Transient stagnation flow

Equation 11.131 assumes that the total surface site density T is constant. Section 17.7.1 uses the equation above in the formulation of a transient stagnation flow problem, for example. 

In the steady stagnation-flow formulation the thermodymanic pressure may be assumed to be constant and treated as a specified parameter. The small pressure variations in the axial direction, which may be determined from the axial momentum equaiton, become decoupled from the system of governing equations (Section 6.2). The small radial pressure variations associated with the pressure-curvature eigenvalue A are also presumed to be negligible. While this formulation works very well for the steady-state problem, it can lead to significant numerical difficulties in the transient case. A compressible formulation that retains the pressure as a dependent variable (not a fixed parameter) relieves the problem [323],... 

Deriving the compressible, transient form of the stagnation-flow equations follows a procudeure that is largely analogous to the steady-state or the constant-pressure situation. Beginning with the full axisymmetric conservation equations, it is conjectured that the solutions are functions of time t and the axial coordinate z in the following form axial velocity u = u(t, z), scaled radial velocity V(t, z) = v/r, temperature T = T(t, z), and mass fractions y = Yk(t,z). Boundary condition, which are applied at extremeties of the z domain, are radially independent. After some manipulation of the momentum equations, it can be shown that... 

Fig. 17.14 Finite-volume, staggered-grid, spatial-difference stencil for the transient compressible stagnation-flow equations. Grid points, which are at control-volume centers, are used to represent all dependent variables except axial velocity, which is represented at the control-volume faces. The grid indexes are shown on the left and the face indexes on the right. The right-facing protuberance on the stencils indicates where the time derivative is evaluated. For the pressure-eigenvalue equation there is no time derivative.

L.L. Raja, R.J. Kee, and L.R. Petzold. Simulation of the Transient, Compressible, Gas-Dynamic, Behavior of Catalytic-Combustion Ignition in Stagnation Flows. Proc. Combust. Inst., 27 2249-2257,1998. 

FIG. 16.21 Apparent or transient extensional viscosity of the round robin test fluid Ml as a function of Hencky strain, measured in many different devices (lames and Walters, 1993). The various instruments are spin line Binding et al. Ferguson and Hudson Ngyuen et al. horizontal spin line Oliver open siphon Binding et al. stagnation flow. Laun and Hingmann Schweitzer et al. contraction flow. Binding et al. ... 

Transient stagnation-flow models have been used to determine catalytic ignition of CH4/air, CO/air, and H2/air mixtures over noble metals (Deutschmann et ah, 1996 Raja et ah, 1998). Steady-state catalytic stagnation simulations will be presented in Section 5.1, when discussing the validation of surface chemistry. 

Raja LL, Kee RJ, Petzold LR Simulation of the transient, compressible, gas-dynamic behavior of catalytic combustion ignition in stagnation flows, Proc Combust Inst 27 2249—2257, 1998. 

Eigenberger [15] reported that low flow transients coupled with shadowing in mixed phase reactors can cause even greater hot spotting. This amplification was ascribed to the localized consumption of liquid phase reactant stagnated behind an obstruction. With a localized flow interruption caused by a transitory... 

This flow field can be maintained in a steady state, at least in the Eulerian sense, either by use of a four-roll mill [18] as in Figure 2.8.4(a) or by means of opposed jet flow as in Figure 2.8.4(b). However, it is important to note that the flow is still transient in the Lagrangian sense. That is, pure planar extension is confined to the central stagnation... 

Mechanical degradation of polymers has been studied for more than 70 years in several flow fields encompassing strong elongation components. In certain flow fields the streamlines are symmetric with a stagnation point. In the vicinity of the stagnation point, the dwell time of the fluid element is longer than the timescale for coU extension. Such flow is referred to as quasi-steady-state-flow (QSSF). hi most other cases the dwell time is shorter than the coil extension time and the flow is referred to as fast-transient-flow (FTF). 

An experimental stu% was performed to determine fee effect of small water droplets incorpmated into a single-phase stagnation-point flow on heat transfer. Steady state and transient cooling heat transfo erqieriments were carried out to analyze fee characteristics of single-phase and two-phase flows. PIV measurements were made for different air velocities to determine the characteristics of the flow. Water droplets size distribution was also measured. The following conclusions can be made fiom this study ... 

The reactor behavior is similar to that of at the loss of offsite power after the trip of the RCPs at 10 s. The maximum pressure is about 26.8 MPa, the highest among the abnormal transients but is low enough compared to the criterion (28.9 MPa). The hottest cladding temperature increases by about 50°C from the initial value during the flow stagnation caused by the closure of the coolant outlet. 

The WWER-440 simulator (Pactel) exhibits a decrease of the NC flowrate at relatively high mass inventories of the primary loop. The presence of the hot leg loop seal is at the origin of a partial flow stagnation (Fig. 6). Removal of the hot leg loop seal is effective in improving NCP as shown by the calculated WWER-1000 transient. The consideration of a passive system also improves the NCP of the Pactel. 

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