Vorticity streamwise

Figure 10.5 Inlet-normalized vortic-ity thickness vs. streamwise distance without (1) and with (2) radiation...

The effect of heating on the azimuthal and streamwise components of the vorticity field is shown in Fig. 11.1 the effect on the radial component is comparable to that on the azimuthal component, and is therefore not separately shown. The vorticity distributions at the same nondimensional time t = 35 are plotted side by side for the unheated and heated case for each component. The positive and negative values of vorticity are shown by solid and dotted lines, respectively. 

To quantify the vorticity increases due to heating, the total enstrophy and also the enstrophies corresponding to the azimuthal, streamwise, and radial components of vorticity are examined. Computed values are shown using a linear-log scale in Fig. 11.2. In the absence of heating, the total as well as the component enstrophies all fall beyond time t = 25, as would be expected in a fully developed turbulent jet. When heat is applied, there is a virtually exponential rise of the enstrophies after some time. At t = 35, the enstrophies are one order of magnitude higher with heating than without. 

Figure 11.1 Streamwise sections (in the j/z-plane passing through the axis of the jet) of different components of vorticity in the unheated (a), (c) and heated (6), (d) jets at time t = 35 (a), (b) — azimuthal vorticity, (c), (d) — streamwise vorticity. Negative contours are shown using dotted lines in steps of —0.5 starting from —0.5, while positive contours are in solid lines in steps of 0.5 starting from 0.5...

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... 

Figure 13.5 Unsteady nonpremixed combustion and fluid dynamics (a) contours of the vorticity magnitude O in planes indicated to the right (6) cross-sectional averaged measures of instantaneous chemical product and product formation (left frame), instantaneous unconstrained and vorticity-bearing (ff > 5% peak-value) streamwise mass flux Q (right frame). 1 — product, 2 — instantaneous production, 3 — Oo = 0, and 4 flo/f peak — 0.05...

The goal of this work has been to characterize the effects of the unsteady vor-ticity dynamics on jet entrainment and nonpremixed combustion. The main focus of the numerical simulations of rectangular jets has been on the vortic-ity dynamics underlying axis switching when the initial conditions at the jet exit involve laminar conditions, negligible streamwise vorticity, and negligible azimuthal nonuniformities of the momentum thickness. 

Liepmann, D., and M. Gharib. 1992. The role of streamwise vorticity in the near-held entrainment of round jets. J. Fluid Mechanics 245 643-68. 

The modelling of aerodynamic entrainment is based on the close link between particles take-off and turbulent coherent structures above the surface. In fact, some authors [6,7] have experimentally observed that a particle take-off can be associated to the ejection of fluid from the wall region due to the presence of streamwise counter rotating vortices. If it is assumed that the presence of two streamwise counter rotating vortices produces only one ejection, each pair of streamwise vortices is considered as a possibility that a particle takes-off. Thus, for each of these possibilities, a take-olf criterion is tested. 

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). 

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... 

The two-dimensional Navier-Stokes equation is solved in stream function-vorticity formulation, as reported variously in Sengupta et al. (2001, 2003), Sengupta Dipankar (2005). Brinckman Walker (2001) also simulated the burst sequence of turbulent boundary layer excited by streamwise vortices (in X- direction) using the same formulation for which a stream function was defined in the y — z) -plane only. To resolve various small scale events inside the shear layer, the vorticity transport equation (VTE) and the stream function equation (SFE) are solved in the transformed — rj) —... 

Figure 3.8 Stream function (top three panels) and vorticity contours plotted at the indicated times. Same contour values are plotted for each quantity. Arrowheads at the top of each frame indicate the instantaneous streamwise location of the freestream...

Of significant interest are the strong counter-rotating vortices observed in lateral cross-sections. In the region of the sweep, these vortices rotate such that the central area between them is one of downward flow, as shown in Figure 4.11. Following the vortex pair in the streamwise direction, the centres of rotation are observed to be tilted upwards. 

Figure 10.7 Particle Image Velocimetry results on a streamwise plane downstream of Swirler 304545 at 68 scfm, 2-inch diameter exhaust nozzle, and Lmi = O" (a) mean axial velocity component (6) mean tangential velocity component (c) mean radial velocity component (d) vorticity and (e) 3D vector. (Refer color plate, p. VIII.)...

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