Stagnation point

If one can assume that the process in the flow field is adiabatic and that dissipative effects are negligibly small, the flow in the system is isentropic (ds = 0), and then Eq. (1.21) becomes 

The changes in temperature, pressure, and density in a flow field are expressed as a function of Mach number as follows  

However, in practice, it is found that while there is no lift force on such a sphere in a viscous air stream there is an appreciable drag force which varies in a complex way with fluid velocity or Reynolds Number (as will be discussed presently in connection with Fig. 6.5). It was not until the concept of the boundary layer was introduced by Prandtl in the early 1900s that this discrepancy between theory and experiment was explained. 

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Since pipe flow is more nearly isenthalpic, the flash fraction x is found from an enthalpy balance between the stagnation point and a point z downstream. Accounting for changes in potential energy, kinetic energy, and heat added or removed from the pipe Q, x is given by ... 

The energy balance across a pipe from the stagnation point 0 to a point 2 downstream is ... 

This states that the sum of the velocity pressure 0.5pv plus the static pressure / the total pressure, is constant along a streamline. In the case of standard air density (1.2 kg m ), 0.5pv becomes 0.6v. When a Pitot-static tube is immersed into the flow, as in Fig. 12.19, the velocity at the stagnation point at the tube nose is f = 0 and the local static pressure equals the total pressure p,. The flow static pressure p, is measured a short distance downstream from the surface of the tube. The flow velocity is obtained by applying Eq. (12.27) ... 

Fig. 22. Schematic diagram of the opposite jets device with some of the associated streamlines (the x marks the location of the stagnation point). It has been determined that a ratio of d/(2 r0) w 1 — 1.4 constitutes the optimum geometry for extensional viscosity measurements [104]...

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.

Sheu, W.J. and Sivashinsky, G.L, Nonplanar flame configurations in stagnation point flow. Combust. Flame, 84, 221,1991. 

Figure 1. Schematic of the stagnation point flow conflguration.

A number of theoretical (5), (19-23). experimental (24-28) and computational (2), (23), (29-32). studies of premixed flames in a stagnation point flow have appeared recently in the literature. In many of these papers it was found that the Lewis number of the deficient reactant played an important role in the behavior of the flames near extinction. In particular, in the absence of downstream heat loss, it was shown that extinction of strained premixed laminar flames can be accomplished via one of the following two mechanisms. If the Lewis number (the ratio of the thermal diffusivity to the mass diffusivity) of the deficient reactant is greater than a critical value, Lee > 1 then extinction can be achieved by flame stretch alone. In such flames (e.g., rich methane-air and lean propane-air flames) extinction occurs at a finite distance from the plane of symmetry. However, if the Lewis number of the deficient reactant is less than this value (e.g., lean hydrogen-air and lean methane-air flames), then extinction occurs from a combination of flame stretch and incomplete chemical reaction. Based upon these results we anticipate that the Lewis number of hydrogen will play an important role in the extinction process. 

Hydrodynamic theory shows that the thickness, 8, of the boundary layer is not constant but increases with increasing distance y from the flow s stagnation point at the surface (Fig. 4.4) it also depends on the flow velocity ... 

Let CO be the angular velocity of rotation this is equal to Inf where/is the disk frequency or number of revolutions per second. The distance r of any point from the center of the disk is identical with the distance from the flow stagnation point. The hnear velocity of any point on the electrode is cor. We see when substituting these quantities into Eq. (4.34) that the effects of the changes in distance and hnear vefocity mutuaUy cancel, so that the resulting diffusion-layer thickness is independent of distance. 

Ribe NM Smooke MD (1987) A stagnation point flow model for melt extraction from a mantle plume. J Geophys Res 92 6437-6443... 

Weder s experiments were carried out with opposing body forces, and large current oscillations were found as long as the negative thermal densification was smaller than the diffusional densification. [Note that the Grashof numbers in Eq. (41) are based on absolute magnitudes of the density differences.] Local mass-transfer rates oscillated by 50%, and total currents by 4%. When the thermal densification dominated, the stagnation point moved to the other side of the cylinder, while the boundary layer, which separates in purely diffusional free convection, remained attached. 

In region III near the tube center, viscous stresses scale by the tube radius and for small capillary numbers do not significantly distort the bubble shape from a spherical segment. Thus, even though surfactant collects near the front stagnation point (and depletes near the rear stagnation point), the bubble ends are treated as spherical caps at the equilibrium tension, aQ. Region... 

Next, in order to study the stability of the kebabs, the flow rate was set at e = 0.001 and four, initially equilibrated (i.e. in a pre-crystallized conformation), short chains were added per t = 2000 with an initial position of 20ro length units away from the stagnation point in the x and y direction. They form a kebab around the shish which was preformed. This procedure was repeated up to 44 short chains in the kebab as shown in Fig. 31. 

The pitot tube is a device for measuring v(r), the local velocity at a given position in the conduit, as illustrated in Fig. 10-1. The measured velocity is then used in Eq. (10-2) to determine the flow rate. It consists of a differential pressure measuring device (e.g., a manometer, transducer, or DP cell) that measures the pressure difference between two tubes. One tube is attached to a hollow probe that can be positioned at any radial location in the conduit, and the other is attached to the wall of the conduit in the same axial plane as the end of the probe. The local velocity of the streamline that impinges on the end of the probe is v(r). The fluid element that impacts the open end of the probe must come to rest at that point, because there is no flow through the probe or the DP cell this is known as the stagnation point. The Bernoulli equation can be applied to the fluid streamline that impacts the probe tip ... 

With regard to the flow over an immersed body (e.g., a sphere), the boundary layer grows from the impact (stagnation) point along the front of... 

When a thermometer is placed in a flowing gas stream, most of the thermometer s surface has gas flowing past it but a stagnation point occurs at its upstream side. Thus instead of measuring the temperature T, it measures a value that is slightly higher. This can be accommodated by introducing a correction factor known as the recovery factor r/. 

At all values of the particle Reynolds number Rep, the fluid is brought to rest relative to the particle at A, which is therefore a stagnation point where the pressure is higher than in the flowing fluid (see equation 1.19 in... 

Interestingly, the shape of the wake is similar to that developed behind a hypersonic blunt body where the flow converges to form a narrow recompression neck region several body diameters downstream of the rear stagnation point due to strong lateral pressure gradients. The liquid material, that is continuously stripped off from the droplet surface, is accelerated almost instantaneously to the particle velocity behind the wave front and follows the streamline pattern of the wake, suggesting that the droplet is reduced to a fine micromist. 

In the opposed jets design fluid is sucked or pumped into a beaker. The profile which develops is dominantly extensional. In the profiled slot design a rectangular channel is designed such that in the total slip condition an extensional flow develops with a constant rate. The pressure is measured at the stagnation point. Other designs include the open syphon, where fluid is sucked from a beaker through a nozzle which is... 

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