Identifier: TDX:275
Authors: Fabregat Tomàs, Alexandre
Abstract:
The main goal of this work is to study the turbulent heat transfer in a developed channel flow using Direct Numerical Simulations (DNS). These simulations solve explicitly all the scales present in the turbulent flow so, even for moderate Reynolds numbers, the discretization grids need to be fine enough to capture the smallest structures of the flow and, consequently, DNS demands large computational resources. The flow, driven by a mean constant pressure gradient in the streamwise direction, is confined between two smooth, parallel and infinite walls separated a distance 2d.<br/>The turbulent heat transport is studied for three different flow configurations.<br/>Some of them are used as benchmark results for this work. The three cases reported can be summarized as:<br/>· case A: Scalar plume from a line source in a horizontal channel.<br/>· case B:Mixed convection with the gravity vector aligned with the streamwise direction (vertical channel).<br/>· case C: Buoyant plume from a line source in a horizontal channel.<br/>In addition, preliminary results for a turbulent reacting flow in a fully developed channel are also presented.<br/>In the case B heat flux results from a temperature difference between the channel walls. The gravity vector is aligned with the streamwise direction and the Grashof, Reynolds and Prandtl numbers are Gr = 9.6 · 106, Ret = 150 and Pr = 0.71 respectively. Close to the hot wall, buoyancy acts aligned to the flow direction imposed by the mean pressure gradient so velocities are generally increased in comparison with a purely forced convection flow. Oppositely, near the cold wall, buoyancy is opposed to the flow and consequently velocities are decreased.<br/>Cases A and C are similar because in both cases a hot fluid is released within a cold background flow through a line source vertically centered in the wall-normal direction located at the inlet. The height of the source is 0.054d. The injected hot fluid disperses forming a hot plume that is convected downstream between the two adiabatic walls of the channel.<br/>The difference between cases A and C lies in the fact that for case A heat and momentum are decoupled and temperature acts as an scalar. Advection and diffusion are the only phenomena responsible for the evolution of the plume. On the other hand, in case C, buoyancy couples heat and momentum and, consequently, the plume floats drifting upward as it advances in the channel due to its lower density. In case C, the streamwise direction is not homogenous because of the coupling between heat and momentum. To guarantee developed conditions at the inlet of the channel it has been necessary to attach a buffer domain just before the computational domain. In this buffer domain, the momentum transport equations for a fully developed channel are solved with the same resolution used in the main domain.<br/>The results of cases A and B have been used to validate the 3DINAMICS CFD code by comparison with data reported in the literature. This code is written in FORTRAN 90 and parallelized using the Message Passing Interface (MPI-CH<br/>library). It uses the second order in time Crank-Nicholson scheme to integrate numerically the transport equations which are discretized spatially using the centered second-order finite volume approach.<br/>The analysis of averaged turbulent quantities and the contributions of the different terms of the time-averaged transport equations is used to show how buoyancy affects the turbulent transport of momentum and heat along the channel.<br/>Finally, following a similar configuration than that of case A, a chemical reactant<br/>A released through line source reacts with a background reactant B following a second order chemical reaction with Damkh¨oler number of 1. Preliminary results for turbulent species transport are also included in this work.<br/>Special attention have been devoted to the discretization of the advective terms to avoid non-realistic values of the variables because of the non-linearities of the transport equations. The conservative non-reflecting boundary conditions have been implemented at the outlet to simulate the convected outflow when the streamwise direction can not be considered homogeneous, as in case C. For homogeneous directions, periodic boundary conditions have been used.<br/>Large grid resolutions (up to 8 million grid nodes for case C including the buffer region) demand important computational resources. A parallel Multigrid solver has substituted the previous conjugate gradient method to solve the Poisson equation in the pressure calculation. This step was the most expensive in terms of CPU costs. The Multigrid method efficiency has been compared with two different versions of the conjugate gradient approach and it has been demonstrated that this method is the most efficient in terms of CPU time although the current algorithmcan be improved to enhance the scalability inmultiprocessor computers.
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