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The pivotal proposal of this work is to present a reliable algorithm based on the local fractional homotopy perturbation Sumudu transform technique for solving a local fractional Tricomi equation occurring in fractal transonic flow. The proposed technique provides the results without any transformation of the equation into discrete counterparts or imposing restrictive assumptions and is completely free of round-off errors. The results of the scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.

Purpose This paper aims to improve Reynolds-averaged Navier Stokes (RANS) turbulence models using a data-driven approach based on machine learning (ML). A special focus is put on determining the optimal input features used for the ML model. Design/methodology/approach The field inversion and machine learning (FIML) approach is applied to the negative Spalart-Allmaras turbulence model for transonic flows over an airfoil where shock-induced separation occurs. Findings Optimal input features and an ML model are developed, which improve the existing negative Spalart-Allmaras turbulence model with respect to shock-induced flow separation. Originality/value A comprehensive workflow is demonstrated that yields insights on which input features and which ML model should be used in the context of the FIML approach

The paper presents mathematical modelling of steam condensation in the atmospheric air transonic flows. A single-fluid model was employed. The model was validated against the in-house experimental studies of internal flow in nozzles and against benchmark tests available in literature i.e., RAE2822 transonic airfoil. The impact of air relative humidity on the condensation process under transonic flow conditions was examined. The paper shows that the impact of the condensation process in air transonic flow is non-negligible and has to be taken under consideration in flow simulations. The presence of air contaminants in form of small particles was considered too. Their crucial role in the change of the transonic flow structure was numerically confirmed.

In this paper, the prediction of the unsteady flow field over typical high aspect ratio (AR) wings in the transonic flow regime but below the sonic Mach number is of interest. The methodology adopted is a computational approach based on the transonic small disturbance unsteady potential equation. It is shown that the higher AR wings generally have a higher lift coefficient as well as a higher lift-to-drag ratio. With NASA’s common research model (CRM) wing, there is an increase in maximum lift with increasing AR while the induced drag is almost the same. There is also an optimum sweep angle, which is different for each angle-of-attack so that variable sweep lifting surfaces may be designed to provide optimum solutions. The computed flutter speeds indicate an expected reduction with increasing AR.

Control laws for implementing active flutter suppression are generally derived from linear aeroelastic models. In this paper, families of control laws for implementing an active flutter suppression system were initially designed using linearised aeroelastic models based on the doublet lattice method after ignoring the aerodynamic loads associated with relatively faster time scales. Using these preliminary sets of control laws and the nonlinear transonic small disturbance theory, near-optimum control laws were chosen in the transonic domain to maximally increase the flutter speed of a typical aircraft wing by at least 16% or more. Thus it is shown that it is feasible to systematically design near-optimal control laws for active flutter suppression using computational models in transonic flow. The doublet lattice method coupled with the zeroth-order matrix Padé approximant provided the fastest method for synthesising a large number of preliminary control laws. The methodology was successfully demonstrated by applying it to two benchmarking examples.

Mesh-agnostic models have advantages in processing flow field data with various topologies and densities, and they can easily incorporate partial differential equations. Beyond physics-informed neural networks, mesh-agnostic models have been studied for data-driven predictions of simple flows. In this study, a data-driven mesh-agnostic model is proposed to predict the transonic flow field of various supercritical airfoils. The model consists of two subnetworks, i.e., ShapeNet and HyperNet. ShapeNet is an implicit neural representation used to predict spatial bases of the flow field. HyperNet is a simple neural network that determines the weights of these bases. The input of ShapeNet is extended to ensure accurate prediction for different airfoil geometries. To reduce overfitting while capturing shock waves and boundary layers, a multi-resolution ShapeNet combining two activation functions is proposed. Additionally, a physics-guided loss function is proposed to enhance accuracy. The proposed model is trained and tested on various supercritical airfoils under different free-stream conditions. Results show that the model can effectively utilize airfoil samples with different grid sizes and distributions, and it can accurately predict the shock wave and boundary layer velocity profile. The proposed mesh-agnostic model can be used as a decoder in any conventional models, contributing to their application in complex and three-dimensional geometries.

Understanding shock wave behavior in supersonic flow environments is critical for optimizing the aerodynamic performance of turbomachinery components. This study introduces a novel transonic linear cascade design, focusing on advanced blade manufacturing and experimental validation. Blades were 3D-printed using Inconel 625, enabling tight control over the geometry and surface quality, which were verified through extensive dimensional accuracy assessments and surface finish quality checks using coordinate measuring machines (CMMs). Numerical simulations were performed using Ansys CFX with an implicit pressure-based solver and high-order numerical schemes to accurately model the shock wave phenomena. To validate the simulations, experimental tests were conducted using Schlieren visualization, ensuring high fidelity in capturing the shock wave dynamics. A custom-designed test rig was commissioned to replicate the specific requirements of the cascade, enabling stable and repeatable testing conditions. Experiments were conducted at three different inlet pressures (0.7-bar, 0.8-bar, and 0.9-bar gauges) at a constant temperature of 21 °C. Results indicated that the shock wave intensity and position are highly sensitive to the inlet pressure, with higher pressures producing more intense and extensive shock waves. While the numerical simulations aligned broadly with the experimental observations, discrepancies at finer flow scales suggest the need for the further refinement of the computational models to capture detailed flow phenomena accurately.

The aim of this paper is to develop a profile of axisymmetric minimum length nozzle giving a uniform and parallel flow at the exit section. The study is done at high temperature, lower than the dissociation threshold of the molecules. The design is made by the method of characteristics (MOC). The variation of the specific heats with the temperature is considered. The numerical results have been validated with CFD simulation Ansys-Fluent software. The second part of this study is to calculate and analyze the transonic flow field of this supersonic nozzle. The computation of the flow field characteristics at the throat is thus essential to the nozzle developed thrust value and therefore to the aircraft or rocket it propels. An investigation was conducted to analyze the effects of parameters on the position of the sonic line. These parameters include stagnation temperature T0, radius of the nozzle, types of gases, and exit Mach number ME.

This paper presents a focusing schlieren system designed for the investigation of transonic turbine tip-leakage flows. In the first part, the functional principle and the design of the system are presented. Major design considerations and necessary trade-offs are discussed. The key optical properties, e.g., depth of focus, are verified by means of a simple bench test. In the second part, results of an idealized tip-clearance model as well as linear cascade tests at engine representative Reynolds and Mach numbers are presented and discussed. The focusing schlieren system, designed for minimum depth of focus, has been found to be well suited for the investigation of three-dimensional transonic flow fields in turbomachinery applications. The schlieren images show the origin and growth of the tip-leakage vortex on the blade suction side. A complex shock system was observed in the tip region, and the tip-leakage vortex was found to interact with the suction side part of the trailing edge shock system. The results indicate that transonic vortex shedding is suppressed in the tip region at an exit Mach number around M 2 , i s = 0.8.

Both smooth subsonic and transonic spiral flows to steady Euler–Poisson system with nonzero angular velocity and vorticity in a concentric cylinder are studied. On the one hand, we investigate the structural stability of smooth cylindrically symmetric subsonic flows under three-dimensional perturbations on the inner and outer cylinders. On the other hand, the structural stability of smooth transonic flows under the axi-symmetric perturbations is examined. There are no any restrictions on the background subsonic and transonic solutions. A deformation-curl-Poisson decomposition to the steady Euler–Poisson system is utilized to deal with the hyperbolic-elliptic mixed structure in the subsonic region. We emphasize that there is a special structure of the steady Euler–Poisson system which yields a priori estimates and uniqueness of the linearized elliptic system.