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This study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.

Exact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).

Two total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.

No thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy.

In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence.

In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient.

The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

A numerical analysis is given for the prediction of unsteady, two‐dimensional fluid flow induced by a heat and mass source in an initially closed cavity which is vented when the internal overpressure reaches a certain level. A modified ICE technique is used for solving the Navier–Stokes equations governing a compressible flow at a low Mach number and high temperature. Particular attention is focused on the treatment of the boundary conditions on the vent surface. This has been treated by an original procedure using the resolution of a Riemann problem. The configuration investigated may be viewed as a test problem which allows simulation of the ventilation and cooling of such cavities. The injection of hot gases is found to play a key role on the temperature field in the enclosure, whereas the vent seems to produce a distortion of the dynamic flow‐field only. When the injection of hot gases is stopped, the enclosure heat transfer is strongly influenced by the vent. A comparison with the results obtained when the radiative heat transfer between the walls of the enclosure is considered, indicate that radiation dominates the heat transfer in the enclosure and alters the flow patterns significantly.

The purpose of this paper is to study the unsteady caivitating flows in centrifugal pump, especially for improving the turbulence model to obtain highly resolution results-capable of predicting the cavitation inception, shedding off and collapse procedures.

Both numerical simulations and experimental visualizations were performed in the present paper. An improved RCD turbulence models was proposed by considering three corrected methods: the rotating corrected method, the compressible corrected method and the turbulent viscosity corrected method. Unsteady RANS computations were conducted to compare with the experiments.

The comparison of pump cavitation performance showed that the RCD turbulence model obtained better performance both in non-cavitation and cavitation conditions. The visualization of the cavitation evolution was recorded to validate the unsteady simulations. Good agreement was noticed between calculations and visualizations. It is indicated the RCD model can successfully capture the bubbles detachment and collapse at the rear of the cavity region, since it effectively reduces the eddy viscosity in the multiphase region of liquid and vapor. Furthermore, the eddy viscosity, the instantaneous pressure and density distribution were investigated. The effectiveness of the compressibility was found. Meanwhile, the influence of the rotating corrected method on prediction was explored. It is found that the RCD model solved more unsteady flow characteristics.

The current work presented a turbulence model which was much more suitable for predicting the cavitating flow in centrifugal pump.

This paper aims to study the magneto-radiative gas (water vapor) on an unsmooth boundary.

This paper provided a numerical treatment via the implicit Chebyshev pseudo-spectral method to investigate unsteady compressible magneto-radiative gas (water vapor Pr = 1) flow near a heated vertical wavy wall through porous medium in the presence of inclined magnetic field. The impacts of viscous dissipation, temperature-dependent fluid properties, thermal conductivity and viscosity in the presence of nonlinear thermal radiation are studied. The sinusoidal surface is transformed into a flat one using a suitable transformation. The comparison figures of published data with the present outcomes illustrate a good match. The present steady-state outcomes are presented for the temperature, velocity, Nusselt number and the shearing stress through figures for several interested physical parameters, namely, compressibility, magnetic, radiation, viscosity–temperature variation, thermal conductivity–temperature variation, surface sinusoidal waveform and porous parameters.

The present numerical outcomes confirm the importance of applying nonlinear thermal radiation cases in all studies that investigate heat transfer under the influence of thermal radiation.

A mathematical model is established for a wavy boundary, and Chebyshev pseudo-spectral method is adopted for the numerical study.

Relevant analyses are presented on the base of the compressible vortex method for simulating the development of two or three co-rotating vortices with different characteristic Mach numbers. The paper aims to discuss this issue.

In addition to having vorticity and dilatation properties, the vortex particles also carry density, enthalpy, and entropy. Taking co-rotating vortices in two-dimensional unsteady compressible flow for an example, truncation of unbounded domains via a nonreflecting boundary condition was considered in order to make the method computationally efficient.

For two identical vortices, the effect of the vortex Mach number on merging process is not evident; if two vortices have the same circulation rather than different radiuses, the vorticity and dilatation fields of the vortex under a vortex Mach number will be absorbed by the vortex under a higher vortex Mach number. For three vortices, if the original arrangement of the vortices is changed, the evolvement of the vorticity and dilatation fields is different.

The paper reveals new mechanism of the three co-rotating vortices by a feasible compressible vortex method.

A generalized variational principle of 2D unsteady compressible flow around oscillating airfoils is established directly from the governing equations and boundary/initial conditions via the semi‐inverse method proposed by He. In this method, an energy integral with an unknown F is used as a trial‐functional. The identification of the unknown F is similar to the identification of the Lagrange multiplier. Based on the variational theory with variable domain, a variational principle for the inverse problem (given as the time‐averaged pressure over the airfoil contour, while the corresponding airfoil shape is unknown) is constructed, and all the boundary/initial conditions are converted into natural ones, leading to well‐posedness and the unique solution of the inverse problems.

