scholarly journals Transonic flow over localised heating elements in boundary layers

2018 ◽  
Vol 844 ◽  
pp. 746-765 ◽  
Author(s):  
A. F. Aljohani ◽  
J. S. B. Gajjar
Keyword(s):  
Supersonic Flow ◽  
Transonic Flow ◽  
Energy Equation ◽  
Flat Surface ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Upper Deck ◽  
Lower Deck

The problem of transonic flow past an array of micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface is investigated using the triple-deck theory. The compressible Navier–Stokes equations supplemented by the energy equation are considered for large Reynolds numbers. The triple-deck problem is formulated with the aid of the method of matched expansions. The resulting nonlinear viscous lower deck problem, coupled with the upper deck problem governed by the nonlinear Kármán–Guderley equation, is solved using a numerical method based on Chebyshev collocation and finite differences. Our results show the differences in subsonic and supersonic flow behaviour over heated elements. The results indicate the possibility of using the elements to favourably control the transonic flow field.

scholarly journals Instability of transonic flow past flattened airfoils

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Alexander Kuzmin
Keyword(s):  
Numerical Modeling ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Simulations ◽  
Flow Past ◽  
Coefficient Versus

AbstractTransonic flow past a Whitcomb airfoil and two modifications of it at Reynolds numbers of the order of ten millions is studied. The numerical modeling is based on the system of Reynolds-averaged Navier-Stokes equations. The flow simulations show that variations of the lift coefficient versus the angle of attack become more abrupt with decreasing curvature of the airfoil in the midchord region. This is caused by an instability of closely spaced local supersonic regions on the upper surface of the airfoil.

Influence of Surface Roughness on Shear Flow

2004 ◽  
Vol 71 (4) ◽  
pp. 459-464 ◽  
Author(s):  
S. Bhattacharyya ◽  
S. Mahapatra ◽  
F. T. Smith
Keyword(s):  
Cross Section ◽  
Numerical Solutions ◽  
Flat Surface ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Uniform Shear

The local planar flow of incompressible fluid past an obstacle of semi-circular cross section is considered, the obstacle being mounted on a long flat surface. The far-field motion is one of uniform shear. Direct numerical solutions of the Navier-Stokes equations are described over a range of Reynolds numbers. The downstream eddy length and upstream position of maximum pressure gradient are found to agree with increased Reynolds number theory; in particular the agreement for the former quantity is close for Reynolds numbers above about 50.

scholarly journals Subsonic flow past localised heating elements in boundary layers

2017 ◽  
Vol 821 ◽  
Author(s):  
A. F. Aljohani ◽  
J. S. B. Gajjar
Keyword(s):  
Energy Equation ◽  
Subsonic Flow ◽  
Flat Surface ◽  
Stokes Equations ◽  
Micro Electro Mechanical System ◽  
Navier Stokes ◽  
Mems Devices ◽  
Navier Stokes Equations ◽  
System Type ◽  
Flow Past

The problem of subsonic flow past micro-electro-mechanical-system-type (MEMS-type) heating elements placed on a flat surface, where the MEMS devices have hump-shaped surfaces, is investigated using triple-deck theory. The compressible Navier–Stokes equations supplemented by the energy equation are considered in the limit that the Reynolds number is large. The triple-deck problem is formulated, and the linear and nonlinear analysis and results are presented. The current work is a generalisation of the problem discussed by Koroteev & Lipatov (J. Fluid Mech., vol. 707, 2012, pp. 595–605; Z. Angew. Math. Mech., vol. 77, 2013, pp. 486–493), where the MEMS devices have flat-shaped surfaces. The results show that the hump-shaped heating elements enhance large drops in pressure, and peaks and troughs in the skin friction over the centre of the hump compared with the flat-shaped devices, which may be useful for controlling the flow.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Reynolds Numbers ◽  
Drop Impact ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Viscous Drop

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.

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