Characteristics of the Laminar Boundary Layer
Comparing and contrasting laminar and turbulent flow.
Diving deeper into the properties of the laminar boundary layer.
A focus on the thermodynamics of the laminar boundary layer.
The characteristics of laminar boundary layers govern the relatively ordered behavior of low flow rates
Turn on a sink faucet head slowly enough and you might just see something interesting. At low flow rates, water flows in an overall shape that is easily viewable, but after a certain flow rate, this shape gives way to a chaotic, opaque torrent. The flow speed has an effect, but what is the underlying structure powering the change? The answer is that flows can be categorized as either laminar or turbulent, and each is associated with certain qualities.
To the layperson, “turbulent” is a term that people might have some experience with even if they don’t understand the finer points of the phenomenon. The central difference between the two boils down to the boundary layer – a section of fluid adjacent to a solid body that can vary in size and functionality depending on both the fluid and the solid body. The characteristics of laminar boundary layers are especially noteworthy for their structured nature and the performance benefits they offer.
Describing the Characteristics of Laminar Boundary Layers
As fluid flows past a solid body, a boundary layer is established where the fluid particles will have zero velocity relative to the surface. This property, known as the no-slip condition, exists due to the adhesive forces between the fluid and solid body overcoming the cohesive forces between the particles of the liquid. The presence of the boundary layer can create a continuum of viscosity layers with a low Reynolds number (the ratio of inertial to viscous forces), which increases in viscosity proportionally to the distance away from the boundary layer. This is the case of laminar flow, which is often seen as the preferable state to the closely related turbulent flow due to the reduction in analogous surface-level drag forces.
While well-behaved laminar flow is relatively unstable – given enough distance from the point where fluid passes over a submerged solid body – laminar flow gives way to turbulent flow. A subset of fluid dynamics known as boundary layer control concerns design techniques to maximize the distance before the flow transition. In general, the thickest point of the solid body should be placed as far back from the initial point of the boundary layer to reduce the Reynolds number for the longest possible distance.
What Are Laminar Boundary Layer Properties?
The mechanics of a laminar flow arise due to the ordered behavior of the viscosity layers. As mentioned, viscosity increases linearly away from the surface of the boundary layer, and this can be partitioned into a series of infinitesimally small layers. In this heuristic, layers only slide against adjacent layers – there is no movement of fluid in the direction perpendicular to the surface. Traveling parallel to the surface, there is always some critical distance where laminar flow evolves into turbulent flow, but designs can effectively control where this occurs.
Beyond its behavior, the laminar flow has additional characteristics that make it far preferable to turbulence conditions:
Velocity - In either case, velocity increases moving away from the surface, but it does so much more gradually with laminar flow. Since velocity correlates to shear stress, turbulent flow experiences a sharp spike in shear stress that is disruptive and liable to cause fatigue.
Viscosity - Laminar flow was vaguely quantified with a low Reynolds number, but there is more variance. Within laminar flow conditions, a lower Reynolds number causes the envelope of the viscous laminar region to expand around the solid body, while a higher Reynolds number causes it to contract. This viscous layer remains even at Reynolds numbers within the turbulent region, but it shrinks even further to encompass only the boundary layer. The viscosity within the envelope acts as something analogous to light moving through a medium compared to a vacuum: streamlines are bent and deflected into more circuitous routes around the solid body compared to the surrounding inviscid flow.
Thermodynamics of the Laminar Boundary Layer
Laminar flow can further be examined from a thermodynamics perspective. Just like the discussed velocity gradient beginning with the no-slip condition at the solid body before smoothly transitioning to the inviscid region, temperature experiences a gradual growth or decay (depending on the relative temperatures of the fluid and the solid body). Other similarities exist:
While it is impossible to indicate an exact point where the boundary layer gives way to the surrounding fluid, the parameters of the envelope (including its thickness) are well-defined with the 99% boundary layer condition.
Heat transfer can only occur between adjacent slices of the boundary layer much the same as the movement of fluid within the layer; heat transfer for turbulent flow can instead flow in the perpendicular direction to the solid body directly (improving the heat exchange capabilities between fluid and solid body).
There are a few methods to calculate the thickness of the thermal envelope for laminar flow:
99% boundary layer thickness - To simplify an asymptotic approach from the temperature of the solid body to that of the fluid far enough to be negligibly affected by the temperature, an engineering solution is to take the 99% temperature of the unaffected fluid as the distance where the boundary delineates. The equation changes dramatically depending on the geometry of the solid body.
Thermal displacement thickness - Instead of assuming a continuous temperature gradient, temperatures taken at certain distances from the solid body are assumed to be step-wise shifts. The envelope can then be built by numerically integrating these values.
Moment - As the temperature profile for laminar flow very closely emulates Gaussian distribution, integration methods can be used to model the thermal profile throughout its extents, and not just at the boundary.
Ensure a Smooth Workflow With Cadence CFD Simulations
The characteristics of the laminar boundary layer are of critical importance in a bevy of applications due to their mechanical properties. Cadence CFD software precisely models laminar flow conditions for smooth sailing. Preparing for turbulence is also a necessity when determining the seaworthiness of any vessel, and the close relation of the two flow characteristics can be quickly and comprehensively handled with cutting-edge Cadence solutions.
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