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The indefinite nature of the mixed finite element formulation of the Navier‐Stokes equations is treated by segregation of the variables. The segregation algorithm assembles the coefficients which correspond to the velocity variables in the upper part of the equation matrix and the coefficients which corresponds to the pressure variables in the lower part of the equation matrix. During the incomplete; elimination of the velocity matrix, fill‐in will occur in the pressure matrix, hence, divisions with zero are avoided. The fill‐in rule applied here is related to the location of the node in the finite element mesh, rather than the magnitude of the fill‐in or the magnitude of the coefficient at the location of the fill‐in. Different orders of fill‐in are explored for ILU preconditioning of the mixed finite element formulation of the Navier‐Stokes equations in two dimensions.

Steady‐state two‐dimensional solutions to the full compressible Navier‐Stokes equations are computed for laminar convective motion of a gas in a square cavity with large horizontal temperature differences. No Boussinesq or low‐Mach number approximations of the Navier‐Stokes equations are used. Results for air are presented. The ideal‐gas law is used and viscosity is given by Sutherland’s law. An accurate low‐Mach number solver is developed. Here an explicit third‐order discretization for the convective part and a line‐implicit central discretization for the acoustic part and for the diffusive part are used. The semi‐implicit line method is formulated in multistage form. Multigrid is used as the acceleration technique. Owing to the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low Mach number stiffness is treated by a preconditioning technique. By a combination of the preconditioning technique, the semi‐implicit discretization and the multigrid formulation a convergence behaviour is obtained which is independent of grid size, grid aspect ratio, Mach number and Rayleigh number. Grid converged results are shown for a variety of Rayleigh numbers.

A software package is developed for the modelling and animation of viscous incompressible fluids. The full time‐dependent Navier‐Stokes equations are used to simulate 2D and 3D incompressible fluid phenomena which include shallow and deep fluid flow, transient dynamic flow, vorticity and splashing in simulated physical environments. The package also allows the inclusion of variously shaped and spaced static or moving obstacles that are fully submerged or penetrate the fluid surface. Stable numerical analysis techniques based on finite‐differences are used for the solution of the Navier‐Stokes equations. To model free‐surface fluids, a technique based on the Marker‐and‐Cell method is presented. Based on the fluid’s pressure and velocities obtained from the solution of the Navier‐Stokes equations this technique allows modelling of the fluid’s free surface either by solving a surface equation of by tracking the motion of marker particles. The latter technique is suitable for visualization of splashing and vorticity. Furthermore, an editing tool is developed for easy definition of a physical‐world which includes obstacles, boundaries and fluid properties such as viscosity, initial velocity and pressure. Using the editor, complex fluid simulations can be performed without prior knowledge of the underlying fluid dynamics equations. Finally, depending on the application fluid rendering techniques are developed using standard Silicon Graphics workstation hardware routines.

Unsteady compressible, axisymmetric Navier‐Stokes equations are solved for a flow over a forward facing spike attached to a heat shield for a freestream Mach number range of 1.3‐4.5. A numerical simulation is carried out using a finite‐volume discretization technique in conjunction with a multistage Runge‐Kutta time‐stepping scheme. Comparisons have been made with experimental results such as surface oil flow visualisation, schlieren picture and surface pressure distribution. A good agreement is found between them. Computed results show that lengths of the separated region on the spike are influenced by freestream Mach number. The interaction between the shear layer on the spike and the conical‐reattachment shock wave causes the peak wall pressure and heat flux on the heat shield. The peak heat flux is shown to be a function of freestream Mach number and increases with increase in freestream Mach number.

Fluid flows in pipes whose cross-sectional area are increasing in the stream-wise direction are prone to separation of the recirculation region. This paper aims to investigate such fluid flow in expansion pipe systems using direct numerical simulations. The flow in circular diverging pipes with different diverging half angles, namely, 45, 26, 14, 7.2 and 4.7 degrees, are considered. The flow is fed by a fully developed laminar parabolic velocity profile at its inlet and is connected to a long straight circular pipe at its downstream to characterise recirculation zone and skin friction coefficient in the laminar regime. The flow is considered linearly stable for Reynolds numbers sufficiently below natural transition. A perturbation is added to the inlet fully developed laminar velocity profile to test the flow response to finite amplitude disturbances and to characterise sub-critical transition.

Direct numerical simulations of the Navier–Stokes equations have been solved using a spectral element method.

It is found that the onset of disordered motion and the dynamics of the localised turbulence patch are controlled by the Reynolds number, the perturbation amplitude and the half angle of the pipe.

The authors clarify different stages of flow behaviour under the finite amplitude perturbations and shed more light to flow physics such as existence of Kelvin–Helmholtz instabilities as well as mechanism of turbulent puff shedding in diverging pipe flows.

