Sentence examples for closure relations to from inspiring English sources

Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows.

Recently, the authors have extended the validation of this set of closure relations to the "pseudo-homogeneous" flow regime, by comparing the numerical predictions to a comprehensive experimental dataset (gas holdup, bubble size distributions and local flow measurements).

Since it is not feasible to simulate an entire industrial-scale bubble column in full detail from first principles (direct numerical simulations), higher-level models rely on algebraic closure relations to account for the most important physical phenomena prevailing at the smallest length and time scales, while keeping computational demands low.

For further explanations about the underlying bio-medical processes and respective closure relations to (1) we refer to [9].

The field boundaries and different types of closure relations required to close the model are briefly discussed.

Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest.

The closure relation corresponding to these pairs is formulated in the following important corollary.

Two closure relations are needed to predict these flow rates: the first closure relation expresses that the volume of solid injected into the airlift remains constant; the second closure relation expresses a global balance between the difference of column height in the riser and the downcomer and the total pressure drop in the airlift.

The favorable comparisons and simplicity of the proposed closure relations are promising, aiming to practical application.

Special attention is paid to closure relations involving pressure terms at the gas liquid interface.

In this paper, the validation of this set of closure relations has been extended to the pseudo-homogeneous flow regime characterized by a wide spectrum of bubble sizes and typically associated with the large sparger openings used in industrial applications in large-scale bubble columns, thus establishing a first step towards the simulation of industrial-scale reactors.