scholarly journals Mass balance errors when solving the convective form of the transport equation in transient flow problems

2004 ◽  
Vol 40 (5) ◽  
Author(s):  
Maarten W. Saaltink ◽  
Jesús Carrera ◽  
Sebastià Olivella
Keyword(s):  
Transport Equation ◽  
Mass Balance ◽  
Transient Flow ◽  
Flow Problems

A New Formulation for Computational Fluid Dynamics

1979 ◽  
Vol 101 (4) ◽  
pp. 453-460
Author(s):  
D. B. Reed ◽  
W. L. Oberkampf
Keyword(s):  
Fluid Dynamics ◽  
Boundary Conditions ◽  
Transport Equation ◽  
Mesh Size ◽  
Channel Length ◽  
Test Case ◽  
Parallel Plates ◽  
Flow Problems ◽  
Vector Quantity ◽  
New Formulation

A new vector quantity in fluid dynamics is defined and a vector transport equation for the quantity is derived. The new vector quantity is defined as the curl of the vorticity and is referred to as the angular vorticity. The transport equation for the new quantity is derived by taking the curl of the vorticity transport equation. The new transport equation combined with Poisson type velocity equations comprises the new angular vorticity-velocity formulation. The major advantage of the new formulaton is that computational boundary conditions for through-flow problems may be significantly relaxed. Boundary conditions for the newly defined variable are derived. A simple test case of laminar incompressible planar flow between parallel plates was executed to determine if the new formulation would produce results comparable to previous solutions. Numerical experiments were conducted using channel length, mesh size, and Reynolds number as parameters. The results are compared to values obtained by other investigators. The results show that the angular vorticity formulation is a feasible method for solution of fluid flow problems where fully developed flow is not attained.

scholarly journals Computational flow analysis of the washout of an aortic valve by means of Eulerian transport equation

2019 ◽  
Vol 5 (1) ◽  
pp. 123-126
Author(s):  
Michael Stiehm ◽  
Finja Borowski ◽  
Sebastian Kaule ◽  
Robert Ott ◽  
Sylvia Pfensig ◽  
...  
Keyword(s):  
Aortic Valve ◽  
Flow Field ◽  
Transport Equation ◽  
Residence Time ◽  
Transient Flow ◽  
Numerical Study ◽  
Main Flow ◽  
Elastic Behavior ◽  
Time Step ◽  
Valve Thrombosis

AbstractAlthough the development of the transcatheter aortic valve (TAV) has saved many lives of inoperable patients and has a very good clinical outcome, concerns about valve thrombosis are increasing. Due to the potential risk of late clinically relevant events, the US Food and Drug Administration (FDA) suggests a careful systematic investigation of thrombosis and reduced leaflet motion related to hemodynamic changes induced by TAV implantation. Furthermore, recently published position papers of the ISO working group address numerical and experimental flow field assessment of TAV. In particular, pathologically high shear rates and a reduced washout of the sinuses may increase the risk of valve thrombosis and should therefore be investigated. By means of fluid-structure interaction (FSI) as a powerful in silico tool, the transient flow field in an aortic valve was analyzed. A linear elastic behavior was assumed for leaflet material properties (Young modulus: 10 MPa, Poisson ratio: 0.46 and leaflet material density: 1000 kg/m3) and blood was specified as a homogeneous, Newtonian and incompressible fluid (fluid density: 1060 kg/m3 and a dynamic viscosity: 0.0035 Pa s). In this numerical study we present a Eulerian approach, which is based on transport equation of the residence time (RT) as a passively transported scalar. It can be clearly seen that the RT is significantly higher in the sinus referred to the main flow. At time step t = 0.25 s, the average residence time in the main flow is RTavg ≈ 0.05 s, whereas RT ≈ 0.25 s in the sinus. In particular, RT is a valuable hemodynamic metric to quantify the washout of the sinus in order to evaluate the thrombogenic potential of TAV devices. Further studies will concentrate on particle image velocimetry measurements for validation purposes. In particular the velocity in the sinus and therefore the washout is one important hemodynamic key feature that has to be improved for future TAV designs.

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