Supersonic Flow Research Articles

Investigation of viscous supersonic laminar flows around F-16 airfoil: experimental, numerical, and analytical approaches

Abstract This research paper primarily focuses on the behavior of viscous supersonic laminar flows around the F-16’s NACA 64A-204 airfoil, while also extending its scope to Shock-Wave/Boundary-Layer Interactions. The aim is to evaluate and compare methodologies for accurately characterizing these crucial aerodynamic phenomena. A unique experimental setup was developed, featuring mock-ups of F-16 airfoil equipped with pressure taps, and tested in the Supersonic Burst Wind Tunnel AF300. Computational Fluid Dynamics simulations were conducted using Ansys Fluent 2022 R2 and were supplemented by our previously established analytical model was adapted to our specific airfoil case, following calculations of the wing section equation. Key aerodynamic parameters such as lift coefficient, drag coefficient, Local Mach numbers, and the characteristics of the shock waves formed around the airfoil were examined. The study validates the NACA 64A-204 mock-up, with average errors for key parameters and 1st and 2nd Pressure Taps between the three adopted approaches remaining below 2.5%. The findings contribute valuable insights into the fundamental physics of viscous supersonic laminar flows, offering immediate applications to the design of high-speed aircraft and other advanced aerospace technologies. Additionally, the validated mock-up enhances the research capabilities of the Supersonic Burst Wind Tunnel AF300. Ultimately, this study serves as a foundational reference for optimizing aerodynamic surfaces, thereby facilitating advancements in key vehicle performance metrics such as manoeuvrability and fuel efficiency.

A hybrid computational approach for modeling cold spray deposition

Cold spray (CS) is a cold-state technology that uses high-velocity supersonic gas flow to propel and deposit powder particles onto a substrate surface. The design and optimization of the cold spray deposition process were recently achieved via the experimental trial-and-error approach, which is laborious and costly. The present study presents a computationally efficient hybrid method for simulating cold spray coating deposition, applied explicitly to Ni coating used for wear applications. The model effectively synergizes meshless and meshed computational schemes in predicting the thermo-mechanical deformation of the impacting Ni particles and SS304 steel substrate. During the simulations, the point cloud (PC) of deformed particle domains is converted into a high-quality finite element (FE) mesh with novel PC processing algorithms. The simulations are carried out for various particle characteristics and spraying conditions. The numerical predictions are validated by comparing them with other numerical schemes and previous experimental studies. The main results indicate that the kinetic energy and morphology of the impacting Ni particles strongly influence plastic deformation and temperature rise in the substrate and predeposited coating particles. Plastic deformation is more prominent at the particle edges and mating material interfaces. At the same time, the temperature rise does not reach the melting point but can allow for recrystallization near highly localized regions of the coating microstructure, even at lower deposition rates. Compressive residual stresses are also observed across the coating and substrate layers, with a non-uniform and nonlinear residual stress field due to complex interactions among neighboring particles. The study aims to provide a robust numerical framework for designing and optimizing cold spray deposition parameters for industrial coatings, bridging the knowledge gap and enabling efficient and cost-effective simulations for process optimization.

Numerical simulation of rarefied supersonic flows using a fourth-order maximum-entropy moment method with interpolative closure

Maximum-entropy moment methods allow for the modeling of gases from the continuum regime to strongly rarefied conditions. The development of approximated solutions to the entropy maximization problem has made these methods computationally affordable. In this work, we apply a fourth-order maximum-entropy moment method to the study of supersonic rarefied flows. For such conditions, we compare the maximum-entropy solutions to results obtained from the kinetic theory of gases at different Knudsen numbers. The analysis is performed for both a simplified model of a gas with a single translational degree of freedom (5-moment system) and for a typical gas with three degrees of freedom (14-moment system). The maximum-entropy method is applied to the study of the Sod shock-tube problem at various rarefaction levels, and to the simulation of two-dimensional low-collisional crossed supersonic jets. We show that, in rarefied supersonic conditions, it is important to employ accurate estimates of the wave speeds. Since analytical expressions are not presently available, we propose an approximation, valid for the 14-moment system. In these conditions, the solution of the maximum-entropy system is shown to realize large degrees of non-equilibrium and to approach the Junk subspace, yet provides a good overall accuracy and agreement with the kinetic theory. Numerical procedures for reaching second-order accurate discretizations are discussed, as well as the implementation of the 14-moment solver on Graphics Processing Units (GPUs).

