Steady Penetration of a Rigid Cone With a Rough Wall Into a Power-Law Viscous Solid

1991 ◽  
Vol 58 (4) ◽  
pp. 872-880 ◽  
Author(s):  
N. A. Fleck ◽  
D. Durban
Keyword(s):  
Boundary Layer ◽  
Strain Rate ◽  
Power Law ◽  
Eigenvalue Analysis ◽  
Rough Wall ◽  
Wall Friction ◽  
Stress Fields ◽  
Wall Roughness ◽  
Perfectly Plastic ◽  
Special Cases

Singular strain rate and stress fields are examined at the tip of a rigid conical indentor penetrating an incompressible viscous solid. Attention is focused on friction effects induced by wall roughness. The problem is formulated within the usual framework of eigenvalue analysis of locally singular fields. Some special cases are investigated further with emphasis on a boundary layer expansion for the rigid/perfectly plastic solid sliding along the perfectly rough wall. It has been found that the level of singularity increases as the cone becomes sharper and the wall friction decreases. Numerical results, presented for a variety of cases, suggest a boundary layer build up for sharp cones with rough walls.

Power Law Velocity Profile in the Turbulent Boundary Layer on Transitional Rough Surfaces

2007 ◽  
Vol 129 (8) ◽  
pp. 1083-1100 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Boundary Layer ◽  
Functional Equation ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Power Law ◽  
Wall Roughness ◽  
Closure Model ◽  
Log Law

A new approach to scaling of transitional wall roughness in turbulent flow is introduced by a new nondimensional roughness scale ϕ. This scale gives rise to an inner viscous length scale ϕν∕uτ, inner wall transitional variable, roughness friction Reynolds number, and roughness Reynolds number. The velocity distribution, just above the roughness level, turns out to be a universal relationship for all kinds of roughness (transitional, fully smooth, and fully rough surfaces), but depends implicitly on roughness scale. The open turbulent boundary layer equations, without any closure model, have been analyzed in the inner wall and outer wake layers, and matching by the Izakson-Millikan-Kolmogorov hypothesis leads to an open functional equation. An alternate open functional equation is obtained from the ratio of two successive derivatives of the basic functional equation of Izakson and Millikan, which admits two functional solutions: the power law velocity profile and the log law velocity profile. The envelope of the skin friction power law gives the log law, as well as the power law index and prefactor as the functions of roughness friction Reynolds number or skin friction coefficient as appropriate. All the results for power law and log law velocity and skin friction distributions, as well as power law constants are explicitly independent of the transitional wall roughness. The universality of these relations is supported very well by extensive experimental data from transitional rough walls for various different types of roughnesses. On the other hand, there are no universal scalings in traditional variables, and different expressions are needed for various types of roughness, such as inflectional roughness, monotonic roughness, and others. To the lowest order, the outer layer flow is governed by the nonlinear turbulent wake equations that match with the power law theory as well as log law theory, in the overlap region. These outer equations are in equilibrium for constant value of m, the pressure gradient parameter, and under constant eddy viscosity closure model, the analytical and numerical solutions are presented.

Singular Fields in Plane-Strain Penetration

1991 ◽  
Vol 58 (4) ◽  
pp. 910-915 ◽  
Author(s):  
David Durban ◽  
Omri Rand
Keyword(s):  
Boundary Layer ◽  
Strain Rate ◽  
Plane Strain ◽  
Constitutive Relation ◽  
Solid Material ◽  
Material Behavior ◽  
Wall Friction ◽  
Friction Factors ◽  
Hardening Parameter ◽  
Strain Rate Hardening

Local singular fields are investigated in the vicinity of the vertex of a sharp wedge that penetrates a viscous solid. Material behavior is modeled by the usual powerlaw constitutive relation. Wall friction is accounted for by imposing friction factors along the walls of the wedge. The case of a Newtonian fluid is investigated analytically, and sample numerical results are presented for nonlinear strain rate hardening. It is shown that the exponent of strain rate singularity increases as the wedge becomes sharper and smoother. Increasing the hardening parameter also results in a stronger strain rate singularity. High levels of wall friction induce an intensive shear boundary layer near the wall.

