Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

Kitsios, Vassili; Sekimoto, Atsushi; Atkinson, Callum; Sillero, Juan A.; Borrell, Guillem; Gungor, Ayse G.; Jiménez, Javier; Soria, Julio

doi:10.1017/jfm.2017.549

Cited by 80 publications

(117 citation statements)

References 47 publications

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“…Mellor and Gibson (1966) defined the pressure velocity u p = δ * /ρdP e /dx, which is related to the Clauser pressure-gradient parameter as β 2 = u p /u τ . Similarly, it is possible to define an outer-scaled APG parameter as u p /U e , as in the study by Kitsios et al (2017), who also considered a strongly-decelerated APG with β = 39. The ratio u p /U e is shown in Figure 7 for the four wing cases under consideration.…”

Section: Boundary-layer Developmentmentioning

confidence: 99%

“…The use of β to characterize the pressuregradient magnitude and to identify near-equilibrium TBLs was introduced by Clauser (1954Clauser ( , 1956, together with Mellor and Gibson (1966), who developed a theoretical framework for such TBLs. Although in the very strong APG conditions beyond x ss /c 0.95 the β parameter may not be adequate to characterize the effect of the pressure gradient on the TBL (as in the work by Kitsios et al (2017)), the APG on the flow upstream can be assessed in terms of β. The fact that the lower-Re wings are subjected to a larger u p /U e ratio is connected to their stronger wall-normal velocity, as discussed below.…”

Section: Boundary-layer Developmentmentioning

confidence: 99%

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Turbulent boundary layers around wing sections up to Rec=1,000,000

Vinuesa

Negi

Atzori

et al. 2018

International Journal of Heat and Fluid Flow

126

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Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we analyze four cases at Reynolds numbers based on freestream velocity and chord length ranging from Re c = 100, 000 to 1, 000, 000, all of them with 5 • angle of attack. The results of four well-resolved large-eddy simulations (LESs) are used to characterize the effect of Reynolds number on APG TBLs subjected to approximately the same pressure-gradient distribution (defined by the Clauser pressure-gradient parameter β). Comparisons of the wing profiles with zeropressure-gradient (ZPG) data at matched friction Reynolds numbers reveal that, for approximately the same β distribution, the lower-Reynolds-number boundary layers are more sensitive to pressure-gradient effects. This is reflected in the values of the inner-scaled edge velocity U + e , the shape factor H, the components of the Reynolds-stress tensor in the outer region and the outer-region production of turbulent kinetic energy. This conclusion is supported by the larger wall-normal velocities and outer-scaled fluctuations observed in the lower-Re c cases. Thus, our results suggest that two complementing mechanisms contribute to the development of the outer region in TBLs and the formation of large-scale energetic structures: one mechanism associated with the increase in Reynolds number, and another one connected to the APG. Future extensions of the present work will be aimed at studying the differences in the outer-region energizing mechanisms due to APGs and

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Section: Boundary-layer Developmentmentioning

confidence: 99%

Section: Boundary-layer Developmentmentioning

confidence: 99%

Turbulent boundary layers around wing sections up to Rec=1,000,000

Vinuesa

Negi

Atzori

et al. 2018

International Journal of Heat and Fluid Flow

126

View full text Add to dashboard Cite

show abstract

“…The latter case is the one considered in the present work for adverse-pressure-gradient turbulent boundary layers. This explains the lower values of the shape factor obtained by Clauser 3 and Lee 26 compared to the higher (close to separation) values of Stratford 27 , Mellor and Gibson 19 or Kitsios et al 28 for the same value of m. Besides, Schofield also found that near-equilibrium is not possible when m < −0.3 which is a threshold in accordance with the results of Head 23 and close to the value of −1/3 given by Townsend 20 . These two conclusions are also observable in the work of Clauser 3 .…”

Section: Please Cite This Article As Doi:101063/15125496mentioning

confidence: 76%

Effects of upstream perturbations on the solution of the laminar and fully turbulent boundary layer equations with pressure gradients

2019

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The aim of this work is to contribute to the understanding of sensitivity of boundary layers to the upstream boundary condition and history effects for both laminar and fully turbulent states in equilibrium conditions as well as some non-equilibrium turbulent boundary layers. Solutions of the two-dimensional boundary layer equations are obtained numerically for this study together with the RANS (Reynolds-averaged Navier-Stokes) approach for turbulence modeling. The external pressure gradient is imposed through an evolution of the external velocity of the form U e ∝ (x − x 0) m , and boundary layers are initialized from a profile giving a perturbed shape factor. It is found that laminar boundary layers require very long distances for convergence towards the non-disturbed profiles in terms of the initial boundary layer thickness (∼ 10 4 δ in) and that this distance is dependent on m. In turbulent boundary layers much shorter distances, although still large (∼ 10 2 δ in), are observed and they are also dependent on m. The maximum adverse pressure gradient for which convergence to a reference solution is possible is also studied finding that there is no limit for attached laminar boundary layers, whereas turbulent boundary layers do not converge once they are out of equilibrium. The convergence distances in turbulent boundary layers are also studied in terms of the turnover length (δU + e) because it has been shown to be more appropriate to refer the convergence distance to this length rather than the boundary layer thickness. The values for convergence using this criterion are extended to pressure gradient boundary layers. Moreover an equivalent criterion is proposed and studied for laminar boundary layers based on the viscous characteristic time.

