Large-eddy simulation and streamline coordinate analysis of flow over an axisymmetric hull

2021 ◽  
Vol 926 ◽  
Author(s):  
Nicholas Morse ◽  
Krishnan Mahesh
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Streamwise Pressure Gradient

A new perspective on the analysis of turbulent boundary layers on streamlined bodies is provided by deriving the axisymmetric Reynolds-averaged Navier–Stokes equations in an orthogonal coordinate system aligned with streamlines, streamline-normal lines and the plane of symmetry. Wall-resolved large-eddy simulation using an unstructured overset method is performed to study flow about the axisymmetric DARPA SUBOFF hull at a Reynolds number of $Re_L = 1.1 \times 10^{6}$ based on the hull length and free-stream velocity. The streamline-normal coordinate is naturally normal to the wall at the hull surface and perpendicular to the free-stream velocity far from the body, which is critical for studying bodies with concave streamwise curvature. The momentum equations naturally reduce to the differential form of Bernoulli's equation and the $s$ – $n$ Euler equation for curved streamlines outside of the boundary layer. In the curved laminar boundary layer at the front of the hull, the streamline momentum equation represents a balance of the streamwise advection, streamwise pressure gradient and viscous stress, while the streamline-normal equation is a balance between the streamline-normal pressure gradient and centripetal acceleration. In the turbulent boundary layer on the mid-hull, the curvature terms and streamwise pressure gradient are negligible and the results conform to traditional analysis of flat-plate boundary layers. In the thick stern boundary layer, the curvature and streamwise pressure gradient terms reappear to balance the turbulent and viscous stresses. This balance explains the characteristic variation of static pressure observed for thick boundary layers at the tails of axisymmetric bodies.

Three-dimensional laminar boundary layers in crosswise pressure gradients

1974 ◽  
Vol 66 (4) ◽  
pp. 641-655 ◽  
Author(s):  
J. H. Horlock ◽  
A. K. Lewkowicz ◽  
J. Wordsworth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Laminar Boundary Layers ◽  
The Cross

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.

scholarly journals Large-eddy simulation of laminar transonic buffet

2018 ◽  
Vol 850 ◽  
pp. 156-178 ◽  
Author(s):  
Julien Dandois ◽  
Ivan Mary ◽  
Vincent Brion
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Separation Bubble ◽  
Oscillation Amplitude ◽  
Boundary Layer Separation ◽  
Stream Velocity ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Shock Oscillation ◽  
Transonic Buffet

A large-eddy simulation of laminar transonic buffet on an airfoil at a Mach number $M=0.735$, an angle of attack $\unicode[STIX]{x1D6FC}=4^{\circ }$, a Reynolds number $Re_{c}=3\times 10^{6}$ has been carried out. The boundary layer is laminar up to the shock foot and laminar/turbulent transition occurs in the separation bubble at the shock foot. Contrary to the turbulent case for which wall pressure spectra are characterised by well-marked peaks at low frequencies ($St=f\cdot c/U_{\infty }\simeq 0.06{-}0.07$, where $St$ is the Strouhal number, $f$ the shock oscillation frequency, $c$ the chord length and $U_{\infty }$ the free-stream velocity), in the laminar case, there are also well-marked peaks but at a much higher frequency ($St=1.2$). The shock oscillation amplitude is also lower: 6 % of chord and limited to the shock foot area in the laminar case instead of 20 % with a whole shock oscillation and intermittent boundary layer separation and reattachment in the turbulent case. The analysis of the phase-averaged fields allowed linking of the frequency of the laminar transonic buffet to a separation bubble breathing phenomenon associated with a vortex shedding mechanism. These vortices are convected at $U_{c}/U_{\infty }\simeq 0.4$ (where $U_{c}$ is the convection velocity). The main finding of the present paper is that the higher frequency of the shock oscillation in the laminar regime is due to a different mechanism than in the turbulent one: laminar transonic buffet is due to a separation bubble breathing phenomenon occurring at the shock foot.

Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers

1997 ◽  
Vol 336 ◽  
pp. 151-182 ◽  
Author(s):  
BRANKO KOSOVIĆ
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Boundary Layers ◽  
Nonlinear Model ◽  
High Reynolds Number ◽  
Subgrid Scale ◽  
Eddy Simulation ◽  
Large Eddy ◽  
High Reynolds

It has been recognized that the subgrid-scale (SGS) parameterization represents a critical component of a successful large-eddy simulation (LES). Commonly used linear SGS models produce erroneous mean velocity profiles in LES of high-Reynolds-number boundary layer flows. Although recently proposed approaches to solving this problem have resulted in significant improvements, questions about the true nature of the SGS problem in shear-driven high-Reynolds-number flows remain open.We argue that the SGS models must capture inertial transfer effects including backscatter of energy as well as its redistribution among the normal SGS stress components. These effects are the consequence of nonlinear interactions and anisotropy. In our modelling procedure we adopt a phenomenological approach whereby the SGS stresses are related to the resolved velocity gradients. We show that since the SGS stress tensor is not frame indifferent a more general nonlinear model can be applied to the SGS parameterization. We develop a nonlinear SGS model capable of reproducing the effects of SGS anisotropy characteristic for shear-driven boundary layers. The results obtained using the nonlinear model for the LES of a neutral shear-driven atmospheric boundary layer show a significant improvement in prediction of the non-dimensional shear and low-order statistics compared to the linear Smagorinsky-type models. These results also demonstrate a profound effect of the SGS model on the flow structures.

scholarly journals Large-eddy simulation of the zero-pressure-gradient turbulent boundary layer up to Reθ = O(1012)

