Boundary layer

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https://en.wikipedia.org/wiki/Boundary_layer 

 

For fluid flow along walls, see fluid dynamics. For the concept in asymptotic analysis, see Method of matched asymptotic expansions.

The boundary layer around a human hand, schlieren photograph. The boundary layer is the bright-green border, most visible on the back of the hand (click for high-res image).

In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer.

The air next to a human is heated resulting in gravity-induced convective airflow, airflow which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boundary layer is the air layer (~ 1 km) near the ground. It is affected by the surface; day-night heat flows caused by the sun heating the ground, moisture, or momentum transfer to or from the surface.

Types of boundary layer

Boundary layer visualization, showing transition from laminar to turbulent condition

Laminar boundary layers can be loosely classified according to their structure and the circumstances under which they are created. The thin shear layer which develops on an oscillating body is an example of a Stokes boundary layer, while the Blasius boundary layer refers to the well-known similarity solution near an attached flat plate held in an oncoming unidirectional flow and Falkner–Skan boundary layer, a generalization of Blasius profile. When a fluid rotates and viscous forces are balanced by the Coriolis effect (rather than convective inertia), an Ekman layer forms. In the theory of heat transfer, a thermal boundary layer occurs. A surface can have multiple types of boundary layer simultaneously.

The viscous nature of airflow reduces the local velocities on a surface and is responsible for skin friction. The layer of air over the wing's surface that is slowed down or stopped by viscosity, is the boundary layer. There are two different types of boundary layer flow: laminar and turbulent.

Laminar boundary layer flow

The laminar boundary is a very smooth flow, while the turbulent boundary layer contains swirls or "eddies." The laminar flow creates less skin friction drag than the turbulent flow, but is less stable. Boundary layer flow over a wing surface begins as a smooth laminar flow. As the flow continues back from the leading edge, the laminar boundary layer increases in thickness.

Turbulent boundary layer flow

At some distance back from the leading edge, the smooth laminar flow breaks down and transitions to a turbulent flow. From a drag standpoint, it is advisable to have the transition from laminar to turbulent flow as far aft on the wing as possible, or have a large amount of the wing surface within the laminar portion of the boundary layer. The low energy laminar flow, however, tends to break down more suddenly than the turbulent layer.

The Prandtl boundary layer concept

Ludwig Prandtl

Laminar boundary layer velocity profile

The aerodynamic boundary layer was first hypothesized by Ludwig Prandtl in a paper presented on August 12, 1904 at the third International Congress of Mathematicians in Heidelberg, Germany. It simplifies the equations of fluid flow by dividing the flow field into two areas: one inside the boundary layer, dominated by viscosity and creating the majority of drag experienced by the boundary body; and one outside the boundary layer, where viscosity can be neglected without significant effects on the solution. This allows a closed-form solution for the flow in both areas by making significant simplifications of the full Navier–Stokes equations. The same hypothesis is applicable to other fluids (besides air) with moderate to low viscosity such as water. For the case where there is a temperature difference between the surface and the bulk fluid, it is found that the majority of the heat transfer to and from a body takes place in the vicinity of the velocity boundary layer. This again allows the equations to be simplified in the flow field outside the boundary layer. The pressure distribution throughout the boundary layer in the direction normal to the surface (such as an airfoil) remains relatively constant throughout the boundary layer, and is the same as on the surface itself.

The thickness of the velocity boundary layer is normally defined as the distance from the solid body to the point at which the viscous flow velocity is 99% of the freestream velocity (the surface velocity of an inviscid flow). Displacement thickness is an alternative definition stating that the boundary layer represents a deficit in mass flow compared to inviscid flow with slip at the wall. It is the distance by which the wall would have to be displaced in the inviscid case to give the same total mass flow as the viscous case. The no-slip condition requires the flow velocity at the surface of a solid object be zero and the fluid temperature be equal to the temperature of the surface. The flow velocity will then increase rapidly within the boundary layer, governed by the boundary layer equations, below.

The thermal boundary layer thickness is similarly the distance from the body at which the temperature is 99% of the freestream temperature. The ratio of the two thicknesses is governed by the Prandtl number. If the Prandtl number is 1, the two boundary layers are the same thickness. If the Prandtl number is greater than 1, the thermal boundary layer is thinner than the velocity boundary layer. If the Prandtl number is less than 1, which is the case for air at standard conditions, the thermal boundary layer is thicker than the velocity boundary layer.

In high-performance designs, such as gliders and commercial aircraft, much attention is paid to controlling the behavior of the boundary layer to minimize drag. Two effects have to be considered. First, the boundary layer adds to the effective thickness of the body, through the displacement thickness, hence increasing the pressure drag. Secondly, the shear forces at the surface of the wing create skin friction drag.

At high Reynolds numbers, typical of full-sized aircraft, it is desirable to have a laminar boundary layer. This results in a lower skin friction due to the characteristic velocity profile of laminar flow. However, the boundary layer inevitably thickens and becomes less stable as the flow develops along the body, and eventually becomes turbulent, the process known as boundary layer transition. One way of dealing with this problem is to suck the boundary layer away through a porous surface (see Boundary layer suction). This can reduce drag, but is usually impractical due to its mechanical complexity and the power required to move the air and dispose of it. Natural laminar flow (NLF) techniques push the boundary layer transition aft by reshaping the airfoil or fuselage so that its thickest point is more aft and less thick. This reduces the velocities in the leading part and the same Reynolds number is achieved with a greater length.

At lower Reynolds numbers, such as those seen with model aircraft, it is relatively easy to maintain laminar flow. This gives low skin friction, which is desirable. However, the same velocity profile which gives the laminar boundary layer its low skin friction also causes it to be badly affected by adverse pressure gradients. As the pressure begins to recover over the rear part of the wing chord, a laminar boundary layer will tend to separate from the surface. Such flow separation causes a large increase in the pressure drag, since it greatly increases the effective size of the wing section. In these cases, it can be advantageous to deliberately trip the boundary layer into turbulence at a point prior to the location of laminar separation, using a turbulator. The fuller velocity profile of the turbulent boundary layer allows it to sustain the adverse pressure gradient without separating. Thus, although the skin friction is increased, overall drag is decreased. This is the principle behind the dimpling on golf balls, as well as vortex generators on aircraft. Special wing sections have also been designed which tailor the pressure recovery so laminar separation is reduced or even eliminated. This represents an optimum compromise between the pressure drag from flow separation and skin friction from induced turbulence.

When using half-models in wind tunnels, a peniche is sometimes used to reduce or eliminate the effect of the boundary layer.

Boundary layer equations

The deduction of the boundary layer equations was one of the most important advances in fluid dynamics. Using an order of magnitude analysis, the well-known governing Navier–Stokes equations of viscous fluid flow can be greatly simplified within the boundary layer. Notably, the characteristic of the partial differential equations (PDE) becomes parabolic, rather than the elliptical form of the full Navier–Stokes equations. This greatly simplifies the solution of the equations. By making the boundary layer approximation, the flow is divided into an inviscid portion (which is easy to solve by a number of methods) and the boundary layer, which is governed by an easier to solve PDE. The continuity and Navier–Stokes equations for a two-dimensional steady incompressible flow in Cartesian coordinates are given by

${\displaystyle \frac{\mathrm{\partial }u}{\mathrm{\partial }x}+\frac{\mathrm{\partial }\upsilon }{\mathrm{\partial }y}=0}$

${\displaystyle u\frac{\mathrm{\partial }u}{\mathrm{\partial }x}+\upsilon \frac{\mathrm{\partial }u}{\mathrm{\partial }y}=-\frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }x}+\nu \left(\frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{y}^2}\right)}$

${\displaystyle u\frac{\mathrm{\partial }\upsilon }{\mathrm{\partial }x}+\upsilon \frac{\mathrm{\partial }\upsilon }{\mathrm{\partial }y}=-\frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }y}+\nu \left(\frac{{\mathrm{\partial }}^2\upsilon }{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^2\upsilon }{\mathrm{\partial }{y}^2}\right)}$

where ${\displaystyle u}$ and ${\displaystyle \upsilon }$ are the velocity components, ${\displaystyle \rho }$ is the density, ${\displaystyle p}$ is the pressure, and ${\displaystyle \nu }$ is the kinematic viscosity of the fluid at a point.

