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Fig. 12 Flat plate and cone intermittency (y) curves for several spot generation rates n computed at the conditions of shot 2776. These curves have been transformed by the Narasimha (1957) linearizing function F(y)

Figure 12 Flat plate and cone intermittency (y) curves for several spot generation rates n computed at the conditions of shot 2776. These curves have been transformed by the Narasimha (1957) linearizing function F(y)

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Fig. 1 Schematic depiction of a triangular turbulent spot, with the velocities at the leading and trailing edges labeled as U,, and U,,, and the spreading angle labeled as a, the spreading angle with respect to the velocity vector at the boundary layer edge. Both U,, and U,, are some fraction of U,. Not depicted is U,,, the spot peak heating veloc- ity
Fig. 1 Schematic depiction of a triangular turbulent spot, with the velocities at the leading and trailing edges labeled as U,, and U,,, and the spreading angle labeled as a, the spreading angle with respect to the velocity vector at the boundary layer edge. Both U,, and U,, are some fraction of U,. Not depicted is U,,, the spot peak heating veloc- ity
Fig. 2 Four frames from shot 2698 covering a total time of 0.3 ms, during which a turbulent spot is observed near the tip and propagates downstream. This example was chosen because the spot is well- isolated and happens to be approximately centered on the developed cone surface. Thermocouple locations are indicated by small circles
Fig. 2 Four frames from shot 2698 covering a total time of 0.3 ms, during which a turbulent spot is observed near the tip and propagates downstream. This example was chosen because the spot is well- isolated and happens to be approximately centered on the developed cone surface. Thermocouple locations are indicated by small circles
Fig. 3 A spot observed as a localized region of increased heat flux typically lasting for 20-30 time steps (0.1-0.15 ms) over an individ- ual gauge, during shot 2700 along one ray of gauges between TC16 and TC80, tracked in successive heat transfer (in MW/m7) versus time plots. The steady test time for this experiment begins at 1.0 ms
Fig. 3 A spot observed as a localized region of increased heat flux typically lasting for 20-30 time steps (0.1-0.15 ms) over an individ- ual gauge, during shot 2700 along one ray of gauges between TC16 and TC80, tracked in successive heat transfer (in MW/m7) versus time plots. The steady test time for this experiment begins at 1.0 ms
Fig. 6 Leading edge and trailing edge velocities for all spots nor- malized by U,, with average normalized velocities (C,,, C,, and C,,) depicted as lines with uncertainty zones
Fig. 6 Leading edge and trailing edge velocities for all spots nor- malized by U,, with average normalized velocities (C,,, C,, and C,,) depicted as lines with uncertainty zones
Each of these spots was isolated enough to distinguish as a distinct phenomenon on the cone during the steady test time, and was observed tc propagate downstream over three or more heat transfer gauges, permitting the measurement of leading edge, trailing edge, and peak heating velocities. For tests 2737, 2809-2818, the balance of the composition was air. There were various extents of nonequilibrium and dissociation in all cases; the computed boundary layer edge conditions (species, temperature and pressure) are tabulated in Jewell and Shepherd (2014)
Each of these spots was isolated enough to distinguish as a distinct phenomenon on the cone during the steady test time, and was observed tc propagate downstream over three or more heat transfer gauges, permitting the measurement of leading edge, trailing edge, and peak heating velocities. For tests 2737, 2809-2818, the balance of the composition was air. There were various extents of nonequilibrium and dissociation in all cases; the computed boundary layer edge conditions (species, temperature and pressure) are tabulated in Jewell and Shepherd (2014)
Fig. 8 Flat plate and cone intermittency y and curves for n = 4 x 10° computed at shot 2776 conditions, compared with the relevant univer- sal intermittency curves. Excellent agreement is obtained Fig. 7 Schematic depiction of a triangular turbulent spot on the developed surface of a cone, with the velocities at the leading and trailing edges labeled as U,, and U,,, and the angle at which additional fluid is entrained in the spot as it moves labeled as a, the spreading angle with respect to the velocity at the boundary layer edge, U,. In this coordinate system, the boundary layer edge velocity acting on the spots has a transverse component
Fig. 8 Flat plate and cone intermittency y and curves for n = 4 x 10° computed at shot 2776 conditions, compared with the relevant univer- sal intermittency curves. Excellent agreement is obtained Fig. 7 Schematic depiction of a triangular turbulent spot on the developed surface of a cone, with the velocities at the leading and trailing edges labeled as U,, and U,,, and the angle at which additional fluid is entrained in the spot as it moves labeled as a, the spreading angle with respect to the velocity at the boundary layer edge, U,. In this coordinate system, the boundary layer edge velocity acting on the spots has a transverse component
Fig. 10 Path of a single centered spot in angular coordinates with spreading angle a = 2.5° generated at x7, = 0.389, for a cylinder (top) and an axisymmetric cone with 5° half-angle (bottom), both 1 m long with circumference of 0.220 m at the transition point Fig. 9 Path of a single centered spot with spreading angle a = 2.5° generated at x7, = 0.389, for a plate or cylinder (top) and an axisym- metric cone with 5° half-angle (bottom). While the growth profile of a spot in both geometries is similar, the increasing total surface area of the cone with respect to x means that each spot covers a smaller circumferential fraction of the surface, as shown in Fig. 10