The design of a space launcher requires some considerations about the unsteady loads and heat transfer occurring at the base of the structure. In particular, these phenomena are predominant during the early stage of the flight. This paper aims to evaluate the ability of the unstructured, high order finite-volume CFD solver FLUSEPA, developed by Airbus Safran Launchers, to accurately describe these phenomena.

This paper first performs a steady simulation on a base flow around a four-clustered rocket configuration. Results are compared with NASA experiments and Loci-CHEM simulations. Then, unsteady simulations of supersonic H2/air reacting mixing layer based on the experiment of Miller, Bowman and Mungal are performed. Three meshes with different cells number are used to study the impact of spatial resolution. Instantaneous and time-averaged concentrations are compared with the combined OH/acetone planar laser-induced fluorescence imaging from the experiment.

FLUSEPA satisfactorily predicts the base heat flux at the base of a four-clustered rocket configuration. NASA Loci-CHEM reactive simulations indicate that afterburning plays an important role and should not be neglected. The unsteady reactive computation of a supersonic mixing layer shows that FLUSEPA is also able to accurately predict flow structures and interactions. However, the complexity of the experiment and the lack of details concerning the facility prevents from obtaining satisfactory converged results.

This study is the first step on the development of a cost-effective method aiming at predicting unsteady loads and heat transfer on space launchers using an unsteady and reactive model for the CDF calculations. It uses original techniques such as conservative CHIMERA-like overset grids, local re-centering of fluxes and local adaptive time-stepping to reduce computational cost while being robust and accurate.

The flux vector splitting (FVS) schemes are known for their higher resistance to shock instabilities and carbuncle phenomena in high-speed flow computations, which are generally accompanied by relatively large numerical diffusion. However, it is desirable to control the numerical diffusion of FVS schemes inside the boundary layer for improved accuracy in viscous flow computations. This study aims to develop a new methodology for controlling the numerical diffusion of FVS schemes for viscous flow computations with the help of a recently developed boundary layer sensor.

The governing equations are solved using a cell-centered finite volume approach and Euler time integration. The gradients in the viscous fluxes are evaluated by applying the Green’s theorem. For the inviscid fluxes, a new approach is introduced, where the original upwind formulation of an FVS scheme is first cast into an equivalent central discretization along with a numerical diffusion term. Subsequently, the numerical diffusion is scaled down by using a novel scaling function that operates based on a boundary layer sensor. The effectiveness of the approach is demonstrated by applying the same on van Leer’s FVS and AUSM schemes. The resulting schemes are named as Diffusion-Regulated van Leer’s FVS-Viscous (DRvLFV) and Diffusion-Regulated AUSM-Viscous (DRAUSMV) schemes.

The numerical tests show that the DRvLFV scheme shows significant improvement over its parent scheme in resolving the skin friction and wall heat flux profiles. The DRAUSMV scheme is also found marginally more accurate than its parent scheme. However, stability requirements limit the scaling down of only the numerical diffusion term corresponding to the acoustic part of the AUSM scheme.

To the best of the authors’ knowledge, this is the first successful attempt to regulate the numerical diffusion of FVS schemes inside boundary layers by applying a novel scaling function to their artificial viscosity forms. The new methodology can reduce the erroneous smearing of boundary layers by FVS schemes in high-speed flow applications.

This paper aims to improve the computational efficiency and to achieve high-order accuracy for the computation of helicopter rotor unsteady flows in forward flight during the industrial preliminary design stage.

The integral arbitrary Lagrangian–Eulerian form of unsteady compressible Navier–Stokes equations with low Mach number preconditioned pseudo time terms based on non-inertial frame of reference undergoing rotating and translating was derived and discretized in the framework of multi-block structured finite volume grid using three types of spatial reconstruction schemes, i.e. the third-order accurate monotonic upwind scheme for conservation laws, the fifth-order accurate weighted essentially non-oscillatory and the fifth-order accurate weighted compact nonlinear schemes.

The results show that the present non-inertial computational method can obtain comparable results with other methods, such as the dynamic overset method, and make sure that the higher-order spatial schemes can significantly improve the tip vortex resolution.

The computational grid used by the present method remained static during the whole unsteady computation process, with only local deformations induced by blade cyclic pitch and other operating motions, which greatly reduced the complexity of grid motion and enhanced the efficiency and robustness.