8 results
Effect of small roughness elements on thermal statistics of a turbulent boundary layer at moderate Reynolds number
- Ali Doosttalab, Guillermo Araya, Jensen Newman, Ronald J. Adrian, Kenneth Jansen, Luciano Castillo
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- Journal of Fluid Mechanics / Volume 787 / 25 January 2016
- Published online by Cambridge University Press:
- 08 December 2015, pp. 84-115
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A zero-pressure-gradient turbulent boundary layer flowing over a transitionally rough surface (24-grit sandpaper) with $k^{+}\approx 11$ and a momentum-thickness Reynolds number of approximately 2400 is studied using direct numerical simulation (DNS). Heat transfer between the isothermal rough surface and the turbulent flow with molecular Prandtl number $Pr=0.71$ is simulated. The dynamic multiscale approach developed by Araya et al. (J. Fluid Mech., vol. 670, 2011, pp. 581–605) is employed to prescribe realistic time-dependent thermal inflow boundary conditions. In general, the rough surface reduces mean and fluctuating temperature profiles with respect to the smooth surface flow when normalized by Wang & Castillo (J. Turbul., vol. 4, 2003, 006) inner/outer scaling. It is shown that the Reynolds analogy does not hold for $y^{+}<9$. In this region the value of the turbulent Prandtl number departs substantially from unity. Above this region the Reynolds analogy is only approximately valid, with the turbulent Prandtl number decreasing from 1 to 0.7 across the boundary layer for rough and smooth walls. In comparison with the smooth-wall case, the turbulent transport of heat per unit mass, $\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$, towards the wall is enhanced in the buffer layer, but the transport of $\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$ away from the wall is reduced in the outer layer for the rough case; similar behaviour is found for the vertical transport of turbulent momentum per unit mass, $\overline{v^{\prime }u^{\prime }v^{\prime }}$. Above the roughness sublayer (3$k$–5$k$) it is found that most of the temperature field statistics, including higher-order moments and conditional averages, are highly similar for the smooth and rough surface flow, showing that the Townsend’s Reynolds number similarity hypothesis applies for the thermal field as well as the velocity field for the Reynolds number and $k^{+}$ considered in this study.
The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers
- Guillermo Araya, Luciano Castillo, Fazle Hussain
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- Journal of Fluid Mechanics / Volume 775 / 25 July 2015
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- 19 June 2015, pp. 189-200
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Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, $\overline{u^{\prime }v^{\prime }}^{+}$, monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. $-\overline{u^{\prime }v^{\prime }}^{+}=-(1/A_{uv})\ln y^{+}+B_{uv}$) in the mesolayer region (e.g. $50\leqslant y^{+}\leqslant 170$). The thickness of the log layer of $\overline{u^{\prime }v^{\prime }}^{+}$ increases with the streamwise distance and with the pressure gradient strength, extending over a large portion of the TBL thickness (up to 55 %). Simulations reveal that $V^{+}\,\partial U^{+}/\partial y^{+}\sim 1/y^{+}\sim \partial \overline{u^{\prime }v^{\prime }}^{+}/\partial y^{+}$, resulting in a logarithmic $\overline{u^{\prime }v^{\prime }}^{+}$ profile. Also, $V^{+}\sim -y^{+}$ is no longer negligible as in zero-pressure-gradient (ZPG) flows. Other experimental/numerical data at similar favourable-pressure-gradient (FPG) strengths also show the presence of a log region in $\overline{u^{\prime }v^{\prime }}^{+}$. This log region in $\overline{u^{\prime }v^{\prime }}^{+}$ is larger in sink flows than in other spatially developing FPG flows. The latter flows exhibit the presence of a small power-law region in $\overline{u^{\prime }v^{\prime }}^{+}$, which is non-existent in sink flows.
