Sonic Conditions Research Articles

Behaviour of Whitcomb Integral Supercritical airfoil at various angles of attack in sonic condition using CFD

Understanding the aerodynamic behaviour of an airfoil is crucial for evaluating its performance in generating lift and drag. In this study, the aerodynamic performance of the Whitcomb Integral Supercritical Airfoil is analysed across a range of angles of attack—specifically, 2°, 4°, 6°, 8°, and 10°—under sonic conditions. The primary objective is to investigate and characterize the lift and drag properties exhibited by the airfoil at these various angles of attack. This analysis will provide insights into how the airfoil performs in terms of efficiency and stability at sonic speeds.

Numerical characterization of high-pressure hydrogen jets for compression–ignition engines applying real gas thermodynamics

The development of hydrogen-fueled direct-injection compression–ignition engines requires adequate models that can accurately predict the spatial development and heat release rate of a jet at high pressure. It is found in literature that the combustion process benefits from minimizing flame–wall interaction, but it is unresearched how to achieve this. Jet theory can greatly reduce research efforts, only its validity is uncertain for hydrogen injections at relevant conditions. This work checks the validity via a parametric study performed with Computational Fluid Dynamics simulations. Sonic conditions are imposed at the nozzle exit, using different equations of state. It is found that real gas behavior needs to be used to compute these conditions and to model the jet dynamics. Furthermore, jet theory shows qualitative agreement with the simulation results. Finally, the heat release rate of a multi-hole injector appears insensitive to injection properties, but jet penetration can be controlled.

Flow and Performance Characterization of Rotating Detonation Combustor Integrated with Various Convergent Nozzles

In this study, convergent nozzles of various area ratios (ARs) are used downstream of an annular rotating detonation combustor (RDC) to increase the operating pressure and approach sonic conditions at the nozzle throat. Reactant methane and oxygen-enriched air (67% O2 and 33% N2 by volume) are supplied in counterflow arrangement from two separate plenums located at the base of the RDC annulus. Based on experimentation, a total mass flow rate of 0.32 kg/s was chosen to achieve stable, single-wave mode RDC operation for all test cases, allowing for one-to-one comparisons. The internal performance of the RDC was characterized by ion probes and pressure measurements (wall static and oscillating) in supply plenums and across different axial locations of the combustor. Particle image velocimetry (PIV) at 100 kHz was utilized to measure axial and circumferential velocity components within a two-dimensional region of interest located downstream of the converging nozzle exit. Results show higher internal performance of the RDC with increasing AR of the convergent nozzle. PIV measurement illustrated that the flow oscillation amplitudes decrease with an increasing AR of the converging nozzle. The exit flow contained significant nonuniformity and unsteadiness even with a converging nozzle of AR 2.0, indicating incomplete choking of the flow at the nozzle throat.

Development of Node-centered finite-volume diffusion method on triangle mesh for detonation propagation simulation in insensitive high explosives

This study presents a numerical simulation of detonation waves in insensitive high explosives (IHE). A direct numerical simulation (DNS) method of detonation waves propagation was developed. It solves two-dimensional reactive Euler equations by using a semi-discrete node-centered finite-volume (NCFV) scheme on triangle mesh. Employing ZND model analytical solution as the initial condition, the upper and lower boundary conditions were designed as local sonic equilibrium conditions. The DNS method was validated using steady detonation wave propagation experimental results for tri-amino-tri-nitro-benzene (TATB) based explosives. The two-dimensional steady detonation propagation of the circular arc experiments was completed using a non-embedded technique (electric and optical fibre probe velocimetry). The comparison results demonstrate that the numerical method can provide a good prediction of the pseudo-steady-state detonation wave front propagation and the angular speed.

