# Vol.4 : Computational Turbulent Incompressible Flow

## Forum.Flying History

September 24, 2007, at 09:28 AM by 82.183.149.16 -
Changed line 20 from:

so determined that the separation point of the flow occured at the trailing edge of the wing,

to:

so determined that the flow separated at the trailing edge of the wing,

September 24, 2007, at 09:27 AM by 82.183.149.16 -
Changed lines 52-54 from:

from the instability a low-pressure turbulent wake would develop effectively generating lift. Thus flying in a real imperfect World is possible, but not in a fictional prefect World.

to:

from the instability a low-pressure turbulent wake always develops effectively generating stable lift. Thus stable flying in a real imperfect World is possible, but not in a fictional prefect World.

Changed lines 56-57 from:

is similar to the vortex in a bathtub drain.

to:

is similar to the vortex generated in a bathtub drain, also referred to as vortex stretching.

Changed lines 59-60 from:

Vol 4 opens the possibility that the lift and drag of the turbulent flow around an entire aircraft can be accurately simulated by G2 for the Euler equations (Euler/G2)

to:

Vol 4 opens the possibility that the lift and drag of the turbulent flow around an entire aircraft can be accurately simulated by G2 for the Euler equations (Euler/G2)

September 24, 2007, at 09:23 AM by 82.183.149.16 -
Changed line 25 from:

and mathematical order seemd to be resurrected: Indeed powered flight

to:

and mathematical order seemed to be resurrected: Indeed powered flight

September 24, 2007, at 09:22 AM by 82.183.149.16 -
Changed line 4 from:

why it is than some heavier that air objects air can fly but others cannot?

to:

why it is than some heavier-than-air objects can fly, but others cannot?

Changed lines 8-15 from:

d'Alembert had showed in 1752 that in potential flow both the lift and drag is zero, and Newton had shown using a particle model of air flow that the lift was way too small to allow powered heavier than air flight, and none of da Vincis human powered flying machines could get off the ground. So from both mathematical and practical point of view the old dream of flying like the birds seemed out of reach for humanity, when the two brothers Orwille and Wilbur Wright in 1903 showed that powered heavier than air flight indeed was possible.

to:

d'Alembert showed in 1752 that in potential flow both the lift and drag is zero, supporting Newton´s prediction using a particle model of air flow of a very small lift, and da Vinci´s unsuccessful attempts of human powered flying machines. So from both mathematical and practical point of view the old dream of flying like the birds seemed out of reach for humans, when the two brothers Orwille and Wilbur Wright in 1903 showed that powered heavier-than-air flight, indeed was possible.

Changed lines 17-18 from:

potential solution of a wing section, by adding a rotational flow creating an unsymmetric pressure distribution with substantial lift, with the rotation and resulting lift

to:

potential solution of a wing section, by adding a flow circulating around the wing creating an unsymmetric pressure distribution with substantial lift, with the circulation and resulting lift

Changed lines 23-24 from:

In 1904 Prandtl presented his resolution of d'Alembert's paradox of zero lift based on boundary layer effects of vanishing viscosity,

to:

Further, in 1904 Prandtl presented his resolution of d'Alembert's paradox of zero lift based on laminar boundary layer effects of vanishing viscosity,

Changed lines 29-30 from:

Vol 4 shows that Prandtl's resolution is incorrect, and asks from where the Kutta-Jukowski condition comes?

to:

Vol 4 shows that Prandtl's resolution is incorrect and that there is no large scale circulation around a wing and asks from where the Kutta-Jukowski condition comes?

Changed lines 33-35 from:

Vol 4 shows that the answer is no, because the true turbulent nature of the flow has to be taken into account, and it is not in classical aero dynamics. Without turbulence, there would be no lift,

to:

Vol 4 shows that the answer is NO, because the true turbulent nature of the flow has to be taken into account, and it is not in classical aero dynamics of laminar boundary layer theory and Kutta-Jukowski potential flow.

