Profile inlet velocity

Figure 3-18. Typical inlet velocity profile for an industrial gas turbine.

There is a natural draw rate for a rotating disk that depends on the rotation rate. Both the radial velocity and the circumferential velocity vanish outside the viscous boundary layer. The only parameter in the equations is the Prandtl number in the energy equation. Clearly, there is a very large effect of Prandtl number on the temperature profile and heat transfer at the surface. For constant properties, however, the energy-equation solution does not affect the velocity distributions. For problems including chemistry and complex transport, there is still a natural draw rate for a given rotation rate. However, the actual inlet velocity depends on the particular flow circumstances—there is no universal correlation. 

Fig. 6.22 Nondimensional streamlines and velocity profiles for an isothermal tubular flow with purely radial inlet velocity. The streamlines shown are for a Reynolds number of 1. The nondimensional velocity profiles are shown for Reynolds numbers of 1, 10, and 100.

Based on the shapes of the velocity profiles, describe the boundary-layer thickness as a function of inlet velocity. 

Consider the flow of an incompressible fluid in the entry region of a circular duct, assuming that the inlet velocity profile is flat. As is often the case, the problem can be generalized by casting into a nondimensional form. A set of nondimensional variables may be chosen as... 

Explore the effects of flow rate by increasing the inlet velocity to mo = 50,100, and 200 cm/s. Explain the differences in gas-phase composition and deposition profiles in terms of the competition among alternative reaction paths and residence times. 

Fig. 17.2 Gas-phase profiles of SiELi and SiH2 for wafer-surface temperatures of 800 K, 925 K, and 1300 K. The wafer-to-showerhead separation is 3 cm. In all cases the total pressure is one atmosphere, the inlet velocity is 100 cm/s, and the inlet mixture is 0.17 % SiELj in He.

Despite the flow fields being very different between the burner-stabilized and wall-stabilized cases, the flame structure itself is remarkably similar. The lower panels of Fig. 17.4 show exploded views of the species profiles within the narrow flame zone. As long as the flame is burning, it appears as though the increasing inlet velocity simply translates the flame from right to left. 

A sufficiently high inlet velocity will cause the flame to be extinguished [270]. There are two reasons for the extinction. One is heat loss to the wall, which reduces the flame temperature and hence the chemical reaction rates. The second, and perhaps less obvious, is strain extinction. As the inlet velocity increases and the boundary layer thins, the radial velocity increases (the general shape of the radial velocity profiles are shown in Fig.6.6). As the radial velocity increases, the residence time in the flame zone also decreases. The reduced residence time, in turn, limits the time available for the relatively slow radical-recombination reactions to keep the flame temperature high. Reduced temperature and residence time limit the relatively slow the chain-branching reaction H + O2 OH + O, which is needed to sustain a flame. Ultimately a flame cannot be sustained [214],... 

Consider the two axial-velocity profiles in Fig. 17.10 that correspond to the low-strain solution in Fig. 17.9. While at the symmetry plane both solutions must have zero velocity, the inlet-velocity boundary conditions are quite different. In the finite-gap case (here the gap is 3.5 mm), the inlet velocity is specified directly (here as 250 cm/s). In the semiinfinite case, the inlet cannot be specified. Instead, the velocity gradient a = du/dz is specified, with the velocity itself growing linearly away from the surface. In the finite-gap case the strain rate is determined by evaluating the velocity gradient just ahead of the flame, where there is a region in which the velocity gradient is reasonably linear. In the semi-infinite case, the velocity gradient is specified directly, whereas in the finite-gap case it must be evaluated from the solution. 

The inlet velocity profile and temperature profile are given as... 

At the inlet to the finite element domain, the flow is parallel so the equations of the lubrication approximation are used to specify the inlet velocity profile. These equations are integrated from -oo to the inlet, generating an equation relating the flow rate to the inlet pressure. The remaining boundary conditions are as shown in Figure 3. The only complexity here is that the fluid traction, n T, at the free surface has to be specified as a boundary condition on the momentum equation. A force balance there gives, in dimensionless form,... 

Numerical model calculations using the CFD code FLUENT 6.1 were performed to evaluate the time dependent behavior of fires ignited within a homogeneous porous canopy. These were compared with flow behavior from a similar fire in the absence of the canopy. Consideration was given to the effects of grid resolution, turbulence model (/c-RANS versus LES), wind speed (Uh = 0, 1, 2, 5 m/s), fire intensity (Q = 20, 50, 100 kW/m3), and inlet velocity profile (a = 0 or 0.14). The development of velocities, turbulence intensity, static pressure, and temperature fields were examined for such examples. Typical results are discussed below. 