The approximation states that, for a sufficiently high Reynolds number the flow over a surface can be divided into an outer region of inviscid flow unaffected by viscosity (the majority of the flow), and a region close to the surface where viscosity is important (the boundary layer). Let ${\displaystyle u}$ and ${\displaystyle \upsilon }$ be streamwise and transverse (wall normal) velocities respectively inside the boundary layer. Using scale analysis, it can be shown that the above equations of motion reduce within the boundary layer to become

${\displaystyle u\frac{\mathrm{\partial }u}{\mathrm{\partial }x}+\upsilon \frac{\mathrm{\partial }u}{\mathrm{\partial }y}=-\frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }x}+\nu \frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{y}^2}}$

${\displaystyle \frac{1}{\rho }\frac{\mathrm{\partial }p}{\mathrm{\partial }y}=0}$

and if the fluid is incompressible (as liquids are under standard conditions):

${\displaystyle \frac{\mathrm{\partial }u}{\mathrm{\partial }x}+\frac{\mathrm{\partial }\upsilon }{\mathrm{\partial }y}=0}$

The order of magnitude analysis assumes the streamwise length scale significantly larger than the transverse length scale inside the boundary layer. It follows that variations in properties in the streamwise direction are generally much lower than those in the wall normal direction. Apply this to the continuity equation shows that ${\displaystyle \upsilon }$, the wall normal velocity, is small compared with ${\displaystyle u}$ the streamwise velocity.

Since the static pressure ${\displaystyle p}$ is independent of ${\displaystyle y}$, then pressure at the edge of the boundary layer is the pressure throughout the boundary layer at a given streamwise position. The external pressure may be obtained through an application of Bernoulli's equation. Let ${\displaystyle U}$ be the fluid velocity outside the boundary layer, where ${\displaystyle u}$ and ${\displaystyle U}$ are both parallel. This gives upon substituting for ${\displaystyle p}$ the following result

${\displaystyle u\frac{\mathrm{\partial }u}{\mathrm{\partial }x}+\upsilon \frac{\mathrm{\partial }u}{\mathrm{\partial }y}=U\frac{dU}{dx}+\nu \frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{y}^2}}$

For a flow in which the static pressure ${\displaystyle p}$ also does not change in the direction of the flow

${\displaystyle \frac{dp}{dx}=0}$

so ${\displaystyle U}$ remains constant.

Therefore, the equation of motion simplifies to become

${\displaystyle u\frac{\mathrm{\partial }u}{\mathrm{\partial }x}+\upsilon \frac{\mathrm{\partial }u}{\mathrm{\partial }y}=\nu \frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{y}^2}}$

These approximations are used in a variety of practical flow problems of scientific and engineering interest. The above analysis is for any instantaneous laminar or turbulent boundary layer, but is used mainly in laminar flow studies since the mean flow is also the instantaneous flow because there are no velocity fluctuations present. This simplified equation is a parabolic PDE and can be solved using a similarity solution often referred to as the Blasius boundary layer.

Prandtl's transposition theorem

Prandtl observed that from any solution ${\displaystyle u(x,y,t),v(x,y,t)}$ which satisfies the boundary layer equations, further solution ${\displaystyle u^{\ast }(x,y,t),v^{\ast }(x,y,t)}$, which is also satisfying the boundary layer equations, can be constructed by writing

${\displaystyle u^{\ast }(x,y,t)=u(x,y+f(x),t),v^{\ast }(x,y,t)=v(x,y+f(x),t)-f^{\prime }(x)u(x,y+f(x),t)}$

where ${\displaystyle f(x)}$ is arbitrary. Since the solution is not unique from mathematical perspective, to the solution can added any one of an infinite set of eigenfunctions as shown by Stewartson and Paul A. Libby.

Von Kármán momentum integral

Von Kármán derived the integral equation by integrating the boundary layer equation across the boundary layer in 1921. The equation is

${\displaystyle \frac{{\tau }_w}{\rho U^2}=\frac{1}{U^2}\frac{\mathrm{\partial }}{\mathrm{\partial }t}(U{\delta }_1)+\frac{\mathrm{\partial }{\delta }_2}{\mathrm{\partial }x}+\frac{2{\delta }_2+{\delta }_1}{U}\frac{\mathrm{\partial }U}{\mathrm{\partial }x}+\frac{v_w}{U}}$

where

${\displaystyle {\tau }_w=\mu {\left(\frac{\mathrm{\partial }u}{\mathrm{\partial }y}\right)}_{y=0},v_w=v(x,0,t),{\delta }_1={\int }_0^{\mathrm{\infty }}\left(1-\frac{u}{U}\right)dy,{\delta }_2={\int }_0^{\mathrm{\infty }}\frac{u}{U}\left(1-\frac{u}{U}\right)dy}$

${\displaystyle {\tau }_w}$ is the wall shear stress, ${\displaystyle v_w}$ is the suction/injection velocity at the wall, ${\displaystyle {\delta }_1}$ is the displacement thickness and ${\displaystyle {\delta }_2}$ is the momentum thickness. Kármán–Pohlhausen Approximation is derived from this equation.

Energy integral

The energy integral was derived by Wieghardt.

${\displaystyle \frac{2\epsilon }{\rho U^3}=\frac{1}{U}\frac{\mathrm{\partial }}{\mathrm{\partial }t}({\delta }_1+{\delta }_2)+\frac{2{\delta }_2}{U^2}\frac{\mathrm{\partial }U}{\mathrm{\partial }t}+\frac{1}{U^3}\frac{\mathrm{\partial }}{\mathrm{\partial }x}(U^3{\delta }_3)+\frac{v_w}{U}}$

where

${\displaystyle \epsilon ={\int }_0^{\mathrm{\infty }}\mu {\left(\frac{\mathrm{\partial }u}{\mathrm{\partial }y}\right)}^{2}dy,{\delta }_3={\int }_0^{\mathrm{\infty }}\frac{u}{U}\left(1-\frac{u^2}{U^2}\right)dy}$

${\displaystyle \epsilon }$ is the energy dissipation rate due to viscosity across the boundary layer and ${\displaystyle {\delta }_3}$ is the energy thickness.

Von Mises transformation

For steady two-dimensional boundary layers, von Mises introduced a transformation which takes ${\displaystyle x}$ and ${\displaystyle \psi }$(stream function) as independent variables instead of ${\displaystyle x}$ and ${\displaystyle y}$ and uses a dependent variable ${\displaystyle \chi =U^2-u^2}$ instead of ${\displaystyle u}$. The boundary layer equation then become

${\displaystyle \frac{\mathrm{\partial }\chi }{\mathrm{\partial }x}=\nu \sqrt{U^2-\chi }\frac{{\mathrm{\partial }}^2\chi }{\mathrm{\partial }{\psi }^2}}$

The original variables are recovered from

${\displaystyle y=\int \sqrt{U^2-\chi }d\psi ,u=\sqrt{U^2-\chi },v=u\int \frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(\frac{1}{u}\right)d\psi .}$

This transformation is later extended to compressible boundary layer by von Kármán and HS Tsien.

