Supersonic Nozzle Flow Research Articles

Comparative Study on the Application Efficacy of Small Disturbance Equation versus One-Dimensional Euler Equation in Nozzle Flow Analysis

This paper presents a numerical simulation study of subsonic and supersonic nozzle flow regimes utilizing the Small Disturbance Equation (SDE), implemented through Python to analyze flow stability under various boundary conditions. The SDE, extensively applied in aerospace, meteorology, and fluid mechanics, offers a critical framework for examining aircraft stability and maneuverability, essential for ensuring flight safety. Additionally, its application extends to spacecraft stability and control in aerospace science. The findings from this study reveal that subsonic flows, characterized by their stability and smoothness, respond more predictably under varying boundary conditions compared to their supersonic counterparts. Conversely, supersonic flows demonstrate increased sensitivity to changes in boundary conditions, resulting in more complex flow patterns. This sensitivity underscores the need for precise control mechanisms in supersonic applications to maintain flow stability and ensure the safety and efficiency of aerospace operations. The simulations underscore the practical importance of the SDE in advancing the understanding of dynamic flow problems across different scientific and engineering disciplines.

A general drag coefficient model for a spherical particle incorporating rarefaction and particle-to-gas temperature ratio effects

A concept and model of two critical Reynolds numbers Rep,cr1 and Rep,cr2 corresponding respectively to onsets of drag crisis and recovery are proposed. A drag model at limits of zero particle Mach and Knudsen numbers is constructed. On this basis, we develop a general drag coefficient model applicable for a spherical particle traveling in a gas by using a large number of available data derived from the previous experiments, direct numerical simulations and direct simulation Monte-Carlo methods. The scope of applicability of the proposed drag model covers all flow regimes relative to the particle characterized by particle Reynolds and Mach (or Knudsen) numbers and different particle-to-gas temperature ratios. Its comparison with two latest general drag models shows the significantly smaller relative error. Furthermore, quasi-one dimensional simulations against two supersonic nozzle gas-particle flow experiments are conducted with an in-house code to validate its accuracy in comparison with the two drag models.

Вплив детонаційної хвилі на перерозширений надзвуковий потік газу в со-плі

This paper proposes to use the detonation process to solve the problem of controlling highly maneuverable flying vehicles. The goal of the work is to study a new way of the thrust vector control of a rocket engine using the effect of a detonation shock wave on the gas flow in the nozzle. It is known that the method of thrust vector control by gas injection into the supersonic nozzle area of a rocket engine features one of the lowest losses of specific momentum and a high response speed and produces a significant lateral force. However, for the current level of rocket technology, there is a need to improve these characteristics. Detonation is considered as a method to intensify processes that affect the main gas flow and produce a lateral force. Its features make it possible to develop a system for pulse trajectory correction. In order to study the features of such a system, experimental studies of the detonation wave effect on a supersonic nozzle flow were conducted. A nozzle model and a gas generator for initiating a detonation wave interacting with the main supersonic air flow were developed and made. In the course of experiments, the effect of separation of the main flow from the nozzle wall by the detonation wave during the nozzle operation in the overexpansion mode was revealed. The duration of this effect was much longer than that of the detonation product effect on the main air flow in the nozzle, thus allowing it to be used in the development of a new thrust vector control method. To better understand the experimental results, a numerical simulation of the detonation wave propagation in a supersonic flow was carried out for the test conditions. The simulation was carried out in a non-stationary 2D formulation using the Solid Works software package. The goal of the simulation was to estimate the flow structure and the value of the relative lateral force produced by the change of this structure during detonation product injection into the supersonic nozzle area. The time evolution of the pressure field was obtained. The relative lateral force produced by detonation product injection into the supersonic air flow in the nozzle was determined. The presented features and method of jet engine thrust vector control may be used in unmanned systems operating in a wide range of speeds.

