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A flux‐difference splitting based on the polynomial character of the flux vectors is applied to steady Euler equations, discretized with a vertex‐centred finite volume method. In first order accurate form, a discrete set of equations is obtained which is both conservative and positive. Due to the positivity, the set of equations can be solved by collective relaxation methods in multigrid form. A full multigrid method based on successive relaxation, full weighting, bilinear interpolation and W‐cycle is used. Second order accuracy is obtained by the Chakravarthy‐Osher flux‐extrapolation technique, using the Roe‐Chakravarthy minmod limiter. In second order form, direct relaxation of the discrete equations is no longer possible due to the loss of positivity. A defect‐correction is used in order to solve the second order system.

Applicability of two k‐ω hybrid RANS/LES and a k‐ω RANS models is studied for simulation of round impinging jets at nozzle‐plate distance H/D=2 with Reynolds number 70000, H/D=2 with Reynolds number 5000 and H/D=10 with Reynolds number 5000 (D is the nozzle exit diameter). The aim is to verify two concepts of unified hybrid RANS/LES formulations, one of DES (Detached Eddy Simulation) type and one of LNS (Limited Number Scales) type in analysis of impinging jet flow and heat transfer. The grid resolution requirements are also discussed.

The simulations are performed with two k‐ω based hybrid RANS/LES models of very different nature, one of DES type and one of LNS type, and the RANS k‐ω model. For the lower Reynolds number (5000), also dynamic Smagorinsky LES is done. Both hybrid model formulations converge to the same RANS k‐ω model in the near‐wall region and have the same Smagorinsky limit on fine isotropic grids in the LES mode of the hybrid models.

With the hybrid RANS/LES models, improved fluid flow and heat transfer results are obtained compared to RANS, in the impact region and in the developing wall‐jet region. For accurate predictions at low nozzle‐plate distance, where the impact region is in the core of the jet, it is necessary to sufficiently resolve the formation and breakup of the near‐wall vortices in the jet impingement region and the developing wall‐jet region, as these determine largely the level of fluctuating velocity and the heat transfer. This requires high grid resolution for high Reynolds number, while the grid resolution requirements stay modest for low Reynolds number.

The paper demonstrates that two formulations of hybrid RANS/LES models of different nature, one of DES type and one of LES type, lead to equivalent results. Consistency has been guaranteed in the sense that the RANS limit of both models is the same and that the LES limit on fine, isotropic, grids is the same. In the intermediate range, however, the repartition into resolved and modelled fluctuations may differ considerably.

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.

The influence of computational aspects on simulation results is quantitatively investigated for the specific case of a turbulent piloted jet diffusion flame (Sandia Flame D). It is illustrated that, with a fixed turbulence and chemistry model, the results can heavily depend on the numerical aspects. The influence of inlet boundary conditions has already been discussed in an earlier paper. In this work, attention is focused onto the order of accuracy of the spatial discretization in the numerical scheme and onto the position of the outlet boundary. It is stressed that the purpose is not to judge the quality of the applied models, but to illustrate the possible impact of numerical influence factors. The conclusion is a warning message and a demonstration that all numerical aspects must be completely described when calculation results are presented.

In this study, Benchmark solutions are derived for the problem of two‐dimensional laminar flow of air in a square cavity which is heated on the left, cooled on the right and insulated on the top and bottom boundaries. The temperature differences between the hot and cold walls are large. Neither Boussinesq nor low‐Mach number approximations of the Navier‐Stokes equations are used. The ideal‐gas law is used and the viscosity is given by Sutherland's law. A constant Prandtl number is assumed. The computational method is completely described by Vierendeels et al. Grid converged results with an accuracy of 4 up to 5 digits are obtained for different Rayleigh numbers and temperature differences.

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The extended scheme is applied to the steady‐state heat transfer of axisymmetric turbulent jets, impinging onto a flat plate. Firstly, the low‐Reynolds version of the standard k‐ε model is employed. As is well known, the classical k‐ε turbulence model fails to predict the heat transfer of impinging jets adequately. A non‐linear k‐ε model, with improved ε‐equation, yields much better results. The numerical treatment of the higher order terms in this model is described. The effect on the heat transfer predictions of a variable turbulent Prandtl number is shown to be small. It is also verified that the energy equation can be simplified, without affecting the results. Results are presented for the flow field and the local Nusselt number profiles on the plate for impinging jets with different distances between the pipe exit and the flat plate.