Crocco's transformation

For steady two-dimensional compressible boundary layer, Luigi Crocco introduced a transformation which takes ${\displaystyle x}$ and ${\displaystyle u}$ as independent variables instead of ${\displaystyle x}$ and ${\displaystyle y}$ and uses a dependent variable ${\displaystyle \tau =\mu \mathrm{\partial }u/\mathrm{\partial }y}$(shear stress) instead of ${\displaystyle u}$. The boundary layer equation then becomes

${\displaystyle \begin{array}{rl}& \mu \rho u\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(\frac{1}{\tau }\right)+\frac{{\mathrm{\partial }}^2\tau }{\mathrm{\partial }{u}^2}-\mu \frac{dp}{dx}\frac{\mathrm{\partial }}{\mathrm{\partial }u}\left(\frac{1}{\tau }\right)=0,\\ & \text{if }\frac{dp}{dx}=0,\text{ then }\frac{\mu \rho }{{\tau }^2}\frac{\mathrm{\partial }\tau }{\mathrm{\partial }x}=\frac{1}{u}\frac{{\mathrm{\partial }}^2\tau }{\mathrm{\partial }{u}^2}.\end{array}}$

The original coordinate is recovered from

${\displaystyle y=\mu \int \frac{du}{\tau }.}$

Turbulent boundary layers

The treatment of turbulent boundary layers is far more difficult due to the time-dependent variation of the flow properties. One of the most widely used techniques in which turbulent flows are tackled is to apply Reynolds decomposition. Here the instantaneous flow properties are decomposed into a mean and fluctuating component with the assumption that the mean of the fluctuating component is always zero. Applying this technique to the boundary layer equations gives the full turbulent boundary layer equations not often given in literature:

${\displaystyle \frac{\mathrm{\partial }\overline{u}}{\mathrm{\partial }x}+\frac{\mathrm{\partial }\overline{v}}{\mathrm{\partial }y}=0}$

${\displaystyle \overline{u}\frac{\mathrm{\partial }\overline{u}}{\mathrm{\partial }x}+\overline{v}\frac{\mathrm{\partial }\overline{u}}{\mathrm{\partial }y}=-\frac{1}{\rho }\frac{\mathrm{\partial }\overline{p}}{\mathrm{\partial }x}+\nu \left(\frac{{\mathrm{\partial }}^2\overline{u}}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^2\overline{u}}{\mathrm{\partial }{y}^2}\right)-\frac{\mathrm{\partial }}{\mathrm{\partial }y}(\overline{u^{\prime }{v}^{\prime }})-\frac{\mathrm{\partial }}{\mathrm{\partial }x}(\overline{u^{\prime 2}})}$

${\displaystyle \overline{u}\frac{\mathrm{\partial }\overline{v}}{\mathrm{\partial }x}+\overline{v}\frac{\mathrm{\partial }\overline{v}}{\mathrm{\partial }y}=-\frac{1}{\rho }\frac{\mathrm{\partial }\overline{p}}{\mathrm{\partial }y}+\nu \left(\frac{{\mathrm{\partial }}^2\overline{v}}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^2\overline{v}}{\mathrm{\partial }{y}^2}\right)-\frac{\mathrm{\partial }}{\mathrm{\partial }x}(\overline{u^{\prime }{v}^{\prime }})-\frac{\mathrm{\partial }}{\mathrm{\partial }y}(\overline{v^{\prime 2}})}$

Using a similar order-of-magnitude analysis, the above equations can be reduced to leading order terms. By choosing length scales ${\displaystyle \delta }$ for changes in the transverse-direction, and ${\displaystyle L}$ for changes in the streamwise-direction, with ${\displaystyle \delta <<L}$, the x-momentum equation simplifies to:

${\displaystyle \overline{u}\frac{\mathrm{\partial }\overline{u}}{\mathrm{\partial }x}+\overline{v}\frac{\mathrm{\partial }\overline{u}}{\mathrm{\partial }y}=-\frac{1}{\rho }\frac{\mathrm{\partial }\overline{p}}{\mathrm{\partial }x}-\frac{\mathrm{\partial }}{\mathrm{\partial }y}(\overline{u^{\prime }{v}^{\prime }}).}$

This equation does not satisfy the no-slip condition at the wall. Like Prandtl did for his boundary layer equations, a new, smaller length scale must be used to allow the viscous term to become leading order in the momentum equation. By choosing ${\displaystyle \eta <<\delta }$ as the y-scale, the leading order momentum equation for this "inner boundary layer" is given by:

${\displaystyle 0=-\frac{1}{\rho }\frac{\mathrm{\partial }\overline{p}}{\mathrm{\partial }x}+\nu \frac{{\mathrm{\partial }}^2\overline{u}}{\mathrm{\partial }{y}^2}-\frac{\mathrm{\partial }}{\mathrm{\partial }y}(\overline{u^{\prime }{v}^{\prime }}).}$

In the limit of infinite Reynolds number, the pressure gradient term can be shown to have no effect on the inner region of the turbulent boundary layer. The new "inner length scale" ${\displaystyle \eta }$ is a viscous length scale, and is of order ${\displaystyle \frac{\nu }{u_{\ast }}}$, with ${\displaystyle u_{\ast }}$ being the velocity scale of the turbulent fluctuations, in this case a friction velocity.

Unlike the laminar boundary layer equations, the presence of two regimes governed by different sets of flow scales (i.e. the inner and outer scaling) has made finding a universal similarity solution for the turbulent boundary layer difficult and controversial. To find a similarity solution that spans both regions of the flow, it is necessary to asymptotically match the solutions from both regions of the flow. Such analysis will yield either the so-called log-law or power-law.

Similar approaches to the above analysis has also been applied for thermal boundary layers, using the energy equation in compressible flows.

The additional term ${\displaystyle \overline{u^{\prime }{v}^{\prime }}}$ in the turbulent boundary layer equations is known as the Reynolds shear stress and is unknown a priori. The solution of the turbulent boundary layer equations therefore necessitates the use of a turbulence model, which aims to express the Reynolds shear stress in terms of known flow variables or derivatives. The lack of accuracy and generality of such models is a major obstacle in the successful prediction of turbulent flow properties in modern fluid dynamics.

A constant stress layer exists in the near wall region. Due to the damping of the vertical velocity fluctuations near the wall, the Reynolds stress term will become negligible and we find that a linear velocity profile exists. This is only true for the very near wall region.

Heat and mass transfer

In 1928, the French engineer André Lévêque observed that convective heat transfer in a flowing fluid is affected only by the velocity values very close to the surface. For flows of large Prandtl number, the temperature/mass transition from surface to freestream temperature takes place across a very thin region close to the surface. Therefore, the most important fluid velocities are those inside this very thin region in which the change in velocity can be considered linear with normal distance from the surface. In this way, for

${\displaystyle u(y)=U\left[1-\frac{(y-h{)}^2}{h^2}\right]=U\frac{y}{h}\left[2-\frac{y}{h}\right],}$

when ${\displaystyle y\to 0}$, then

${\displaystyle u(y)\approx 2U\frac{y}{h}=\theta y,}$

where θ is the tangent of the Poiseuille parabola intersecting the wall. Although Lévêque's solution was specific to heat transfer into a Poiseuille flow, his insight helped lead other scientists to an exact solution of the thermal boundary-layer problem. Schuh observed that in a boundary-layer, u is again a linear function of y, but that in this case, the wall tangent is a function of x. He expressed this with a modified version of Lévêque's profile,

${\displaystyle u(y)=\theta (x)y.}$

This results in a very good approximation, even for low ${\displaystyle Pr}$ numbers, so that only liquid metals with ${\displaystyle Pr}$ much less than 1 cannot be treated this way. In 1962, Kestin and Persen published a paper describing solutions for heat transfer when the thermal boundary layer is contained entirely within the momentum layer and for various wall temperature distributions. For the problem of a flat plate with a temperature jump at ${\displaystyle x=x_0}$, they propose a substitution that reduces the parabolic thermal boundary-layer equation to an ordinary differential equation. The solution to this equation, the temperature at any point in the fluid, can be expressed as an incomplete gamma function. Schlichting proposed an equivalent substitution that reduces the thermal boundary-layer equation to an ordinary differential equation whose solution is the same incomplete gamma function.

Convective transfer constants from boundary layer analysis

Paul Richard Heinrich Blasius derived an exact solution to the above laminar boundary layer equations. The thickness of the boundary layer ${\displaystyle \delta }$ is a function of the Reynolds number for laminar flow.