Numerical Study of the Effect of Primary Nozzle Geometry on Supersonic Gas-Solid Jet of Bypass Injected Dry Powder Fire Extinguishing Device

A two-way coupled model between polydisperse particle phases with compressible gases and a density-based coupling implicit solution method, combining the third-order MUSCL with QUICK spatial discretization scheme and the second-order temporal discretization scheme, are constructed based on the discrete-phase model (DPM) and the stochastic wander model (DRWM) in the Eulerian–Lagrangian framework in conjunction with a unitary particulate source (PSIC) approach and the SST k-ω turbulence model. The accuracy of the numerical prediction method is verified using previous supersonic nozzle gas-solid two-phase flow experiments. Numerical simulation of a two-phase jet of dry powder extinguishing agent gas with pilot-type supersonic nozzle was performed to analyze the influence of geometrical parameters, such as the length ratio rL and the area ratio rA of the main nozzle on the two-phase flow field, as well as on the jet performance indexes, such as the particle mean velocity vp,a, velocity inhomogeneity Φvp, particle dispersion Ψp, particle mean acceleration ap,a, etc. By analyzing the parameters, we indicate the requirements for the combination of jet performance metrics for different flame types such as penetrating, spreading, and dispersing.

Wind tunnel's supersonic CD nozzle design and flow analysis

Wind tunnel's supersonic CD nozzle design and flow analysis

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.

Керування вектором тяги шляхом вдува продуктів детонації в надзвукову частину сопла

To solve the problem of satellite control and stabilization in emergencies, it is proposed to use a detonation rocket engine, which enables active maneuvering to avoid a collision with space debris. The goal of this work is to study a new way of rocket engine thrust vector control by acting with a detonation shock wave on the gas flow in the nozzle. A detonation wave in a supersonic flow in a nozzle was numerically simulated. The simulation was conducted in a non-stationary plane formulation at different angles of inclination of the detonation gas generator that initiates a detonation shock wave to the combustion chamber axis with the use of SolidWorks application software for the 11D25 engine of the Cyclone-3 third stage. The simulation results were used to pre-optimize the location of the detonation gas generator on the nozzle wall. It was found that the effect of the detonation wave on the main gas flow in the nozzle is caused by two force factors: the first is due to the reactive force produced by the detonation product injection into the nozzle and a high-pressure zone on the wall where the detonation gas generator is mounted, and the second is due to a change in pressure distribution over the nozzle surface. In order to increase the effect of the shock wave, the detonation products must be injected parallel to the main gas flow in the nozzle or at some angle. The simulation showed the drawbacks and advantages of detonation product injection at different angles. The detonation wave effect on a supersonic nozzle flow was studied experimentally. A system was developed to record the shock detonation wave propagation using a heat meter. A special nozzle model and a gas generator were developed to initiate a detonation wave interacting with a supersonic air flow. It was found out how the detonation wave separates the main flow from the nozzle walls in the overexpanded mode. The results may be used in the space-rocket industry to provide upper stage maneuvering to avoid a collision with space debris.

NIMOC: A design and analysis tool for supersonic nozzles under non-ideal compressible flow conditions

A computational tool for non-ideal supersonic nozzle flows is developed to perform direct design of nozzle geometries and flow analysis of shock-free off-design conditions. So-called non-ideal flows are characterized by the departure of the fluid thermodynamics from the ideal-gas law, which is the case of supersonic expansions close to the critical point, either in the superheated vapour or in the supercritical region. Deviations from the ideal-gas model of remarkable significance are observed in connection with, but not limited to, fluids made of complex molecules. NIMOC (Non-Ideal Method Of Characteristics) implements a formulation of the Method Of Characteristics (MOC) valid for non-ideal flows: the classical formulation of the MOC is complemented with state-of-the-art nonlinear multiparameter Equations of State (EoS) implemented in external thermodynamic libraries. NIMOC implements a two-dimensional and axisymmetric formulation of the MOC, which is applied to the solution of the isentropic expansion through nozzles of different geometrical configurations: straight-axis symmetric and axisymmetric conventional wind-tunnel nozzles, straight-axis symmetric and axisymmetric minimum-length nozzles, and asymmetric nozzles with curved meanline. Results are presented, which demonstrate nozzle design and flow analysis in the presence of paradigmatic non-ideal flow phenomena. Verification of MOC computations is performed by means of inviscid Computational Fluid Dynamics (CFD) simulations and experimental data. Results are presented for selected geometrical configurations.

Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows

Viscous effects on an ideal gas flow in a supersonic convergent–divergent nozzle are a well-studied subject in classical gas dynamics. However, the ideal assumption fails on fluids that exhibit complex behaviours such as near-critical-region and non-ideal dense vapours. Under those conditions, a realistic equation of state (EOS) plays a vital role for a precise and realistic computation. This work examines the problem for solving the quasi-one-dimensional viscous compressible flow using a realistic EOS. The governing equations are discretised and solved using the fourth-order Runge–Kutta method coupled with a state-of-the-art EOS to calculate the thermodynamic properties. The role of the Grüneisen parameter along with viscous and real gas effects and their influence on the sonic point formation are discussed. The study shows that the flow may not achieve the supersonic regime for any pressure ratio depending on the combination of that parameter and the normalised friction factor. In addition, the analysis yields the discharge coefficient and the isentropic nozzle efficiency, which may achieve maximum values as a function of the stagnation conditions. Finally, the study also evaluates the formation and intensity of normal shock waves by using the Rankine–Hugoniot relations, which now depend on the real gas and viscous effects in opposition to the inviscid solution. Moreover, the methodology used captures the sonic point and shock wave position by a space marching algorithm using the Brent method for scalar minimisation. Experimental data available in the open literature corroborate the approach.

Prediction and visualization of supersonic nozzle flows using OpenFOAM

Prediction and visualization of supersonic nozzle flows using OpenFOAM

Evaluation of Injection Strategies in Supersonic Nozzle Flow

The ability to manipulate shock patterns in a supersonic nozzle flow with fluidic injection is investigated numerically using Large Eddy Simulations. Various injector configurations in the proximity of the nozzle throat are screened for numerous injection pressures. We demonstrate that fluidic injection can split the original, single shock pattern into two weaker shock patterns. For intermediate injection pressures, a permanent shock structure in the exhaust can be avoided. The nozzle flow can be manipulated beneficially to increase thrust or match the static pressure at the discharge. The shock pattern evolution of injected stream is described over various pressure ratios. We find that the penetration depth into the supersonic crossflow is deeper with subsonic injection. The tight arrangement of the injectors can provoke additional counter-rotating vortex pairs in between the injection.

Two semi-analytical approaches for solving condensation shocks in supersonic nozzle flows

The paper describes two methods for solving condensation shocks in steady-state quasi-one- dimensional flows. A single-fluid-model has been implemented by solving the algebraic form of compressible flow conservation equations, in conjunction with nucleation and droplet growth laws from gas-kinetic theory. The second method assumes the condensation shock problem as a flow discontinuity, the downstream state of the shock being defined as a weak-detonation, and determined from intersections on the Rayleigh and Hugoniot curves. Both approximations have been implemented with complex multi-parameter equations-of-state based on the Helmholtz free energy, taking into account the non-ideal gas flow behavior of steam and carbon dioxide. In order to reproduce operating conditions of engineering applications, where non-equilibrium condensation occurs such as steam turbines, injectors, supercritical carbon dioxide compressors and supersonic gas flow separators. Both gas-kinetic and flow discontinuity approaches have been tested for several nozzle geometries and results have been compared with low- and high-pressure experimental data of steam and carbon dioxide. The results show that both models are able to model properly the pressure recovery that occurs in supersonic condensing flows. It has been found a low deviation 4% from experimental data of steam, and deviations within 8 % were found for the carbon dioxide case. The average droplet radius size distribution obtained from the droplet growth model is in the same order of magnitude of that of reported by experimental data available in open literature. Finally both methods were implemented in a converging-diverging nozzle of a carbon dioxide ejector in order to explore the effects of the stagnation temperature and to determine conditions free of condensation.

Three-Dimensional Structure of Non-Equilibrium Homogeneous Condensation Flow in a Supersonic Rectangular Nozzle

Numerical simulations have been carried out for a supersonic three-dimensional rectangular arc nozzle, where a secondary flow toward the center of the curvature occurs due to the shape of the nozzle. It is known that secondary flow causes longitudinal vortices to form near the wall of the nozzle corner, making the nozzle outlet flow unstable and induces loss of transport energy. When the working fluid is a condensable gas with relatively large latent heat such as moist air or steam, rapid accelerated expansion in the nozzle causes non-equilibrium condensation due to supersaturation. After the release of latent heat during phase transition, nozzle flow continues expanding at an equilibrium saturation condition. In the absence of foreign particles, e.g. ions or dust particles, condensation nuclei are formed in the gas itself causing non-equilibrium homogeneous condensation. Supersonic nozzle flow properties vary considerably due to the occurrence of condensation phenomenon. The objective of this study is to investigate the effect of non-equilibrium homogeneous condensation on the longitudinal vortices which form in the range close to the corner of rectangular arc nozzle numerically.