Fig. 10 Path of a single centered spot in angular coordinates with spreading angle a = 2.5° generated at x7, = 0.389, for a cylinder (top) and an axisymmetric cone with 5° half-angle (bottom), both 1 m long with circumference of 0.220 m at the transition point Fig. 9 Path of a single centered spot with spreading angle a = 2.5° generated at x7, = 0.389, for a plate or cylinder (top) and an axisym- metric cone with 5° half-angle (bottom). While the growth profile of a spot in both geometries is similar, the increasing total surface area of the cone with respect to x means that each spot covers a smaller circumferential fraction of the surface, as shown in Fig. 10
Fig. 11 Flat plate and cone intermittency (y) curves for several spot generation rates n computed at the conditions of shot 2776
Fig. 11 Flat plate and cone intermittency (y) curves for several spot generation rates n computed at the conditions of shot 2776
For each experiment record ed in Jewell (2014) and Jewell and Shepherd (2014) for which both transition onset and transition completion are c early observed, a set of simu- lations are run varying the spot generation parameter n, with spots generated randomly along the band defined by Xx = Xp, at a rate defined by t of that band and the input n. he product of the circumference For each case, a total of 10 ms of test time is run (discarding the first 2(1 — x7,)/U. ms to allow time for the spots to fully develop), with a time step
For each experiment record ed in Jewell (2014) and Jewell and Shepherd (2014) for which both transition onset and transition completion are c early observed, a set of simu- lations are run varying the spot generation parameter n, with spots generated randomly along the band defined by Xx = Xp, at a rate defined by t of that band and the input n. he product of the circumference For each case, a total of 10 ms of test time is run (discarding the first 2(1 — x7,)/U. ms to allow time for the spots to fully develop), with a time step
Fig. 14 Experimentally measured distance between transition onset and transition completion for shot 2740. The contour plot (bottom) presents the average heat flux during the test time over the surface of the cone. On the Re vs. St plot (top), a line is fit through the tran- sitional region, and the transition onset location x7, is taken as the intersection of the fit with the laminar correlation. The transition completion location X7,comp 18 taken as the intersection of the fit with the White and Christoph (1972) turbulent correlation. The distance between the two points is Ax,,
Fig. 14 Experimentally measured distance between transition onset and transition completion for shot 2740. The contour plot (bottom) presents the average heat flux during the test time over the surface of the cone. On the Re vs. St plot (top), a line is fit through the tran- sitional region, and the transition onset location x7, is taken as the intersection of the fit with the laminar correlation. The transition completion location X7,comp 18 taken as the intersection of the fit with the White and Christoph (1972) turbulent correlation. The distance between the two points is Ax,,
Fig. 15 Spot generation rates for the present data compared with the results from Mee and Tanguy (2015)
Fig. 15 Spot generation rates for the present data compared with the results from Mee and Tanguy (2015)
Fig. 16 Computed and experimental transition distance Ax, for shot 2740
Fig. 16 Computed and experimental transition distance Ax, for shot 2740
The calculated spot spreading angle (a) and boundary layer edge unit Reynolds number (unit Re) are included along with other relevant paran eters Table 2 Spot generation rates computed via the mechanistic process described in Sect. 3 for transition onset-completion length (Ax;,) during the present test campaign, taken from 17 tests for which clear transition onset (x7,) and transition completion (%7,comp) locations were observed
The calculated spot spreading angle (a) and boundary layer edge unit Reynolds number (unit Re) are included along with other relevant paran eters Table 2 Spot generation rates computed via the mechanistic process described in Sect. 3 for transition onset-completion length (Ax;,) during the present test campaign, taken from 17 tests for which clear transition onset (x7,) and transition completion (%7,comp) locations were observed
Fig. 17 Experimental transition distance Ax;, compared with Ax, computed via the mechanistic process described in Sect. 3 for shot 2740 with C,, = 0.5, which was the value used by Mee and Tanguy (2015). Compared with the computations in Fig. 16, the matching value of n for the observed transition length drops by 3.4 x 10° spots/ m/s. This accounts for most of the difference between the present computations and those of Mee and Tanguy (2015)
Fig. 17 Experimental transition distance Ax;, compared with Ax, computed via the mechanistic process described in Sect. 3 for shot 2740 with C,, = 0.5, which was the value used by Mee and Tanguy (2015). Compared with the computations in Fig. 16, the matching value of n for the observed transition length drops by 3.4 x 10° spots/ m/s. This accounts for most of the difference between the present computations and those of Mee and Tanguy (2015)
* Value not reported > Calculated by the present authors from other reported values © Spot “wing tip” convection velocity Table 3 Results from past spot propagation studies, based on super- sonic and hypersonic experiments (Zanchetta and Hillier 1996; Fiala et al. 2006; Mee 2002; Clark et al. 1994) and computations [Krishnan and Sandham (2006), two results from Jocksch and Kleiser (2008), Jocksch (2009) and Sivasubramanian and Fasel (2010)] reported for a range of conditions and presented together with the results from the present study
* Value not reported > Calculated by the present authors from other reported values © Spot “wing tip” convection velocity Table 3 Results from past spot propagation studies, based on super- sonic and hypersonic experiments (Zanchetta and Hillier 1996; Fiala et al. 2006; Mee 2002; Clark et al. 1994) and computations [Krishnan and Sandham (2006), two results from Jocksch and Kleiser (2008), Jocksch (2009) and Sivasubramanian and Fasel (2010)] reported for a range of conditions and presented together with the results from the present study
Related topics:
Turbulent FlowsCompressible Fluid DynamicsHypersonic AerothermodynamicsShock Tubes
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