${\displaystyle \delta \approx 5.0\frac{x}{\sqrt{Re}}}$

${\displaystyle \delta }$ = the thickness of the boundary layer: the region of flow where the velocity is less than 99% of the far field velocity ${\displaystyle v_{\mathrm{\infty }}}$; ${\displaystyle x}$ is position along the semi-infinite plate, and ${\displaystyle Re}$ is the Reynolds Number given by ${\displaystyle \rho v_{\mathrm{\infty }}x/\mu }$ (${\displaystyle \rho =}$ density and ${\displaystyle \mu =}$ dynamic viscosity).

The Blasius solution uses boundary conditions in a dimensionless form:

${\displaystyle \frac{v_x-v_S}{v_{\mathrm{\infty }}-v_S}=\frac{v_x}{v_{\mathrm{\infty }}}=\frac{v_y}{v_{\mathrm{\infty }}}=0}$     at     ${\displaystyle y=0}$

${\displaystyle \frac{v_x-v_S}{v_{\mathrm{\infty }}-v_S}=\frac{v_x}{v_{\mathrm{\infty }}}=1}$     at     ${\displaystyle y=\mathrm{\infty }}$ and ${\displaystyle x=0}$

Velocity Boundary Layer (Top, orange) and Temperature Boundary Layer (Bottom, green) share a functional form due to similarity in the Momentum/Energy Balances and boundary conditions.

Note that in many cases, the no-slip boundary condition holds that ${\displaystyle v_S}$, the fluid velocity at the surface of the plate equals the velocity of the plate at all locations. If the plate is not moving, then ${\displaystyle v_S=0}$. A much more complicated derivation is required if fluid slip is allowed.

In fact, the Blasius solution for laminar velocity profile in the boundary layer above a semi-infinite plate can be easily extended to describe Thermal and Concentration boundary layers for heat and mass transfer respectively. Rather than the differential x-momentum balance (equation of motion), this uses a similarly derived Energy and Mass balance:

Energy:         ${\displaystyle v_x\frac{\mathrm{\partial }T}{\mathrm{\partial }x}+v_y\frac{\mathrm{\partial }T}{\mathrm{\partial }y}=\frac{k}{\rho C_p}\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{y}^2}}$

Mass:           ${\displaystyle v_x\frac{\mathrm{\partial }{c}_A}{\mathrm{\partial }x}+v_y\frac{\mathrm{\partial }{c}_A}{\mathrm{\partial }y}=D_{AB}\frac{{\mathrm{\partial }}^2{c}_A}{\mathrm{\partial }{y}^2}}$

For the momentum balance, kinematic viscosity ${\displaystyle \nu }$ can be considered to be the momentum diffusivity. In the energy balance this is replaced by thermal diffusivity ${\displaystyle \alpha =k/\rho C_P}$, and by mass diffusivity ${\displaystyle D_{AB}}$ in the mass balance. In thermal diffusivity of a substance, ${\displaystyle k}$ is its thermal conductivity, ${\displaystyle \rho }$ is its density and ${\displaystyle C_P}$ is its heat capacity. Subscript AB denotes diffusivity of species A diffusing into species B.

Under the assumption that ${\displaystyle \alpha =D_{AB}=\nu }$, these equations become equivalent to the momentum balance. Thus, for Prandtl number ${\displaystyle Pr=\nu /\alpha =1}$ and Schmidt number ${\displaystyle Sc=\nu /D_{AB}=1}$ the Blasius solution applies directly.

Accordingly, this derivation uses a related form of the boundary conditions, replacing ${\displaystyle v}$ with ${\displaystyle T}$ or ${\displaystyle c_A}$ (absolute temperature or concentration of species A). The subscript S denotes a surface condition.

${\displaystyle \frac{v_x-v_S}{v_{\mathrm{\infty }}-v_S}=\frac{T-T_S}{T_{\mathrm{\infty }}-T_S}=\frac{c_A-c_{AS}}{c_{A\mathrm{\infty }}-c_{AS}}=0}$     at     ${\displaystyle y=0}$

${\displaystyle \frac{v_x-v_S}{v_{\mathrm{\infty }}-v_S}=\frac{T-T_S}{T_{\mathrm{\infty }}-T_S}=\frac{c_A-c_{AS}}{c_{A\mathrm{\infty }}-c_{AS}}=1}$     at     ${\displaystyle y=\mathrm{\infty }}$ and ${\displaystyle x=0}$

Using the streamline function Blasius obtained the following solution for the shear stress at the surface of the plate.

${\displaystyle {\tau }_0={\left(\frac{\mathrm{\partial }{v}_x}{\mathrm{\partial }y}\right)}_{y=0}=0.332\frac{v_{\mathrm{\infty }}}{x}R{e}^{1/2}}$

And via the boundary conditions, it is known that

${\displaystyle \frac{v_x-v_S}{v_{\mathrm{\infty }}-v_S}=\frac{T-T_S}{T_{\mathrm{\infty }}-T_S}=\frac{c_A-c_{AS}}{c_{A\mathrm{\infty }}-c_{AS}}}$

We are given the following relations for heat/mass flux out of the surface of the plate

${\displaystyle {\left(\frac{\mathrm{\partial }T}{\mathrm{\partial }y}\right)}_{y=0}=0.332\frac{T_{\mathrm{\infty }}-T_S}{x}R{e}^{1/2}}$

${\displaystyle {\left(\frac{\mathrm{\partial }{c}_A}{\mathrm{\partial }y}\right)}_{y=0}=0.332\frac{c_{A\mathrm{\infty }}-c_{AS}}{x}R{e}^{1/2}}$

So for ${\displaystyle Pr=Sc=1}$

${\displaystyle \delta ={\delta }_T={\delta }_c=\frac{5.0x}{\sqrt{Re}}}$

where ${\displaystyle {\delta }_T,{\delta }_c}$ are the regions of flow where ${\displaystyle T}$ and ${\displaystyle c_A}$ are less than 99% of their far field values.

Because the Prandtl number of a particular fluid is not often unity, German engineer E. Polhausen who worked with Ludwig Prandtl attempted to empirically extend these equations to apply for ${\displaystyle Pr\ne 1}$. His results can be applied to ${\displaystyle Sc}$ as well. He found that for Prandtl number greater than 0.6, the thermal boundary layer thickness was approximately given by:

Plot showing the relative thickness in the Thermal boundary layer versus the Velocity boundary layer (in red) for various Prandtl Numbers. For ${\displaystyle Pr=1}$, the two are equal.

${\displaystyle \frac{\delta }{{\delta }_T}=P{r}^{1/3}}$          and therefore          ${\displaystyle \frac{\delta }{{\delta }_c}=S{c}^{1/3}}$

From this solution, it is possible to characterize the convective heat/mass transfer constants based on the region of boundary layer flow. Fourier's law of conduction and Newton's Law of Cooling are combined with the flux term derived above and the boundary layer thickness.

${\displaystyle \frac{q}{A}=-k{\left(\frac{\mathrm{\partial }T}{\mathrm{\partial }y}\right)}_{y=0}=h_x(T_S-T_{\mathrm{\infty }})}$

${\displaystyle h_x=0.332\frac{k}{x}R{e}_x^{1/2}P{r}^{1/3}}$

This gives the local convective constant ${\displaystyle h_x}$ at one point on the semi-infinite plane. Integrating over the length of the plate gives an average

${\displaystyle h_L=0.664\frac{k}{x}R{e}_L^{1/2}P{r}^{1/3}}$

Following the derivation with mass transfer terms (${\displaystyle k}$ = convective mass transfer constant, ${\displaystyle D_{AB}}$ = diffusivity of species A into species B, ${\displaystyle Sc=\nu /D_{AB}}$ ), the following solutions are obtained:

${\displaystyle k_x^{\prime }=0.332\frac{D_{AB}}{x}R{e}_x^{1/2}S{c}^{1/3}}$

${\displaystyle k_L^{\prime }=0.664\frac{D_{AB}}{x}R{e}_L^{1/2}S{c}^{1/3}}$

These solutions apply for laminar flow with a Prandtl/Schmidt number greater than 0.6.