Role of magnetic pressure forces in fluctuation dynamo saturation

ABSTRACT Using magnetohydrodynamic simulations of fluctuation dynamos in turbulent flows with rms Mach numbers $\mathcal {M}_{\rm rms}= 0.2, 1.1$, and 3, we show that magnetic pressure forces play a crucial role in dynamo saturation in supersonic flows. First, as expected when pressure forces oppose compression, an increase in anticorrelation between density and magnetic field strengths obtains even in subsonic flows with the anticorrelation arising from the intense but rarer magnetic structures. In supersonic flows, due to stronger compressive motions density and magnetic field strength continue to maintain a positive correlation. However, the degree of positive correlation decreases as the dynamo saturates. Secondly, we find that the unit vectors of ∇ρ and ∇B2 are preferentially antiparallel to each other in subsonic flows. This is indicative of magnetic pressure opposing compression. This antiparallel alignment persists in transonic and supersonic flows at dynamo saturation. However, compressive motions also lead to the emergence of a parallel alignment in these flows. Finally, we consider the work done against the components of the Lorentz force and the different sources of magnetic energy growth and dissipation. We show that while in subsonic flows, suppression of field line stretching is dominant in saturating the dynamo, the picture is different in supersonic flows. Both field line stretching and compression initially amplifies the field. However, growing magnetic pressure opposes further compression of magnetic flux which tends to reduce the compressive motions. Simultaneously, field line stretching also reduces. But, suppression of compressive amplification dominates the saturation of the dynamo.

Analysis of the effect of turbulent inflow on the flow-field and noise of supersonic jet flow using large eddy simulation

The impact of inflow flow state on the flow-field and far-field noise of supersonic jet flow has been studied. A new turbulent inflow boundary condition based on the synthetic eddy method is implemented in an in-house LES code. The implementation was validated using a turbulent channel flow. Simulation results of an under-expanded supersonic jet with a converging nozzle have shown that turbulent inflow leads to thicker and turbulent initial shear layer with rich vortical structures. The thick initial shear layer hinders the growth of flow instability and break the acoustic feedback loop, which is vital to the generation of screech tone. The alternation of the flow-field by the turbulent inflow also leads to changes in the far-field noise radiation. The screech tone is eliminated, the noise in the downstream direction is considerably suppressed, and the noise radiates in the upstream direction is slightly amplified.

Large-Eddy Simulation of the unsteady supersonic flow around a Mars entry capsule at different angles of attack

Time-evolving high-fidelity simulations of an entry capsule in a supersonic flight regime have been performed at different angles of attack (0∘,5∘,10∘ and 15∘) in Mars' atmosphere. The aim is to contribute to the understanding of the critical unsteady phenomena that arise during the descent phase, gaining insights on the optimal design choices to ensure a safe atmospheric entry and a successful landing procedure. Turbulent structures effectively solved via Implicit Large-Eddy Simulation technique allow us to evaluate the flow properties and the capsule's response both in space and time, placing special attention to the analysis of the turbulent motions responsible for the oscillatory and unsteady dynamics. Ultimately, Proper Orthogonal Decomposition is employed to provide a low-order model of the wake dynamics.

Effect of unsteady supersonic flow on detonation under different hot jet initiation conditions

To understand the actual operation of detonation engines, it is of great significance to simulate the detonation characteristics after being affected by unsteady supersonic flow. Adaptive mesh refinement method and single-step chemical reaction model were used for simulation calculations. The Navier–Stokes equations and hybrid sixth-order weighted essentially non-oscillatory centered difference scheme was adopted in this study. Three different amplitudes of disturbances (0.1, 0.2, and 0.3) and two hot jet injection times were analyzed. The results showed that a moderate disturbance can improve the stability of detonation wave under the ideal hot jet injection time. It allows detonation wave to stay in the combustion chamber for a longer time, which is beneficial for the release of thrust performance. Although the stability of detonation wave is significantly different between the low and high-amplitude disturbances, the residence time of detonation wave is close to the steady flow case under ideal initiation conditions. When the ignition time is insufficient, successful detonation can occur with low and medium-amplitude disturbances. However, the ignition delay was significantly prolonged with medium-amplitude disturbance. There was also greater instability, which is detrimental to the thrust release. When the inflow has a high-amplitude disturbance, the detonation wave fails to ignite due to insufficient energy.

