摘要:

AbstractBoundary value problems for Stokes and Navier‐Stokes equations with non‐standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux. First, a variational formulation is introduced which is shown to be equivalent to the Stokes equations with the non‐standard boundary conditions under consideration. The existence and uniqueness of the solution of the variational problem are studied. Secondly, most of the results obtained for the Stokes equations are extended to the case of the Navier‐Stokes equations. The final section is devoted to numerical experiments, flows in pipes and physiologica

ISSN:0271-2091    

DOI:10.1002/fld.1650200402

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractNumerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non‐zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non‐staggered grid and a modified Crank‐Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer (Re) is 100. The Womersley number (Nw) ranges from 0 to 50, with the corresponding Strouhal number (St) ranging from 0 to 3·98. The constriction opening ratio (d/D) and thickness ratio (h/D) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. ForNw≤ 1 and St≤ 1·56 x 10−3the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δp) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasingNwandSt, the phase angle between the flow rate and the dp/dz becomes larger and has its maximum value of 90° atNw= 50 andSt= 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non‐zero mean velocity sinusoidal flow has the smallest. For largerNwandStthe fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases forNwranging from 0 to 4·2, while this length becomes very small atNw= 50 andSt= 3·98. The deceleration tends to enlarge the recirculation region and this effect appears forNw≥ 3 andSt≥ 1·43×10−2. Linear relations exist between the flow rate and the instantaneous maximum values of veloci

ISSN:0271-2091    

DOI:10.1002/fld.1650200403

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractNumerical solutions to the three‐dimensional, unsteady, incompressible Reynolds‐averaged Navier‐Stokes equations have been obtained for bubble‐type vortex breakdown. Two different turbulence models were employed: (1) standardK‐ε and (2) an explicit, regularized algebraic Reynolds stress model. Results are computed at a Reynolds number of 10,000. The algebraic Reynolds stress model produced a breakdown bubble with a larger length‐to‐diameter ratio than did theK‐ε model. Breakdown also occurred at lower levels of adverse pressure gradient for the algebraic stress model than for theK‐ε model. In each case single‐cell breakdown structures resulted. This is contrasted with numerical calculations for laminar breakdown which reveal the existence of complex multicell bubbl

ISSN:0271-2091    

DOI:10.1002/fld.1650200404

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractWe consider steady state and time‐dependent flows of chemically reactive polymeric systems in two‐dimensional geometries. A numerical simulation tool is proposed for predicting the evolution of the macroscopic velocity, temperature, stress and species concentration fields in such flows. We formulate a general mathematical model on the basis of the first principles of continuum mechanics, which includes a description of the non‐liner coupling between kinematics, heat transfer and chemical kinetics. The resulting set of non‐linear partial differential equations is solved numerically by means of appropriate finite element techniques. We have implemented the resulting numerical model in the general‐purpose POLYFLOWRsoftware developed in Louvain‐la‐Neuve, Belgium. Simulation results for various steady state and time‐dependent reactive flo

ISSN:0271-2091    

DOI:10.1002/fld.1650200405

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650200406

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650200407

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650200401

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY