Modeling of turbulence-interface interaction in two-fluid systems
Final Report Abstract
The joint reserach project concerned development of a physical model for the interactions between non-broken interface and turbulence and development of new numerical methods appropriate for this study. We considered an intermittency function γ denoting the probability of finding the water phase at a given point of the flow and at a given time. The function γ is defined as the ensemble average of the Heaviside function γ(x, t) = χ(x, t) where χ(x, t) = 1 if the point x is in the water at time t and χ(x, t) = 0 otherwise, cf. Fig. 1a. The region were 0 < γ < 1 is called the ”intermittency region” or the ”surface layer”. Within the research project, a priori tests were first performed in order to check the predictions of the model for turbulence-interface interactions in the intermittency zone previously proposed. Moreover, models for the unclosed contraction term in the γ equation for the Favre-averaged quantities was proposed and compared with results of a priori tests. Improvements of the original model equation were proposed. Another direction of study was connected with the symmetry method, which provides restrictions on the proposed form of the model. It was shown that the model for the γ equation is invariant under classical symmetry groups of Navier-Stokes equations for two fluids. Apart from this, within the present project it was shown that when a probabilistc description of turbulent flow in terms of probability density functions (pdf’s) is used, additional symmetries arise. These new symmetries are connected with the intermittent laminar-turbulent or two-phase flows. As far as the numerical issues are concerned, the solution and discretization of the intermittency region evolution equation in the framework of the conservative level-set method was investigated. We first employed numerical schemes proposed in the literature and found that when the large number of re-initialization steps is used during reconstruction of the intermittency region evolution, the strong artificial deformations of the interface are induced. These artifical deformations occur due to the accumulation of errors, which are a result of erroneous discretization of the counteracting diffusive and compressive terms in γ re-initialization equation. We have put forward a new re-initialization method based on the stationary solution of the intermittency region evolution equation. This approach allows for the first time to conjoin the conservative level-set function γ and the related signed distance function ψ0 (γ) in the consistent re-initialization procedure. Moreover, consistently with the discretization of the γ re-initialization equation, the procedure for computation of higher-order γ spatial derivatives is proposed. The latter approach allows to achieve the second order convergence rate during computations of the interface curvature.
Publications
- (2013) Modelling of turbulence-interface interactions by means of the intermittency region approach: a priori study, Proc. 8th Int. Conf. Multiphase Flow, May, Jeju, Korea
Waclawczyk M., Waclawczyk T.
- (2014) Modelling of turbulence-interface interactions in stratified two-phase flows, Journal of Physics: Conference Series 530, 012050
Waclawczyk, T., Waclawczyk, M. and Kraheberger, S. V.
(See online at https://doi.org/10.1088/1742-6596/530/1/012050) - (2014) Statistical symmetries of the Lundgren-Monin-Novikov hierarchy, Phys. Rev. E 90, 013022
Waclawczyk M., Staffolani N., Oberlack, M., Rosteck, A., Wilczek, M., Friedrich R.
(See online at https://doi.org/10.1103/PhysRevE.90.013022) - (2014) Towards statistical modeling of turbulent separated two-phase flows with the diffuse interface method, Proc. 2nd Int. Conf. Num. Meth. Multiphase Flow, Darmstadt, Germany
Waclawczyk, T., Waclawczyk, M.
- (2015) A priori study for the modelling of velocity-interface correlations in the stratified air-water flows, Int. J. Heat and Fluid Flow, 52, 40-49
Waclawczyk M., Waclawczyk T.
(See online at https://doi.org/10.1016/j.ijheatfluidflow.2014.11.004)
