Chapter 5 Single-Point QNS Measurements 5. Overview A total of 46 primary test cases were evaluated using the QNS technique. These cases duplicated the 8 studied by Ainley [] and extend the parameters examined which include a total of 8 particle time constants, 5 drift velocities, and two Reynolds numbers. Table (5.) shows the test matrix that was completed with the new QNS particle advancement scheme. In addition, a number of other cases were run to con- rm specic characteristics though the data is not directly presented in this chapter. Each of the cases was comprised of 00 individual runs which lasted between 7 and 2 seconds each. Individual runs were composed of between 200 and 900 velocity measurements from the LDV probe. These were each individually ltered before being postprocessed. The rst 2500 ms of each data set was eliminated to guarantee the emulated particle was up to speed and following the ow with no `memory' of its initial startup. This was tested and conrmed empirically by changing the cuto time until results no longer changed (Section 6.2). Velocity autocorrelations and energy spectra of the particle and the uid from within the p-l reference frame are discussed in the following sections. In the interest of saving space, only a subsection of the data is presented directly with additional 44
cases found in the appendix. Specic plots in this chapter were chosen to demonstrate the trends observed in the autocorrelation and spectra plots with specic exceptions noted. Re Drift % Particle Time Constant (ms) 50 250 350 500 700 800 000 200 3300 0.2 2.5 4.0 6.0 3300 5.2 2.5 4.0 6.0 3300 7.5.2 2.5 4.0 6.0 3300 0.2 2.5 4.0 6.0 6600 0 2.6 4.4 6. 8.8 2.3 7.5 6600 2.5 2.6 4.4 6. 8.8 2.3 7.5 6600 5 2.6 4.4 6. 8.8 2.3 7.5 6600 7.5 2.6 4.4 6. 8.8 2.3 7.5 6600 0 2.6 4.4 6. 8.8 2.3 7.5 Table 5.: Primary test matrix with St k for each case studied. 5.2 Velocity Autocorrelations Gravity has a profound eect on the behavior of particles suspended within a turbulent ow. With gravity acting against the streamwise direction, uid velocity autocorrelations in the streamnormal are highly aected by a change in gravity. As the drift velocity increases, the particles pass through uid neighborhoods more quickly, causing the correlation times to decrease. This is the `crossing trajectories' eect that is can be seen in the data. 45
Fluid velocity autocorrelations at both a Reynolds number of 3300 and 6600 show eects of crossing trajectories. The behavior is most easily seen in the streamnormal data where the uid autocorrelations of of each drift case signicantly deviates from one another (gure 5.). With the crossing trajectories eect, larger drift velocities cause correlation times to decrease. The Re = 3300 data is considerably noisier but shows similar trends as well (appendix A). 0.8 S g = 0.00 S g = 0.66 S g =.33 S g =.97 S g = 2.59 0.6 R ii / u 2 0.4 0.2 0-0.2 0 2 4 6 8 0 2 4 6 Time / T p Figure 5.: Streamnormal uid autocorrelation (Re=6600 p = 250ms). Surprisingly, particle velocity autocorrelations in the streamwise direction show very little eect from changes in the drift velocity (gure 5.2). The streamnormal data does show consequences from the crossing trajectory eect (gure 5.3) but it seems to diminish with the large time constants. The streamwise particle data also shows similar deviations at a much reduced level. Though gravity eects the uid velocity autocorrelations in the p-l reference frame, the particle velocity autocorrelations are not as severely aected at larger Stokes numbers (O(0)). 46
0.8 S g = 0.00 S g = 0.68 S g =.47 S g = 2.4 S g = 2.78 0.6 R ii / u 2 0.4 0.2 0-0.2 0 2 3 4 5 6 7 8 Time / T p Figure 5.2: Streamwise particle autocorrelation (Re=6600 p = 500ms). 0.8 S g = 0.00 S g = 0.66 S g =.33 S g =.97 S g = 2.59 0.6 R ii / u 2 0.4 0.2 0-0.2 0 2 4 6 8 0 2 4 6 Time / T p Figure 5.3: Streamnormal particle autocorrelation (Re=6600 p = 250ms). 47
The velocity of particles with greater inertia stay correlated longer than their smaller counterparts due to the lag introduced by their time constant. On average the particles will see a larger uctuating uid velocity component but will respond less vigorously therefore extending the correlation. The eect does not extend linearly with particle time constant. When the particle velocity autocorrelations are normalized by the particle time constant, it is seen that smaller particles stay correlated a greater number of time constants though this still translates to a shorter real time (gures 5.4 and 5.5). As discussed by Ainley [] and Wells and Stock [20], uid correlation times seem to be only weakly aected by particle response. Streamnormal and streamwise uid autocorrelations seem to be unaected by variation of time constant within the range of limits tested (gure 5.5). 0.8 St k = 2.63 St k = 4.39 St k = 6.4 St k = 8.77 St k = 2.28 St k = 7.54 0.6 R ii / u 2 0.4 0.2 0-0.2 0 5 0 5 20 25 30 Time / T p Figure 5.4: Streamnormal particle autocorrelation (Re=6600 Drift = 0%). 48
0.8 T p = 50 ms T p = 250 ms T p = 350 ms T p = 500 ms T p = 700 ms T p = 000 ms 0.6 R ii / u 2 0.4 0.2 0-0.2 0 500 000 500 2000 2500 3000 Time (ms) Figure 5.5: Streamnormal uid autocorrelation (Re=6600 Drift = 0%). Additional autocorrelation plots can be found in the appendix. The oscillatory nature of the streamwise uid autocorrelations of the 50 ms particle at Re=6600 is believed to be due to the traverse approaching its natural frequency with slight oscillations showing up in the measured uid velocities. These are equivalent to the natural frequency of the traverse system, aggravated as the particle time constant approached the natural period of the vertical traverse extrusion. More mysterious is similar behavior that appears in the streamnormal direction at Re=3300 (gure 5.0). 5.3 Fluid and Particle Energy Spectra The turbulent energy being dissipated represents the inherent energy of the ow with the energy being dissipated directly related to the energy added to the system. In the case of the water channels, the water pump that pushes the water through 49