Study on combustion characteristics of sinusoidal hydrogen pulsed jet with different frequencies in supersonic flows

Pulsed jets can effectively improve mixing and combustion efficiencies, while sinusoidal pulsed jets have the advantages of good performance and simple setup. Therefore, the three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations and Shear Stress Transfer k-omega model (SST) are utilized to study the combustion characteristics of sinusoidal pulsed jets with three different frequencies and steady jet in order to obtain an approach to improve the combustion performance in the supersonic flow. In the current study, the combustion performances of the steady jet and the pulsed jets with an equal average momentum flux ratio to the steady jet are compared and analyzed, and the instantaneous combustion characteristics of four different time points in one cycle of the pulsed jets are analyzed in detail. The obtained results show that the pulsed jet can obviously improve the combustion efficiency, although the total pressure loss is slightly larger than that of the steady jet. On the whole, the pulsed jets have a good impact on the combustion performance of the combustor, and the combustion performance of the f = 20 kHz pulsed jet case is the best in this study.

Uncertainty quantification and identification of SST turbulence model parameters based on Bayesian optimization algorithm in supersonic flow

AbstractThe Reynolds‐Averaged Navier–Stokes (RANS) model is the main model in engineering applications today. However, the normal value of the closure coefficient of the RANS turbulence model is determined based on some simple basic flows and may no longer be applicable for complex flows. In this paper, the closure coefficient of shear stress transport (SST) turbulence model is recalibrated by combining Bayesian method and particle swarm optimization algorithm, so as to improve the numerical simulation accuracy of wall pressure in supersonic flow. First, the obtained prior samples were numerically calculated, and the Sobol index of the closure coefficient was calculated by sensitivity analysis method to characterize the sensitivity of the wall pressure to the model parameters. Second, combined with the uncertainty of propagation parameters by non‐intrusive polynomial chaos (NIPC). Finally, Bayesian optimization is used to quantify the uncertainty and obtain the maximum likelihood function estimation and optimal parameters. The results show that the maximum relative error of wall pressure predicted by the SST turbulence model decreases from 29.71% to 9.00%, and the average relative error decreases from 9.86% to 3.67% through the parameter calibration of Bayesian optimization method. In addition, the system evaluated the calibration effect of three criteria, and the calibration results parameters under the three criteria were all better than the calculated results of the nominal values. Meanwhile, the velocity profile and density profile of the flow field were also analyzed. Finally, the same calibration method was applied to the supersonic hollow cylinder and BSL (Baseline) turbulence model, and the same calibration results were obtained, which verified the universality of the calibration method.

Analysis of influencing factors on numerical simulation of transverse jet in supersonic flow

Numerical simulation is becoming an important research method in the field of supersonic flow. Its accuracy and reliability have always been the key to its further application and the focus of current researches. In this study, a series of numerical simulations of transverse supersonic jet in supersonic free flow are carried out based on Reynolds averaged (RANS) solver. Firstly, the flow field structure obtained by different calculation cases is studied, and the mechanism of the difference of flow field structure is described. Furthermore, by changing the accuracy of difference scheme for the convection term and the turbulence model, the different simulation results are compared with the experimental data. The deviation from numerical simulation compared with the experiment is further analyzed to clarify the critical factors affecting the calculation reliability. The results show that improving the accuracy of the scheme cannot effectively improve the calculation results, while choosing an appropriate turbulence model can be helpful to improve the calculation accuracy. When the numerical simulation of jet flow mixing in supersonic flow field is carried out, the conclusions of this study can provide a support for determining the numerical model method and error analysis.