Naval architecture

Many of the principles that apply to aircraft also apply to ships, submarines, and offshore platforms.

For ships, unlike aircraft, one deals with incompressible flows, where change in water density is negligible (a pressure rise close to 1000kPa leads to a change of only 2–3 kg/m³). This field of fluid dynamics is called hydrodynamics. A ship engineer designs for hydrodynamics first, and for strength only later. The boundary layer development, breakdown, and separation become critical because the high viscosity of water produces high shear stresses.

Boundary layer turbine

This effect was exploited in the Tesla turbine, patented by Nikola Tesla in 1913. It is referred to as a bladeless turbine because it uses the boundary layer effect and not a fluid impinging upon the blades as in a conventional turbine. Boundary layer turbines are also known as cohesion-type turbine, bladeless turbine, and Prandtl layer turbine (after Ludwig Prandtl).

Predicting transient boundary layer thickness in a cylinder using dimensional analysis

By using the transient and viscous force equations for a cylindrical flow you can predict the transient boundary layer thickness by finding the Womersley Number (${\displaystyle N_w}$).

Transient Force = ${\displaystyle \rho vw}$

Viscous Force = ${\displaystyle \frac{\mu v}{{\delta }_1^2}}$

Setting them equal to each other gives:

${\displaystyle \rho vw=\frac{\mu v}{{\delta }_1^2}}$

Solving for delta gives:

${\displaystyle {\delta }_1=\sqrt{\frac{\mu }{\rho w}}=\sqrt{\frac{v}{w}}}$

In dimensionless form:

${\displaystyle \frac{L}{{\delta }_1}=L\sqrt{\frac{w}{v}}=N_w}$

where ${\displaystyle N_w}$ = Womersley Number; ${\displaystyle \rho }$ = density; ${\displaystyle v}$ = velocity; ${\displaystyle w=}$ ?; ${\displaystyle {\delta }_1}$ = length of transient boundary layer; ${\displaystyle \mu }$ = viscosity; ${\displaystyle L}$ = characteristic length.

Predicting convective flow conditions at the boundary layer in a cylinder using dimensional analysis

By using the convective and viscous force equations at the boundary layer for a cylindrical flow you can predict the convective flow conditions at the boundary layer by finding the dimensionless Reynolds Number (${\displaystyle Re}$).

Convective force: $\frac{{\displaystyle \rho v^2}}{L}$

Viscous force: ${\displaystyle \frac{\mu v}{{\delta }_2^2}}$

Setting them equal to each other gives:

${\displaystyle \frac{\rho v^2}{L}=\frac{\mu v}{{\delta }_2^2}}$

Solving for delta gives:

${\displaystyle {\delta }_2=\sqrt{\frac{\mu L}{\rho v}}}$

In dimensionless form:

${\displaystyle \frac{L}{{\delta }_2}=\sqrt{\frac{\rho vL}{\mu }}=\sqrt{Re}}$

where ${\displaystyle Re}$ = Reynolds Number; ${\displaystyle \rho }$ = density; ${\displaystyle v}$ = velocity; ${\displaystyle {\delta }_2}$ = length of convective boundary layer; ${\displaystyle \mu }$ = viscosity; ${\displaystyle L}$ = characteristic length.

Boundary layer ingestion

Boundary layer ingestion promises an increase in aircraft fuel efficiency with an aft-mounted propulsor ingesting the slow fuselage boundary layer and re-energising the wake to reduce drag and improve propulsive efficiency. To operate in distorted airflow, the fan is heavier and its efficiency is reduced, and its integration is challenging. It is used in concepts like the Aurora D8 or the French research agency Onera’s Nova, saving 5% in cruise by ingesting 40% of the fuselage boundary layer.

Airbus presented the Nautilius concept at the ICAS congress in September 2018: to ingest all the fuselage boundary layer, while minimizing the azimuthal flow distortion, the fuselage splits into two spindles with 13-18:1 bypass ratio fans. Propulsive efficiencies are up to 90% like counter-rotating open rotors with smaller, lighter, less complex and noisy engines. It could lower fuel burn by over 10% compared to a usual underwing 15:1 bypass ratio engine.

Esoteric programming language

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Esoteric_programming_language

An esoteric programming language (sometimes shortened to esolang) is a programming language designed to test the boundaries of computer programming language design, as a proof of concept, as software art, as a hacking interface to another language (particularly functional programming or procedural programming languages), or as a joke. The use of the word esoteric distinguishes them from languages that working developers use to write software. The creators of most esolangs do not intend them to be used for mainstream programming, although some esoteric features, such as visuospatial syntax, have inspired practical applications in the arts. Such languages are often popular among hackers and hobbyists.

Usability is rarely a goal for designers of esoteric programming languages; often their design leads to quite the opposite. Their usual aim is to remove or replace conventional language features while still maintaining a language that is Turing-complete, or even one for which the computational class is unknown.

History

The earliest, and still the canonical example of an esoteric programming language, is INTERCAL, designed in 1972 by Don Woods and James M. Lyon, who said that their intention was to create a programming language unlike any with which they were familiar. It parodied elements of established programming languages of the day such as Fortran, COBOL and assembly language.

For many years, INTERCAL was represented only by paper copies of the INTERCAL manual. Its revival in 1990 as an implementation in C under Unix stimulated a wave of interest in the intentional design of esoteric computer languages.

In 1993, Wouter van Oortmerssen created FALSE, a small stack-oriented programming language with syntax designed to make the code inherently obfuscated, confusing and unreadable. Its compiler is only 1024 bytes in size. This inspired Urban Müller to create an even smaller language, the now-infamous Brainfuck, which consists of only eight recognized characters. Along with Chris Pressey's Befunge (like FALSE, but with a two-dimensional instruction pointer), Brainfuck is now one of the best-supported esoteric programming languages, with canonical examples of minimal Turing tarpits and needlessly obfuscated language features. Brainfuck is related to the P′′ family of Turing machines.

Common features

While esoteric programming languages differ in many ways, there are some common traits that characterize many languages, such as parody, minimalism, and the goal of making programming difficult. Many esoteric programming languages, such as brainfuck, and similar, use single characters as commands, however, it isn't uncommon for languages to read line by line like conventional programming languages.

Unique data representations

Conventional imperative programming languages typically allow data to be stored in variables, but esoteric languages may utilize different methods of storing and accessing data. Languages like Brainfuck and Malbolge only permit data to be read through a single pointer, which must be moved to a location of interest before data is read. Others, like Befunge and Shakespeare, utilize one or more stacks to hold data, leading to a manner of execution akin to Reverse Polish notation. Finally, there are languages which explore alternative forms of number representation: the Brainfuck variant Boolfuck only permits operations on single bits, while Malbolge and INTERCAL variant TriINTERCAL replace bits altogether with a base 3 ternary system.

Unique instruction representations

Esoteric languages also showcase unique ways of representing program instructions. Some languages, such as Befunge and Piet, represent programs in two or more dimensions, with program control moving around in multiple possible directions through the program. This differs from conventional languages in which a program is a set of instructions usually encountered in sequence. Other languages modify instructions to appear in an unusual form, often one that can be read by humans with an alternate meaning to the underlying instructions. Shakespeare achieves this by making all programs resemble Shakespearian plays. Chef achieves the same by having all programs be recipes. Chef is particularly notable in that some have created programs that successfully function both as a program and as a recipe, demonstrating the ability of the language to produce this double meaning.

Difficulty to read and write

Many esoteric programming languages are designed to produce code that is deeply obfuscated, making it difficult to read and to write. The purpose of this may be to provide an interesting puzzle or challenge for program writers: Malbolge for instance was explicitly designed to be challenging, and so it has features like self-modifying code and highly counterintuitive operations. On the other hand, some esoteric languages become difficult to write due to their other design choices. Brainfuck is committed to the idea of a minimalist instruction set, so even though its instructions are straightforward in principle, the code that arises is difficult for a human to read. INTERCAL's difficulty arises as a result of the choice to avoid operations used in any other programming language, which stems from its origin as a parody of other languages.

