Search results for: boussinesq

Authors: Qaisar Ali, Waqar A. Khan, Shafiq R. Qureshi

Abstract:

Heat transfer in Power Law Fluids across cylindrical surfaces has copious engineering applications. These applications comprises of areas such as underwater pollution, bio medical engineering, filtration systems, chemical, petroleum, polymer, food processing, recovery of geothermal energy, crude oil extraction, pharmaceutical and thermal energy storage. The quantum of research work with diversified conditions to study the effects of combined heat transfer and fluid flow across porous media has increased considerably over last few decades. The most non-Newtonian fluids of practical interest are highly viscous and therefore are often processed in the laminar flow regime. Several studies have been performed to investigate the effects of free and mixed convection in Newtonian fluids along vertical and horizontal cylinder embedded in a saturated porous medium, whereas very few analysis have been performed on Power law fluids along wedge. In this study, boundary layer analysis under the effects of radiation-mixed convection in power law fluids along vertical wedge in porous medium have been investigated using an implicit finite difference method (Keller box method). Steady, 2-D laminar flow has been considered under prescribed surface heat flux condition. Darcy, Boussinesq and Roseland approximations are assumed to be valid. Neglecting viscous dissipation effects and the radiate heat flux in the flow direction, the boundary layer equations governing mixed convection flow over a vertical wedge are transformed into dimensionless form. The single mathematical model represents the case for vertical wedge, cone and plate by introducing the geometry parameter. Both similar and Non- similar solutions have been obtained and results for Non similar case have been presented/ plotted. Effects of radiation parameter, variable heat flux parameter, wedge angle parameter ‘m’ and mixed convection parameter have been studied for both Newtonian and Non-Newtonian fluids. The results are also compared with the available data for the analysis of heat transfer in the prescribed range of parameters and found in good agreement. Results for the details of dimensionless local Nusselt number, temperature and velocity fields have also been presented for both Newtonian and Non-Newtonian fluids. Analysis of data revealed that as the radiation parameter or wedge angle is increased, the Nusselt number decreases whereas it increases with increase in the value of heat flux parameter at a given value of mixed convection parameter. Also, it is observed that as viscosity increases, the skin friction co-efficient increases which tends to reduce the velocity. Moreover, pseudo plastic fluids are more heat conductive than Newtonian and dilatant fluids respectively. All fluids behave identically in pure forced convection domain.

Keywords: porous medium, power law fluids, surface heat flux, vertical wedge

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Authors: Sagar Saroha, Sawan S. Sinha, Sunil Lakshmipathy

Abstract:

Reynolds averaged Navier-Stokes (RANS) model is the popular computational tool for prediction of turbulent flows. Being computationally less expensive as compared to direct numerical simulation (DNS), RANS has received wide acceptance in industry and research community as well. However, for high Reynolds number flows, the traditional RANS approach based on the Boussinesq hypothesis is incapacitated to capture all the essential flow characteristics, and thus, its performance is restricted in high Reynolds number flows of practical interest. RANS performance turns out to be inadequate in regimes like flow over curved surfaces, flows with rapid changes in the mean strain rate, duct flows involving secondary streamlines and three-dimensional separated flows. In the recent decade, partially averaged Navier-Stokes (PANS) methodology has gained acceptability among seamless bridging methods of turbulence- placed between DNS and RANS. PANS methodology, being a scale resolving bridging method, is inherently more suitable than RANS for simulating turbulent flows. The superior ability of PANS method has been demonstrated for some cases like swirling flows, high-speed mixing environment, and high Reynolds number turbulent flows. In our work, we intend to evaluate PANS in case of separated turbulent flows past bluff bodies -which is of broad aerodynamic research and industrial application. PANS equations, being derived from base RANS, continue to inherit the inadequacies from the parent RANS model based on linear eddy-viscosity model (LEVM) closure. To enhance PANS’ capabilities for simulating separated flows, the shortcomings of the LEVM closure need to be addressed. Inabilities of the LEVMs have inspired the development of non-linear eddy viscosity models (NLEVM). To explore the potential improvement in PANS performance, in our study we evaluate the PANS behavior in conjugation with NLEVM. Our work can be categorized into three significant steps: (i) Extraction of PANS version of NLEVM from RANS model, (ii) testing the model in the homogeneous turbulence environment and (iii) application and evaluation of the model in the canonical case of separated non-homogeneous flow field (flow past prismatic bodies and bodies of revolution at high Reynolds number). PANS version of NLEVM shall be derived and implemented in OpenFOAM -an open source solver. Homogeneous flows evaluation will comprise the study of the influence of the PANS’ filter-width control parameter on the turbulent stresses; the homogeneous analysis performed over typical velocity fields and asymptotic analysis of Reynolds stress tensor. Non-homogeneous flow case will include the study of mean integrated quantities and various instantaneous flow field features including wake structures. Performance of PANS + NLEVM shall be compared against the LEVM based PANS and LEVM based RANS. This assessment will contribute to significant improvement of the predictive ability of the computational fluid dynamics (CFD) tools in massively separated turbulent flows past bluff bodies.

Keywords: bridging methods of turbulence, high Re-CFD, non-linear PANS, separated turbulent flows

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