Next, change the problem slightly and take the inlet velocity as the fully developed velocity profile. 

Figure 10.7. Streamlines (cz) and inlet velocity profile b for flow in pipe with parabolic inlet velocity profile.

You can solve the problem with an inlet velocity that is flat thus you find the entry length it takes to achieve fully developed turbulent flow, and the velocity profile downstream is the fully developed one. When you solve for a kinematic viscosity of 10 m /s (water), diameter of 0.05 m (about 2 inches) and a velocity of 2 m/s (a common optimal velocity), you will obtain a Reynolds number of 10. ... 

Figure 11.2 (a) Turbulent pipe-flow (open symbols) and GEAE LM-6000 (filled symbols) radial profiles of inlet velocity components (normalized by the peak mean inlet axial velocity) for S = 0.56 1 — axial U 2 — tangential W and 3 — radial V. [b) Sensitivity of LM-6000 normalized centerline velocity to choice of floating inflow boundary condition streamwise variable is scaled with inlet diameter R previous LES [3] 1 — fine grid 2 — coarse grid (fix T and V ) present work 3 — MILES (fix p and V) 4 — MILES (fix Po and float V ) and -5 — OEEV M (fix p and V ). 

The sensitivity of the axisymmetric combustor flow dynamics to the actual choice of inlet velocity conditions was also examined. Figure 11.3 compares the results of initializing the simulations with the turbulent-pipe or LM-6000 swirling conditions and otherwise identical initial conditions S = 0.56, Uo — 100 m/s, STP). The flow visualizations depict the significant effects on the combustor vortex dynamics of changing the specifics of the velocity profiles used to initialize the LES, with noticeably more-axisymmetric features observed in the flow features for the LM-6000 case. The LM-6000 initial velocity conditions (Fig. 11.2a) involve a peak tangential velocity component located farther away from the axis and a more moderate radial gradient of the axial velocity. A clear consequence of these initial condition specifics, apparent in Fig. 11.3a, is that the LM-6000... 

The locations of the boundaries between the three annular passages are shown on the abscissa. Compared to the top-hat inlet velocity profiles discussed above, TARS velocity profiles involve a much more complex structure, with the more noticeable aspect being the annular axial TARS velocities with a characteristic well around the axis — as opposed to the simpler top-hat velocities in Fig. 11.2a. All TARS cases reported in this chapter involve unconfined conditions downstream of the fuel-injector nozzle. 

This approach to defining the inlet velocity profiles does not account for important effects of the sudden expansion and adverse pressure gradients due to swirl, namely, the rapid decay of the axial velocity magnitude (e.g., Fig. 11.2a) and significant reduction of the inner slope of the axial velocity profile (e.g.. Fig. 11.8). A challenging additional difficulty relates to emulating (even at axisymmetric profiles) the turbulent intensities in Fig. 11.56 ... 

Other extended Graetz problems in which the effect of viscous dissipation, inlet velocity, and temperature profiles are considered are reviewed in detail by Shah and London [1]. 

Figure 7 Velocity profile in a simulated gravity separator inlet liquid section inlet velocity 0.5 m/s.

The inlet velocity significantly modifies the Nu and Sh number profiles near the entrance, as shown in Figure 10.11. As the velocity increases, a lar r axial distance is required for the thermal boundary layer to develop fully. Hence Nu and Sh approach their asymptotic values more gradually. In contrast, other parameters, such as the wall conductivity (kg), heat loss coefficient (hj) to the environment and equivalence ratio (([)), do not have an effect on the Sh profile. While the Nu profile is also independent of these parameters, the location of the discontinuity in the Nu profile shifts due to a shift in the boundary between preheating/combustion and post-combustion zones. 

The boundary constraints used in pipe flow regimes are inlet velocity profile, zero velocity on solid non-slip walls, and stress free (or for long pipes developed flow) exit conditions. In shell and tube systems with solid and porous walls, used in thickening of suspensions by cross-flow filtration, a different set of boundary conditions must be given. These are the inlet velocity profile, zero velocity on outer shell s solid walls, stress-free conditions at the exit, and the following Darcy flow conditions on porous wall ... 

To get uniform volumetric flow where the above criteria cannot be met, it is necessary to calculate the velocity from each orifice, then calculate flie area required to get flie necessary volumetric flow. To do this it is necessary to calculate the pressure profile in the distributor at all the various points. This would be a very complicated procedure and is seldom done. This mefliod is not discussed here. Only a simplified procedure is presented and is only valid for inlet velocities between 6 and 14 feet per second. 

Inlet Boundary Conditions We assume a parabolic inlet velocity profile for fully developed laminar flow in the axial direction of the inlet side as... 

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