Velocity streamwise

Average fluid temperature Average velocity Normalized local velocity Streamwise velocity... 

The other method is the prescribed velocity (PV) method. In this method only the streamwise velocity component U and the temperature profile are prescribed inside the volume ab. The remaining variables ( V, W, k, and e) are solved for as usual in the whole room, including the ab volume. The temperature level has to be readjusted after each iteration to ensure conservation of energy. 

In the laminar region the rms of streamwise velocity fluctuations was expected to be zero (Sharp et al. 2001). Figure 3.10 shows that the first evidence of transition, in the form of an abrupt increase in the rms, occurs at 1,800 < Re < 2,200, in full agreement with the flow resistance data. There was no evidence of transition below these values. Thus, the behavior of the flow in micro-tubes, at least down to a 50 pm diameter, shows no perceptible differences with the macro-scale flow. 

Hao et al. (2007) investigated the water flow in a glass tube with diameter of 230 Lim using micro particle velocimetry. The streamwise and mean velocity profile and turbulence intensities were measured at Reynolds number ranging from 1,540 to 2,960. Experimental results indicate that the transition from laminar to turbulent flow occurs at Re = 1,700—1,900 and the turbulence becomes fully developed at Re > 2,500. 

For a typical case, an axisymmetric jet with a mean velocity of 100 m/s flows through the cylindrical inlet of diameter D into a cylindrical combustion chamber of twice the diameter. An annular or central exit at the end of the combustion chamber is modeled to produce choked flow. Particles are injected from the inlet-combustor junction with a streamwise velocity of 50 m/s and zero radial velocity. If the number of particles is small (that is, for low-mass loadings), the effect of the particles on the flow can be neglected. Still the flow has an effect on the particles that depends on parameters such as the size and density of the particles. Such systems are called one-way coupled systems and are discussed next. 

Figure 11.5 shows the computed entraining velocity fields at the widest transverse cross-sections at t = 35 in the heated and unheated jets. (This corresponds to looking at the flow in the plane of the cross-section of the spatially developing jet.) The figure shows velocity vectors in the ambient fluid, and contours of streamwise vorticity within the jet. 

Figure 11.5 Comparison of computed entraining velocity fields at the widest transverse sections of the (a) unheated and (6) heated jet at time t = 35. The contonrs of streamwise vorticity, at intervals of 0.5, are shown using solid lines for positive values, and dotted lines for negative values. Contour for level 0 is not shown... 

The vortex structures appear with statistical spatial periodicities, whose values are dependent on the flow properties and velocity, and on the presence or not of particles. Jimenez and Moin [8] have obtained, by numerical simulations, the values of average spatial periodicities of appearing in the spanwise and streamwise directions of the flow which are respectively, Xz+ 100 and Xx+ 250-300. 

Fig. 1 shows the number of taking-off possibilities over the bed surface if it is assumed that each box, which contains an ejection, is associated with a possibility of taking-off. The numbers of possibilities of taking-off along the spanwise and streamwise directions of the bed are equal respectively to l/Xz and L/Xx. Consequently, they depend on the flow velocity. 

The orthogonal-plane PIV technique is recently proposed for investigating the 3D characteristics of the coherent structures in a turbulent boundary layer flow (Hambleton et al., 2006 Kim et al., 2006). The hardware components and principle of this technique are the same as polarization-based dual-plane PIV. The only difference is to set up both laser sheets mutually perpendicular to each other instead of parallel to each other in the dual-plane PIV system. This allows for measuring velocity distributions in both streamwise-spanwise and streamwise-wall-normal planes simultaneously, so that the salient features of the coherent structures in a turbulent boundary layer flow as the legs and the head of the hairpin vortices can be detected (Hambleton et al., 2006 Kim et al., 2006). 

Figure 2.29 (a) Phase speed of first five modes as functions of (jSr), (b) Streamwise component of group velocity of first five modes as functions of (/ r) (c) spanwise component of group velocity of first five modes as functions of (/ r)... 

Figure 2.34 Streamwise disturbance velocity component plotted at a height y = 0.3<5 for the pure convection case (c = U ) at the indicated times, when solution is obtained by solving the Navier-Stokes equation for the problem shown in Fig.2.30...

In the table, the initial condition t = 0) identifies the packets at a non-dimensional distance of IOOtt -with packets identified by their location outside the computational domain and those entering the domain at later times indicated by asterisks. Due to higher damping rate of both upstream and downstream modes, solution at very early times consists of only the local solution- as discussed with respect to the results in Fig. 2.19. We note six disturbance packets at t = 0, exactly at the same streamwise locations exactly below the freestream vortices. Subsequently at t = 100, two clusters would have been noted at x = 400 and at x = 715, if the disturbance field would have moved with c = Uoo One notes two smaller peaks at these two locations at t = 100. However, the major peaks are at the locations indicated by the quantities within parentheses in Table 2.3. These are exactly at those locations, if one calculated the disturbance clusters to move with the group velocity V o = 0.5f/oo with respect to the corresponding source i.e. the free stream vortices. This is verified for the clusters location at... 

Figure 3.11 Flow profiles and schematic of co-ordinate systems for flow past a swept-back wing, (a) Notation and co-ordinate system (b) Streamwise and cross-flow mean velocity profiles and (c) Attachment-line flow...

Figure 4.3 Streamwise distm-bance velocity component plotted as function of x at indicated times for Re = 1000 at y = 0.278...

The necessary condition for the creation of a forerunner is found by looking at the receptivity solutions for points C and D, with the former having a single stable mode and latter with two damped modes. Results are shown in Fig. 4.4 for the streamwise perturbation velocity, at the indicated large time. 

Further properties of spatio-temporally growing wave-front were studied in Sengupta et al. (2006a). It was investigated by exciting the Blasius boundary layer at a frequency that corresponds to the point on branch 11 of the neutral curve at wq = 0.1307 for Re = 1000. Computed streamwise perturbation velocity at different time instants are shown in Fig. 4.7. 

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