NPR for NPR£1.92. The thrust co-efficient of all the theoretical, predicted inviscid and predicted viscous solutions reduce with increase in NPR upto a certain value of NPR and then starts increasing. The predicted viscous results (shock structure, shock location, size of normal shock, aftershock and asymmetric lambda shocks) are close to the experiments in most of the cases. The aftershock phenomenon provides dual mode flow at the exit of the nozzle.

Effect of Relative Jet Temperature in Supersonic Dual-Impinging Jets

Short takeoff and vertical landing aircraft configurations involve multiple jets that impinge onto the deck surface in tandem and lead to several adverse effects. This study reports on the experimental characterization of supersonic dual-impinging jets by systematically varying their relative jet temperature. A sonic converging and Mach 1.5 converging–diverging (CD) nozzles are employed. The expansion ratio of the converging nozzle is maintained at 0.96, 1.19, and 1.59, and the CD nozzle is operated at a fixed nozzle pressure ratio of 3. The temperature ratio of the jet from the CD nozzle is varied from 1.0, 1.3, and 1.7. For a fixed momentum of the jet pair, an increase in jet temperature intensified the nearfield noise and unsteadiness on the impingement surface. At short impingement heights, resonance in the heated jet was the primary source of unsteadiness. At a fixed impingement height, an increase in jet temperature led to a systematic increase in tonal frequency, while jet instability mode shapes were retained. Furthermore, the mean flowfield of sonic jet and fountain regions remain unaffected, and an increase in supersonic jet velocity is observed. This is also accompanied by an increase in unsteadiness in the fountain upwash.

A Numerical Simulation of the Underwater Supersonic Gas Jet Evolution and Its Induced Noise

To explore the complex flow field and noise characteristics of underwater high-speed gas jets, the mixture multiphase model, large eddy simulation method, and Ffowcs Williams–Hawking (FW–H) acoustic model were used for simulations, and the numerical methods were validated by the gas jet noise experimental results. The results revealed that during the initial stages, the jet collided with the water surface and created low-pressure high-temperature gas bubbles, accompanied by much high-frequency noise. When the jet reached its maximum length, its impact weakened, the bubble broke, the jet transformed into a conical shape, and the jet noise changed from high- to low-frequency. The pressure fluctuation peaked near the position at which the Mach number reached 1, indicating that the jet was the most unstable at the sonic point. Additionally, at low frequencies, the sound pressure levels between jets with different nozzle pressure ratios were similar, whereas above 400 Hz, under-expanded jets had higher sound pressure levels. This paper provides theoretical guidance for the study of underwater jet noise.

Simulation Investigation on the Structure and Its Influence on the Impinging Pressure of the Carbon Dioxide Jet.

An improved understanding of the mechanisms of SC-CO2 jet drilling technology is important for the application of this new technology. The flow field structure and dynamic fluctuation of SC-CO2 jets are the key factors affecting the jet erosion performance. To improve the erosion performance of the SC-CO2 jet, it is necessary to study the relationship between the different flow fields of the jet. In this study, a numerical simulation model for SC-CO2 jet drilling technology is established. Based on the modified real-gas model, the pressure distribution and flow field characteristics of the SC-CO2 jet were obtained by the simulation investigation, and the reliability of the model was verified. The results show that the flow field structure of a supercritical CO2 jet has typical compressible flow field characteristics. As the jet is fully expanded, its pressure fluctuation is slight and less affected by the distance between the nozzle and the wall. When the jet is in the state of under-expansion, the flow field structure characteristics have a significant impact on the pressure distribution and peak pressure. At the same time, when the distance is large, when nozzle pressure ratio = 5, the pressure ratio has a more significant impact on the flow field and the pressure peak and distribution. The pressure distribution of different flow fields should be fully considered in the application.

