An official website of the United States government
Direct numerical simulations of spanwise-rotating turbulent channel flow with a parabolic bump on the bottom wall are employed to investigate the effects of rotation on flow separation. Four rotation rates,$$Ro_b := 2\varOmega H/U_b = \pm 0.42$$,$$\pm$$1.0, are compared with the non-rotating scenario. The mild adverse pressure gradient induced by the lee side of the bump allows for a variable pressure-induced separation. The separation region is reduced (increased) when the bump is on the anti-cyclonic (cyclonic) side of the channel, compared with the non-rotating separation. The total drag is reduced in all rotating cases. Through several mechanisms, rotation alters the onset of separation, reattachment and wake recovery. The mean momentum deficit is found to be the key. A physical interpretation of the ratio between the system rotation and mean shear vorticity,$$S:=\varOmega /\varOmega _s$$, provides the mechanisms regarding stability thresholds$$S=-0.5$$and$$-$$1. The rotation effects are explained accordingly, with reference to the dynamics of several flow structures. For anti-cyclonic separation, particularly, the interaction between the Taylor–Görtler vortices and hairpin vortices of wall-bounded turbulence is proven to be responsible for the breakdown of the separating shear layer. A generalized argument is made regarding the essential role of near-wall deceleration and resultant ejection of enhanced hairpin vortices in destabilizing an anti-cyclonic flow. This mechanism is anticipated to have broad impacts on other applications in analogy to rotating shear flows, such as thermal convection and boundary layers over concave walls.
more »
« less
Optimal wall shapes and flows for steady planar convection
We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer ($$Nu$$) between hot and cold walls, for a given rate of viscous dissipation by the flow ($$Pe^2$$), with no-slip boundary conditions at the walls. In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical non-zero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a$$Pe^{-1/3}$$scaling of horizontal lengths. The corresponding rate of heat transfer$$Nu \sim Pe^{2/3}$$. We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large$$Pe$$.
more »
« less
- Award ID(s):
- 2204900
- PAR ID:
- 10535894
- Publisher / Repository:
- Cambridge Univ Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 984
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A lubrication analysis is presented for the resistances between permeable spherical particles in near contact,$$h_0/a\ll 1$$, where$$h_0$$is the minimum separation between the particles, and$$a=a_1 a_2/(a_1+a_2)$$is the reduced radius. Darcy's law is used to describe the flow inside the permeable particles and no-slip boundary conditions are applied at the particle surfaces. The weak permeability regime$$K=k/a^{2} \ll 1$$is considered, where$$k=\frac {1}{2}(k_1+k_2)$$is the mean permeability. Particle permeability enters the lubrication resistances through two functions of$$q=K^{-2/5}h_0/a$$, one describing axisymmetric motions, the other transverse. These functions are obtained by solving an integral equation for the pressure in the near-contact region. The set of resistance functions thus obtained provide the complete set of near-contact resistance functions for permeable spheres and match asymptotically to the standard hard-sphere resistances that describe pairwise hydrodynamic interactions away from the near-contact region. The results show that permeability removes the contact singularity for non-shearing particle motions, allowing rolling without slip and finite separation velocities between touching particles. Axisymmetric and transverse mobility functions are presented that describe relative particle motion under the action of prescribed forces and in linear flows. At contact, the axisymmetric mobility under the action of oppositely directed forces is$$U/U_0=d_0K^{2/5}$$, where$$U$$is the relative velocity,$$U_0$$is the velocity in the absence of hydrodynamic interactions and$$d_0=1.332$$. Under the action of a constant tangential force, a particle in contact with a permeable half-space rolls without slipping with velocity$$U/U_0=d_1(d_2+\log K^{-1})^{-1}$$, where$$d_1=3.125$$and$$d_2=6.666$$; in shear flow, the same expression holds with$$d_1=7.280$$.more » « less
-
Pressure-driven flows of viscoelastic fluids in narrow non-uniform geometries are common in physiological flows and various industrial applications. For such flows, one of the main interests is understanding the relationship between the flow rate$$q$$and the pressure drop$$\Delta p$$, which, to date, is studied primarily using numerical simulations. We analyse the flow of the Oldroyd-B fluid in slowly varying arbitrarily shaped, contracting channels and present a theoretical framework for calculating the$$q-\Delta p$$relation. We apply lubrication theory and consider the ultra-dilute limit, in which the velocity profile remains parabolic and Newtonian, resulting in a one-way coupling between the velocity and polymer conformation tensor. This one-way coupling enables us to derive closed-form expressions for the conformation tensor and the flow rate–pressure drop relation for arbitrary values of the Deborah number ($$De$$). Furthermore, we provide analytical expressions for the conformation tensor and the$$q-\Delta p$$relation in the high-Deborah-number limit, complementing our previous low-Deborah-number lubrication analysis. We reveal that the pressure drop in the contraction monotonically decreases with$$De$$, having linear scaling at high Deborah numbers, and identify the physical mechanisms governing the pressure drop reduction. We further elucidate the spatial relaxation of elastic stresses and pressure gradient in the exit channel following the contraction and show that the downstream distance required for such relaxation scales linearly with$$De$$.more » « less
-
Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius$$R$$and axial length$$10{\rm \pi} R$$at friction Reynolds numbers up to$$Re_\tau =5200$$using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor$$\lambda$$overshoots by$$2\,\%$$and undershoots by$$0.6\,\%$$the Prandtl friction law at low and high$$Re$$ranges, respectively. In addition,$$\lambda$$in our results is slightly higher than in Pirozzoliet al.(J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichiet al.(Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to$$y^+=250$$, has not yet developed a plateau farther away from the wall in the pipes even for the$$Re_\tau =5200$$cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with$$Re_\tau$$– are lower in the pipe than in the channel, but the difference decreases with increasing$$Re_\tau$$. While the wall value is slightly lower in the channel than in the pipe at the same$$Re_\tau$$, the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a$$k^{-1}$$dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.more » « less
-
The transition to turbulence in a plane Poiseuille flow of dilute polymer solutions is studied by direct numerical simulations of a finitely extensible nonlinear elastic fluid with the Peterlin closure. The range of Reynolds number ($$Re$$)$$2000 \le Re \le 5000$$is studied but with the same level of elasticity in viscoelastic flows. The evolution of a finite-amplitude perturbation and its effects on the transition dynamics are investigated. A viscoelastic flow begins transition at an earlier time than its Newtonian counterparts, but the transition time appears to be insensitive to polymer concentration in the dilute and semi-dilute regimes studied. Increasing polymer concentration, however, decreases the maximum attainable energy growth during the transition process. The critical or minimum perturbation amplitude required to trigger transition is computed. Interestingly, both Newtonian and viscoelastic flows follow almost the same power-law scaling of$$Re^\gamma$$with the critical exponent$$\gamma \approx -1.25$$, which is in close agreement with previous studies. However, a shift downward is observed for viscoelastic flow, suggesting that smaller perturbation amplitudes are required for the transition. A mechanism of the early transition is investigated by the evolution of wall-normal and spanwise velocity fluctuations and flow structure. The early growth of these fluctuations and the formation of quasi-streamwise vortices around low-speed streaks are promoted by polymers, hence causing an early transition. These vortical structures are found to support the critical exponent$$\gamma \approx -1.25$$. Once the transition process is completed, polymers play a role in dampening the wall-normal and spanwise velocity fluctuations and vortices to attain a drag-reduced state in viscoelastic turbulent flows.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2024.202