Different methods for the determination of accurate values for the dissipation rate ϵ at the inlet boundary of a computational domain, are studied. With DNS data for a fully developed channel flow and pipe flow, it is shown that the method suggested by Rhee and Sung (2000), in which the k–ϵ turbulence model is used to compute both k and ϵ from a given velocity profile, is not reliable and can result in very poor results. The method is found to be extremely sensitive to the details of the imposed velocity profile. An alternative procedure is proposed, in which only the ϵ transport equation is employed, with given profiles for the mean velocity and the turbulence kinetic energy. This way, accurate and reliable profiles are obtained for ϵ. Another procedure, based on the turbulent mixing length, was suggested by Jones (1994). The problem. The problem is then shifted towards the determination of the mixing length at the inlet boundary of the computational domain. An expression for this mixing length is proposed in this paper, based on the mentioned DNS data. Finally, the method proposed by Rodi and Scheuerer (1985) is included for comparison reasons. The different procedures are first validated on the fully developed channel and pipe flow. Next, the turbulent flow over a backward‐facing step is considered. Finally, the influence of the inlet boundary condition for ϵ is illustrated in the application of a turbulent piloted jet diffusion flame.

To present conversion of the advection upwind splitting method (AUSM+) from the conventional density‐based and coupled formulation to the pressure‐based and segregated formulation.

The spatial discretization is done by a finite volume method. A collocated grid cell‐center formulation is used. The pressure‐correction procedure is set up in the usual way for a compressible flow problem. The conventional Rhie‐Chow interpolation methodology for the determination of the transporting velocity, and the conventional central interpolation for the pressure at the control volume faces, are replaced by AUSM+ definitions.

The AUSM+ flux definitions are spontaneously well suited for use in a collocated pressure‐correction formulation. The formulation does not require extensions to these flux definitions. As a consequence, the results of a density‐based fully coupled method, are identical to the results of a pressure‐based segregated formulation. The advantage of the pressure‐correction method with respect to the density‐based method, is the higher efficiency for low Mach number applications. The advantage of the AUSM+ flux definition for the transporting velocity with respect to the conventional Rhie‐Chow interpolation, is the improved accuracy in high Mach number flows. As a consequence, the combination of AUSM+ with a pressure‐correction method leads to an algorithm with improved performance for flows at all Mach numbers.

A new methodology, with obvious advantages, is composed by the combination of ingredients from an existing spatial discretization method (AUSM+) and an existing time stepping method (pressure‐correction).

This paper aims to provide improvements to the newest version of the k‐ ω turbulence model of Wilcox for convective heat transfer prediction in turbulent axisymmetric jets impinging onto a flat plate.

Improvements to the heat transfer prediction in the impingement zone are obtained using the stagnation flow parameter of Goldberg and the vortex stretching parameter of Wilcox. The third invariant of the strain rate tensor in the form of Shih et al. and the blending function of Menter are applied in order make negligible the influence of the impingement modifications in the benchmark flows for turbulence models. Further, it is demonstrated that for two‐dimensional jets impinging onto a flat plate the stagnation region Nusselt number predicted by the original k‐ ω model is in good agreement with direct numerical simulation (DNS) and experimental data. Also for two‐dimensional jets, the proposed modification is deactivated.

The proposed modification has been applied to improve the convective heat transfer predictions in the stagnation flow regions of axisymmetric jets impinging onto a flat plate with nozzle‐plate distances H/D = 2, 6, 10 and Reynolds numbers Re = 23,000 and 70,000. Comparison of the predicted and experimental mean and fluctuating velocity profiles is performed. The heat transfer rates along a flat plate are compared to experimental data. Significant improvements are obtained with respect to the original k‐ ω model.

The proposed modification is simple and can be added to the k‐ ω model without causing stability problems in the computations.

The purpose of this paper is to clarify the methodological logic of coproductive research approaches like action research, collaborative research, interactive research and participatory research in a way that can clarify its effectiveness and scientific qualities in high quality knowledge production, and show the way that it can be integrated with institutionalized textbook science.

The paper clarifies the character of coproduction as research methodology concept, the logic of coproductive research approaches, and its characteristics compared to quantitative and qualitative methodology. A model for characterizing research approaches from leading textbook social science is developed to specify the character of coproductive research approaches and support integration in mainstream research methodology discussions.

The paper develops a research methodology framework for coproductive logic and approaches to research, to support the integration of this type of approaches in mainstream research methodology.

The developed model of coproductive research approaches is not empirically described. Therefore, researchers are encouraged to test and further develop the model in relation to cases and designs of research projects.

The paper is helpful for guiding the design of coproductive research in practice, i.e., in research project development or in research methodology education.

The development of coproductive research approaches supports making science relevant and useful for solving pressing problems and improving social conditions. It also is enabling stakeholders to participate in research and development processes, thus the democratization of research and knowledge production.

The paper contributes to integration of the family of coproductive approaches in mainstream research methodology discussion through the development and elaboration of a framework for organizing the description and development of coproductive research approaches. The aim is that the framework is valuable for both academics, practitioners and students in designing coproductive research projects.