ANALYSIS OF THE BIFURCATING DUCT OF AN INLET PARTICLE SEPARATOR IN TRANSONIC FLOW CONDITIONS

Abstract To increase the reliability of turboprop and turboshaft engines in extreme operating conditions, filtering protections such as Inlet Particle Separators (IPS) can be installed at the intake. The flow inside an IPS is highly 3D and unsteady, with fluctuations especially pronounced when transonic conditions are reached. In this paper, we aim at providing the transonic analysis of an industrial IPS designed for aerodynamic lab testing. As a first step, we define the threshold beyond which sonic conditions are reached in the boundary cross sections of the IPS by means of a 1D semi-empirical model. Second, we select a critical configuration, and we perform CFD simulations to analyze the locations and evolution of the transonic flow inside the IPS. Different models are presented, i.e. steady and unsteady Reynolds-Averaged Navier-Stokes, Detached Eddy Simulation and Large Eddy Simulation, characterized by three levels of resolution. The results show the evolution of some transonic shocks: the steady-state model is only providing information on averaged quantities, while the time-resolved simulations offer a more precise overview in the time domain. The analysis in the frequency domain reveals the frequencies of the transonic fluctuations. Finally, we discuss three alternative designs to effectively improve the operating range and mitigate the risks related to the transonic instabilities, comparing the differences in separation efficiency with respect to the baseline case. The results prove that the optimal design choice is given by the trade-off between operating range, pressure losses and separation efficiency.

Mechanically Enhanced Detoxification of Chemical Warfare Agent Simulants by a Two-Dimensional Piezoresponsive Metal-Organic Framework.

Chemical warfare agents (CWAs) refer to toxic chemical substances used in warfare. Recently, CWAs have been a critical threat for public safety due to their high toxicity. Metal-organic frameworks have exhibited great potential in protecting against CWAs due to their high crystallinity, stable structure, large specific surface area, high porosity, and adjustable structure. However, the metal clusters of most reported MOFs might be highly consumed when applied in CWA hydrolysis. Herein, we fabricated a two-dimensional piezoresponsive UiO-66-F4 and subjected it to CWA simulant dimethyl-4-nitrophenyl phosphate (DMNP) detoxification under sonic conditions. The results show that sonication can effectively enhance the removal performance under optimal conditions; the reaction rate constant k was upgraded 45% by sonication. Moreover, the first-principle calculation revealed that the band gap could be further widened with the application of mechanical stress, which was beneficial for the generation of 1O2, thus further upgrading the detoxification performance toward DMNP. This work demonstrated that mechanical vibration could be introduced to CWA protection, but promising applications are rarely reported.

On steady rotational high speed flows: The swirling compressible Trkalian profile with headwall injection

This work considers a uniquely configured swirling motion that develops inside a porous tube due to sidewall injection. The bulk fluid motion is modeled as a steady inviscid Trkalian flow field with a swirl-velocity component that increases linearly along the axis of the chamber. The underlying procedure consists of solving the compressible Bragg–Hawthorne equation using a Rayleigh–Janzen expansion that produces a closed-form approximation for the stream function. Based on the latter, most remaining flow attributes may be readily inferred. Results are then compared to their counterparts obtained using a strictly incompressible Trkalian motion. They are also benchmarked against available compressible solutions in an effort to characterize the dilatational effects caused by flow acceleration in long chambers or chambers with sufficiently large sidewall injection. In addition to the stream function, the velocity, pressure, temperature, and density are evaluated over a range of physical parameters. Finally, the distortions affecting the velocity profiles are characterized and shown to result in a blunter motion near the center and a steeper curvature near the sidewall as a consequence of high-speed flow. In comparison with a non-swirling complex-lamellar solution, we find the Trkalian motion to be generally faster and therefore capable of reaching sonic conditions in a shorter distance from the headwall.

Points of Balance and the Infra-thin in Éliane Radigue’s Endless Music

ABSTRACT This paper examines Éliane Radigue’s ‘musique sans fin’ (endless music) of 1968–1970. The period marks her development of acoustic feedback techniques for free-duration performance, where two or more tape loops are set into asynchronous, continuous mechanical playback. Drawing on interview material with Radigue, critical analysis of her ‘endless music’ works and my own study of audio feedback to identify technical details of her studio practice, I argue the importance of this short, relatively under-researched, but formative period of her composition. In the creative, musical use of acoustic, or ‘Larsen’ feedback, musicians control sounds that resonate in the space between a microphone and a loudspeaker under certain acoustic conditions and there is a thin point of balance between pure feedback tones and distortion. A similar fine balancing point is the basis of Marcel Duchamp’s concept of the ‘infra-thin’ which refers to an almost imperceptible gap between two fluid states or experiences during the creation of a work of art. I have chosen to employ elements of Duchamp’s ‘infra-thin’ to guide my analysis of Radigue’s feedback techniques which are similarly based on an atomic, transformational fluctuation between different sonic conditions.

Sonic–supersonic–shock–subsonic–sonic solution to Euler–Poisson system with varying background charges

In this paper, steady transonic shock solutions to the Euler–Poisson system are investigated with respect to varying background charge. More precisely, the density of the background charge is prescribed as a piecewise constant function whose discontinuity is determined only by the shock front. The Euler–Poisson system with varying background charge can describe the motion of the electrons in the special semiconductor devices. We establish the well-posedness of sonic–supersonic–shock–subsonic–sonic solutions, with sonic physical boundary conditions at the upstream and downstream respectively.

