Direct Numerical Simulation of a Turbulent Spot in a Cone Boundary-Layer at Mach 6

Sivasubramanian, Jayahar; Fasel, Hermann F.

doi:10.2514/6.2010-4599

Cited by 21 publications

(8 citation statements)

References 39 publications

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“…However, all available computational results of spot propagation in hypersonic flow in the present literature survey simulated much higher wall temperature ratios T w /T e than actually occur in reflected shock tunnel experiments (see Tables 1 and 2). The computations of Sivasubramanian and Fasel (2010) are most representative of the present conditions and their spot propagation speeds are reasonably consistent with our experimental results. However, the flow conditions in all of these simulations are essentially nonreactive (cold flow with frozen composition) and the ratios of freestream to wall temperature in the simulations are far from our experimental conditions.…”

Section: Discussionsupporting

confidence: 86%

“…Computational studies of spot propagation in supersonic flows have been carried out by Chong and Zhong (2005), Krishan and Sandham (2006), and Jocksch and Kleiser (2008). Sivasubramanian and Fasel (2010) have carried out DNS of turbulent spot evolution on a cone in Mach 6 cold flow and observed the breakdown of two-dimensional second mode disturbances into a threedimensional wave packet or spot. Selected results of experiments and computations are given in Table 2.…”

Section: Introductionmentioning

confidence: 99%

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Turbulent Spot Observations within a Hypervelocity Boundary Layer on a 5-degree Half-Angle Cone

Jewell

Parziale

Leyva

et al. 2012

42nd AIAA Fluid Dynamics Conference and Exhibit

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Nomenclature C le = U le /U e normalized turbulent spot leading edge propagation rate C m = U m /U e normalized turbulent spot trailing edge propagation rate C te = U te /U e normalized turbulent spot centroid/peak propagation rate M e = boundary layer edge Mach number q  = heat flux (transfer rate) L q  = laminar heat flux T q  = turbulent heat flux Re 1 = unit Reynolds number Re 1e = boundary layer edge unit Reynolds number T e = boundary layer edge temperature T w = wall temperature U e = boundary layer edge velocity α = turbulent spot spreading angle

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Section: Discussionsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Turbulent Spot Observations within a Hypervelocity Boundary Layer on a 5-degree Half-Angle Cone

Jewell

Parziale

Leyva

et al. 2012

42nd AIAA Fluid Dynamics Conference and Exhibit

View full text Add to dashboard Cite

show abstract

“…We assume the underlying assumptions [4] to be fulfilled in the streamwise direction. Figure 4 shows turbulent spots obtained by direct numerical simulations (cases B2 and C of [5], see also [6,7]) with a sketch of the corresponding streamwise-directed wave packet. The leading edges of the spots are faster than the ones of the packets, while for the trailing edges the packet and the spot velocities are equal in the cooled case while in the adiabatic case the result Section 9: Flows and transition is ambigious.…”

Section: Spreading Of Wave Packets and Transitionmentioning

confidence: 99%

Spreading of Linear Disturbances in Boundary Layers at Mach Number Five and the Effect of Wall Cooling

