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A solution algorithm for the numerical calculation of isothermal fluid flow inside gas turbine combustors is presented. The finite‐volume method together with curvilinear non‐orthogonal coordinates and a non‐staggered grid arrangement is employed. Cartesian velocity components are chosen as dependent variables in the momentum equations. The turbulent flow inside the combustor is modelled by the k—ε turbulence model. The grid is generated by solving elliptic equations. This solution algorithm, which can be used on both can‐type and annular combustors, is tested on a water model can‐type combustor because of the availability of geometrical and experimental data for comparison.

WHEN a high‐speed jet aircraft is flying at transonic speeds — near or just above the speed of sound — a large proportion of the total drag of the aircraft will come from the afterbody of the fuselage. This may be as much as 30–40%, which is a very significant amount to the aircraft designer. The flow over the afterbody is also important because it affects the behaviour of the fin, and because if the flow is oscillatory, this can have adverse consequences on the airccraft. The necessity of maximising knowledge of the after‐body flow while minimising the cost of wind‐tunnel and in‐flight testing is bringing computational fluid dynamics (CFD) into prominence. British Aerospace has recently commissioned a study by CHAM (Concentration Heat and Momentum Ltd) in the application of the extremely sophisticated CFD code PHOENICS to the problem. The study has concentrated upon predicting the effect of jet entrainment on the surface pressure distribution around the afterbody, an area which has previously been difficult to model computationally. A large amount of experimental work has already been carried out using wind‐tunnel measurements, and the study sought first to validate the program by reference to experimental data.

This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives are to handle internal and external flows in fairly complex geometries including shock waves, compressible turbulence and heat transfer.

The code is equipped with high-order discretization schemes to improve the computational accuracy of the solution algorithm. Besides, a new method to deal with the geometrical singularities, so-called domain decomposition method (DDM), is implemented. The DDM consists of using two different meshes communicating with each other, where the base mesh is Cartesian and the overlapped one a hollow cylinder.

The robustness of the present implemented code is appraised through several numerical test cases including a vortex advection, supersonic compressible flow over a cylinder, Poiseuille flow, turbulent channel and pipe flows. The results obtained here are in an excellent agreement when compared to the experimental data and the previous direct numerical simulation (DNS). As for the DDM strategy, it was successful as simulation time is clearly decreased and the connection between the two subdomains does not create spurious oscillations.

In sum, the developed solver was capable of solving, accurately and with high-precision, two- and three-dimensional compressible flows including fairly complex geometries. It is noted that the data provided by the DNS of supersonic pipe flows are not abundant in the literature and therefore will be available online for the community.

This paper aims to predict aerodynamic heating through the efficient solution of three‐dimensional viscous shock layer (VSL) equations, using axisymmetric analog.

The three‐dimensional VSL equations are written in the curvilinear streamline coordinate system. In these equations, normal momentum equation is replaced by Maslen's pressure relation. In addition to this, axisymmetric analog is implemented along the streamlines through assuming a zero value for circumferential velocity component. In this case, three‐dimensional VSL equations are reduced into an axisymmetric form, which can be solved much easier.

It is demonstrated that the solution of three‐dimensional VSL equations in the curvilinear streamline coordinate system, using axisymmetric analog, has made it possible to predict convective heat fluxes in both windward and leeward regions. Moreover, in comparison with the 3D VSL methods, the present approach dramatically reduces the CPU time of calculations. Comparison with the experimental and numerical data shows a good agreement between both of these data and the present results.

This method is an excellent tool for parametric study and preliminary design of hypersonic vehicles.

This method can predict convective heat flux in the leeward region where other similar methods are not applicable. In addition to this the present method is faster than other methods of solution for the 3D VSL equations.

A systematic, non‐orthogonal FDTD algorithm for the unified and fully dual construction of curvilinear PMLs in 3‐D lossy electromagnetic and advective acoustic problems, is presented in this paper. Postulating a consistent mathematical formulation, the novel methodology introduces a set of general vector parametric equations that describe wave propagation in both media and facilitate the effective treatment of the remarkably complex, arbitrarily‐aligned (non‐uniform) source or mean flow terms, particularly at low frequencies. The discretization procedure is performed via accurate higher‐order FDTD topological concepts, which along with a well‐posed variable transformation, suppress the undesired lattice dispersion and anisotropy errors. Hence, due to these additional degrees of design freedom and their optimal establishment, the new stable PMLs (split‐field or Maxwellian) accomplish a critical attenuation of the evanescent, vorticity or elastic wave families by carefully accounting for every loss mechanism. Numerical investigation reveals the superiority of the proposed technique in terms of various open‐region, waveguide and ducted‐domain simulations.

Stochastic uncertainties in material parameters have a significant impact on the analysis of real-world electromagnetic compatibility (EMC) problems. Conventional approaches via the Monte-Carlo scheme attempt to provide viable solutions, yet at the expense of prohibitively elongated simulations and system overhead, due to the large amount of statistical implementations. The purpose of this paper is to introduce a 3-D stochastic finite-difference time-domain (S-FDTD) technique for the accurate modelling of generalised EMC applications with highly random media properties, while concurrently offering fast and economical single-run realisations.