Novel Quasi-One-Dimensional Analysis of a Choked Transonic Reacting Flow with Finite-Rate Chemistry

A numerically accurate method for solving quasi-one-dimensional transonic flow with a system of ordinary differential equations (ODEs) has been developed to estimate the performance of a high-speed propulsion system. Specifically, ramjet engines are thermally choked in the combustor region. for which the solution processes undergo a mathematical singularity problem. This singularity incurs various numerical difficulties because the derivatives are indeterminate at the sonic condition and the solution cannot march in the streamwise direction, requiring special numerical treatment. To overcome this issue, two solution processes are augmented in the ODE system: coordinate transform, and solution extrapolation from the equivalent subsonic system. An additional variable is defined to convert the spatial coordinate into a dependent variable that characterizes the transonic flow only by the solution curve passing through the critical point. After the transformation, solution variables are extrapolated from the subsonic solutions obtained with a predicted critical (sonic) condition via a forward iterative shooting method such that the flow properties are smoothly varying both upstream and downstream of the critical point. As a result, there is a good agreement in the predicted critical point with the theoretical location. Moreover, the new method successfully yields the transonic solution without any abrupt or discontinuous changes in flow properties including species fractions, which is almost impossible with existing methods.

Comparison of the different shapes of extruded annular nozzle on the fuel mixing of the hydrogen jet at supersonic combustion chamber

The fuel mixing mechanism is a critical aspect of the propulsion system of hypersonic vehicles. This study aimed to comprehensively investigate a novel jet configuration that enhances fuel mixing in the combustion chamber. The primary objective was to analyze the significance of vortexes in fuel distribution within the combustion chamber. Computational fluid dynamics was used to investigate the three-dimensional structure of the transverse fuel jet released from an extruded nozzle in a supersonic free stream. The influence of jet type (circular and lobe structure nozzles) and nozzle height was fully explored in this research. The free stream air jet was supersonic (Mach = 4), and the hydrogen jet was injected using various annular nozzles in sonic condition. The results obtained show that the use of an annular circular nozzle is efficient in fuel mixing behind the extruded nozzle. Additionally, fuel mixing improves by approximately 90% when the height of the extruded 3-lobe injector is increased by twice its original length.

Soundscape components inform acoustic index patterns and refine estimates of bird species richness

Ecoacoustic monitoring has proliferated as autonomous recording units (ARU) have become more accessible. ARUs provide a non-invasive, passive method to assess ecosystem dynamics related to vocalizing animal behavior and human activity. With the ever-increasing volume of acoustic data, the field has grappled with summarizing ecologically meaningful patterns in recordings. Almost 70 acoustic indices have been developed that offer summarized measurements of bioacoustic activity and ecosystem conditions. However, their systematic relationships to ecologically meaningful patterns in varying sonic conditions are inconsistent and lead to non-trivial interpretations. We used an acoustic dataset of over 725,000 min of recordings across 1,195 sites in Sonoma County, California, to evaluate the relationship between 15 established acoustic indices and sonic conditions summarized using five soundscape components classified using a convolutional neural network: anthropophony (anthropogenic sounds), biophony (biotic sounds), geophony (wind and rain), quiet (lack of emergent sound), and interference (ARU feedback). We used generalized additive models to assess acoustic indices and biophony as ecoacoustic indicators of avian diversity. Models that included soundscape components explained acoustic indices with varying degrees of performance (avg. adj-R2 = 0.61 ± 0.16; n = 1,195). For example, we found the normalized difference soundscape index was the most sensitive index to biophony while being less influenced by ambient sound. However, all indices were affected by non-biotic sound sources to varying degrees. We found that biophony and acoustic indices combined were highly predictive in modeling bird species richness (deviance = 65.8%; RMSE = 3.9 species; n = 1,185 sites) for targeted, morning-only recording periods. Our analyses demonstrate the confounding effects of non-biotic soundscape components on acoustic indices, and we recommend that applications be based on anticipated sonic environments. For instance, in the presence of extensive rain and wind, we suggest using an index minimally affected by geophony. Furthermore, we provide evidence that a measure of biodiversity (bird species richness) is related to the aggregate biotic acoustic activity (biophony). This established relationship adds to recent work that identifies biophony as a reliable and generalizable ecoacoustic measure of biodiversity.