Experimental investigation on supersonic film cooling of hypersonic optical dome under different nozzle pressure ratios

When an aircraft flies at hypersonic speeds in the atmosphere, its optical window is subjected to severe aerodynamic heating. To investigate the supersonic film cooling laws of hypersonic optical dome, three supersonic (Mach 2.35) film generation devices with different jet outlet heights (1 mm, 2 mm, 3 mm) were designed. The experiments were conducted in a hypersonic (Mach 7.1) gun wind tunnel. The NPR (nozzle pressure ratio = jet outlet static pressure/nearby mainstream static pressure) ranged from 0 to 2.3. The heat flux on the window surface was measured by the thin film resistance thermometer. Experimental results indicate that, under different jet outlet heights, the film cooling effectiveness increased gradually as the NPR increased, corresponding to an increase in effective cooling length. The existing similarity parameters for film cooling could effectively predict the effective cooling length of supersonic film when NPR = 1. However, the prediction effect deviated significantly when NPR ≠ 1. Moreover, the effective cooling length corresponding to the unit mass flow rate of the coolant first increased and then decreased with the increase of NPR, and there existed an optimal solution. Furthermore, with the same coolant mass flow rate, higher jet Mach number lead to better supersonic film cooling performance.

Altitude-compensating axisymmetric supersonic nozzle design and flow analysis

Altitude-adapted nozzles are designed to facilitate flow adaptation during rocket ascent in the atmosphere, without requiring mechanical activation. As a consequence, the performance of the nozzle is significantly improved. The aim of this study is to develop a new profile of axisymmetric supersonic nozzles adapted at altitude (Dual Bell Nozzle with Central Body), which is characterized by an E-D nozzle as a basic profile. The performances obtained for this nozzle (E-D Nozzle) are then compared to those of a Plug nozzle. The E-D nozzle shows significant performance advantages over the Plug nozzle, including a 13.02% increase in thrust, knowing that the length of the E-D nozzle is half that of the Plug nozzle under the same design conditions. Finally, viscous calculations using the k-ω SST turbulence model were conducted to compare the performance of the dual bell nozzle with central body (DBNCB) and the E-D nozzle with the same cross-sectional ratio, and to assess the impact of nozzle pressure ratio (NPR) variations on the operation mode of the DBNCB. The results obtained show that the DBNCB offers the best performance in most phases of flight.

Performance of double expansion ramp nozzle

Additional thrust gained by expanding the supersonic stream emerging from a convergent–divergent (C–D) nozzle through a symmetric double expansion ramp nozzle (DERN) connected to the nozzle is experimentally investigated. Thrust augmentation caused by the DERN of design Mach number 3.5 attached to a full and a half convergent–divergent (C–D) nozzle of design Mach number 1.5 is studied. The nozzle pressure ratios (NPRs) studied are 3, 4, 5, 5.45, and 6. The ramp angles of the symmetric double expansion ramp nozzle studied were 18° and 22°. It is found that an additional thrust of around 44% can be derived with the DERN in the presence of a favorable gradient of +36%, corresponding to NPR 5.

The influence of cryogenic temperature on the shock structure of impinging under-expanded flow over a convex surface

This study comprehensively investigates the effect of cryogenic nozzle inlet temperature on the flow structure and interactions of an under-expanded supersonic jet with a spherical solid surface. A combined experimental and numerical approach was employed to achieve this goal, utilizing high-speed Z-type schlieren visualization and Reynolds-averaged Navier–Stokes simulations with a Redlich–Kwong real gas equation of state. This study is significant as it addresses a relatively unexplored area of research on the flow structure of the cryogenic under-expanded supersonic jet. The study examines the shock pattern and interaction region through varying static inlet temperature (Tin = 178–290 K) and nozzle pressure ratio (NPR 5–14). Additionally, parameters including nozzle exit-to-throat area ratio (A/A* = 1.277), the distance between the sphere and the nozzle (1.5 cm), and the diameter of the sphere (d = 1.5 cm) were considered fixed. The results show that the supersonic jet exhibits a change in shock patterns in the first shock cell concerning the location and width of the Mach disk, accompanied by a shift in the location of the last shock crossing point and the shock plate. The simulation provides a more detailed insight into the flow, indicating a temperature drop to 105 K in the case of the cryogenic nozzle inlet. At such a low temperature, the compressibility factor exhibits a 5% reduction from unity, while in the case of the ambient nozzle inlet, the minimum temperature at the nozzle exit reached 170 K, leading to only a 1% drop in the compressibility factor, which is negligible. It triggers different flow structures concerning the nozzle inlet temperature. These findings can contribute to the complex flow structures of supersonic jets seen in different industrial and scientific fields.