DNS of a turbulent boundary layer with surface roughness
- James Cardillo, Yi Chen, Guillermo Araya, Jensen Newman, Kenneth Jansen, Luciano Castillo
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- Journal:
- Journal of Fluid Mechanics / Volume 729 / 25 August 2013
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- 24 July 2013, pp. 603-637
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A pioneer direct numerical simulation (DNS) of a turbulent boundary layer at $R{e}_{\theta } = 2077{{\unicode{x2013}}}2439$, was performed, on a rough surface and with a zero pressure gradient (ZPG). The boundary layer was subjected to transitional, 24-grit sandpaper surface roughness, with a roughness parameter of ${k}^{+ } \simeq 11$. The computational method involves a synergy of the dynamic multi-scale approach devised by Araya et al. (2011) for prescribing inlet turbulent boundary conditions and a new methodology for mapping high-resolution topographical surface data into a computational fluid dynamics (CFD) environment. It is shown here that the dynamic multi-scale approach can be successfully extended to simulations which incorporate surface roughness. The DNS results demonstrate good agreement with the laser Doppler anemometry (LDA) measurements performed by Brzek et al. (2008) and Schultz & Flack (2003) under similar conditions in terms of mean velocity profiles, Reynolds stresses and flow parameters, such as the skin friction coefficient, boundary and momentum thicknesses. Further, it is demonstrated that the effects of the surface roughness on the Reynolds stresses, at the values of $R{e}_{\theta } = 2077{{\unicode{x2013}}}2439$, are scale-dependent. Roughness effects were mainly manifested up to $y/ \delta \approx 0. 1$. Generally speaking, it was observed that inner peak values of Reynolds stresses increased when considering outer units. However, decreases were seen in inner units. In the outer region, the most significant differences between the present DNS smooth and rough cases were computed in the wall-normal component $\langle {v}^{\prime 2} \rangle $ of the Reynolds stresses and in the Reynolds shear stresses $\langle {u}^{\prime } {v}^{\prime } \rangle $ in outer units. From the resulting flow fields a proper orthogonal decomposition (POD) analysis is performed and the effects of the surface roughness are distinctly observed in the most energetic POD modes. The POD analysis shows that the surface roughness causes a redistribution of the kinetic energy amongst the POD modes with energy being shifted from low-order to high-order modes in the rough case versus the smooth case. Also, the roughness causes a marked decrease in the characteristic wavelengths observed in the POD modes, particularly in the streamwise component of the velocity field. Low-order modes of the streamwise component demonstrated characteristic wavelengths of the order of $3\delta $ in the smooth case, whereas the same modes for the rough case demonstrated characteristic wavelengths of only $\delta $.
A dynamic multi-scale approach for turbulent inflow boundary conditions in spatially developing flows
- GUILLERMO ARAYA, LUCIANO CASTILLO, CHARLES MENEVEAU, KENNETH JANSEN
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- Journal of Fluid Mechanics / Volume 670 / 10 March 2011
- Published online by Cambridge University Press:
- 22 February 2011, pp. 581-605
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A dynamic method for prescribing realistic inflow boundary conditions is presented for simulations of spatially developing turbulent boundary layers. The approach is based on the rescaling–recycling method proposed by Lund, Wu & Squires (J. Comput. Phys, vol. 140, 1998, pp. 233–258) and the multi-scale method developed by Araya, Jansen & Castillo (J. Turbul., vol. 10, no. 36, 2009, pp. 1–33). The rescaling process requires prior knowledge about how the velocity and length scales are related between the inlet and recycle stations. Here a dynamic approach is proposed in which such information is deduced dynamically by involving an additional plane, the so-called test plane located between the inlet and recycle stations. The approach distinguishes between the inner and outer regions of the boundary layer and enables the use of multiple velocity scales. This flexibility allows applications to boundary layer flows with pressure gradients and avoids the need to prescribe empirically the friction velocity and other flow parameters at the inlet of the domain. The dynamic method is tested in direct numerical simulations of zero, favourable and adverse pressure gradient flows. The dynamically obtained scaling exponents for the downstream evolution of boundary layer parameters are found to fluctuate in time, but on average they agree with the expected values for zero, favourable and adverse pressure gradient flows. Comparisons of the results with data from experiments, and from other direct numerical simulations that use much longer computational domains to capture laminar-to-turbulence transition, demonstrate the suitability of the proposed dynamic method.