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“…All turbulent terms (3.7)-(3.15) and the viscosity (3.16) are represented analogously to the analysis of George & Castillo (1993) as products of an x-dependent and an η-dependent quantity. In contrast to most previous incompressible analyses, where the displacement thickness δ * is anticipated as length scale L 0 (x) for the outer scaling (Townsend 1956b;Castillo et al 2004;Kitsios et al 2016Kitsios et al , 2017,…”

Section: Outer-layer Ansatz Functionsmentioning

confidence: 80%

“…Thus, the similarity analysis itself only provides templates for conditions that must be fulfilled by possible characteristic scales in case of self-similarity; consequently, without the specific choice of scales, the results are not applicable to real flow data. In analogy to the analysis of incompressible TBLs, such as by George & Castillo (1993), Castillo et al (2004), Maciel et al (2006) and Kitsios et al (2016Kitsios et al ( , 2017, see § 2.2.2, a separation-of-variables approach is used for the present analysis. Every quantity Ψ (x, y) of the compressible two-dimensional boundary-layer equations is hereby assumed to consist of a combination of ansatz functions; for example, Ψ (x, y) = Φ(x)φ(η), where Φ(x) and φ(η) depend only on either the streamwise position x or the wall-normal position η = y/L 0 (x).…”

Section: Methodsmentioning

confidence: 99%

Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer

et al. 2019

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A thorough self-similarity analysis is presented to investigate the properties of self-similarity for the outer layer of compressible turbulent boundary layers. The results are validated using the compressible and quasi-incompressible direct numerical simulation (DNS) data shown and discussed in the first part of this study; see Wenzel et al. (J. Fluid Mech., vol. 880, 2019, pp. 239–283). The analysis is carried out for a general set of characteristic scales, and conditions are derived which have to be fulfilled by these sets in case of self-similarity. To evaluate the main findings derived, four sets of characteristic scales are proposed and tested. These represent compressible extensions of the incompressible edge scaling, friction scaling, Zagarola–Smits scaling and a newly defined Rotta–Clauser scaling. Their scaling success is assessed by checking the collapse of flow-field profiles extracted at various streamwise positions, being normalized by the respective scales. For a good set of scales, most conditions derived in the analysis are fulfilled. As suggested by the data investigated, approximate self-similarity can be achieved for the mean-flow distributions of the velocity, mass flux and total enthalpy and the turbulent terms. Self-similarity thus can be stated to be achievable to a very high degree in the compressible regime. Revealed by the analysis and confirmed by the DNS data, this state is predicted by the compressible pressure-gradient boundary-layer growth parameter $\unicode[STIX]{x1D6EC}_{c}$, which is similar to the incompressible one found by related incompressible studies. Using appropriate adaption, $\unicode[STIX]{x1D6EC}_{c}$ values become comparable for compressible and incompressible pressure-gradient cases with similar wall-normal shear-stress distributions. The Rotta–Clauser parameter in its traditional form $\unicode[STIX]{x1D6FD}_{K}=(\unicode[STIX]{x1D6FF}_{K}^{\ast }/\bar{\unicode[STIX]{x1D70F}}_{w})(\text{d}p_{e}/\text{d}x)$ with the kinematic (incompressible) displacement thickness $\unicode[STIX]{x1D6FF}_{K}^{\ast }$ is shown to be a valid parameter of the form $\unicode[STIX]{x1D6EC}_{c}$ and hence still is a good indicator for equilibrium flow in the compressible regime at the finite Reynolds numbers considered. Furthermore, the analysis reveals that the often neglected derivative of the length scale, $\text{d}L_{0}/\text{d}x$, can be incorporated, which was found to have an important influence on the scaling success of common ‘low-Reynolds-number’ DNS data; this holds for both incompressible and compressible flow. Especially for the scaling of the $\bar{\unicode[STIX]{x1D70C}}\widetilde{u^{\prime \prime }v^{\prime \prime }}$ stress and thus also the wall shear stress $\bar{\unicode[STIX]{x1D70F}}_{w}$, the inclusion of $\text{d}L_{0}/\text{d}x$ leads to palpable improvements.

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Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

Cited by 80 publications

References 47 publications

Turbulent boundary layers around wing sections up to Rec=1,000,000

Turbulent boundary layers around wing sections up to Rec=1,000,000

Effects of upstream perturbations on the solution of the laminar and fully turbulent boundary layer equations with pressure gradients

Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer

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