The proposed method establishes the concept of covariant/contravariant metrics for robust tessellations of arbitrarily curved structures and derives the mean value and standard deviation of the generated fields in a single-run. Also, the critical case of geometrical and physical uncertainties is handled via an optimal parameterisation, which locally reforms the curvilinear grid. In order to pursue extra speed efficiency, code implementation is conducted through contemporary graphics processor units and parallel programming.

The curvilinear S-FDTD algorithm is proven very precise and stable, compared to existing multiple-realisation approaches, in the analysis of statistically-varying problems. Moreover, its generalised formulation allows the effective treatment of realistic structures with arbitrarily curved geometries, unlike staircase schemes. Finally, the GPU-based enhancements accomplish notably accelerated simulations that may exceed the level of 120 times. Conclusively, the featured technique can successfully attain highly accurate results with very limited system requirements.

Development of a generalised curvilinear S-FDTD methodology, based on a covariant/contravariant algorithm. Incorporation of the important geometric/physical uncertainties through a locally adaptive curved mesh. Speed advancement via modern GPU and CUDA programming which leads to reliable estimations, even for abrupt statistical media parameter fluctuations.

The purpose of this paper was to determine the influence of a number of measured points on results of measurements of turbine blades, which are the parts of aircraft engines. The selection of a number of points is the part of a measurement strategy in the coordinate measuring technique and determines the accuracy of measurements.

Numerical and experimental investigations were conducted. The measurements were simulated using different numbers of measured points. The simulated measurements were performed for the selected dispersion of measured points. The dispersion reflected the inaccuracy of a manufacturing process of the considered product and the uncertainty of measurements of curvilinear surfaces. To verify the accuracy of the numerical studies, experimental research was conducted. The real measurements were conducted using the selected coordinate measuring machine.

The gained results following the simulations can be very useful when selecting the appropriate number of measured points. The chosen number of points may be used during real measurements of turbine blades conducted on coordinate measuring machines. The results of numerical research indicate that there should be used the average radii of leading and trailing edges to increase the accuracy of measurements. The results of real coordinate measurements confirmed the results of simulation studies.

The main novelty of the paper is the presented methodology for determining the influence of measured points on results of measurements. The presented methodology helps the user of a coordinate measuring system select the appropriate measurement strategy of free-form surfaces applied in the aerospace industry.

This paper aims to develop an efficient numerical method for simulating multicomponent flows by solving the system of conservative equations closed by a general two parameters equation of state.

A finite difference method for solving the two‐dimensional Euler or Navier‐Stokes equations for multicomponent flows in a general curvilinear coordinate system is developed. The system of conservative equations (mass, momentum and energy) is closed with a general two parameters equation of state (ρe=(p+γp_∞)/(γ−1)), which, associated to a γ‐formulation, allows easy computation of multicomponent flows. In order to enforce the stability of the numerical scheme, the Roe's flux‐difference splitting is adopted for the numerical treatment of the inviscid fluxes. The method is adapted to treat also unsteady flows by implementing an explicit Euler scheme.

The method was applied to compute various configurations of flows, ranging from incompressible to compressible fluid, including cases of single component flows or multicomponent ones. Computations show that the use of primitive variables instead of conservative ones, especially at low Mach numbers, improves the iteration process when the resolution is performed with a relaxation procedure such as Gauss‐Seidel method. Simulations of compressible flows with a strong shock show the ability of the present method to capture shocks correctly even with the use of primitive variables. To complete numerical tests, flows involving two fluids with the presence of interactions between a shock and a discontinuity surface have been treated successfully. Also, a case of cavitating flow has been considered in this work.

The present method permits the simulation of a large variety of multicomponent complexes flows with an efficient numerical taking advantage of Roe's flux‐difference splitting in curvilinear coordinate system.

A numerical model for solving either elastic‐plastic, elastic‐viscoplastic or purely viscoplastic deformation of thin sheets is presented, using a membrane mechanical approach. The finite element method is used associated with an incremental procedure. The mechanical equations are the principle of virtual work written in terms of plane stress, which is solved at the end of each increment, and an incremental semi‐implicit flow rule obtained by the time integration of the constitutive equations over the increment. These equations are written using curvilinear coordinates, and membrane elements are used to discretize them. The resolution method is the Newton‐Raphson algorithm. The contact algorithm is presented and allows for applications to cold stretching and deep‐drawing problems and to the superplastic forming of thin sheets.

An attempt has been made to solve the heat conduction equation in a multiconnected domain using both boundary fitted coordinate system and finite element method. It has been found that boundary fitted coordinate system takes significantly less time in setting up the grid lines or mesh points compared to the finite element method of ANSYS. It has also been established that the former method takes much less time in obtaining a grid independent solution of the temperature field compared to the later one.