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Optimal two-dimensional roughness for transition delay in high-speed boundary layer
- Reza Jahanbakhshi, Tamer A. Zaki
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- Journal:
- Journal of Fluid Mechanics / Volume 968 / 10 August 2023
- Published online by Cambridge University Press:
- 07 August 2023, A24
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The influence of surface roughness on transition to turbulence in a Mach 4.5 boundary layer is studied using direct numerical simulations. Transition is initiated by the nonlinearly most dangerous inflow disturbance, which causes the earliest possible breakdown on a flat plate for the prescribed inflow energy and Mach number. This disturbance primarily comprises two normal second-mode instability waves and an oblique first mode. When localized roughness is introduced, its shape and location relative to the synchronization points of the inflow waves are confirmed to have a clear impact on the amplification of the second-mode instabilities. The change in modal amplification coincides with the change in the height of the near-wall region where the instability wave speed is supersonic relative to the mean flow; the net effect of a protruding roughness is destabilizing when placed upstream of the synchronization point and stabilizing when placed downstream. Assessment of the effect of the roughness location is followed by an optimization of the roughness height, abruptness and width with the objective of achieving maximum transition delay. The optimization is performed using an ensemble-variational (EnVar) approach, while the location of the roughness is fixed upstream of the synchronization points of the two second-mode waves. The optimal roughness disrupts the phase of the near-wall pressure waves, suppresses the amplification of the primary instability waves and mitigates the nonlinear interactions that lead to breakdown to turbulence. The outcome is a sustained non-turbulent flow throughout the computational domain.
Optimal heat flux for delaying transition to turbulence in a high-speed boundary layer
- Reza Jahanbakhshi, Tamer A. Zaki
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- Journal:
- Journal of Fluid Mechanics / Volume 916 / 10 June 2021
- Published online by Cambridge University Press:
- 14 April 2021, A46
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The optimal steady wall heat flux is sought to delay transition to turbulence in a Mach 4.5 boundary layer, when the free stream disturbance is the nonlinearly most dangerous condition that causes the earliest breakdown to turbulence in the adiabatic flow. The transition-delay strategy is pursued using direct numerical simulations, and the problem is formulated as a constrained optimization where the objective is to minimize the viscous drag force and the control vector is the heat flux at the wall. The optimization is performed using an ensemble-variational approach. The algorithm identifies regions of the flow that are most sensitive to thermal treatment: most of the heating and cooling is applied upstream of the synchronization point of the slow and the fast modes. Attenuation of key instability waves by the optimal heat flux mitigates the nonlinear interactions that preceded breakdown to turbulence in the reference flow, and hence transition is appreciably delayed. Detailed analysis of the acoustic, entropic and solenoidal components of the momentum density vector reveals the stabilizing effects of the optimal heat flux. In addition, the influence of the thermal treatment is not limited to the pretransitional flow where it is concentrated, but rather it persists downstream even within the newly formed fully turbulent boundary layer.
Nonlinearly most dangerous disturbance for high-speed boundary-layer transition
- Reza Jahanbakhshi, Tamer A. Zaki
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- Journal:
- Journal of Fluid Mechanics / Volume 876 / 10 October 2019
- Published online by Cambridge University Press:
- 31 July 2019, pp. 87-121
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Laminar-to-turbulent transition in a zero-pressure-gradient boundary layer at Mach 4.5 is studied using direct numerical simulations. For a given level of total disturbance energy, the inflow spectrum was designed to correspond to the nonlinearly most dangerous condition that leads to the earliest possible transition Reynolds number. The synthesis of the inlet disturbance is formulated as a constrained optimization, where the control vector is comprised of the amplitudes and relative phases of the inlet modes; the constraints are the prescribed total energy and that the flow evolution satisfies the full nonlinear compressible Navier–Stokes equations; the cost function is defined in terms of the mean skin-friction coefficient and, once maximized, ensures the earliest possible transition location. An ensemble-variational (EnVar) technique is developed to solve the optimization problem. Starting from an initial guess, here a broadband disturbance, EnVar updates the estimate of the control vector at the end of each iteration using the gradient of the cost function, which is evaluated from the outcomes of an ensemble of possible solutions. Two inflow conditions are computed, each corresponding to a different level of energy, and their spectra are contrasted: the lower-energy case includes two normal acoustic waves and one oblique vorticity perturbation, whereas the higher-energy condition consists of oblique acoustic and vorticity waves. The focus is placed on the former case because it cannot be categorized as any of the classical breakdown scenarios (fundamental, subharmonic or oblique), while the higher-energy condition undergoes a second-mode oblique transition. At the lower energy level, the instability wave that initiates the rapid breakdown to turbulence is not present at the inlet plane. Instead, it appears at a downstream location after a series of nonlinear interactions that spur the fastest onset of turbulence. The results from the nonlinearly most potent inflow condition are also compared to other inlet disturbances that are selected solely based on linear theory, and which all yield relatively delayed transition onset.