A General Strategy to Extend Turbulence Models to Rough Surfaces: Application to Smith’s k-L Model

2007 ◽  
Vol 129 (10) ◽  
pp. 1245-1254 ◽  
Author(s):  
B. Aupoix
Keyword(s):  
Boundary Layer ◽  
Turbulence Model ◽  
General Procedure ◽  
Turbulence Models ◽  
Wall Friction ◽  
General Strategy ◽  
Wall Roughness ◽  
Wide Range ◽  
Hypersonic Shock ◽  
The Right

A general procedure to extend turbulence models to account for wall roughness, in the framework of the equivalent sand grain approach, is proposed. It is based on the prescription of the turbulent quantities at the wall to reproduce the shift of the logarithmic profile and hence provide the right increase in wall friction. This approach was previously applied to Spalart and Allmaras one equation (1992, “A One-Equation Turbulence Model for Aerodynamic. Flows,” 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA paper No. 92-0439;1994, ibid, Rech. Aerosp. 1, pp. 5–21). Here, the strategy is detailed and applied to Smith’s two-equation k-L model (1995, “Prediction of Hypersonic Shock Wave Turbulent Boundary Layer Interactions With The k-l Two Equaton Turbulence Model,” 33rd Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper No. 95-0232). The final model form is given. The so-modified Spalart and Allmaras and Smith models were tested on a large variety of test cases, covering a wide range of roughness and boundary layer Reynolds numbers and compared with other models. These tests confirm the validity of the approach to extend any turbulence model to account for wall roughness. They also point out the deficiency of some models to cope with small roughness levels as well as the drawbacks of present correlations to estimate the equivalent sand grain roughness.

Non-similar solution of free convective flow of power law nanofluids in porous medium along a vertical cone and plate with thermal and mass convective boundary conditions

2015 ◽  
Vol 93 (10) ◽  
pp. 1144-1155 ◽  
Author(s):  
W.A. Khan ◽  
M. Jashim Uddin ◽  
A.I.M. Ismail
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Power Law ◽  
Similar Solution ◽  
Convective Boundary Conditions ◽  
Concentration Increase ◽  
Vertical Cone ◽  
Convective Boundary ◽  
Special Cases

This paper investigates non-similar solution of free convective boundary layer flow of a viscous incompressible fluid along a vertical cone and plate embedded in a Darcian porous medium filled with power law non-Newtonian nanofluids. The effects of the thermal and mass convective boundary conditions are taken into account, which makes the present analysis practically applicable. The governing boundary layer equations are converted into a system of non-similar differential equations by using suitable transformations before being solved numerically. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, and the local Nusselt and Sherwood numbers are reported. It is found that the velocity, temperature, and concentration increase with mass transfer velocity for both the vertical plate and cone. Further, the velocity reduces whilst the temperature and concentration increase with increasing buoyancy ratio parameter for all three types of nanofluids in the case of both geometries. The local Nusselt and the local Sherwood numbers are found to be higher for dilatant nanofluids than pseudoplastic nanofluids and Newtonian fluids in each case. The numerical results for special cases are compared with the published data and an excellent agreement has been found.

Power Law Turbulent Velocity Profile in Transitional Rough Pipes

2005 ◽  
Vol 128 (3) ◽  
pp. 548-558 ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena ◽  
Afzal Bushra
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Power Law ◽  
Roughness Parameter ◽  
Rough Wall ◽  
Wall Roughness ◽  
Velocity Shift ◽  
Normal Wall ◽  
Good Support ◽  
Grain Roughness