The purpose of this paper is to investigate airfoil’s tonal noise reduction mechanism when deploying surface irregularities, such as surface waviness by means of spatial stability analyses.

Flow field calculations over smooth and wavy-surface NACA 0012 airfoils at 2° angle of attack and at Reynolds number of 200,000 are performed using the large eddy simulation (LES) approach. Three geometrical configurations are considered: a smooth NACA 0012 airfoil, wavy surface on the suction side (SS) and wavy surface on the pressure side (PS). The spatial stability analyses using the LES-generated flow fields are conducted and validated against the Orr-Sommerfeld stability analysis for the smooth airfoil configuration.

The spatial stability analyses show that inclusion of the wavy-type modification on the SS of the airfoil does not lead to altering of the acoustic feedback loop mechanism, with respect to the mechanism observed for the smooth airfoil configuration. In contrast, applying the surface modifications to the airfoil PS leads to a significant reduction of the amplification range of disturbances in the vicinity of the trailing edge for the frequency of the acoustic feedback loop mechanism.

The spatial analyses using, for example, LES-generated flow fields can be widely used to determine acoustic sources and associated distributions of amplifications for a wide range of applications in the aeroacoustics.

The spatial stability analysis approach based on flow fields computed a priori using the LES method has been introduced, validated and used to determine behaviour of the acoustic feedback loop when accurate reconstruction of geometry effects is required.

The purpose of this paper is the theoretical presentation of tensorial formulation with surface mobility forces and numerical verification of Reynolds thermal transpiration law in a contemporary experiment with nanoflow.

The velocity profiles in a single microchannel are calculated by solving the momentum equations and using thermal transpiration force as the boundary conditions. The mass flow rate and pressure of unstationary thermal transpiration modeling of the benchmark experiment has been achieved by the implementation of the thermal transpiration mobility force closure for the thermal momentum accommodation coefficient.

An original and easy-to-implement method has been developed to numerically prove that at the final equilibrium, i.e. zero-flow state, there is a connection between the Poiseuille flow in the center of channel and counter thermal transpiration flow on the surface. The numerical implementation of the Reynolds model of thermal transpiration has been performed, and its usefulness for the description of the benchmark experiment has been verified.

The simplified procedure requires the measurement or assumption of the helium-glass slip length.

The procedure can be very useful in the design of micro-electro-mechanical systems and nano-electro-mechanical systems, especially for accommodation pumping.

The paper discussed possible constitutive equations in the transpiration shell-like layer. The new approach can be helpful for modeling phenomena occurring at a fluid–solid phase interface at the micro- and nanoscales.

An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The purpose of this paper is to show that the Class‐Shape‐Refinement‐Transformation method in combination with an Euler/adjoint solver provides an efficient and intuitive way of optimizing aircraft shapes.

The Class‐Shape‐Transformation method was used to parameterize the aircraft shape and the flow was computed using an in‐house Euler code. An adjoint solver implemented into the Euler code was used to compute the required gradients and a trust‐region reflective algorithm was employed to perform the actual optimization.

The results of two aerodynamic shape optimization test cases are presented. Both cases used a blended‐wing‐body reference geometry as their initial input. It was shown that using a two‐step approach, a considerable improvement of the lift‐to‐drag ratio in the order of 20‐30 per cent could be achieved. The work presented in this paper proves that the CSRT method is a very intuitive and effective way of parameterizating aircraft shapes. It was also shown that using an adjoint algorithm provides the computational efficiency necessary to perform true three‐dimensional shape optimization.

The novelty of the algorithm lies in the use of the Class‐Shape‐Refinement‐Transformation method for parameterization and its coupling to the Euler and adjoint codes.

Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations.

Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes.

It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall cavity. In all the cases the results agree very well with exemplary solutions.

A staggered or half-staggered grid arrangement is usually used for the projection method for both constant and low Mach number flows. The staggered approach ensures stability and strong pressure-velocity coupling. In the paper a high-order compact method has been implemented in the framework of low Mach number approximation on collocated meshes. The resulting algorithm is accurate, robust for large density variations and is almost free from the pressure oscillations.

The purpose of this paper is to investigate the problem of entropy generation around a spinning/non‐spinning solid sphere subjected to uniform heat flux boundary condition in the forced‐convection regime.

The governing continuity, momentum, energy and entropy generation equations are numerically solved for a wide range of the controlling parameters; Reynolds number and the dimensionless spin number.

The dimensionless overall total entropy generation increases with the dimensionless spin number. The effect of increasing the spin number on the fluid‐friction component of entropy generation is more significant compared to its effect on heat transfer entropy generation.

Since the boundary‐layer analysis is used, the flow is presented up to only the point of external flow separation.

Entropy generation analysis can be used to evaluate the design of many heat transfer systems and suggest design improvements.

A review in the open literature indicated that no study is available for the entropy generation in the unconfined flow case about a spinning sphere.