A Modeling of Toms Effect Based on the Discrete Element Model

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A model to simulate the drag reductoin by dilute addition of polymer or surfactant (Toms effect) is proposed based on the discrete element model. The dimension of the discrete element, which represents the polymer or the rod-like micelle, is very small compared to that of the velocity fluctuation of the fluid. So it is assumed that the element is in equilibrium state in the fluid and turns to the direction of an eigenvector of the velocity gradient tensor. And the macroscopic effect of the discrete elements is modeled as the stress assuming the elements are independent each other. Direct numerical simulations are carried out with this new model using the rigid dumbbell element as a discrete element model and it is shown that the drag reduction up to 37% drag reduction rate is reproduced. In addition the followings are indicated as concluding remarks. (1)The drag reduction can be reproduced without assuming the macrostructures formed as the network of elongated polymers or rod-like micelles. (2)The drag reduction and the stress deficit can be reproduced without the elasticity.In addition study, new character is added on the model, say, the dumbbell element which simulate a polymer can be cut by the stretching force in the fluid. Simulations of 2D channel flows (Re_τ=120-600) are carried out and the drag reduction up to 50% drag reduction rate is reproduced by the modified model.