Near-Bed Flow Mechanisms Around a Circular Marine Pipeline Close to a Flat Seabed in the Subcritical Flow Regime Using a k-ɛ Model

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Muk Chen Ong ◽  
Torbjørn Utnes ◽  
Lars Erik ◽  
Dag Myrhaug ◽  
Bjørnar Pettersen
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Flow Regime ◽  
Boundary Layer Thickness ◽  
Friction Velocity ◽  
Lift Coefficient ◽  
Pressure Coefficient ◽  
Mean Pressure ◽  
Flow Mechanisms ◽  
The Mean

Flow mechanisms around a two-dimensional (2D) circular marine pipeline close to a flat seabed have been investigated using the 2D unsteady Reynolds-averaged Navier–Stokes (URANS) equations with a standard high Reynolds number k-ɛ model. The Reynolds number (based on the free stream velocity and cylinder diameter) ranges from 1 × 104 to 4.8 × 104 in the subcritical flow regime. The objective of the present study is to show a thorough documentation of the applicability of the k-ɛ model for engineering design within this flow regime by means of a careful comparison with available experimental data. The inflow boundary layer thickness and the Reynolds numbers in the present simulations are set according to published experimental data, with which the simulations are compared. Detailed comparisons with the experimental data for small gap ratios are provided and discussed. The effects of the gap to diameter ratio and the inflow boundary layer thickness have been studied. Although under-predictions of the essential hydrodynamic quantities (e.g., time-averaged drag coefficient, time-averaged lift coefficient, root-mean-square fluctuating lift coefficient, and mean pressure coefficient at the back of the pipeline) are observed due to the limitation of the turbulence model, the present approach is capable of providing good qualitative agreement with the published experimental data. The vortex shedding mechanisms have been investigated, and satisfactory predictions are obtained. The mean pressure coefficient and the mean friction velocity along the flat seabed are predicted reasonably well as compared with published experimental and numerical results. The mean seabed friction velocity at the gap is much larger for small gaps than for large gaps; thus, the bedload sediment transport is much larger for small gaps than for large gaps.

Interference effects of three consecutive wall-mounted cubes placed in deep turbulent boundary layer

2014 ◽  
Vol 756 ◽  
pp. 165-190
Author(s):  
Hee Chang Lim ◽  
Masaaki Ohba
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Coefficient ◽  
Azimuth Angle ◽  
Pressure Variation ◽  
Interference Effects ◽  
Detached Eddy Simulation ◽  
Eddy Simulation ◽  
Mean Pressure ◽  
The Mean

AbstractIn this study we undertook various calculations of the turbulent flow around a building in close proximity to neighbouring obstacles, with the aim of gaining an understanding of the velocity and the surface-pressure variations with respect to the azimuth angle of wind direction and the gap distance between the obstacles. This paper presents the effects of flow interference among consecutive cubes for azimuth angles of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta = 0$, 15, 30, and $45^{\circ }$ and gap distances of $G = 0.5{h}, 1.0{h}, 1.5{h}$, and $\infty $ (i.e. a single cube), where $h$ is the cube height, placed in a turbulent boundary layer. A transient detached eddy simulation (DES) was carried out to calculate the highly complicated flow domain around the three wall-mounted cubes to observe the fluctuating pressure, which substantially contributes to the suction pressure when there is separation and reattachment around the leading and trailing edges of the cubes. In addition, the results indicate that an increasing azimuth angle increases the pressure variation on the centre cube of the three parallel-aligned cubes. The mean pressure variation can even change from negative to positive on the side face. Owing to interference effects, the mean pressure coefficient of the centre cube of the three parallel-aligned cubes was generally lower than the coefficient of the single cube and tended to increase depending on the gap distance. Furthermore, when the three consecutive cubes are in a tandem arrangement, the gap distance has little influence on the first cube but results in significant interference effects on the second and third cubes.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Bingham Fluid Flow in the Entrance Region of a Pipe

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Basma Baioumy ◽  
Rachid Chebbi ◽  
Nabil Abdel Jabbar
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Bingham Fluid ◽  
Entrance Region ◽  
Integral Model ◽  
Fully Developed Flow

Abstract Laminar Bingham fluid flow in the entrance region of a circular pipe is investigated using a momentum integral model. The fully developed flow is uniform in the core region, while the velocity changes in the annular part of the cross section of the pipe. The inlet-filled region concept is adopted. In the inlet region, the boundary layer thickness increases until the size of the plug flow area reaches the fully developed flow size. The model converges to the fully developed solution in the filled region. The model provides the velocity, pressure drop, and skin friction coefficient profiles. The pressure drop results are in good agreement with published experimental data. The flow results asymptotically converge to the fully developed values. In addition, the results are consistent with published Newtonian fluid flow experimental data and theoretical results for the boundary layer thickness, pressure drop, and centerline velocity for small values of the Bingham number.