Experiments on water vapour condensation within supersonic nozzle flow generated by an impulse tunnel

An impulse facility for analysis of water vapour nozzle flows using both shock tunnel and Ludwieg tube operating modes has been developed and tested at the University of Southern Queensland. Unique high-speed flow visualisation of the water vapour condensation shock has been acquired in the throat region of a nominally two-dimensional convergent-divergent nozzle with a 120 mm2 throat area. This paper presents the facility performance and the time-resolved visualisation results for the nozzle flow, and the results are analysed with the aid of image post-processing tools and quasi-one-dimensional (Q1D) thermodynamic calculations. The experiments have produced qualitative and quantitative data on the flow conditions at four different relative humidity values from 25% to 100%, and over a range of nozzle supply temperatures between 293 K and 343 K. The direct measurement of the pressures and wave speeds within the tunnel resulted in a good agreement with the ideal gas Q1D calculations, particularly for the first incident shocks and expansion waves. Differences progressively increased with the number of reflections, due to the effect of viscous dissipation and the non-ideal end-wall interaction caused by the presence of the nozzle inlet. Moreover, flow visualizations of the location and orientation of both the weak disturbance waves and the condensation shock enabled the investigation of the supersonic water vapour condensation within the nozzle of this impulse facility. Based on these measurements, the nozzle flow downstream of the condensation shock was demonstrated to have a lower Mach number relative to the dry nitrogen flow case. This phenomenon is due to the phase change heat release, which appeared to be more significant when the condensation shock intensity was higher. Although further development of the apparatus is possible, the impulse test-rig configuration that we have developed permits a relatively high flow rate of test gas for a short period of time, leading to significantly reduced operating expenses relative to a continuous flow facility with the same mass flow rate. It is therefore suggested that future studies further improve and test the impulse facility techniques for studying condensation phenomena as a potential alternative to high-power, continuous flow facilities.

Study of Deformation and Breakup of Submillimeter Droplets’ Spray in a Supersonic Nozzle Flow

The problem of secondary atomization of droplets is crucial for many applications. In high-speed flows, fine atomization usually takes place, and the breakup of small droplets determines the final products of atomization. An experimental study of deformation and breakup of 15–60 µm size droplets in an accelerated flow inside a converging–diverging nozzle is considered in the paper. Particle image velocimetry and shadow photography were employed in the experiments. Results of gas and liquid phase flow measurements and visualization are presented and analyzed, including gas and droplets’ velocity, shape and size distributions of droplets. Weber numbers for droplets’ breakup are reported. For those small droplets at low Weber numbers, the presence of well-known droplets’ breakup morphology is confirmed, and rare “pulling” breakup mode is detected and qualitatively described. For the “pulling” breakup mode, a consideration, explaining its development in smaller droplets through shear stress effect, is provided.

Numerical simulation of an over-expanded supersonic and subsonic industrial nozzle flow relevant to flaring system

Flaring in oil and gas production is the controlled burning of unwanted exhaust gases to enhance safety. To improve flare combustion, gas flares are equipped with air nozzles that introduce extra oxygen and improve mixing in the combustion zone. These nozzles are operated in the subsonic, sonic, or supersonic regimes. In this paper, we are concerned with turbulence modeling of the jet flow exiting from a particular convergent–divergent nozzle used in flare systems. That nozzle has convergent and divergent sections that are connected via a throat section with a finite length and constant diameter. The Realizable k – ε and SST k – ω models are used to study the compressible flow within the nozzle. The velocity profiles, turbulent kinetic energy, Mach number profiles, and entrainment rate coefficients predicted by both turbulence models are compared for nozzle pressure ratios in the range 1.18 ≤ NPR ≤ 1.78. It is shown that both turbulence models predict nearly identical flow evolution along the nozzle. When the flow becomes supersonic, the shock surface, and consequently nozzle outlet velocity profiles, predicted by the SST k – ω model deviates slightly from the other model. The differences, however, become negligible a couple of diameters downstream of the nozzle outlet.

