Turbulent Boundary Layer - Assignment Example

Turbulent Boundary Layer Controlling turbulence and ultimately relaminarization has been a dream for many engineers and scientists. There have been many control strategies investigate in the past. These strategies have included feedback-control techniques and open loop in the form of wall motion or body force. Studies have shown that crude oscillation of the wall decreases turbulence. Direct numerical simulations were applied in the first studies of turbulent flows over an oscillating wall. In most numerical work, the wall oscillation is imposed through a wall velocity (W) in the spanwise direction in the form of W=Wmsin(ωt), (1) Where Wm is the maximum wall velocity and w is the angular frequency of the wall oscillation, which is related to the period (T) through w=2πr/T. The oscillation in time may not be practical to implement in an engineering application which has recently led researchers to consider a steady variation in the streamwise direction along the plate instead of a time dependent forcing. In this case, the wall velocity (W) is imposed in the from of W=Wm sin(kx), (2) Where k is the wavenumber of the spatial oscillation, which is related to the wavelength (λx) through k=2π/λx. The work on the type of spatial oscillation been performed using DNS of flow through the combination of spatial and temporal wall oscillation. Only marginal improvement on the drag reduction was obtained (Skote, 2011). The numerical code and grid are the same as in the previous simulation of an oscillating turbulent boundary layer by Yudhistira and Skote who also showed that the grid is sufficiently fine. In developing the code a pseudo-spectral method is employed (Skote, 2011). All quantities are nondimensionalized by the free stream velocity (U) and the displacement thickness at the starting point of the simulation where flow is laminar. The Reynolds number based on the momentum thickness is varies between 418 and 750 in the region for the unmanipulated boundary. Modifications have been made thus allowing for streamwise modulation of the spanwise wall velocity. Resolutions used for the simulation were 800 modes in streamwise direction, 201 in wall-normal direction, and 144 mode in the spanwise direction. The sampling time for reference case was 6000 in time units. In the simulation presented, the maximum wall velocity and wavelength are set to 0.857 and 58.17, respectively. The wall forcing is of the same magnitude as the freestream velocity and the flow therefore deviates substantially from the unmanipulated boundary layer. Additional simulation is required so that investigation of a much weaker and more practical wall forcing is got (Skote, 2011). The qualitative similarity between responses to temporal and spatial forces strengthens the theory advanced by Viotti. The theory is that temporal forcing could be translated to spatial forcing through the use of a convection velocity of near wall turbulence fluctuations. This relates to the oscillations period and wavelength through (λx+ =Um+T+. For direction comparison between present spatial case and temporal simulation, T+) would be set to 130 if the estimate value of U+w=10 is used. Spatial oscillation which is observed in the DR is stationary statistically and relates with wall velocity oscillation. For further investigations, DR taken from two intervals which are equal of 4000 in units of simulation units corresponds to 4500 viscous units. The difference in DR from the two intervals is at it highest 1.5% and this is an indicator that DR can be converged statistically. The amplitude and phase the same for two intervals thus demonstrating that the oscillations of the DR does not represent a transcient phenomenon. The DR shows an oscillatory distribution which has a wavenumber that is twice that of the wall velocity. In comparing the DR and the wall velocity oscillation, it is clear that the maximum DR is observed in places at which wall velocity is at maximum or minimum and the minimum in DR relates to positions at which wall velocity is zero. Studying a snapshot of turbulent velocity can provide some insight into the oscillating behaviour of the DR (Skote, 2011). Direct numerical simulations have been carried out with the aim of studying the effect of a stationary distribution spanwise well velocity which oscillates in the streamwise direction or even a turbulent boundary layer. A spatially developing flow with the type of force has been studied for the first time. The part of the boundary layers that flows over an alternating wall velocity section gets affected to a large extent when drag reduction gets close to 50%. This exhibits an oscillatory distribution which has a wavenumber that is twice the wall velocity that is imposed. The maximum drag reduction takes place when the wall velocity is at its peak. The minimum drag occurs where the wall velocity is zero. Comparisons of mean spanwise velocity profiles with analytical solution to laminar Navier-Stokes equations portray very good agreement (Skote, 2011). The streamwise velocity profile is a clear indicator that the thickening of the sublayer which is viscous when scaled with local friction velocity and upward shifting of the logarithmic region when scaled with the reference friction velocity. An estimation of the power consumption which is ideal indicates that with the present of forcing magnitude more energy is hence required for spatial oscillation than what is saved through drag reduction (Skote, 2011). Waves of spanwise velocity are imposed on the walls of turbulent flow channel. These are studied by the way of direct numerical simulations. What is considered are sinusoidal waves, which have spanwise velocity which vary in time and get modulated in space along streamwise direction. The speed of the phase could be null, negative or positive. This means that waves could be stationary or could be traveling forward or backward in the direction of the mean flow. Such a forcing does include two cases two techniques which are known for reduction of friction drag. The oscillating wall technique which is a travelling wave which have an infinite phase speed and another one which was recently proposed on steady distribution of spanwise velocity where a wave has a zero phase speed. The travelling waves change the friction drag to some extent. Waves which travel at a slow speed travel forward and bring about a significant reduction of drag which can relminarize the flow at values which are low of the Reynolds numbers. Faster waves produce an outcome which is completely different which is known as drag increase (Skote, 2011). Waves which are faster produce what is known as drag reduction effect also. Backward travelling waves, when they cause a reduction of drag, act in a manner which is similar to the oscillating wall with a resulting efficiency in energy. In physics which is concerned with fluid mechanics, a boundary layer refers to a layer of fluid which is in the immediate vicinity of a bounding surface where effects of viscosity are found to be significant. In the atmosphere of the earth, the boundary of the planet is a layer of air which is near the ground and is affected by heat present during the day, moisture or even momentum which is transferred to the surface or from the surface. On the wing of an aircraft the boundary layer refers to the part of the flow which is close to the wing (Skote, 2011). At this point, viscous forces cause a distortion to non viscous flow in the surrounding. Laminar boundary can be grouped by reference to their structure or the circumstances surrounding their creation. The thin shear layer which develop on a body which is oscillating provides an examples of stokes boundary layer. The Blasius boundary layer is used in reference to similarities which are known as solution and are near a flat plate which is attached in a unidirectional flow which is oncoming. When a fluid rotates and Coriosis effect balances them, a layer known as Ekman layers is formed. In the heat transfer theory, thermal boundary layers then occur. Therefore, a surface with many types of boundary layers can occur at the same time (Skote, 2011). The aerodynamics boundary was defined for the first time by Ludwig Prandtl through a paper that he presented in the year 1904. This was at the International Congress of Mathematicians. This definition simplified equations of fluid flow through division of the flow field into two areas (Skote, 2011). The first area was the one inside the boundary layer which dominated by viscosity and majority of drag which was experienced by the boundary body. The other is one which is outside the boundary layer. In this second area, viscosity can be neglected and this does not bring about significant effects on the solution. This makes room for a solution which is closed from for the flows in the two areas. This provides a simplification of the Navier-Stokes equations. The majority of heat transfer from a body and to it happens within the boundary layer. This allows the equation to be simplified in the layer of the boundary and this means that the equation can be simplified in the flow field which is outside the boundary layer. The distribution of the pressure on the boundary layer in the direction which is normal to the surface does not change throughout the boundary layer and this does not change on the surface (Skote, 2011). References Skote, M. (2011).Turbulent boundary layer flow subject to streamwise oscillation of spanwise wall-velocity. School of Mechanical and Aerospace Engineering, Nanyang Technological University: Singapore. Read More