Jocksch

Kleiser

2015

Proc Appl Math and Mech

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We determine inviscid eigensolutions in zero pressure gradient flat plate boundary layers at Mach number five and evaluate the eigensolutions with the method of steepest descent. The resulting wave packets show that with wall cooling the tail of the packets becomes slower. Although the boundary layers investigated are all convectively unstable we interpret the slow tail of the wave packets as a trend towards an absolute instability. From a comparison of the wave packets with turbulent spot transition, we conclude that for wall cooling the general transition properties are close to those of an absolutely unstable flow. Laminar boundary layers and linear instabilitiesThe linear stability properties of boundary layers are fundamental to the understanding of the laminar-turbulent transition process. Compressible boundary layers have special linear stability properties, such as the presence of inviscid instabilities [1]. In this contribution we focus on inviscid linear stability eigensolutions of zero pressure gradient flat plate boundary layers at Mach number M = 5 without and with wall cooling. The spreading of linear disturbances in these boundary layers is investigated and its relation to the transition process [2, 3] is discussed.The undisturbed stationary, two-dimensional base flow is obtained from the boundary layer equations for a perfect gas with a ratio of specific heats γ = 1.4 and a constant Prandtl number of P r = 0.72. At M = 5 inviscid instabilities are present in the boundary layer [1] which we compute with a local eigenvalue solver based on a shooting method [3]. The resulting complex dispersion relation ω(α), where ω = ω r + i ω i is the frequency and α = α r + i α i is the wavelength, is shown in Fig. 1 for the first and the second modes [1,5]. Eigensolutions propagating in oblique directions can be determined as if they were two-dimensional but with a base flow projected into their propagation direction [1]. Spreading of wave packets and transitionWe use the method of steepest descent [4] to determine the spreading of localised disturbances. The solutions are wave packets described by rays x/t = ∂ω/∂α with ∂ 2 ω/∂α 2 = 0 of constant growth α i x/t − ω i in the limit of time t → ∞. Since the method provides the solution for this limit and inviscid instabilities are eigensolutions far downstream in the boundary layer (also in the limit t → ∞) the method appears to be well suited for the problem.In the case of an adiabatic wall we analyse modes 1 and 2 separately. The results are shown in Fig. 2. For every ray the solution with largest growth represents the resulting wave packet. For the streamwise direction shown in Fig. 2, the solution of mode 2 shows higher growth rates throughout than the solution of mode 1. Thus mode 1 is negligible compared to mode 2, which dominates the wave packet.The amplification of higher modes by wall cooling T w = T ∞ results in wave packets of larger extent (Fig. 2). The packet has the special property of very high wave numbers at the trailing edge which propagates slo...

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“…8 Recent direct numerical simulation (DNS) efforts have computed the pressure field for wave packets and developing turbulent spots in hypersonic boundary layers. [9][10][11][12] Recent experimental measurements have also measured the internal structure of spots in pressure data under a hypersonic boundary layer. [13][14][15][16] These measurements were made on the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT).…”

Section: Introductionmentioning

confidence: 99%

A Preliminary Study of the Longitudinal Merging of Instability Wave Packets and Turbulent Spots in a Hypersonic Boundary Layer

Casper

Beresh

Schneider

2012

42nd AIAA Fluid Dynamics Conference and Exhibit

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The longitudinal merging of wave packets and turbulent spots in a hypersonic boundary layer was studied on the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel. Two pulsed glow perturbations were created in rapid succession to generate two closely spaced disturbances. The time between the perturbations was varied from run to run to simulate longitudinal merging. Preliminary results suggest that the growth of the trailing disturbance seems to be suppressed by the presence of the leading disturbance. Conversely, the core of the leading disturbance appears unaffected by the presence of the trailing disturbance and behaves as if isolated. This result is consistent with low-speed studies as well as DNS computations of longitudinal merging. However, the present results may be influenced by the perturber performance and therefore further studies of longitudinal merging are necessary to confirm the effect on the internal pressure structure of the interacting disturbances. NomenclatureM freestream Mach number p pressure fluctuation, p − p ∞ (Pa) p ∞ freestream static pressure (Pa) P 0 tunnel stagnation pressure (kPa) Re freestream unit Reynolds number (1/m) T 0 tunnel stagnation temperature (K) ∆t p time between pairs of glow perturbations (ms) U ∞ freestream velocity (m/s) y tunnel spanwise coordinate measured from the centerline of the perturber along the circumference of the wall, positive to the right looking upstream (m) z tunnel axial coordinate with variable origin (m) z tunnel axial coordinate measured from throat (m)

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Direct Numerical Simulation of a Turbulent Spot in a Cone Boundary-Layer at Mach 6

Cited by 21 publications

References 39 publications

Turbulent Spot Observations within a Hypervelocity Boundary Layer on a 5-degree Half-Angle Cone

Turbulent Spot Observations within a Hypervelocity Boundary Layer on a 5-degree Half-Angle Cone

Spreading of Linear Disturbances in Boundary Layers at Mach Number Five and the Effect of Wall Cooling

A Preliminary Study of the Longitudinal Merging of Instability Wave Packets and Turbulent Spots in a Hypersonic Boundary Layer

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