Supersonic jet and nozzle flows in uniform-flow and free-vortex aerodynamic windows of gas lasers

The mathematical models and computational tools for design, analysis and predictions of supersonic jet and nozzle flows in the aerodynamic windows of high-power gas lasers are considered. The steady-state Euler equations describing strong shock waves, contact discontinuities, rarefaction waves and their interactions are solved with the finite-volume solver and space-marching method. The results of numerical simulation of steady-state supersonic flows of inviscid compressible gas in nozzles and under- and over-expanded jets are obtained and analyzed for different pressure ratios in the laser cavity and ambient atmosphere. The flowfields corresponding to the uniform velocity profile and free-vortex velocity profile in the outlet nozzle boundary are compared. Nozzle profiling tools are developed on the basis of numerical solution of a sequence of direct problems. The aerodynamic performance of the window is evaluated in terms of the simulated laser cavity pressure and plenum pressure of the free-vortex supply nozzle. The pressure support characteristic for the aerodynamic window is established by determining the ambient to cavity pressure ratio over a range of aerodynamic window supply pressures.

Invariants of velocity gradient tensor in supersonic turbulent pipe, nozzle, and diffuser flows

Velocity gradient tensor (VGT) analysis of high-order accurate direct numerical simulation data of supersonic pipe, nozzle, and diffuser flows at computationally moderate Reynolds numbers is performed. Joint probability density functions of second and third invariants of the VGT conditioned on positive and negative dilatation levels are presented in the near-wall viscous layer, buffer layer, log layer, and core region of these flows. For flow regions with positive dilatation, there is a preference for unstable flow topologies, while regions with negative dilatation show a preference for stable flow topologies.

Comparative CFD analysis of a 2D supersonic nozzle flow with jet tab and jet vane

Comparative CFD analysis of a 2D supersonic nozzle flow with jet tab and jet vane

Experimental observation of non-ideal expanding flows of Siloxane MDM vapor for ORC applications

Extensive experimental results characterizing the supersonic expansion of an organic vapor in non-ideal conditions are reported in this paper for the first time. The collected data also allowed the assessment of the accuracy of Computational Fluid Dynamic (CFD) tools employed to predict the non-ideal behavior of such flows, including the consistency of thermodynamic models adopted.The investigation has been carried out on the converging-diverging nozzle test section of the Test Rig for Organic VApors (TROVA), at the Laboratory of Compressible fluid-dynamics for Renewable Energy Application (CREA) of Politecnico di Milano. Supersonic nozzle flow was chosen as the simplest one of significance for organic Rankine cycle (ORC) turbine channels.The working fluid under scrutiny is Siloxane MDM, a widely employed compound for high temperature ORCs. MDM vapor expands through the TROVA nozzle at moderate non-ideal conditions in the close proximity of the vapor saturation curve. This is the region where ORC expanders typically operate, thus proving the relevance of the investigation for the ORC community. Indeed, detailed experimental data representative of typical ORC expansions were lacking in the open literature up to date.Two different nozzle geometries, featuring exit Mach number of 2.0 and 1.5 respectively, were tested, exploring a wide range of thermodynamic inlet conditions and diverse levels of non-ideality, from moderate non-ideal state, indicated by a compressibility factor Z = Pv/RT ≃ 0.80, to dilute gas conditions, Z ≥ 0.97. Maximum operating total pressure and temperature are Pt ≃ 5 bar and TT ≃ 250 °C. The nozzle flow is characterized in terms of total pressure, total temperature, static pressure at discrete locations along the nozzle axis, and schlieren imaging. In contrast to the well known case of polytropic ideal gas, the vapor expansion through the nozzle is found to be dependent on the inlet conditions, thus proving the non-ideal character of the flow. This influence is found to be consistent with the one predicted by the quasi-1D theory coupled with simple non-ideal gas models.Experimental data at the nozzle centerline are compared with those resulting from a two-dimensional viscous CFD calculation carried out using the SU2 software suite and the improved Peng Robinson Stryjek Vera (iPRSV) thermodynamic model. A very good accordance is found, demonstrating the high accuracy of the applied tools.