Parody and spoof

One of the aims of esoteric programming languages is to parody or spoof existing languages and trends in the field of programming. For instance, the first esoteric language INTERCAL began as a spoof of languages used in the 1960's, such as APL, Fortran, and COBOL. INTERCAL's rules appear to be the inverse of rules in these other languages. However, the subject of parody is not always another established programming language. Shakespeare can be viewed as spoofing the structure of Shakespearean plays, for instance. The language Ook! is a parody of Brainfuck, where Brainfuck's eight commands are replaced by various orangutang sounds like "Ook. Ook?"

Examples

See also: List of programming languages by type § Esoteric languages

Befunge

Befunge allows the instruction pointer to roam in multiple dimensions through the code. For example, the following program displays "Hello World" by pushing the characters in reverse order onto the stack, then printing the characters in a loop which circulates clockwise through the instructions >, :, v, _, ,, and ^.

 "dlroW olleH">:v
              ^,_@

There are many versions of Befunge, the most common being Befunge-93, which is named as such because it was released in 1993.

Binary combinatory logic

Binary combinatory logic, otherwise known as binary lambda calculus, is designed from an algorithmic information theory perspective to allow for the densest possible code with the most minimal means, featuring a 29-byte self interpreter, a 21-byte prime number sieve, and a 112-byte Brainfuck interpreter.

Brainfuck

Brainfuck is designed for extreme minimalism and leads to obfuscated code, with programs containing only eight distinct characters. The following program outputs "Hello, world!":

++++++++++[>+++++++>++++++++++>+++<<<-]>++.>+.+++++++
 ..+++.>++.<<+++++++++++++++.>.+++.------.--------.>+.

All characters other than +-<>,.[] are ignored.

Chicken

Chicken has just three tokens, the word "chicken", " " (the space character), and "\n". The compiler interprets the amount of "chickens" on a line as an opcode instruction which it uses to manipulate data on a stack. A simple chicken program can contain dozens of lines with nothing but the word "chicken" repeated countless times. Chicken was invented by Torbjörn Söderstedt who drew his inspiration for the language from a parody of a scientific dissertation.

Chef

Chef is a stack-oriented programming language created by David Morgan-Mar, designed to make programs look like cooking recipes. Programs consist of a title, a list of variables and their data values, and a list of stack manipulation instructions. A joking design principle states that "program recipes should not only generate valid output, but be easy to prepare and delicious", and Morgan-Mar notes that an example Hello World program with "101 eggs" and "111 cups oil" would produce "a lot of food for one person."

FRACTRAN

A FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input ${\displaystyle n}$. The program is run by multiplying the integer ${\displaystyle n}$ by the first fraction ${\displaystyle f}$ in the list for which ${\displaystyle nf}$ is an integer. The integer ${\displaystyle n}$ is then replaced by ${\displaystyle nf}$ and the rule is repeated. If no fraction in the list produces an integer when multiplied by ${\displaystyle n}$, the program halts. FRACTRAN was invented by mathematician John Conway.

GolfScript

Programs in GolfScript, a language created for code golf, consist of lists of items, each of which is pushed onto the stack as it is encountered, with the exception of variables which have code blocks as their value, in which case the code is executed.

INTERCAL

INTERCAL, short for "Compiler Language With No Pronounceable Acronym", was created in 1972 as a parody to satirize aspects of the various programming languages at the time.

JSFuck

JSFuck is an esoteric programming style of JavaScript, where code is written using only six characters: [, ], (, ), !, and +. Unlike Brainfuck, which requires its own compiler or interpreter, JSFuck is valid JavaScript code, meaning JSFuck programs can be run in any web browser or engine that interprets JavaScript. It has been used in a number of cross-site scripting (XSS) attacks on websites such as eBay due to its ability to evade cross-site scripting detection filters.

LOLCODE

LOLCODE is designed to resemble the speech of lolcats. The following is the "Hello World" example:

HAI
CAN HAS STDIO?
VISIBLE "HAI WORLD!"
KTHXBYE

While the semantics of LOLCODE is not unusual, its syntax has been described as a linguistic phenomenon, representing an unusual example of informal speech and internet slang in programming.

Malbolge

Malbolge (named after the 8th circle of Hell) was designed to be the most difficult and esoteric programming language. Among other features, code is self-modifying by design and the effect of an instruction depends on its address in memory.

Piet

Piet program that prints 'Piet'

A "Hello World" program in Piet

Piet is a language designed by David Morgan-Mar, whose programs are bitmaps that look like abstract art. The execution is guided by a "pointer" that moves around the image, from one continuous coloured region to the next. Procedures are carried out when the pointer exits a region.

There are 20 colours for which behaviour is specified: 18 "colourful" colours, which are ordered by a 6-step hue cycle and a 3-step brightness cycle; and black and white, which are not ordered. When exiting a "colourful" colour and entering another one, the performed procedure is determined by the number of steps of change in hue and brightness. Black cannot be entered; when the pointer tries to enter a black region, the rules of choosing the next block are changed instead. If all possible rules are tried, the program terminates. Regions outside the borders of the image are also treated as black. White does not perform operations, but allows the pointer to "pass through". The behaviour of colours other than the 20 specified is left to the compiler or interpreter.

Variables are stored in memory as signed integers in a single stack. Most specified procedures deal with operations on that stack, while others deal with input/output and with the rules by which the compilation pointer moves.

Piet was named after the Dutch painter Piet Mondrian. The original intended name, Mondrian, was already taken by an open-source statistical data-visualization system.

Rockstar

Rockstar is a computer programming language designed for creating programs that are also hair metal power ballads. It was created by Dylan Beattie.

Shakespeare

Shakespeare is designed to make programs look like Shakespearean plays. For example, the following statement declares a point in the program which can be reached via a GOTO-type statement:

 Act I: Hamlet's insults and flattery.

Storyteller

Storyteller is a computer programming language designed to make programs look like rich, emotional narrative.

Unlambda

Unlambda is a minimalist functional programming language based on SKI calculus, but combined with first-class continuations and imperative I/O (with input usually requiring the use of continuations).

Whitespace

Whitespace uses only whitespace characters (space, tab, and return), ignoring all other characters, which can therefore be used for comments. This is the reverse of many traditional languages, which do not distinguish between different whitespace characters, treating tab and space the same. It also allows Whitespace programs to be hidden in the source code of programs in languages like C.

Cultural context

The cultural context of esolangs has been studied by Geoff Cox, who writes that esolangs "shift attention from command and control toward cultural expression and refusal", seeing esolangs as similar to code art and code poetry, such as Mez Breeze's mezangelle. Daniel Temkin describes Brainfuck as "refusing to ease the boundary between human expression and assembly code and thereby taking us on a ludicrous journey of logic," exposing the inherent conflict between human thinking and computer logic. He connects programming within an esolang to performing an event score such as those of the Fluxus movement, where playing out the rules of the logic in code makes the point of view of the language clear.

Phenolic content in wine

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Phenolic_content_in_wine 

The phenolic compounds in Syrah grapes contribute to the taste, color and mouthfeel of the wine.

The phenolic content in wine refers to the phenolic compounds—natural phenol and polyphenols—in wine, which include a large group of several hundred chemical compounds that affect the taste, color and mouthfeel of wine. These compounds include phenolic acids, stilbenoids, flavonols, dihydroflavonols, anthocyanins, flavanol monomers (catechins) and flavanol polymers (proanthocyanidins). This large group of natural phenols can be broadly separated into two categories, flavonoids and non-flavonoids. Flavonoids include the anthocyanins and tannins which contribute to the color and mouthfeel of the wine. The non-flavonoids include the stilbenoids such as resveratrol and phenolic acids such as benzoic, caffeic and cinnamic acids.

