A Simplified CFD Model With Multi-Periodic Boundary Conditions for Cross Wavy Channels

2011 ◽  
Author(s):  
L. X. Du ◽  
M. Zeng ◽  
Q. W. Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Flow Direction ◽  
Wave Length ◽  
Three Dimensional ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
The Cross ◽  
Wavy Channels

The compact and efficient primary surface heat exchangers are often used as recuperators in microturbine regenerative cycle systems. In the present study, the flow and the heat transfer performance of the cross wavy (CW) ducts have been simulated by three-dimensional models. The hydrodynamic diameters of the models are 1.689mm. Navier-Stokes and energy equations are solved by COMSOL3.5. Because one single wavy cell will overlap more than one adjacent channel, multi-periodic boundary conditions are especially adopted to simplify the calculations. Multi-periodic boundary conditions have been proved to have more reasonable flow field and heat transfer coefficient compared with the literature results. A dimensionless parameter L/A (wave length L, internal height of the corrugation in flow direction A) is defined as the optimization target. The numerical results indicated that when L/A = 6, the CW channel has the best comprehensive performance in all the cases. The comprehensive performances of the CW ducts are evaluated by the j/f (heat transfer factor j and friction factor f). The flow and heat transfer characteristics are much more complex in the cross wavy channels, especially when L/A is small.

Transient Heat Transfer of a Hollow Cylinder Subjected to Periodic Boundary Conditions

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Yujia Sun ◽  
Xiaobing Zhang
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Hollow Cylinder ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Transient Heat Transfer ◽  
Maximum Temperature ◽  
Water Cooling ◽  
Chromium Plating ◽  
Inner Surface

The purpose of this paper is to study the transient temperature responses of a hollow cylinder subjected to periodic boundary conditions, which comprises with a short heating period (a few milliseconds) and a relative long cooling period (a few seconds). During the heating process, the inner surface is under complex convection heat transfer condition, which is not so easy to approximate. This paper first calculated the gas temperature history and the convective heat transfer coefficient history between the gas flow and the inner surface and then they were applied to the inner surface as boundary conditions. Finite element analysis was used to solve the transient heat transfer equations of the hollow cylinder. Results show that the inner surface is under strong thermal impact and large temperature gradient occurs in the region adjacent to the inner surface. Sometimes chromium plating and water cooling are used to relief the thermal shock of a tube under such thermal conditions. The effects of these methods are analyzed, and it indicates that the chromium plating can reduce the maximum temperature of the inner surface for the first cycle during periodic heating and the water cooling method can reduce the growth trend of the maximum temperature for sustained conditions. We also investigate the effects of different parameters on the maximum temperature of the inner surface, like chromium thickness, water velocity, channel diameter, and number of cooling channels.

scholarly journals Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions

2013 ◽  
Vol 45 (3) ◽  
pp. 742-772
Author(s):  
G. N. Milstein ◽  
M. V. Tretyakov
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Weak Sense ◽  
Periodic Boundary Conditions ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Probabilistic Nature

We propose and study a number of layer methods for Navier‒Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic.

scholarly journals Limits of the Stokes and Navier–Stokes equations in a punctured periodic domain

2019 ◽  
Vol 18 (02) ◽  
pp. 211-235
Author(s):  
Michel Chipot ◽  
Jérôme Droniou ◽  
Gabriela Planas ◽  
James C. Robinson ◽  
Wei Xue
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Periodic Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Periodic Domain ◽  
Navier Stokes Equations ◽  
Forcing Function ◽  
Connected Set

We treat three problems on a two-dimensional “punctured periodic domain”: we take [Formula: see text], where [Formula: see text] and [Formula: see text] is the closure of an open connected set that is star-shaped with respect to [Formula: see text] and has a [Formula: see text] boundary. We impose periodic boundary conditions on the boundary of [Formula: see text], and Dirichlet boundary conditions on [Formula: see text]. In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent Navier–Stokes equations, all with a fixed forcing function [Formula: see text], and examine the behavior of solutions as [Formula: see text]. In all three cases we show convergence of the solutions to those of the limiting problem, i.e. the problem posed on all of [Formula: see text] with periodic boundary conditions.

scholarly journals Computation of Flutter of Turbomachinery Cascades Using a Parallel Unsteady Navier-Stokes Code

1998 ◽  
Author(s):  
Shanhong Ji ◽  
Feng Liu
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Unsteady Flows ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Multiple Passage ◽  
Parallel Code

A quasi-three-dimensional multigrid Navier-Stokes solver on single and multiple passage domains is presented for solving unsteady flows around oscillating turbine and compressor blades. The conventional “direct store” method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the Message Passing Interface (MPI) standard is developed for multiple passage computations. In the parallel multiple passage computations, the phase-shifted periodic boundary condition is converted to simple in-phase periodic condition. Euler and Navier-Stokes solutions are obtained for unsteady flows through an oscillating turbine cascade blade row with both the sequential and the parallel code. It is found that the parallel code offers almost linear speedup with multiple CPUs. In addition, significant improvement is achieved in convergence of the computation to a periodic unsteady state in the parallel multiple passage computations due to the use of in-phase periodic boundary conditions as compared to that in the single passage computations with phase-lagged periodic boundary conditions via the “direct store” method. The parallel Navier-Stokes code is also used to calculate the flow through an oscillating compressor cascade. Results are compared with experimental data and computations by other authors.

Sign in / Sign up

Export Citation Format

Share Document