Vol 4 shows that without turbulence, there would be no lift,

Changed lines 41-43 from:

Vol 4 shows that the turbulent flow around a wing generates a lift increasing with the angle of attack up to around 20 degrees, whereafter it quickly drops and the drag increases drastically corresponding to stall. The lift is generated because the wing redirects the flow of air to a downward direction

to:

Vol 4 shows more precisely that the turbulent flow around a wing generates a lift increasing with the angle of attack up to around 20 degrees, whereafter it quickly drops and the drag increases drastically corresponding to stall. The lift is generated because the wing redirects the flow of air to a downward direction

Changed lines 44-48 from:

downwash. If there is downwash, then there is lift. The book shows that downwash occurs because of the generation of turbulent streamwise vorticity with low pressure at the trailing edge, which depletes the high pressure of the potential solution with zero lift. The turbulent streamwise vorticity is similar to the vortex in a bathtub drain, and forms a wake attaching to the trailing edge, which also generates drag. There is thus no lift without drag.

to:

downwash. If there is downwash, then there is lift.

Vol 4 shows that downwash occurs because of the generation of turbulent streamwise vorticity with low pressure at the trailing edge, which depletes the high pressure of the potential solution with zero lift, which is not realized because of exponential instability at the trailing edge.

Vol 4 shows that in a fictional ideal perfect mathematical World of infinite precision, the potential solution with zero lift could occur and thus prevent flying. However, in the real imperfect World in which we live, the potential solution could never occur because of exponential instability, and from the instability a low-pressure turbulent wake would develop effectively generating lift. Thus flying in a real imperfect World is possible, but not in a fictional prefect World.

Vol 4 shows that the turbulent streamwise vorticity generated at the trailing edge, is similar to the vortex in a bathtub drain.

September 23, 2007, at 04:53 PM by 82.183.149.16 -
Changed lines 37-46 from:

Vol 4 shows that the turbulent flow around a wing generates a lift increasing with the angles of attack up to around 20 degrees whereafter it quickly drops and the drag increases drastically corresponding to stall. The lift is generated by the unsymmetric position of the separation which occurs at the trailing edge for small angles of attack, but moves forward on the upper wing surface for larger angles, while the drag is generated by turbulent vortex stretching at the separation point.

Vol 4 shows that the flow is turbulent in a thin wake attaching to the trailing edge for the small angle of attack of 2-4 degrees at crusing speed, while for the large angle of attack of about 16-20 degrees at take off and landing the flow separates to turbulent flow close to the leading edge.

Vol 4 shows that the lift and drag of the turbulent flow around an entire aircraft can be accurately simulated

to:

Vol 4 shows that the turbulent flow around a wing generates a lift increasing with the angle of attack up to around 20 degrees, whereafter it quickly drops and the drag increases drastically corresponding to stall. The lift is generated because the wing redirects the flow of air to a downward direction after the wing (referred to as downwash), and the key question to answer is why a wing generates downwash. If there is downwash, then there is lift. The book shows that downwash occurs because of the generation of turbulent streamwise vorticity with low pressure at the trailing edge, which depletes the high pressure of the potential solution with zero lift. The turbulent streamwise vorticity is similar to the vortex in a bathtub drain, and forms a wake attaching to the trailing edge, which also generates drag. There is thus no lift without drag.

Vol 4 opens the possibility that the lift and drag of the turbulent flow around an entire aircraft can be accurately simulated

March 21, 2007, at 10:51 PM by Johan Hoffman -
Changed lines 50-57 from:

mesh points with a reduction factor of 10 millions.

to:

mesh points with a reduction factor of 10 millions.

March 18, 2007, at 09:19 PM by claes -
Changed lines 47-48 from:

by Euler/G2 without resolving the boundary layers, thereby reducing the number of mesh points from the

to:

by G2 for the Euler equations (Euler/G2) without resolving the boundary layers, thereby reducing the number of mesh points from the

March 17, 2007, at 08:40 AM by claes -
Changed line 49 from:

with a reduction factor of 10 millions.

to:

mesh points with a reduction factor of 10 millions.

March 17, 2007, at 08:39 AM by claes -
Changed lines 48-49 from:

commonly predicted impossible 10^16 to the entirely possible around 10^8.

to:

commonly predicted impossible 10 millions times 10 millions to the entirely possible around 10 millions with a reduction factor of 10 millions.

March 17, 2007, at 08:38 AM by claes -
Changed line 42 from:

The flow is turbulent in a thin wake attaching to the trailing

to:

Vol 4 shows that the flow is turbulent in a thin wake attaching to the trailing

March 17, 2007, at 08:37 AM by claes -
March 17, 2007, at 08:37 AM by claes -
Changed lines 40-43 from:

for small angles of attack, but moves forward on the upper wing surface for larger angles, while the drag is generated by turbulent vortex stretching at the separation point. The flow is turbulent in a thin wake attaching to the trailing edge for the small angle of attack of around 2 degrees at crusing speed, while for the angle of attack of about 16 degrees at take off the flow separates to turbulent flow close to the leading edge.

to:

for small angles of attack, but moves forward on the upper wing surface for larger angles, while the drag is generated by turbulent vortex stretching at the separation point.