Viscous superlayer in a reacting compressible turbulent mixing layer
- Reza Jahanbakhshi, Cyrus K. Madnia
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- Journal:
- Journal of Fluid Mechanics / Volume 848 / 10 August 2018
- Published online by Cambridge University Press:
- 13 June 2018, pp. 743-755
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Direct numerical simulations of temporally evolving reacting compressible mixing layers have been performed to study the viscous superlayer (VSL) at the outer edge of the interface layer. Budgets of the transport equation of enstrophy conditioned on the normal distance from the turbulent/non-turbulent interface are used to examine the features of the VSL. A new method is introduced to detect and to quantify the thickness of the VSL in reacting compressible flows. It involves finding the correlation coefficient of the viscous diffusion term with the viscous dissipation term. It is shown that, while compressibility seems to have little effect on the thickness of the VSL, as the level of heat release increases, the thickness of this layer decreases. Furthermore, it is observed that a thinner VSL propagates slower, resulting in a decrease of the rate of entrainment into the mixing layer.
The effect of heat release on the entrainment in a turbulent mixing layer
- Reza Jahanbakhshi, Cyrus K. Madnia
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- Journal:
- Journal of Fluid Mechanics / Volume 844 / 10 June 2018
- Published online by Cambridge University Press:
- 03 April 2018, pp. 92-126
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Direct numerical simulations of a temporally evolving compressible reacting mixing layer have been performed to study the entrainment of the irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). In order to study the effects of heat release and interaction of the flame with the TNTI on turbulence several cases with different heat release levels, $Q$, and stoichiometric mixture fractions are chosen for the simulations with the highest opted value for $Q$ corresponding to hydrogen combustion in air. The combustion is mimicked by a one-step irreversible global reaction, and infinitely fast chemistry approximation is used to compute the species mass fractions. Entrainment is studied via two mechanisms: nibbling, considered as the vorticity transport across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. As the level of heat release increases, the total entrained mass flow rate into the mixing layer decreases. In a reacting mixing layer by increasing the heat release rate, the mass flow rate due to nibbling is shown to decrease mostly due to a reduction of the local entrainment velocity, while the surface area of the TNTI does not change significantly. It is also observed that nibbling is a viscous dominated mechanism in non-reacting flows, whereas it is mostly carried out by inviscid terms in reacting flows with high level of heat release. The contribution of the engulfment to entrainment is small for the non-reacting mixing layers, while mass flow rate due to engulfment can constitute close to 40 % of the total entrainment in reacting cases. This increase is primarily related to a decrease of entrained mass flow rate due to nibbling, while the entrained mass flow rate due to engulfment does not change significantly in reacting cases. It is shown that the total entrained mass flow rate in reacting and non-reacting compressible mixing layers can be estimated from an expression containing the convective Mach number and the density change due to heat release.
Entrainment in a compressible turbulent shear layer
- Reza Jahanbakhshi, Cyrus K. Madnia
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- Journal:
- Journal of Fluid Mechanics / Volume 797 / 25 June 2016
- Published online by Cambridge University Press:
- 24 May 2016, pp. 564-603
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Direct numerical simulations (DNS) of temporally evolving shear layers have been performed to study the entrainment of irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). Four cases with convective Mach number from 0.2 to 1.8 are used. Entrainment is studied via two mechanisms; nibbling, considered as vorticity diffusion across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. The mass flow rate due to nibbling is calculated as the product of the entrained mass flux with the surface area of the TNTI. It is found that increasing the convective Mach number results in a decrease of the average entrained mass flux and the surface area of the TNTI. For the incompressible shear layer the local entrained mass flux is shown to be highly correlated with the viscous terms. However, as the convective Mach number increases, the mass fluxes due to the baroclinic and the dilatation terms play a more important role in the local entrainment process. It is observed that the entrained mass flux is dependent on the local dilatation and geometrical shape of the TNTI. For a compressible shear layer, most of the entrainment of the irrotational flow into the turbulent region due to nibbling is associated with the compressed regions on the TNTI. As the convective Mach number increases, the percentage of the compressed regions on the TNTI decreases, resulting in a reduction of the average entrained mass flux. It is also shown that the local shape of the interface, looking from the turbulent region, is dominated by concave shaped surfaces with radii of curvature of the order of the Taylor length scale. The average entrained mass flux is found to be larger on highly curved concave shaped surfaces regardless of the level of dilatation. The mass fluxes due to vortex stretching, baroclinic torque and the shear stress/density gradient terms are weak functions of the local curvatures on the TNTI, whereas the mass fluxes due to dilatation and viscous diffusion plus the viscous dissipation terms have a stronger dependency on the local curvatures. As the convective Mach number increases, the probability of finding highly curved concave shaped surfaces on the TNTI decreases, whereas the probability of finding flatter concave and convex shaped surfaces increases. This results in a decrease of the average entrained mass flux across the TNTI. Similar to the previous works on jets, the results show that the contribution of the engulfment to the total entrainment is small for both incompressible and compressible mixing layers. It is also shown that increasing the convective Mach number decreases the velocities associated with the entrainment, i.e. induced velocity, boundary entrainment velocity and local entrainment velocity.