Flow structure and parameter evaluation of conical convergent–divergent nozzle supersonic jet flows

Supersonic gas jets in conical convergent–divergent nozzles are studied numerically using the OpenFOAM rhoCentralFoam solver. The spatiotemporal evolution of the jet flow field is analyzed. The influence of the operating conditions on the flow field is studied parametrically, including the nozzle pressure ratio (NPR), area ratio, and throat position. The behaviors and mechanisms of the double-diamond structure, throat wave, and exit wave are interpreted in detail. The results show that a conical convergent–divergent nozzle always generates shock waves. The throat shock reaches its maximum length during the initial stage, then becomes slightly shorter before becoming stationary, dominated by the exit velocity. Furthermore, it is shown that the jet flow changes from overexpansion to underexpansion with increasing NPR. With an increasing area ratio, the trend is the opposite. The throat position affects the jet divergence angle at the nozzle exit, consequently causing a variation in the core radius of the jet. It is further shown that the double-diamond structure does not always appear. The throat shock angle, exit wave angle, and shear layer width directly affect the shape of the double-diamond structure. The favorable pressure gradient of the nozzle ultimately dominates the changes in the length of the throat wave and exit wave.

Super-resolution of time-resolved three-dimensional density fields of the B mode in an underexpanded screeching jet

The estimation of time-resolved three-dimensional (3D) density fields of an underexpanded jet at the nozzle pressure ratio of 2.42, a so-called “spatiotemporal super-resolution” was conducted using non-time-resolved three-dimensional background-oriented schlieren (3D-BOS) and time-resolved microphone measurements. This approach aims to reconstruct three-dimensional density fields associated with the intermittent and switching behavior of the B mode of a screeching jet from the microphone data by constructing a linear regression model. An azimuthal Fourier decomposition is applied to the 3D-BOS and microphone data, and the proper orthogonal decomposition (POD) is performed for each of their azimuthal Fourier modes. The m=1 azimuthal Fourier mode is dominant in both cases, and the leading two POD modes in the m=1 azimuthal mode of the microphone data are associated with the B mode. The linear regression model is constructed from the POD modes of the m=1 azimuthal 3D-BOS data and the first two microphone POD modes of the m=1 azimuthal mode of the microphone data. The three-dimensional density fields reconstructed from each POD mode of the m=1 azimuthal mode of the microphone data have helical structures with opposite rotation directions. The amplitudes of those POD modes change with time, and the azimuthal structure associated with the B mode is determined depending on those amplitudes. The present result showed that intermittency in the flapping to helical structures and their strength can be interpreted by the temporal changes in the strengths of two rotating helical structures with opposite rotation directions.

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.

Effect of free boundary on the performance of single expansion nozzle

Abstract Effect of free boundary on the flow field characteristics of a single expansion nozzle has been studied experimentally and computationally. The single expansion nozzles studied in this investigation are a convergent-divergent nozzle of rectangular cross-section with convergent-divergent wall on one side and a flat wall on the opposite side, and an identical convergent-divergent ramp with its top open to atmosphere. The studies have been carried out at nozzle pressure ratios 2, 3, 4 and 5. The results show that the single expansion nozzle with wall boundary is able to deliver the flow with Mach number around 1.5, at nozzle pressure ratios of 4 and 5 even with the single expansion. The nozzle with free boundary, the wall static pressure is appreciably lower than that of nozzle with closed boundary and the exit Mach number is 1.5 for NPR 4 and 1.75 for NPR 5. That is, at the exit, the single expansion nozzle with free boundary delivers higher Mach number compared to single expansion nozzle with wall boundary for NPR 5.