Alternate power law velocity profile u+=Aζα in transitional rough pipe fully turbulent flow, has been proposed, in terms of new appropriate inner rough wall variables (ζ=Z+∕ϕ, uϕ=u∕ϕ), and new parameters Rϕ=Rτ∕ϕ termed as the roughness friction Reynolds number, Reϕ=Re∕ϕ termed as the roughness Reynolds number and ϕ termed as roughness scale (along with normal wall coordinate Z=y+ϵr where ϵr is the shift of the origin of boundary layer due to the rough wall, Z+=Zuτ∕ν and u+=u∕uτ). The envelope of the power law shows that the power law constants α and A depend on the parameter Rϕ (i.e., α=α(Rϕ) and A=A(Rϕ)) but explicitly independent of the wall roughness parameter h∕δ (roughness height h in pipe of radius δ). The roughness scale ϕ has been related to the roughness function ΔU+ of Clauser representing the velocity shift caused by wall roughness. The present results of the velocity profile, just slightly above the wall roughness level h, remain valid for all types of wall roughness. The data of Nikuradse for sand-grain roughness, in transitional and fully rough pipes, has been considered, which provides good support to the predictions of an alternate power law velocity profile, based on single parameter Rϕ, the roughness friction Reynolds number.

The Effects of Upstream Wall Roughness On the Spatio-Temporal Characteristics of Flow Separations Induced by a Forward-Facing Step

2021 ◽  
Author(s):  
Sedem Kumahor ◽  
Xingjun Fang ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Reverse Flow ◽  
Rough Wall ◽  
Step Height ◽  
Stream Velocity ◽  
Wall Roughness ◽  
Mean Flow ◽  
Flow Area ◽  
Separation Bubbles ◽  
Forward Facing Step

Abstract Separating and reattaching turbulent flows induced by a forward-facing step submerged in thick oncoming turbulent boundary layers (TBL) developed over smooth and rough upstream walls were investigated using time-resolved particle image velocimetry. The examined upstream walls resulted in smooth, transitionally rough and fully rough wall conditions. The upstream boundary layer thicknesses were 4.3 and 6.7 times the step height in the smooth and rough wall cases, respectively. The Reynolds number based on the step height and free-stream velocity was 7800. The effects of upstream wall roughness on the mean flow characteristics, Reynolds stresses defined in both Cartesian and curvilinear coordinate systems as well as the unsteadiness of the turbulent separation bubbles were critically examined. The results show that upstream wall roughness increases the boundary layer thickness and turbulence intensity and consequently, promotes early mean flow reattachment over the step. Distinct regions of significantly elevated vertical Reynolds normal stress and Reynolds shear stress were observed upstream of the step in the fully rough wall case compared to the smooth wall case. Proper orthogonal decomposition (POD) and the reverse flow area over the step were employed to investigate the unsteadiness of the separation bubbles. The first POD mode coefficient and the reverse flow area over the step were well correlated and exhibited the same dominant frequency.

The Effects of Upstream Wall Roughness on the Spatio-Temporal Characteristics of Flow Separations Induced by a Forward-Facing Step

2020 ◽  
Author(s):  
Sedem Kumahor ◽  
Xingjun Fang ◽  
Ali Nematollahi ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Leading Edge ◽  
Rough Wall ◽  
Step Height ◽  
Stream Velocity ◽  
Wall Roughness ◽  
Smooth Wall ◽  
Frequency Spectra ◽  
Forward Facing Step

Abstract The unsteady characteristics of flow separations induced by a forward-facing step immersed in thick oncoming turbulent boundary layers developed over smooth and fully rough upstream walls were experimentally studied using time-resolved particle image velocimetry. The upstream boundary layer thicknesses were 4.3 and 6.7 times the step height in the smooth and fully rough wall cases, respectively. The Reynolds number based on the step height and free-stream velocity was 7800. The effects of upstream wall roughness on the instantaneous separated shear layer, frequency spectra and two-point correlations are critically examined. Proper orthogonal decomposition (POD) is employed to investigate the mechanism underlying the unsteadiness of turbulent separation bubbles over the step. The first two POD modes exhibit the same topology in both cases. The energy fraction of the first mode is significantly larger in the rough wall case, signifying the enhanced large-scale motion residing in the incoming turbulent boundary layer. The correlation between the reverse flow area over the step and the first POD mode coefficient is much stronger in the rough wall case than in the smooth wall case. High levels of vertical fluctuating velocity immediately upstream of the leading edge of the step is mostly associated with the first POD mode in the rough wall case, but is further influenced by the higher POD modes in the smooth wall case. Irrespective of the upstream wall roughness, the vertical fluctuating velocity over the step are mostly induced by vortex shedding motion from the leading edge of the step.

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