Stability of Parker's Steady Solar Wind Solution in the Subcritical Region

Parker’s steady solar wind solution (PSSWS) is a physically acceptable solution describing a smooth acceleration of the solar wind to supersonic speeds. Parker proposed that PSSWS possesses an intrinsic stability, like a “stable attractor” of this dynamical system. With a view to give a systematic analytical development, we restrict ourselves to the subcritical region inside the Parker critical point (PCP) where the solar wind goes through sonic flow conditions. This enables one to avoid the singularity at PCP plaguing the linear stability problem. Following Parker, we approximate the corona in the subcritical region by a static atmosphere and amend it to include an azimuthal flow and a weak radial flow. These physical simplifications enable us to pose a Sturm–Liouville problem for linearized perturbations about PSSWS. PSSWS is shown to have an intrinsic stability in the subcritical region, while leaving the solar coronal base in a state of (1) rest, (2) corotation with the Sun, and (3) slow radial motion. This result is also shown to hold when a diabatic flow in near-isothermal conditions is included in Parker’s model to explicitly account for the extended coronal heating. The isothermal gas assumption in Parker’s model is then relaxed, and a more realistic barotropic fluid representing variable extended active coronal heating conditions is considered for the gas flow. The stability of PSSWS, as the solar wind flow emerges from a state of rest at the solar surface, is shown to continue to hold.

Using an optimisation strategy to design a supercritical CO2 radial inflow turbine transonic stator

During the operation of supercritical CO (sCO) radial inflow turbines (RITs), sonic conditions may happen, which will decrease their efficiency. Non-standard design geometries are needed to reduce the losses. However, modifying the turbine geometry is a challenge, especially as the optimum shape may be non-intuitive; commercial computational fluid dynamics (CFD) software is not friendly towards automation by surrogate scripts, and the traditional design method for blade passage shape is not suited to the optimisation of aerodynamic turbine design. Hence, in this study, a stator nozzle for a 120 kW sCO RIT, whose geometries are obtained from in-house preliminary design code TOPGEN, has been optimised with a modularised geometry optimiser. To parametrise the geometry, a parametrised stator mesh generator based on a meridional streamline is developed. Bulk CFD simulations are carried out with OpenFOAM, to form a Pareto front with a vector of 14 variables. Three final stators have been selected: they are the optimised Mach number distribution (), the optimised outlet flow angle distribution () and a compromise case. The the outlet boundary properties of these stators are extracted and discussed. The optimised case has the shortest divergent nozzle, returns the best and the least loss; the optimised case has the longest divergent nozzle and returns a better-uniformed outlet flow; the compromise case has the medium length of the divergent case. All these stators have fixed mass flow rates to allow de-coupling of the upstream system from the rotor. This study will ultimately benefit the development of the sCO power cycle.

A new statistical approach to identify critical mass flow rate in CO2 nozzles near saturation conditions

The pressing needs to increase efficiency in heat pumps require refined design of various system components. In common reverse cycles, the throttling valve performs pure energy dissipation, and therefore it is well suited to be replaced by technologies such as ejectors and turbines, to augment system performance. In both two-phase turbines and two-phase ejectors a supersonic convergent-divergent nozzle is commonly required, which is responsible for accelerating the refrigerant fluid from the high-pressure part (e.g. condenser) to the low pressure part (e.g. evaporator). In the design phase of these nozzles, the accurate prediction of the maximum mass flow rate, also known as the critical mass flow rate, is particularly complex due to the two-phase nature of the expansion. In this paper, a new statistical approach to determine the value of the critical mass flow rate for CO2, as refrigerant fluid, is presented and assessed. This approach is based on the MF (Massflow Factor) parameter, which well correlates the value of mass flow rate in sonic conditions. The relationship shown here is based on open experimental information and it is validated on data from the open literature and the industry. The relative error on critical flow rate is less than 15% in the validation range, placing this statistical approach at a level of accuracy comparable to other physical models. An example of design is provided in this paper to demonstrate the potential of the relationship found. This approach provides the designer with a straightforward and validated basis for a reliable preliminary design of expanding two-phase nozzles.