Experimental Investigation of a Turbulent Boundary Layer Subjected to an Adverse Pressure Gradient

2011 ◽  
Author(s):  
Takanori Nakamura ◽  
Takatsugu Kameda ◽  
Shinsuke Mochizuki
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Friction Velocity ◽  
Adverse Pressure Gradient ◽  
Turbulent Intensity ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Velocity Scale ◽  
The Mean ◽  
The Law

Experiments were performed to investigate the effect of an adverse pressure gradient on the mean velocity and turbulent intensity profiles for an equilibrium boundary layer. The equilibrium boundary layer, which makes self-similar profiles, was constructed using a power law distribution of free stream velocity. The exponent of the law was adjusted to −0.188. The wall shear stress was measured with a drag balance by a floating element. The investigation of the law of the wall and the similarity of the streamwise turbulent intensity profile was made using both a friction velocity and new proposed velocity scale. The velocity scale is derived from the boundary layer equation. The mean velocity gradient profile normalized with the height and the new velocity scale exists the region where the value is almost constant. The turbulent intensity profiles normalized with the friction velocity strongly depend on the nondimensional pressure gradient near the wall. However, by mean of the local velocity scale, the profiles might be achieved to be similar with that of a zero pressure gradient.

scholarly journals Euler Solutions for Transonic Oscillating Cascade Flows Using Dynamic Triangular Meshes

1993 ◽  
Author(s):  
C. J. Hwang ◽  
S. Y. Yang
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Transonic Flow ◽  
Lift Coefficient ◽  
Pressure Coefficient ◽  
Oscillation Amplitude ◽  
Time History ◽  
Present Approach ◽  
Instantaneous Pressure ◽  
Interblade Phase Angle

The modified total-variation-diminishing scheme and an improved dynamic triangular mesh algorithm are presented to investigate the transonic oscillating cascade flows. In a Cartesian coordinate system, the unsteady Euler equations are solved. To validate the accuracy of the present approach, transonic flow around single NACA 0012 airfoil pitching harmonically about the quarter chord is computed first. The calculated instantaneous pressure coefficient distributions during a cycle of motion compare well with the related numerical and experimental data. To further evaluate the present approach involving nonzero interblade phase angle, the calculations of transonic flow around oscillating cascade of two unstaggered NACA 0006 blades with interblade phase angle equal to 180 deg are performed. From the instantaneous pressure coefficient distributions and time history of lift coefficient, the present approach, where a simple spatial treatment is utilized on the periodic boundaries, gives satisfactory results. By using the above solution procedure, transonic flows around oscillating cascade of four biconvex blades with different oscillation amplitudes, reduced frequencies and interblade phase angles are investigated. From the distributions of magnitude and phase angle of the dynamic pressure difference coefficient, the present numerical results show better agreement with the experimental data than those from the linearized theory in most of the cases. For every quarter of one cycle, the pressure contours repeat and proceed one pitch distance in the upward or downward direction for interblade phase angle equal to −90 deg or 90 deg, respectively. The unsteady pressure wave and shock behaviors are observed. From the lift coefficient distributions, it is further confirmed that the oscillation amplitude, interblade phase angle and reduced frequency all have significant effects on the transonic oscillating cascade flows.

The Effects of Surface Roughness on the Mean Velocity Profile in a Turbulent Boundary Layer

2002 ◽  
Vol 124 (3) ◽  
pp. 664-670 ◽  
Author(s):  
Donald J. Bergstrom ◽  
Nathan A. Kotey ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Friction Velocity ◽  
Outer Region ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Outer Flow ◽  
The Mean

Experimental measurements of the mean velocity profile in a canonical turbulent boundary layer are obtained for four different surface roughness conditions, as well as a smooth wall, at moderate Reynolds numbers in a wind tunnel. The mean streamwise velocity component is fitted to a correlation which allows both the strength of the wake, Π, and friction velocity, Uτ, to vary. The results show that the type of surface roughness affects the mean defect profile in the outer region of the turbulent boundary layer, as well as determining the value of the skin friction. The defect profiles normalized by the friction velocity were approximately independent of Reynolds number, while those normalized using the free stream velocity were not. The fact that the outer flow is significantly affected by the specific roughness characteristics at the wall implies that rough wall boundary layers are more complex than the wall similarity hypothesis would allow.