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- The Cambridge Dictionary of Christianity
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- 20 September 2010, pp xi-xliv
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The rough favourable pressure gradient turbulent boundary layer
- RAÚL BAYOÁN CAL, BRIAN BRZEK, T. GUNNAR JOHANSSON, LUCIANO CASTILLO
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- Journal of Fluid Mechanics / Volume 641 / 25 December 2009
- Published online by Cambridge University Press:
- 25 November 2009, pp. 129-155
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Laser Doppler anemometry measurements of the mean velocity and Reynolds stresses are carried out for a rough-surface favourable pressure gradient turbulent boundary layer. The experimental data is compared with smooth favourable pressure gradient and rough zero-pressure gradient data. The velocity and Reynolds stress profiles are normalized using various scalings such as the friction velocity and free stream velocity. In the velocity profiles, the effects of roughness are removed when using the friction velocity. The effects of pressure gradient are not absorbed. When using the free stream velocity, the scaling is more effective absorbing the pressure gradient effects. However, the effects of roughness are almost removed, while the effects of pressure gradient are still observed on the outer flow, when the mean deficit velocity profiles are normalized by the U∞ δ∗/δ scaling. Furthermore, when scaled with U2∞, the 〈u2〉 component of the Reynolds stress augments due to the rough surface despite the imposed favourable pressure gradient; when using the friction velocity scaling u∗2, it is dampened. It becomes ‘flatter’ in the inner region mainly due to the rough surface, which destroys the coherent structures of the flow and promotes isotropy. Similarly, the pressure gradient imposed on the flow decreases the magnitude of the Reynolds stress profiles especially on the 〈v2〉 and -〈uv〉 components for the u∗2 or U∞2 scaling. These effects are reflected in the boundary layer parameter δ∗/δ, which increase due to roughness, but decrease due to the favourable pressure gradient. Additionally, the pressure parameter Λ found not to be in equilibrium, describes the development of the turbulent boundary layer, with no influence of the roughness linked to this parameter. These measurements are the first with an extensive number of downstream locations (11). This makes it possible to compute the required x-dependence for the production term and the wall shear stress from the full integrated boundary layer equation. The finding indicates that the skin friction coefficient depends on the favourable pressure gradient condition and surface roughness.
Effects of free-stream turbulence on rough surface turbulent boundary layers
- BRIAN BRZEK, SHEILLA TORRES-NIEVES, JOSÉ LEBRÓN, RAÚL CAL, CHARLES MENEVEAU, LUCIANO CASTILLO
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- Journal of Fluid Mechanics / Volume 635 / 25 September 2009
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- 10 September 2009, pp. 207-243
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Several effects of nearly isotropic free-stream turbulence in transitionally rough turbulent boundary layers are studied using data obtained from laser Doppler anemometry measurements. The free-stream turbulence is generated with the use of an active grid, resulting in free-stream turbulence levels of up to 6.2%. The rough surface is characterized by a roughness parameter k+ ≈ 53, and measurements are performed at Reynolds numbers of up to Reθ = 11300. It is confirmed that the free-stream turbulence significantly alters the mean velocity deficit profiles in the outer region of the boundary layer. Consequently, the previously observed ability of the Zagarola & Smits (J. Fluid Mech., vol. 373, 1998, p. 33) velocity scale U∞δ*/δ to collapse results from both smooth and rough surface boundary layers, no longer applies in this boundary layer subjected to high free-stream turbulence. In inner variables, the wake region is significantly reduced with increasing free-stream turbulence, leading to decreased mean velocity gradient and production of Reynolds stress components. The effects of free-stream turbulence are clearly identifiable and significant augmentation of the streamwise Reynolds stress profiles throughout the entire boundary layer are observed, all