First, an off-topic question: How does one begin a new paragraph when responding to a quote? A double shows up on the composition screen as beginning a new paragraph…but the transmitted post is displayed as one huge paragraph.
Thanks in advance for any replies. In the meantime, I’ve inserted a /P to indicate the start of a new paragraph.
Now back to the topic at hand (and I apologize for the lack of paragraphs and the resulting difficulty in reading the post).
Quote:
……to redirect the flow takes energy , the bernoulli effect takes energy as well ,
but the bernoulli effect can redirect the flow without an angle of attack ,…
/P In the Physical explaination, it is the Coanda Effect that redirects the flow (and it does not require that there be a speed difference between the two sides to effect this redirection). The Coanda effect also does not require an angle of attack for an asymmetric foil (i.e. with camber) to generate lift at zero angle of attack. /P By way of example, consider a flat surface with some angle of attack, alpha, moving (planing) across the surface of water. If the velocity is "high", virtually all the lift generated by this surface is the result of the downward momentum imparted to the water moving under the hull (at slower speeds, buoyancy makes an increasing contribution to the pressure exerted on the bottom of the hull). /P The magnitude of the lift is related to the rate of change of vertical momentum imparted to the water per unit time--and hence proportinal to the density of the fluid, the square of the velocity of the fluid, the wetted area of the surface, the (effective) thickness of the layer of water affected, and the sine of the angle-of-attack. /P Now let's assume that the water level is raised so that the thin plate is totally submerged (but remains at the same angle-of-attack, and moves through the water at the same speed). Now one has the lift generated by the deflection of the water passing under the plate, plus any lift created by water moving along and down the upper side of the plate. Within limits (e.g. the stall angle), the Coanda effect causes the water on the upper side of the plate to follow this path, hence if the thickness of the layer of water flowing over the upper side of the plate, and deflected downward by the angle-of-attack of the plate is the same as for the lower surface, one would expect that the lift would be doubled. In fact, it is slightly more than doubled (e.g. a factor of about 2.06x versus 2.00x). /P Why? One explanation might be that the difference is a consequence of the Bernoulli effect. A possible alternative is that the thickness of the upper layer that is affected by the presence of the inclined plate is greater than the thickness of the analogous layer flowing under the plate. /P But there is another complication. Although the total lift with flow past both sides is approximately double the total lift with the flow past only one side, measurements show that substantially more than half the total lift is a consequence of the flow over the upper face of the plate, and substantially less than half the total lift is a consequence of the flow over the lower face of the plate. What happened to reduce the lift generated by the lower face as a result of simply immersing the plate deeper in the water? /P One contributor is that the mass (per unit time) of water in the lower layer has been reduced, while the mass (per unit time) of water in the uper layer has been increased. When the plate was at the surface, all the water lying below the leading edge of the plate went under the plate; when the plate is immersed, a portion of the flow approaching the plate from slightly below the leading edge slows down, reverses course, and flows up the plate (and counter to the overall flow), wraps around the leading edge, and flows down along the upper surface. The greater the angle of attack, the more this "stagnation" point marking the point of separation between the water flowing over, and the water flowing under, the plate, the more this point moves down the lower face of the plate (and when the angle of attack becomes 90-degrees--i.e. vertical--the stagnation point lies at the middle of the plate). /P Now consider a foil consisting of a flat lower face, and a convex upper face, with a sharp leading edge where the curved and flat surfaces intersect. The plate is oriented so that the angle of attack is zero (i.e. the plate is horizontal). Water moving under the foil is not deflected downward, and hence contributes nothing to the lift. On the other hand, water moving over the foil is initially deflected upward (imparted upward momentum), then (via the Coanda effect) its upward motion fades and reverses to a downward sloping path as it moves past the thickest section of the foil and toward the trailing edge. As it leaves the trailing edge of the foil, its direction of motion is aligned with approximately the slope of the rear section of the foil--and hence downward as well as aft. Since this downward motion means that downward momentum has been imparted to the water flowing over the foil, a lift force is imparted to the foil. /P [An aside: As the flows over the top of the foil and below the foil merge beyond the trailing edge, they mix and the downward momentum of the upper flow is reduced, while the lower flow is imparted a downward momentum. Since momentum, unlike energy, is a conserved quantity, the end result is that the mixture has the same downward momentum as the flow over the upper layer just prior to reaching the trailing edge] /P End result? Lift is generated by an asymmetric foil without any need to invoke the Bernoulli effect. That is not to say that the Bernoulli effect cannot contribute to the lift, only that it is not required--and whether any Bernoulli effect is additive or subtractive will depend on the relative speeds on the two sides of the foil. Estimates of the Bernoulli effect contribution indicate that the contribution is small compared in comparison with the lift associated with the imparting of vertical momentum to the water moving around the foil as a consequence of the Coanda effect. /P By conceptually rotating our hypothetical foil so as to make the angle of attack become increasingly negative, it is obvious that at some negative angle (e.g. approximately one half the included angle between the upper and lower faces of the foil near the trailing edge), the lift force will be reduced to zero--and any further negative rotation will lead to a downward directed lift force. /P In this example, for conceptual ease it was assumed that the leading edge was sharp. However, a sharp leading edge can have adverse effects (in terms of the lift/drag ratio) at positive angles of attack. As noted above, with a positive angle of attack, the stagnation point begins to move along the lower surface, causing a flow to develop that reverses course at the stagnation point, moves forward (and upward), and around the leading edge, before moving back along the upper face of the foil. If the leading edge of the foil is not sufficiently rounded, as the flow rounds the leading edge, it can separate from the surface of the foil, then reattach farther back on the upper foil surface. This can have adverse effects on the lift/drag characteristics of the foil. These become even more pronounced as the angle of attack (and lift force) are increased, leading to premature stalling. This is the reason that thin foils (e.g. the Venetian shade-like thin foil) have earlier stall angles, lower maximum lift coeffients, and increased drag at large angles of attack, compared with foiled sections with more rounded leading edges. /P retroman wrote: <div class="bb-quote">Quote:<blockquote class="bb-quote-body">
……On the other hand, the Bernoulli effect is stronger in water, since that is a different medium than air (e.g., water is much more viscuous)……
/P As long as one avoids operating at low pressures that lead to cavitation (liquid evaporating to a gas) or ventilation (entrainment of air into a low pressure void), and at speeds that are well below the speed of sound (Mach # <<1), the dynamic properties of a fluid (gas or liquid) flow are scaled by the Reynolds number (equal to the product of the flow speed times a characteristic length of the object divided by the kinematic viscosity)--not solely by the viscosity. So if two identical (except for gas vs liquid) flow situations have large and equal Reynolds numbers, the flow dynamics should be identical, and the Bernoulli effects equal. Moreover, at low Reynolds numbers, the effects of viscosity and the accompany dissipation of energy should diminish, rather than increase, the Bernoulli effect (since the latter implicitly assumes the conservation of energy). /P MT