Flow stagnation

It was proposed by the author (Stralmann et al., 1988) that thermophores is could be used to suppress particle deposition on wafers during clean room operations in the microelectronics industry. To estimate the effect of an applied temperature gradient on particle deposition, the flow of filtered air over the surface of a horizontal wafer can be approximated by a stagnation flow (Fig. 3.12), For both the plane and axially symmetric stagnation flows, the gas velocity component normal to the surface and the temperature fields depend only on the distance from the surface. In the absence of natural convection, the gas velocity normal to the surface in the neighborhood of the plane stagnation flow is 

Thus Sjr is proportional to the square root of the thermophoretic coefficient, the temperature 

Values of 5df based on the first term of the expansion of the velocity near the surface compare well with numerically computed values based on the complete velocity and temperature distributions. Calculations of iat for alumina and copper particles (0.5 dp 2 /im) indicate that for temperature differences as small as 10°C the dust-free space would be thick enough to prevent particle deposition. 

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In vertical unidirectional airflow benches, the area along the vertical wall in front of the operator is usually entirely or partially open. When the other side walls reach down to the working surface in the bench a stagnation flow with stationary vortices is usually created as shown in Fig. 10.53. 

Fig. 2.8 Schematic representation of an experimental set-up for a liquid metal impingement/stagnation flow. Reprinted from Miner and Ghoshal (2004) with permission...

Figure 4.1.2 is a photograph of a coimterflow burner assembly. The experimental particle paths in this cold, nonreacting, counterflow stagnation flow can be visualized by the illumination of a laser sheet. The flow is seeded by submicron droplets of a silicone fluid (poly-dimethylsiloxane) with a viscosity of 50 centistokes and density of 970 kg/m, produced by a nebulizer. The well-defined stagnation-point flow is quite evident. A direct photograph of the coimterflow, premixed, twin flames established in this burner system is shown in Figure 4.1.3. It can be observed that despite the edge effects.

Tsuji, Ft. and Yamaoka, 1., Structure and extinction of near-limit flames in a stagnation flow, Proc. Combust. Inst., 19,1533,1982. 

Although a nearly planar premixed turbulent flame is maintained in the stagnation-flow burning configuration (3), the divergence of flow-field streamlines results in mean strain rates which also modify the turbulent flame structure and burning rates. 

In Fig. 15.4, the measured turbulent flame speeds, normalized with mixture-specific laminar flame velocities obtained recently by Vagelopoulos et al. [14], are compared with experimental and theoretical results obtained in earlier studies. Also shown in the figure are the measurements made by Abdel-Gayed et al. [3] for methane-air mixtures with = 0.9 and = 1 a correlation of measured turbulent flame speeds with intensity obtained by Cheng and Shepherd [1] for rod-stabilized v-flames, tube-stabilized conical flames, and stagnation-flow stabilized flames, Ut/Ul = l + i.2 u /U ) a correlation of measured turbulent flame... 

The adiabatic surface temperature (for stagnation flow) and the adiabatic PSR temperature are shown in Fig. 26.4a as a function of the inlet fuel composition. The residence time in the PSR is simply taken as the inverse of the hydrodynamic strain rate. In both cases, the adiabatic temperature exhibits a maximum near the stoichiometric composition. The limits of the adiabatic operation are 8% and 70% inlet H2 in air for the stagnation reactor. For a PSR, the corresponding limits are 12% and 77% inlet H2 in air. Beyond these compositions, the heat generated from the chemical reactions is not sufficient to sustain combustion. 

As already noted in Section IV,B, turbulence can be described in the plane normal to the main flow by the stagnation flow pattern. For steady laminar stagnation flow, u = aDx and v = — a y far from the solid surface and [2]... 

Stagnation flow configuration Photograph of a premixed C z/Hz/Oz flame depositing diamond film... 

Flat flames can be made to impinge onto surfaces. Such strained flames can be used for a variety of purposes. On the one hand, these flames can be used in the laboratory to study the effects of strain on flame structure, and thus improve understanding of the fluid-mechanical effects encountered in turbulent flows. It may also be interesting to discover how a cool surface (e.g., an engine or furnace wall) affects flame structure. Even though the stagnation-flow situation is two-dimensional in the sense that there are two velocity components, the problem can be reduced to a one-dimensional model by similarity, as addressed in the book. 

Fig. 2.23 Computational solution to a CVD reactor, stagnation-flow problem. The white arrows illustrate the streamlines, and the color (grayscale) illustrates the temperature field. Flow enters both through a porous showerhead assembly and through an annular channel adjacent to the outer wall. The exhaust exits downward through the annular channel. The process is running at a reduced pressure of 10,000 Pa (approximately one-tenth of atmospheric pressure). The fluid properties are those for air.

The flow at high Rep approaches the planar, finite-gap, stagnation flow between parallel plates. In this case, the injection velocity V dominates over the initial velocity U that enters the channel. The system of equations developed here are essentially the same as those for finite-gap planar stagnation flow. Indeed, it is only the relationship between K and the axial pressure gradient that distinguishes the two flows. 

Stagnation flows represent a very important class of flow configurations wherein the steady-state Navier-Stokes equations, together with thermal-energy and species-continuity equations, reduce to systems of ordinary-differential-equation boundary-value problems. Some of these flows have great practical value in applications, such as chemical-vapor-deposition reactors for electronic thin-film growth. They are also widely used in combustion research to study the effects of fluid-mechanical strain on flame behavior. 

Stagnation flows can be viewed either as a similarity reduction of the flow equations in a boundary-layer region or as an exact reduction of the Navier-Stokes equations under certain simplifying assumptions. Depending on the circumstances of a particular problem of interest, one or the other view may be more natural. In either case, the same governing equations emerge, with the differences being in boundary conditions. The alternatives are explored in later sections, where particular problems and boundary conditions are discussed. 

Historically variations of stagnation flows have been classified and analyzed according to the particular circumstances of the outer flows. Examples are stagnation flows, as developed by Hiemenz [429], and rotating-disk flows, as developed by Von Karman [429]. When one reads the literature on these flows, it is usually not apparent that the viscous-... 

A principal assumption for similarity is that there exists a viscous boundary layer in which the temperature and species composition depend on only one independent variable. The velocity distribution, however, may be two- or even three-dimensional, although in a very special way that requires some scaled velocities to have only one-dimensional content. The fact that there is only one independent variable implies an infinite domain in directions orthogonal to the remaining independent variable. Of course, no real problems have infinite extent. Therefore to be of practical value, it is important that there be real situations for which the assumptions are sufficiently valid. Essentially the assumptions are valid in situations where the viscous boundary-layer thickness is small relative to the lateral extent of the problem. There will always be regions where edge effects interrupt the similarity. The following section provides some physical evidence that supports the notion that there are situations in which the stagnation-flow assumptions are valid. 

Not all reactor designs and operating conditions lead to the stagnation-flow similarity regimes illustrated in Fig. 6.1. Buoyancy-induced flow, owing to large temperature gra-... 

Several investigators have studied the potentially complex flow in actual stagnation-flow reactors, using two-and three-dimensional Navier-Stokes simulations [116,117,133,183, 203,228,348,419] and flow visualization [45], Generally speaking, the departure from... 

Deriving the axisymmetric stagnation-flow equations begins with the steady-state three-dimensional Navier-Stokes equations (Eqs. 3.58, 3.60, and 3.60), but considering flow only in the z-r plane. In general, there may be a circumferential velocity component ui, but there cannot be variations of any variable in the circumferential direction 0. The derivation depends on two principal conjectures. First, the velocity field is presumed to be described in terms of a streamfunction that has the separable form... 

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