2011 ◽  
Vol 686 ◽  
pp. 507-533 ◽  
Author(s):  
M. Inoue ◽  
D. I. Pullin
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Turbulent Boundary Layer ◽  
Large Eddy Simulation ◽  
Pressure Gradient ◽  
Skin Friction Coefficient ◽  
Smooth Wall ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Near Wall

AbstractA near-wall subgrid-scale (SGS) model is used to perform large-eddy simulation (LES) of the developing, smooth-wall, zero-pressure-gradient flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. Large-eddy simulations of the turbulent boundary layer are reported at Reynolds numbers ${\mathit{Re}}_{\theta } $ based on the free-stream velocity and the momentum thickness in the range ${\mathit{Re}}_{\theta } = 1{0}^{3} \text{{\ndash}} 1{0}^{12} $. Results include the inverse square-root skin-friction coefficient, $ \sqrt{2/ {C}_{f} } $, velocity profiles, the shape factor $H$, the von Kármán ‘constant’ and the Coles wake factor as functions of ${\mathit{Re}}_{\theta } $. Comparisons with some direct numerical simulation (DNS) and experiment are made including turbulent intensity data from atmospheric-layer measurements at ${\mathit{Re}}_{\theta } = O(1{0}^{6} )$. At extremely large ${\mathit{Re}}_{\theta } $, the empirical Coles–Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that LES is suggestive of the asymptotic, infinite Reynolds number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum ${\mathit{Re}}_{\theta } $ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger ${\mathit{Re}}_{\theta } $ could be achieved with quad- or higher-precision arithmetic.

Darryl E. Metzger Memorial Session Paper: The Streamwise Development of Go¨rtler Vortices in a Favorable Pressure Gradient

1996 ◽  
Vol 118 (1) ◽  
pp. 162-171 ◽  
Author(s):  
M. V. Finnis ◽  
A. Brown
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Velocity Gradient ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Velocity Variation ◽  
Radius Of Curvature ◽  
Stream Velocity ◽  
Mean Flow ◽  
Favorable Pressure Gradient

Measurements are presented of the streamwise velocity variation within a laminar boundary layer on a concave surface of 4 m radius of curvature for which the free-stream velocity gradient factor (ν/U02)dU0/dx was approximately 1 × 10−6. The stream velocity variation was consistent with the presence of counterrotating vortices resulting from the Go¨rtler instability. The vortices exhibited exponential growth over the streamwise extent of the measurements to a disturbance amplitude of approximately 13 percent of the local free-stream velocity. The vortex growth rates were found to be less than those for a zero velocity gradient factor, indicating that a favorable pressure gradient stabilizes the flow with respect to the Go¨rtler instability. Boundary layer profiles at local upwash and downwash positions are compared with the linear theory for which the mean flow was modeled using the Pohlhausen approximation to the solution of the boundary layer equations. The agreement between the measured and predicted profiles indicates that the linear stability theory can provide a fair approximation to the small amplitude growth of the Go¨rtler instability.

Natural Transition of Boundary Layers—The Effects of Turbulence, Pressure Gradient, and Flow History

1980 ◽  
Vol 22 (5) ◽  
pp. 213-228 ◽  
Author(s):  
B. J. Abu-Ghannam ◽  
R. Shaw
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Stream Velocity ◽  
Hot Wire ◽  
Empirical Relationships ◽  
Free Stream Turbulence ◽  
Turbomachinery Blades ◽  
Low Speed Wind Tunnel

Natural transition of boundary layers is investigated for a flat plate in a low-speed wind tunnel with free-stream turbulence intensities ranging from 0.3 to 5 per cent, and with pressure-gradient histories typical of turbomachinery blades without separation. Empirical relationships are proposed for the prediction of the start and end of transition, as well as the development of the boundary layer during transition. These relations are based on the recent measurements made with a hot-wire anemometer, and augmented, mainly for the start of transition, by results of previously reported research. Finally, these experimental relationships are used in conjunction with well established methods to predict the entire unseparated boundary layer. To utilize the prediction, all that is required is a knowledge of the free-stream turbulence level and the free-stream velocity distribution, which itself can be derived from potential flow theory.

Toward Cost-Effective Boundary Layer Transition Computations With Large-Eddy Simulation

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Solkeun Jee ◽  
Jongwook Joo ◽  
Ray-Sing Lin
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Boundary Layers ◽  
Stability Theory ◽  
Boundary Layer Stability ◽  
Computational Domain ◽  
Nonlinear Interactions ◽  
Eddy Simulation ◽  
Subgrid Model ◽  
Large Eddy

An efficient large-eddy simulation (LES) approach is investigated for laminar-to-turbulent transition in boundary layers. This approach incorporates the boundary-layer stability theory. Primary instability and subharmonic perturbations determined by the boundary-layer stability theory are assigned as forcing at the inlet of the LES computational domain. This LES approach reproduces the spatial development of instabilities in the boundary layer, as observed in wind tunnel experiments. Detailed linear growth and nonlinear interactions that lead to the H-type breakdown are well captured and compared well to previous direct numerical simulation (DNS). Requirements in the spatial resolution in the transition region are investigated with connections to the resolution in turbulent boundary layers. It is shown that the subgrid model used in this study is apparently dormant in the overall transitional region, allowing the right level of the growth of small-amplitude instabilities and their nonlinear interactions. The subgrid model becomes active near the end of the transition where the length scales of high-order instabilities become smaller in size compared to the given grid resolution. Current results demonstrate the benefit of the boundary-layer forcing method for the computational cost reduction.

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