Supersonic Flow past a Sharp Plate with Surface Anomalous Glow Discharge in a Magnetic Field

The electrodynamic structure of an anomalous glow discharge between two plane electrodes located on the surface of a sharp plate in supersonic flow of molecular nitrogen is studied numerically in a wide range of Mach numbers using a modified ambipolar model of quasi-neutral electric-discharge plasma. The ambipolar diffusion coefficient and the effective ionization rate are modified while taking into account the external magnetic field. The problem is solved in the two-dimensional x–y formulation, when the external magnetic field strength is directed in the positive or negative direction of the z axis. The parameters of anomalous glow discharge are numerically studied in the pressure range p = 0.14–5 Torr and the voltage drops on the quasineutral current column of discharge plasma V = 30–320 V. The main problem parameters which make it possible to obtain a reasonable agreement with the available experimental data are determined.

Application of multi-extruded fuel injectors for mixing enhancement of hydrogen gas at scramjet engine: computational study.

Scramjet engines are considered a highly promising technology for improving high-speed flight. In this study, we investigate the effects of using multi-extruded nozzles on fuel mixing and distribution inside the combustion chamber at supersonic flow. Additionally, we explore the impact of an inner air jet on fuel mixing in annular nozzles. To model fuel penetration in the combustor, we employ a computational technique. Our study compares the roles of three different extruded injectors on fuel diffusion and distribution at supersonic cross-flow. Our findings reveal that the use of an inner air jet increases fuel mixing in the annular jet, while the use of extruded nozzles improves fuel distribution by enhancing the vortices between injectors. These results demonstrate the potential benefits of incorporating multi-extruded nozzles and inner air jets in the design of scramjet engines.

Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field

We study the impact of compressibility on two-dimensional turbulent flows, such as those modeling astrophysical disks. We demonstrate that the direction of cascade undergoes continuous transition as the Mach number Ma increases, from inverse at Ma = 0, to direct at . Thus, at comparable amounts of energy flow from the pumping scale to large and small scales, in accord with previous data. For supersonic turbulence with the cascade is direct, as in three dimensions, which results in multifractal density field. For that regime () we derive a Kolmogorov-type law for potential forcing and obtain an explicit expression for the third order correlation tensor of the velocity. We further show that all third order structure functions are zero up to first order in the inertial range scales, which is in sharp contrast with incompressible turbulence where the third order structure function, that describes the energy flux associated with the energy cascade is non-zero. The properties of compressible turbulence have significant implications on the amplification of magnetic fields in conducting fluids. We thus demonstrate that imposing external magnetic field on compressible flows of conducting fluids allows to manipulate the flow producing possibly large changes even at small Mach numbers. Thus Zeldovich’s antidynamo theorem, by which at Ma = 0 the magnetic field is zero in the steady state, must be used with caution. Real flows have finite Ma and, however small it is, for large enough values of I, the magnetic flux through the disk, the magnetic field changes the flow appreciably, or rearranges it completely. This renders the limit Ma → 0 singular for non-zero values of I. Of particular interest is the effect of the density multifractality, at which is relevant for astrophysical disks. We demonstrate that in that regime, in the presence of non-zero I the magnetic field energy is enhanced by a large factor as compared to its estimates based on the mean field. Finally, based on the insights described above, we propose a novel two-dimensional Burgers’ turbulence, whose three-dimensional counterpart is used for studies of the large-scale structure of the Universe, as a model for supersonic two-dimensional magnetohydrodynamic flows.

Intelligent flow field reconstruction based on proper orthogonal decomposition dimensionality reduction and improved multi-branch convolution fusion

The rapid and accurate reconstruction of the supersonic combustor flow field is of great significance for sensing and predicting the combustion state. Existing deep learning methods pay less attention to the convergence speed of flow field reconstruction, which results in longer training and prediction times for the models. This study proposes a method for reconstructing the flow field in supersonic combustor by combining a reduced-order model based on proper orthogonal decomposition (POD) with a multi-branch convolutional neural network. This method first analyzes the effectiveness of POD reconstruction. Then, based on the wall pressure data of the supersonic engine combustor, it performs flow field image reconstruction. Finally, through error calculation and gradient updating with low-resolution principal component flow field shadow images obtained from the POD algorithm, the high-precision and efficient prediction of flow field images is achieved. Different equivalence ratio hydrogen fuel combustion experiments were conducted in a pulsed combustion wind tunnel with an incoming flow Mach number of 2.5. The learning model was trained and tested using the dataset obtained from these experiments. Numerous experiments demonstrated that the model can effectively reconstruct the wave structures of complex flow fields. Multiple evaluation indicators indicated that the reconstructed flow field of the combustor shows good agreement with that obtained from ground wind tunnel testing. Furthermore, after introducing the POD dimensionality reduction model, the training time was reduced by 32.03%, effectively improving the training time complexity of the model.

