Propagation of uncertainty in a rotating pipe mechanism to generate an impinging swirling jet flow for heat transfer from a flat plate

In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for uncertainty quantification in the computational heat transfer by forced convection is applied to the two-step simulation of the mechanical design of a swirling jet flow generated by a rotating pipe (Simulation 1) impinging on a flat plate (Simulation 2). This is the first probabilistic uncertainty analysis on computational heat transfer by impinging jets in the literature. The conclusion drawn from the analysis of this frequent engineering application is that the simulated system does not exhibit a significant sensitivity to stochastic variations of model input parameters, over the tested uncertainty ranges. Additionally, a set of non-linear regression models for the stochastic velocity and turbulent profiles for the pipe nozzle are created and tested, since impinging jets for heat transfer at Reynolds number of Re = 23000 are very frequent in the literature, but stochastic inlet conditions have never been provided. Numerical results demonstrate a negligible difference in the predicted convective heat transfer with respect to the use of the profiles simulated via CFD. These suggested surrogate models can be directly embedded onto other engineering applications (e.g. arrays of jets, jet flows impinging on plates with different shapes, inlet piping in combustion, chemical mixing, etc.) in which a realistic swirling flow under uncertainty can be of interest

Meshless Local Petrov-Galerkin Simulation of Buoyancy-Driven Fluid Flow and Heat Transfer in a Cavity with Wavy Side Walls

As some new applications of the meshless local Petrov-Galerkin method (MLPG) with unity as the test function, a number of buoyancy-driven fluid flow natural convection heat transfer problems in cavities with differentially-heated wavy side walls were analyzed. Cavities with a single wavy wall on one side as well as two wavy walls erected on both sides were considered. For the cases of the double wavy walls, two different configurations in terms of the two walls facing each other on the two sides of the cavities symmetrically or non-symmetrically were investigated. All the simulations performed in this work were based on the stream function-vorticity formulation. The work of this study is focused on the cavities filled with incompressible and laminar flow of air with a Prandtl number of 0.71. The moving least-squares interpolations of the field variables were employed in these MLPG numerical calculations. Appropriate parametric and characteristic studies were carried out on all the wavy wall-cavities considered. The analysis focused on the effects of the dimensionless amplitudes, wall's number of undulations, and different Rayleigh numbers on the fluid flow and natural convection heat transfer within the considered enclosures. The results of the MLPG-new applications show smooth Nusselt number distributions and the occurrences of the distributions maxima and minima in the close proximity of the crests and troughs, respectively, as they were supposed to. The logical behavior of the streamlines and the isotherms affected by the appropriate parameters and geometrical characters prove the total validity and feasibility of the code for the new considered applications

Meshless Local Petrov-Galerkin Method with Unity Test Function for Non-Isothermal Fluid Flow

The meshless local Petrov-Galerkin (MLPG) method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for different test cases. This present study considers the implementation of the method on a non-isothermal lid-driven cavity flow, the lid-driven cavity flow with an inlet and outlet, and also on the non-isothermal flow over an obstacle. Nonuniform point distribution is employed for all the test cases for the numerical simulations. The flow streamlines for each test case is depicted. The L2-norm of the error as a function of the size of the control volumes is presented for moderate Reynolds numbers and the rate of convergence of the method is established. Close agreements of the obtained results with those of the other numerical techniques show that the proposed method is applicable in solving a variety of non-isothermal fluid flow problems

MLPG Application of Nanofluid Flow Mixed Convection Heat Transfer in a Wavy Wall Cavity

Procuring a numerical solution through an application of the meshless local Petrov-Galerkin method (MLPG) on the fluid flow and mixed convection in a complex geometry cavity filled with a nanofluid is the scope of the present study. The cavity considered is a square enclosure having a lower temperature sliding lid at the top, a differentially higher temperature wavy wall at the bottom, and two thermally insulated walls on the sides. The nanofluid medium used is a water-based nanofluid, Al2O3-water with various volume fractions of its solid. To carry out the numerical simulations, the developed governing equations are determined in terms of the stream function-vorticity formulation. The weighting function in the weak formulation of the governing equations is taken as unity, and the field variables are approximated using the MLS interpolation. Capability as well as adaptability of the proposed meshless technique is ascertained by close comparisons of the illustrated results obtained through the mesh-free method with those obtained through a traditional method already existing in the literature. Effective viscosity and thermal conductivity of the solid-liquid mixture are determined using the Brinkman and Maxwell models, respectively. A parametric study conducted through the present method to gain insight into the nanofluid convective heat transfer performance shows rational and deducible results. The study reveals that, distributions of the local Nusselt number along the wavy hot wall closely follow the pattern of the wall's geometry for different Richardson numbers and the nanoparticles volume fractions considered

Inclination angle implications for fluid flow and mixed convection in complex geometry enclosure-meshless numerical analyses

The meshless local Petrov-Galerkin (MLPG) method is extended to analyze the mixed convection and fluid flow in an inclined two-dimensional lid-driven cavity. The enclosure considered comprises two insulated vertical walls and a wavy bottom wall which is subjected to a higher constant temperature than its top counterpart, the sliding lid. For the proposed scheme, the stream function formulation with a weighting function of unity is employed. The simulation results reveal that the local Nusselt number increases with a clockwise increase in the inclination angle. Also, a decrease in the aspect ratio results in an increase in the hot wavy wall average Nusselt number