Finite point based numerical study on the unsteady laminar wake behind square cylinders

Abstract

PurposeThe purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.Design/methodology/approachThe numerical method that has been developed is based on a finite point formulation characterised by its weak connectivity requirements. This formulation allows for a patched unstructured approach to computational domain modelling that is of interest for industrial applications. Time evolution of pressure is computed by using a pseudo‐compressibility relaxation model that is based on physical considerations.FindingsThis model is characterised by the fact that no sub‐iterations on a numerical pseudo‐time are required so that computational efficiency is increased. Algorithm stability requires the use of second and fourth order artificial viscosity operators that effectively change the order of the equations. A discussion is included regarding the boundary conditions for these operators that do not influence vortex shedding behaviour.Research limitations/implicationsBearing in mind the industrial drive (MEMS design) that the authors have in mind, solver validation has been addressed at two levels: global coefficients (lift, drag and Strouhal number) were compared with those published in the specialised literature, while local velocity and rms profiles were compared with those obtained after performing a specific low velocity wind tunnel testing campaign (Reynolds numbers in the range from 110 to 268).Practical implicationsA sensitivity analysis of the results obtained is presented and it shows that the solver numerical robustness makes it amenable for project oriented applications.Originality/valueThe formulation being presented is competitive and could be considered as a potential alternative to other approaches.

Laminar heat transfer enhancement downstream of a backward facing step by using a pulsating flow

“…In particular, we compared our computed global flow parameters (drag, lift and Strouhal number) with those reported in the literature [32]. Also, we performed a dedicated experimental campaign in a low Reynolds number wind tunnel to validate solver results with regard to time-averaged local flow variables (velocity profiles) and rms values in the unsteady wake behind a square cylinder [33].…”

“…Regarding spatial discretisation, we use the Finite Point formulation developed by Mendez and Velazquez [32,33] whose main features are: Spatial derivatives are computed by using a least squares approximation in a cloud of points. Second order Taylor polynomials are used as the approximating functions…”

Coupling Between Thermal Oscillations in the Surface of a Micro-Cylinder and Vortex Shedding

“…We follow a finite point approach, similar to the one presented in Méndez and Velazquez [15,16] for incompressible flows, where local functional approximations oí the variables are second-order Taylor polynomials:…”

“…Sensitivity of the results with regard to time step is presented in Table 3. The criterion to make a fair comparison between cases has been to use a constant valué of £ 2p , S,4 P , S,4u, an d ^4TÍ see definition (16). Baseline case used for comparison has been case 11.…”

A method to generate computationally efficient reduced order models

“…In addition, in order to avoid numerical instabilities, four stabilizing terms are added in the left hand sides Eqs. (5)- (8) [20]. Each CFD run, to obtain each steady state, typically (depending on the flow parameters) requires a CPU time of the order of 6 h on a desktop PC.…”