A. Goulas

Estimate of the truncation error of a finite volume discretisation of the Navier-Stokes equations on colocated grids

A methodology is proposed for the calculation of the truncation error of finite volume discretizations of the incompressible Navier–Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier–Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretizations of the incompressible Navier–Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure part of the mass fluxes is not dependent on the coefficients of the linearized momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two-dimensional flows, but extension to three-dimensional cases should not pose problems. Copyright

Efficient treatment of complex geometries for large eddy simulations of turbulent flows

Abstract Incompressible turbulent flow over a backward facing step at Reh=5100 is investigated by large eddy simulations (LES). The ratio of the oncoming boundary layer thickness δ to the step height h was set to 1.2. Additionally channel flows at various Reτ numbers are presented for the validation of the numerical code. The results are compared with existing DNS and experimental databases. The present study focuses on different procedures for LES of engineering problems in complex geometries using structured rectangular grids. Two different methods that are able to treat complex geometrical configurations are implemented, examined and compared; namely the domain decomposition approach based on Schur’s complement and the immersed boundary method. In the present study both methods make use of a fast direct Poisson’s pressure solver based on a heavily modified version of the public domain package FISHPAK . The latter was optimised and fully parallelised for shared memory architectures, for solutions on rectangular grids stretched in one or two directions. The resulting code reaches performances of 1.0 μs/node/iter, allowing low cost computations on grids of the order of million points. The main objective of the present study was to investigate the potential of different methods for LES in complex geometrical configurations like bluff body flows and wakes. One of the main findings is that careful selection of numerical methods and implementation techniques can lead to accurate and very efficient codes, where the geometric complexity does not lead to algorithmic or numerical complexity.

Transition on a flat plate with a semi-circular leading edge under uniform and positive shear free-stream flow

Abstract The effect of the free-stream velocity profile on the transition from laminar to turbulent flow on a flat plate was studied experimentally and numerically and it is presented in this paper. The flows investigated are based on the T3L test case of the ERCOFTAC Special Investigation Group for transition. According to this test case, the boundary layer development on a flat plate with a semi-circular leading edge is examined by means of transition due to separation, under various free-stream conditions concerning the turbulence intensity and velocity magnitude. In the present work, two free-stream velocity distributions were studied. The first was a uniform velocity one and the second, with a mean shear velocity profile with positive gradient, ∂ U / ∂ y=27.7 s −1 . Measurements using hot-wire anemometry were taken in two primary regions: far upstream of the flat plate to observe the velocity and turbulence distributions and near the flat plate to capture the boundary layer development and the transition phenomenon. The effect of the two free-stream velocity distributions was studied and it was shown that for both velocity distributions a recirculation region of the flow occurred near the flat plate wall that led to transition dominated by the boundary layer separation. For the positive velocity gradient the separation region was smaller compared to the case of uniform free-stream profile. Both cases were also studied computationally. Two widely used linear eddy-viscosity turbulence models, the k – e and the k – ω with specific low Reynolds formulations were applied and in addition, a non-linear eddy-viscosity based on the k – e model has been implemented. In general, all the k – e models gave satisfactory predictions for both flow cases regarding the predicted velocity distributions, while the k – ω model gave poor results. Concerning the longitudinal Reynolds stress distributions in the near-wall region, the non-linear k – e model gave the best predictions inside the separation zone but it over predicted the corresponding values beyond the reattachment point while beyond the separation the linear models predicted the longitudinal stresses in a more satisfactory way.

Finite volume adaptive solutions using SIMPLE as smoother

This paper describes a new multilevel procedure that can solve the discrete Navier-Stokes system arising from finite volume discretizations on composite grids, which may consist of more than one level. SIMPLE is used and tested as the smoother, but the multilevel procedure is such that it does not exclude the use of other smoothers. Local refinement is guided by a criterion based on an estimate of the truncation error. The numerical experiments presented test not only the behaviour of the multilevel algebraic solver, but also the efficiency of local refinement based on this particular criterion.

Numerical experiments on the efficiency of local grid refinement based on truncation error estimates

Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a coarser grid and applying the coarse grid discrete operator. The complication that high truncation error develops at grid level interfaces is also investigated and several treatments are tested.

CFD Modeling and LDA Measurements for the Air-Flow in an Aero Engine Front Bearing Chamber

The continuous development of aero engines toward lighter but yet more compact designs, without decreasing their efficiency, has led to gradually increasing demands on the lubrication system, such as the bearing chambers of an aero engine. For this reason, it is of particular importance to increase the level of understanding of the flow field inside the bearing chamber in order to optimize its design and improve its performance. The flow field inside a bearing chamber is complicated since there is a strong interaction between the sealing air-flow and the flow of lubrication oil, and both of them are affected by and interacting with the geometry of the chamber and the rotating shaft. In order to understand the flow field development and, as a next step, to optimize the aero engine bearing chamber performance, in relation to the lubrication and heat transfer capabilities, the behavior of this interaction must be investigated. In this work, an investigation of the air-flow field development inside the front bearing chamber of an aero engine is attempted. The front bearing chamber is divided into two separate sections. The flow from the first section passes through the bearing and the bearing holding structure to the second one where the vent and the scavenging system are located. The investigation was performed with the combined use of experimental measurements and computational fluid dynamics (CFD) modeling. The experimental measurements were carried out using a laser Doppler anemometry system in an experimental rig, which consists of a 1:1 model of the front bearing chamber of an aero engine. Tests were carried out at real operating conditions both for the air-flow and for the lubricant oil-flow and for a range of shaft rotating speeds. The CFD modeling was performed using a commercial CFD package. Particularly, the air-flow through the bearing itself was modeled, adopting a porous medium technique, the parameters of which were developed in conjunction with the experiments. A satisfactory quantitative agreement between the experimental measurements and the CFD computations was achieved. At the same time, the effect of the important parameters such as the air and oil mass flow, together with the shaft rotational speed, and the effect of the chamber geometry were identified. The conclusions can be exploited in future attempts in combination with the CFD model developed in order to optimize the efficiency of the lubrication and cooling system. The latter forms the main target of this work, which is the development of a useful engineering tool capable of predicting the flow field inside the aero engine bearing, which can be used subsequently for optimization purposes.