the way down to the inner region. In contrast, the Reynolds wall-normal and shear stress profiles increase due to free-stream turbulence only in the outer part of the boundary layer due to the blocking effect of the wall. As a consequence, there is a significant portion of the boundary layer in which the addition of nearly isotropic turbulence in the free-stream, results in significant increases in anisotropy of the turbulence. To quantify which turbulence length scales contribute to this trend, second-order structure functions are examined at various distances from the wall. Results show that the anisotropy created by adding nearly isotropic turbulence in the free-stream resides mostly in the larger scales of the flow. Furthermore, by analysing the streamwise Reynolds stress equation, it can be predicted that it is the wall-normal gradient of 〈u2v〉 term that is responsible for the increase in 〈u2〉 profiles throughout the boundary layer (i.e. an efficient turbulent transport of turbulence away from the wall). Furthermore, a noticeable difference between the triple correlations for smooth and rough surfaces exists in the inner region, but no significant differences are seen due to free-stream turbulence. In addition, the boundary layer parameters δ*/δ95, H and cf are also evaluated from the experimental data. The flow parameters δ*/δ95 and H are found to increase due to roughness, but decrease due to free-stream turbulence, which has significance for flow control, particularly in delaying separation. Increases in cf due to high free-stream turbulence are also observed, associated with increased momentum flux towards the wall.
A theory for turbulent pipe and channel flows
- MARTIN WOSNIK, LUCIANO CASTILLO, WILLIAM K. GEORGE
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- Journal:
- Journal of Fluid Mechanics / Volume 421 / 25 October 2000
- Published online by Cambridge University Press:
- 02 November 2000, pp. 115-145
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A theory for fully developed turbulent pipe and channel flows is proposed which extends the classical analysis to include the effects of finite Reynolds number. The proper scaling for these flows at finite Reynolds number is developed from dimensional and physical considerations using the Reynolds-averaged Navier–Stokes equations. In the limit of infinite Reynolds number, these reduce to the familiar law of the wall and velocity deficit law respectively.
The fact that both scaled profiles describe the entire flow for finite values of Reynolds number but reduce to inner and outer profiles is used to determine their functional forms in the ‘overlap’ region which both retain in the limit. This overlap region corresponds to the constant, Reynolds shear stress region (30 < y+ < 0.1R+ approximately, where R+ = u*R/v). The profiles in this overlap region are logarithmic, but in the variable y + a where a is an offset. Unlike the classical theory, the additive parameters, Bi, Bo, and log coefficient, 1/κ, depend on R+. They are asymptotically constant, however, and are linked by a constraint equation. The corresponding friction law is also logarithmic and entirely determined by the velocity profile parameters, or vice versa.
It is also argued that there exists a mesolayer near the bottom of the overlap region approximately bounded by 30 < y+ < 300 where there is not the necessary scale separation between the energy and dissipation ranges for inertially dominated turbulence. As a consequence, the Reynolds stress and mean flow retain a Reynolds number dependence, even though the terms explicitly containing the viscosity are negligible in the single-point Reynolds-averaged equations. A simple turbulence model shows that the offset parameter a accounts for the mesolayer, and because of it a logarithmic behaviour in y applies only beyond y+ > 300, well outside where it has commonly been sought.
The experimental data from the superpipe experiment and DNS of channel flow are carefully examined and shown to be in excellent agreement with the new theory over the entire range 1.8 × 102 < R+ < 5.3 × 105. The Reynolds number dependence of all the parameters and the friction law can be determined from the single empirical function, H = A/(ln R+)α for α > 0, just as for boundary layers. The Reynolds number dependence of the parameters diminishes very slowly with increasing Reynolds number, and the asymptotic behaviour is reached only when R+ [Gt ] 105.