Phonon motion around (2+1)-dimensional acoustic black hole

We study motion of a phonon, a particle representing the quanta of the sound wave in the (2+1) spacetime of the acoustic analogous axially symmetric black hole, so-called acoustic (sonic) black hole. Similar to the real objects known as black holes in relativity theories, the phenomenon called acoustic black hole possesses the ergoregion whose area is increasing with increasing rotation of the black hole, leading to more phonons being affected by the supersonic flow. It is found that phonons in the ergoregion of an acoustic black hole behave differently than those outside of it. Specifically, we found that the phonons in the ergoregion are affected by the supersonic flow of the fluid, causing them to move in different directions than those outside the ergoregion. Moreover, we presented calculations of the deflection angle and time delay of the phonon in the field of the acoustic black hole in the weak field regime that can be useful to test the geometry of the acoustic black hole in the laboratory.

Experimental investigation of heating augmentation by particle kinetic energy conversion in dust-laden supersonic flows

The presence of particles in supersonic flows can cause significant increases in stagnation point heat fluxes (Dunbar et al. in AIAA J 13:908–912, 1975). This effect is commonly named ‘particle-induced heat flux augmentation’ or just ‘heating augmentation.’ Heating augmentation can be described as the sum of the conversion of kinetic energy of the particles into thermal energy, characterized by the energy conversion efficiency, also called accommodation coefficient, and the increase of convective heat flux (Polezhaev et al. in High Temp 30:1147–1153, 1992; Vasilevskii and Osiptsov in Experimental and numerical study of heat transfer on a blunt body in dusty hypersonic flow 33rd thermophysics conference, American Institute of Aeronautics and Astronautics, 1999). Although the accommodation coefficient is fundamental for heating augmentation characterization, there is only a small number of experimental datasets for it. This work focusses on the experimental determination of the accommodation coefficient in flow regimes at Mach number 2.1, Reynolds number, based on the probe nose diameter, from approx. 6e5 to 1.8e6, and nominal particle sizes of approx. 20 µm. The decrease of particle velocity and kinetic energy flux in the shock layer is measured with highly resolved shadowgraphy for individual particles. The particle kinetic energy flux is decreased by 29% on average by particle deceleration in the shock layer. Negligible kinetic energy fluxes of rebounded particles were measured. The accommodation coefficient is approx. 0.36 for Al2O3 and SiO2 particles, while it is approx. 0.09 for MgO particles. Hence, it is significantly smaller than the widely used value of 0.7, based on the study of (Fleener and Watson in Convective heating in dust-laden hypersonic flows 8th thermophysics conference, 1973), but in good agreement with values given in (Hove and Shih in Reentry vehicle stagnation region heat transfer in particle environments 15th aerospace sciences meeting, 1977) and (Molleson and Stasenko in High Temp 55:87–94, 2017. https://doi.org/10.1134/S0018151X1701014X ). No difference between erosive and elastic particle reflection mode was detected on the conversion efficiency. The data from a simplification of the modeling approach of the conversion efficiency for elastic particle reflection by Molleson and Stasenko (2017) are in poor agreement with experimental data.

