Combined effects of suction/injection and exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow: a semi-analytical approach

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Analytical Approach ◽  
Time Dependent ◽  
Combined Effects ◽  
Dean Flow

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Hydrodynamic effect of slip boundaries and exponentially decaying/growing time-dependent pressure gradient on Dean flow

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Velocity Shear ◽  
Time Dependent ◽  
Hydrodynamic Effect ◽  
Shear Stresses ◽  
Step Method ◽  
Dean Flow ◽  
Dean Vortices ◽  
Riemann Sum ◽  
Hydrodynamic Behaviour

AbstractHydrodynamic behaviour of slip flow and radially applied exponential time-dependent pressure gradient in a curvilinear concentric cylinder is examined. A two-step method of solution has been utilized in resolving the governing momentum equation. Accordingly, the exact solution of the time-dependent partial differential equation is derived in terms of the Laplace parameter. Afterwards, the Laplace domain solution is then inverted to time domain using a numerical-based inverting scheme known as Riemann-sum approximation. The effect of various dimensionless parameters involved in the problem on the Dean velocity, shear stresses and Dean vortices is discussed with the aid of graphs. It is found that maximum Dean velocity is due to an exponentially growing time-dependent pressure gradient and slip wall coefficient. Stability of the Dean vortices is achieved by suppressing time, wall slippage and inducing an exponentially decaying time-dependent pressure gradient.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

2003 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Combined Effects ◽  
Pressure Gradients ◽  
Smooth Wall ◽  
Reynolds Analogy ◽  
Integral Boundary ◽  
Favorable Pressure Gradient

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number (Rex≅900,000). An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy (2St/cf). Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

Time-Dependent Laminar Flow in Curved Channels

1970 ◽  
Vol 37 (3) ◽  
pp. 838-843 ◽  
Author(s):  
R. J. Nunge
Keyword(s):  
Laminar Flow ◽  
Pressure Gradient ◽  
Constant Pressure ◽  
Time Dependent ◽  
Pressure Gradients ◽  
Straight Channel ◽  
Curvature Ratio ◽  
Curved Channels ◽  
Developing Flow ◽  
Time Required

The velocity distribution for time-dependent laminar flow in curved channels is derived. The analysis applies to flows with pressure gradients which are arbitrary functions of time. Numerical results are obtained for developing flow due to a constant pressure gradient. Developing flow in a straight channel is also discussed and it is found that the curvature ratio has only a small effect on the time required to reach the fully developed state.

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

2018 ◽  
Vol 32 (8) ◽  
pp. 3537-3545 ◽  
Author(s):  
Mohsen Rezaei ◽  
Mehrdad Poursina ◽  
Shahram Hadian Jazi ◽  
Farhad Haji Aboutalebi
Keyword(s):  
Analytical Approach ◽  
Planetary Gear ◽  
Gear System ◽  
Time Dependent ◽  
Mesh Stiffness ◽  
Planetary Gear System

Steady flow in a helically symmetric pipe

1998 ◽  
Vol 370 ◽  
pp. 297-320 ◽  
Author(s):  
L. ZABIELSKI ◽  
A. J. MESTEL
Keyword(s):  
Pressure Gradient ◽  
Steady Flow ◽  
Three Dimensional ◽  
Arterial System ◽  
Fully Developed Flow ◽  
Irrotational Flow ◽  
Dean Flow ◽  
Steady Pressure ◽  
Helical Pipe ◽  
Curvature And Torsion

Fully developed flow in an infinite helically coiled pipe is studied, motivated by physiological applications. Most of the bends in the mammalian arterial system curve in a genuinely three-dimensional way, so that the arterial centreline has not only curvature but torsion and can be modelled by a helix. Flow in a helically symmetric pipe generalizes related problems in axisymmetry (Dean flow) and two-dimensionality, but the geometry ensures that even irrotational flow has a cross-pipe component. Fully developed helical flows driven by a steady pressure gradient are studied analytically and numerically. Varying the radius and pitch of the helical pipe, the effects of curvature and torsion on the flow are investigated.

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