The flow is turbulent in a thin wake attaching to the trailing edge for the small angle of attack of 2-4 degrees at crusing speed, while for the large angle of attack of about 16-20 degrees at take off and landing the flow separates to turbulent flow close to the leading edge.

March 17, 2007, at 08:35 AM by claes -
Changed lines 23-24 from:

of zero lift, and mathematical order seemd to be resurrected: Indeed powered flight

to:

of zero lift based on boundary layer effects of vanishing viscosity, and mathematical order seemd to be resurrected: Indeed powered flight

Changed lines 32-33 from:

has to be taken into account, and it is not. Without turbulence, there would be no lift,

to:

has to be taken into account, and it is not in classical aero dynamics. Without turbulence, there would be no lift,

Changed lines 40-42 from:

for small angles of attack, but before for larger angles, while the drag is generated by turbulent vortex stretching at the separation point.

to:

for small angles of attack, but moves forward on the upper wing surface for larger angles, while the drag is generated by turbulent vortex stretching at the separation point. The flow is turbulent in a thin wake attaching to the trailing edge for the small angle of attack of around 2 degrees at crusing speed, while for the angle of attack of about 16 degrees at take off the flow separates to turbulent flow close to the leading edge.

March 17, 2007, at 08:24 AM by claes -
Changed line 19 from:

so determined that the separation point of the flow occured at the trailing edge of the wing

to:

so determined that the separation point of the flow occured at the trailing edge of the wing,

March 16, 2007, at 03:58 PM by claes -
Changed line 4 from:

why it is than some heavier than air objects air can fly but others cannot?

to:

why it is than some heavier that air objects air can fly but others cannot?

Changed lines 6-8 from:

object can be created balancing the gravitational force.

to:

object can be created balancing the gravitational force.

Changed lines 20-21 from:

referred to as the Kutta-Jukowski condition?

to:

referred to as the Kutta-Jukowski condition.

Changed line 27 from:

Vol 4 shows that Prandtl's resolution is incorrect, and asks from where does the Kutta-Jukowski condition come?

to:

Vol 4 shows that Prandtl's resolution is incorrect, and asks from where the Kutta-Jukowski condition comes?

Changed lines 30-31 from:

Vol 4 shows that the answer is no, because the turbulent nature of the flow has to be taken into account. Without turbulence, there would be no lift,

to:

Vol 4 shows that the answer is no, because the true turbulent nature of the flow has to be taken into account, and it is not. Without turbulence, there would be no lift,

March 16, 2007, at 03:55 PM by claes -
Changed line 23 from:

to:

In 1904 Prandtl presented his resolution of d'Alembert's paradox

Changed lines 25-31 from:

was possible as predicted by mathematics!

But the book shows that Prandtl's resolution is incorrect, and from where does really the Kutta-Jukowski condition come? Does really commonly accepted fluid dynamics show that flying is possible?

The book shows that the answer is no, and that the turbulent nature of the flow

to:

was possible as predicted by mathematics! But only after flying was demonstrated to be possible in practice!

Vol 4 shows that Prandtl's resolution is incorrect, and asks from where does the Kutta-Jukowski condition come? Does really commonly accepted fluid dynamics show that flying is possible?

Vol 4 shows that the answer is no, because the turbulent nature of the flow

Changed line 36 from:

The book shows that the turbulent flow around a wing generates a lift increasing with the angles of attack

to:

Vol 4 shows that the turbulent flow around a wing generates a lift increasing with the angles of attack

Changed lines 38-40 from:

to stall. The lift is generated by the unsymmetric position of the separation at the trailing edge for small angles of attack, while the drag is generated by turbulent vortex stretching at the trailing edge.

to:

to stall. The lift is generated by the unsymmetric position of the separation which occurs at the trailing edge for small angles of attack, but before for larger angles, while the drag is generated by turbulent vortex stretching at the separation point.