Corrugation geometry effect on jet mixing

An experimental investigation was carried out to assess the mixing promoting efficiency of rectangular, semicircular, and triangular corrugations at the edges of rectangular tabs. Mixing promoting capability of two rectangular tabs with aspect ratio of 1.0, 1.5, and 2.0, with rectangular, semicircular, and triangular corrugations over their edges, located diametrically opposite at the exit of a convergent–divergent Mach 1.73 nozzle was studied. Pressure measurements and optical flow visualization were carried out. The nozzle pressure ratios (NPRs) studied were 4, 5, 6, 7 and 8, in order to cover different levels of expansion at the nozzle exit. At NPR 4, Mach 1.73 nozzle is overexpanded, with about 23% adverse pressure gradient. At NPR 5, the adverse pressure gradient is just 3%. At NPR 6, 7, and 8, the jet is underexpanded with favorable pressure gradients of 16%, 36%, and 55%, respectively. The corrugated tabs were found to be efficient mixing promoters, leading to shorter core and weaker shocks in the core than the uncontrolled jet. The mixing effectiveness of the corrugated tab is found to increase with increase in NPR. The core length reduction associated with all the corrugations is found to increase with increase in tab aspect ratio. At the almost correctly expanded state, for aspect ratio 1, rectangular corrugation is found to be the most efficient mixing promoter, causing a core length reduction of almost 100%, followed by the triangular and semicircular corrugations, leading to a 77% and 73% reduction, respectively. For aspect ratios 1.5 and 2.0, triangular corrugation is found to be the most efficient mixing promoter, causing a core length reduction of almost 100%, followed by the rectangular and semicircular corrugations. The shadowgraph images of the controlled and uncontrolled jets demonstrate the effectiveness of the corrugated tabs in weakening the waves in the jet core.

A novel thrust vector nozzle with conical surface based on Coanda effect

In this paper, a novel thrust vector control method based on Coanda effect is proposed for conical surface. The effect of thrust vector control is studied by computation fluid dynamic (CFD) numerical simulation. When there is no side plate on both sides of Coanda surface, there are large vortex structures on both sides of nozzle wake, and the vector control cannot be realized. After adding the side plate, the comprehensive control of the pitch and yaw thrust vectors was realized. When the nozzle pressure ratio (NPR) is 2~2.4, the pitch and yaw vector angles decreased with the increase of NPR, and the maximum pitch vector angle is 8°. And the yaw vector angle is 8°.

Influence of orifice thickness on the flow field of co-flow jets

The present study analyses the numerical simulation results of subsonic flow through co-flow orifices. Analysis is done on the effects of modifying orifice thickness on the co-flow jet characteristics. The combined frontal area of the co-flow jet and central jet is maintained constant (20 mm2). The primary orifice diameter (D) is kept as 3mm and the orifice thickness, i.e the co-flow jet is formed as four segments of a concentric circle around the core jet, and the edge distance between them ranges from 0.16D to 0.5D. The 0.16D co-flow is shown to lengthen the potential core of the main jet at nozzle pressure ratios of 1.2, 1.4, 1.6, and 1.8, but the 0.33D co-flow and the 0.5D co-flow shorten the potential core length, enhancing mixing. The present study analyses the Mach numbers that correspond to the Nozzle Pressure ratios of 1.2, 1.4, 1.6, and 1.8, which are 0.517, 0.71, 0.84, and 0.96, respectively. The 0.5D annular gap is found to be more effective which boosts primary jet mixing.

Numerical investigation on thrust characteristics of an annular expansion–deflection nozzle

The thrust characteristics of a large-expansion-ratio annular expansion–deflection (ED) nozzle are investigated based on detailed flow pattern simulations. The purpose is to build a bridge between the nozzle internal flow pattern and nozzle thrust performance. The present work traces flow parameters along typical streamlines to demonstrate the nozzle flow pattern, partitions the nozzle exit plane based on its flow features to evaluate thrust contributions of each thrust coefficient contributor in different sub-areas, and monitors flow parameter distributions in the nozzle exit plane at 22 nozzle pressure ratios to interpret the developing histories of nozzle thrust coefficients. The present simulations show that the shocks generated in open wake mode are both inevitable and indispensable, while the shocks generated in closed wake mode contribute negatively to thrust performance. Three basic requests for designing a high-performance ED nozzle are clarified, which are to ensure high-quality expansion at the nozzle throat, to smooth out the reflected shock in open wake mode, and to diminish the strong near-wall shock generated in closed wake mode. An interesting and counter-intuitive phenomenon, namely, the existence of the reflected shock in open wake mode not only consumes the ability of the exhaust flow to do work but also improves the overall nozzle thrust performance, is explained. This is because the reflected shock deflects lateral-going exhaust flow to the axial direction. When this reflected shock disappears, a sudden drop in the nozzle thrust coefficient history takes place.