Research on time sequence prediction of supersonic cascade flow field based on compressed sensing artificial neural network

The aviation engine that achieves efficient energy conversion is the core power equipment for low-carbon navigation, and the thermal components represented by the combustion chamber greatly affect the stable state of the compressor cascade flow field. Accurate, comprehensive and promptly monitoring of the compressor cascade flow state is related to the safe operation of the engine. A flow field time sequence prediction framework named compressed convolutional gate recurrent unit (CC-GRU) was proposed in this study to predict future supersonic cascade flow parameters based on the flow field at previous moments. CC-GRU embedded convolution into gate recurrent unit (GRU) to deal with the complex spatial-temporal behavior of supersonic cascade flow field. Firstly, unsteady numerical simulations driven by linear changes in back pressure were carried out, and the dataset for model training and validation was obtained to verify the feasibility of time sequence prediction of the cascade flow field. The verification results indicate that the framework can comprehensively predict the flow field with high back pressure in the future according to the flow field with low back pressure in the past period, and further validated the effectiveness of the proposed time sequence prediction model in ground wind tunnel experiments. The CC-GRU model can accurately capture the fine shock wave structure and flow separation zone, with a relative error of less than 10% in predicting the pressure field, and is mainly concentrated within the shock wave structure. Therefore, this research provides new research perspective and technical support for comprehensive and promptly condition monitoring of supersonic cascade flow field.

Modelling the Wall Pressure Fluctuations on the VEGA-C Launcher in Supersonic Conditions

The prediction of pressure fluctuations generated over the external surface of aerospace launchers during the atmospheric flight remains a challenging task due to the complexity of the geometry and the effects of compressibility at high supersonic Mach numbers. An experimental database is here analysed to the scope of providing a procedure to model and predict the relevant statistics of the wall pressure fluctuations generated by a supersonic flow overflowing the VEGA-C Launcher Vehicle. Data have been obtained in an extensive Wind Tunnel test campaign carried out in the trisonic wind tunnel of the National Institute for Aerospace Research (INCAS) in Bucharest. Wall-mounted pressure transducers allowed for the computation of the pressure Auto- and Cross-spectra over the fourth (the payload region) and third stages of the launcher model. Coherence functions are modelled through exponential-like analytical functions following the approaches usually adopted in canonical boundary layer flows, whereas the auto-spectra models are based on polynomial fits. The approach adopted for the achievement of proper non-dimensional quantities as well as the procedure implemented for the full-scale extrapolation is presented and discussed.

Blade tip leakage flow and heat transfer characteristics over a gas turbine blade at subsonic and transonic exit conditions

The present study numerically investigates the blade tip leakage flow (TLF) over a gas turbine blade cascade at low speed ( M ex = 0.1) and transonic ( M ex = 0.92) blade exit Mach numbers, with and without shroud motion. Various blade tip flow phenomena like flow separation and reattachment, flow choking, shock-boundary layer interaction (SBLI), and tip leakage vortex (TLV) are studied, and their influence on the heat transfer coefficient (HTC) distributions over the blade tip and near tip blade suction surface is investigated. The study has found some new zones of heat transfer due to the interaction of horseshoe vortices (HSV) with the blade tip. In addition to the primary TLV, a secondary TLV is formed, which increases near tip blade suction surface heat transfer. The flow transitions to supersonic speed in the aft portion of the blade tip for the transonic case resulting in complex heat transfer distribution due to SBLI, compared to near-uniform distribution for the low speed case. This supersonic flow results in a smaller flow separation zone near the aft portion of the pressure side tip edge for the transonic case compared to the low speed case. The qualitative nature of HTC near the leading edge of the blade tip resembles for low speed and transonic cases. However, near the trailing edge of the blade tip, the qualitative nature of HTC for the transonic case shows a substantial difference due to supersonic flow compared to the low speed case.

A computational study of leading-edge wall cooling effect on shock wave–boundary layer interaction in forward-facing step

A computational study has been done to understand the effect of leading-edge wall cooling on shock wave–boundary layer interaction. Shock wave–boundary layer interaction is studied over a forward-facing step at supersonic Mach 2.5. The study was carried out using Ansys. The work aims to explore the implementation of wall cooling at the leading edge as a separation control strategy for supersonic forward-facing step-induced flow separation. We use a finite-volume method based on upwind flux difference splitting and second-order upwind flow discretization. The simulation results are validated with the available experimental data. Furthermore, using numerical simulations, we found that the separation bubble size was reduced by 18.36% when the walls were marginally cooled to 150 K, while the separation was reduced by 32.65% when the walls were strongly cooled to 100 K.