On the Implementation of Stream-Wise Periodic Boundary Conditions

Abstract

Fully-developed periodic boundary conditions have frequently been employed to perform calculations on the performance of typical elements of heat exchangers. Many such calculations have been achieved by transforming the equations of motion to obtain a new set of state variables which are cyclic in the stream-wise direction. In others, primitive variables, based on substitution schemes are employed. In this paper; a review of existing procedures is provided, and a new method is proposed. The method is based on the use of primitive variables with periodic boundary conditions combined with the use of slip values. Either pressure difference or mass flow rate may be prescribed, and both constant wall temperature and constant heat flux wall conditions may be considered. The example of an offset-fin plate-fin heat exchanger is used to illustrate the application of the procedure. The scope and limitations of the method are discussed in detail, and the mathematical basis by which the method may be extended to the consideration of problems involving mass transfer, with associated continuity, momentum, and species source/sinks is proposed. INTRODUCTIONIn the application of computational fluid dynamics to heat exchanger design, it has long been recognized that much computational effort may be spared by considering elements deep within the design where the flow is 'fully-developed'; for example; Thom and Alpelt [1], LeFeuvre [2], and Massey [3] considered fully-developed flow in tube banks assuming a cyclical 2-D stream function/vorticity formulation. In [2,3] temperature was also solved-for.More recently, the equations of motion are usually solved in terms of primitive variables, for which the steady-state form is typically written, subject to certain simplifications, as:

A Fundamental Investigation of Gas/Solid Heat and Mass Transfer in Structured Catalysts Based on Periodic Open Cellular Structures (POCS)

“…POCS fluid dynamic behavior is investigated in the fully developed regime, neglecting any influences due to entrance effects and lateral constraints. To describe and analyze the fully developed regime in POCS, periodic boundary conditions are implemented for all the relevant variables. ,, Under fully developed flow conditions, the physical properties of interest (i.e., fluid specific flow rate, pressure, composition, and temperature) are reduced to periodic functions in the streamwise and transverse directions. Details on the implementation of periodic boundary conditions for compressible flows in the three-dimensional space are reported in the Supporting Information, Section 1.3.…”