Onset conditions for Mach disk formation in underexpanded jet flows

In this study, the formation conditions of the Mach disk in an underexpanded jet flow were numerically and theoretically investigated under sonic injection conditions and the assumption of an axisymmetric flow. The numerical results demonstrated that the threshold nozzle-pressure ratio (NPR) at which the Mach disk occurred was situated between 3.03 and 3.12, which is lower than those reported in the previous studies. Since the oscillation frequency of the Mach disk was approximately constant over a wide range of NPRs and the amplitude was weak, it was regarded as a steady shock. In addition, the Mach disk was found to form when the total pressure loss reached approximately 40%. To predict the appearance of the Mach disk, we proposed a theoretical model based on a quasi-one-dimensional flow by considering the Mach disk as a normal shock wave on the axis. Based only on injection and ambient conditions, the total-pressure loss ratio derived from the model was in good agreement with that obtained from the numerical simulations, indicating that the proposed model provides useful knowledge for Mach disk occurrence prediction.

An improved shock wave capturing method in high Mach numbers

This study describes an improved scheme that can suppress numerical instabilities caused by calculating strong shock waves at high Mach numbers. The current scheme combines a clear detection of shock waves based on a sonic point condition with a hybrid numerical flux used in a dissipative scheme and a low-precision interpolation only near shock waves. This scheme is easily obtained by combining existing schemes often used in hypersonic flows. Its performance in a two-dimensional system is compared to existing schemes using two inviscid flows at Mach numbers 15 and 20. The results show that the scheme outperforms existing schemes in terms of improving accuracy around shock waves. It is also discovered that this scheme can prevent nonphysical numerical oscillations caused by a mismatch between grid and local-shock forms. The significance of the scheme is demonstrated in the interaction field between the normal shock wave and the boundary layer in competition between viscosity and numerical dissipations. Therefore, the current scheme is useful in a high-Mach-number problem.

Thermodynamic perfect fluid spheres admitting an orthogonal flat synchronization

We analyze the interpretation of the spherically symmetric perfect fluid solutions that admit a flat synchronization orthogonal to the fluid flow as a thermodynamic perfect fluid in local thermal equilibrium. The ideal gas sonic condition is examined for this family of metrics, and the macroscopic conditions for physical reality are accurately tested for some specific solutions.

Effects of circular and non-circular nozzle exit geometries on subsonic and supersonic jet propagations

The mixing enhancement and core length reduction of a jet without significant loss of thrust are essential for reducing infrared radiation, mitigating aeroacoustic noise, improving combustion characteristics, and thrust vectoring. The jet mixing can be improved by manipulating the flow behavior. In subsonic and sonic jets, the flow manipulation may be achieved by utilizing nozzles with non-circular geometries that shed vortices of varying size due to their non-uniform azimuth curvatures. Non-uniform vortices generate differential spreading along the nozzle’s perimeter, causing axis switching and improving entrainment characteristics. Therefore, the present study examines the effects of two non-circular nozzle exit shapes (elliptic and square) on the mixing augmenting efficacy at subsonic and sonic flow conditions. The circular nozzle is tested for comparison. Both quantitative and qualitative analyses evaluate the efficacy of nozzles with non-circular exit geometries. Among the configurations investigated, the elliptic nozzle is superior in shortening the potential core length and enhancing the jet spread. A maximum reduction of 18.75% in core length with rapid jet decay was accomplished with the elliptic nozzle. The measurement of pressure profiles at different streamwise locations reveals that the spread rate is greater for elliptic and square jets than their circular counterpart. The elliptic jet exhibits the highest spread along the minor-axis direction compared to the major-axis direction. The differential jet spread rate in the elliptical jet causes an early axis-switching––direct evidence of mixing augmentation. Shadowgraph images show the asymmetric pattern of shock cell structures and differential spreading in elliptic and square jets.

Secondary flow choking in axisymmetric supersonic air ejector with adjustable motive nozzle

Supersonic ejectors have many applications across engineering, but their broader utilization is prevented by their generally low efficiency, which is related to a lack of understanding of the processes within them. This paper presents experimental and numerical analyses of the choking phenomenon within an axisymmetric supersonic air ejector with an adjustable motive nozzle. The effects of the operating and geometric conditions on the flow within the ejector were studied in detail. Five motive nozzle configurations were considered, and the results showed that the specific nozzle position (xp) could be changed to influence the choking of the secondary flow and hence achieve different working regimes while keeping the operating conditions constant. At xp = 1 or 2 mm, the secondary flow reached sonic conditions before even entering the mixing chamber and therefore before mixing with the primary flow. At xp = 3–5 mm, choking occurred within the mixing chamber, and two different choking mechanisms were identified. These results may serve as background for better understanding of flow choking in supersonic ejectors.