the system adds the energy which is dissipated. The largest eddies formed from the wall shear take energy from the ow while a cascading eect begins that passes this energy from the largest integral scales down to the smallest Kolmogoro scales where it is nally dissipated as heat. The uid and particle spectra can be obtained from the velocity autocorrelations and show the amount of energy present at each of the cascading scales. Since the pump has to add a signicantly dierent amount of energy to the system to change the mean velocity (Reynolds number), the power spectra changes depending upon the Reynolds number tested. A particle traveling through regions of the ow has uctuating components at characteristic frequencies. The energy measured at the various uctuating frequencies vary depending upon the uid region being sampled which is itself dependent upon the particle's inertia and the gravitational drift. These factors inuence the path a typical particle takes through the ow with a corresponding change in the uid spectra. Since the energy spectra is derived from the velocity autocorrelation, it follows that the same patterns are found within. As expected, changes in particle inertia and gravitational drift modify the trajectory of a typical particle with corresponding changes in the particle and uid spectra. The streamnormal energy spectra shows the greatest inuence from gravitational drift. Figures (5.6 and 5.7) show that both the uid and particle power spectra are aected by drift. The particle spectra shows an immediate consequence of `crossing trajectories', namely that the particle sees more high frequency energy as the particle is rapidly pulled through uid neighborhoods with correspondingly rapid uctuations in relative uid velocity. Relatively less energy is seen at the lower frequencies for the same reason though dividing by u' obscures that the total energy is less for larger values of g. The changes in the uid spectra are less pronounced but still does show less low frequency energy and more high with an increase in drift from an external acceleration on a particle of constant inertia. 50
00 0 S g = 0.00 S g = 0.68 S g =.47 S g = 2.4 S g = 2.78-5/3 slope S ii / u 2 0. 0.0 0.00 0. 0 f (Hz) Figure 5.6: Streamnormal particle energy spectra (Re=6600 p = 500ms). 00 0 S g = 0.00 S g = 0.68 S g =.47 S g = 2.4 S g = 2.78-5/3 slope 0. S ii / u 2 0.0 0.00 0.000 e-005 0. 0 f (Hz) Figure 5.7: Streamnormal uid energy spectra (Re=6600 p = 500ms). 5
The streamwise particle spectra also shows the same behavior. Though the eect is much smaller than the streamnormal component, there is slightly more energy at the high frequencies in cases of higher drift as the particle is pulled through uid neighborhoods. The uid spectra shows very little eect from g and any eect is dicult to distinguish from noise. The particle Stokes number has an eect on the energy spectra. The streamwise and streamnormal particle spectra (gure 5.8) all show more high frequency energy at the smaller Stokes numbers. This directly follows from the response time of the particle which determines the types of frequencies the particle responds to. The smaller particles are much more responsive to the high frequencies while larger particles are less aected. The uid spectra in both the streamwise and streamnormal (gure 5.9) directions show that particles with less inertia spend more time in areas of rapid uid uctuations. This could potentially be a result of preferential concentration since the smaller particles are the most likely to concentrate at their Stokes numbers. Streamwise uid energy spectra deviate with both gravitational drift and particle inertia. When the particle St k = O(), particles with smaller drift velocities see more high frequency uid uctuations than particles with larger drift velocities. Taking the view that this is the result of preferential concentration, it is immediately clear that increasing gravity reduces the range where preferential concentration occurs. 52
00 0 St k = 2.63 St k = 4.39 St k = 6.4 St k = 8.77 St k = 2.28 St k = 7.54-5/3 slope S ii / u 2 0. 0.0 0.00 0.000 0. 0 f (Hz) Figure 5.8: Streamnormal particle energy spectra (Re=6600, Drift = 0%). 53
00 0 St k = 2.63 St k = 4.39 St k = 6.4 St k = 8.77 St k = 2.28 St k = 7.54-5/3 slope 0. S ii / u 2 0.0 0.00 0.000 e-005 0. 0 f (Hz) Figure 5.9: Streamnormal uid energy spectra (Re=6600, Drift = 0%). One note worthy of mention is the unusual behavior found in the Re = 3300 streamnormal energy spectra (gure 5.0). At approximately the frequency of the moving Eulerian integral scale, an unusual blip occurs in the spectra which corresponds to the oscillations seen in the uid autocorrelations. This integral scale placement is perhaps a coincidence with no pronounced eect seen in the Re=6600 data. The most likely cause is assumed to be noise within the system, though it is interesting to ponder the possibility that the behavior is caused by a particle moving between laminar and turbulent regions of the Re=3300 transition ow. 54
00 0 St k =.24 St k = 2.49 St k = 3.98 St k = 5.97-5/3 slope 0. S ii / u 2 0.0 0.00 0.000 e-005 0. 0 f (Hz) Figure 5.0: Streamnormal uid energy spectra (Re=3300, Drift = 0%). 55