Origin of the phenolic compounds

The natural phenols are not evenly distributed within the fruit. Phenolic acids are largely present in the pulp, anthocyanins and stilbenoids in the skin, and other phenols (catechins, proanthocyanidins and flavonols) in the skin and the seeds. During the growth cycle of the grapevine, sunlight will increase the concentration of phenolics in the grape berries, their development being an important component of canopy management. The proportion of the different phenols in any one wine will therefore vary according to the type of vinification. Red wine will be richer in phenols abundant in the skin and seeds, such as anthocyanin, proanthocyanidins and flavonols, whereas the phenols in white wine will essentially originate from the pulp, and these will be the phenolic acids together with lower amounts of catechins and stilbenes. Red wines will also have the phenols found in white wines.

Wine simple phenols are further transformed during wine aging into complex molecules formed notably by the condensation of proanthocyanidins and anthocyanins, which explains the modification in the color. Anthocyanins react with catechins, proanthocyanidins and other wine components during wine aging to form new polymeric pigments resulting in a modification of the wine color and a lower astringency. Average total polyphenol content measured by the Folin method is 216 mg/100 ml for red wine and 32 mg/100 ml for white wine. The content of phenols in rosé wine (82 mg/100 ml) is intermediate between that in red and white wines.

In winemaking, the process of maceration or "skin contact" is used to increase the concentration of phenols in wine. Phenolic acids are found in the pulp or juice of the wine and can be commonly found in white wines which usually do not go through a maceration period. The process of oak aging can also introduce phenolic compounds into wine, most notably vanillin which adds vanilla aroma to wines.

Most wine phenols are classified as secondary metabolites and were not thought to be active in the primary metabolism and function of the grapevine. However, there is evidence that in some plants flavonoids play a role as endogenous regulators of auxin transport. They are water-soluble and are usually secreted into the vacuole of the grapevine as glycosides.

Grape polyphenols

Vitis vinifera produces many phenolic compounds. There is a varietal effect on the relative composition.

Flavonoids

Main article: Flavonoids

The process of maceration or extended skin contact allows the extraction of phenolic compounds (including those that form a wine's color) from the skins of the grape into the wine.

In red wine, up to 90% of the wine's phenolic content falls under the classification of flavonoids. These phenols, mainly derived from the stems, seeds and skins are often leached out of the grape during the maceration period of winemaking. The amount of phenols leached is known as extraction. These compounds contribute to the astringency, color and mouthfeel of the wine. In white wines the number of flavonoids is reduced due to the lesser contact with the skins that they receive during winemaking. There is on-going study into the health benefits of wine derived from the antioxidant and chemopreventive properties of flavonoids.

Flavonols

Main article: Flavonols

Within the flavonoid category is a subcategory known as flavonols, which includes the yellow pigment - quercetin. Like other flavonoids, the concentration of flavonols in the grape berries increases as they are exposed to sunlight. Wine grapes facing too much sun exposure can see an accelerated ripening period, leading to a lessened ability for the synthesis of flavonols. Some viticulturalists will use measurement of flavonols such as quercetin as an indication of a vineyard's sun exposure and the effectiveness of canopy management techniques.

Anthocyanins

Main article: Anthocyanin

Anthocyanins are phenolic compounds found throughout the plant kingdom, being frequently responsible for the blue to red colors found in flowers, fruits and leaves. In wine grapes, they develop during the stage of veraison, when the skin of red wine grapes changes color from green to red to black. As the sugars in the grape increase during ripening so does the concentration of anthocyanins. An issue associated with climate change has been the accumulation of sugars within the grape accelerating rapidly and outpacing the accumulation of anthocyanins. This leaves viticulturists with the choice of harvesting grapes with too high sugar content or with too low anthocyanin content. In most grapes anthocyanins are found only in the outer cell layers of the skin, leaving the grape juice inside virtually colorless. Therefore, to get color pigmentation in the wine, the fermenting must needs to be in contact with the grape skins in order for the anthocyanins to be extracted. Hence, white wine can be made from red wine grapes in the same way that many white sparkling wines are made from the red wine grapes of Pinot noir and Pinot Meunier. The exception to this is the small class of grapes known as teinturiers, such as Alicante Bouschet, which have a small amount of anthocyanins in the pulp that produces pigmented juice.

There are several types of anthocyanins (as the glycoside) found in wine grapes which are responsible for the vast range of coloring from ruby red through to dark black found in wine grapes. Ampelographers can use this observation to assist in the identification of different grape varieties. The European vine family Vitis vinifera is characterized by anthocyanins that are composed of only one molecule of glucose while non-vinifera vines such as hybrids and the American Vitis labrusca will have anthocyanins with two molecules. This phenomenon is due to a double mutation in the anthocyanin 5-O-glucosyltransferase gene of V. vinifera. In the mid-20th century, French ampelographers used this knowledge to test the various vine varieties throughout France to identify which vineyards still contained non-vinifera plantings.

Red-berried Pinot grape varieties are also known to not synthesize para-coumaroylated or acetylated anthocyanins as other varieties do.

Tempranillo has a high pH level which means that there is a higher concentration of blue and colorless anthocyanin pigments in the wine. The resulting wine's coloring will have more blue hues than bright ruby red hues.

The color variation in the finished red wine is partly derived from the ionization of anthocyanin pigments caused by the acidity of the wine. In this case, the three types of anthocyanin pigments are red, blue and colorless with the concentration of those various pigments dictating the color of the wine. A wine with low pH (and such greater acidity) will have a higher occurrence of ionized anthocyanins which will increase the amount of bright red pigments. Wines with a higher pH will have a higher concentration of blue and colorless pigments. As the wine ages, anthocyanins will react with other acids and compounds in wines such as tannins, pyruvic acid and acetaldehyde which will change the color of the wine, causing it to develop more "brick red" hues. These molecules will link up to create polymers that eventually exceed their solubility and become sediment at the bottom of wine bottles. Pyranoanthocyanins are chemical compounds formed in red wines by yeast during fermentation processes or during controlled oxygenation processes during the aging of wine.

Tannins

Main article: Tannin

Tannins refer to the diverse group of chemical compounds in wine that can affect the color, aging ability and texture of the wine. While tannins cannot be smelled or tasted, they can be perceived during wine tasting by the tactile drying sensation and sense of bitterness that they can leave in the mouth. This is due to the tendency of tannins to react with proteins, such as the ones found in saliva. In food and wine pairing, foods that are high in proteins (such as red meat) are often paired with tannic wines to minimize the astringency of tannins. However, many wine drinkers find the perception of tannins to be a positive trait—especially as it relates to mouthfeel. The management of tannins in the winemaking process is a key component in the resulting quality.

Tannins are found in the skin, stems, and seeds of wine grapes but can also be introduced to the wine through the use of oak barrels and chips or with the addition of tannin powder. The natural tannins found in grapes are known as proanthocyanidins due to their ability to release red anthocyanin pigments when they are heated in an acidic solution. Grape extracts are mainly rich in monomers and small oligomers (mean degree of polymerization < 8). Grape seed extracts contain three monomers (catechin, epicatechin and epicatechin gallate) and procyanidin oligomers. Grape skin extracts contain four monomers (catechin, epicatechin, gallocatechin and epigallocatechin), as well as procyanidins and prodelphinidins oligomers. The tannins are formed by enzymes during metabolic processes of the grapevine. The amount of tannins found naturally in grapes varies depending on the variety with Cabernet Sauvignon, Nebbiolo, Syrah and Tannat being 4 of the most tannic grape varieties. The reaction of tannins and anthocyanins with the phenolic compound catechins creates another class of tannins known as pigmented tannins which influence the color of red wine. Commercial preparations of tannins, known as enological tannins, made from oak wood, grape seed and skin, plant gall, chestnut, quebracho, gambier and myrobalan fruits, can be added at different stages of the wine production to improve color durability. The tannins derived from oak influence are known as "hydrolysable tannins" being created from the ellagic and gallic acid found in the wood.

Fermenting with the stem, seeds and skin will increase the tannin content of the wine.