Direct simulation of the turbulent boundary layer along a compression ramp at M = 3 and Reθ = 1685

2000 ◽  
Vol 420 ◽  
pp. 47-83 ◽  
Author(s):  
NIKOLAUS A. ADAMS
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Shear Stresses ◽  
Numerical Representation ◽  
Computational Domain ◽  
The Mean ◽  
Compression Ramp

The turbulent boundary layer along a compression ramp with a deflection angle of 18° at a free-stream Mach number of M = 3 and a Reynolds number of Reθ = 1685 with respect to free-stream quantities and mean momentum thickness at inflow is studied by direct numerical simulation. The conservation equations for mass, momentum, and energy are solved in generalized coordinates using a 5th-order hybrid compact- finite-difference-ENO scheme for the spatial discretization of the convective fluxes and 6th-order central compact finite differences for the diffusive fluxes. For time advancement a 3rd-order Runge–Kutta scheme is used. The computational domain is discretized with about 15 × 106 grid points. Turbulent inflow data are provided by a separate zero-pressure-gradient boundary-layer simulation. For statistical analysis, the flow is sampled 600 times over about 385 characteristic timescales δ0/U∞, defined by the mean boundary-layer thickness at inflow and the free-stream velocity. Diagnostics show that the numerical representation of the flow field is sufficiently well resolved.Near the corner, a small area of separated flow develops. The shock motion is limited to less than about 10% of the mean boundary-layer thickness. The shock oscillates slightly around its mean location with a frequency of similar magnitude to the bursting frequency of the incoming boundary layer. Turbulent fluctuations are significantly amplified owing to the shock–boundary-layer interaction. Reynolds-stress maxima are amplified by a factor of about 4. Turbulent normal and shear stresses are amplified differently, resulting in a change of the structure parameter. Compressibility affects the turbulence structure in the interaction area around the corner and during the relaxation after reattachment downstream of the corner. Correlations involving pressure fluctuations are significantly enhanced in these regions. The strong Reynolds analogy which suggests a perfect correlation between velocity and temperature fluctuations is found to be invalid in the interaction area.

Pulmonary hysteresis

1962 ◽  
Vol 17 (1) ◽  
pp. 51-53 ◽  
Author(s):  
G. Cavagna ◽  
G. Brandi ◽  
F. Saibene ◽  
G. Torelli
Keyword(s):  
Experimental Data ◽  
Airway Resistance ◽  
Human Lung ◽  
Minute Ventilation ◽  
Mean Flow ◽  
Mean Pressure ◽  
The Mean

The pressure-volume (P-V) diagram of the human lung was recorded on three subjects at minute ventilation from 2.5 to 180 liters/min. The area included between the inspiratory and expiratory curve is the expression of the work necessary to overcome a) airway resistance to the flow, b) lung viscosity, and c) eventual pulmonary hysteresis. From the experimental data the mean pressure (Pm) and the mean flow (Vm) have been calculated, and the mean pressure plotted against the mean flow; the extrapolation of the Pm data to Vm = o leads to a positive value of Pm of 0.5-0.9 cm H2O, and this is interpreted as being due to pulmonary hysteresis. This is almost equal to the pressure necessary to overcome the airway resistance and the lung viscosity during respiration at rest. Submitted on April 17, 1961

Euler Solutions for Transonic Oscillating Cascade Flows Using Dynamic Triangular Meshes

1995 ◽  
Vol 117 (3) ◽  
pp. 393-400 ◽  
Author(s):  
C. J. Hwang ◽  
S. Y. Yang
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Transonic Flow ◽  
Lift Coefficient ◽  
Pressure Coefficient ◽  
Oscillation Amplitude ◽  
Time History ◽  
Present Approach ◽  
Instantaneous Pressure ◽  
Interblade Phase Angle

The modified total-variation-diminishing scheme and an improved dynamic triangular mesh algorithm are presented to investigate the transonic oscillating cascade flows. In a Cartesian coordinate system, the unsteady Euler equations are solved. To validate the accuracy of the present approach, transonic flow around a single NACA 0012 airfoil pitching harmonically about the quarter chord is computed first. The calculated instantaneous pressure coefficient distribution during a cycle of motion compare well with the related numerical and experimental data. To evaluate further the present approach involving nonzero interblade phase angle, the calculations of transonic flow around an oscillating cascade of two unstaggered NACA 0006 blades with interblade phase angle equal to 180 deg are performed. From the instantaneous pressure coefficient distributions and time history of lift coefficient, the present approach, where a simple spatial treatment is utilized on the periodic boundaries, gives satisfactory results. By using this solution procedure, transonic flows around an oscillating cascade of four biconvex blades with different oscillation amplitudes, reduced frequencies, and interblade phase angles are investigated. From the distributions of magnitude and phase angle of the dynamic pressure difference coefficient, the present numerical results show better agreement with the experimental data than those from the linearized theory in most of the cases. For every quarter of one cycle, the pressure contours repeat and proceed one pitch distance in the upward or downward direction for interblade phase angle equal to −90 deg or 90 deg, respectively. The unsteady pressure wave and shock behaviors are observed. From the lift coefficient distributions, it is further confirmed that the oscillation amplitude, interblade phase angle, and reduced frequency all have significant effects on the transonic oscillating cascade flows.

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