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This thesis is an attempt to assess some of the effects that electroquasistatic body forces exert on turbulent internally forced convective flows. In order to do that, a stochastic turbulence model is employed, namely, the One-Dimensional Turbulence (ODT) model.
The reduced dimensionality of ODT demands a reduction of the Navier-Stokes equations (and in this case, also the Maxwell equations), into a 1-D system. This is done by performing an asymptotic analysis in terms of the nondimensional numbers of the flow. Also, a validation step due to the relative novel character of the cylindrical ODT formulation is done for an incompressible and constant properties flow regime and a variable density flow regime. The validation is presented for both the temporal (T-ODT) and a novel spatial (S-ODT) formulation in both planar and cylindrical geometries. Results in the constant property case show that wall normal (and radial) profiles, in both the T-ODT and S-ODT formulations, show good agreement with each other and to the data of Direct Numerical Simulations (DNSs). For the evaluated variable density heated pipe flow, gradients at the wall can be better reproduced with S-ODT.
After validating the model, ODT is applied first into a planar configuration which emulates the flow in a wire-plate Electrostatic Precipitator (ESP). For this flow, the additional input energy due to the electroquasistatic body force has an effect on the modification of the bulk velocity, and subsequently, the skin friction coefficient. Some qualitative DNS trends are confirmed with ODT, such as the localized increase of the Reynolds stress, as a consequence of increased eddy activity close to the discharge electrodes. Next, the results of ODT simulations in a cylindrical wire-tube ESP are presented. Here, ODT results are compared to experimental results. ODT results for global integral quantities such as the streamwise pressure gradient and the Nusselt number enhancement ratio are able to match in a reasonable way the experimental results. The competing relevance between the EHD contribution to turbulence by momentum, and by affecting the temperature and density due to the Joule heating effect is also analyzed, showing the leading order relevance of the former one. Specifically for the Nusselt number results, the sensitivity of the EHD flow to transition effects is shown to be very significant.
This thesis may open the door to a vast new field of phenomena which can not only serve for the further validation of the ODT model against DNSs or experiments, but also for the real use of ODT in applications which are so far inaccessible for traditional DNSs.
The continual optimization process for more efficiency of industrial flows has raised the need for providing deeper understanding of turbulence. These details can be provided by direct numerical simulation (DNS), which is impossible for most flows with current computers. Therefore, progress in optimizing Reynolds averaged Navier-Stokes (RANS) and large eddy simulation (LES) modeling strategies will need to continue. Another ansatz is the reduction to 2D or 1D models to reduce the numerical cost.
One dimensional turbulence (ODT) as presented by A. R. Kerstein is a new modeling strategy that reduces the 3D simulation to a 1D line of sight through the flow region. Due to the higher resolution afforded by the 1D model, it is possible to simulate even the smallest scales and to provide insight into turbulence statistics.
To assess the advantages and disadvantages of the model, ODT has to be validated against several flows. Within this thesis, ODT is validated against the channel flow, the passive scalar transport and the channel flow with a fluctuating pressure gradient. These flows are simplified test cases for the phenomena present in single-phase industrial flows. ODT produces meaningful results for friction Reynolds numbers up to Reτ = 6·10⁵ and for Prandtl numbers from Pr = 0.025 to 50. Statistics of the wall shear stress are presented and the influence of pressure fluctuations is discussed.
Based on these channel results, the non-breaking and breaking jet are simulated. While the former is a simplified case of a free-surface flow, the latter is of primary interest for spray formation and fuel injection. Detailed statistics of the TKE budgets and the breakup are presented. As the last case, the cloud top of a stratocumulus-topped boundary layer (STBL) was simulated. The case combines the interaction of an active and a passive scalar. It further combines the simulation of a stable and an unstable stratified region that suppresses and enhances turbulence respectively. The simulations reproduce the entrainment velocity and generate comparable mean and flux profiles compared to DNSs.