Vol 4 shows that the lift and drag of the turbulent flow around an entire aircraft can be accurately simulated by Euler/G2 without resolving the boundary layers, thereby reducing the number of mesh points from the commonly predicted impossible 10^16 to the entirely possible around 10^8.

March 16, 2007, at 10:29 AM by claes -
Changed line 28 from:

the Kutta-Jukowski condition come? Does real mathematical fluid dynamics show that

to:

the Kutta-Jukowski condition come? Does really commonly accepted fluid dynamics show that

The book shows that the answer is no, and that the turbulent nature of the flow has to be taken into account. Without turbulence, there would be no lift, and with turbulence the lift comes along with drag, so flying consumes energy, which the migrating birds know very well, as well as the airline companies.

The book shows that the turbulent flow around a wing generates a lift increasing with the angles of attack up to around 20 degrees whereafter it quickly drops and the drag increases drastically corresponding to stall. The lift is generated by the unsymmetric position of the separation at the trailing edge for small angles of attack, while the drag is generated by turbulent vortex stretching at the trailing edge.

March 16, 2007, at 10:21 AM by claes -
Changed lines 17-18 from:

Quickly thereafter, the mathematicians Kutta and Jukowski changed the zero drag potential solution of a wing section by adding a rotational flow creating an unsymmetric

to:

Quickly thereafter, the mathematicians Kutta and Jukowski changed the zero lift potential solution of a wing section, by adding a rotational flow creating an unsymmetric

Changed lines 20-21 from:

so determined that the separation point of the flow occured at the trailing edge of the wing.

to:

so determined that the separation point of the flow occured at the trailing edge of the wing referred to as the Kutta-Jukowski condition?

But the book shows that Prandtl's resolution is incorrect, and from where does really the Kutta-Jukowski condition come? Does real mathematical fluid dynamics show that flying is possible?

March 16, 2007, at 10:17 AM by claes -
Changed lines 14-26 from:

when the brothers Wright in 1903 showed that powered heavier

to:

when the two brothers Orwille and Wilbur Wright in 1903 showed that powered heavier than air flight indeed was possible.

Quickly thereafter, the mathematicians Kutta and Jukowski changed the zero drag potential solution of a wing section by adding a rotational flow creating an unsymmetric pressure distribution with substantial lift, with the rotation and resulting lift so determined that the separation point of the flow occured at the trailing edge of the wing.

In 1904 Prandtle in addition presented his resolution of d'Alembert's paradox of zero lift, and mathematical order seemd to be resurrected: Indeed powered flight was possible as predicted by mathematics!

March 16, 2007, at 10:10 AM by claes -
Changed line 3 from:

Since the dawn of history man has asked upon observation of flying birds

to:

Since the dawn of history man has asked upon observation of flying birds,

Changed lines 5-6 from:

The critical question is how a lift force can be created balancing the gravitational

to:

The critical question is how a lift force from the pressure distribution around the object can be created balancing the gravitational

March 16, 2007, at 08:52 AM by claes -
Deleted line 4:
Changed lines 10-11 from:

to allow powered heavier than air flight. So from mathematical point

to:

to allow powered heavier than air flight, and none of da Vincis human powered flying machines could get off the ground. So from both mathematical and practical point

Changed line 13 from:

although Icaros had managed to escape and da Vinci

to:

when the brothers Wright in 1903 showed that powered heavier

March 16, 2007, at 08:48 AM by claes -
Changed lines 3-4 from:

Why is it than some heavier than air objects air can fly but others cannot?

to:

Since the dawn of history man has asked upon observation of flying birds why it is than some heavier than air objects air can fly but others cannot?

Changed lines 7-8 from:

force. d'Alembert had showed in 1752 that in potential flow both the lift and drag is zero, and Newton

to:

force.

d'Alembert had showed in 1752 that in potential flow both the lift and drag is zero, and Newton had shown using a particle model of air flow that the lift was way too small to allow powered heavier than air flight. So from mathematical point of view the old dream of flying like the birds seemed out of reach for humanity, although Icaros had managed to escape and da Vinci

March 16, 2007, at 08:37 AM by claes -
Changed lines 3-7 from:

Why is it than some heavier than air objects air can fly but others cannot?

to:

Why is it than some heavier than air objects air can fly but others cannot?

The critical question is how a lift force can be created balancing the gravitational force. d'Alembert had showed in 1752 that in potential flow both the lift and drag is zero, and Newton

March 16, 2007, at 08:20 AM by claes -