In the vineyards, there is also a growing distinction being made between "ripe" and "unripe" tannins present in the grape. This "physiological ripeness", which is roughly determined by tasting the grapes off the vines, is being used along with sugar levels as a determination of when to harvest. The idea is that "riper" tannins will taste softer but still impart some of the texture components found favorable in wine. In winemaking, the amount of the time that the must spends in contact with the grape skins, stems and seeds will influence the amount of tannins that are present in the wine with wines subjected to longer maceration period having more tannin extract. Following harvest, stems are normally picked out and discarded prior to fermentation but some winemakers may intentionally leave in a few stems for varieties low in tannins (like Pinot noir) in order to increase the tannic extract in the wine. If there is an excess in the amount of tannins in the wine, winemakers can use various fining agents like albumin, casein and gelatin that can bind to tannins molecule and precipitate them out as sediments. As a wine ages, tannins will form long polymerized chains which come across to a taster as "softer" and less tannic. This process can be accelerated by exposing the wine to oxygen, which oxidize tannins to quinone-like compounds that are polymerization-prone. The winemaking technique of micro-oxygenation and decanting wine use oxygen to partially mimic the effect of aging on tannins.

A study in wine production and consumption has shown that tannins, in the form of proanthocyanidins, have a beneficial effect on vascular health. The study showed that tannins suppressed production of the peptide responsible for hardening arteries. To support their findings, the study also points out that wines from the regions of southwest France and Sardinia are particularly rich in proanthocyanidins, and that these regions also produce populations with longer life spans.

Reactions of tannins with the phenolic compound anthocyanidins creates another class of tannins known as pigmented tannins which influences the color of red wine.

Addition of enological tannins

Commercial preparations of tannins, known as enological tannins, made from oak wood, grape seed and skin, plant gall, chestnut, quebracho, gambier and myrobalan fruits, can be added at different stages of the wine production to improve color durability.

Effects of tannins on the drinkability and aging potential of wine

Tannins are a natural preservative in wine. Un-aged wines with high tannin content can be less palatable than wines with a lower level of tannins. Tannins can be described as leaving a dry and puckered feeling with a "furriness" in the mouth that can be compared to a stewed tea, which is also very tannic. This effect is particularly profound when drinking tannic wines without the benefit of food.

Many wine lovers see natural tannins (found particularly in varietals such as Cabernet Sauvignon and often accentuated by heavy oak barrel aging) as a sign of potential longevity and ageability. Tannins impart a mouth-puckering astringency when the wine is young but "resolve" (through a chemical process called polymerization) into delicious and complex elements of "bottle bouquet" when the wine is cellared under appropriate temperature conditions, preferably in the range of a constant 55 to 60 °F (13 to 16 °C). Such wines mellow and improve with age with the tannic "backbone" helping the wine survive for as long as 40 years or more. In many regions (such as in Bordeaux), tannic grapes such as Cabernet Sauvignon are blended with lower-tannin grapes such as Merlot or Cabernet Franc, diluting the tannic characteristics. White wines and wines that are vinified to be drunk young (for examples, see nouveau wines) typically have lower tannin levels.

Other flavonoids

Flavan-3-ols (catechins) are flavonoids that contribute to the construction of various tannins and contribute to the perception of bitterness in wine. They are found in highest concentrations in grape seeds but are also in the skin and stems. Catechins play a role in the microbial defense of the grape berry, being produced in higher concentrations by the grape vines when it is being attacked by grape diseases such as downy mildew. Because of that grape vines in cool, damp climates produce catechins at high levels than vines in dry, hot climates. Together with anthocyanins and tannins they increase the stability of a wines color-meaning that a wine will be able to maintain its coloring for a longer period of time. The amount of catechins present varies among grape varieties with varietals like Pinot noir having high concentrations while Merlot and especially Syrah have very low levels. As an antioxidant, there are some studies into the health benefits of moderate consumption of wines high in catechins.

In red grapes, the main flavonol is on average quercetin, followed by myricetin, kaempferol, laricitrin, isorhamnetin, and syringetin. In white grapes, the main flavonol is quercetin, followed by kaempferol and isorhamnetin. The delphinidin-like flavonols myricetin, laricitrin, and syringetin are missing in all white varieties, indicating that the enzyme flavonoid 3',5'-hydroxylase is not expressed in white grape varieties.

Myricetin, laricitrin and syringetin, flavonols which are present in red grape varieties only, can be found in red wine.

Non-flavonoids

See also: Wine and health

Hydroxycinnamic acids

Hydroxycinnamic acids are the most important group of nonflavonoid phenols in wine. The four most abundant ones are the tartaric acid esters trans-caftaric, cis- and trans-coutaric, and trans-fertaric acids. In wine they are present also in the free form (trans-caffeic, trans-p-coumaric, and trans-ferulic acids).

Stilbenoids

V. vinifera also produces stilbenoids.

Resveratrol is found in highest concentration in the skins of wine grapes. The accumulation in ripe berries of different concentrations of both bound and free resveratrols depends on the maturity level and is highly variable according to the genotype. Both red and white wine grape varieties contain resveratrol, but more frequent skin contact and maceration leads to red wines normally having ten times more resveratrol than white wines. Resveratrol produced by grape vines provides defense against microbes, and production can be further artificially stimulated by ultraviolet radiation. Grapevines in cool, damp regions with higher risk of grape diseases, such as Bordeaux and Burgundy, tend to produce grapes with higher levels of resveratrol than warmer, drier wine regions such as California and Australia. Different grape varieties tend to have differing levels, with Muscadines and the Pinot family having high levels while the Cabernet family has lower levels of resveratrol. In the late 20th century interest in the possible health benefits of resveratrol in wine was spurred by discussion of the French paradox involving the health of wine drinkers in France.

Piceatannol is also present in grape  from where it can be extracted and found in red wine.

Phenolic acids

Vanillin is a phenolic aldehyde most commonly associated with the vanilla notes in wines that have been aged in oak. Trace amounts of vanillin are found naturally in grapes, but they are most prominent in the lignin structure of oak barrels. Newer barrels will impart more vanillin, with the concentration present decreasing with each subsequent usage.

Phenols from oak ageing

Phenolic compounds like tannins and vanillin can be extracted from aging in oak wine barrels.

Oak barrel will add compounds such as vanillin and hydrolysable tannins (ellagitannins). The hydrolyzable tannins present in oak are derived from lignin structures in the wood. They help protect the wine from oxidation and reduction.

4-Ethylphenol and 4-ethylguaiacol are produced during ageing of red wine in oak barrels that are infected by brettanomyces .

Natural phenols and polyphenols from cork stoppers

Extracted cork closure inscribed with "Bottled at origin" in Spanish

Low molecular weight polyphenols, as well as ellagitannins, are susceptible to be extracted from cork stoppers into the wine. The identified polyphenols are gallic, protocatechuic, vanillic, caffeic, ferulic, and ellagic acids; protocatechuic, vanillic, coniferyl, and sinapic aldehydes; the coumarins aesculetin and scopoletin; the ellagitannins are roburins A and E, grandinin, vescalagin and castalagin.

Guaiacol is one of the molecules responsible for the cork taint wine fault.

Phenolic content in relation with wine making techniques

Extraction levels in relation with grape pressing techniques

Flash release is a technique used in wine pressing. The technique allows for a better extraction of phenolic compounds.

Microoxygeneation

The exposure of wine to oxygen in limited quantities affects phenolic content.

Phenolic compounds found in wine

LC chromatograms at 280 nm of a pinot red wine (top), a Beaujolais rosé (middle) and a white wine (bottom). The picture shows peaks corresponding to the different phenolic compounds. The hump between 9 and 15 minutes corresponds to the presence of tannins, mostly present in the red wine.

Effects

Polyphenol compounds may interact with volatiles and contribute to the aromas in wine. Although wine polyphenols are speculated to provide antioxidant or other benefits, there is little evidence that wine polyphenols actually have any effect in humans. Limited preliminary research indicates that wine polyphenols may decrease platelet aggregation, enhance fibrinolysis, and increase HDL cholesterol, but high-quality clinical trials have not confirmed such effects, as of 2017.