Changes in psychophysiological processing of vision in myasthenia gravis

OBJECTIVE To investigate the possibility of impaired central nervous system (CNS) cholinergic transmission in myasthenia gravis (MG), and the effect of eye movements and particularly of micromovements in the psychophysiology of vision. MATERIALS AND METHODS Fourteen patients with clinical manifestations of external ophthalmoplegia due to different causes (nine patients with myasthenia gravis and five with ocular myopathy) were examined. Simultaneous recording of eye movements (optical method) and pattern reversal-visual evoked potentials (PR-VEPs) were performed. RESULTS Eye micromovements during fixation were impaired in both groups. A statistically significant difference (P < 0.01) was found in the amplitude of P100 of PR-VEPs before and after treatment in MG patients, and also between normal controls and MG patients before (P < 0.001) and after treatment (P < 0.01). P100 latency of the PR-VEPs in MG patients before and after treatment was delayed compared to normal controls, while there were no differences between ocular myopathy patients and normal controls. CONCLUSION The eye movement impairment observed in MG patients is not sufficient to explain abnormal PR-VEPs detected in these patients. These results provide neurophysiological evidence of impaired cholinergic transmission in the central nervous system in patients with MG and suggest that PR-VEPs offer an easily applicable non-invasive method to study the central effects of MG.

Modelling Operation of System of Recuperative Heat Exchangers for Aero Engine with Combined Use of Porosity Model and Thermo-Mechanical Model

Abstract The present work describes an effort to model the operation of a system of recuperative heat exchangers of an aero engine for real engine operating conditions. The modelling was performed with the combined use of a porous medium model and a thermo mechanical model. The porous medium model was taking into account the heat transfer and pressure loss behaviour of the heat exchangers while the thermo mechanical one was used for the calculation of the wall temperature distribution of the elliptic tubes of the heat exchangers. As it is presented, the combined use of these models can provide a useful tool which can help in the prediction of the macroscopic behaviour of the system of recuperative heat exchangers of the aero engine which can be used for optimization purposes and numerical studies.

Large-amplitude interfacial waves on a linear shear flow in the presence of a current

The properties of two-dimensional steady periodic interfacial gravity waves between two fluids in relative motion and of constant vorticities and finite depths are investigated analytically and numerically. Particular attention is given to the effect of uniform vorticity, in the presence of a current velocity, on the two factors (identified in the literature as dynamical and geometrical limits) which limit the existence of steady gravity wave solutions. The dynamical limit to the existence of steady solutions is found to be significantly influenced by the uniform vorticity of the lower fluid. In particular, the effect of non-zero vorticity is qualitatively different between a very shallow and a relatively deep lower fluid

The effect of negative shear on the transitional separated flow around a semi-circular leading edge

Abstract The effect of a negative free-stream mean-shear velocity distribution on the boundary layer development on a flat plate with a semi-circular leading edge is studied experimentally and computationally. The geometry is the same as in the T3L test case of the ERCOFTAC Special Interest Group on Transition. The existence of a negative shear is related to the transition of the boundary layer from laminar to turbulent through separation. The flow investigated here has the same general characteristics as the one presented in a recent work by the authors, Palikaras et al. [Int. J. Heat Fluid Flow 23 (2002) 455–470], where the boundary layer development has been studied under free-stream conditions of uniform and positive mean-shear velocity distributions. The negative shear flow in the core region of the wind tunnel has a value ∂ U / ∂ y=−27.7 s−1, which is the opposite to the case examined by Palikaras et al. [Int. J. Heat Fluid Flow 23 (2002) 455–470]. In the first part of the paper, a detailed description of the flow is given. The measured quantities are presented, discussed and compared with the computational analysis in order to obtain a complete picture of the investigated flow. For the computations, the non-linear k–e model of Craft et al. [Int. J. Heat Fluid Flow 17 (1996) 108–115] is used, and satisfactory predictions are reported. In the second part, a detailed comparison of the results with the cases of uniform and positive mean-shear velocity inlet distribution is carried out. In the case of negative mean velocity the separated boundary layer leads to a larger reverse flow region than the two other cases. A relation is observed between the location of the stagnation point at the leading edge and the presence or absence of shear. When mean shear is present, depending on the sign, there is a movement of the stagnation point away from the symmetry line of the flat plate and it is believed that this is the driving mechanism that affects the boundary layer development and the longitudinal size of the reverse flow region. This remark is supported by the observation that for all the three cases studied, the longitudinal RMS distribution above the reverse flow region and in the free-stream region has the same values.